Advances in Optics Reviews Vol. 3

Advances in Optics: Reviews Book Series, Volume 3 Sergey Y. Yurish Editor Advances in Optics: Reviews Book Series, Volume 3 International Frequency Sensor Association Publishing Sergey Y. Yurish Editor Advances in Optics: Reviews Book Series, Vol. 3 Published by International Frequency Sensor Association (IFSA) Publishing, S. L., 2018 E-mail (for print book orders and customer service enquires): ifsa.books@sensorsportal.com Visit our Home Page on http://www.sensorsportal.com Advances in Optics: Reviews, Vol. 1 is an open access book which means that all content is freely available without charge to the user or his/her institution. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles, or use them for any other lawful purpose, without asking prior permission from the publisher or the authors. This is in accordance with the BOAI definition of open access. Neither the authors nor International Frequency Sensor Association Publishing accept any responsibility or liability for loss or damage occasioned to any person or property through using the material, instructions, methods or ideas contained herein, or acting or refraining from acting as a result of such use. ISBN: 978-84-697-9439-5, e-ISBN: 978-84-697-9440-1 BN-20180420-XX BIC: TTB Acknowledgments As Editor I would like to express my undying gratitude to all authors, editorial staff, reviewers and others who actively participated in this book. We want also to express our gratitude to all their families, friends and colleagues for their help and understanding. Contents Contents Contents............................................................................................................................ 7 Contributors................................................................................................................... 15 Preface ............................................................................................................................ 19 1. Health and Wellness Fiber Optic Sensors in IoT Application............................... 21 1.1. Introduction ...................................................................................................................... 21 1.2. Internet of Things ............................................................................................................. 22 1.2.1. Communication Models Used by IoT .................................................................................... 24 1.2.2. Main Existing Applications of IoT ........................................................................................ 26 1.2.3. Leading Companies .............................................................................................................. 27 1.3. Fiber Optic Sensors for Health and Wellness Application ............................................... 28 1.3.1. Working Principles and Applications ................................................................................... 29 1.3.1.1. Intensity-Modulated Fiber Optic Sensors ................................................................... 30 1.3.1.2. Interferometric Fiber Optic Sensors ........................................................................... 33 1.3.1.3. Wavelength-Modulated Sensors ................................................................................. 35 1.3.2. Multicore Fiber ..................................................................................................................... 37 1.4. IoT Systems for the Family Based on Fiber Optic Sensor ............................................... 38 1.5. Conclusion and Future Prospect ....................................................................................... 41 References ............................................................................................................................... 41 2. Multi-Point Temperature Sensor Consisting of AWG, SOA, and FBGs in Linear-Cavity Fiber Lasing System ................................................................... 49 2.1. Introduction ...................................................................................................................... 49 2.2. Linear-Cavity Fiber Sensor Consisting of SOA, AWG, and FBGs.................................. 50 2.3. Analysis of Multi-Channel Lasing ................................................................................... 52 2.3.1. Analysis for SOA Nonlinearity .............................................................................................. 52 2.3.2. Analysis of Multi-Wavelength Lasing ................................................................................... 54 2.4. Experimental Results ....................................................................................................... 56 2.4.1. SOA Nonlinearity .................................................................................................................. 56 2.4.2. ASE Spectrum and AWG Transmittance ............................................................................... 57 2.4.3. Multi-Wavelength Lasing ...................................................................................................... 58 2.4.4. Two-Wavelength Lasing with FBGs...................................................................................... 60 2.4.5. Simultaneous Temperature Sensing ...................................................................................... 62 2.4.6. Increase of the Temperature Sensing Range ......................................................................... 63 2.5. Conclusion ....................................................................................................................... 64 Acknowledgements ................................................................................................................. 64 References ............................................................................................................................... 65 Appendix ................................................................................................................................. 66 3. Review of Fabry-Pérot Fiber Sensors ...................................................................... 69 3.1. Introduction ...................................................................................................................... 69 3.2. Basic Theory .................................................................................................................... 70 3.3. Applications ..................................................................................................................... 71 7 Advances in Optics: Reviews. Book Series, Vol. 3 3.3.1. Strain Sensing ....................................................................................................................... 71 3.3.1.1. Prolate Spheroidal FP Cavity Strain Sensor ...............................................................71 3.3.1.2. Spherical FP Cavity Strain Sensor ..............................................................................75 3.3.1.3. Cylindrical FP Cavity Strain Sensor ...........................................................................76 3.3.1.4. Analysis of Temperature Sensitivity for the Fiber FP Strain Sensor ..........................83 3.3.1.5. Summary of this Section ............................................................................................. 84 3.3.2. Refractive Index Sensing ....................................................................................................... 84 3.3.2.1. Method of Measuring Fluid RI in FP Cavity ..............................................................84 3.3.2.2. Method of Measuring Fluid RI out of FP Cavity ........................................................88 3.3.2.3. Summary of this Section ............................................................................................. 91 3.3.3. Temperature Sensing............................................................................................................. 92 3.3.3.1. Theory ........................................................................................................................92 3.3.3.2. Applications of Temperature Sensor Based on FPI ....................................................93 3.3.3.3. Summary of this Section ............................................................................................. 98 3.4. Concluding Remarks and Perspectives ............................................................................. 98 References ............................................................................................................................... 99 4. Multi-Parameter Integrated Optical Sensor Based on Multimode Interference and Microring Resonator Structures ............................................. 103 4.1. Introduction..................................................................................................................... 103 4.2. Multimode Interference Structures ................................................................................. 104 4.3. Microring Resonator ....................................................................................................... 105 4.4. Two-Parameter Sensor Based on 4×4 MMI and Resonator Structure ............................ 106 4.5. Three-Parameter Sensor Based on 6×6 MMI and Resonator Structure .......................... 114 4.6. Four-Parameter Sensor Based on 8×8 MMI and Resonator Structure ............................ 118 4.7. Conclusions..................................................................................................................... 125 References ............................................................................................................................. 125 5. Coherent Gradient Sensor for Curvature Measurement in Extreme Environments .......................................................................................................... 129 5.1. Introduction..................................................................................................................... 129 5.2. The CGS System............................................................................................................. 130 5.3. Curvature Measurements in Cryogenic Medium ............................................................ 134 5.3.1. Governing Equations .......................................................................................................... 134 5.3.2. Error Analysis ..................................................................................................................... 136 5.3.3. Curvature Measurement in Cryogenic Vacuum Chamber .................................................. 138 5.4. Curvature Measurements in Multiple Media .................................................................. 139 5.4.1. Refraction Analysis ............................................................................................................. 139 5.4.2. Experiment Verification ...................................................................................................... 140 5.5. The Multiplication Method for Sparse Interferometric Fringes ...................................... 144 Acknowledgements................................................................................................................ 151 References ............................................................................................................................. 151 6. Photo-Emf Sensors and Talbot Effect: Measurement of Displacement and Vibration .......................................................................................................... 153 6.1. Introduction..................................................................................................................... 153 6.2. Non-Steady-State Photo-Electromotive Force Effect ..................................................... 155 6.3. Applications .................................................................................................................... 159 6.3.1. Measurements of Displacements ......................................................................................... 159 8 Contents 6.3.2. Determination of Low Frequency, Out-of-Plane Vibrations ............................................... 162 6.4. Conclusions .................................................................................................................... 165 References ............................................................................................................................. 166 7. Advances in Label-Free Sensing of Bacteria by Light Diffraction Phenomenon............................................................................................................ 169 7.1. Introduction .................................................................................................................... 169 7.2. The Biophysical Model of the Bacterial Colony ............................................................ 170 7.3. The Optical System for Analysis of Light Diffraction on Bacterial Colonies ............... 178 7.3.1. The Optical Wave Field Transformation in Proposed Optical System ............................... 179 7.3.2. The Configuration of the Experimental Optical System for Bacteria Identification ........... 183 7.4. Bacteria Identification Based on Fresnel Diffraction Patterns of Bacterial Colonies.... 184 7.4.1. The Bacteria Sample Preparation ....................................................................................... 184 7.4.2. The Experimental Fresnel Diffraction Patterns of Bacterial Colonies ............................... 185 7.4.3. The Analysis of the Diffraction Patterns ............................................................................. 188 7.5. The Use of the Fresnel Diffraction Patterns of Bacterial Colonies for Evaluation of the Efficiency of Antibacterial Factors ..................................................................... 190 7.6. The Perspectives for Exploiting of Light Diffraction on Bacterial Colonies Using Digital Holography ............................................................................................. 193 7.7. Conclusions .................................................................................................................... 194 Acknowledgements ............................................................................................................... 194 References ............................................................................................................................. 194 8. Integrated Terahertz Planar Waveguides for Molecular Sensing ..................... 197 8.1. Introduction .................................................................................................................... 197 8.2. THz Frequency Sensitive Detection ............................................................................... 198 8.2.1. Waveguide Configuration and Terahertz Spectral Characterization .................................. 198 8.2.2. Integration of a Superstrate and the Sensing Method ......................................................... 201 8.3. Phase Sensitive Detection .............................................................................................. 204 8.3.1. Waveguide Configuration and Terahertz Spectral Characterization .................................. 204 8.3.2. Integration of a Superstrate and the Sensing Method ......................................................... 206 8.4. Conclusions .................................................................................................................... 210 Acknowledgements ............................................................................................................... 210 References ............................................................................................................................. 210 9. Integrated-Optics Solutions for Biomedical Optical Imaging ............................. 213 9.1. Introduction .................................................................................................................... 213 9.2. Designs at 1300 nm ........................................................................................................ 214 9.2.1. Material System .................................................................................................................. 214 9.2.2. Working Principle of the Electro-Optic Switch ................................................................... 214 9.2.3. Akinetic Beam Scanner Layout and Its Working Principle ................................................. 216 9.2.4. Multiple-Reference TD-OCT Layout and Its Working Principle......................................... 217 9.2.5. Design Parameters of the Electro-Optic Switch ................................................................. 217 9.2.6. Two-Mode Interference Beam Splitter/Combiner Design ................................................... 219 9.3. High-Speed Spectrometer Designs ................................................................................. 220 9.3.1. Material System at 800 nm.................................................................................................. 221 9.3.2. Electro-Optic Switch Design at 800 nm .............................................................................. 222 9 Advances in Optics: Reviews. Book Series, Vol. 3 9.3.3. Ultrahigh-Resolution Spectrometer Layout and Its Working Principle .............................. 223 9.3.4. Broadband Spectrometer Layout and Its Working Principle .............................................. 225 9.4. Conclusions..................................................................................................................... 226 Acknowledgements................................................................................................................ 226 References ............................................................................................................................. 227 10. Video Based Heart Rate Estimation Using Facial Images from Video Sequences ............................................................................................ 229 10.1. Introduction................................................................................................................... 229 10.2. Introduction to Component Analysis ............................................................................ 232 10.2.1. Independent Component Analysis ..................................................................................... 232 10.2.2. Principal Component Analysis .......................................................................................... 232 10.3. Dynamic Heart Rate Estimation Using Component Analysis....................................... 233 10.3.1. Experimental Setup ........................................................................................................... 233 10.3.2. Experimental Results Using ICA Method .......................................................................... 234 10.3.3. Experimental Results Using PCA ...................................................................................... 236 10.4. Distance between the Subject and Video Camera......................................................... 238 10.4.1. Varying Distance with Fixed Video Duration ................................................................... 239 10.4.2. Fixed Distance with Varying Video Duration ................................................................... 241 10.5. Conclusion .................................................................................................................... 242 References ............................................................................................................................. 244 11. Implementing Differential Signalling in Free Space Optical Communication Link ............................................................................................. 247 11.1. Introduction to Free Space Optics................................................................................. 247 11.2. FSO Communications ................................................................................................... 249 11.2.1. Background ....................................................................................................................... 249 11.2.2. FSO Structure ................................................................................................................... 251 11.3. Turbulence .................................................................................................................... 256 11.4. Channel Model.............................................................................................................. 259 11.5. Differential Signalling .................................................................................................. 261 11.6. Differential Signalling Configuration ........................................................................... 263 11.7. Differential Signalling and Turbulence......................................................................... 264 11.7.1. Optimal Detection Threshold Level .................................................................................. 264 11.7.2. Correlation between Channels .......................................................................................... 265 11.7.3. Channel Modelling ............................................................................................................ 266 11.7.4. BER Expression................................................................................................................. 269 11.7.5. Numerical Analysis ........................................................................................................... 270 11.7.6. Atmospheric Turbulence Experiment ................................................................................ 278 11.8. Differential Signalling and Pointing Errors .................................................................. 283 11.8.1. Channel Modelling ............................................................................................................ 283 11.8.2. Pointing Errors Experiment .............................................................................................. 286 11.9. Differential Signalling and Manchester Code ............................................................... 290 11.9.1. System Configuration ........................................................................................................ 290 11.9.2. Manchester Code Experiment ........................................................................................... 291 11.10. Summary ..................................................................................................................... 294 References ............................................................................................................................. 295 10 Contents 12. Fabrications of Holographic Optical Elements in Polycarbonate for Holographic Weapon Sight Application ........................................................ 301 12.1. Introduction .................................................................................................................. 301 12.2. Material and Methods................................................................................................... 302 12.3. Experimental Arrangement .......................................................................................... 304 12.3.1. Fabrication Details of Reticle HOE in AgH ..................................................................... 304 12.3.2. Direct Fabrication of HOEs in Photoresist ...................................................................... 305 12.3.3. Transfer of HOE into PR and PC ..................................................................................... 306 12.4. Result and Discussion .................................................................................................. 307 12.5. Conclusion ................................................................................................................... 311 Acknowledgment .................................................................................................................. 311 References ............................................................................................................................. 312 13. Optical Methods for the Characterization of PV Solar Concentrators ........... 315 13.1. Introduction .................................................................................................................. 315 13.2. Theoretical Aspects of SC Irradiation and Definition of New Optical Quantities ....... 323 13.2.1. Direct Collimated Irradiation ........................................................................................... 323 13.2.2. Direct Lambertian Irradiation .......................................................................................... 329 13.2.3. Inverse Lambertian Irradiation......................................................................................... 332 13.2.4. Mixed Lambertian Irradiation .......................................................................................... 335 13.3. Equivalence between DCM and ILM ........................................................................... 338 13.4. Real Prototypes of Nonimaging Solar Concentrators................................................... 342 13.5. Practical Application of the SC Characterization Methods .......................................... 346 13.5.1. Application of the DCM Method ....................................................................................... 346 13.5.2. Application of the ILM Method (Parretta-Method)........................................................... 353 13.5.3. The Application of DLCM Method .................................................................................... 364 13.5.3.1. Optical Efficiency Measurements........................................................................... 366 13.5.3.2. Beam Exit Angle Measurements ............................................................................ 366 13.5.4. The Application of the PH-Method (Parretta-Herrero Method) ....................................... 367 13.6. Experimental Results.................................................................................................... 369 13.6.1 The Truncated and Squared CPC (TS-CPC) ..................................................................... 369 13.6.1.1. Local Optical Efficiency by the Laser Method (DLCM) ........................................ 369 13.6.1.2. Beam Exit Angle Measurements ............................................................................ 373 13.6.1.3. Optical Efficiency by DCM and ILM ..................................................................... 376 13.6.1.4. Local Optical Efficiency by ILLM ......................................................................... 378 13.6.2. The (Virtual) Half-Truncated CPC (HT-CPC) ................................................................. 381 13.6.2.1. Local Optical Efficiency by ILLM ......................................................................... 381 13.6.3. The Truncated CPC (T-CPC) ........................................................................................... 383 13.6.3.1. Optical Efficiency by ILM ..................................................................................... 383 13.6.4. The Rondine Concentrators .............................................................................................. 385 13.6.4.1. Optical Efficiency by DCM and ILM ..................................................................... 385 13.6.4.2. Optical Efficiency by Parretta-Method and Parretta-Herrero Method .................... 388 13.6.5. The PhoCUS Concentrator ............................................................................................... 391 13.6.5.1. Optical Simulations ................................................................................................ 391 13.6.5.2. Experimental Measurements .................................................................................. 393 13.7. Conclusions .................................................................................................................. 394 Acknowledgements ............................................................................................................... 395 References ............................................................................................................................. 396 Appendix 13.A ...................................................................................................................... 400 Appendix 13.B ...................................................................................................................... 402 11 Advances in Optics: Reviews. Book Series, Vol. 3 Appendix 13.C ....................................................................................................................... 408 Appendix 13.D ....................................................................................................................... 411 14. Determination of the Heights of the Smoke-Plume Layering in the Vicinity of Wildfires and Prescribed Burns ....................................................................... 417 14.1. Introduction................................................................................................................... 417 14.2. Determination of the Heights of the Smoke-Plume Layering in the Vicinity of Wildfires: Theory and Data Processing Methodology............................................... 419 14.3. Some Results of Lidar Profiling of the Smoke-Polluted Atmosphere in the Vicinity of Spotted Wildfires ............................................................................... 423 14.4. Determination of the Heights of the Smoke-Plume Layering in the Vicinity of Prescribed Burns ........................................................................................................ 426 14.5. Summary ....................................................................................................................... 431 References ............................................................................................................................. 432 15. Precision Glass Molding........................................................................................ 435 15.1. Introduction................................................................................................................... 435 15.2. An Introduction to PGM ............................................................................................... 437 15.3. Selection of Glass and Preparation of Its Preform ........................................................ 438 15.4. Precision Mold Fabrication ........................................................................................... 439 15.4.1. Mold Materials in PGM .................................................................................................... 439 15.4.2. Mold Fabrications............................................................................................................. 441 15.4.2.1. Macro Mold Fabrication ......................................................................................... 441 15.4.2.2. Micro Mold Fabrication .......................................................................................... 443 15.5. PGM Process ................................................................................................................ 444 15.5.1. Stages in a PGM Process .................................................................................................. 444 15.5.2. Finite Element Analysis..................................................................................................... 445 15.5.2.1. Constitutive Modeling of Optical Glass.................................................................. 445 15.5.2.2. Mechanisms of Profile Distortion ........................................................................... 446 15.5.2.3. Residual Stresses .................................................................................................... 448 15.6. Quality Inspection Techniques ..................................................................................... 450 15.6.1. Surface Characterization .................................................................................................. 450 15.6.2. Residual Stress Characterization ...................................................................................... 451 15.6.3. Micro-Optics Characterization and Standardization ........................................................ 451 15.7. Optimization of PGM Process ...................................................................................... 453 15.7.1. Optimization Strategy........................................................................................................ 453 15.7.2. Mold Shape Optimization .................................................................................................. 454 15.7.3. Residual Stress Optimization ............................................................................................ 456 15.7.4. Multi-Objective Optimization ............................................................................................ 456 15.8. Summary ....................................................................................................................... 458 Acknowledgements................................................................................................................ 458 References ............................................................................................................................. 458 16. Deterministic Loose Abrasive Wear in Conventional Grinding-Polishing Machines ................................................................................................................. 467 16.1. Introduction................................................................................................................... 467 16.2. Abrasive Wear Theory .................................................................................................. 468 16.3. Conventional Grinding-Polishing Machines ................................................................. 469 12 Contents 16.4. Relative Velocities between an Arbitrary Pair of Points .............................................. 471 16.5. Upper Disk Relative Velocity ...................................................................................... 472 16.5.1. First Relative Velocity Contribution (V0) Approximate Calculation ................................. 472 16.5.2. Second Relative Velocity Contribution (V1) ..................................................................... 473 16.5.3. Third Relative Velocity Contribution (V2) ......................................................................... 474 16.5.4. Vector Addition of Three Relative Velocity Contributions ................................................ 476 16.6. Lower Disk Relative Velocity ...................................................................................... 476 16.6.1. Approximate Calculation of the First Relative Velocity Component (V0) ......................... 476 16.6.2. Calculation of the Relative Velocity Second Component (V1) ........................................... 477 16.6.3. General Expression for the Third Relative Velocity Component (V2) ............................... 478 16.6.4. Vector Addition of Three Relative Velocity Contributions ................................................ 480 16.7. Boundary Conditions in Abrasive Wear Process ......................................................... 481 16.8. Pressure Distribution within Disks Contact Area ......................................................... 481 16.9. Arm Stroke Adjustments (Controlling Curvature Radius and Figure) ......................... 482 16.10. Simulation and Real Optical Manufacturing .............................................................. 482 16.11. Concluding Remarks .................................................................................................. 484 Acknowledgment .................................................................................................................. 484 References ............................................................................................................................. 485 17. Quantitative Phase Microscopy and Tomography with Spatially Incoherent Light ..................................................................................................... 487 17.1. Introduction .................................................................................................................. 487 17.2. Concepts of Coherence................................................................................................. 489 17.2.1. Temporal Coherence......................................................................................................... 489 17.2.2. Spatial Coherence ............................................................................................................. 490 17.2.2.1. Transverse Spatial Coherence................................................................................. 491 17.2.2.2. Longitudinal Spatial Coherence ............................................................................. 492 17.3. Synthesis of Low Spatial and High Temporal Coherent light Source .......................... 493 17.3.1. Experimental Details ........................................................................................................ 495 17.4. Phase Retrieval Algorithm ........................................................................................... 496 17.4.1. Five Step Algorithm .......................................................................................................... 496 17.4.2. Fourier Transform Algorithm ........................................................................................... 497 17.5. Characterization of System Parameters ........................................................................ 498 17.5.1. Temporal and Spatial Phase Noise ................................................................................... 498 17.5.2. Transverse Resolution....................................................................................................... 499 17.5.3. Axial Resolution ................................................................................................................ 499 17.6. Spatial Phase Noise Comparison in Case of Direct Laser and Synthesized Light Source .................................................................................................................. 501 17.6.1. Standard Flat Mirror ........................................................................................................ 501 17.6.2. Human Red Blood Cells .................................................................................................... 502 17.7. Quantitative Phase Imaging of Industrial and Biological Cells Using Pseudo Thermal Light Source.................................................................................................... 503 17.7.1. QPI of Standard Waveguide ............................................................................................. 503 17.7.2. QPI of Human RBCs ......................................................................................................... 503 17.7.3. QPI of Onion Cells ........................................................................................................... 505 17.8. Profilometry and Optical Coherence Tomography ...................................................... 506 17.8.1. Profilometry of Standard Gauge Block and Indian Five Rupee Coin ............................... 506 17.8.2. OCT of Multilayered Onion Sample ................................................................................. 507 13 Advances in Optics: Reviews. Book Series, Vol. 3 17.9. Conclusions................................................................................................................... 508 Acknowledgements................................................................................................................ 509 References ............................................................................................................................. 509 Index ............................................................................................................................. 513 14 Contributors Contributors Mojtaba Mansour Abadi School of Engineering, University of Glasgow, Glasgow, Scotland, UK Azeem Ahmad Department of Physics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India, E-mail: ahmadazeem870@gmail.com Luis C. Alvarez-Nuñez Universidad Nacional Autónoma de México, Instituto de Astronomía, Ciudad Universitaria, Mexico City, Mexico, E-mail: lalvarez@astro.unam.mx Anatoly Babchenko Lev Academic Center, Faculty of Engineering, Department of Applied Physics/Electro-Optics Engineering, Jerusalem, Israel Igor Buzalewicz Bio-Optics Group, Department of Biomedical Engineering, Faculty of Fundamental Problems of Technology, Wroclaw University of Science and Technology, 27 Wybrzeze S. Wyspianskiego St., 50-3708, Wroclaw, Poland Oscar Chapa Universidad Nacional Autónoma de México, Instituto de Astronomía, Ciudad Universitaria, Mexico City, Mexico P.-J. Chen Dept. of Optical Science, Tokushima University, Japan Dept. of Electronic Engineering, National Taiwan University of Science and Technology, Taiwan Ilan Gadasi Lev Academic Center, Faculty of Engineering, Department of Applied Physics/Electro-Optics Engineering, Jerusalem, Israel Ying Guo Harbin Institute of Technology, China W. M. Hao Missoula Fire Sciences Laboratory, Missoula, Montana, 59808, USA B. Imran Akca Institute for Lasers, Life and Biophotonics Amsterdam, Department of Physics and Astronomy, VU University Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands Carolina Keiman Universidad Nacional Autónoma de México, Instituto de Astronomía, Ciudad Universitaria, Mexico City, Mexico 15 Advances in Optics: Reviews. Book Series, Vol. 3 H. Kishikawa Department of Optical Science, Tokushima University, Japan N. Korneev National Institute for Astrophysics, Optics and Electronics, A.P. 51, Puebla 72000, Mexico V. Kovalev Missoula Fire Sciences Laboratory, Missoula, Montana, 59808, USA Katarzyna Kowal Bio-Optics Group, Department of Biomedical Engineering, Faculty of Fundamental Problems of Technology, Wroclaw University of Science and Technology, 27 Wybrzeze S. Wyspianskiego St., 50-3708, Wroclaw, Poland Trung-Thanh Le International School (VNU-IS), Vietnam National University (VNU), 144 Xuan Thuy, Cau Giay, Hanoi, Vietnam S.-K. Liaw Dept. of Electronic Engineering, National Taiwan University of Science and Technology, Taiwan Mariusz Linard Bio-Optics Group, Department of Biomedical Engineering, Faculty of Fundamental Problems of Technology, Wroclaw University of Science and Technology, 27 Wybrzeze S. Wyspianskiego St., 50-3708, Wroclaw, Poland S.-S. Ling Department of Electrical Engineering, Faculty of Engineering, University of Malaya, Kuala Lumpur, 50603, Malaysia, E-mail: s.shiling@hotmail.com Cong Liu Key Laboratory of Mechanics on Disaster and Environment in Western China attached to the Ministry of Education of China, Lanzhou University, Lanzhou, Gansu 730000, PR China Department of Mechanics and Engineering Sciences, College of Civil Engineering and Mechanics, Lanzhou University, Lanzhou, Gansu 730000, PR China Weidong Liu Laboratory for Precision and Nano Processing Technologies, School of Mechanical and Manufacturing Engineering, University of New South Wales, NSW 2052 Australia Ja-Yu Lu Department of Photonics, National Cheng Kung University, Tainan 70101, Taiwan E-mail: jayu@mail.ncku.edu.tw S. Mansurova National Institute for Astrophysics, Optics and Electronics, A.P. 51, Puebla 72000, Mexico 16 Contributors Dalip Singh Mehta Department of Physics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India, E-mail: mehtads@physics.iitd.ac.in M. Okada Dept. of Optical Science, Tokushima University, Japan Antonio Parretta Physics and Earth Science Department, University of Ferrara, Italy A. Petkov Missoula Fire Sciences Laboratory, Missoula, Montana, 59808, USA Halina Podbielska Bio-Optics Group, Department of Biomedical Engineering, Faculty of Fundamental Problems of Technology, Wroclaw University of Science and Technology, 27 Wybrzeze S. Wyspianskiego St., 50-3708, Wroclaw, Poland Raveendran P. Department of Electrical Engineering, Faculty of Engineering, University of Malaya, Kuala Lumpur, 50603, Malaysia, E-mail: ravee@um.edu.my P. Rodriguez National Institute for Astrophysics, Optics and Electronics, A.P. 51, Puebla 72000, Mexico D. Sanchez de la Llave National Institute for Astrophysics, Optics and Electronics, A.P. 51, Puebla 72000, Mexico Chandar Shekar Department of Physics, KASC, G.N Mills post, Coimbatore -641029, Tamilnadu, India Agnieszka Suchwałko QUANTUP, Wrocław, Poland K. Takahashi Dept. of Optical Science, Tokushima University, Japan S. Urbanski Missoula Fire Sciences Laboratory, Missoula, Montana, 59808, USA Vadivelan V. R&D Department, Ignetta holographic (P) Ltd, Madukkari, Coimbatore – 641105, Tamilnadu, India Department of Physics, KASC, G.N Mills post, Coimbatore -641029, Tamilnadu, India C. Wold Missoula Fire Sciences Laboratory, Missoula, Montana, 59808, USA 17 Advances in Optics: Reviews. Book Series, Vol. 3 Borwen You Division of Applied Physics, Faculty of Pure and Applied Sciences, University of Tsukuba, Tennodai 1-1-1, Tsukuba, Japan Y.-L. Yu Dept. of Electronic Engineering, National Taiwan University of Science and Technology, Taiwan Y. P. Yu Department of Computer Science and Mathematics, Faculty of Computing and Information Technology, Tunku Abdul Rahman University College, 53300, Malaysia, E-mail: yuyp@acd.tarc.edu.my Ping Yuan Harbin Institute of Technology, China Ariel Zev Lev Academic Center, Faculty of Engineering, Department of Applied Physics/Electro-Optics Engineering, Jerusalem, Israel Liangchi Zhang Laboratory for Precision and Nano Processing Technologies, School of Mechanical and Manufacturing Engineering, University of New South Wales, NSW 2052 Australia Xingyi Zhang Key Laboratory of Mechanics on Disaster and Environment in Western China attached to the Ministry of Education of China, Lanzhou University, Lanzhou, Gansu 730000, PR China Department of Mechanics and Engineering Sciences, College of Civil Engineering and Mechanics, Lanzhou University, Lanzhou, Gansu 730000, PR China E-mail: zhangxingyi@lzu.edu.cn, Tel: +86-931-8914560. Yundong Zhang Harbin Institute of Technology, China Li Zhao Harbin Institute of Technology, China Youhe Zhou Key Laboratory of Mechanics on Disaster and Environment in Western China attached to the Ministry of Education of China, Lanzhou University, Lanzhou, Gansu 730000, PR China Department of Mechanics and Engineering Sciences, College of Civil Engineering and Mechanics, Lanzhou University, Lanzhou, Gansu 730000, PR China Fuxing Zhu Harbin Institute of Technology, China 18 Preface Preface It is my great pleasure to introduce the third volume of new Book Series ‘Advances in Optics: Reviews’ started by the IFSA Publishing in 2018. Three volumes were published in this year. The ‘Advances in Optics: Reviews’ Book Series is published as an Open Access Books in order to significantly increase the reach and impact of these volumes, which also published in two formats: electronic (pdf) with full-color illustrations and print (paperback). The third of three volumes of this Book Series has organized by topics of high interest. In order to offer a fast and easy reading of each topic, every chapter in this book is independent and self-contained. All chapters have the same structure: first an introduction to specific topic under study; second particular field description including sensing or/and measuring applications. Each of chapter is ending by complete list of carefully selected references with books, journals, conference proceedings and web sites. The Vol.3 is devoted to various topics of applied optics and contains 17 chapters written by 49 experts in the field from 14 countries: Australia, China, India, Israel, Italy, Japan, Malaysia, Mexico, The Netherlands, Poland, Taiwan, UK, USA and Vietnam. ‘Advances in Optics: Reviews’ Book Series is a comprehensive study of the field of optics, which provides readers with the most up-to-date coverage of optics, photonics and lasers with a good balance of practical and theoretical aspects. Directed towards both physicists and engineers this Book Series is also suitable for audiences focusing on applications of optics. A clear comprehensive presentation makes these books work well as both a teaching resources and a reference books. The book is intended for researchers and scientists in physics and optics, in academia and industry, as well as postgraduate students. I shall gratefully receive any advices, comments, suggestions and notes from readers to make the next volumes of ‘Advances in Optics: Reviews’ Book Series very interesting and useful. Dr. Sergey Y. Yurish Editor IFSA Publishing Barcelona, Spain 19 Chapter 1. Health and Wellness Fiber Optic Sensors in IoT Application Chapter 1 Health and Wellness Fiber Optic Sensors in IoT Application Anatoly Babchenko, Ariel Zev and Ilan Gadasi1 1.1. Introduction Things around us have been connected for decades. Car door openers, TV remote controls and other devices have been part of our life for generations. Industrial and medical applications of these technologies are also nothing new. In fact, even Internet connected to the physical world via smart sensors (“Internet of Things”) is not a recent invention; it was proposed around thirty years ago. However, recent developments in both sensors, especially fiber optic sensors, and networks are enabling a much greater range of connected objects and devices. The potential applications of these new systems are virtually limitless, and they have the ability to greatly improve quality of life. In this chapter, we explore a wide range of topics related to Internet of Things (IoT) and fiber optic sensors’ applications for health and wellness monitoring. Health and wellness represent one of the most attractive areas for IoT [1] and the current review is related directly to this field. The real-world example have been provided to give the reader practical insights into the successful development of IoT system for child’s wellness monitoring. The chapter is organized as follows (Fig. 1.1). Section 1.1 introduces Internet of Things systems - a reality that surrounds us and intersects with many aspects of our lives. Section 1.2 presents Fiber Optic Sensors for health and wellness monitoring that will play a central role in providing the success of IoT in these applications. Section 1.3 shows IoT with fiber optic sensing technology designed for child’s wellness monitoring. The conclusion is drawn in Section 1.4. Anatoly Babchenko Lev Academic Center, Faculty of Engineering, Department of Applied Physics/Electro-Optics Engineering Jerusalem, Israel 21 Advances in Optics: Reviews. Book Series, Vol. 3 Fig. 1.1. Overview structure. 1.2. Internet of Things A reality of Internet of Things has changed the world in which we live. The term “Internet of Things” was first used by British technology pioneer Kevin Ashton to describe a system where the Internet is connected to the physical world via sensors [2]. Ashton illustrated the power of connecting Radio-Frequency Identification tags used in corporate supply chains to the Internet in order to count and track goods without the need for human intervention. The concept of combining computers and networks to control devices has been around for decades. Early Machine to Machine (M2M) applications have typically sent all remote data from the devices to the data centre for processing [3-5]. However, as more data is generated at the edge in real-time, a greater need for real time decision making also at the edge will be required. Many of these early applications, however, were not based on Internet Protocol (IP) and Internet standards. One of the first Internet Protocol “devices” has been developed by Simon Hackett and John Romkey, becoming the hit of the 1990 Interop. They connected a Sunbeam Deluxe Automatic Radiant Control Toaster to the Internet with TCP/IP networking, and controlled with a Simple Networking Management Protocol Management Information Base (SNMP MIB). Other “thing” was the internet-connected soda vending machine that 22 Chapter 1. Health and Wellness Fiber Optic Sensors in IoT Application allows customers to check the availability status of soda remotely using a finger interface. Originally developed circa 1982 by a group of students at Carnegie Mellon University, the machine became known as one of the very first Internet appliances and inspired a number of modified versions allowing people to queue their purchases on the machine remotely via Internet, such as the Trojan Room Coffee Pot. A design student at Brunel University, UK, has developed a toaster that takes meteorological information from the internet and then browns his bread with an image of what weather to expect on the way to work. The experiment was adopted later by Electrolux to produce a more detailed weather report. All these freakish beginnings helped create the ground for today’s IoT that is rapidly becoming a part of every aspect of our lives. The IoT was added to the 2011 annual Gartner Hype Cycle (Fig. 1.2) that tracks technology life-cycles from "technology trigger" to "plateau of productivity" and has hit the Hype Cycle's "Peak of Inflated Expectations" in 2014 [6]. Fig. 1.2. Gartner Hype Cycle for Emerging Technologies, 2014. According to the McKinsey Global Institute [7] IoT has a total potential economic impact of $3.9 trillion to $11.1 trillion a year by 2025 and Morgan Stanley projects 75 billion networked devices/objects by 2020 [8]. Business-to-business applications of IoT systems certainly capture more value than consumer uses, although consumer application, such as health and wellness, attract more and more attention [9] and can create significant value in near future. The healthcare is 23 Advances in Optics: Reviews. Book Series, Vol. 3 shifting from reactive approach towards health conditions to a more proactive approach in terms of early detection of conditions, prevention and well-being management. Physical condition monitoring, their automated processing and automatic management of individual well-being based on IoT technologies [10] will play a key role in providing better healthcare services and improving the quality of life. Advances in IoT and sensors technologies have made possible the connection of more and more devices to the Internet. This is leading to a new wave of applications that have the potential to dramatically improve the way people work, learn and live. Sensors play a key role in connecting the physical world with the digital world and they are in the core of IoT [11]. For example, home-based environmental monitors allow people to track ambient air quality. They can use this data to either modify their environment or alter their behaviour in order to maintain their health and wellness [12]. Some, like the U.K.-based technology and development organization The Technology Partnership, argue that IoT should really be called the Internet of Sensors (IoS) [13]. In the IoT, things at the edge can create significantly large amounts of data. Transmitting all that data to the cloud and transmitting response data back demands wide bandwidth and requires a considerable amount of time. Rather than having to be transmitted to the cloud the data from sensors or internet can be processed locally in smart devices with a fog (fog is a cloud close to the ground) computing data processing [14-15]. Companies that adopt fog computing gain deeper and faster insights, leading to increased business agility, higher service levels, and improved safety. 1.2.1. Communication Models Used by IoT The Internet of Things is connecting various sensors and devices, based on them. The basic principle of every IoT is how devices/sensors connect and communicate. Internet Architecture Board – a group within the Internet Society that oversees the technical evolution of the Internet – defined four common communication models used by IoT [16]: Device-to-Device, Device-to-Cloud, Device-to-Gateway, and Back-End Data-Sharing. Device-to-device (Fig. 1.3) communication represents two or more devices/sensors that directly connect and communicate between one another. This model is commonly used in home IoT systems to transfer small data packets of information between sensors at a relatively low data rate. Device-to-device is used in wearable IoT devices like a heart rate or breathing efforts monitor connected to a smartwatch where data doesn’t necessarily have to be shared with multiple people. Fig. 1.3. Device-to-device model. 24 Chapter 1. Health and Wellness Fiber Optic Sensors in IoT Application Device-to-Cloud (Fig. 1.4) communication involves an IoT devices/sensors connecting directly to an Internet cloud service to exchange data and control message traffic. It often uses traditional wired Ethernet or Wi-Fi connections, but can also use mobile technology. Cloud connectivity lets the big amount of users to obtain remote access to various sensors and applications. It also gives an opportunity for big data processing and potentially supports pushing software updates to the devices. This model can be used for various health and wellness IoT systems. Fig. 1.4. Device-to-Cloud model. Device-to-Gateway (Fig. 1.5) is a model where IoT devices connect to an intermediary device to access a cloud service. The example can be a fitness device that connects to the cloud through a smartphone app like in Nike personal trainer system. Fig. 1.5. Device-to-Gateway model. Back-End Data-Sharing (Fig. 1.6) model refers to a communication architecture that enables users to export and analyze smart object data from a cloud service in combination with data from other sources. An example of this model is a fitness tracking application MapMyFitness [17]. It compiles fitness data from various devices like Fitbit, Adidas miCoach and Wahoo Bike Cadence Sensor. This means an exercise can be analyzed from the viewpoint of various sensors. 25 Advances in Optics: Reviews. Book Series, Vol. 3 Fig. 1.6. Back-End Data-Sharing model. 1.2.2. Main Existing Applications of IoT At present, a wide range of industry sectors are considering the potential for incorporating IoT technology into their products, services, and operations [18-19]. Here are the main applications of IoT devices and sensor systems: Health and wellness [20-23]. Disease management; wearables, devices attached to (including smart bed, chair, etc.) or inside the human body - to monitor and maintain human health and wellness; sport and fitness. Sensors - pressure, acceleration, shape/form, temperature, chemical, bio sensors. Wearable IoT systems have many forms, such as glasses, watches, helmet, jewelry, collar, wristband, belts, rings, gloves, body-wear clothing, shoes and socks. Smart home [24-26]. Home and building automation with controllers and monitoring devices for security, garage, fire alarm, water, light, home electronics (TV, airconditioner, refrigerator, etc.) and network. Sensors - temperature, humidity, chemical, imaging, motion, power. Transportation [27-28]. Devices inside staying or moving vehicles including cars, trucks, trains, ships and aircraft. Sensors - gyroscope, velocity, temperature, humidity, pressure, chemical. City [29]. Systems in and outside urban environments, streets, buildings, railroad tracks, autonomous vehicles (outside urban locations), flight navigation, real-time routing, connected navigation, shipment tracking. Sensors - gyroscope, environmental monitoring, chemical, light, noise, traffic control, structural health monitoring. Others: security and public safety [30]. Factories, farms, hospitals and clinics [31], stores, banks, restaurants, arenas; consumers [32]. 26 Chapter 1. Health and Wellness Fiber Optic Sensors in IoT Application 1.2.3. Leading Companies Here are the leading companies that have ventured into the IoT world. Medtronic’s Continuous Glucose Monitoring [33] is a wearable device that displays a constant reading of a diabetic’s blood glucose level. A tiny electrode is inserted under the skin, which then transmits the glucose reading via wireless radio frequency to a display device. CellNovo [34] who have developed the world’s first mobile diabetes management system. The device has a built-in insulin pump and monitoring system that records glucose level and activity monitor to track and record exercise. It can detect possible hypos and hypers before they happen, warning the user before it’s too late. GlowCap device from Vitality [35]. This is an IoT digitized medicine bottle that can be programmed so that when the user needs to take their tablet, it flashes and sounds notifications as a reminder. It also records when the bottle is opened and sends information back to the clinic to inform them. It even features a button at the bottom of the bottle, that when pressed, automatically orders the next prescription/order from the pharmacy. AliveCor [36] heart monitor. Traces standard ECG heart rhythms with a mobile device monitor. Qualcomm Life’s [37] wireless health system stores medical data in a cloud-based platform from various medical devices. Facilitates continuum of care and improves health care delivery. Fitbit Flex [38] tracks activity, calories burned, diet, and sleep. Zephyr’s BioHarmess [39] captures and transmits comprehensive physiological data. BodyMedia’s [40] on-body monitoring system collects information on temperature, moisture, and movement. Wireless blood pressure wrist monitor by iHealth [41] tracks changes in pulse rate, systolic and diastolic blood pressure. Ring [42] is a connected doorbell and home security solution used for home automation and for helping disabled or the elderly. It alerts users to motion as soon as it’s detected, so they can remotely monitor their door. A doorbell with a built-in camera, motion sensor and two-way communication allows a house owner to check on who is at the door or even nearby before ever getting near opening it. Philips’ Hue Light Bulbs and Bridge [38] provide a bridge and connected bulbs that allow the user to control their home lighting from the palm of their hand. 27 Advances in Optics: Reviews. Book Series, Vol. 3 iRobot’s Roomba [43] is a smart vacuum cleaner equipped with iAdapt technology, a system of software and sensors that enables Roomba to find its way around a home of any shape or size. Ralph Lauren’s Polo Tech Shirt [44] is a shirt with conductive threads woven into it and relays information like heart rate and breathing data to a Bluetooth-connected iPhone or iPad. Nest [38], is a smart thermostat that’s connected to the internet. The Nest learns family’s routines and will automatically adjust the temperature. Samsung SmartThings [45] system controls lights, locks, plugs, thermostats, cameras, and speakers from a central hub that can be accessed from a smartphone, as well as a wide range of sensors that can be used with the system to create a security solution that’s integrated with all of the other electronics at home. Cisco’s Connected Factory [46] is a remote monitoring and access technology to the equipment used in manufacturing. DHL’s IoT Tracking and Monitoring [47] released a report detailing some potential uses of IoT technology that includes vehicle monitoring and maintenance, real-time tracking of packages, environmental sensors in shipping containers, informationgathering on employees and tools, and a number of safety-enhancing features for vehicles and people. Ericsson Maritime ICT [48] which provides infrastructure for ships, ports and terminals. Via its 'Maritime ICT Cloud' system, the company uses sensors on its ships to monitor vessel location, speed and the temperature for heat sensitive cargo, all in real-time. 1.3. Fiber Optic Sensors for Health and Wellness Application Fiber Optic Sensors represent a technology that can be successfully applied to a multitude of sensing applications. Pressure, stress, strain, vibration, temperature, displacement, concentration, density, temperature, or chemical composition are just some of the phenomena that can be measured [49]. A huge number of fiber optic sensing devices for biomedical applications have been designed in the last years. The most reported fiber optic sensors are for biological, biomechanical, and physiological parameters. For biological purposes, several optical devices have been developed [50-51] to target cells and proteins, identify DNA markers or to measure humidity/moisture. In the field of biomechanics, sensors based on optical fibers are presented to measure displacement, force, acceleration, angle and pressure [52]. Human physiological parameters such as respiratory rate [53], temperature [54], pH [55] or heart beat [56] can be monitored with fiber optic sensors. From a biomedical engineering point of view, optical fibers and sensors based on them, possess many advantages that could be wisely used for health and wellness monitoring. Some of them are briefly explained below: 28 Chapter 1. Health and Wellness Fiber Optic Sensors in IoT Application 1. Biomedical compatibility. The material of optical fiber sensing element does not present side effects when attached to person, embedded in his/her organs or placed in biological substance [57]. 2. Small Size and Light Weight. The size and weight of the optical fiber are very small (approximately 100 μm). The fiber can be embedded, into the fabric for example, and to measure in real time various body’s parameters [58]. 3. Low Cost. Optical fibers, both polymer and silica, are cheap materials for final application. 4. Flexibility. An optical fiber can reach almost any place in the human body and measure it during surgery or other medical procedures. For instance, a guiding catheter introduced into the coronary artery, and blood pressure measured by the fiber optic sensor [59]. 5. Reliability. The issue of reliability of optical fiber and sensors becomes increasingly important, as they are more and more frequently used in applications where a failure of the sensor might have dramatic consequences on patient’s health or life. An example of such an application is integrated microfluidic chip for glucose detection [60]. 1.3.1. Working Principles and Applications It is not possible to describe all the working principles and applications of fiber optic sensors in one chapter. However fiber optic sensors for health and wellness can be easily classified into five major categories according to the location of the sensor application. 1. Sensors attached or embedded into expandable belts, patches, helmets or special garments (gloves, shoes, smart textiles) as well as affixed directly to the body, measuring pressure, angle, strain, vibration, temperature, displacement or density. 2. Sensors placed in a mouth, an ear, a nostril or oxygen mask, measuring temperature, humidity, pressure or force of inhaled/exhaled air (flow). 3. Sensors attached to chairs, placed on/in/under a bed mattress, or embedded into cushion, measuring the strain, pressure, or force caused by respiration, heart or other physiological functions. 4. In-vivo sensors placed or implanted inside a human body (heart, blood vessels etc.), measuring pressure, temperature and density. 5. Sensors used in laboratory for in-vitro tests, measuring chemical composition. The growing interest in the smart fiber optic sensors for health and well-being applications is driven by the success of IoT, as the next evolution of the Internet. These sensors allow the measurement of various biophysical parameters employing a large number of configurations and working principles [61]. Fiber optics sensors can be classified under two major categories: the sensing location and the operating principal. Depending on 29 Advances in Optics: Reviews. Book Series, Vol. 3 location of sensor, a fiber sensor can be classified to intrinsic or extrinsic. In intrinsic sensors, the internal property of the optical fiber itself converts the environmental changes into a modulation of optical signal. In contrast to intrinsic, in extrinsic sensor the modulation takes place outside the fiber. In this case the fiber merely acts as a conduit to transport light signal to and from the sensor head. Based on the operating principal and demodulation technique, fiber optic sensors can be classified into few major categories: intensity, phase, wavelength, polarisation and distributed sensors (Brillouin, Raman and Rayleigh). 1.3.1.1. Intensity-Modulated Fiber Optic Sensors An intensity-modulated sensor relies on variations of the radiant power transmitted through an optical fiber with respect to the measurand. A wide range of sensors based on intensity modulation have previously been studied and tested on patients to monitor their physiological parameters. Fig 1.7 (a, b), 8 show how intensity-based optical fiber extrinsic and intrinsic sensors monitor human seated spinal posture [62]. In one of the optical sensor for back-pain patients [63] the bending angle of spine is measured as the angle between the emitting and receiving fibers that changed. Two separate configurations of the sensor are considered: fiber longitudinal displacement loss (Fig. 1.7 (a)) and fiber tilt angle loss (Fig. 1.7 (b)). The light intensity decreases with the increase in the gap between emitting and receiving fibers as well as increases in bending angle between them. Fig. 1.7. (a) Spine-bending sensor with a fiber gap; (b) Fiber tilt angle. Another sensor (Fig. 1.8) has been designed using side-polished plastic optical fiber [64]. This work describes the evaluation of a wearable bending optical fiber sensor for monitoring seated spinal posture. It is also possible to measure the direction of the bending throughout the measurement. If the polished area is at the external side (convex) of the bending fiber, more light will escape the fiber, thus giving a higher attenuation and vice versa. 30 Chapter 1. Health and Wellness Fiber Optic Sensors in IoT Application Fig. 1.8. Side polished optical fiber for bending sensor. Other solutions utilising intensity-modulated sensors have been developed [65]. In this model, the area of polymer optical fiber is replaced by a uniform layer with a complex refractive index. The changes in the absorption characteristics of the polymer depend on the environmental properties in the sensing area and the light intensity changes as a result of light attenuation in this imperfected fiber. Micro and macrobending fiber-optic sensors In sensors measuring transmission loss caused by micro changes of the shape of an optical fiber or in fiber bends with a radius of curvature well above the fiber diameter, i.e., in socalled micro- and macro bend sensors, respectively, the intensity of the light reaching the receiver is measured. Various human body movements (caused by respiration and heart function, among other things) are a complicating factor since these movements produce micro- and macrobends of fibers with a variable radius of curvature. Thus, along the axis of a bent fiber, the layout of the mode fields continuously changes as the energy radiates; this is seen in the form of light intensity changes at the receiver. The measuring system for micro- and macrobend sensors is distinguished by a simple design for the sensors alone as well as for the associated transceiver modules (light source and photodetector). The sensors can be embedded in a cushion, mattress, armchair, on which the patient sits or lies during monitoring, or, special garments (textiles) affixed directly to the body, which are worn by the monitored person. A micro-bending fiber based sensor was reported in [66]. Authors propose a smart cushion for heart rate monitoring. The cushion consists of an integrated micro-bending fiber sensor and a new heart rate extraction algorithm. The principle of using micro-bending fiber sensor for heart rate measurement is based on Ballistocardiogram, which measures the body vibration caused by the heartbeat. The sensor contains a section of multimode fiber clamped between a pair of micro-benders, as shown in Fig. 1.9. As the displacement between two micro-benders changes, the light intensity of the clamped multimode fiber changes with subject’s body vibrations caused by respiration/heart beating, i.e. the light intensity in the micro-bending fiber is modulated by the body vibrations. This modulated signal is picked up by a detector inside the optical transceiver. The main problem associated with the use of microbending devices is the narrow range of displacement measurement. 31 Advances in Optics: Reviews. Book Series, Vol. 3 Fig. 1.9. Micro-bending fiber sensor. The macro-bending effect is used for many applications and one of them is measuring human body motions. Transmitted light power in the silica optical fiber decreases exponentially when the fiber is bended. By using several optical fiber curvature sensors, it is possible to measure two or more degrees of freedom of motion. One classic example is the use of simple silica fiber to determine angular movements of human joints. Kyoobin Lee et al. [67] presented the application for physically handicapped persons whose arms are disabled. The wearable master device is used for human shoulder motions. It has also shown that a subject can control a two-wheeled mobile robot like a wheelchair. Another example [68] demonstrates the feasibility of using flexible polymer optical fibers to measure the respiratory rate and to evaluate the type of breathing. The fibers that react to applied pressure were integrated into a carrier fabric to form a wearable sensing system. This wearable system enables to keep track of the way of breathing (diaphragmatic, upper costal and mixed) when the sensor is placed at different positions of the torso. In their study Jao-Hwa Kuang et al. [69] presented a sensitive plastic optical fiber displacement sensor based on cyclic bending. The POF sensor is pressed by cylindrical models without surface damage. Dual bending model is used to increase the sensitivity of the POF displacement sensor. The results showed that the sensitivity can be improved by regulating the number of rollers, the distance between top and bottom plates, and the interval between two rollers. Sensors based on the polymer optical fiber macrobending technique have a wide measurement range, but within this range, the resolution is very low. Polymer optical fiber with disturbance on the outer and/or inner side of a U-shaped bent fiber (Fig. 1.10) can be utilized as a displacement, high sensitive sensor [70] for different medical applications, such as respiratory monitoring [71] or smart bed [72]. Use of a graded-index fiber instead of a step-index fiber for bending measurements resulted in an increase in sensitivity [73]. The fiber deformation sensor with the highest sensitivity to bending (15 half-loops, 3 imperfection areas), had a change in radius with a resolution of 20 µm, over a range from 25 to 50 mm. Additional sensitivity to bending and optimization of the sensor can be obtained by varying the different abrasion angle, imperfection location angle, imperfection displacement and V-grove cavity depth, and by splitting the imperfections into multiple small imperfections rather than a single large imperfection [74]. 32 Chapter 1. Health and Wellness Fiber Optic Sensors in IoT Application Fig. 1.10. U-shaped fiber optic sensing element. Hetero-core optical fiber The development of a new sensitive glove is described in [75] using hetero-core fiberoptic nerve sensors, in which the glove not only works as a motion capture tool but also as a tactile sensing device and detects the angles of finger joints. Hetero-core optical fibers are fabricated by inserting a small portion of fiber with a smaller core diameter into two identical fibers with larger core diameters which is illustrated in Fig. 1.11. The cladding diameters of the fibers should be the same. The principle behind the phenomenon is the same with the evanescent wave sensors, but hetero-core optical fibers are easier to fabricate, since control of section length is easier compared to etching. Fig. 1.11. Hetero-core optical fiber structure. Hetero-core fiber optic sensors have great sensitivity because of the mode coupling taking place at the splice region. Since some of the power is coupled to the cladding, the leakage gets easier by an external effect which is to be detected. Since there is a great difference in core diameters, light can largely leak into the cladding part after the splice. Because of this structure, the light in the cladding may be affected by environmental conditions easily. 1.3.1.2. Interferometric Fiber Optic Sensors Another important type of a medical fiber optic sensor due to their very high sensitivities is sensors using in-fiber interferometry. Interferometric sensor relies on induced phase 33 Advances in Optics: Reviews. Book Series, Vol. 3 change in light propagating through the optical fiber. Fiber optic interferometers have been developed in their most popular configurations, i.e., Michelson, Mach-Zehnder, and Sagnac interferometers [76-77] and also fiber-optic speckle interferometry that, for example, have been used for a human vital signs monitoring [78]. W. B. Spillmann Jr et al. [79] presented the result aimed at the development of a smart bed to non-intrusively monitor patient respiration, heart rate and movement using spatially distributed integrating multimode fiber optic sensors. The system consists of two spatially integrating fiber optic sensors, one of which is based on inter-modal interference and the other on mode conversion. The sensing fiber is integrated into a bed. The basic concept is that any patient movement that also moved an optical fiber within the specified area would produce a change in optical signal that would indicate patient movement. The physical repetitive movement caused by respiration or heart pumping is contained within the signal as well and can be extracted via appropriate signal processing. Two different modal modulation approaches are used with 200 μm core step index silica multimode optical fibers excited by a coherent laser source. The fiber is arranged on the mattress in two sinusoidal overlapping patterns arranged orthogonal to each other so that the fiber in each pattern crossed the fiber in the other pattern at an angle of 90°. In the statistical mode sensing all guided modes of the fiber are excited and then detected by a low cost digital camera. This is shown schematically in Fig. 1.12. Fig. 1.12. Interferometric fiber optic sensor. In the interferometric fiber-optic bending sensors, the light is split and guided along two different paths, or it is coupled into different optical modes. Recombination of light from the different paths or modes generates interference pattern that is sensitive to fiber bending. Various implementations of the interferometric fiber-optic bending sensors have been proposed, including sensor based on: multimode interference [80], single mode structure [81] and photonics crystal fiber [82]. H. Qu et al. [83] demonstrated an interferometric fiber-optic bending/nano-displacement sensor based on a plastic dual-core fiber with one end coated with a silver mirror. The two fiber cores are first excited with the same laser beam, the light in each core is then back-reflected at the mirror-coated fiber-end, and, finally, the light from the two cores is made to interfere at the coupling end. Bending of the fiber leads to shifting interference fringes that can be interrogated 34 Chapter 1. Health and Wellness Fiber Optic Sensors in IoT Application with a photodetector. Experimentally it was found that the resolution of the sensor is ~3 × 10-4 m-1 for sensing of bending curvature, as well as ~70 nm for sensing of displacement of the fiber tip. 1.3.1.3. Wavelength-Modulated Sensors Fibers with replaced cladding Various techniques have been devised by which a measured modifies the spectrum of a guided light is being measured. A simple example includes glucose fiber optic sensor. A fiber based pH meter has been developed in which the cladding material is replaced with polyaniline polymer, a polymer with broad sensitivity to pH [84]. The sensor is modified by using glucose oxidase immobilised on the polyaniline polymer surface (an enzyme which converts glucose to glucuronic acid, resulting in a pH change) to predict glucose concentration [85]. The near-IR evanescent wave sensor was converted into a glucose sensor by immobilizing glucose oxidase on the surface of the polymer. The enzyme converted glucose to gluconic acid and the resulting pH change was used to predict glucose concentrations. Standard errors of prediction for the concentration range of 0 to 20 mM were 0.25 mM for distilled water and 0.8 mM for buffer solutions. Lossy Mode Resonances (LMR) One of the most relevant factors that make LMRs a good choice for optical fiber sensors (humidity sensors) development is their ability to generate an optical phenomenon that can be detected by the wavelength detection method with the same material that acts as the sensitive layer to the parameter to be measured. The structure of a LMR-based device consists of a waveguide, which allows for accessing the evanescent field, coated with a thin film of the appropriate material. The condition for LMR generation is that the real part of the thin film permittivity is positive and higher in magnitude than both its own imaginary part and the real part of the material surrounding the thin film [86]. LMRs are generated when there is a resonant coupling of light to modes guided in the external coating. The large amount of available materials enables the development of optical fiber sensors for a wide range of applications [87-88]. Fiber Bragg Grating (FBG) FBG sensors have caught attention in the last decade, due to their distinguishing advantages when compared with other sensors. First, they are not sensitive to the light source amplitude fluctuations, since the readout mechanism is based on wavelength instead of light intensity. Second, the Bragg structure is directly written into the fiber core, keeping the overall fiber structure unaffected. FBG sensors are becoming increasingly attractive for healthcare and different wellbeing application [89-90]. Fiber Bragg Gratings are fibers that reflect particular wavelengths of light and transmit all others. This is achieved by creating a periodic variation in the refractive index of the fiber core. At each periodic refraction change, a small amount of light is reflected. All the 35 Advances in Optics: Reviews. Book Series, Vol. 3 reflected light signals combine coherently to one large reflection at a particular wavelength when the grating period is approximately half the input light's wavelength. This is referred to as the Bragg condition, and the wavelength at which this reflection occurs is called the Bragg wavelength. Light signals at wavelengths other than the Bragg wavelength, which are not phase matched, are essentially transparent [91]. This principle is shown in Fig. 1.13. Fig. 1.13. Fiber Bragg Grating. For example, Kalinowski et al. [92] presented the application of FBG for the measurement of bone deformation under load. As the FBG is sensitive to both temperature and deformation, the two parameters can be measured simultaneously using two FBGs with different thermal and deformation sensitivities [93]. FBG sensors have several advantages over existing imaging modalities and measuring methods, which make them well-suited for use in a clinical environment, especially for a flexible surgical instruments. Flexible minimally invasive surgical instruments can be used to reach difficult-to-reach locations within the human body. Accurately steering these instruments requires information about the shape of the instrument. In order for FBGs to measure shape and 3D deformations in general they are used in orthogonally arranged arrays where each FBG measures one component of the 3D strain as a wavelength shift of its reflection spectrum peak [94]. 3D shape sensing could be realised with series of FBGs embedded off axis along different directions inside optical fibers [95]. A novel approach has been recently demonstrated for 3D shape sensing by using two weakly titled Bragg gratings spliced together such that their tilt plane directions are oriented ~90 degree from each other [96-97]. The transmission spectrum of this device has two resonances that respond differentially to bending along perpendicular directions, one for each of the tilted FBG. Results demonstrate that bending directions from 0 to 180 degrees and curvature magnitudes between 0 and 3 m−1 can be extracted from each pair of resonance transmission values in a single measurement using unpolarized light. The measurement sensitivities obtained from the two TFBGs range from −0.33 to + 0.21 dB/m-1, depending on orientation. Another example of FBG’s biomedical usage is a skin layer that can be easily attached to the subject’s body under monitoring. The solution relies on the development of a methodology to embed FBG sensors on a flexible polyvinyl chloride skin foil [98], using standard industrial fabrication processes. It is possible to achieve a good bonding between the sensor and the foil, which allows the sensor to track with success the applied 36 Chapter 1. Health and Wellness Fiber Optic Sensors in IoT Application displacement to the foil. A linear response of the sensor with a slope of 7.8 nm per 1 % elongation emphasizes its performance. Long-period fiber gratings (LPG) Long-period fiber gratings (LPG) consist of a periodic modification of the refractive index of the core (Fig. 1.14) of a single-mode optical fiber [99]. In opposition to FBG, which have a sub-micron period and couple light from the forward-propagating mode of the optical fiber to a backward counter-propagating mode, LPGs have a period typically in the range of 100 μm to 1 mm. This provokes in LPGs a coupling of light between the guided core mode and various co-propagating cladding modes. Coupling to the cladding modes is wavelength selective, resulting in a series of attenuation bends in the transmission spectrum. Fig. 1.14. Long-period fiber gratings. A long period grating coated with hydrogel has been developed [100] for monitoring the relative humidity (RH) level which has an important influence on several biomedical processes [101]. The response wavelength of the LPG varies with the changes of the relative humidity. The changes are based on the effect of the hydrogel thin film, the index of which increases with the increasing RH. Experiment shows that the hydrogel-coated LPG sensor is highly sensitive between 38.9 % and 100 % RH, and behaves linearly with humidity with an accuracy of ±2.3 % RH. The feasibility to monitor health condition (breathing efforts) of patients was demonstrated [102], by using silica fiber sensor woven into bandage or attached onto garment based on LPGs technique. However, the poor compatibility of the sensors with industrial textile processes limits their use for medical monitoring purposes. 1.3.2. Multicore Fiber Recently, there has been increased interest in fiber optic sensors for medical applications based on multicore fibers. These include distributed temperature [103], strain [104], and shape [105]. 37 Advances in Optics: Reviews. Book Series, Vol. 3 The complete integrated optical fiber assembly suitable for shape sensing has been developed [106]. Shape sensing using optical fibers exploit the strain sensitivity of light propagating in an optical fiber waveguide core. When such a core is offset from the center of a fiber it experiences a strain that depends on the curvature of the fiber. With more than one offset core, the direction of the bend may also be determined. Sensitivity to fiber twist can be introduced by adding a permanent twist to the outer fiber cores. In this way, when the fiber is twisted, the outer cores will all be strained in the same way, while the center remains unstrained. Several fiber designs used to satisfy this set of sensing requirements. The most straightforward design has offset cores at equal radius surrounding a central core. The module consists of a length (> 1 m) of twisted multicore optical fiber with fiber Bragg gratings inscribed along its length. The fiber has a compact 180 micron coated diameter, a twist of 50 turns per meter and grating reflectivities greater than 0.01 % per cm of array, suitable for high efficiency scatter measurements over many meters of fiber. Light signals from a series of fiber Bragg gratings (FBGs) inscribed along the length of a single-core optical fiber (SCF) can quantify the strain, temperature, and pressure experienced by that fiber. The technical team at FBGS (Jena, Germany) inscribed a high density of FBGs within a multicore fiber (MCF) using their draw-tower grating (DTG) technology to perform shape sensing [107]. To identify two- or three-dimensional spatial information, either multiple SCFs must be integrated into a multifiber bundle or, a single MCF can be used. DTG-MCF sensors are mechanically robust, lightweight and compact, immune to ionized radiation, and inert-beneficial attributes when integrated with advanced minimally invasive devices targeted for clinical diagnostic, therapeutic, or monitoring applications. Another interesting type of a fiber bending sensor is based on multicore fiber and long period fiber gratings [108]. Long period grating was UV inscribed into a multicore fiber consisting of 120 single mode cores. The multicore fiber that hosts the grating was fusion spliced into a single mode fiber at both ends. The spectral characteristics of this device were a function of fiber’s curvature. The device yielded a significant spectral sensitivity as high as 1.23 nm/m-1 and 3.57 dB/m-1 to the ultra-low curvature values from 0 to 1 m-1. 1.4. IoT Systems for the Family Based on Fiber Optic Sensor In this section, we will introduce an IoT platform, applied in a Device-to-Cloud communication model (Fig. 1.4), for family wellness based on fiber optic sensors. This IoT system combines different modules that are suitable for different family members. Each module is built from a variety of objects (Things) - sensors and electronic devices. The sensors monitor and collect in real time the different physiological parameters which are then sent to the cloud and processed there. In case any deviation from norms in the wellness/health properties is identified, an algorithm in the cloud generates a command to provide an appropriate response for correction of the deviated parameter. The response occurs automatically using the internet so that the system runs by itself without any human intervention. In that configuration, the objects 'sense' their environment, 'talk' to each other and react respectively to a given situation. 38 Chapter 1. Health and Wellness Fiber Optic Sensors in IoT Application As can be seen in Fig. 1.15, the system consists of objects, communication components and cloud. Each sensing object monitors continuously and consistently several physiological parameters of the users: breathing depth, exhalation and inhalation time, pulse rate, etc. In each module, a microprocessor samples the data from the sensors and performs an initial processing of calculating the health/wellness properties. A Wi-Fi communication component sends the processed data to the cloud for storing. Additional information is collected to the cloud from websites - the weather condition and typical physiological parameters of the person according to his/her age. The data from the sensors is analyzed according to an algorithm in the cloud along with the data from the internet and the stored data in the cloud. Then, the algorithm generates an "action parameter" – a command to execute the appropriate reaction based on the identified scenario. The action parameter activates the dedicated device in the module automatically so that each different action parameter causes a different automatic response. Fig. 1.15. IoT system diagram. The objects part is modular so that other modules with suitable sensors and devices can be connected to the system. 39 Advances in Optics: Reviews. Book Series, Vol. 3 The system objects act according to different situations and they are connected to each member of the family: child, baby, adults, or disabled and elderly, so that the system improves their life and prevents disaster from happening. The system's modules working principle is described as follows: 1. Child module - The child is wearing a respiration [53, 71] and a pulse sensors [109]. In order to ignore the measurement’s noises, the respiration sensor samples each time five cycles of breath and the processor calculates the average exhalation and inhalation time and depth of breathing. The whole health/wellness history of the child is stored and every time new information is received, it is analyzed and the action parameter is generated as follows: if, for example, the breathing depth is 30 % lower than normal, or when the breathing rate is slower or faster by 50 % than the typical, an alarm SMS message is sent to the parents. In a more unusual case, when the change in breathing depth is 70 % lower than normal, or the breathing rate is abnormal compared to the age of the child, an alert is sent immediately to an ambulance service with the child's location. 2. Disabled and elderly module - a sensor [110] that samples the temperature in the environment of the human is installed. In addition, breathing and pulse sensors are installed in the chair. The data is received in the cloud, and as explained above, it is processed with additional data. Depending on the outside weather conditions, taken from a weather site, the cloud algorithm decides how to respond. If it is a summer day and the temperature in the human environment is higher than 28 degrees Celsius, the cloud triggers the air conditioner at home. Alternatively, on a winter day when the temperature is below 21 degrees Celsius, the cloud sends a command to activate the heating system or the radiator. Additionally, a motion sensor is attached to the human body. In case of recognizing a fall of the human, the system alerts the disabled or elderly's family and calls for help automatically. 3. Baby's cradle module – breathing and temperature sensors are installed in the cradle and monitor these parameters. The optimal temperature for the baby's environment, especially in the first year, is between 20-22 degrees Celsius [111]. When the temperature in the bed area is not suitable, the cloud sends an order to activate heating or cooling of the bed in order to reach the optimal temperature. Additionally, the cloud learns to recognize when the baby is calm using a motion sensor. When the baby is restless, the cloud generates a comment to activate a relaxing music in the bed until the parent or the nanny arrives. 4. Adults module – studies have shown [112] that maintaining an optimal body temperature enhances the human performance including working memory, subjective alertness and visual attention. The adult module contains a temperature sensor, which is attached to the adult body and measures the body temperature. The adult wears a unique cloth or shoe with a built-in temperature regulator which is triggered by the cloud. The system receives the body temperature and, combined with the area temperature, determines the optimal temperature and activates the temperature regulator accordingly. This IoT system introduces how things (objects) communicate between them. The main peculiarity of such a system isn't inherent in sending the wellness/health information to 40 Chapter 1. Health and Wellness Fiber Optic Sensors in IoT Application the doctor in real time, but in the system that reacts autonomously. In addition the combination of data from physical sensors can be combined with an appropriate internet data. These kind of systems presents the real IoT system – the ability of things to speak between them and act by themselves. Moreover, the system is modular and can be combined with many more objects having a lot more capabilities for identifying different situations, act automatically and improve the family wellness. The system introduced the enormous potential inherent in wellness IoT systems particularly and in real IoT systems in general. Such systems can 'sense' their environment, use virtual sensors data by collecting it from the internet, act autonomously according to identified situations without any human intervention and bring us closer to an automatic world. 1.5. Conclusion and Future Prospect Since the discovery of IoT, there has been tremendous increase in the number of publications in the field and different applications based on these systems have been demonstrated. In recent years, IoT has slowly developed into a useful platform that has potential applications in manufacturing, healthcare, insurance, business services, airline, media and entertainment. In particular, the biomedical applications of Internet of Things have motivated leading researchers and companies to develop very efficient sensing systems based on IoT platform. Internet of Things devices such as fitness trackers, skin sensors, glucose meters and cardiac monitors have created a thriving industry that not only puts people in control of their vital health parameters, but also enables them to engage with healthcare providers in new ways. It should be mentioned that the recent developments in fiber optic sensor technology have contributed largely for the advancement of IoT based applications. It is now possible to obtain very sensitive, reliable, as well as small size and cost structures, that in conjunction with IoT health and wellness system have the ability to greatly improve health outcomes, quality of life and real-time support or intervention. Today it is becoming common practice for patients to track their physiological parameters at home and send the data wirelessly to medical centers or private doctors. It is also routine for doctors to see images in their smartphones and forward them over the Internet to be reviewed by specialists anywhere and anytime. We now already have tools like patient’s data and non-invasive sensor technologies to help us increase medication adherence and allow people to better manage their own health with reduced costs. In the near future, we hope, most of the sensing devices will be communicating on our behalf—they will be interacting with the physical and virtual worlds more than interacting with us. This will be the true realization of the idea of Internet of Things. References [1]. Z. Pang, Technologies and architectures of the Internet of Things (IoT) for health and wellbeing, MS Thesis, KTH Royal Institute of Technology, Stockholm, Sweden, Jan. 2013. 41 Advances in Optics: Reviews. Book Series, Vol. 3 [2]. [3]. [4]. [5]. [6]. [7]. [8]. [9]. [10]. [11]. [12]. [13]. [14]. [15]. [16]. [17]. [18]. [19]. [20]. [21]. [22]. [23]. 42 K. 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Hernández-Rivera, A. S. Sánchez-Sánchez, E. Villarreal-Calva, Electrically insulated sensing of respiratory rate and heartbeat using optical fibers, Sensors, Vol. 14, Issue 11, 2014, pp. 21523-21534. [110]. OMEGA, Fiber-Optic Temperature Measurement, http://www.omega.com/prodinfo/fiberoptic-temperature-measurement.html [111]. Baby Gooroo, What is the ideal temperature for my baby's room? https://babygooroo.com/articles/what-is-the-ideal-temperature-for-my-babys-room [112]. K. P. Wright, J. T. Hull, C. A Czeisler, Relationship between alertness, performance, and body temperature in humans, American Journal of Physiology-Regulatory, Integrative and Comparative Physiology, Vol. 283, Issue 6, 2002, pp. R1370-R1377. 47 Chapter 2. Multi-Point Temperature Sensor Consisting of AWG, SOA, and FBGs in Linear-Cavity Fiber Lasing System Chapter 2 Multi-Point Temperature Sensor Consisting of AWG, SOA, and FBGs in Linear-Cavity Fiber Lasing System Hiroki Kishikawa, Mao Okada, Kazuto Takahashi, Po-Jung Chen, Nobuo Goto, Yi-Lin Yu and Shien-Kuei Liaw1 2.1. Introduction Optical fiber sensing has been extensively studied in various areas, such as aging deterioration measurements of constructed buildings, seismic measurement, environmental measurement, etc. Optical fiber sensing systems are classified into two configurations. One consists of an optical source, an optical fiber transmission line, and sensing elements; the other is formed from a fiber lasing system, including sensing elements in the cavity [1-6]. Compared to the former, the latter systems have advantages such as higher resolution for wavelength-shift induced by a sensing element and higher signal-to-noise ratio (SNR). By employing a fiber Bragg grating (FBG) as the sensing element, the reflecting center wavelength can be shifted due to environmental change in temperature or in tension. In our proposed fiber sensing system, multi-point temperature or tension can be detected by employing multiple FBG elements and an arrayed waveguide grating (AWG) as an optical wavelength multi-/demultiplexer. By adopting the AWG, optical insertion loss in the cavity can be reduced. A flat-top filtering response can be easily realized by appropriate design of the integrated waveguide in the pattern of the AWG [7, 8]. In fiber lasing systems, an erbium-doped fiber amplifier (EDFA), Raman fiber amplifier, and semiconductor optical amplifier (SOA) have been employed as gain components. We consider multi-wavelength simultaneous lasing to measure temperature or tension at multiple points. To realize multi-wavelength lasing, the amplifier has to be carefully selected. When the EDFA is employed in the system, the homogeneous broadening of erbium ions limits the number of lasing wavelengths. Therefore, special lasing configurations have been proposed for multi-wavelength operation by using EDFA H. Kishikawa Dept. of Optical Science, Tokushima University, Japan 49 Advances in Optics: Reviews. Book Series, Vol. 3 [9, 10]. On the contrary, SOAs show the inhomogeneous broadening properties, which makes it possible to operate lasing at multiple wavelengths [11]. SOAs, however, have lower saturation output power compared with EDFAs, which limits the multi-wavelength lasing power. Pleros et al. reported simultaneous 38 wavelength lasing at 50 GHz spacing across a 15-nm spectral window by using two SOAs in a feedback loop [12]. Mode-locked pulse lasing at multiple wavelengths was used to identify each of the serially connected FBGs [13]. To identify each of the serial FBGs, a spectral encoding method was employed in the system [14]. Wavelength-swept pulses were also employed for multi-position fiber loop ring-down sensor array [15]. The SOAs have attracted much interest in not only optical fiber communication systems but also integrated optic devices. In optical amplification, linear amplification is required to avoid signal degradation. On the other hand, in optical signal processing using SOAs, optical nonlinearity in SOAs has been effectively used in a variety of signal processing circuits [16-18]. We consider optical lasing at multiple wavelengths. The number of wavelength channels is limited by amplifiable wavelength range, optical nonlinearity, and gain saturation in the SOA. In the proposed fiber sensing system, multi-wavelength lasing is obtained by using a single SOA [19]. Temperature at multiple points is detected by employing multiple FBG elements and an AWG. Although the SOA has a potential of multi-wavelength lasing, the number of actual lasing wavelengths is affected by physical parameters, such as the reflectivity of each FBG, cavity loss, and gain saturation of the SOA. However, there have been few studies reporting effects of such parameters in multi-point sensing systems with SOAs and FBGs. Therefore, the objective of this study is to theoretically and experimentally evaluate the influence of physical parameters with multi-point sensing characteristics by using a single SOA and multiple FBGs. Moreover, multiwavelength lasing characteristics on unequal reflecting power on each channel are especially revealed. In addition, the advantages are also clarified in the proposed sensing system configuration, employing parallel FBGs that are connected to demultiplexed ports of an AWG. By using such a star configuration, it is easy to equalize the reflecting power of each channel by using variable optical attenuators on FGBs with various reflectivities. Furthermore, it would be resilient to fiber failures [20], which means that the reliability and robustness against unexpected breakdown in a certain FBG sensing element can be improved. 2.2. Linear-Cavity Fiber Sensor Consisting of SOA, AWG, and FBGs The proposed fiber sensing system consists of multiple linear cavities lasing at different wavelengths as shown in Fig. 2.1(a). The SOA placed in the linear-cavity amplifies multiwavelength signals propagating in both directions. The AWG plays a role as a multi/demultiplexer. The passband filtering response of the AWG is schematically illustrated in Fig. 2.1(b), where a flat-top filtering passband is assumed. The base of the wavelength interval of the multi-channel lasing is lasing, which is equal to the channel interval of the AWG. The AWG demultiplexes the optical signals propagating in the right-hand direction into N signals having different wavelengths i, i = 1, … , N. The signal at wavelength i in port i is reflected by the FBG. The wavelength of each FBG is designed to be at the 50 Chapter 2. Multi-Point Temperature Sensor Consisting of AWG, SOA, and FBGs in Linear-Cavity Fiber Lasing System center of the AWG passband of each channel. The wavelength multiplexed signals propagating in the left-hand direction are amplified by the SOA. The left-end wavelengthindependent loop mirror reflects all the channel signals, where a part of the signals is coupled out for detection. The lasing spectra are also schematically shown in Fig. 2.1 (b). Since the FBG reflection wavelength depends on its environment, an environmental change results in wavelength-shift shift,i of the lasing wavelength. The maximum amount of shift,i has to be less than half of the bandwidth of each channel, AWG_FT ∕ 2. FBG 1 Loop mirror SOA 2 AWG N Detection of wavelength shift Linear cavity (a) Linear-cavity multi-channel fiber sensing system; Filtering response in AWG 1 2  shift, i N  AWG_FT   lasing (b) Lasing spectrum with AWG filtering characteristics. Fig. 2.1. Multi-point sensing system consisting of an SOA, an AWG, and FBGs. When multi-wavelength signals are amplified with the SOA, optical nonlinearity becomes an important issue. The gain saturation in the SOA limits the number of lasing channels. The induced four-wave-mixing (FWM) nonlinearity may result in degradation of sensing preciseness. When wavelengths in two neighbor lasing channels come closer each other, the amplified gain for two channels becomes unequal as discussed in Section 2.3.1. This inequality in gain might result in disappear of one of the two lasing channels. 51 Advances in Optics: Reviews. Book Series, Vol. 3 2.3. Analysis of Multi-Channel Lasing 2.3.1. Analysis for SOA Nonlinearity Optical multi-channel signal behavior through SOA amplification has been studied by many researchers. Nonlinear phenomena for multi-wavelength signals are induced by gain saturation [21] and FWM [22-24]. The wavelength range available for amplification depends on the material gain [25]. These factors cause restriction on the number of wavelength channels and sensing preciseness. The mechanism of FWM in an SOA is explained as follows [21]: interference of multiwavelength signals coupled in the SOA induces amplitude variation at the beat frequencies of the signals. Since the amplitude varying signal induces carrier variation, stimulated emission results in variation of the refractive index as well as gain variation. These gain and refractive-index variations not only modulate the incident signals but also generate sideband signals with the interval of the beat frequencies. In this section, we analyze the multi-channel signal behavior through an SOA based on the analysis reported by Connelly [26]. The analysis is composed of the traveling-wave equations for signal fields and spontaneous emission, carrier–density rate equation, and material gain modeling as discussed in Appendix. The numerical simulation was performed by using OptiSystem (Optiwave Systems Inc.). The simulated wavelength dependence of the optical gain through an SOA is shown in Fig. 2.2(a), where the SOA current I is assumed to be 130 mA. The optical input power is −10 dBm. The wavelength range for gain larger than 20 dB is evaluated to be around 50 nm. When the input optical power increases, the gain is saturated as shown in Fig. 2.2(b), where wavelength  is 1570 nm and the current I is 130 mA. The optical gain of 25 dB is expected for an input power less than −20 dBm. The gain saturation is a major factor that limits the channel number for multi-channel amplification. 22 21 Input power: -10dBm 30 130mA Gain (dB) Gain (dB) 20 19 18 17 16 1500 =1570nm 25 I=130mA 20 15 10 5 1520 1540 1560 1580 Optical wavelength (nm) (a) Gain as a function of wavelength 1600 0 -30 -20 -10 0 Input power (dBm) (b) Gain as a function of input power at  = 1570 nm Fig. 2.2. Calculated SOA gain at electric current of I = 130 mA. 52 10 Chapter 2. Multi-Point Temperature Sensor Consisting of AWG, SOA, and FBGs in Linear-Cavity Fiber Lasing System We consider simultaneous amplification for two signals at different wavelengths. When the wavelength interval decreases, the gain for the longer wavelength signal increases, whereas that for the shorter wavelength signal decreases due to FWM [23]. Fig. 2.3(a) shows the simulated gain for the longer (fixed at  = 1570 nm) and the shorter wavelength signals as a function of the wavelength interval. The input power is changed as a parameter. The induced FWM intensities are shown in Fig. 2.3(b). The generated FWM signals decrease with the wavelength interval. This gain deviation would complicate the diagnosis of its source as a result of the FWM effect or the interrogated environmental change. It would also affect the multi-channel lasing characteristics described in the following subsection. 5 20 0 FWM intensity (dBm) Gain (dB) 15 10 5 -10dBm_Long -10dBm_Short -5dBm_Long -5dBm_Short 0dBm_Long 0dBm_Short 0 -5 -10 0.0 0.5 1.0 1.5 2.0 Wavelength interval (nm) 2.5 -10dBm_Long -10dBm_Short -5dBm_Long -5dBm_Short 0dBm_Long 0dBm_Short -5 -10 -15 -20 -25 -30 3.0 0.0 (a) Gain at two wavelengths 0.5 1.0 1.5 2.0 Wavelength interval (nm) 2.5 3.0 (b) Generated FWM intensities Fig. 2.3. Simulated characteristics of two-wavelength amplification as a function of the wavelength interval, where input power is changed as a parameter. The SOA current is 130 mA. Finally, we investigate nonlinearity for amplification of multiple signals with equal interval. Fig. 2.4(a) shows output signal intensities as a function of optical frequency for cases of 4, 8, and 16 channels. The multiple signals have equal frequency separation. It is found that FWM signals are generated. The gain at the wavelengths of the input signals is shown in Fig. 2.4(b). The gain decreases with the input power due to gain saturation. The maximum number of multi-channel amplification is restricted depending on the input optical power. 25 5 4ch, 0dBm 8ch, 0dBm -15 8ch, -10dBm -20 8ch, -20dBm -25 16ch, 0dBm -30 16ch, -10dBm 16ch, -20dBm -35 -40 190 191 192 193 194 195 Optical frequency (THz) (a) Output intensities 4ch, -10dBm 15 4ch, -20dBm -10 4ch, 0dBm 20 4ch, -10dBm -5 Gain (dB) Output intensity (dBm) 0 4ch, -20dBm 8ch, 0dBm 10 8ch, -10dBm 5 8ch, -20dBm 16ch, 0dBm 0 16ch, -10dBm -5 -10 16ch, -20dBm 190 191 192 193 194 195 Optical frequency (THz) (b) Gain Fig. 2.4. Output intensities for multiple signal amplification. 53 Advances in Optics: Reviews. Book Series, Vol. 3 2.3.2. Analysis of Multi-Wavelength Lasing The proposed sensor system consists of a single SOA as the gain component for lasing. The number of channels at different wavelengths is limited due to the gain saturation in the SOA, as discussed in the previous section. The gain saturation, however, can be avoided by decreasing the incident optical power even if the channel number is large. In this section, we consider the lasing power of each channel by using a model shown in Fig. 2.5. FBG_1 FBG 1 MIRROR Loop mirror 1 AWG 2 AWG SOA FBG_N N Fig. 2.5. A model to calculate lasing powers for multi-wavelength operation. Each signal propagating in the left-hand direction at wavelength i has an optical power of Iai and Ibi, i = 1,…,N at the entrance and the exit of the SOA, respectively. The signal propagating in the right-hand direction after the SOA has an optical power of Ici. The gain of the SOA for a one-way path GS and a round-trip path GR are expressed as Ibi ∕ Iai and Ici ∕ Iai, respectively. Both are calculated numerically by using the SOA analysis model, which is described above, as shown in Fig. 2.6(a) where the optical wavelength of 1570 nm and the injection current of 130 mA are assumed. The reflectance at the left loop mirror, including the power-splitting loss for detection, is denoted by MIRROR. We assume MIRROR = 1 in this calculation. For weak incident power, the round-trip gain is higher due to the double path amplification. On the contrary, for stronger incident power, the oneway gain is higher due to the gain saturation. The total optical power propagating in the left-hand direction at the entrance of the SOA ISUM is given by ∑ (2.1) . The round-trip gain in the SOA, being denoted by GR(ISUM), depends on ISUM. The nonlinear effect of FWM is ignored in this analysis, and the gain for each wavelength is assumed to be identical. The transmittance of the AWG, including the insertion loss, is denoted by AWG; the reflectance at each FBG i is denoted by FBG_i. The total gain at i through a cavity is written as 54 _ . (2.2) Chapter 2. Multi-Point Temperature Sensor Consisting of AWG, SOA, and FBGs in Linear-Cavity Fiber Lasing System 40 Round-trip Gain (dB) 30 One-way 20 10 0 -10 -30 -20 -10 0 10 Optical input power (dBm) Total gain through linear cavity (dB) (a) Optical gain for one-way path and round-trip path through an SOA 10 N=1 N=2 N=4 N=8 N=16 N=32 N=1 N=2 N=4 N=8 N=16 N=32 5 0 -5 -10 -25 -20 -15 -10 -5 0  overall= ‐10dB ‐15dB 5 Optical power per channel (dBm) (b) Optical gain through the linear-cavity sensor as a function of optical intensity I 0 at the entrance of the SOA Fig. 2.6. Simulated results with the model of Fig. 2.5. The lasing condition in gain is given by (2.3) 1. We assume that Iai = I0, i = 1,…,N and the overall transmittance due to the losses is _ . (2.4) The total gain Gcavity is calculated as a function of I0 in Fig. 2.6(b), where the channel number N is varied as a parameter. It is found that the lasing power per channel decreases with N. As an example, the lasing power at the entrance of the SOA is around −8.5 dBm and −13.3 dBm for N = 8 with overall = −10 dB and −15 dB, respectively. The lasing power is increased by 3 dB by decreasing N to half, that is N = 4. 55 Advances in Optics: Reviews. Book Series, Vol. 3 2.4. Experimental Results 2.4.1. SOA Nonlinearity The nonlinearities in multi-channel amplification were experimentally verified with an SOA (Inphenix, IPSAD1502-214) using an experimental setup shown in Fig. 2.7. The measured wavelength dependence of the gain is shown in Fig. 2.8 (a), where a wavelength-variable laser source (Anritsu, MG9638A) and a spectrum analyzer (Anritsu, MS9710C) were used. At wavelength of 1570 nm, the maximum gain of 14.6 dB was obtained for input power of -20 dBm with injection current of 150 mA. When the input power was increased, the gain decreased due to gain saturation as shown in Fig. 2.8 (b), where the incident wavelength is 1570 nm. LD1 LD2 LDN 1 2 WDM signals Variable attenuator Combiner N SOA Optical spectrum analyzer Optical spectrum analyzer Fig. 2.7. Experimental setup for measuring multi-channel SOA amplification. 20 15 Input power ‐20 dBm =1570nm 10 0 Gain (dB) Gain (dB) 10 -10 100 mA 100 mA 0 120 mA -20 5 120 mA 150 mA 150 mA -30 1500 1510 1520 1530 1540 1550 1560 Optical wavelength (nm) 1570 (a) Gain as a function of wavelength 1580 -5 -50 -40 -30 -20 -10 Input Power (dBm) 0 10 (b) Gain as a function of input power Fig. 2.8. Measured results of optical gain characteristics for an SOA. Next, the nonlinearity due to FWM was measured for optical inputs at two wavelengths. The incident wavelengths, short and long, were varied as shown in Fig. 2.9 (a), where multi-channel laser sources (Anritsu, MU952601A, MU952602A) were used. The gain at the two wavelengths is plotted as a function of wavelength interval in (b). The gain at long was larger than that atshort as theoretically discussed in Fig. 2.3. The generated FWM intensities are shown in (c). The FWM at the shorter wavelength was larger than that at 56 Chapter 2. Multi-Point Temperature Sensor Consisting of AWG, SOA, and FBGs in Linear-Cavity Fiber Lasing System the longer wavelength. The increase of the gain at long in wider wavelength interval is considered to be caused by the wavelength dependence of the gain shown in Fig. 2.8 (a). 9 lambda1 long 1569 lambda2 short 1568 8 lambda1 long 1567 Gain (dB) Incident wavelength (nm) 1570 lambda2 short 1566 7 1565 1564 0 1 2 3 4 Wavelength interval (nm) 5 6 (a) Two incident wavelengths 6 0 1 2 3 4 Wavelength interval (nm) 5 6 (b) Gain at two wavelengths FWM intensity (dBm) -20 FWM1 FWM short -25 FWM long FWM2 -30 -35 -40 -45 0 1 2 3 4 Wavelength interval (nm) 5 6 (c) Generated FWM intensities Fig. 2.9. Measured characteristics of two-wavelength amplification as a function of the wavelength interval, where the SOA current is 150 mA. Finally, four-channel simultaneous amplification was demonstrated. The four input channels were set to have equal frequency interval of 200 GHz. The output intensities including FWM signals are shown in Fig. 2.10 (a). FWM signals were not observed for input of -20 dBm. The output intensities for larger incident power are restricted due to gain saturation. The gain at the four signal wavelengths are shown in (b). 2.4.2. ASE Spectrum and AWG Transmittance In order to assess the gain spectrum of an SOA (Inphenix, IPSAD1502-214) used in the experiment, we measured the amplified spontaneous emission (ASE) noise spectrum with no optical input at the SOA input port as shown by the dashed curve in Fig. 2.11. The current to the SOA was 120 mA. The wavelength resolution of the optical spectrum analyzer (Anritsu, MS9710C) was 0.05 nm. The maximum gain of the SOA is expected at around 1540 nm. When the ASE noise was input in the AWG (Accelink, 32-channel 57 Advances in Optics: Reviews. Book Series, Vol. 3 10 16 0 14 12 -10 0dBm -20 -20dBm -10dBm -30 Gain (dB) Output intensity (dBm) Athermal AWGMux or Demux), having 100-GHz frequency spacing, the output spectra at ports 1 and 2 were measured as shown by the solid and dotted curves, respectively, in Fig. 2.11. Although the output wavelength at port 1 of the AWG was designed to be 1535.2 nm, the other peaks were observed at 1488.0 nm and 1585.6 nm due to the periodical properties of the AWG. The frequency difference of the outputs between ports 1 and 2 was 100 GHz (≃0.8 nm in 1550-nm band). 10 8 6 4 -40 0dBm -10dBm -20dBm 2 0 1564 -50 1558 1560 1562 1564 1566 1568 1570 1572 1574 1576 1565 Optical wavelength (nm) 1566 1567 1568 1569 1570 Optical wavelength (nm) (a) Output intensities (b) Gain Fig. 2.10. Measured characteristics of multi-channel amplification as a function of optical wavelength. Input power is changed as a parameter. The SOA current is 150 mA. Optical Output (dBm) -20 ch1 ch2 ASE -30 -40 -50 -60 -70 1450 1500 1550 1600 1650 Wavelength (nm) Fig. 2.11. ASE spectrum from the SOA and the spectrum at channels 1 and 2 after passing through the AWG. 2.4.3. Multi-Wavelength Lasing We demonstrated multi-channel lasing with the setup shown in Fig. 2.12. The cavity consists of the SOA, the AWG, and fiber mirror reflectors at the end of the demultiplexed channels; a fiber loop mirror consists of a circulator, a 99:1 coupler, and a polarization controller. The AWG has a non-uniform insertion loss of 4.01–4.53 dB among ports with a 1-dB passband of 0.45 nm and 20 dB passband of 1.14 nm. The round-trip insertion loss 58 Chapter 2. Multi-Point Temperature Sensor Consisting of AWG, SOA, and FBGs in Linear-Cavity Fiber Lasing System of the AWG, the circulator, and the 99:1 coupler are approximately 8.6 dB, 1.47 dB, and 0.57 dB, respectively. Therefore, the total cavity loss is estimated to be around 10.64 dB. When the Nreflected output ports of the AWG were terminated by the fiber mirror reflectors, the lasing Nreflected wavelengths were observed at the measured port, as shown in Fig. 2.13. The number of the port terminated with the fiber mirror reflectors was changed from one to eight. The averaged power per channel decreased with the number of channels due to the gain saturation, as shown in Fig. 2.13 (b), where the lasing power was −32.6 dBm for Nreflected = 8. On the other hand, the lasing power was doubled by decreasing the lasing channel number to half, as mentioned in the simulated result shown in Fig. 2.6 (b). 1 2 Pol. controller Circulator 1:32 AWG SOA 99:1 coupler Fiber mirror reflector  Nrefl ected N Optical spectrum analyzer Fig. 2.12. Experimental setup for multi-channel lasing. -20 -40 1 -60 2 -80 3 1584 4 1586 5 1588 6 1590 7 1592 8 (a) Lasing spectrum Output Average Power (dBm) Output Power (dBm) -22 -24 -26 -28 -30 -32 -34 11 2 3 4 Number of Channels 5 6 7 8 (b) Output averaged power per channel for multi-channel lasing. Fig. 2.13. Measured results when the number of reflected channels is changed from 1 to 8. Next, we demonstrated the difference in multi-channel lasing between SOA and EDFA as the amplifier. The amplifier was placed in the left-hand side loop mirror as shown in Fig. 2.14. In this setup, the optical signal passes through the amplifier only in a single path. The eight output ports from the AWG are terminated with fiber reflector mirrors. The lasing output was observed as shown in Fig. 2.15. In the case of EDFA, lasing 59 Advances in Optics: Reviews. Book Series, Vol. 3 spectrum at one channel was observed. This is due to the homogeneous broadening in amplification with the EDFA. Therefore, SOA is superior in multi-channel lasing operation. 1 2 Pol. controller SOA or EDFA Circulator 1:32 AWG 99:1 coupler  Nrefl ected Fiber mirror reflector N Optical spectrum analyzer Fig. 2.14. Experimental setup to demonstrate the difference in lasing between SOA and EDFA. -30 SOA Optical power (dBm) Optical power (dBm) -30 -40 -50 -60 1540 1542 1544 Wavelength (nm) 1546 1548 (a) SOA EDFA -40 -50 -60 1540 1542 1544 Wavelength (nm) 1546 1548 (b) EDFA Fig. 2.15. Lasing output spectra for amplifier of (a) SOA and (b) EDFA. 2.4.4. Two-Wavelength Lasing with FBGs To verify multi-channel sensing, we demonstrated two-channel temperature sensing with two FBGs. The FBGs [channel 6: grating length (L) = 10 mm,  = 1539.872 nm, −3 dB bandwidth (BW at −3 dB) = 0.227 nm, reflectivity (R) = 97.04 %, sidelobe suppression rate (SLSR) = 15.40 dB; channel 9: L = 10 mm,  = 1542.122 nm, BW at −3 dB = 0.236 nm, R = 97.57 %, SLSR = 23.02 dB] were connected at ports 6 and 9 through variable attenuators, as shown in Fig. 2.16. Optical lasing spectra measured at the detection port at room temperature are shown in Fig. 2.17. The lasing characteristics at two channels were measured by varying the attenuator in channel 6, as shown in Fig. 2.18. When the transmittance decreased with the increase of the attenuation in channel 6, the lasing output at channel 6 decreased. On the contrary, the lasing output at channel 9 decreased when the transmittance of channel 6 increased. 60 Chapter 2. Multi-Point Temperature Sensor Consisting of AWG, SOA, and FBGs in Linear-Cavity Fiber Lasing System Simultaneous lasing with equal power was obtained with the transmittance of 0.68. Thus, the attenuation in both channels should be adjusted to achieve an equal lasing output power. The AWG used in the experiment had Gaussian-like filtering characteristics, as shown in Fig. 2.19, where the transmittance at channels from 6 to 9 were plotted. Variable attenuator Pol. controller Circulator Water bath Ch.6 1:32 AWG SOA FBG Ch.9 99:1 coupler Optical spectrum analyzer Hot plate Fig. 2.16. Experimental setup for two-channel temperature sensing. Output Power (dBm) -20 Ch.6 -30 Ch.9 -40 -50 -60 -70 1536 1538 1540 Wavelength (nm) 1542 1544 Fig. 2.17. Lasing spectra with two FBGs at room temperature. Optical Output Power (dBm) -10 -20 -30 Ch.6 -40 Ch.9 -50 -60 0 0.2 0.4 0.6 0.8 Transmission Ratio of Attenuator in Channel 6 1 Fig. 2.18. Output power at two channels with varying the attenuator in channel 6. 61 Advances in Optics: Reviews. Book Series, Vol. 3 Fig. 2.19. Transmission characteristics of the AWG at ports 6 to 9. 2.4.5. Simultaneous Temperature Sensing The temperature at the FBG in channel 9 was measured as shown in Fig. 2.20 (a), where the FBG in channel 6 was removed. The output power as a function of wavelength obtained from Fig. 2.20 (a) is plotted in Fig. 2.20 (b). Since the transmittance of the AWG in channel 9 started to decrease at the wavelength corresponding to a temperature higher than around 60 °C, the output power decreased. The ratio of the wavelength change to the temperature change was around 6.4 pm/deg. A similar result was also confirmed by using the FBG in channel 6 as shown in Fig. 2.21. The ratio of the wavelength change to the temperature change was also around 6.4 pm/deg. Note that the reason that the measured wavelength was changed almost in steps of 0.025 nm was due to the wavelength resolution of the optical spectrum analyzer. 1541.85 1541.75 -25 1541.70 Output Power Wavelength -30 1541.65 1541.60 1541.55 -35 1541.50 Channel 9 -40 10 30 50 70 Temperature (degree) 1541.45 90 1541.40 (a) Output power and the wavelength vs. temperature Optical Output Power (dBm) -20 1541.80 Wavelength (nm) Optical Output Power (dBm) -20 -25 -30 -35 -40 1541.4 1541.5 1541.6 1541.7 Wavelength (nm) 1541.8 1541.9 (b) Output power vs. wavelength Fig. 2.20. Temperature measurement result by using an FBG only in channel 9. Fig. 2.22 shows an example of simultaneous temperature measurement with two FBGs. The temperature of the FBG in channel 9 was varied while the FBG in channel 6 was kept at room temperature. Since the loss in channel 9 increased as the temperature increased more than around 50°, the lasing power in channel 9 decreased gradually with the 62 Chapter 2. Multi-Point Temperature Sensor Consisting of AWG, SOA, and FBGs in Linear-Cavity Fiber Lasing System temperature, whereas the power in channel 6 increased by about 3 dB with the temperature. A similar result of two-channel measurement also was confirmed when the temperature at the FBG in channel 6 is varied as shown in Fig. 2.23. -20 1539.50 1539.40 Output Power 1539.35 Wavelength -30 1539.30 1539.25 -35 1539.20 Channel 6 -40 10 20 30 40 50 Temperature (degree) 60 Wavelength (nm) 1539.45 -25 70 Optical Output Power (dBm) Optical Output Power (dBm) -20 -25 -30 -35 -40 1539.1 1539.15 1539.2 1539.3 1539.4 1539.5 Wavelength (nm) (a) Output power and the wavelength vs. temperature (b) Output power vs. wavelength -25 1539.45 1539.40 -30 Output Power Wavelength -35 1539.35 1539.30 -40 1539.25 -45 -50 1539.20 Channel 6 10 20 30 40 50 Temperature in Channel 9 (degree) 60 1539.15 Channel 6 (fixed temp.) Channel 9 (varied temp.) -20 1541.80 -25 1541.75 1541.70 -30 Output Power Wavelength -35 1541.65 1541.60 1541.55 -40 1541.50 -45 -50 Channel 9 10 (a) Channel 6 20 30 40 50 Temperature in Channel 9 (degree) Wavelength (nm) 1539.50 Wavelength (nm) -20 Optical Output Power (dBm) Optical Output Power (dBm) Fig. 2.21. Temperature measurement result by using an FBG only in channel 6. 1541.45 60 1541.40 (b) Channel 9 Fig. 2.22. Simultaneous temperature measurement result using FBGs in channels 6 and 9, where the temperature at channel 6 was kept fixed at room temperature and that at channel 9 was varied. 2.4.6. Increase of the Temperature Sensing Range The measured temperature range in the experimental results is mainly restricted by the facility limitations. The maximum operating temperature of the utilized FBGs is 80 °C due to the coating material of their fibers. Besides, the AWG has the non-flat-top passband profile for each wavelength channel, as shown in Fig. 2.19. By employing an FBG with wider operating temperature and a flat-top AWG having 200 GHz bandwidth with suitable central wavelengths, for example, the measured temperature range can be more than doubled. 63 Advances in Optics: Reviews. Book Series, Vol. 3 Output Power Wavelength -30 1539.40 1539.35 -35 1539.30 -40 1539.25 -45 -50 1539.20 Channel 6 10 20 30 40 Temperature (degree) (a) Channel 6 50 1539.15 Optical Output Power (dBm) 1539.45 -25 Channel 6 (varied temp.) Channel 9 (fixed temp.) -20 1541.80 -25 1541.75 Output Power -30 1541.70 Wavelength -35 1541.65 1541.60 -40 1541.55 1541.50 -45 -50 1541.45 Channel 9 10 20 30 40 Temperature (degree) Wavelength (nm) 1539.50 Wavelength (nm) Optical Output Power (dBm) -20 50 1541.40 (b) Channel 9 Fig. 2.23. Simultaneous temperature measurement result using FBGs in channels 6 and 9, where the temperature at channel 9 was kept fixed at room temperature and that at channel 6 was varied. Advantages of the proposed system configuration are that it can provide easy equalization of power of each lasing wavelength channel as well as resilience to fiber failures by exploiting the star configuration of the sensing elements. Moreover, the sensing physical parameters can be simply measured by detecting the wavelength shift of the lasing lines. 2.5. Conclusion Multi-channel amplification with an SOA was investigated for the proposed linear-cavity sensing system. The lasing condition for multi-channel operation was clarified numerically by considering the gain saturation in the SOA. The gain saturation limits the maximum number of channels and the lasing power per channel. The multi-wavelength lasing was experimentally demonstrated up to eight channels, where fiber mirror reflectors were employed instead of FBGs. The lasing power was doubled by decreasing the lasing channel number to half and by decreasing the number of the reflectors. This result agrees well with theoretical analysis. To demonstrate multi-point sensing, two FBGs were employed at two ports of the AWG. Since the filtering response of the AWG was not in a flat-top profile, the lasing power decreased when the lasing wavelength shifted to the edge of the AWG channel. It was found that equalization of loss in each channel was indispensable for multiple simultaneous sensing. By adopting a flat-top AWG, stable multi-point sensing is expected over a wide range of temperatures. Acknowledgements This research was supported in part by Collaborative Research Project between National Taiwan University of Science and Technology and Tokushima University. 64 Chapter 2. Multi-Point Temperature Sensor Consisting of AWG, SOA, and FBGs in Linear-Cavity Fiber Lasing System References [1]. S. Kim, J. Kwon, S. Kim, B. Lee, Multiplexed strain sensor using fiber grating-tuned fiber laser with a semiconductor optical amplifier, IEEE Photon. Technol. Lett., Vol. 13, Issue 4, April 2001, pp. 350-351. [2]. S.-K. Liaw, Y.-W. Lee, H.-W. Huang, W.-F. Wu, Multi-wavelength linear-cavity SOA-based laser array for long-haul sensing, IEEE Sensor J., Vol. 15, Issue 6, June 2015, pp. 3353-3358. [3]. C.-S. Shin, S.-K. Liaw, S.-W. Yang, Post-impact fatigue damage monitoring using fiber Bragg grating sensors, Sensors, Vol. 14, Issue 3, March 2014, pp. 4144-4153. [4]. S. Diaz, D. Leandro, M. Lopez-Amo, Stable multiwavelength erbium fiber ring laser with optical feedback for remote sensing, IEEE/OSA J. Lightw. Technol., Vol. 33, Issue 12, Jun. 2015, pp. 2439-2444. [5]. M. Bravo, V. DeMiguel-Soto, A. Ortigosa, M. Lopez-Amo, Fully switchable multiwavelength fiber lasers based on random distributed feedback for sensors interrogation, IEEE/OSA J. Lightw. Technol., Vol. 33, Issue 12, June 2015, pp. 2598-2604. [6]. H. D. Lee, G. H. Kim, T. J. Eom, M. Y. Jeong, and C. -S. Kim, Linearized wavelength interrogation system of fiber Bragg grating strain sensor based on wavelength-swept active mode locking fiber laser, IEEE/OSA J. Lightw. Technol., Vol. 33, Issue 12, June 2015, pp. 2617-2622. [7]. S. Pathak, M. Vanslembrouck, P. Dumon, D. Van Thourhout, W. Bogaerts, Optimized silicon AWG with flattened spectral response using an MMI aperture, IEEE/OSA J. Lightw. Technol., Vol. 31, Issue 1, January 2013, pp. 87-93. [8]. K. Okamoto, Fundamentals of Optical Waveguides, 2nd Ed., Elsevier, Amsterdam, Boston, 2006. [9]. A. Bellemare, M. Karásek, M. Rochellte, S. LaRochelle, M. Têtu, Room temperature multifrequency erbium-doped fiber lasers anchored on the ITU frequency grid, IEEE/OSA J. Lightw. Technol., Vol. 18, Issue 6, June 2000, pp. 825-831. [10]. S. Diaz, A. B. Socorro, R. M. Manuel, R. Fernandez, I. Monasterio, Stable multi-wavelength fiber lasers for temperature measurements using an optical loop mirror, Appl. Opt., Vol. 55, Issue 29, Oct. 2016, pp. 8385-8389. [11]. H.-Y. Hsu, Y.-L. Yu, C.-C. Tsai, S.-K. Liaw, N.-K. Chen, W.-F. Wu, Semiconductor optical amplifier based multi-wavelength lasers in 0.4 nm channel spacing, Laser Physics, Vol. 23, Issue 9, August 2013, pp. 95-104. [12]. N. Pleros, C. Bintjas, M. Kalyvas, G. Theophilopoulos, K. Yiannopoulos, S. Sygletos, H. Avramopoulos, Multiwavelength and power equalized SOA laser sources, IEEE Photon. Technol. Lett., Vol. 14, Issue 5, May 2002, pp. 693-695. [13]. M. Fernandez-Vallejo, D. Ardanaz, M. Lopez-Amo, Optimization of the available spectrum of a WDM sensors network using a modelocked laser, IEEE/OSA J. Lightwave Technol., Vol. 33, Issue 22, November 2015, pp. 4627-4631. [14]. A. Triana, D. Pastor, M. Varon, Overlap-proof fiber Bragg grating sensing system using spectral encoding, IEEE Photon. Technol. Lett., Vol. 28, Issue 7, Apr. 2016, pp. 744-747. [15]. R. Li, C. Tian, Y. Zhang, J. Zhang, X. Chen, S. Liu, Simultaneous measurement of force and temperature by a multi-position fiber loop ringdown sensor array, IEEE/OSA J. Lightwave Technol., Issue 33, Issue 17, September 2015, pp. 3607-3612. [16]. R. J. Manning, A. D. Ellis, A. J. Poustie, K. J. Blow, Semiconductor laser amplifiers for ultrafast all-optical signal processing, J. Opt. Soc. Am. B, Vol. 14, Issue 11, November 1997, pp. 3204-3216. [17]. K. Tajima, S. Nakamura, Y. Ueno, Ultrafast all-optical signal processing with symmetric Mach-Zehnder type all-optical switches, Opt. Quantum Electron., Vol. 33, Issue 7-10, July 2001, pp. 875-897. 65 Advances in Optics: Reviews. Book Series, Vol. 3 [18]. V. Lal, M. L. Masanovic, J. A. Summers, G. Fish, D. J. Blumenthal, Monolithic wavelength converters for high-speed packet-switched optical networks, IEEE J. of Sel. Topics in Quantum. Electron., Vol. 13, Issue 1, January-February 2007, pp. 49-57. [19]. H. Kishikawa, M. Okada, K. Takahashi, P.-J. Chen, N. Goto, Y.-L. Yu, S.-K. Liaw, MultiPoint temperature sensing using linear-cavity lasing system, Applied Optics, Vol. 56, Issue 11, April 2017, pp. 3206-3212. [20]. M. Fernandez-Vallejo, S. Díaz, R. A. Perez-Herrera, D. Passaro, S. Selleri, M. A. Quintela, J. M. López Higuera, M. Lopez-Amo, Resilient long-distance sensor system using a multiwavelength Raman laser, Meas. Sci. Technol., Vol. 21, Issue 9, September 2010, 094017. [21]. K. Inoue, Crosstalk and its power penalty in multichannel transmission due to gain saturation in a semiconductor laser amplifier, IEEE/OSA J. Lightw. Technol., Vol. 7, Issue 7, July 1989, pp. 1118-1124. [22]. K. Inoue, T. Mukai, T. Saitoh, Nearly degenerate four-wave mixing in a traveling-wave semiconductor laser amplifier, Appl. Phys. Lett., Vol. 51, Issue 14, October 1987, pp. 1051-1053. [23]. G. P. Agrawal, I. M. Habbab, Effect of four-wave mixing on multichannel amplification in semiconductor laser amplifiers, IEEE J. Quant. Electron., Vol. 26, Issue 3, March 1990, pp. 501-505. 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Appendix Equations Used in SOA Analysis The analysis composed of the traveling-wave equations for signal fields and spontaneous emission, carrier-density rate equation, and material gain modeling based on [26]. at The signals are assumed to be composed Ns components having power of frequencies νk, k = 1,..., Ns. The fields of each incident signal in SOA is assumed to be sum of and propagating to +z and −z directions, respectively. Photon rate per second is given by by . The traveling-wave equations for Γ Γ 66 , , and , are given (2.A1) Chapter 2. Multi-Point Temperature Sensor Consisting of AWG, SOA, and FBGs in Linear-Cavity Fiber Lasing System where βk is the propagation constant,  is optical confinement factor,  is loss coefficient, gm is material gain coefficient, and n is conduction band carrier density. To model spontaneous emission, noise photons are assumed to exist only at discrete frequencies νj, j = 0,..., Nm − 1, corresponding to integer multiples of cavity resonance. and are Traveling-wave equations for spontaneous emission of photon rates, given by Γ , Γ , , where Rsp is the spontaneous emitted noise coupled into , and (2.A2) , . The rate equation for carrier density n is given by ∑ ∑ , , (2.A3) , where Kj equals to unity for zero facet reflectivity, I is the current, d is the active region thickness, and W is the active region width. The recombination rate R(n) is given by , (2.A4) where Rrad and Rnrad are the radiative and non-radiative carrier recombination rates, respectively. These rates can be expressed as , . (2.A5) , where Arad and Brad are the linear and bimolecular radiation recombination coefficients, Anrad is the linear non-radiative recombination coefficient due to traps in the semiconductor material, Bnrad is the non-radiative bimolecular recombination, Caug is the Auger recombination coefficient, and Dleak is the recombination due to leakage effects. Material gain coefficient gm can be modeled as , √ ⁄ , (2.A6) where c is the speed of light in vacuum, n1 is the active region refractive index,  is the radiative carrier recombination lifetime, h is the Planck’s constant, me and mhh are the conductive band (CB) electron and valence band (VB) heavy hole effective masses, respectively, Eg is the bandgap energy, and fc and fv are the Fermi-Dirac distributions in CB and VB. 67 Chapter 3. Review of Fabry-Pérot Fiber Sensors Chapter 3 Review of Fabry-Pérot Fiber Sensors Yundong Zhang, Li Zhao, Fuxing Zhu, Ying Guo, Ping Yuan1 3.1. Introduction Fabry-Pérot interferometers (FPIs) have been widely used as optical fiber sensors in health monitoring of composite materials, civil engineering structures, space aircrafts, and medicine, etc. Owing to their advantages, such as compactness, simple configuration, small size, high sensitivity, fast responses, good repeatability, etc., which makes them suitable for the detection of physical and chemical parameters such as temperature, strain, refractive index (RI), transverse load, gas phase concentrations and so on. The fiber FP sensor is based on the multi-beam interference principle to detect the changes of the external parameters. The FP cavity has two parallel separated reflective surfaces which can partially reflect the lead-in optical signals. The beams reflected by the surfaces will interfere when they come back into the lead-in fiber. When the FP cavity is subjected to external parameters (strain, deformation, displacement, temperature, refractive index), there would be a phase difference change between the two reflected beams, resulting in a shift of reflection spectrum. Thus, the change of external parameters can be known. With the aim of forming FP cavities in optical fibers, two parallel separated interfaces which can partially reflect the lead-in optical signals are required to be made in optical fibers. For this purpose, considerable techniques have been developed, such as the earlier manual bonding techniques, inserting a section of hollow core fiber or hollow core photonic crystal fiber between two sections of single-mode fibers (SMFs), splicing different fibers in series, film coating techniques, direct micromachining using focused femtosecond laser beam, and using chemical etching method to form a microcavity in fiber. Different shapes of cavities have been developed according to the different fabricating method. Such as ellipsoidal cavities, spherical shape, cylindrical shape and so on. Different FP cavity structures correspond to different sensing sensitivity. How to simplify the fabricating method as well as improve the sensitivity of the FPIs is a long- Yundong Zhang Harbin Institute of Technology, China 69 Advances in Optics: Reviews. Book Series, Vol. 3 term goal. What’s more, realizing the simultaneous measurement for different parameters in a single FPI is also a focus of the study. In this chapter, we present a comprehensive overview of the FP fiber sensor technology, classified according to their applications, including FP fiber sensors for strain measurement, temperature measurement, refractive index (RI) measurement and so on. The fundamental principles of the FP fiber sensors are detailed. Each application is reviewed in turn, key recent researches that contributions to the developing of the FP fiber sensors are highlighted and discussed. Finally, we give a forward-looking perspective and discuss the outlook of the FP based fiber sensors considering how can FP fiber sensors step forward. 3.2. Basic Theory The intensity of the interference fringe of air cavity FPI in the reflection spectrum can be expressed as I =I1 +I 2 +2 I1 I 2 cos  , (3.1) where I1 and I2 are the intensities of light reflected at the two cavity interfaces, respectively, and φ is the phase different shift between the two reflected lights.  4  nL , (3.2) where λ is the wavelength of the incident light, n is the RI of the medium in cavity, is the FP cavity length. When    2m  1  , m is an integer, the minimum interference intensity occurs: m  4nL . 2m  1 (3.3) Free spectral range (FSR), namely the fringe spacing or period of the FPI spectrum at λ, can be given by FSR  2 2nL , (3.4) where λ is the wavelength of light, n is the refractive index (RI) of the medium inside the FP cavity. In experiment, L is not convenient for direct measurement, so it is usually calculated by FSR. The interference fringe contrast of the reflecting spectrum is V: 70 Chapter 3. Review of Fabry-Pérot Fiber Sensors V I max  I min , I max  I min (3.5) where Imax is the maximum of interference spectral intensity, Imin is the minimum of interference spectral intensity. 3.3. Applications 3.3.1. Strain Sensing The intrinsic optical fiber sensors based on FP cavities prove to be suitable for strain sensing and have been used successfully for health monitoring of the large civil engineering structures, composite materials, spacecraft, and so on, due to their distinct advantages such as low cost, compactness, high sensitivity and low temperature cross sensitivity. Regarding the optical fiber FPIs, varieties of FP cavities with different shapes were designed and fabricated, for instance, the prolate spheroidal shape FP cavities [1-3], quasi-spherical FP cavities [4], and FP cavities based on a tube [5-10]. Developing FPIs which have a high strain sensitivity and a low thermal sensitivity is the goal people pursuit. In this section, an overview of the accomplishments in the field of optical fiber FPIs for strain sensing is reported. According to the shape of the FP cavity, we classify the optical fiber FPIs into 3 types: spheroidal shape FP cavities, quasispherical FP cavities, and cylindrical FP cavities. 3.3.1.1. Prolate Spheroidal FP Cavity Strain Sensor What kind of fiber FP cavity shape can help to improve the strain sensitivity is of utmost importance. Besides, the relationship between the strain sensitivity and the length of the FP cavity is another key point to research. But For a long time, researchers didn’t have a systematic investigation to the above questions. Some authors even assume that the strain sensitivity of a FPI is independent of the cavity size and it can be enhanced solely by choosing longer wavelengths. Till 2012, F. C. Favero et al. investigated the relationship between the FPIs cavity shape and the strain sensitivity, and demonstrated that the strain sensitivity of FPIs with spheroidal cavities can be controlled through the dimensions of the spheroid [1]. When FPI cavities like those described in Fig. 3.1 is subjected to axial strain, it will experience both axial deformation  d , and transversal deformation  r , the shift of the interference pattern of a FPI with quasi-spherical or spheroidal cavity is proportional to  r . That is to say, the strain sensitivity is proportional to  r . d d  r 3  E   R2 2  r  1    .  d 4  K   r 2 3  d (3.6) 71 Advances in Optics: Reviews. Book Series, Vol. 3 Fig. 3.1. Diagram of a FPI with (a) spherical and (b) prolate spheroidal air cavity. In Eq. (3.6), E is the Young’s modulus, K is the bulk modulus, d is the polar radius and r is the equator radius. Plot the term  r  d as a function of the polar radius d, considering both the quasi- spherical cavity(r ≈ d) and the prolate spheroidal cavity. We can easily find that when the cavity has spherical shape, the term  r  d decrease as the cavity becomes smaller. However, in Fig. 3.2(b), the result is quite opposite to the former situation, when the cavity has spheroidal shape,  r  d increase as the cavity becomes smaller. For the same spheroid diameter, the term  r  d increases with the increase of r. That means the prolate spheroidal FP cavities corresponds to higher strain sensitivity. The theoretical analysis here provides us a way to enhance the sensitivity for different kind of FPIs. Fig. 3.2. (a) Theoretical value of δr/δd as a function of d of a quasi-spherical cavity; (b) a prolate spheroidal cavity for different values of r. In all cases r > d. By fusion splicing SMF to PCF, prolate spheroidal FP cavities are fabricated, as shown in Fig. 3.3. To verify whether the experimental results fit well with the theoretical analysis, FPIs with cavities of sizes of 10  60 µm and 29  40 µm were subjected to the strain tests. The experimental results are shown in Fig. 3.4. The strain sensitivity of the FPI with large d and small r was found to be 3.5 pm/µε, while the prolate one with small d and large r was 72 Chapter 3. Review of Fabry-Pérot Fiber Sensors 10.3 pm/µε. Thus, the results fit very well with the theoretical analysis of spheroidal cavities presented above. Fig. 3.3. Schematic diagram of the interrogation set-up. Fig. 3.4. (a) Reflection spectra at different strains observed in a FPI whose cavity had prolate spheroidal shape and dimensions of 10  60 µm; (b) Interference pattern shifts vs strain observed in FPIs with cavity size of 10  60 µm (dots) and cavity size of 29  40 µm (stars). The presented FPIs also exhibit a low temperature sensitivity (~0.95 pm/°C). This means that for the fiber FP sensor with cavity size of 10  60 µm, the temperature-induced strain error is only 0.09 µε/°C. In 2014, Yiping Wang et al. demonstrated a simple technique to create prolate spheroidal FP cavity in fiber directly [2]. They coated a liquid film on the hemispherical end surface of the SMFs, when the liquid films were overlapped, arc discharge was done, then two fiber ends were spliced with each other and a prolate spheroidal air bubble was created in the spliced joint. Using the above method, prolate spheroidal air bubbles with different cavity lengths of 79, 70, 58, 54, and 46 μm were achieved, as shown in Figs. 3.5 (a)-3.5 (e). The corresponding reflection spectra of the air-cavity-based FPIs are illustrated in Figs. 3.5(f)3.5(j), respectively, in which the FSR of the interference fringes is 14.9, 16.8, 20.8, 22.8, and 26.4 nm, respectively. As the cavity length decrease from 79 to 46 μm, the 73 Advances in Optics: Reviews. Book Series, Vol. 3 corresponding FSR around 1530 nm increases gradually from 14.9 to 26.4 nm, which is in accordance well with the FSR theory. Fig. 3.5. (a), (b), (c), (d), and (e) Microscope images of the created prolate spheroidal air bubble with a cavity length of 79, 70, 58, 54, and 46 μm, respectively; (f)–(j) the corresponding reflection spectra of the prolate spheroidal air-cavity-based FPI. (ER, extinction ratio). Then the response of the FPI with different cavity lengths to the applied tensile strain was investigated. The experiment results show that the shorter length the FP cavity is, a higher strain sensitivity the FPI has. Hence the strain sensitivity of the air-cavity-based FPI fiber sensor can be enhanced by means of shortening the cavity length. The strain sensitivity of the air-cavity-based FPI was enhanced from 2.9 pm/με to 6.0 pm/με while the cavity length was shortened from 79 to 46 μm. This is of great consistence with the conclusion proposed in [1]. A FPI sample with cavity length of 46 μm was used to investigate the temperature responses. The dip wavelength in the reflection spectrum was shifted toward a longer wavelength with a low temperature sensitivity of 1.1 pm/°C. In 2012, Yun-jiang Rao et al. reported an easy fabricated and low-cost fiber optical FPI strain sensor whose cavity is a microscopic prolate spheroidal air bubble [3]. The bubble is formed by fusion splicing together two sections of single-mode fibers (SMFs) with cleaved flat tip and arc fusion induced hemispherical tip, respectively. The schematic of the sensor system with highlighting detail structure of the proposed sensor head is shown in Fig. 3.6. The effect of strain variation on the spectrum shifts were experimentally investigated in two FPIs, both with cavity lengths ~91 μm. The experimental results show that sensor 1 has a higher strain sensitivity of 4.2 pm/με and sensor 2 has a relatively lower strain sensitivity of 4.0 pm/με. The authors also stated that since the refractive index of the medium inside the bubble does not change with strain, the spectrum shift depends solely 74 Chapter 3. Review of Fabry-Pérot Fiber Sensors on the length of the cavity L. If the FPI sensors have larger bubble diameter (cavity length) L and thinner bubble outer cladding than theirs, they are more susceptible to the axial stress, and thus have higher strain sensitivity. But for this point of view, the authors didn’t give the experimental data to support. Considering the FP cavity is formed by a prolate spheroidal air bubble, this kind of FPI maybe more susceptible to the axial stress if they have shorter bubble diameter (cavity length). And it’s certain that thinner bubble outer cladding help to enhance the strain sensitivity. Fig. 3.6. Schematic of the sensor system (top) with highlighting detail structure of the proposed sensor head. The inset in the middle is the microscope photograph of a fabricated microbubble sensor. The temperature tests show that sensitivity of this FPI is only 0.828 pm/°C for sensor 1 and 0.868 pm/°C for sensor 2 in a range of temperature from 100 °C to 950 °C. As for the fore-mentioned three works, all the FPI strain sensors are based on the prolate spheroidal FP air cavities, during the strain measure experiments, the smaller FP cavity lengths corresponds to higher strain sensitivity, conversely, as the FP cavity length become larger, the sensitivity of the FPI strain sensor decreases gradually. Thus, for the prolate spheroidal FP cavity based fiber strain sensor, the sensitivity can be increased by shortening their cavity length. In general, they all show high strain sensitivity and low temperature cross sensitivity, which may become suitable candidates as strain sensors to be used in the practical applications. 3.3.1.2. Spherical FP Cavity Strain Sensor In this section, let’s take a look at the situation when the FP cavity is a spherical one. In 2009, Joel Villatoro et al. reported a FP strain sensor based on index guiding photonic crystal fiber, whose cavity is a spherical air bubble [4]. When splicing is done, the micro air holes in the cladding collapse over a few hundred micrometers and are trapped inside the PCF, thus, forming a spherical micro bubble, the diameter of the bubbles was in a range of 20–25 μm. The cross section of the PCF and the diagram of the interrogation setup are shown in Fig. 3.7. 75 Advances in Optics: Reviews. Book Series, Vol. 3 Fig. 3.7. Diagram of the interrogation setup highlighting the zone of the splice. The 25 μm diameter spherical air cavity was subjected to strain ranging from 0 to 5000 με, and the observation was carried out at wavelength 1290 ± 40 nm. The 58 μm diameter bubble was also subjected to the same strain range, but the shift was measured at wavelength 1550 ± 30 nm. The strain sensitivity of the interferometer with the smaller cavity was 0.62 pm/με, while that of the interferometer with the larger cavity was 2.7 pm/με. So, for the spherical FP cavity, the strain sensitivity increases when the FPI has larger FP cavity length. The experimental result is opposite to the former situation when the cavity has spheroidal shape. These two types are in agreement with the theory proposed in [1]. 3.3.1.3. Cylindrical FP Cavity Strain Sensor Apart from the aforementioned FP cavities, there are also some FP cavities formed by inserting a section of hollow tube or hollow core PCF into SMFs, or just using the fs laser to fabricate a notch on the fiber. FP cavities formed by this way usually have cylindrical or rectangular shape. In 2016, Yong Zhao et al. demonstrated a kind of in-fiber rectangular air FP strain sensor with different cavity lengths [5]. They show that the shorter length the cavity has, the higher strain sensitivity the sensor obtains. The strain sensitivity of in-fiber rectangular air FP sensor with a cavity length of 35 µm can be up to 2.23 pm/με. Fig. 3.8 shows that the in-fiber air FP cavity, which is formed by splicing a section of hollow-core fiber (HCF) with a diameter of 50/125 µm (hole/outer clad) between SMFs. Three FP cavities fabricated are show in Fig. 3.8 (c), in which the lengths of the middle HCF segments are 35 µm, 50 µm, 100 µm, respectively. Through formula derivation, the sensitivity of optical microcavity tension sensor can be can be expressed as follow: K 76 dip F =dip  L , LF (3.7) Chapter 3. Review of Fabry-Pérot Fiber Sensors where K is the sensitivity of sensor, λ is the dip of the reflection spectrum, F is the axial tension, and L is the microcavity length. By formula (3.7), when F is the constant, the sensitivity of optical microcavity tension sensor mainly depends on ΔL/L. That means higher ΔL/L value corresponds to higher strain sensitivity. Fig. 3.8. Preparation process of in-fiber air FP cavity: (a) Welding process of SMF-HCF; (b) Cutting process base on HFCP, and (c) Physical map of FP platform. Fig. 3.9 shows the relationship between L and ΔL/L. When cavity length L varies, ΔL increases with the increase of cavity length L, but ΔL/L reduces with the increase of cavity length L. According to the formula (3.7), what really matters is the ΔL/L value, thus, high strain sensitivity can be obtained by reducing the cavity length L (namely, increasing the ΔL/L value). Fig. 3.9. The relationship diagram between cavity length L and ΔL/L. Fig. 3.10 shows the shift observed as a function of strain in two samples. The strain sensitivity of the 35 µm FP cavity is measured to be 2.23 pm/με, while that the strain sensitivity of the 75 µm FP cavity is 1.12 pm/με. The experimental results and the theory are in agreement, the shorter length the cavity has, the higher strain sensitivity the sensor obtains. 77 Advances in Optics: Reviews. Book Series, Vol. 3 Fig. 3.10. Reflection spectrum and strain sensitivity of in-fiber rectangular air FP sensor with different cavity length 35 µm and 75 µm. The temperature sensing properties of the in-fiber rectangular air FP sensor with cavity length of 35 µm has a low temperature sensitivity of only 0.32 pm/°C. According to the strain and temperature sensitivity of the interference fringe, the temperature-induced strain measurement error is about 0.15 με/°C. Therefore, the temperature disturbance can be ignored in the condition of small temperature fluctuations. In 2012, Marta S. Ferreira et al. proposed a FP strain sensor based on hollow-core ring photonic crystal fiber [6]. The FP cavity was constituted by splicing a small section of hollow-core ring photonic crystal fiber (HCR PCF) between two sections of SMFs. Through numerical simulation, the authors demonstrate that as the FP cavity length decreases, there is a significant increase in the normalized strain coefficient, as shown in Fig. 3.11. As the FP cavity approaches 40 μm, and decreases furthermore, there is a significant increase on the strain sensitivity. The experimental setup is shown in Fig. 3.12. The cross section image of this fiber can be seen at the lower right corner in Fig. 3.12. As expected, this figure illustrates that the strain sensitivity strongly depends on the sensing head length. Longer FP cavities exhibited lower strain sensitivity. In fact, the smaller the sensing head, the higher its sensitivity. Sensitivities of 3.12 pm/με, 3.79 pm/με, 6.16 pm/με, 15.43 pm/με were respectively obtained for the 906 μm, 207 μm, 35 μm, 13 μm sensing heads. The 207 μm long FP cavity was subjected to temperature variations from the room temperature (~26 °C) to 83 °C. The experimental result shows a very low temperature 78 Chapter 3. Review of Fabry-Pérot Fiber Sensors sensitivity of only 0.81 pm/°C, that is to say, the proposed sensing heads in this work are insensitive to temperature variations. Fig. 3.11. Theoretical response of the normalized strain coefficient with the FP cavity length, for three different single mode fibers: SMF28, SM800 and SM1500. Fig. 3.12. Scheme of the experimental setup. In 2007, Yunjiang Rao et al. first demonstrated to directly fabricate a micro in-line FPI (MFPI) by using a near-infrared femtosecond (fs) laser [7]. Fig. 3.13(a) displays the microscope picture of MFPI with 80 μm cavity length based on the SMF. Fig. 3.13 (b) displays the microscope picture of MFPI with 75 μm cavity length based on the PCF. The dependence of wavelength shift of the SMF-MFPI sensor and the PCF-MFPI sensor on the applied strain are experimentally studied and the results are presented in Fig. 3.14(a) and Fig. 3.14(b), respectively. The strain sensitivity of the SMF-MFPI sensor and the PCF-MFPI sensor are 0.006 nm/με and 0.0045 nm/με, respectively. Hence, the SMF-MFPI sensor is more sensitive to strain than the PCF-MFPI sensor. 79 Advances in Optics: Reviews. Book Series, Vol. 3 Fig. 3.13. (a) MFPI with 80 μm cavity length based on SMF; (b) MFPI with 75 μm cavity length based on PCF. Fig. 3.14. Relationship between the applied strain and wavelength-shift of the (a) SMF-MFPI; (b) the PCF-MFPI. The temperature sensitivity of the MFPI sensors are also studied. For a temperature range from 20 °C to 100 °C, the temperature sensitivity of the SMF-MFPI is -0.0021 nm/°C which is close to that of the PCF-MFPI sensor, i.e. -0.002 nm/°C. It should be noted that it is negative because the two end-faces would expand towards the cavity center with the increment of temperature, leading to such a decrease in cavity length. With the increase of the temperature, the wavelengths of both the sensors shift towards the short-wavelength direction. In 2015, Marta S. Ferreira et al. proposed a FP cavity based on a new silica tube [8]. The one shown in Fig. 3.15 is drawn under the pressure p = 2300 Pa, which was chosen to be used as the sensing element. Fig. 3.15. Micrograph of drawn fiber when the pressure p = 2300 Pa. 80 Chapter 3. Review of Fabry-Pérot Fiber Sensors The FP cavity shown in Fig. 3.16 can be produced by splicing a short section of the silica tube between SMFs. Fig. 3.16. Scheme of the experimental setup. A microscope photograph of one FP cavity is also shown. The wavelength responses of different sensing heads are exhibited in Fig. 3.17(a). As expected, the smaller the sensing head, the higher its sensitivity. For the sensing heads with lengths of 17 μm, 51 μm, 70 μm and 198 μm, the obtained strain sensitivities are 13.9 pm/με, 6.0 pm/με, 4.6 pm/με and 3.5 pm/με, respectively. Fig. 3.17. (a) FP cavity sensors response to the applied strain (b) The 198 μm long FP cavity sensor response to temperature. The temperature responses were also investigated. The 198 μm long FP sensing head was subjected to a temperature variation of ~900 °C and a sensitivity of 0.85 pm/°C was obtained, which indicates that this sensor has a cross sensitivity of only ~0.18 με/°C. In 2017, Yi Liu et al. proposed a fiber FP sensor based on micro-cavity plugged by cantilever taper with super long active-length, this fiber FP sensor exhibits ultra-high strain sensitivity [9]. The FPI based on the micro-cavity plugged by cantilever taper with ultra-long activelength is shown in Fig. 3.18, the FP interference length of the FPI based on the micro81 Advances in Optics: Reviews. Book Series, Vol. 3 cavity plugged by cantilever taper is L1, and it is less than the hollow tube length L2. The length L3 of the cantilever taper in the hollow tube can be calculated by L2-L1. Fig. 3.18. The diagram of the FPI based on the micro-cavity plugged by cantilever taper with ultra-long active-length. The stain force sensitivity of the FPI based on the micro-cavity plugged by cantilever taper can be written as: m m L2 = . F AE L1 (3.8) From Eq. (3.8) it can be seen that if the sensing wavelength is fixed, the stain force sensitivity is proportional to the value L2/L1. Therefore, the stain force sensitivity of the FPI can be improved greatly by increasing the hollow tube length L2 or decreasing the FP interference length L1. Then different lengths of cavities are fabricated, the structure A, B and C are (138 µm, 1100 µm), (26 µm, 810 µm) and (3.5 µm, 1360 µm), respectively. The strain force sensitivity of the fabricated fiber inline FP micro-cavity, plugged by cantilever taper are investigated. The changes in the reflection spectra of the three structures with different strain forces are shown in Figs. 3.5(a)–3.5(c), respectively. The results of the three structures were all linear fitted, which are shown in Fig. 3.5(d). The strain force sensitivity of the fiber inline FP micro-cavity C plugged by cantilever taper reached as high as 841.59 nm/N, which equivalents the strain sensitivity of 559 pm/µɛ. By increasing the value of L2/L1, the measured strain force sensitivity of the structure is improved greatly. The sensitivity is approximately proportional to the value L2/L1, which is in accordance with Eq. (3.8). To investigate the crosstalk of the temperature on the strain force sensing, the fiber inline FP micro-cavity C plugged by cantilever taper was placed in air environment in a tube furnace, which was heated from 25 °C to 55 °C with the interval of about 5 °C. When the temperature increases, the interference peak shifted to shorter wavelength direction as the increase of the temperature, and the temperature sensitivity is only 11 pm/°C. However, this temperature sensitivity is pretty high compared to the previous reported ones. In 2014, Shen Liu et al. demonstrated an improved technique and create a unique rectangular air bubble by means of splicing two sections of standard single mode fibers together and tapering the splicing joint [10]. 82 Chapter 3. Review of Fabry-Pérot Fiber Sensors To investigate the strain sensitivity difference between the rectangular and elliptical air bubbles, four samples are used, two rectangular air bubble sample, two elliptical air bubbles, as shown in Fig. 3.19. The fringe dips of the four samples shifted linearly toward a longer wavelength with the increased tensile strain. The strain sensitivity of S1, S2, S3 and S4 was calculated to be 3.0, 29.0, 3.5 and 43.0 pm/με, respectively, by applying a linear fitting of the experimental data. So the strain sensitivity of the rectangular air bubble samples is about nine and twelve times higher than that of the elliptical air bubbles, which indicates that the rectangular air bubble can significantly enhance the strain sensitivity of the air-cavity-based FPI. By using a commercial software, i.e. ANSYS, stress distribution and the deformation of the air cavity under an applied tensile strain is studied, the results show that under the applied tensile strain, the stress distributed on the silica wall of an infiber air bubble sharply increases with the applied tensile strain in case such an air bubble has a rectangular shape and is created in the fused taper. Fig. 3.19. Four in-fiber air bubble samples. In order to study the stress distribution and the deformation of the air cavity under an applied tensile strain, simulation models were established by use of a commercial software, i.e. ANSYS. So the stress distributed on the silica wall of an in-fiber air bubble sharply increases with the applied tensile strain in case such an air bubble has a rectangular shape and is created in the fused taper, which agrees well with the experimental results. 3.3.1.4. Analysis of Temperature Sensitivity for the Fiber FP Strain Sensor The relationship of the cavity length change and the interference pattern shift: ΔL/L= Δλ/λ. Thus, the thermal interference pattern shift sensitivity of 0.95 pm/°C at 1550 nm is equal to ΔL/L = 6.12  107 /°C, this result agrees well with the thermal expansion coefficient of pure silica 5.5 107 /°C. It should be noted that for the air-cavity based fiber FP sensor, the temperature sensitivity is all around 1 pm/°C. The wavelength shift of air cavity to temperature can be given by   L n =  T  L  T n  T          ,  (3.9) 83 Advances in Optics: Reviews. Book Series, Vol. 3 where ε = 5.5 107 and κ = 1.0  105 are the thermal expansion coefficient and the thermo-optic coefficient for pure silica respectively. For the air cavity, the thermo-optic coefficient can be neglected. So the temperature of this kind of FPI sensor is only influenced by silica thermal expansion. Taking the thermal expansion coefficient of silica at wavelength 1550 nm, we get Δλ/T ≈ 0.85 pm/°C. 3.3.1.5. Summary of this Section In this section, we summarized the application of the fiber strain sensor based on FP cavity. According to their shape, they are divided into three categories to introduce. Finally, the temperature characteristics of the FP cavity based fiber strain sensors are analyzed and discussed. Using the same principle, the FP fiber sensor can also be used to measure some other parameters, such as transversal load [11]. 3.3.2. Refractive Index Sensing Refractive index is one of the most important physical parameters. In our daily life, the refractive index (RI) of the fluid (liquid, gas) is often needed to be measured, and people already developed lots of methods to measure refractive index. The optical fiber FP sensor based on the principle of beam interference is widely used as RI sensor, which has high RI sensitivity and is temperature insensitive. There are many types of FP fiber sensors to measure the RI. In this work, they are divided into two categories, one is the method of measuring the fluid RI in the FP cavity, the other is measuring the fluid RI out of the FP cavity. 3.3.2.1. Method of Measuring Fluid RI in FP Cavity 3.3.2.1.1. The Principle of Measuring the Fluid RI in FP Cavity Here we consider a FP cavity model like this: etching a micro-hole in the end of the fiber, and the fiber tip is spliced together with another SMF tip with micro-hole. Then a microchannel is machined vertically to the FP cavity, which allows the RI liquid to flow in or out of the FP cavity, as shown in Fig. 3.20. The micro-channel is fabricated at the cladding, so the size of the micro-channel affects the time of RI liquid flow in (or out of) the FPI cavity and the physical strength of the sensor. But it will not affect the experimental results. When the beam is transmitted to the FP cavity, it will reflect at the two surfaces of the FP cavity. From the Fresnel formula, the reflectivities of the two reflecting surfaces are 2   2 n n  ; R  n1  n2 R1   0 1 , 2 n0  n1  n2  n1  where n0 and n2 are the RI of the fiber core, n1 is the RI of the medium in cavity. 84 (3.10) Chapter 3. Review of Fabry-Pérot Fiber Sensors Fig. 3.20. Diagram of a FPI with air cavity. To avoid the Fresnel reflection at the fiber end, we angle the end of the fiber >8°, [12]. Since the reflectivity of the two reflecting surfaces is very low [13], when the medium in cavity is air or water, the reflectivity is about 0.035 and 0.002, respectively, thus we ignore the multiple reflections in the cavity. The FPI can be treated as a two-beam interferometer and the interference spectrum can be expressed as Equation (3.10). For Equation (3.3), the refractive index is a function of wavelength, L is constant. Differentiating both sides of Equation (3.3) with respect to n , we can obtain n d n 1  2 0.   n    n  dn (3.11) So the RI sensitivity of the sensor can be expressed as S d  n dn   n n . (3.12) In Equation (3.12), it can be seen that the wavelength shift of the interference spectrum is linear with the change in the refractive index of the medium filled in the cavity. Using long wavelength lasers is helpful in improving the sensitivity of the sensor. The sensitivity of the RI is proportional to the wavelength. Thus, it is necessary to indicate the wavelength we use when describing the RI sensitivity. In Equation (3.2), n and L are functions of temperature,  is constant relative to temperature, simplifying both sides of Equation (3.2) with respect to T, we get the temperature sensitivity, d 4  dn dL  n ,   L dt 2m  1  dt dt  (3.13) where dn dt is the thermo-optic coefficient of medium in cavity, it is very small when the medium is air. dL is the thermal expansion coefficient of fiber material, which is also dt very small. It is 0.55  106 /°C for SMF-28 fiber. 85 Advances in Optics: Reviews. Book Series, Vol. 3 3.3.2.1.2. RI Sensing Experiments In 2012, C. R. Liao et al proposed a FP cavity sensor which was etched by laser to measure the RI of a liquid [14] as shown in Fig. 3.21. In the range of 1.31-1.39, the transmission dip wavelength shift towards longer wavelengths with the increase of the refractive index. And the refractive index has a linear relationship with the wavelength of interference dip. Increasing the temperature from 24 to 100 °C, the temperature sensitivity obtained is 4.8 pm/°C at 1554 nm, and the RI sensitivity obtained is 994 nm/RIU with extremely low temperature cross-sensitivity of 4.8 106 RIU/°C. Three different lengths of dielectric cavity are tested. The results show that the FSR decreases with the increase of cavity length, and the intensity of reflected light increases with the increase of cavity length, because the two reflection surfaces within the fiber core are nearly in parallel with a larger radius of the FP cavity, and the reflected light intensity can be enhanced. Fig. 3.21. FPI cavity with the micro-channel. In 2014, Chuang Wu et al. proposed a method for measuring the RI of a liquid in a C-shaped fiber FP cavity [13]. The structure is formed using a C-type open fiber welded two-stage single-mode fiber as shown in Fig. 3.22. In the experiment, the refractive index is changed from 1.33 to 1.36, and the sensitivity is 1368 nm/RIU at 1600 nm. The temperature is heated from room temperature to 600 °C and the sensitivity of the temperature is only 0.42 pm/°C, so temperature cross-sensitivity is 3.04  107 RIU/°C. They also point out that shorter cavities produce a wider range of measurements with greater detection limits. In 2016, ZeJin Lu et al proposed a fast response FP structure based on photonic crystal fiber to measure the RI of the liquid [15]. The structure is shown in Fig. 3.23. The micropores of the photonic crystal fiber in the structure increase its response speed. The response time of water and ethanol is measured to be less than 359 ms and 23 ms, respectively. Ethanol concentration increases from 0 to 19.11 %, the RI sensitivity is 1635.62 nm/RIU at 1500 nm. The temperature increases from 25 °C to 200 °C and the 86 Chapter 3. Review of Fabry-Pérot Fiber Sensors temperature sensitivity is 0.29 pm/°C. The temperature cross-sensitivity 1.77  107 RIU/°C. is Fig. 3.22. C-type FP cavity sensor structure. Fig. 3.23. Fast response photonic crystal FP cavity sensor. In 2012, De-wen Duan et al. proposed a method for measuring the RI of gas using a FP cavity [12], as shown in Fig. 3.24. The gas to be measured enters the FP cavity to change the RI, where the change in RI is achieved by increasing the gas pressure, meanwhile the effect of pressure on FP cavity structure is ignored. When the temperature changes from 30 °C to 300 °C, the wavelength changes by 0.06 nm, so the temperature sensitivity is 2.2 104 nm/°C. When the pressure increases by 700 kPa, the change in RI is 2.14365  103 , so the range of the sensor is limited. The sensitivity of the sensor is 1542 nm/RIU at 1550 mn. In summary, the RI sensitivity is pretty high which can reach 1635.62 nm/RIU at 1500 nm when the liquid and gas fill into the FP Cavity, and the temperature sensitivity is usually less than 1 pm/°C. The temperature cross-over sensitivity is typically at 107 RIU/°C. The sensor responds very quickly, the measurement time is basically dependent on the time of fluid flows into the FP cavity. But its production process is complex, it requires laser etching, fiber splicing and other processes. Besides, the sensor is not convenient to clean. 87 Advances in Optics: Reviews. Book Series, Vol. 3 Fig. 3.24. Gas refractive index measurement experimental structure. 3.3.2.2. Method of Measuring Fluid RI out of FP Cavity 3.3.2.2.1. The Principle of Measuring the Fluid RI out of the FP Cavity Etching a microcavity at the end of the fiber, and splicing two fibers can form an air microcavity. This air chamber is the first FP cavity. Cut the end of the fiber and keep the end face clean, so that the reflected light can be returned by the same way at surface 3, the structure is shown in Fig. 3.25. Fig. 3.25. The structure of the sensor. The reflecting surface 2 and the reflecting surface 3 form a second FP cavity. The reflection light of the two FP cavities will interfere in the fiber, and the change of the RI at the end face can be calculated by demodulating the change of the interference light. The reflection surface of the FP cavity is the interface between the fiber and the air. For the air cavity, the reflectance of the two surfaces is equal 2 n 1   0.034  1 , R1  R2   0  n  1 0   88 (3.14) Chapter 3. Review of Fabry-Pérot Fiber Sensors where n0 is the RI of the fiber. The left side of the interface 3 is optical fiber and the right side is fluid medium. The refractive index of the medium on both sides of the interface 3 is different, the beam will be transmitted and reflected at the interface 3, but we only care about the reflected light and ignore the transmitted light. The reflectance of the interface 3 is: 2  n  n'  R3   0 ' , n n  0   (3.15) where n ' is the RI of the fluid, R1 and R2 are certain, so R3 will directly affect the intensity of interference light. The total reflected electric field Er is thus given by Er  R1 Ei  1  A1 1     1  R1  R2 Ei e  j 2  L1  j  1  A1 1  A2 1     1  R1  R3 Ei e for n'  n0 ,  j  2 L1  2 L2  Er  R1 Ei  1  A1 1     1  R1  R2 Ei e j 2  L1  j  1  A1 1  A2 1     1  R1  R3 Ei e   j  2 L1  2 L2   j  for n0  n' , (3.16) where Ei is the input electric field; A1, A2, and A3 are the transmission loss factors at reflection surfaces; βis the propagation constant of the guided mode of the fiber;α is the loss factor of cavity 1. There is a πphase shift at reflection surface 2. When n ' > n0 , there is also a π phase shift at reflection surface 3, where we only talk about Er for n '  n0 . So the normalized reflection spectrum RFP    is given by: RFP     2 Er  R1  1  A1  1     1  R1  R2 2 Ei 2  1  A1  1  A2  1     1  R1  2 2 2 2 2 1  R  2 2 R3 2 R1 R3 1   1  A1 1  A2 1  R1 1  R2  cos  2 R2 R3 1    2 R1 R2 1   1  A1 1  R1  cos  2 4  L1  n0 L2   1  A  1  A 1  R  1  R  cos  4 2 L  2 1 2 2 1 1  4 L1 2    for n '  n0 .  nL      0 (3.17) 2 From Eqs. (3.16), we obtain that only the reflection coefficient R3 depends on the RI to be measured, and RFP    is independent of the power of the input light. 89 Advances in Optics: Reviews. Book Series, Vol. 3 The corresponding fringe contrast is given by R    for n'  n0 . V  10 log10  FP 2   R   1  FP  (3.18) Using Eqs. (3.16) and Eq. (3.17), we obtain that the maximum fringe contrast V (in dB) varies linearly with n ' as V 10 E  n0  n ' , n0 F log e 10 (3.19) where: F  R1  1  A1  1    1  R1  R2  2 R1 R2 1   1  A1 1  R1  ; 2 2 2 E  2 R1 1   1  A1 1  A2 1  R1 1  R2   2 R2 1    1  A1  1  A2 1  R1  1  R2  . 2 2 2 The plus and minus signs are for n '  n0 and n0  n ' , respectively. If R ,  ,  and other parameters are determined, we can obtain the RI of fluid by detecting the change of V. We obtain the RI of fluid by detecting the change of V. In the experiment, fluid does not need to flow into the FP cavity, so it will affect R3 and V. The sensor head needs to be immersed in the solution, each time after the measurement, the sensor is rinsed with Propyl alcohol carefully until the original spectrum is restored and no residual liquid is left. 3.3.2.2.2. Experimental Introduction and Result Analysis In 2008, W. J. Liu et al proposed a method for measuring the RI of liquid with an air FP cavity [16] as shown in Fig. 3.25. The experimental results show that reducing the cavity loss (  ) and transmission loss (A) can improve the refractive index sensitivity. The sensor can supply a measurement of almost any liquid which possess larger RI than air, as long as it is not very closed to the fiber index n0 , if n '  n0 , the fringe contrast will become zero. The refractive index increases from 1.0 to 1.441, the RI sensitivity is 37 dB/RIU. The refractive index increases from 1.33 to 1.441, the RI sensitivity is 27 dB/RIU. The refractive index increases from 1.45 to 1.62, the RI sensitivity is 24 dB/RIU. For different RI of the liquid, the sensitivity will be different. What’s more, the sensor is temperature insensitive. In 2013, Mingshun Jiang et al. proposed a novel TiO2 nanoparticle thin film coated optical fiber FP sensor for RI sensing [17] as shown in Fig. 3.26. The film increases the reflectivity of the interface 4. The reflectivity of interface 4 is changed with different liquids. Over the RI range from 1.333 to 1.8423, the RI sensitivity is 69.38 dB/RIU. The sensor is also temperature insensitive. 90 Chapter 3. Review of Fabry-Pérot Fiber Sensors Fig. 3.26. FP cavity sensing structure. In 2016, Xiaohui Liu et al. proposed an optical fiber FP interferometer based on hollowcore photonic crystal fiber (HCPCF) for RI sensing [18]. The sensor is formed by splicing both ends of a short section of HCPCF to SMFs. As is shown in Fig. 3.27, over a RI range of 1.312 to 1.42, the RI sensitivity is -136 dB/RIU at 1550 nm. The resolution of the sensor is 7 105 RIU. Increasing the temperature from 30°C to 90°C, the temperature sensitivity of the sensor is 10.7 pm /°C. Fig. 3.27. Hollow photonic crystal fiber FP sensor. In conclusion, the method of measuring fluid RI out of FP cavity is by analyzing the variation of the fringe contrast, rather than the wavelength shift of the interference fringe. This type of sensor does not need to fabricate micro-channels on the FP cavity, so it is robust in structure and simple to construct compared with the method of measuring fluid RI in FP cavity. However, the cleaning process of the sensor needs to be very careful to avoid damaging the reflective interface. 3.3.2.3. Summary of this Section In this section, we describe two types of FP RI fiber sensors which are insensitive to temperature. The method of measuring fluid RI in the FP cavity analyzes the wavelength shifts of a point (usually interference spectrum dip) to detect the change of fluid RI. This kind of RI sensors have high sensitivity and fast response, but the microchannel reduces its structural strength. The method of measuring fluid RI out of FP cavity analyzes the variation of the fringe contrast, which does not require the fabrication of micro-channels in the FP cavity, so that its structural strength is higher and easy to construct. 91 Advances in Optics: Reviews. Book Series, Vol. 3 Although lots of ways have been explored to measure the RI, and the sensitivity is pretty high, the study of FP cavity based fiber sensors is still in process. Only by making prominent FP fiber RI sensors, which possess features such as high sensitivity, strong structural strength, low interference, compactness and so on, can it be used widely in practical applications. 3.3.3. Temperature Sensing Temperature is one of the most basic physical quantities in science and technology. Physics, chemistry, thermodynamics, flight mechanics, hydrodynamics and other disciplines are inseparable from temperature measurement. It is also one of the most common and important parameters in industrial production. The quality of the product is closely related to the temperature in many industries. Fiber FP cavity temperature sensor has been widely used, because it has a small size, light weight, anti-electromagnetic interference ability, resistance to harsh environments, high sensitivity, resist harsh environments, simple structure, low production cost advantages. 3.3.3.1. Theory Fiber optical FP sensor is characterized by a single fiber using multi-beam interference to detect. In general, the round-trip optical path length (OPL) of an FP cavity is simply given by: lOPL  2 nL , (3.20) where n is the refractive index and L is the physical length of the cavity, the OPL depends on temperature. For a FPI, the relationship between the free space range (FSR) and the interferometer length L is:   2 2 neff L , (3.21) where λ is the wavelength of light, neff is the effective refraction index (ERI). The light in the fiber first reflect at the first mirror, the reflection light intensity is I1, then reflect at the second mirror, the reflection light intensity is I2, the two reflected light will interference after encountering, the interference between I1 and I2 can be expressed as: I  I1  I 2  2 I  I cos( 1 2 4 neff L   0 ) , (3.22) where neff is the effective refractive index neff of the fundamental mode, L is the length of the FP cavity, λ is the free space wavelength, and φ0 is initial phase. Assuming φ0 = 0, for a certain spectrum peak, the phase difference value of the optical phase shift Δϕ as a function of temperature is given by: 92 Chapter 3. Review of Fabry-Pérot Fiber Sensors   = 4 neff L   2m , 4 nL  1 dn 1 dL   T ,   n dT L dT  (3.23) where m is the integer, φ is the phase. Thus, the wavelength of the peak km is given by: m  2 neff L m . (3.24) When the FPI is subjected to temperature variation, the effective refractive index neff and the fiber length L will change due to thermo-optic effect and thermal-expansion, which can be expressed as: ( neff neff  L 1 )   , L T (3.25) where the thermo-optic coefficient δ = 6.45  10 6 /°C and thermal expansion coefficient  = 5.5x10 7 /°C for silica, respectively. The temperature sensitivity of the FPI is: L  m (   ) . T (3.26) Therefore, the temperature variation can be measured by detecting the output light spectrum of the FPI. 3.3.3.2. Applications of Temperature Sensor Based on FPI In this part, the principle, application and development trend of the FP fiber temperature sensor are introduced. The temperature sensing head are classified into two types according to their structure. The first type is by splicing one fiber section to another, thus forming the FP cavity, for simplicity, we call it splicing type FP cavity. The second type is by coating a thin film at the end of the fiber and forming the FP cavity, we call this kind of sensing head coating type FP cavity. 3.3.3.2.1. Splicing Type FP Fiber Optic Sensor The extrinsic FP fiber temperature sensors, the FP cavity is formed between the two end faces of the fiber, the air cavity has a small thermal expansion coefficient. Although the external FPI is relatively simple and low cost, its drawbacks are obvious, like low coupling efficiency, requiring calibration and tight packaging etc., all of these things limit the development of extrinsic FPIs. To overcome this problem, special fiber is adopted by 93 Advances in Optics: Reviews. Book Series, Vol. 3 many researcher. By splicing a small section of the special fiber into two SMFs, high temperature sensitivities can be achieved. What’s more, it is low cost, robust and easy to fabricate. In 2015, Peng Zhang et al. demonstrated a FPI-based high temperature fiber sensor fabricated by splicing two single mode fibers (SMFs) to both ends of a section of simplified hollow core fiber (SHCF) with a certain length and cleaving one of the two SMFs to a designed length [19]. The highest temperature sensitivity is 1.019 nm/°C for the envelope under temperature range from 250 to 300 °C. The fiber sensor can be operated in the temperature measurement range from 20 to 1050 °C. The configuration of the SHCF-based FPI fiber-optic sensor head is shown in Fig. 3.28. The use of this fiber can increase the effective reflected power at the splice point, which is different from the use of solid PCF that has a large refractive index. Fig. 3.28. Configuration of the SHCF-based FPI sensor (a) and cross section of SHCF (b). In 2008, Hae Young Choi et al. demonstrated a compact FPI fiber sensor suitable for hightemperature sensing [20]. The sensor head consists of two FP cavities formed by fusion splicing a short segment of hollow-core fiber and single-mode fiber at the end of a PCF. The schematic of the proposed sensor system is presented in Fig. 3.29. The SMF part is used as the main sensing area, and the HOF air cavity part is used as the auxiliary sensing cavity. The temperature response of the proposed sensor is measured up to 1000 °C and analyzed in the spatial frequency domain of the reflection spectrum. Fig. 3.29. Schematic of the sensor system (top) and the detail structure of the proposed sensor head (bottom). The inset in the middle is the microscope photograph of a fabricated sensor head. 94 Chapter 3. Review of Fabry-Pérot Fiber Sensors In 2015, the temperature sensor proposed by Xinghu Fu et al. exhibits a relatively high sensitivity [21]. The fiber FP temperature sensor is fabricated by just splicing photonic crystal fiber (PCF) and a section of single-mode fiber (SMF) together. Fig. 3.30 shows the schematic design. With the temperature increasing, due to the thermal-optic effect and the thermal-expansion effect of the fiber, both the RI of the core and the distance between the two reflectors increase, thus leading to the wavelengths shift toward longer wavelength. Four wavelength dips are selected as the observing points, in the temperature range of 30-80°C, the highest sensitivity is 11.12 pm/°C. Fig. 3.30. (a) Schematic diagram of the FPI sensor (b) Microscope images of the two reflection surfaces. In 2013 Wei Peng et al. constructed a miniature FPI temperature sensor based on a dualcore photonic crystal fiber (DCPCF) [22]. Fig. 3.31 shows a schematic design of the proposed DCPCF-based FPI sensor. The DCPFC has two symmetric silica cores that separated by one air hole in the center point of the fiber, thus the light guided by SMF will partially reflect at the fiber-air interface at the splicing point because of the Fresnel reflection. The rest of the light will be guided through the core and reflected back at the cleave ends of the DCPCF, finally recoupled into the SMF again. These two beams will interfere and the interferometric spectrum can be used for sensing. The temperature response of two sensors with PCF lengths of 164 and 953 μm has been characterized, respectively. The temperature sensitivities are 13.17 pm/°C for the 164 μm long FPI and 13.18 pm/°C for the 953 μm long FPI in a temperature range of 40-480 °C. Fig. 3.31. Schematics of DCPCF-based fiber optic FPI sensor system: (a) Sensor structure and operating mechanism; (b) Microscope photograph of the DCPCF and splicing processing. 95 Advances in Optics: Reviews. Book Series, Vol. 3 In 2011, D. W. Duan et al. designed a novel compact FPI which can measure temperature up to 1000 [23]. The sensor is formed by fusion splicing two sections of SMFs with a large lateral offset. The temperature responses of the FPI based on larger lateral offset splicing induced by two parallel separated mirrors are demonstrated. The sensor has been tested under high temperature, showing a high sensitivity of 41 nm/°C. The schematic of sensor system and detailed structure of proposed sensor head is shown in Fig. 3.32. This larger lateral offset splicing can excite higher order cladding modes, thus increasing the sensitivity of sensor. Fig. 3.32. Schematic of sensor system (top) and detailed structure of proposed sensor head (bottom). In 2015, Chen Pengfei et al. proposed a FP air cavity which can be created by splicing a special sapphire-derived fiber with SMF directly and cleaving the pigtail of the sapphirederived fiber subsequently [24]. The microphotography of the FP cavity fabrication process is shown in Fig. 3.33. This FP interferometer shows a high sensitivity to temperature of about 15.7 pm/°C within the temperature range up to 1000 °C. Fig. 3.33. The microphotography of the FP cavity fabrication by using sapphire-derived fiber, (a) well aligned fibers; (b) air cavity created at the splicing point, and (c) Fabry-Perot fabricated in the sapphire-derived fiber. 96 Chapter 3. Review of Fabry-Pérot Fiber Sensors 3.3.3.2.2. Coating Type FP Fiber Optic Sensor In this section, the FP cavity is formed by thin films made in different material, the outer temperature have great influences on the length of the FP cavity. Thus, it can possess extremely high temperature sensitivity. Besides, some material can be operated under high temperature, so they appeared to be suitable for high temperature sensing. In 2015 Jinesh Mathew et al. presented an in-fiber FP fiber sensor for high-temperature sensing [25]. The sensor has been demonstrated for high-temperature sensing up to 1100 °C. As shown in Fig. 3.34 (a), the FP cavity is formed between a reflective in-fiber metallic splice and the air-fiber boundary at the end of the sensor head, to make it more compact, a second FPI is fabricated where the sensor is in a reduced diameter. The sensitivity increases with longer FP cavity length. Fig. 3.34. Basic structure of the optical fibre sensor; (a) Image of the fabricated 125 μm diameter sensor; (b) Image of the fabricated 50 μm sensor. Similarly, they demonstrated two types of FP fiber sensors, SMF-Cr-SMF, and SMF-CrPCF. Both are tested over a temperature range from room temperature up to 1100 °C with good repeatability. In 2016, Iván Hernández-Romano et al. proposed a similar structure used for low temperature sensing [26]. The sensor head consists of FP micro-cavity formed by an internal mirror made of a thin titanium dioxide (TiO2) film and a segment of SMF covered with Poly (dimethylsiloxane) (PDMS). The structure of the sensing head is shown in Fig. 3.35. In this design, the RI of PDMS varies according to the temperature, the temperature change can be detected by the amplitude variation of the interference pattern. By monitoring the extinction ratio of the interference pattern, a temperature sensitivity of 0.13 dB/℃ was observed in the temperature range of 22 °C - 60 °C. In 2014, M. J˛edrzejewska-Szczerska et al. demonstrated a novel optical fiber sensor of temperature using a thin ZnO layer [27]. The ZnO layer was coated on SMF and thus a FP cavity was built. The ZnO thin films can be used in two basic extrinsic FPI types, as shown in Fig. 3.36. The sensitivity of temperature measurement is measured to be 0.05 nm/°C in the temperature range from 50 to 300 °C. 97 Advances in Optics: Reviews. Book Series, Vol. 3 Fig. 3.35. Schematic diagram of the sensing head. Fig. 3.36. FP interferometer with the cavity made of a ZnO layer: (a) Symmetric configuration; (b) Asymmetric configuration; h is the thickness of the cavity, M1, M2 are the cavity mirrors. 3.3.3.2.3. Other Types In addition to the above mentioned splicing and coating method, there are some other special methods using FP cavity for temperature sensing. Such as a sapphire fiber extrinsic FP interferometer for ultrahigh temperature [28], a U-shaped optical FPI is constructed for high temperature sensing [29], and fiber FPI assisted with iron V-groove for temperature measurement [30]. 3.3.3.3. Summary of this Section In summary, we divided the FP temperature sensor into two types, splicing type and coating type. The measuring temperature range of the splicing type is lower than coated type, but it possesses higher sensitivity. The coating type FPI can measure higher temperature, because the thin films which constructed the FP is made from special materials can work in high temperature. 3.4. Concluding Remarks and Perspectives In the past few decades, optical fiber sensors have been widely used in sensing applications of various fields. Different fiber sensors based on various principles have 98 Chapter 3. Review of Fabry-Pérot Fiber Sensors been proposed [31, 32]. Among which, FP cavity based fiber sensors possess the advantages of compactness, simple configuration, small size, high sensitivity, fast responses etc., which make them attractive for sensing applications in industry. This chapter reviewed the typical intrinsic FP fiber sensors. The fundamental principles of the FP fiber sensors are discussed in detail. Each application is reviewed in turn, key recent researches and their contributions for the development of the FP fiber sensors are highlighted and discussed. Some methods for fabricating FP fiber sensors are described according to their operating principles, fabrication methods, and application fields. 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Wang, FabryPerot cavity based on sapphire-derived fiber for high temperature sensor, in Proceedings of the International Conference on Optical Fibre Sensors (OFS’15), Society of Photo-Optical Instrumentation Engineers, Curitiba, Brazil, 2015, 96347T. [25]. J. Mathew, O. Schneller, D. Polyzos, D. Havermann, R. M. Carter, W. N. MacPherson, D. P. Hand, R. J. Maier, In-fiber Fabry-Perot cavity sensor for high-temperature applications, J. Lightw. Technol., Vol. 33, 2015, pp. 2419-2425. [26]. I. Hernández-Romano, M. A. Cruz-Garcia, C. Morenohernández, D. Monzónhernández, E. O. Lópezfigueroa, Optical fiber temperature sensor based on a microcavity with polymer overlay, Opt. Express, Vol. 24, 2016, pp. 5654-5661. [27]. M. Jędrzejewska-Szczerska, P. Wierzba, A. A. Chaaya, M. Bechelany, P. Miele, R. Viter, A. Mazikowski, K. Karpienko, M. Wróbel, ALD thin ZnO layer as an active medium in a fiber-optic Fabry-Perot interferometer, Sens. & Actuators A Phys., Vol. 221, 2015, pp. 88-94. [28]. Z. P. Tian, Z. H. Yu, B. Liu, A. B. Wang, Sourceless optical fiber high temperature sensor, Opt. Lett., Vol. 41, 2016, pp. 195-198. 100 Chapter 3. Review of Fabry-Pérot Fiber Sensors [29]. L. Yuan, X. Lan, J. Huang, H. Z. Wang, B. K. Cheng, J. Liu, H. Xiao, Miniaturized optical fiber Fabry-Perot interferometer fabricated by femtosecond laser irradiation and selective chemical etching, in Proceedings of the Conference Advanced Fabrication Technologies for Micro/Nano Optics and Photonics VII, Society of Photo-Optical Instrumentation Engineers, San Francisco, CA, USA, 2014, 89741A. [30]. X. D. Wen, T. G. Ning, Y. Bai, C. Li, J. Li, C. B. Zhang, Ultrasensitive temperature fiber sensor based on Fabry-Pérot interferometer assisted with iron V-groove, Opt. Express, Vol. 23, 2015, pp. 11526-11536. [31]. J. F. Wang, Y. D. Zhang, X. N. Zhang, H. Tian, H. Wu, Y. X. Cai, J. Zhang, P. Yuan, Enhancing the sensitivity of fiber Mach–Zehnder interferometers using slow and fast light, Opt. Lett., Vol. 36, 2011, pp. 3173-3175. [32]. J. F. Wang, Y. D. Zhang, J. Zhang, Y. X. Cai, X. N. Zhang, P. Yuan, Simultaneous observation of superluminal and slow light propagation in a nested fiber ring resonator, Opt. Express, Vol. 18, 2010, pp. 13180-13186. 101 Chapter 4. Multi-Parameter Integrated Optical Sensor Based on Multimode Interference and Microring Resonator Structures Chapter 4 Multi-Parameter Integrated Optical Sensor Based on Multimode Interference and Microring Resonator Structures Trung-Thanh Le1 4.1. Introduction Current approaches to the real time analysis of chemical and biological sensing applications utilize systematic approaches such as mass spectrometry for detection. Such systems are expensive, heavy and cannot monolithically integrated in one single chip [1]. Electronic sensors use metallic probes which produces electro-magnetic noise, which can disturb the electro-magnetic field being measured. This can be avoided in the case of using integrated optical sensors. Integrated optical sensors are very attractive due to their advantages of high sensitivity and ultra-wide bandwidth, low detection limit, compactness and immunity to electromagnetic interference [2, 3]. Optical sensors have been used widely in many applications such as biomedical research, healthcare and environmental monitoring. Typically, detection can be made by the optical absorption of the analytes, optic spectroscopy or the refractive index change [1]. The two former methods can be directly obtained by measuring optical intensity. The third method is to monitor various chemical and biological systems via sensing of the change in refractive index [4]. Optical waveguide devices can perform as refractive index sensors particularly when the analyte becomes a physical part of the device, such as waveguide cladding. In this case, the evanescent portion of the guided mode within the cladding will overlap and interact with the analyte. The measurement of the refractive index change of the guided mode of the optical waveguides requires a special structure to convert the refractive index change into detectable signals. A number of refractive index sensors based on optical waveguide structures have been reported, including Bragg grating sensors, directional coupler Trung-Thanh Le International School (VNU-IS), Vietnam National University (VNU), Cau Giay, Hanoi, Vietnam 103 Advances in Optics: Reviews. Book Series, Vol. 3 sensors, Mach- Zehnder interferometer (MZI) sensors, microring resonator sensors and surface plasmon resonance sensors [1, 4-7]. Recently, the use of optical microring resonators as sensors [2, 6] is becoming one of the most attractive candidates for optical sensing applications because of its ultra-compact size and easy to realize an array of sensors with a large scale integration [8-10]. When detecting target chemicals by using microring resonator sensors, one can use a certain chemical binding on the surface. There are two ways to measure the presence of the target chemicals. One is to measure the shift of the resonant wavelength and the other is to measure the optical intensity with a fixed wavelength. In the literature, some highly sensitive resonator sensors based on polymer and silicon microring and disk resonators have been developed [11-14]. However, multichannel sensors based on silicon waveguides and MMI structures, which have ultra-small bends due to the high refractive index contrast and are compatible with the existing CMOS fabrication technologies, are not presented much. In order to achieve multichannel capability, multiplexed single microring resonators must be used. This leads to large footprint area and low sensitivity. For example, recent results on using single microring resonators for glucose and ethanol detection showed that sensitivity of 108 nm/RIU [2, 15], 200 nm/RIU [16] or using microfluidics with grating for ethanol sensor with a sensitivity of 50 nm/RIU [17]. Silicon waveguide based sensors has attracted much attention for realizing ultra-compact and cheap optical sensors. In addition, the reported sensors can be capable of determining only one chemical or biological element. The sensing structures based on one microring resonator or Mach Zender interferometer can only provide a small sensitivity and single anylate detection [13]. Therefore, in this study, we present new structures for achieving a highly sensitive and multichannel sensor. Our structures are based on only 4×4, 6×6 and 8×8 multimode interference (MMI) coupler assisted microring resonators for two, three and four parameter sensors. The proposed sensors provide very high sensitivity compared with the conventional MZI sensor. In addition, it can measure multi-parameter target chemicals and biological elements simultaneously. 4.2. Multimode Interference Structures The conventional MMI coupler has a structure consisting of a homogeneous planar multimode waveguide region connected to a number of single mode access waveguides. The MMI region is sufficiently wide to support a large number of lateral modes. There are three main interference mechanisms. These mechanisms depend upon the locations of the access waveguides [18]. The first is the general interference (GI) mechanism which is independent of the modal excitation. The second is the restricted interference (RI) mechanism, in which excitation inputs are placed at some special positions so that certain modes are not excited. The last mechanism is the symmetric interference (SI), in which the excitation input is located at the centre of the multimode section. 104 Chapter 4. Multi-Parameter Integrated Optical Sensor Based on Multimode Interference and Microring Resonator Structures The characteristics of an MMI device can be described by a transfer matrix [19-21]. This transfer matrix is a very useful tool for analyzing cascaded MMI structures. The phase ij associated with imaging an input i to an output j in an MMI coupler. These phases ij form a matrix  , with i representing the row number, and j representing the column number. Then the transfer matrix of the MMI coupler  is directly related to  , and the output field distribution emerging from the MMI coupler can be written as b  Ma , (4.1) where a  [a1 a 2 . . . a N ]T , b  [b1 b 2 . . . b N ]T and M  [mij ]NxN . The superscript T indicates the transpose of a matrix. a i (I = 1,..,N) is the complex field amplitude at input waveguide i and b j (j = 1,..,N) is the complex field amplitude at output waveguide j. Elements of the transfer matrix M are mij  m ji  Aije jij , where A ij is the field amplitude transfer coefficient and ij is the phase shift when imaging from input i to output j. 4.3. Microring Resonator Consider a curved waveguide having a radius R connected to an MMI coupler to form a single microresonator as shown in Fig. 4.1. Fig. 4.1. The structure of a microresonator using a 2×2 MMI coupler. If the common phase factor 0 of the MMI coupler is factored out for simplicity, then the complex amplitudes of the input signals a i (i=1, 2) and output signals b j (j=1, 2) are related through the transfer matrix of the 2×2 MMI coupler [22] b = Ma , (4.2) 105 Advances in Optics: Reviews. Book Series, Vol. 3  τ where M =  *  -κ κ , a  [a1 a 2 ]T and b  [b1 b2 ]T . * τ  (4.3) Here  and  are the amplitude transmission and coupling coefficients of the coupler, respectively. The superscripts * and T denote the complex conjugate and the transpose of 2 2 a matrix, respectively. For a lossless coupler,     1 . A plot of the transmission characteristics as a function of microresonator loss factor (  ), with transmission coefficient  as parameter, is presented in Fig. 4.2. The transmission loss factor  is   exp(0 LR ) , where L R is the total length of the racetrack (or ring) waveguide and 0 (dB / cm) is the transmission loss coefficient. Fig. 4.2. The transmission characteristic of a single microresonator based on a 2×2 MMI. By rapidly changing the loss/gain or the coupling coefficient of the coupler, optical modulators and optical switches can be created. In addition, a single microresonator can be used as an optical notch filter. The spectral response of the microresonator is shown in Fig. 4.3, for a loss factor of α = 0.7. Here,  is the phase accumulated inside the microresonator,   0 (2R  L') , where 0 is the propagation constant, L ' is the length shown in Fig. 4.3 and R is the radius of the curved waveguide. The simulations show that the largest extinction ratio can be achieved with critical coupling that is when the loss factor  equals the transmission coefficient  (    ). 4.4. Two-Parameter Sensor Based on 4×4 MMI and Resonator Structure We present a structure for achieving a highly sensitive and multichannel sensor. Our structure is based on only one 4×4 multimode interference (MMI) coupler assisted microring resonators [23, 24]. The proposed sensors provide very high sensitivity compared with the conventional MZI sensors. In addition, it can measure two different 106 Chapter 4. Multi-Parameter Integrated Optical Sensor Based on Multimode Interference and Microring Resonator Structures and independent target chemicals and biological elements simultaneously. We investigate the use of our proposed structure to glucose and ethanol sensing at the same time. The proposed sensor based on 4×4 multimode interference and microring resonator structures is shown in Fig. 4.4. The two MMI couplers are identical. The two 4×4 MMI couplers have the same width WMMI and length LMMI . Fig. 4.3. Transmission characteristic of a single microresonator. Fig. 4.4. Schematic of the new sensor using 4×4 MMI couplers and microring resonators. In this structure, there are two sensing windows having lengths Larm1 , Larm2 . As with the conventional MZI sensor device, segments of two MZI arms overlap with the flow channel, forming two separate sensing regions. The other two MZI arms isolated from the analyte by the micro fluidic substrate. The MMI coupler consists of a multimode optical waveguide that can support a number of modes [25]. In order to launch and extract light from the multimode region, a number of single mode access waveguides are placed at the input and output planes. If there are N input waveguides and M output waveguides, then the device is called an NxM MMI coupler. 107 Advances in Optics: Reviews. Book Series, Vol. 3 In this study, the access waveguides are identical single mode waveguides with width Wa . The input and output waveguides are located at [18] 1 W x i  (i  ) MMI , (i = 0, 1,…, N-1). 2 N (4.4) The electrical field inside the MMI coupler can be expressed by [19] E(x,z)  exp( jkz) M  m 1 Em exp( j m2  m z)sin( x). 4 WMMI (4.5) 3L  , where L  is the beat 2 length of the MMI coupler [26]. One can prove that the normalized optical powers transmitted through the proposed sensor at wavelengths on resonance with the microring resonators are given by [9] If we choose the MMI coupler having a length of L MMI  2  1   1  cos( 2 )  T1    ,  1   cos( 1 )  1  2  (4.6) 2  2    2  cos( 2 )  T2    , 1   cos( 2 )  2 2   (4.7) 1  ) 2  sin( 2 ), and  2  cos( 2 ) ; 1 , 2 are the 2 2 2 2 phase differences between two arms of the MZI, respectively; 1 ,  2 are round trip transmissions of light propagation through the two microring resonators [27]. where 1  sin( 1 ) , 1  cos( In this study, the locations of input, output waveguides, MMI width and length are carefully designed, so the desired characteristics of the MMI coupler can be achieved. It is now shown that the proposed sensor can be realized using silicon nanowire waveguides [28, 29]. By using the numerical method, the optimal width of the MMI is calculated to be WMMI  6 m for high performance and compact device. The core thickness is h co = 220 nm. The access waveguide is tapered from a width of 500 nm to a width of 800 nm to improve device performance. It is assumed that the designs are for the transverse electric (TE) polarization at a central optical wavelength   1550 nm . The FDTD simulations for sensing operation when input signal is at port 1 and port 2 for 108 Chapter 4. Multi-Parameter Integrated Optical Sensor Based on Multimode Interference and Microring Resonator Structures glucose and ethanol sensing are shown in Fig. 4.5 (a) and 4.5 (b), respectively. The mask design for the whole sensor structure using CMOS technology is shown in Fig. 4.5 (c). (a) Input 1, glucose sensing (b) Input 2, Ethanol sensing (c) Mask design Fig. 4.5. FDTD simulations for two-channel sensors (a) glucose; (b) Ethanol and (c) mask design. The proposed structure can be viewed as a sensor with two channel sensing windows, which are separated with two power transmission characteristics T1 , T2 and sensitivities S1 , S2 . When the analyte is presented, the resonance wavelengths are shifted. As the result, the proposed sensors are able to monitor two target chemicals simultaneously and their sensitivities can be expressed by: S1  1  , S2  2 , n c n c (4.8) where 1 and 2 are resonance wavelengths of the transmissions at output 1 and 2, respectively. For the conventional sensor based on MZI structure, the relative phase shift  between two MZI arms and the optical power transmitted through the MZI can be made a function of the environmental refractive index, via the modal effective index n eff . The transmission at the bar port of the MZI structure can be given by [1] 109 Advances in Optics: Reviews. Book Series, Vol. 3 TMZI  cos 2 (  ), 2 (4.9) where   2Larm (n eff ,a  n eff ,0 ) /  , Larm is the interaction length of the MZI arm, n eff ,a is effective refractive index in the interaction arm when the ambient analyte is presented and n eff ,0 is effective refractive index of the reference arm. The sensitivity S MZI of the MZI sensor is defined as a change in normalized transmission per unit change in the refractive index and can be expressed as SMZI  TMZI , n c (4.10) where n c is the cover medium refractive index or the refractive index of the analyte. The sensitivity of the MZI sensor can be rewritten by SMZI  TMZI TMZI n eff ,a .  n c n eff ,a n c The waveguide sensitivity parameter n eff ,a n c theorem for optical waveguides [1]: n eff ,a n c  nc n eff ,a  can be calculated using the variation 2 E a (x, y) dxdy analyte  (4.11) 2 E a (x, y) dxdy , (4.12)  where E a (x, y) is the transverse field profile of the optical mode within the sensing region, calculated assuming a dielectric material with index n c occupies the appropriate part of the cross-section. The integral in the numerator is carried out over the fraction of the waveguide cross-section occupied by the analyte and the integral in the denominator is carried out over the whole cross-section. For sensing applications, sensor should have steeper slopes on the transmission and phase shift curve for higher sensitivity. From (4.9) and (4.10), we see that the sensitivity of the MZI sensor is maximized at phase shift   0.5 . Therefore, the sensitivity of the MZI sensor can be enhanced by increasing the sensing window length L a or increasing the n eff ,a , which can be obtained by properly designing optical waveguide sensitivity factor n c waveguide structure. In this chapter, we present a new sensor structure based on microring resonators for very high sensitive and multi-channel sensing applications. 110 Chapter 4. Multi-Parameter Integrated Optical Sensor Based on Multimode Interference and Microring Resonator Structures S1 / SMZI From equations (4.8) and (4.10), the ratio of the sensitivities of the proposed sensor and the conventional MZI sensor can be numerically evaluated. The sensitivity enhancement factor S1 / SMZI can be calculated for values of 1 between 0 and 1 is plotted in Fig. 4.6. For 1  0.99 , an enhancement factor of approximately 10 is obtained. The similar results can be achieved for other sensing arms. Round trip 1 Fig. 4.6. Sensitivity enhancement factor for the proposed sensor, calculated with the first sensing arm. In general, our proposed structure can be used for detection of chemical and biological elements by using both surface and homogeneous mechanisms. Without loss of generality, we applied our structure to detection of glucose and ethanol sensing as an example. The refractive indexes of the glucose ( n glucose ) and ethanol ( n EtOH ) can be calculated from the concentration (C %) based on experimental results at wavelength 1550 nm by [30-32] n glucose  0.2015  [C]  1.3292, (4.13) n EtOH  1.3292  a[C]  b[C]2 , (4.14) where a  (8.4535  104 ) and b  (4.8294  106 ) . The refractive indexes of the glucose and EtOH at different concentrations are shown in Fig. 4.7. In our design, the silicon waveguide with a height of 220 nm, width of 500 nm is used for single mode operation. The wavelength is at 1550 nm. It is assumed that the interaction lengths for glucose and ethanol sensing arms are 100 m . By using the finite difference method (FDM), the effective refractive indexes of the waveguide at different concentration is shown in Fig. 4.8. The glucose solutions with concentrations of 0 %, 0.2 % and 0.4 % and Ethanol concentrations of 0 %, 3 % and 6 % are induced to the device. The resonance wavelength shifts corresponding to the concentrations can be measured by the optical spectrometer as 111 Advances in Optics: Reviews. Book Series, Vol. 3 shown in Fig. 4.9 for glucose and Fig. 4.10 for ethanol. For each 0.2 % increment of the glucose concentration, the resonance wavelength shifts of about 105 pm is achieved. This is a greatly higher order than that of the recent conventional sensor based on single microring resonator [31, 33]. For each 3 % increment of the ethanol concentration, the resonance wavelength shifts of about 1.5×104 pm is achieved. Fig. 4.7. Refractive indexes of the glucose and ethanol vs. concentations. Fig. 4.8. Effective refractive indexes of the waveguide with glucose and ethanol cover at different concentrations. 112 Chapter 4. Multi-Parameter Integrated Optical Sensor Based on Multimode Interference and Microring Resonator Structures Fig. 4.9. Resonance wavelength shift at different glucose concentrations. Fig. 4.10. Resonance wavelength shift at different ethanol concentrations. By measuring the resonance wavelength shift (  ), the glucose concentration is detected. The sensitivity of the glucose sensor can be calculated by Sglu cos e    9000(nm/ RIU). n (4.15) Our sensor provides the sensitivity of 9000 nm/RIU compared with a sensitivity of 170 nm/RIU [33]. In addition to the sensitivity, the detection limit (DL) is another important parameter. For the refractive index sensing, the DL presents for the smallest ambient refractive index change, which can be accurately measured. The Detection limit (DL) can be calculated as the ratio of the resonance wavelength resolution  to the sensitivity Sglu cose by [34] 113 Advances in Optics: Reviews. Book Series, Vol. 3 DL   Sglu cose , (4.16) 2 2 2 where   amp  noise   temp induced  spec  res , amp  noise is the standard deviation of the spectral variation which is determined by the Q factor and extinction ratio, tempinduced is the standard deviation induced by noises in the sensing systems and spec  res is resulted from the spectral resolution of the optical spectrometer. In our sensor design, we use the optical refractometer with a resolution of 20 pm, the detection limit of our sensor is calculated to be 2×10-4, compared with a detection limit of 1.78×10-5 of single microring resonator sensor [35]. The sensitivity of the ethanol sensor is calculated to be SEtOH  6000 (nm/ RIU) and detection limit is 1.3×10-5. It is noted that silicon waveguides are highly sensitive to temperature fluctuations due to the high thermo-optic coefficient (TOC) of silicon ( TOCSi  1.86 104 K 1 ). As a result, the sensing performance will be affected due to the phase drift. In order to overcome the effect of the temperature and phase fluctuations, we can use some approaches including of both active and passive methods. For example, the local heating of silicon itself to dynamically compensate for any temperature fluctuations [36], material cladding with negative thermo-optic coefficient [37-40], MZI cascading intensity interrogation [14], control of the thermal drift by tailoring the degree of optical confinement in silicon waveguides with different waveguide widths [41], ultra-thin silicon waveguides [42] can be used for reducing the thermal drift. 4.5. Three-Parameter Sensor Based on 6×6 MMI and Resonator Structure The proposed sensor based on 6×6 multimode interference and microring resonator structures is shown in Fig. 4.11 [9]. The two MMI couplers are identical. The two 6×6 MMI couplers have the same width WMMI and length L MMI . In this structure, there are three sensing windows having lengths L a1 , L a 2 , L a 3 . As with the conventional MZI sensor device, segments of four MZI arms having lengths L a1 , L a 2 , L a 3 overlap with the flow channel, forming three separate sensing regions. The other three MZI arms isolated from the analyte by the micro fluidic circuit’s substrate. If we choose the MMI coupler having a length of LMMI  3L , where L  is the beat 2  ; the MMI coupler is characterized by a transfer 1  2 matrix M. We can prove that the overall transfer matrix S of both the MMI coupler and combiner in Fig. 4.11 is expressed by length of the MMI coupler, L   114 Chapter 4. Multi-Parameter Integrated Optical Sensor Based on Multimode Interference and Microring Resonator Structures Fig. 4.11. Schematic of the new sensor using 6×6 MMI couplers and microring resonators. Four arms of the MZI is exposed to the analyte within the interaction regions  j e 4   0   1  0 S=  2 0    0  3 e j 4  0 e j 0  4 0 0 0 0 0  j e4 3 j e 4 j e 3 4 e j  4 0 e j 3 4 e j 3 4 0 0 0 0 0 0 3 j e 4 0 0  j e4 0 0 0 0 e j  4        .        (4.17) This matrix can be considered as consisting of four separate sub-matrices which describe four 2×2 3 dB MMI couplers, both having the transfer matrix  j 1 e 4 M2   2  j 3 4 e e j e 3 4 j  4    1 j 4 1 j  e  j 1 .  2     (4.18) Relations between the complex amplitudes a 1 , a 2 ,..., a 6 at the input ports and d1 , d 2 ,..., d 6 at the output ports can be expressed in terms of the transfer matrices of the 3 dB MMI couplers and the phase shifters as follows 115 Advances in Optics: Reviews. Book Series, Vol. 3 1 2  1  *  1 1   a1    , 1*   a 6  (4.19) 2 2  2  *  2  2  a 2    , *2   a 5  (4.20) 1 2  3  *  3 3   a 3    , *3   a 4  (4.21) j  d1   d   je  6 j d 2   d   je  5 j  d3   d   je  4     1  ), 1  cos( 1 ) ; 2  sin( 2 ), 2  cos( 2 ) ; 3  sin( 3 ), 3  cos( 3 ) ; 2 2 2 2 2 2 1 ,  2 ,  3 are the phase differences between two arms of the MZI, respectively. where 1  sin( One can prove that the normalized optical powers transmitted through the proposed sensor at wavelengths on resonance with the microring resonators are given by 2 T1  T2  T3  d1 a1 d2 a2 d3 a3 2 2 2  1   1  cos( 2 )   ,  1   1  1 cos( 2 )    (4.22) 2  2   2  cos( 2 )  2   1   2 cos( 2 )     ,     3   3  cos( 2 )  3   1   3 cos( 2 )     ,    (4.23) 2 (4.24) where 1 ,  2 , and  3 are round trip transmissions of light propagation through the four microring resonators [27] depending the losses of light propagation from output ports d 4, d5 , d 6 back to input ports a 4, a 5 , a 5 ; for a lossless resonator   1 . The proposed structure can be viewed as a sensor with four channel sensing windows, which are separated with four power transmission characteristics T1 , T2 , and T3 and four sensitivities S1 , S2 and S3 . This means that the proposed sensor is able to monitor four target chemicals simultaneously. Their sensitivities can be expressed by: 116 Chapter 4. Multi-Parameter Integrated Optical Sensor Based on Multimode Interference and Microring Resonator Structures S1  T T1 T , S2  2 , S3  3 . n c n c n c (4.25) Fig. 4.12 compares the normalized transmission for the proposed sensor with 1  0.99 and 0.90 to that for the conventional MZI, as functions of the total relative phase  . Given that the sensitivity is linearly proportional to the slope of the power transfer characteristics. Fig. 4.12 shows that the proposed sensor should have a higher sensitivity to a change in the refractive index of the analyte than the conventional MZI, when biased for operation with the region of large slope near 1  0 . Fig. 4.12. Normalized optical transmissions as functions of total relative phase for the proposed sensor with 1  0.99 and 0.90 and conventional MZI sensor. It is now shown that the proposed sensor can be realized using silicon nanowire waveguides. The width of the MMI is WMMI  8.4 m and the core thickness is h co = 220 nm. The access waveguide is tapered to a width of 0.8 µm to improve device performance. It is assumed that the designs are for the transverse electric (TE) polarization at a central optical wavelength   1550 nm . The first 6×6 MMI coupler is now optimized by using the 3D BPM. Fig. 4.13 (a) shows the normalized output powers at the bar and cross ports at different MMI lengths for a signal presented at input port 1 of the MMI coupler. From this simulation result, the optimized length of MMI calculated to be L MMI  273.5 m . The field propagation through the 6×6 MMI coupler at this optimized length is plotted in Fig. 4.13 (b). The relation between the effective index n eff ,a and the ambient index or cladding index n analyte  n c is achieved by using the beam propagation method (BPM). From this 117 Advances in Optics: Reviews. Book Series, Vol. 3 relationship, we achieve the waveguide sensitivity factor n eff ,a n c . Fig. 4.14 shows the effective index change n eff ,a due to the ambient change for silicon nanowire waveguides having a width of 500 nm. We can see that effective index n eff ,a increases almost linearly in the change in the refractive index of ambient material, i.e., the waveguide sensitivity factor is almost a constant. (a) Normalized output powers vs MMI length. (b) Field propagation. Fig. 4.13. BPM simulation results: (a) Normalized output powers vs the length of the 6×6 MMI coupler, and (b) field propagation at the optimized MMI length. From the simulation results of Fig. 4.14, the sensitivities of the proposed sensor and the conventional MZI with the active region length of L a  100 m and L a  500 m are plotted in Fig. 4.15. The simulations obviously show that the sensitivity of the proposed sensor is much higher than the sensitivity of the conventional MZI sensor. 4.6. Four-Parameter Sensor Based on 8×8 MMI and Resonator Structure The proposed sensor based on 8×8 multimode interference and microring resonator structures is shown in Fig. 4.16 [43]. The two 8×8 MMI couplers have the same width WMMI and length L MMI . There are four sensing windows having lengths L a1 , L a 2 , L a 3 , L a 4 . As with the conventional MZI sensor device, segments of four MZI arms having lengths L a1 , L a 2 , L a 3 , L a 4 overlap with the flow channel, forming four separate sensing regions. As a result, this structure can be used to detect four chemical or analyates at the same time. If we choose the MMI coupler having a length of L 2  3L  / 4 , the overall transfer matrix S of both the MMI coupler and combiner of length L MMI  3L  / 2 is expressed by [43] 118 Chapter 4. Multi-Parameter Integrated Optical Sensor Based on Multimode Interference and Microring Resonator Structures (a) (b) (c) Fig. 4.14. (a) The change of the effective index as the increase of refractive index of the analyte for silicon nanowire waveguides; (b) optical field profile for n analyte  1.33 and (c) optical field profile for n analyte  1.34 . Fig. 4.15. Sensitivity of the proposed sensor for sensing window S1 and the conventional MZI sensor versus the round trip loss of the first microring resonator. 119 Advances in Optics: Reviews. Book Series, Vol. 3 Fig. 4.16. Schematic of the new sensor using 8×8 MMI couplers and microring resonators.  j e 4   0    0   1  0 S= 2  0   0    0  3  j4 e 0 e j  4 0 3 4 0 0 0 0 0 0 0 0 0 e j 3 4 e j 0 0  j e4 0 0  j e4 0 0  j e4 3 j e 4 0 0 0 0 0 e 0 0 0 0 3 j e 4  j e4 0 0 0 0 j 3 4 0 e j  4 0 3 j e 4 0 0 0 0  j e4 0 0 0 0 0 0 e j  4          .           (4.26) The 3D-BPM simulations for optimised designs of 8×8 MMI structures based on an SOI channel waveguide having a width of WMMI  9 m are shown in Fig. 4.17. The optimised length calculated to be L MMI  382 m . It is note that the complete device is also equivalent to four separate 2×2 MMI-based microresonators. Each microresonator may have different transmission characteristics such as different quality factor (Q), different free spectral range (FSR) and different bandwidth. The 3D-BPM simulations show that the device performs the functions as predicted by the theory. However, when the signal is applied to input port 1, then 3D-BPM simulations show that at the optimised length of L MMI  382 m , the computed excess loss is 1.08 dB and the imbalance is 0.11 dB. The normalized output powers at the bar and cross ports at different MMI lengths for a signal at input port 1 are shown in Fig. 4.18. 120 Chapter 4. Multi-Parameter Integrated Optical Sensor Based on Multimode Interference and Microring Resonator Structures (a) (b) Fig. 4.17. 3D-BPM simulations of an 8×8 MMI structure used in a microresonator for two cases (a) the signal entered at input port 1, and (b) signal entered at input port 2. Fig. 4.18. Normalized output powers at the bar and cross ports as functions of the MMI length for the signal at input port 1. The complex amplitudes at the output ports of the sensor structure in Fig. 4.16 can be expressed by    j  1 1   a1   c1  1 j 4 1 j e j 0  1 j 4 1 j  a1  2 e e je   (4.27)  *  c  ,  j 1   j 1 a  * 2    0 1 2   8  8  1 1  a 8  1 1  c2  1 j 4 1 j e j e  c   j 1  2   0  7 2  j 1 j j  a 2  4 e   j 1 a   je 1 2   7 0 1 2 2  2  *  2  2  a 2    , *2  a 7  (4.28) 121 Advances in Optics: Reviews. Book Series, Vol. 3   c3  1 j 4 1 j e j e  c   j 1  2   0  6   j 1 j 1  3 j  a 3  4 2 e je   *   j 1 a  1 2   6  3  c4  1 j 4 1 j e j e  c   j 1  2   0  5  j 1 j j  a 4  4 e   j 1  a   je 1 2   5 3 0 1 0 1 4 2 2  4  *  4 3   a 3    , *3  a 6   4  a 4    , *4   a 5  (4.29) (4.30) where a  [a1 a 2 a 3 a 4 a 5 a 6 a 7 a 8 ]T is the input field and c  [c1 c 2 c3 c 4 c5 c 6 c 7 c8 ]T 1    ), 1  cos( 1 ); 2  sin( 2 ), 2  cos( 2 ); 2 2 2 2 3 3 4 4 3  sin( ), 3  cos( ) ; 4  sin( ), 4  cos( ) . 1 ,  2 , 3 and  4 are the 2 2 2 2 is the output field and 1  sin( phase differences between two arms of the MZI, respectively. The normalized optical powers transmitted through the proposed sensor at wavelengths on resonance with the microring resonators are given by T1  c1 a1 c T2  2 a2 c T3  3 a3 T4  c4 a4 2 2 2 2 2  1  1  cos( 2 )  1   1  1 cos( 2 )     ,     2   2  cos( 2 )  2   1   2 cos( 2 )     ,     3   3  cos( 2 )  3  1   3 cos( 2 )     ,     4   4  cos( 2 )  4   1   4 cos( 2 )     ,    (4.31) 2 (4.32) 2 (4.33) 2 (4.34) where 1 ,  2 ,  3 , and  4 are round trip transmissions of light propagation through the four microring resonators [27] depending the losses of light propagation from output ports c5, c6 , c7 , c8 back to input ports a 5, a 6 , a 7 , a 8 ; for a lossless resonator   1 . The proposed structure can be viewed as a sensor with four channel sensing windows, which 122 Chapter 4. Multi-Parameter Integrated Optical Sensor Based on Multimode Interference and Microring Resonator Structures are separated with four power transmission characteristics T1 , T2 , T3 , T4 and four sensitivities S1 , S2 , S3 , S4 . This means that the proposed sensor is able to monitor four target chemicals simultaneously. Their sensitivities can be expressed by: S1  T T1 T T , S2  2 , S3  3 , S4  4 . n c n c n c n c (4.35) Fig. 4.19 compares the normalized transmission for the proposed sensor with 1  0.99, 0.98, 0.97 and 0.90 to that for the conventional MZI, as functions of the total relative phase  . Given that the sensitivity is linearly proportional to the slope of the power transfer characteristics. Fig. 4.3 shows that the proposed sensor should have a higher sensitivity to a change in the refractive index of the analyte than the conventional MZI, when biased for operation with the region of large slope near 1  0 . Fig. 4.19. Normalized optical transmissions as functions of total relative phase for the proposed sensor with 1  0.99, 0.98, 0.97 and 0.90 and conventional MZI sensor. Fig. 4.20 shows the effective index change n eff ,a due to the ambient change for silicon nanowire waveguides having a width of 500 nm. From this simulation, one can see that the effective index n eff ,a increases almost linearly in the change in the refractive index of ambient material, i.e., the waveguide sensitivity factor is almost a constant. From the simulation results of Fig. 4.20, the sensitivities of the proposed sensor and the conventional MZI with the active region length of La  50 m , La  100 m and La  500 m are plotted in Fig. 4.21. The simulations obviously show that the sensitivity of the proposed sensor is much higher than the sensitivity of the conventional MZI sensor. 123 n eff ,a Advances in Optics: Reviews. Book Series, Vol. 3 n analyte (a) (b) (c) Fig. 4.20. (a) The change of the effective index as the increase of refractive index of the analyte for silicon nanowire waveguides, (b) optical field profile for n analyte  1.33 and (c) optical field profile for n analyte  1.335 . Fig. 4.21. Sensitivity of the proposed sensor for sensing window S1 and the conventional MZI sensor versus the round trip transmissivity of the first microring resonator. 124 Chapter 4. Multi-Parameter Integrated Optical Sensor Based on Multimode Interference and Microring Resonator Structures 4.7. Conclusions We have presented novel sensor structures based on the integration of 4×4, 6×6 and 8×8 multimode interference structure and microring resonators. The proposed sensor structures can detect two, three and four chemical or biological elements simultaneously. Our sensor structure can be realized on silicon photonics that has advantages of compatibility with CMOS fabrication technology and compactness. 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Li, Ethanol sensor based on microring resonator, Advanced Materials Research, Vol. 655-657, 2013, pp. 669-672. [36]. S. Manipatruni, R. K. Dokania, B. Schmidt, et al., Wide temperature range operation of micrometer-scale silicon electro-optic modulators, Optics Letters, Vol. 33, 2008, pp. 2185-2187. 126 Chapter 4. Multi-Parameter Integrated Optical Sensor Based on Multimode Interference and Microring Resonator Structures [37]. M. Han, A. Wang, Temperature compensation of optical microresonators using a surface layer with negative thermo-optic coefficient, Optics Letters, Vol. 32, 2007, pp. 1800-1802. [38]. K. B. Gylfason, A. M. Romero, H. Sohlström, Reducing the temperature sensitivity of SOI waveguide-based biosensors, Proceedings of SPIE, Vol. 8431, 2012, pp. 84310F (1-15). [39]. C.-T. Wang, C.-Y. Wang, J.-H. Yu, et al., Highly sensitive optical temperature sensor based on a SiN micro-ring resonator with liquid crystal cladding, Optics Express, Vol. 24, 2016, pp. 1002-1007. [40]. F. Qiu, F. Yu, A. M. Spring, et al., Athermal silicon nitride ring resonator by photobleaching of Disperse Red 1-doped poly (methyl methacrylate) polymer, Optics Letters, Vol. 37, 2012, pp. 4086-4088. [41]. B. Guha, B. B. C. Kyotoku, M. Lipson, CMOS-compatible athermal silicon microring resonators, Optics Express, Vol. 18, 2010, pp. 3487-3493. [42]. S. T. Fard, V. Donzella, S. A. Schmidt, et al., Performance of ultra-thin SOI-based resonators for sensing applications, Optics Express, Vol. 22, 2014, pp. 14166-14179. [43]. T.-T. Le, The design of microresonators based on multimode interference couplers on an SOI platform, in Proceedings of the 3rd International Conference on Communications and Electronics (ICCE’10), Nha Trang, Vietnam, 11-13 August, 2010. 127 Chapter 5. Coherent Gradient Sensor for Curvature Measurement in Extreme Environments Chapter 5 Coherent Gradient Sensor for Curvature Measurement in Extreme Environments Cong Liu, Xingyi Zhang and Youhe Zhou1 5.1. Introduction Due to the merits of the real-time, full-field, non-contact and non-intrusive, the coherent gradient sensor (CGS), as a lateral shearing interferometry, has a wide application in measurements of gradients [1] and curvatures [2-5], especially in the deformation state of field of crack tip [6-8] at room temperature or thin solid film-substrate structure in high temperature with an ignored air refraction [9]. On the contrary, with decrease of the environment temperature, the influences of air refraction cannot be ignored, so the investigation on the CGS at cryogenic temperature [10] is necessary and important for its practical applications [11, 12]. In the first section of this chapter, we will briefly introduce the measurement theory of the CGS method. And in the second section, the error factor dependent on air refraction at low temperature is discussed, as well as the effects of transparent interface reflection and refraction on the interferogram. Some thin filmstructures always work in the multi-media, thus in the third section, we present the study of the effect of refraction of multi-layer media and we suggest a modification factor to eliminate the difference between the experimental measurement and the actual value. Subsequently, the modification factor is verified through gradients and curvatures measurements of specimen immerged into water and silicone oil, respectively. Finally, to process the sparse fringes [13], often encountered in measurements of small gradients or curvatures, an arbitrary integral-multiple fringe multiplication method is proposed and testified by optical-elastic experimental results, this is accounted in the fourth last section of this chapter. Cong Liu Department of Mechanics and Engineering Sciences, College of Civil Engineering and Mechanics, Key Laboratory of Mechanics on Disaster and Environment in Western China attached to the Ministry of Education of China, Lanzhou University, Lanzhou, Gansu, PR China 129 Advances in Optics: Reviews. Book Series, Vol. 3 5.2. The CGS System Fig. 5.1 displays the schematic of the CGS system. The surface of film is illuminated by collimated laser beam through the reflection of beam splitter (Fig. 5.1(a)). The reflective plane wave which includes information of deformation state of film is passed into the CGS system (Fig. 5.1(b)). The surface can be expressed as a function of (x, y). z  f ( x, y ) or F ( x, y, z )  z  f ( x, y )  0 . (5.1) Fig. 5.1. Schematic of the CGS. The normal vector of the reflective surface is equal to the following equation: N F  f x ex  f y e y  e z  . F 1  fx2  f y2 The reflective plane wave propagation vector of wave plane d can be described: 130 (5.2) Chapter 5. Coherent Gradient Sensor for Curvature Measurement in Extreme Environments d  (2e z  N ) N  e z   e x   e y   e z  where:   2(  f x e x  f y e y  e z ) 1  fx2  f y2  ez , (5.3) 1  f x2  f y2 2 f y 2 f x   , , .  1  f x2  f y2 1  f x2  f y2 1  f x2  f y2 The propagation vector of wave plane d becomes d 1 , d0 , and d 1 after diffraction from grating G1. At this situation, d0  d , d1  1d0 , (5.4) where  1 is the rotation tensor whose components are given by: 0 1  1   0 cos 0  sin  0   sin   . cos  (5.5) Form the equation (5.3) to (5.5), one can gain: d1  [ e x  ( cos   sin  )e y  ( cos   sin  )e z ] , (5.6) OA  d1  e z  OA ( cos   sin  )   , (5.7) OB  d0  e z  OB    , (5.8) OC  d1  e z  OC ( cos   sin  )   . (5.9) At the front the second grating G2, the wave equation is displayed as following: E1  a1 exp[i ( kd1  OA  kd1  x)]  a1 exp[i ( k (  )  kd1  x)] ,  cos   sin  E0  a0 exp[i (kd 0  OB  kd 0  x)]  a0 exp[i (k E1  a1 exp[i ( kd 1  OC  kd 1  x)]  a1 exp[i ( k    kd 0  x)] ,   cos    sin   kd 1  x)] . (5.10) (5.11) (5.12) Then the second diffraction happens after passing through the grating G2. The light becomes E(1,1) , E(1,0) , E(1,1) , E(0,1) , E(0,0) , E(0,1) , E( 1,1) , E( 1,0) , and E( 1,1) (Fig. 5.1(b)). The propagation vectors of E(1,0) and E(0,1) are equal to d1 . These E(1,1) , E(0,0) and 131 Advances in Optics: Reviews. Book Series, Vol. 3 E( 1,1) are equal to d0 , and these E(0,1) and E(1,0) are d 1 . E(1,0) , E(0,1) and E(1,1) , E(0,0) , E( 1,1) and E(0,1) , E(1,0) can make interference fringes respectively. However, only interferometric fringes of E(1,0) , E(0,1) and E(0,1) , E( 1,0) which are considered. Then we can separate these situations into A and B: A. Interference fringes made by E(1,0) and E(0,1) E(1,0)  a1 exp[i ( kd1  OA  kd1  x)]  a1 exp[i ( k (   cos    sin  )  kd1  x)] ,  E(0,1)  a0 exp[i (kd 0  OB  kd1  x)]  a0 exp[i ( k ( )  kd1  x)] . (5.13) (5.14)  The intensity function in image plane is I1 , I 2 , respectively. I1    E(1,0) 2  , I 2    E(0,1) 2  . (5.15) The intensity of E(1,0) , E(0,1) together is shown as the following equation: 2 2 I  I 1  I 2  I 12   [ a1 2  a0 2  a1 a 2 cos( kd 1  x  kd 1  x  k   k  cos    sin  )] , (5.16) which can be written as: I  I c   a1a2  cos{k [  (cos   1)   sin  ]} ,  ( cos    sin  ) (5.17) a12  a22 . Considering the small  , we can use approximation   sin  . 2 The above equation becomes: where I c   I  I c   a1a2 cos( k  2 ). (5.18) Then the fringe distribution is gained while: k  2  2n , n  0, 1, 2, ... B. Interference fringes made by E( 1,0) and E(0,1) : 132 (5.19) Chapter 5. Coherent Gradient Sensor for Curvature Measurement in Extreme Environments E(0,1)  a0 exp[i (kd 0  OB  kd 1  x)]  a0 exp[i ( k E( 1,0)  a1 exp[i ( kd 1  OC  kd 1  x)]  a1 exp[i ( k    kd 1  x)] ,   cos    sin  (5.20)  kd 1  x)] , (5.21) also one can get: 2 2 I  I 1  I 2  I 12   [ a1 2  a0 2  a1 a 2 cos( kd 1  x  kd 1  x  k   k  cos    sin  )] , (5.22) which can be written as I  I c   a1a2  cos{k [  (cos   1)   sin  ]} ,  ( cos    sin  ) (5.23) a12  a22 . Same as case A, we gain the equation (5.18) once again. Then we 2 prove the equivalence of these two situations. where I c   Substituting  ,  ,  of the Eq. (5.3) into the Eq. (5.19) and considering that 2  k , p  , one can get:   2 (1   f ) 2 np , n  0, 1, 2,...... . fy  [ ] 2 2 1  f (5.24) When the principal direction is oriented coinciding with the x-axis, one can gain: 2 fx  [ (1   f ) 2 mp , m  0, 1, 2,...... . ] 2 2 1  f (5.25) The curvatures of film can be expressed as k xx  k yy  k xy  f xx 2 x 1 f  f 2 y f yy 2 x 1 f  f 2 y f xy 2 x 1 f  f 2 y    f xx 1  f 2 f yy 1  f 2 f xy 1  f 2 , (5.26) , (5.27) . (5.28) 133 Advances in Optics: Reviews. Book Series, Vol. 3 2 Assuming f  1 , substituting Eq. (5.24) and (5.25) into (5.26)-(5.28), the relationships between fringes and curvatures can be showed as followings: kxx  k xx   2 f ( x, y ) p n ( x )  ( ), x 2 2 x (5.29) kyy  2 f (x, y) p n( y) ),  ( 2 y y2 (5.30) p n( y ) 2 f ( x, y) p n( x) ) ( ).  ( 2 y 2 x xy (5.31) 5.3. Curvature Measurements in Cryogenic Medium 5.3.1. Governing Equations When measurement of the curvature of film-substrate structure is operated at low temperature, the variation of refractive index caused by temperature change should be considered. Fig. 5.2 displays the interface refraction at different temperature. Generally, the relationship between the refractive index and temperature can be displayed as: n1 (T )  1  n0  1 , 1  T where  is the constant of 0.00367C 1 . Fig. 5.2. Schematic of the refraction in the interface with different temperature. The propagation vector of the light from the film's surface becomes 134 (5.32) Chapter 5. Coherent Gradient Sensor for Curvature Measurement in Extreme Environments d '  (2ez  N)N  ez  2( f xex  f ye y  ez ) 1  f x2  f y2  ez . (5.33) The propagation vector changes after the light passing though the interface between the air at room temperature (the refractive index is equal to n 2 ) and low temperature (the refractive index is equal to n1). According to the refraction law, one can get: n1  sin 1  n2  sin  2 . (5.34) The incidence vector and refraction vector are coplanar and related by: n1 n d ' (cos  2  1 cos 1 )e z , n2 n2 d where cos 1  d ' e z  1  f 2 1  f 2 sin 1  1  cos12  (5.35) , (5.36) 2 f 1  f 2 . (5.37) From Eq. (5.34) one can gain: sin  2  n1 2 f  n2 1  f 2 , (5.38) 2 cos2  1  sin 2  2 n22 (1  f )2  n12  4 f 2 n2 (1  f ) 2 . (5.39) Substituting Eq. (5.33), Eq. (5.36) and Eq. (5.39) into Eq. (5.35): d   ex   ey   ez  n1 n2 2 d ' ( n 22 (1   f ) 2  n12  4  f 2 n 2 (1   f ) 2  n1 1   f  n2 1   f 2 2 2 )e z , 2 f, y n22 (1  f )2  n12  4 f n1 n1         , , where 2 1  f, x2  f, 2y n2 1  f, x2  f, y2 n2 n2 (1  f ) 2 f, x (5.40) 2 Then substitute  ,  ,  into Eq. (5.19), one can obtain a new description between gradients and fringes: 135 Advances in Optics: Reviews. Book Series, Vol. 3 fy  fx  2 2 2 2 2 2 2 np n2 (1   f )  4 n1  f  2 2 n1 n2 (1   f ) 2 2 2 mp n2 (1  f )  4n1 f  2 2 n1n2 (1  f ) , n  0, 1, 2,... , (5.41) , m  0, 1, 2,... . (5.42) Same as above, we substitute Eq. (5.41) and (5.42) into Eqs. (5.26)-(5.28) with assumption 2 f  1 , the new relationship between fringes and curvatures can be given as k xy  k xx  n2 p n( x ) ( ) , n  0, 1, 2,... ,  n1 2 x (5.43) k yy  n2 p n ( y )  ( ) , n  0, 1, 2,... , n1 2 y (5.44) n2 p n ( y ) n p n ( x ) ( ) 2  ( ) , n  0, 1, 2,... .  n1 2 x n1 2 y (5.45) 5.3.2. Error Analysis 2 Define   max( f ) in the whole plane, then substitute Eq. (5.41) and (5.42) into Eqs. (5.26)-(5.28), one can see: k xx  n22 (1   )2  4n12  p n( x ) ( ), 2 x (5.46)  p n( y ) ( ), 2 y (5.47) n2 (1   )2  4n12 p n( y ) p n( x )  ( ) 2 ( ). 3 2 y 2 x 2 n1n2 (1   ) (5.48) n1n2 (1   ) k yy  n22 (1   )2  4n12 n1n2 (1   ) k xy  n22 (1   )2  4n12 n1n2 (1   ) 3 2 3 2  A Taylor expansion is made on the factor 3 2 n22 (1   )2  4n12 2 n1n2 (1   ) n22 (1   )2  4n12 2 n1n2 (1   ) 136 3 2  3 2 , n2 n22  8n12     ( 2 ) . n1 2n1n2 (5.49) Chapter 5. Coherent Gradient Sensor for Curvature Measurement in Extreme Environments The systemic absolute error limits are described as: ekxx  k xx  k xx  8n12  n22 p n( x ) ( ),   2n1n2 2 x (5.50) ekyy  k yy  k yy  8n12  n22 p n ( y ) ( ),   2n1n2 2 y (5.51) 8n12  n22 8n 2  n22 p n( x ) p n ( y ) ( ) 1 ( ),     2n1n2 2 y 2n1n2 2 x (5.52) ekxy  k xy  k xy  and systemic relative error limit is described by: er*kxx  er*kyy  er*kxy  k xx  k xx k xx  k yy  k yy k xx  k xy  k xy k xx  (4 n12 1  ) . n22 2 (5.53) According to the Eq. (5.53), one can see that if the CGS is used in the same medium, that 7 is to say n1  n2 , the Eq. (5.53) is equal to  . The change of the relative error limit 2 2 2 factor 4n1 n2  1 2 with temperature is displayed in Fig. 5.3. One can see that with the decrease of the ambient temperature, the systematic relative error limit increases with a negative exponential law. In addition, based on the Eqs. (5.43)-(5.45), the curvature of the film, which includes the modifying factor n2 n1 , there are valuable for the two mediums measurements even temperature is not change. 3.508 3.507 3.506 Error Factor 3.505 3.504 3.503 3.502 3.501 3.500 3.499 3.498 50 100 150 200 250 300 350 400 450 500 Temperature (K) Fig. 5.3. The relationship between the temperature and the relative error limit factor. In this figure, the horizontal ordinate is temperature, and the vertical ordinate is equal to the factor 4n1 n2  1 2 , 2 2 where n2 is the constant and equal to the refractive index at 300K of the light, n1 varies with temperature change. 137 Advances in Optics: Reviews. Book Series, Vol. 3 5.3.3. Curvature Measurement in Cryogenic Vacuum Chamber In practice, CGS needs to be utilized in a vacuum chamber with temperature variation as showed in Fig. 5.4. Here we take emphasis on the technique how to eliminate the influences of interface on the interferogram. At first, in order to eliminate the disturbance of the reflected beam from the upper surface of the transparent window, a tilt of the transparent window will be conducted, which is illustrated in Fig. 5.5. Fig. 5.4. (a) Schematic of the CGS for cryogenic temperature; (b) photo of the measurement system, in which the number 1 denotes the closed cycle refrigerator (G-M). Fig. 5.5. (a) schematic of the lean of transparent windows,  is the angle between the window and the horizontal plane, l denotes the width of the beam splitter, and h is the distance between the project plane of the transparent window and the bottom surface of the beam splitter, and while the thickness of quartz window is neglected; (b) Schematic of the effects of the quartz window on the interferogram, the dotted lines denote the normal of the window’s surface. In Fig. 5.5 (a), one can see that in order to avoid the reflected light of the transparent window into the CGS system, the angle  between the project plane of the transparent 1  tan 2  h window and the bottom surface of the beam splitter should be satisfied by  . 2 tan  l 138 Chapter 5. Coherent Gradient Sensor for Curvature Measurement in Extreme Environments One can get that the two roots as tan  h h2  2  1 , respectively. Considering the small l l  and h  l , we can obtain that tan  is equal to approximation   tan , thus,  is equal to h h2  2  1 , we can use l l h h2  2  1 approximately. According to l l the law of refraction, one can easily see that there is no effect of the quartz window on the light propagation vector, which has effect on the location of the interferogram only. Thus, the change of the incidence vector will be decided by the air (its refractive index is equal to n 2 ) and the vacuum (the refractive index is equal to n1 ). Based on our previous derivation, the propagation vector of the light from the window's surface is satisfied by n1  n2 , we can obtain d  d' without any modification. 5.4. Curvature Measurements in Multiple Media 5.4.1. Refraction Analysis Taking account of multilayer mediums condition as shown in Fig. 5.6 (a), CGS system is developed to measure the gradient or curvature of a sample in multilayer of mediums. We can derive the equivalent situation by the refraction law:   sinsin sin  m sin  2 sin  3    sin  1 sin  1 sin  2 m m 1  n1 , ( m  2) . nm (5.54) Fig. 5.6. (a) Schematic of the effects of the multilayer medium on the reflection, N denotes the normal line of the specimen surface; (b) the situation which is equal to (a). 139 Advances in Optics: Reviews. Book Series, Vol. 3 It is noted that only the first and last layer of medium have effects on refraction of the light reflecting from the sample surface. Thus we can simplify this situation into just two types of mediums as shown in Fig. 5.6 (b). Without loss generality, The CGS for two types of mediums measurement is illustrated in Fig. 5.7 (a). A collimated laser beam passes through a beam splitter (medium 2) and then directly arrives at the reflecting specimen surface (medium 1). The reflected beam from the specimen is further reflected by the beam splitter and then passes through two Ronchi gratings, G1 and G2 with the same density (50 lines/mm) separated by a distance  . The diffracted beams from the two gratings are converged to interfere using a lens. Either of the ±1 diffraction orders is filtered by the filtering aperture to obtain the interferogram recorded by a CCD camera. Fig. 5.7 (b) is displayed schematic of the refraction, for medium 1, its refractive index is equal to n1 , and for the medium 2, the refractive index equals to n2 . In this scenario, the modified gradients and curvatures can be acquired as same as Eqs. (5.41)-(5.45). Fig. 5.7. (a) Schematic of the CGS system for two types of medium; (b). Schematic of the effects of the different mediums on the interferogram, for the medium 1, refractive index is equal to n1 , and for medium 2, the refractive index is n2 . N denotes the normal line of the specimen surface. 5.4.2. Experiment Verification In order to verify the modified factor experimentally, a standard spherical mirror with diameter of 16 mm and radius of curvature of 8 m is used in the experiments. The CGS system is located in the air (medium 2) and the spherical mirror is immerged into the liquid (medium 1). In this work, the liquid is selected by water and silicone oil. The refractive indexes of the air, water and silicone oil are 1, 1.3 and 1.4, respectively. 140 Chapter 5. Coherent Gradient Sensor for Curvature Measurement in Extreme Environments For the spherical 2 2 mirror, the function of surface can be expressed as 2 f ( x, y )  R  x  y , the gradient (x component) of center line (along x direction) has a theoretical solution as following: f x ( x, y ) y 0  x y 0 64  x 2  y 2 , （ 0.008  x  0.008 ）. (5.55) 2 According to the CGS system (single medium) and with the assumption f  1 , the gradient (x component) of center line of the spherical mirror can be obtained by: f x ( x, y ) y 0  p  ( x, y) 4 y 0 , (5.56) where   x, y  denotes the phase angle, and based on the above theoretical analysis, when the spherical mirror is immerged into the liquid whose refractive index is not equal to that of the air, its gradient (x component) should be expressed as: n1  f x ( x, y ) n2 y 0  p  ( x, y ) 4 y 0 , (5.57) where n1 , n2 denote the refractive indexes of the liquid and air, respectively. The distances  between the two Ronchi gratings G1 and G2 in the CGS system are selected by 25, 30, 35, and 40 mm, respectively. When  is equal to 25 mm, the red fringes in Figs. 5.8 (a), 5.8 (b) and 5.8 (c) represent the contour curves of the specimen surface slope in x direction within three different mediums. Fig. 5.8 (a) is obtained when the specimen is placed in the air, and Figs. 5.8 (b) and 5.8 (c) are obtained when the specimen is immerged into water and silicone oil, while the CGS system is located in the air. The wrapped phase map is calculated by FFT method and shown in Figs. 5.8 (d), 5.8 (e) and 5.8 (f). The theoretical deformation gradients (left part of Eq. (5.57)) and experimental measurements (right part of Eq. (5.57)) are displayed in Fig. 5.9. One can see that the experimental results in three conditions have a favorable comparison with the theoretical analysis except points located at the vicinity of the specimen edge. According to these results, we come to a conclusion that the experimental results gain good agreement with the gradient enlarged by the factor n1 n2 . For this reason, we need to add a modified factor n2 n1 if we want to get the real gradient of the surface. Now, we will verify the modification factor of curvatures by the same experiments. Table 5.1 show the experimental curvatures when the standard spherical mirror is immerged into the air, water and silicone oil. For the spherical mirror used in this paper, the curvature of  xx is equal to 0.125 m-1. One can see that the modified curvatures have little difference comparing with the standard value when the spherical mirror is immerged into water and silicone oil. 141 Advances in Optics: Reviews. Book Series, Vol. 3 Fig. 5.8. Interferogram fringes in x direction and their wrapped phase maps: (a) obtained in the air, (b) obtained in the water, (c) obtained in the silicone oil; (d) wrapped phase map for (a), (e) wrapped phase map for (b), (f) wrapped phase map for (c). Fig. 5.9. Comparison of the experimental results with different  and theoretical calculations of the deformation gradients of the center line (x direction) for the standard spherical mirror. (a) Experiment is carried out in the air; (b) Experiment is carried out in the water, (c) Experiment is carried out in the silicone oil. 142 Chapter 5. Coherent Gradient Sensor for Curvature Measurement in Extreme Environments Table 5.1. List of the experimental results and their modification by n2 n1 in different mediums. Grating space ( ) Experimental curvature (in air) Experimental curvature (in water) Corrected curvature (in water) 25 mm 30 mm 35 mm 40 mm 0.1245 m-1 0.1228 m-1 0.1263 m-1 0.1221 m-1 0.1600 m-1 0.1623 m-1 0.1633 m-1 0.1609 m-1 0.1231 m-1 0.1248 m-1 0.1257 m-1 0.1238 m-1 Experimental Curvature (in silicone oil) 0.1776 m-1 0.1772 m-1 0.1794 m-1 0.1786 m-1 Corrected curvature (in silicone oil) 0.1269 m-1 0.1265 m-1 0.1281 m-1 0.1275 m-1 If the CGS system is applied in single medium, wave length of the incident laser has no effect on the curvature measurements. However, the wave length has effect on the refractive index, which can be expressed as: na b  2  c 4 , (5.58) where n,  denote the refractive index and wave length, respectively, a, b and c are the constant related to medium as in the water condition (a = 1.32, b = 3300, c = 3.2e7). Submitting Eq. (5.58) into the Eq. (5.53), one can obtain the influences of the wave length on the factor of system error. One can see that with decrease of the wave length, the system error factor increases as showed in Fig. 5.10. That is to say, when the CGS system is used in two types of mediums even multilayer of mediums, the lager the wave length of incident laser, the weaker is the system error. 6.75 Error factor 6.70 6.65 6.60 6.55 390 420 450 480 510 540 570 600 630 660 690 720 750 Wave length(nm) Fig. 5.10. The relationship between the wave length and the relative error limit factor. In this figure, the horizontal ordinate is wave length, and the vertical ordinate is equal to the factor 4n12 n22  1 2 , where n2 is refractive index of the air, n1 varies with wave length. 143 Advances in Optics: Reviews. Book Series, Vol. 3 5.5. The Multiplication Method for Sparse Interferometric Fringes For an optical ideal interferometric fringe such as CGS fringe, the form is I (r )  A[1  cos( (r ))] , (5.59) where I (r ), r,  (r ) and A denotes the light intensity of the fringe pattern, coordinate vector, phase and amplitude of the fringe variation, respectively. The phase  (r ) contains the desired information, e. g. strain, stress or deformation gradient. The light intensity of the N-fold order multiplied fringe can be expressed as: I N (r )  A[1  cos(N (r ))] , (5.60) where N (r) is the phase distribution of the multiplied pattern. The phase  (r ) before multiplication and N (r) after multiplication can be considered as two parameters in the algorithm, where the relationship between them gives: N (r)  N   (r)  N  arccos( I (r )  1) . A (5.61) This equation constructs a direct correlation between the Eq. (5.59) and Eq. (5.60). Substituting Eq. (5.61) into Eq. (5.60), one finds: I N (r)  A[1  cos( N  arccos( I (r)  1))] . A (5.62) For the non-ideal fringe pattern, the intensity of which can be expressed as I (r )  I1 (r ) 1  cos  (r )   I b (r )  I random , (5.63) where I (r ) is the intensity of the recorded image, Ib (r) is the intensity of background, I1 (r ) is the amplitude of the fringe variation, and I random is the random noise caused by light source and /or digital recording system. According to the description in the second paragraph, the random item can be reduced by using the filter technique, thus the Eq. (5.63) becomes I (r )  I1 (r ) 1  cos  (r )   I b (r ) . (5.64) When the fringe pattern is normalized, the Eq. (5.64) can be rewritten by I (r )  I1  1  cos  (r )   , 144 (5.65) Chapter 5. Coherent Gradient Sensor for Curvature Measurement in Extreme Environments where I1 denotes the constant amplitude that independent from the point position. The form of the Eq. (5.65) is consistent with the Eq. (5.59), thus our method can also be applicable for the no-ideal fringe pattern. Phase determination by Fourier-transform method is an effective way to obtain the phase information in the whole field. This method is applicable for the multiplied fringe pattern, the Fourier transform of the Eq. (5.59) can be written: I (r)  C0  C(r)  C (r) , (5.66) where C0 is the Fourier transform of the constant I1 , C (r) is the Fourier transform of 1 j (r )  I1e and C (r) is the conjugate of C (r) . So we can filter out the DC term C0 and 2  either the components C (r) or C (r) in frequency domain, if we leave the term C (r) , then we can get the wrapped phase with values between  and  :  (r )  arctan Im C (r )  Re C (r )  . (5.67) After that, phase unwrapping can be proceeds iteratively in x and y-direction: n( x1 , y1 )  0 n( x1 , yi 1 ) if  ( x1 , yi )   ( x1 , yi 1 )    n( x1 , yi )  n( x1 , yi 1 )  1 if ( x1 , yi )   ( x1 , yi 1 )   n( x , y )  1 if ( x , y )   ( x , y )   1 i 1 i 1  1 i 1 i  2,3,...,  n( x j 1 , yi ) if  ( x j , yi )   ( x j 1 , yi )    n( x j , yi )   n( x j 1 , yi )  1 if ( x j , yi )   ( x j 1 , yi )     n( x j 1 , yi )  1 if ( x j , yi )   ( x j 1 , yi )   j  2,3,..., (5.68) unwrep ( x j , yi )   ( x j , yi )  2 n( x j , yi ), i,j=1,2,... . Figs. 5.12(a) and 5.12(b) display the frequency domain of the images obtained by the Fourier transform for the original and processed images as showed in Figs. 5.11(a) and 5.11(b), respectively. The plots of amplitude of corresponding frequency along the centerline in the Figs. 5.12(a) and 5.12(b) are shown in Figs. 5.12(c) and 5.12(d), respectively. We can find that the main frequencies of the multiplied fringe image are separated from the DC component, which allow us to use band-pass filtering and phase unwrapping technique to obtain the phase values in the whole field. Fig. 5.13(a) shows the wrapped phase of the 7-fold multiplied fringe. Based on the relationship between the 145 Advances in Optics: Reviews. Book Series, Vol. 3  (r ) and N (r) in the Eq. (5.61), the distribution of the retrieved relative phase is demonstrated in Fig. 5.13 (b), where the reference phase point is located at the center of the image, and the corresponding phase can be set to zero. Fig. 5.13 (c) shows the information for phase error of the whole field, and also indicates that there is no more than 0.07 phase error besides the margin of the picture. Fig. 5.11. (a) The simulated digital image; (b) the 7-fold multiplied fringe pattern; (c) and (d) show the skeleton lines of the (a) and (b), respectively; (e) the intensity of centerline (seen the red line in (a) and 9 (b)). In summary, the presented method for ideal fringe multiplication has clear mathematics algorithm, which can not only provide a way to extract the skeleton lines, but also separate the main frequency form the DC component in the Fourier transform. Furthermore, the presented method has been realized experimentally. As illustrated in Fig. 5.14, the typical photoelasticity experiment has been arranged. In this study, the light source is replaced by a 17-inch LCD in order to provide nearly uniform illumination, and a photoelastic disk composed by the epoxy resin with diameter of 50 mm and thickness of 5.4 mm is used. When the normal loading of 68.6 N is applied, we obtained a sparse fringe pattern with zero and one order fringes. Fig. 5.15 shows our experimental result. 146 Chapter 5. Coherent Gradient Sensor for Curvature Measurement in Extreme Environments Fig. 5.12. (a) and (b) are the frequency domain of the original and the multiplied image respectively ( To increase the contrast, the displayed intensity I  ln 1  I F  is used, where I F is the amplitude of frequency, however, the intensity in center of (b) appears lower than the two neighboring lobes, this optical illusion is mainly caused by picture zooming out in the text and the displaying function I  ln 1  I F  we used. ); (c) and (d) are the frequency amplitude distribution along centerline of frequency map of the original and the multiplied image respectively. Fig. 5.13. (a) The wrapped phase of multiplied fringes pattern; (b) The unwrapped phase N N distribution of the simulated image; (c) The phase error distribution. 147 Advances in Optics: Reviews. Book Series, Vol. 3 Fig. 5.14. The arrangement of photoelasticity experiment. Fig. 5.15. The original photoelastic fringe obtained in this experiment. For this kind of sparse fringe pattern, the intensity of the recording fringe image can be expressed as I (r)  I1  1  cos( (r))  I b  I random . (5.69) We assume that I1 and I b in Eq. (5.69) are uniform (independent of the coordinate), and they are only affected by the response of the CCD camera. Moreover, we reduce the item of random noise by smooth filtering method. In order to normalize the fringe pattern, we removed two 1/4 wave plates and the specimen at the first, and rotated the analyzer with unvaried interval of 10 degree while recording the intensity of image, which can be written as I  I (r )  I1  1  cos(2   rot   )  I b , (5.70) where  rot denotes the rotation angle of analyzer. The intensity dependent on rotation angle is displayed by the black curve in Fig. 5.16 (a). According to the experimental curve, we can propose a theoretic equation with the constant background I b  I min and constant amplitude I1 =  I max -I min  2 , where I max and I min are on behalf of the maximum and minimum intensity of the recording image, respectively. Based on Eq. (5.70), results are shown as the red curve in Fig. 5.16(a). It is found that there are some or little differences between the experimental and theoretic results. For eliminating these differences, the 148 Chapter 5. Coherent Gradient Sensor for Curvature Measurement in Extreme Environments experimental intensity can be calibrated by using a polynomial fitting function with the maximum order of two. The comparison between the fitted results and the experimental results is displayed in Fig. 5.16 (b). One can see that the fitting polynomial function adequately capture the characteristics of the calibration results. Fig. 5.16. The process of calibration (a) the experimental intensity dependent on rotation degree of analyzer, (b) the fitting function of calibration. In order to obtain the multiplied image for the sparse photoelastic fringe, following steps have been applied. First, the fringe pattern should be calibrated by using the fitting polynomial function. Second, the background intensity I b can be subtracted directly. Third, the processed fringe pattern is multiplied by the method presented. The normalized fringe patterns without and with calibration are shown in Figs. 5.17(a) and 5.17(d), respectively. Figs. 5.17(b) and 5.17(c) show the 15-fold and 23-fold multiplication results of normalized fringe pattern without calibration while the Figs. 5.17(f) and 5.17(g) depict the 15-fold and 23-fold multiplication results of the one with calibration. As shown in the Figs. 5.17(b) and 5.17(c), the fringes are diseased at the left and right sides of the multiplication image, which can be understood as the contribution of the slow change in the illumination intensity. Moreover, other possible reasons for the diseased fringes after multiplication can be considered as that the fringes at the top and bottom of all the multiplication results are not normalized. The dependence of phase on the resultant difference between two principal stresses for the stress-optical law has the form as (1   2 )r   (r)  f , 2 h (5.71) where  (r ) denotes the real phase distribution of the fringe pattern, namely multiplied (r) N , f is the material fringe value (equals to 18.4 kN / m in this work), and h is the thickness of the photoelastic slice. Fig. 5.18 shows the calculated stresses of the 15fold and 23-fold multiplied fringes of the normalization results with and without calibration (along the white line in Figs. 5.17(b), 5.17(c), 5.17(e) and 5.17(f)). The blue line is on behalf of the theoretical results. We can see that the calculated results based on 149 Advances in Optics: Reviews. Book Series, Vol. 3 the multiplication fringes under calibration (dark cyan line and red line) have a good agreement with the analytical results except the margin of the sample. In comparison, the calculated results based on the multiplication fringes without calibration (orange line and dark yellow line) are much bigger than theoretical results, which can cause many errors of analysis. Fig. 5.17. The multiplication result of normalized fringe pattern with and without calibration, (a) the normalized fringe without calibration (only the area interested is shown with mask); (b) the 15-fold multiplication result of (a); (c) the 23-fold multiplication result of (a); (d) the normalized fringe with calibration; (e) the 15-fold multiplication result of (d); (f) the 23-fold multiplication result of (d). 6 1x10 Theory 15-MC 23-MC 15-MNC 23-MNC 5 8x10 5 Stress(Pa) 6x10 5 4x10 5 2x10 0 5 -2x10 -30 -25 -20 -15 -10 -5 0 5 x(mm) 10 15 20 25 30 Fig. 5.18. Comparison the stress distributions along the white line in the Figs. 5.17 (b), 5.17 (c), 5.17 (e) and 5.17 (f) with theory result, in the figure the curve 15-MC stands for 15-fold multiplication of calibrated normalization, 15-MNC stands for 15-fold multiplication of noncalibrated normalization, so do the 23-MC and 23-MNC. 150 Chapter 5. Coherent Gradient Sensor for Curvature Measurement in Extreme Environments Acknowledgements This work is supported by the Fund of Natural Science Foundation of China (No. 11622217 ， 11372121), Innovative Research Group of the National Natural Science Foundation of China (Grant No. 11421062), the National Key Project of Scientific Instrument and Equipment Development (11327802), National Program for Special Support of Top-Notch Young Professionals. This work is also supported by the Fundamental Research Funds for the Central Universities (lzujbky-2017-ot18, lzujbky2017-k18, lzujbky-2016-228) References [1]. H. V. Tippur, S. Krishnaswamy, A. J. Rosakis, A coherent gradient sensor for crack tip deformation measurements: analysis and experimental results, International Journal of Fracture, Vol. 48, 1991, pp. 193-204. [2]. A. Rosakis, R. Singh, Y. Tsuji, E. Kolawa, N. Moore, Full field measurements of curvature using coherent gradient sensing: application to thin film characterization, Thin Solid Films, Vol. 325, 1998, pp. 42-54. [3]. H. Lee, A. J. Rosakis, L. Freund, Full-field optical measurement of curvatures in ultra-thinfilm-substrate systems in the range of geometrically nonlinear deformations, Journal of Applied Physics, Vol. 89, 2001, pp. 6116-6129. [4]. M. A. Brown, T. -S. Park, A. Rosakis, E. Ustundag, Y. Huang, N. Tamura, B. Valek, A comparison of X-ray microdiffraction and coherent gradient sensing in measuring discontinuous curvatures in thin film: substrate systems, Journal of Applied Mechanics, Vol. 73, 2006, pp. 723-729. [5]. M. Budyansky, C. Madormo, J. L. Maciaszek, G. Lykotrafitis, Coherent gradient sensing microscopy (micro-CGS): A microscale curvature detection technique, Optics and Lasers in Engineering, Vol. 49, 2011, pp. 874-879. [6]. S. L. Kramer, M. Mello, G. Ravichandran, K. Bhattacharya, Phase shifting full-field interferometric methods for determination of in-plane tensorial stress, Experimental Mechanics, Vol. 49, 2009, pp. 303-315. [7]. M. Mello, S. Hong, A. Rosakis, Extension of the coherent gradient sensor (CGS) to the combined measurement of in-plane and out-of-plane displacement field gradients, Experimental Mechanics, Vol. 49, 2009, pp. 277-289. [8]. X. Yao, H. Yeh, W. Xu, Fracture investigation at V-notch tip using coherent gradient sensing (CGS), International Journal of Solids and Structures, Vol. 43, 2006, pp. 1189-1200. [9]. X. Dong, X. Feng, K.-C. Hwang, S. Ma, Q. Ma, Full-field measurement of nonuniform stresses of thin films at high temperature, Optics Express, Vol. 19, 2011, pp. 13201-13208. [10]. C. Liu, X. Zhang, J. Zhou, Y. Zhou, A general coherent gradient sensor for film curvature measurements: error analysis without temperature constraint, Optics and Lasers in Engineering, Vol. 51, 2013, pp. 808-812. [11]. C. Liu, X. Zhang, J. Zhou, Y. Zhou, X. Feng, The coherent gradient sensor for film curvature measurements at cryogenic temperature, Optics Express, Vol. 21, 2013, pp. 26352-26362. [12]. X. Zhang, C. Liu, J. Zhou, Y. Zhou, Nonuniform magnetic stresses in high temperature superconducting thin films, Journal of Applied Physics, Vol. 115, 2014, 043911. [13]. C. Liu, X. Zhang, Y. Zhou, Multiplication method for sparse interferometric fringes, Optics Express, Vol. 24, 2016, pp. 7693-7702. 151 Chapter 6. Photo-Emf Sensors and Talbot Effect: Measurement of Displacement and Vibration Chapter 6 Photo-Emf Sensors and Talbot Effect: Measurement of Displacement and Vibration P. Rodriguez, S. Mansurova, N. Korneev and D. Sanchez de la Llave1 6.1. Introduction The near-field diffraction of a periodic object has the special property of repeating itself in intensity at certain propagation distances; this effect is widely known as the Talbot effect [1-3]. In particular, when the object with an amplitude transmittance that is periodic along one axis is illuminated by a monochromatic plane wave (Fig. 6.1), the field distribution at the transmittance plane repeats itself at multiples of the so called Talbot distance. The Talbot distance depends only on two parameters, namely, the illuminating wavelength (λ) and the transmittance spatial period (d). More precisely, for plane wave illumination, the Talbot distance is given by ZT = 2d2∕λ. Grating 1st self‐ image 2st self‐ image Planes of uniform illumination Fig. 6.1. Optical arrangement to observe the Talbot effect or self-imaging phenomenon. P. Rodriguez National Institute for Astrophysics, Optics and Electronics, Puebla, Mexico 153 Advances in Optics: Reviews. Book Series, Vol. 3 It can be observed that between any two consecutive self-images a replica of the grating is also formed but with the contrast inverted, that is, the grating is formed with a lateral displacement of half of the period (d/2). For gratings with an opening ratio of ½ (e. g. Ronchi gratings) there are planes of uniform illumination (i.e. with a visibility equal to zero); the position of these latter planes are given by: Z k  (2k  1) ZT , k  0, 1, 2, ... . 4 (6.1) Hence, by measuring the fringe visibility at an observation plane of interest, the distance between the sinusoidal amplitude grating and the desired observation plane can be unambiguously determined in a distance range of one fourth the Talbot distance, e.g., from z = 0 to z = ZT ∕4. In recent years the Talbot effect and Talbot self-images localization have received much attention, both as a fundamental optical phenomenon and because of its optical applications such as interferometry [4], nanolithography [5], [6] and spectrometry [7, 8]. The Talbot effect also has been exploited for several metrological applications, among them: the measurement of the refractive index [9], the measurement of temperature [10], contouring [11], the measurement of focal length [12], collimation testing [13], wavefront sensors [14, 15] and the measurement of distance and displacement [16-20]. For this latter application, the first proposal [16] relied on measuring the fringe contrast or visibility of the diffracted field intensity and realizing temporal processing of the detected images. Afterward, Schirripa, Spagnolo and Ambrosini proposed a measurement method that used either a cosine or a Ronchi [18] grating and then realized numerical Fourier processing of the detected intensity pattern to determine the distance between the grating and the observation plane. Finally, methods for measuring discrete distances using the Talbot effect were proposed by Metha et al. [19] and Dubey et al. [20]. In [19], two wavelengths were employed to measure a step-height that coincides with the difference between the Talbot distances associated with each of the wavelengths utilized. In [20] a superluminescent diode was employed to provide several wavelengths instead of two. In all of the proposals mentioned above, the fields of interest were detected by a CCD camera and numerical processing of the detected images was required in order to determine its visibility and hence, the propagation distance. Among the image processing methods used to determine the light pattern visibility the root mean square (RMS) method [21], histogram-based method [22, 23] and semivariogram-based method [24, 25] can be mentioned. Despite of their simplicity, all CCD–based methods share common weaknesses, namely, necessity of a filter for avoid the saturation of the camera, sensitivity to the environmental vibrations, and need for additional processing which makes difficult sensing fast changing processes. Recently, the photodetector based on the non-steady-state photo-electromotive force (photo-emf) effect for measuring the visibility and for localizing the Fresnel diffraction patterns (Talbot self-images) generated by a Ronchi grating [26] has been proposed. Photo-emf effect [27] reveals itself as alternating current (ac) induced in a short-circuited 154 Chapter 6. Photo-Emf Sensors and Talbot Effect: Measurement of Displacement and Vibration photoconductive sample by a vibrating non-uniform light distribution. Standard theory developed for the simplest case of sinusoidal light pattern created by the interference of two plane waves predicts, that the output current amplitude is proportional to the square of the light pattern visibility V, which makes the photo-emf based sensors suitable for the direct measurements of the changes on the light pattern contrast. Due to its temporal adaptability to the slow phase drifts [27], this detector possesses additional robustness to the environmental vibrations. For these outstanding properties photo-emf based detector has already been proposed for a number of practical applications. In particular, they are used for detecting vibrations of diffusely scattering objects [28], for measuring the coherent length of several light sources [29], for sensing laser-generated ultrasonic displacements [30], for phase locking of lasers [31], for characterizing femtosecond pulses [32], for the detection of Doppler frequency shift [33] etc. In this chapter we present a comprehensive review of a detection method to measure the displacement and out of plane vibrations of a mirror-like object which combines the Talbot effect with the photo-emf-based detector. The information about displacement is codified in the visibility of the diffracted field; however, in contrast to the previous proposals, the decodification is achieved by direct measurement of the photo-emf current without any image processing. 6.2. Non-Steady-State Photo-Electromotive Force Effect Non-steady-state photo-electromotive force (photo-emf) effect was first described by Petrov et al. [34] in 1990’s. The photo-emf effect manifests itself as an alternating current (ac) through a short-circuited photoconductive sample illuminated by an oscillating nonuniform light distribution. A detailed analysis of photo-emf effect for sinusoidal light distribution can be found in [27] and here it is only briefly discussed. The standard configuration for observing the photo-emf effect is shown in Fig. 6.2. Under illumination by two coherent plane waves, one of which is periodically modulated in phase with the frequency f and amplitude  an oscillating sinusoidal light distribution is created inside photoconductive material: I ( x , t )  I 0 1  V cos Kx   sin(  t )  . (6.2) Here I0 is the average light intensity, K =  is the spatial frequency of the interference pattern, and  is the fringe spacing. This intensity distribution, in its turn, generates a spatially non-uniform distribution of the mobile carriers n(x,t). Mobile charge redistribution due to the diffusion/drift and its subsequent trapping gives rise to a periodical distribution of space charged electric field Esc. The expression for the total current density flowing through the sample is: 155 Advances in Optics: Reviews. Book Series, Vol. 3 J   x , t   e  n  x , t  E sc  x , t   eD  J  n  x, t   E sc  x , t  ,   0 x x (6.3) Lx Ly  EOM V  I2 I1  RL Fig. 6.2. Standard configuration for photo-emf effect. Here I1 and I2 are the intensities of each wave, EOM is the electro-optical modulator, J is the photo-emf current, V is the photo-emf voltage, and RL is the load resistor. where e is the electronic charge,  the mobility, n(x,t) is the density of the mobile photoelectrons in the conduction band, D is the diffusion coefficient,  is the permittivity, and  is the vacuum permittivity. If the Eq. (6.3) is integrated in the interval from 0 to L (the interelectrode spacing), due to the boundary conditions n(0,t) = n(L,t) the averaged diffusion current [the second term of the Eq. (6.3)] caused by the nonuniform photocarriers density, has to be equal to zero:  n  x, t  dx  n  L, t   n  0, t   0. x 0 L  (6.4) Because of the potential nature of the electric field, the averaged displacement current through the sample represented by the third term of the Eq. (6.3) is equal to zero also. Therefore, the density of the total current thought the sample is equal to the drift current:  e J  ( x, t )  E ( x, t ) n( x, t ) dx .  0  (6.5) Under the steady state conditions, the diffusion-driven sinusoidal distribution of Esc is shifted by /4 with respect to the photoconductivity distribution (x), (see Fig. 6.3), therefore the photo-emf current is zero. However, if the intensity distribution shifts, the situation is different. It is assumed that the photoconductivity (x) follows the vibrations of the illuminating intensity distribution 156 Chapter 6. Photo-Emf Sensors and Talbot Effect: Measurement of Displacement and Vibration I(x,t) almost instantaneously, while the distribution Esc(x,t) possesses certain inertia with a response time sc. As a result, the phase shift between mobile carriers concentration distributions n(x,t) and space charge field Esc(x,t) is different from /4 and the non-steadystate photo-electromotive force is created giving rise to alternating current through the short-circuited semiconductor. Photoconductive Material (a) Interference pattern (b) Spatial distributions of light intensity I(x) + + (c) Space charge + + +  (x) - (d) Photoconductivity - - -  (x) - - + x x x (e) Space-charge electric field E (x) sc x Fig. 6.3. Diagram of space-charge electric field Esc generation in a photoconductive sample. To calculate the photo-emf current amplitude, first the complex amplitudes of space charge field distribution, as well as the carriers concentration should be found, solving the standard set of equations, described e.g. in [27]. The solution of Eq. (6.5) can be obtained in the approximation of low amplitude of oscillations (<< 1) and low contrast (V << 1) of the illuminating pattern. As result of this solution, the amplitude of the first harmonic of photo-emf current can be expressed as: J   0  i / 0 V 2 E , D 1  i / 0 4 1  K 2 L2D (6.6) here 0 is the average photoconductivity, LD is the diffusion length of the photocarriers, ED=KkBT/e is the diffusion electric field, and the characteristic cutoff frequency  is defined as:   0   sc1   di 1  K 2 L2D  1 , (6.7) 157 Advances in Optics: Reviews. Book Series, Vol. 3 where sc is the recording/erasure time of the electric field grating, and di = is the dielectric relaxation time of the photoconductive material. Note, that the frequency transfer function of photo-EMF current is similar to the transfer function of RC circuit, i.e. at low frequency the signal grows up to the cutoff frequency , and then has a constant level at frequencies higher than this cutoff frequency (see Fig. 6.4).  Photo‐emf signal J (a.u.) 10 1 0,1 0,01 0,01 0,1 1 10 100 Modulation frequency  (a.u.) Fig. 6.4. Dependence of the first harmonic of photo-emf current J versus the modulation frequency . This kind of transfer function is responsible for the inherent adaptive properties of the photo-emf effect for detection of phase-modulated signals. By the nature of the photoemf, the sensors based on this effect have the ability to compensate slow environmental phase drifts, i.e. possess additional robustness to the environmental pertubations. In addition, these photo-emf sensors possess spatial adaptability to the wavefront irregularities in the interfering beams, since the space charge field and concentration distribution are the exact replica of the intensity distributions, i.e. the detection can be performed in presence of speckle of the illuminating light pattern or aberrations of the interfering beams. For these outstanding properties, the photo-emf based sensors have already been proposed for a number of practical applications as an adaptive detector of phase modulated signal [28-35]. For the experiments presented here, the photo-emf sensor was fabricated from a piece of GaAs:Cr crystal with the dimensions 8 mm x 5 mm x 0.5 mm glueded to a plastic substrate. Two electrodes were deposited on its front surface with silver paint, in such a way that they present an effective interelectrode surface with the dimensions Lx = L ≈ 5 mm and Ly = 5 mm (see Fig. 6.2). The photo-emf signal was measured by connecting the silver electrodes to a lock-in amplifier by means of a coaxial cable. 158 Chapter 6. Photo-Emf Sensors and Talbot Effect: Measurement of Displacement and Vibration 6.3. Applications 6.3.1. Measurements of Displacements A novel approach for measuring distances or displacements using detectors based on the photo-emf sensors was recently demonstrated [36]. Similar to previous techniques, the information about the displacement of the test object is codified in the visibility of the diffracted light by a diffraction grating. The decodification, however, is carried out by direct measurement of the photo-emf electrical current, which is proportional to the square of the visibility of the light pattern [see Eq. (6.6)]; unlike the previous techniques there is no any image processing involved. Analysis of this novel proposal is carried out as follows [26]. Consider a one-dimensional sinusoidal amplitude grating, with the transmission described by following expression: t( x)  1 2   2x  1  m cos d  ,    (6.8) where d is the grating period and m is the grating modulation index. For a plane wave illumination, the near-field intensity distribution at axial distance z from the grating position is given by [37]: I ( x)    2z   2x  1 2 2  2x   cos   m cos   . 1  2m cos 4   d   ZT   d  (6.9) For low values of the grating modulation index (m << 1), it is straightforward to show that the visibility of the diffracted light pattern is  2 z   . V ( z )  2m cos  ZT  (6.10) Therefore by measuring the visibility of the diffracted light pattern, the distance from the grating to the plane of interest (z) can be unambiguously determined in a range of ZT/4. On the other hand, as stated in Section 6.2, the photo-emf current amplitude [Eq. (6.6)] at angular frequency =2f can be written as: J   CI0  V 2 , (6.11) where the factor C groups together the factors that depend on electro-optical parameters of the sample and on spatial (K) and temporal frequencies () of the illuminating pattern, and I0 is the average intensity of the light pattern. 159 Advances in Optics: Reviews. Book Series, Vol. 3 If the sinusoidal amplitude grating described by Eq. (6.8) is set to oscillate (at frequency f) on the direction of its grating vector, the axial dependence of the photo-emf current induced in the photo-emf sensor by the light diffracted on the oscillating grating, is obtained by substitution of Eq. (6.10) into Eq. (6.11):  1 1  2 z   J   4 m 2 CI 0    cos   ,  2 2  ( Z T / 2)   (6.12) where  is the amplitude of the oscillations of the grating which is assumed to be smaller than the period of the grating (<< d). It follows from this latter equation that by measuring this photo-emf current, the distance between the oscillating sinusoidal grating and the photo-emf sensor can be determined in a range of ZT/4 in a linear arrangement. To determine the displacement of a mirror-like object using the photo-emf sensors an optical setup depicted in Fig. 6.5 has been proposed. Translation stage Grating B.S. Collimated beam Lock‐in amplifier  V Piezo electric  S.G. Photo‐emf sensor Fig. 6.5. Experimental setup to measure displacements of a test object with mirror-like surface employing the photo-emf sensor. The test object is mounted on a translation stage. In the setup, a sinusoidal amplitude grating is illuminated by a collimated He-Ne laser beam. The light diffracted by the grating is directed to the test object by a beam splitter (BS) and the light reflected from the mirror-like surface of the object is brought to the surface of the photo-emf sensor. Oscillations are induced to the grating by gluing it to a piezoelectric transducer excited by a signal generator. The period of the sinusoidal amplitude grating used in the experiment was d = 0.1 mm, which in combination with the wavelength of the laser (632.8 nm) results in a Talbot distance ZT = 31.60 mm. The frequency of the oscillations was set at f = 600 Hz, and the excitation voltage was such that the produced amplitude of oscillations was 15 m, much lower than the period of the 160 Chapter 6. Photo-Emf Sensors and Talbot Effect: Measurement of Displacement and Vibration grating. A second He-Ne laser beam was used to provide a background illumination to further decrease the visibility at the surface of the photo-emf sensor described in Section 6.2. The electrical current generated by the photo-emf sensor was measured as voltage drop across the input impedance of the lock-in amplifier, so the measured photoemf signal V can be expressed as:  2 z   , V   V0  VC cos   ZT / 4  (6.13) where V0 is the offset signal, VC is the amplitude of the sinusoidal component. The axial period has been changed accordingly due to the “folded” geometry of the experimental setup. Fig. 6.6 shows the signal from the photo-emf sensor as a function of the displacement of the test object in steps of 0.25 mm. Photo_emf signal, V 1.000 800 600 400 200 0 0 2 4 6 8 10 12 14 Displacement , mm Fig. 6.6. Photo-emf signal as a function of the displacement of the test object. The positions are indicated by the scale of the translational stage. The dots are the experimental values and the solid line is the fit to Eq. (6.13), the fitting values are V0 = 510 V, VC = 416 V and ZT/4 = 8 mm. The light power impinging on the photo-emf sensor from the test object is 0.52 mW and from the background is 0.36 mW. As predicted by the theory [Eq. (6.13)] the photo-emf signal varies as a cosine function of the displacement of the test object. The maximum value of the photo-emf signal corresponds to a test object’s position such that the total distance traveled by the light from the grating to the photo-emf sensor is equal to a multiple of ZT/2, where the visibility of the diffracted light pattern is maximal (11*ZT in this particular configuration). The positions of minimal photo-emf signal correspond to positions of minimal visibility, i.e. to planes of uniform illumination. Note, that as shown in Fig. 6.6 and indicated in Eq. (6.13), around the total propagation distances from the grating to photo-emf sensor equal to z= (2k+1)*(ZT/8), with 161 Advances in Optics: Reviews. Book Series, Vol. 3 k = 0,1,2,…, (the quadrature position), there is a region in which the output signal from the photo-emf sensor is linearly proportional to the displacement of the test object. Fig. 6.7 shows an extended view of the photo-emf signal as a function of 20 m displacements of the test object around the position = 5.25 mm. Experimentally, this relationship holds in a range of 1.5 mm. As far as the power of laser, frequency and amplitude of oscillation of the piezoelectric remain constant, these measurements for determination of the displacement of the test object are quite reproducible, yielding a device with high precision. 6.3.2. Determination of Low Frequency, Out-of-Plane Vibrations Vibration detection systems are widely used in several scientific and technological areas. In the region of high frequency vibrations (greater than 20 kHz) the detection of ultrasound stands out [38]. In the low frequency region (in the order of tens of Hertz) the diagnosis of large civil structures, evaluation of mechanical components and the detection and monitoring of telluric movements are highlighted. Photo‐emf signal,  V 650 600 550 500 450 5,1 5,2 5,3 5,4 5,5 5,6 5,7 5,8 Displacement , mm Fig. 6.7. Photo-emf signal as a function of the displacement of the test object around the position where a linear relation is hold. Optical methods provide different techniques and devices for measuring contactless (i.e. remote) vibrations. Among many others we can mention interferometric and holographic techniques [39], techniques based on self-mixing in laser diodes [40], speckle-based techniques and techniques based in the moire method [41]. In these techniques, the detection and decoding of the signals or images containing the vibration amplitude and frequency of the test object are recorded and stored in a computer for later processing. In interferometric techniques and self-mixing in laser diodes, the use of a photodiode is required; while speckle-based and moire-based techniques require the use of CCD cameras. 162 Chapter 6. Photo-Emf Sensors and Talbot Effect: Measurement of Displacement and Vibration In the following we demonstrate the measuring of low frequency, out-of-plane vibrations of a test object with amplitudes of few microns approximately, using the photo-emf sensors and the Talbot effect. For measuring the amplitude of vibration of a test object with mirror-like surface we used a setup similar that on Fig. 6.5 except for two modifications: the test object (a mirror) was attached to a loudspeaker and the amplified photo-emf signal detected by the lock-in amplifier was displayed and measured by an oscilloscope, as it is depicted in Fig. 6.8. The vibration frequencies of the test object (F) are lower than oscillation frequency of the grating (F << f). If the object under test is vibrating with an amplitude A at the frequency F, the photo-emf signal measured in the oscilloscope UF at frequency F is:  2  z  A sin  2 F    U F  U 0  U C cos  ,   ZT / 4   (6.14) where U0 is the offset signal, UC is the maximum amplitude of the sinusoidal component. F Grating B.S. Collimated beam Lock‐in amplifier Piezo electric UF t Scope S.G. Photo‐emf sensor Fig 6.8. Schematic representation of the optical setup to measure the amplitude of vibration of a test object. Filtering out the offset voltage, placing the photo-emf sensor in a position such that the whole optical arrangement is in the quadrature point, and setting the low amplitudes of vibration A << ZT/8, the linear relation between the amplitude of vibrations and amplitude of the signal at frequency F measured by the oscilloscope is hold: UF  8 U C A . ZT (6.15) 163 Advances in Optics: Reviews. Book Series, Vol. 3 The voltage UC can be considered as a “calibrating” voltage and it can be determined experimentally by moving the object under test a distance larger that ZT/8. As for the previous application the value of the Talbot distance can be also experimentally determined or calculated from the specifications of the grating. So it is evident that by measuring the signal UF the amplitude of vibration of the object under test can be estimated: A ZT UF . 8 U C (6.16) The following experiment presents the determination of the amplitude of vibration of a test object vibrating at a frequency of F = 3 Hz using the proposed method. The experimental conditions were similar to that presented in the previous sub-section. Determination of the “calibrating” voltage and the position where the output signal is linearly proportional to the total distance from the grating to the photo-emf sensor (quadrature position) are obtained by axially translating the test object. Fig. 6.9 shows the oscilloscope trace obtained when the object under test is mechanically translated and it is not vibrating. From this trace and from that (similar to shown in Fig. 6.6) produced by moving the test object in steps of 100 m, the value of the Talbot distance, the “calibrating” voltage and the quadrature positions were obtained. Oscilloscope trace, V 6 5 UC 4 3 2 ZT/4 1 0 ‐6 ‐4 ‐2 0 2 4 6 Time, sec Fig. 6.9. Oscilloscope trace obtained when the test object is mechanically translated along the optical axis. Dashed line is the theoretical fit to Eq. (6.14). Left arrow indicate the quadrature position. The object under test is not vibrating. The measurements of amplitudes of vibration of the test object are performed in the quadrature point (marked with an arrow in the Fig. 6.9). Fig. 6.10 shows the oscilloscope trace when the loudspeaker is excited with a voltage of 1.45 V. 164 Chapter 6. Photo-Emf Sensors and Talbot Effect: Measurement of Displacement and Vibration Osciloscope trace, V 5,5 5,0 UF 4,5 4,0 3,5 ‐1,0 ‐0,5 0,0 0,5 1,0 Time, sec Fig. 6.10. Oscilloscope trace obtained when the test object is vibrating. The loudspeaker is excited at 1.45 V at a frequency of 3 Hz. From this trace the value of the voltage UF is readily obtained. In Fig. 6.11 the dependence of the amplitude of vibration of the test object as a function of the voltage applied to the loudspeaker is plotted. For comparison purposes in the same graph the values of the vibrations amplitudes measured by a Michelson interferometer are plotted. As clearly shown, there is an excellent agreement between the two methods. Am plitude of vibration A,  m 300 200 100 0 0,0 0,5 1,0 1,5 2,0 2,5 Voltage applied to loudspeaker, V Fig. 6.11. Amplitude of vibrations of the test object as a function of the voltage applied to the loudspeaker. Values obtained with (●) the proposed method and with (□) a Michelson interferometer. 6.4. Conclusions The self-imaging phenomenon of a binary grating (or Talbot effect) has been useful for setting up low cost and versatile devices for optical metrology. In some cases, the use of 165 Advances in Optics: Reviews. Book Series, Vol. 3 these devices is limited by the experimental technique employed for determining the visibility of the light diffracted from the grating. As an alternative technique, in this report we have presented the use of photo-emf sensors for measuring the visibility. Sensors based on photo-emf have been mainly used to detect phase-modulated optical signals. They have proved to be cheap, reliable and very robust devices for sensor applications. Here we have used the property that the electrical current induced in photoemf sensor by an oscillating light pattern, in particular by the light diffracted on oscillating diffraction grating, is proportional to the square of the visibility. We have presented two applications using the Talbot effect and the photo-emf sensors, one for measuring the displacements and other for determining the amplitude of vibrations of mirror-like objects using a GaAs: Cr photo-emf sensor. Because of the inherent adaptive properties of the photo-emf sensors, the proposed techniques are very robust to environmental perturbations. In contrast to similar applications, our technique does not require image processing. Because the Talbot distance depends on the period of the grating and the wavelength, the range of measurement can be modified by changing any of these parameters. For measurements of displacements we estimated a resolution better than 10 m in a dynamic range of 1.5 mm, and for the determination of amplitude of vibration, an excellent agreement between our technique and an interferometric one was demonstrated. References [1]. H. F. Talbot Facts related to optical science, Philos. Mag., Vol. 9, Issue 56, 1836, pp. 401-407. [2]. L. Rayleigh, On copying diffraction-gratings, and on some phenomena connected therewith, Philos. Mag., Vol. 11, 1881, pp. 196-205. [3]. K. Patorski, The self-imaging phenomenon and its applications, Prog. Opt., Vol. 27, 1989, pp. 1-108. [4]. S. P. Trivedi, S. Prakash, S. Rana, O. Sasaki, Real-time slope mapping and defect detection in bent plates using Talbot interferometry, Appl. Opt., Vol. 49, Issue 5, 2010, pp. 897-903. [5]. X. Wan, Q. Wang, H. Tao, Nanolithography in the quasi-far field based on the destructive interference effect of surface plasmon polaritons, J. Opt. Soc. Am. A. Opt. Image Sci. 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Trivedi, Optical phase-lock loops with photoconductive semiconductor phase detectors, Opt. Lett., Vol. 19, Issue 11, 1994, pp. 774-776. 167 Advances in Optics: Reviews. Book Series, Vol. 3 [32]. Y. Ding, I. Lahiri, D. D. Nolte, G. J. Dunning, D. M. Pepper, Electric-field correlation of femtosecond pulses by use of a photoelectromotive-force detector, J. Opt. Soc. Am. B Opt. Phys., Vol. 15, Issue 7, 1998, pp. 2013-2017. [33]. S. Mansurova, P. M. Zarate, P. Rodriguez, S. Stepanov, S. Köber, K. Meerholz, Non-steadystate photoelectromotive force effect under linear and periodical phase modulation: application to detection of Doppler frequency shift, Opt. Lett., Vol. 37, Issue 3, 2012, pp. 383-385. [34]. M. P. Petrov, I. A. Sokolov, S. I. Stepanov, G. S. Trofimov, Non-steady-state photoelectromotive-force induced by dynamic gratings in partially compensated photoconductors, J. Appl. Phys., Vol. 68, Issue 5, 1990, pp. 2216-2225. [35]. P. Moreno Zarate, P. Rodriguez, S. Koeber, K. Meerholz, S. Mansurova, Adaptive detection of Doppler frequency shift using ac non-steady-state photo-EMF effect, in Proceedings of the Quantum Electronics and Laser Science Conference (QELS’08), San Jose, CA, USA, 2008, p. JThA50. [36]. P. Rodriguez-Montero, D. Sánchez-de-la-Llave, S. Mansurova, Electro-optical processor for measuring displacement employing the Talbot and the nonsteady-state photo-electromotive force effects, Opt. Lett., Vol. 39, Issue 1, 2014, pp. 104-107. [37]. J. W. Goodman, Introduction to Fourier optics, Quantum and Semiclassical Opt.: J. of the Eur. Opt. Soc. Part B, Vol. 8, Issue 5, 1996, p. 491. [38]. B. C. Scruby, E. L. Drain, Laser Ultrasonics Techniques and Applications, CRC Press, 1990. [39]. C. Shakher, S. Prakash, Monitoring/measurement of out-of-plane vibrations using shearing interferometry and interferometric grating, Opt. Lasers Eng., Vol. 38, Issue 5, 2002, pp. 269-277. [40]. L. Scalise, Y. Yu, G. Giuliani, G. Plantier, T. Bosch, Self-mixing laser diode velocimetry: Application to vibration and velocity measurement, IEEE Trans. Instrum. Meas., Vol. 53, Issue 1, 2004, pp. 223-232. [41]. S. Prakash, S. Upadhyay, C. Shakher, Real time out-of-plane vibration measurement/monitoring using Talbot interferometry, Opt. Lasers Eng., Vol. 33, Issue 4, 2000, pp. 251-259. 168 Chapter 7. Advances in Label-Free Sensing of Bacteria by Light Diffraction Phenomenon Chapter 7 Advances in Label-Free Sensing of Bacteria by Light Diffraction Phenomenon Igor Buzalewicz, Katarzyna Kowal, Mariusz Linard, Agnieszka Suchwałko and Halina Podbielska1 7.1. Introduction Bacteria are found widely throughout nature and the environment in soils, water or the intestinal tract of animals. An average person carries more than 150 kinds of bacteria which exist inside and outside the body [1]. Although the majority of microorganisms can coexist with humans, plants and animals with beneficial relations, some of them are pathogenic and can be the cause of infectious diseases. Bacteria are omnipresent, however, until the establishment of optical microscopy foundations they could not have been observed visually. The optical microscopy and phase-contrast microscopy have created the perspectives for observation of the individual bacteria cells, what led to the recognition of bacteria. Since then, the use of light and optical techniques play a crucial role in the bacteria detection and identification being the basis of the microbiological diagnosis. Nowadays, the continuous increase of the bacteria resistant to commonly used antibacterial chemicals (antibiotics, sterilisation agents etc.) has been observed. National Institute of Allergy and Infectious Diseases [2] reports that the rapid and sensitive detection and accurate identification of bacteria are crucial to facilitate the narrowspectrum therapies by enabling the use of treatments targeted to a specific pathogen. Optical biosensors offer the non-invasive and nondestructive detection since they enable analysis of the amplitude and phase of light modulated by pathogens, instead of pathogens themselves. There is a variety of detection methods which base on principles. Optical techniques used in microbiology include infrared and fluorescence spectroscopy, flow cytometry, chromatography, chemiluminescence analysis, surface plasmon resonance (SPR) phenomena [3-7]. Over the past few years, it was demonstrated that the analysis of light diffraction on bacterial colonies could be used for identification of different bacteria Halina Podbielska Bio-Optics Group, Department of Biomedical Engineering, Faculty of Fundamental Problems of Technology, Wroclaw University of Science and Technology, Wroclaw, Poland 169 Advances in Optics: Reviews. Book Series, Vol. 3 species [8-18]. Diffraction signatures of bacterial colonies exhibit species-/strainsdependent features, which are suitable for bacteria differentiation and characterization. In this chapter, several aspects of the use of light diffraction on bacterial colonies in microbiological diagnosis are discussed. In Section 7.2 the biophysical model of the bacterial colony is described. The relevant properties of the bacterial colonies and their mathematical description are outlined. Section 7.3 discusses a proposed optical method for bacteria identification, followed by the detailed description of the detection system based on Fresnel diffraction patterns. In the last part of the chapter, the efficiency of the proposed optical system is presented as well as the potential alterative applications in microbiological diagnosis. 7.2. The Biophysical Model of the Bacterial Colony The transformation of the light on the bacterial colony, as on all physical objects, is influenced by its physical properties. Therefore to understand the specific light diffraction on the object, it is necessary to identify and characterise these relevant features. In case of bacterial colonies being the biological objects, the most important factors affecting its interaction with the optical field are species-/strains- dependent optical and morphological properties. A single bacterial colony is a monoculture of bacterial cells with the same genotype properties. A bacterial colony is formed by a single bacterial cell, which by metabolising the nutrients of the culture medium and by multiplication is creating a macroscopic structure consisting of the same bacterial cells and intercellular material excreted during the growth process. Therefore, the bacterial colony is a macroscopic biological object consisting of millions of individual bacterial cells, interacting with each other. The morphology of individual bacterial cells (see Fig. 7.1) forming the colony is species-dependent, and it includes various cells’ shapes (rod-shaped, spheroid-shaped, spirals-shaped), their spatial arrangement, appendages as flagella. The bacterial cells of different species and strains metabolise different nutrients, affecting the internal structure of the bacterial colony. The extracellular material fills the space between the individual cells. The oldest bacterial cells are located in the centre of the colony around the primary location where the first cell was initially situated. With the growth of the colony, that central region becomes the thickest area of the sample, with the highest concentration of intracellular material. These factors in conjunction with the dynamics of colony development, bacterial cells’ shape, its motility and spatial arrangement are influencing the colony profile and shape. The high concentration of bacterial cells and the extracellular material can be observed at a central region of the lowest intensity of phase-contrast microscopic images of bacterial colonies (see Fig. 7.2). In case of some bacterial cells containing flagella - structures protruding from the bacterial cell wall and are responsible for bacterial motility, the edges of the bacterial colonies are irregular and crown-like, or annular envelope-like structures are observed around the central region of the colony. These structures are characteristic for 170 Chapter 7. Advances in Label-Free Sensing of Bacteria by Light Diffraction Phenomenon the bacteria colonies formed by the cells exhibiting high mobility on the surface of the solid nutrient medium, which moved outside the central region of the colony. An example of such colony can be colonies formed by the Proteus mirabilis bacteria (see Fig. 7.3). Therefore, it can be seen, that colony morphology can be highly influenced by the shape of individual cells, cell wall components, the extracellular components and cellular response to nutrient availability, oxygen and other gases, salt, acidity, alkalinity, temperature [19]. The differences in bacterial cells structure, metabolism and external factors are also affecting the morphology and optical properties of bacterial colonies and can be used as foundations for their differentiation and characterization. Fig. 7.1. The examples of different morphologies of bacterial cells. Fig. 7.2. The exemplary morphology of bacterial colonies. 171 Advances in Optics: Reviews. Book Series, Vol. 3 Fig. 7.3. The exemplary experimental images of Proteus mirabilis colony recorded by the: (A) scanning confocal microscopy, and (B) phase-contrast microscopy presenting the characteristic structure of the peripheral region of the colony caused by the high motility of the bacterial cells. Depending on the optical properties of the physical object a light wave may be transmitted absorbed, re-emitted with a different wavelength, deflected, diffracted or scattered, what causes a change in the spatial distribution and the amplitude of the incoming optical wave field. Thus, the modulated light wave carries coded amplitude-phase information about the structure of the object. Therefore, the properties of the optical objects may be expressed by the amplitude transmittance function, taking into account the twodimensional distribution of the light transmission coefficient by the object under investigation as well as the two-dimensional distribution of phase changes in the plane of the examined object. This general consideration is also valid in the case of the bacterial colony. The transformation of a light wave on bacterial colonies depends on the properties of the object, which based on the wave optics [20] can be described by the amplitude transmittance function tB(x1, y1, t) which carries information about amplitude and phase modulating properties of the incoming optical wave field. This function can be expressed in the following manner: , , , , Φ , , , (7.1) where TB(x1, y1, t) represents the two-dimensional (2D) light transmission coefficient of bacteria colony and ΦB(x1, y1, t) the total phase delay of the wave field passing through the bacteria colony. This general expression enables the analysis of the complex objects as a light amplitude and phase spatial modulators, which is the most appropriate way to examine the light modulating properties of the biological object and the bacterial colonies particularly. Moreover, it should be pointed out that the bacteria colony is evolving in time, what leads to the temporal changes in the optical and morphological properties. Based on the above-described bacteria species-/strains-dependent object function it is hard to escape from the obvious conclusion that the light transmission properties of the bacterial colony in combination with their phase properties related with colony refractive index distribution and the spatial geometry of the colony will be mostly responsible for the specific amplitude-phase modulation of the illuminating light beam. The light transmission/absorption of bacterial colonies depends not only on the transmission/absorption properties of individual bacterial cells but also on the spatial variation of their density and of the intercellular material excreted during the growth 172 Chapter 7. Advances in Label-Free Sensing of Bacteria by Light Diffraction Phenomenon process, as well as on the changes in the colony thickness. They can be determined using transmission microscopy [21]. Based on wave optics, the complex amplitude U x , y′ of the optical field in the image plane in the transmission mode can be described by the following expression [20]: , ′ | | , , (7.2) where U , is the rescaled complex amplitude of the optical field in the object plane and M determines the transverse magnification of the microscope optical system, x’ = Mx and y’ = My are relationships connecting the coordinates x, y in the object plane with the coordinates x’, y’ in the image plane. Because only the intensity of the optical field is recorded in the conventional transmission microscope, the information about the phase modulation is lost. The intensity of the optical field in the image plane can be described as follows: | , , | ≅ | , | , (7.3) The microscopic image enables obtaining the rescaled two-dimensional transmission , . Therefore, it is possible to determine the transmission coefficient coefficient T T(x’, y’) of the bacterial colony, according to the following expression: , , ̅ , , (7.4) where T(i, j) is the discrete transmission coefficient for the particular pixel (i, j) of the recorded transmission image of the colony, Iob(i, j) is the discrete intensity value of the colony image pixel, and ̅ is the average discrete intensity of the pixels of the nutrient medium image outside the region occupied by the colony. T(i, j) is the relative transmission coefficient of the bacterial colony, normalized to the transmission properties of the nutrient medium on which the colonies are grown. The T(i, j) ∈ < 0; 1 > values are dimensionless units. The value 0 describes the situation of total light attenuation for an opaque object, and value 1 describes total transmission for a transparent object. The representative 2D transmission coefficient of different bacterial colonies are presented in Fig. 7.4. The reduction of the light transmission in the central region of the bacterial colony is caused by the spatial variation of the thickness of bacterial colony, bacteria cells and intercellular material density. The increase of the thickness of the colony leads to the greater light scattering and absorption. This effect is observed for the colonies of spheroid-shaped bacterial cells as Staphylococcus intermedius. These cells are forming the regular convex-shaped profiles colonies. The central region of the colony, near the nutrient medium surface, has the highest mass density as the oldest cells are located there, and the concentration of the extracellular material is the highest. On the other hand, near the colony edges where the 173 Advances in Optics: Reviews. Book Series, Vol. 3 thickness is the lowest, and as a consequence, the light transmission is higher. These features are common among different bacteria species, but they are more evident in the case of the spheroid-shaped bacteria cells (cocci). The symmetry of bacteria cells contributes to the homogeneous internal and external structure of the colony because in this case, the spatial arrangement of bacteria cells does not matter. On the other hand, the colonies of bacteria cells with different morphology (rods-shaped, spirals-shaped) have more inhomogeneous morphology what can be observed in the 2D transmission coefficients maps. The most inhomogeneous morphology and optical properties are common for bacterial cells having flagella structures responsible for high bacterial cells motility on the surface of the nutrient medium. The variations of the different bacteria cells, colony thickness and intracellular material density, can also be observed by phase contrast microscopy technique as shown in Fig. 7.5. Fig. 7.4. The exemplary experimental 2D transmission coefficients maps of the bacterial colony: (A) Bacillus subtilis; (B) Pseudomonas aeruginosa; (C) Staphylococcus intermedius. Fig. 7.5. The exemplary experimental phase-contrast microscopic (objective: 10×) images of bacterial colonies: (A) Proteus mirabilis; (B) Citrobacteri freundii; (C) Staphylococcus aureus. Phase-contrast microscopy can be used to visualize the effect of the spatial distribution of the bacterial cells and the intracellular material concentration on the spatial distribution of the colony thickness, surface roughness and colony profile but also the refractive index 174 Chapter 7. Advances in Label-Free Sensing of Bacteria by Light Diffraction Phenomenon distribution. An increase of the colony thickness and the mass density are indicated by the decrease in the intensity of light. In case of some bacteria species/strains colonies (as Bacillus subtilis and Pseudomonas aeruginosa), the high spatial variations of the colony thickness and the mass density distribution are influencing the heterogeneous spatial distribution of the 2D transmission coefficient. In this case, the strong light scattering and diffraction effects can be observed. Moreover, in some cases when the high local variation of the colony thickness and mass density impacts the roughness of the colony surface, the additional speckle effect contributes to the final light modulation on the bacterial colony. This species-/strains-dependent differences in the colony 2D transmission coefficients’ distribution will affect the optical wave field transformation on the colony. In another word, the light diffraction takes place at boundaries of each zone with different transmission properties in a similar way as in the case of the knife-edge diffraction. As it was mentioned above, the bacterial colonies can be treated as an amplitude and phase spatial modulators of the illuminating optical field. Therefore, it is necessary to describe the phase properties of bacterial colonies which contribute to the phase delays of the incident optical field. The phase delay of the wave field propagating in the medium is related to the optical path length being the product of the geometric length d of the path light follows through the medium and the index of refraction n of the medium through which it propagates: . (7.5) Therefore, the phase delay Φ (x, y) of the wave field can be expressed in the following manner: Φ , , where k is the wavenumber. , (7.6) Spatial geometry of the colony is the main factor influencing the phase delays of the optical field. In the literature, various approaches to the bacteria colonies’ profile shape are presented: a convex shape [13, 22, 23], a thin film with decreasing tailing edge [24] or a Gaussian profile [25, 26]. At the beginning for the simplicity of the general analysis, let’s consider the case when the bacterial colony has a spheroid shape as in case of the Staphylococcus aureus colonies and further on the other approaches of bacterial colony profile (Gaussian profile, profile with two different radii of curvature) will be described. Let’s consider the case of a convex shape of bacterial colony located at the object plane ∞ and rB are defined by (x1, y1) coordinates, where the radiuses of curvatures describing the colony flat input surface (on a nutrient medium) and spherical output surface respectively (see Fig. 7.6 (A)). The total phase delay of the wave field passing through such bacteria colony may be expressed, as: Φ , ∆ , ∆ , , (7.7) 175 Advances in Optics: Reviews. Book Series, Vol. 3 Fig. 7.6. Models of different profiles of bacterial colonies: (A) convex; (B) Gaussian; and (C) convex with two radii of curvature. where nB is the refractive index of the bacteria colony, H0 is the central thickness along the optical axis and ∆ , is the bacteria colony thickness function in the off-axis region. Referring to the assumed geometry of the bacteria colony, the thickness ∆ , can be described using following equation: ∆ , 1 1 . (7.8) If we expand the square root term in power series and simplify it, the thickness function can be described as   x1 , y 1   H 0  x12  y12  1 1   ,   2  r rB  (7.9) and the phase delay as  B  x1 , y1   kn B H 0  k ( n B  1) 1  x12  y12  1    . 2 r r B    (7.10) The convex shape of a bacterial colony and the similarity of the above expression to the phase delay introduced by the conventional optical lens indicate that such colony can exhibit the light focusing properties. Therefore, the total phase delay of the convex-shaped colony can be expressed in the following manner:  B  x1 , y1   kn B H 0  176     kF k x12  y12  kn B H 0  B x12  y12 , 2 fB 2 (7.11) Chapter 7. Advances in Label-Free Sensing of Bacteria by Light Diffraction Phenomenon where 1⁄ 1 and fb is the focal distance of bacterial colony. The convex profile of bacterial colony contributes to the light focusing properties of the colony, as in case of the conventional optical lenses. Finally, in the considered case the amplitude transmittance function of the convex shaped colony can be express as follows: , . , (7.12) Now, let’s consider the case of bacterial colony modeled by Gaussian profile (see Fig. 7.5 (B)) as a bell curve shape with tailing edge [26]. As in the previous case, the central thickness of the colony is expressed by H0 and radius of the colony cross-section is expressed by rB, respectively. The Gaussian function describing the colony profile can be derived from the following equation: , (7.13) . The total phase delay of the wave field passing through such bacteria colony is expressed, as: Φ ∆ , , , , Finally, above equation can be written as: Φ , and the amplitude transmittance function as , , , . , 1 1 (7.14) (7.15) . (7.16) In the case of convex shaped bacterial colony with two different radii of curvature (see Fig. 7.5 (C)) rB1 in the central region of colony (Σ1) and rB2 near the colony edges (Σ2), the total phase delay can be described in a similar way as in case of the convex colony with single radius of curvature, but for each region of colony separately: and Φ , , (7.17) Φ , , (7.18) 1 and 1⁄ 1 and where 1⁄ H1+H2 = H0. Above expression have shown that the convex-shaped bacterial colony 177 Advances in Optics: Reviews. Book Series, Vol. 3 exhibits the light focusing properties, with two different focal lengths in each colony region. The amplitude transmittance function in this case can be expressed as: , , , , , ∈Σ , . (7.19) ∈Σ , The examined the Escherichia coli colonies [22] has shown that analyzed biological object exhibits the light focusing properties similar to the conventional microlenses. It should be pointed out that the conventional optical lens does not change the intensity but induces a nonuniform phase shift of the wave, which transforms into visible intensity variations during the propagation through a suitable distance. However, contrary to the classical lens, the bacterial colony is a semi-transparent object, and the light transmission through the colony will be limited, therefore beside the introduced phase shift, the additional amplitude modulation of incoming wave is observed, and the bacterial colony can be treated as amplitude and phase light modulator. Moreover, it was shown, that the intensity distribution in the focal point is more spread or extended in axial and lateral directions than in case of conventional optical lenses. The bacterial colony can also be considered as an optical diffuser, which is affecting the spread of focal point and spatial light intensity variations in the focal plane. Therefore, for the validation of the most general model of the bacterial colonies the phase delay caused by the colony surface roughness: Φ , , where , , (7.20) should be added to the previously described total phase delays expressed by Eq. (7.11), Eq. (7.15), Eq. (7.17) and Eq. (7.18), or be introduced to the amplitude transmittance function of bacteria colony: , , Φ , Φ , . (7.21) This function describes the amplitude and phase properties of a bacterial colony, which are responsible for specific spatial modulation of the illuminating optical wave field. Moreover, the 2D transmission coefficient and the phase delay associated with colony geometry are describing the complex illuminating optical wave field amplitude and phase modulation. 7.3. The Optical System for Analysis of Light Diffraction on Bacterial Colonies The differences in morphology and optical properties of the bacterial colony can be used as foundations for their differentiation and characterization. Moreover, they are also influencing the illuminating optical wave field, what means that the presence of the species-/strains-dependent light transformation on bacterial colony can provide optical signatures, which can be used for bacteria differentiation and characterization. Nowadays, 178 Chapter 7. Advances in Label-Free Sensing of Bacteria by Light Diffraction Phenomenon two bacteria identification systems based on forward-light scattering or diffraction approaches are developed: BARDOT (Bacterial Rapid Detection using Optical scattering Technology) at Purdue University [8-10] and BISLID (Bacteria Identification System by Light Diffraction) at Wroclaw University of Science and Technology [13-18]. There are also some intermediate approaches based on the both BARDOT and BISLID systems [11, 12]. In BARDOT system, no assumption about the type of the illuminating beam is made. However, in each of the colony illumination using either plane wave (collimated beam), spherical divergent or convergent wave illumination, the angular divergence of diffracted optical wave field is different and in different locations from the colony various diffraction patterns are registered. Based on the configuration of the optical correlators carrying out the optical Fourier transform, the type of the illuminating beam can offer significant advantages, which can improve the conditions of the diffraction patterns registration [27]. The BISLID system is based on the optical system with converging spherical wave illumination, which is generated by the transforming lens located before the object plane, where the bacterial colonies are placed. In the proposed system, it is possible to record both the Fresnel and Fraunhofer diffraction patterns, because the converging spherical wave illumination eliminates the need of large observation distances for recording the Fraunhofer pattern. The extended analysis of the converging spherical wave illumination system properties [28] showed that this system allows to compress and distort the observation space along an optical axis into the finite region of the space between the diffracting object and the Fourier transform plane. Moreover, in this optical system, it is possible to control scaling of the registered diffraction patterns, what enables the fitting the lateral size of the diffraction patterns to the size of the matrix of the camera. It should be pointed out, that the optical system with converging spherical wave illumination possesses more advantages comparing to the other Fourier transform systems. The transforming lens, which is placed in front of the object, must be corrected only for a pair of on-axis points to produce the spherical wave and not for all aberrations in the infinity – focal plane points pairs as in configuration with the plane wave illumination. Therefore, the setup with converging spherical wave illumination is simpler, so the level of coherence noises on optical elements is reduced. Moreover, choosing the same size of the lens as the size of the object allows avoiding the bandwidth limitation of the lens. These properties additionally lower the costs of the system construction. 7.3.1. The Optical Wave Field Transformation in Proposed Optical System To understand the main features of the proposed optical system with the converging spherical wave illumination, it is necessary to present the theoretical model of light transformation [13]. For simplicity, let assume that a coherent plane wave Uin.(x0, y0) = A with the amplitude A, propagating along optical axis z perpendicularly to the (x0, y0) plane, falls on the transforming lens L0. It means that the point light source is located at an infinite distance from the transforming lens (see Fig. 7.7). The lens L0 with the focal distance f is transforming the incident plane wave into the converging spherical wave, which can be described as: 179 Advances in Optics: Reviews. Book Series, Vol. 3 Fig. 7.7. Proposed optical system configuration for characterization of bacteria colonies diffraction patterns: L0 transforming lens in (x0, y0) plane, bacteria colonies on Petri dish in (x1, y1) plane, observation plane (x2, y2). , , , Ψ , , ; (7.22) where λ is the wavelength of the incident wave, F = 1/f, P(x0, y0) is a pupil function of the transforming lens, and the function  x , y , p  represents a Gaussian function Ψ , ; (7.23) . Between the lens L0 and the object plane (x1, y1) located in the distance z1 from the lens, the free propagation takes place. Therefore the optical field can be described using the Fresnel diffraction approximation, as follows: U ( x m 1 , y m 1 )  exp ikz m 1   i z m 1     U x m      i x m 1  x m 2   y m 1  y m 2 , y m exp  z   m 1    C  , Z m 1   U ( x m dx  m dy m , , y m ) x m 1  x m , y m 1  y m , Z m 1 dx m dy m   (7.24) where Z m1  1 zm1 . Finally, the wave field illuminating the object plane can be expressed as:   U in ( x1 , y1 )  C  , Z 1   U out . x 0 , y 0  x1  x 0 , y1  y 0 , Z 1 dx 0 dy 0 ,    180      (7.25) Chapter 7. Advances in Label-Free Sensing of Bacteria by Light Diffraction Phenomenon where C(λ, Z1) is a constant characteristic for Fresnel approximation depending on λ and Z1. Additionally, it was assumed that the colony is fully illuminated by the converging spherical wave, therefore its pupil function can be ignored. After simple transformations and substitutions, the optical wave field Uin.(x1, y1) illuminating the bacterial colony can be expressed, as follows: U in ( x1, y1)  i A Z1  F      C , Z1  x1, y1, Z1F  , Z1  F  (7.26) or after simple transformation, as:  f   Z F  A  exp ikz1  x1, y1, 1 ,  f z   Z1  F    1    Uin ( x1, y1)   (7.27) The above expression represents a spherical wave converging towards the plane z = f and the amplitude changes proportionally to the ratio f/(f-z1), what is in agreement with the geometrical optics predictions. When this wave illuminates the single bacteria colony on Petri dish placed in the object plane (x1, y1), its amplitude and phase are modulated by the analyzed object as it was discussed in the previous sections. The contribution of the nutrient medium and Petri dish is limited to the presence of exponential phase shift along the optical axis, as well as to the attenuation of a primary amplitude of the incident wave. The amplitude and phase transformations on bacteria colony of the wave field Uin.(x0, y0), can be simply presented by , , , . (7.28) Similarly, as in the case of the free propagation of the optical field from the lens L0 to the object plane, we are using the Fresnel approximation to obtain scattered wave field in the observation plane:   U in ( x 2 , y 2 )  C 2  , Z 2   U x1 , y1  x 2  x1 , y 2  y1 , Z 2 dx 1 dy 2 .         (7.29) After rearrangement of Eq. (7.29) and appropriate substitutions, the optical wave field in the observation plane (x2, y2) takes a form:      x , y , Z 2 2 2  1  f fAz U in ( x 2 , y 2 )  C  , Z1 , Z 2       ~ x Z y Z   t b ( x1 , y1 )  x1 , y1 , Z f x 2 2; f y  2 2   (7.30) , where ZF ~ Z  Z2  1 . Z1  F (7.31) 181 Advances in Optics: Reviews. Book Series, Vol. 3 The operator … represents the two-dimensional Fourier transform. It can be seen that 0 Eq. (7.30) is describing the Fresnel transform of the bacteria colony amplitude for transmittance. However, there are some important differences between this expression and the conventional Fresnel diffraction formula known from scalar theory of diffraction. Presented above expression should be considered as a Fresnel diffraction formula for tB(x1, y1) alone, and not for entire scattered wave field U.(x1, y1), as it is commonly ~ regarded. Moreover, the parameter Z is not describing the distance to the observation plane, but rather the nature of diffraction pattern (Fresnel or Fraunhofer), which is observed. If the observation plane is shifted to the back focal plane of the transforming lens, then z1 + z2 = f and the parameter Z~  0 . Moreover, the exponential quadratic phase term inside the two-dimensional Fourier transform is eliminated and Eq. (7.30) takes a form of the Fourier transform of the bacteria colony amplitude transmittance alone representing the Fraunhofer diffraction formula:  fA   x , y , Z  t ( x , y ) x Zˆ y Zˆ U ( x f , y f )  U ( x2 , y2 )  C  , Z1, Z 2   f  z  2 2 2 B 1 1 f x  2 ; f y  2 , 1       (7.32) where Z1F 1 1 Zˆ    . zˆ f  z1 Z 1  F (7.33) If the location of the observation plane ranges from the object plane z = z1 to the Fourier transform plane z = f, then, it is possible to observe the Fresnel diffraction pattern of the ~ object. The scale of the patterns depends directly on the value of the parameter Z and indirectly on the relation between the distance z1 and f (see Fig. 7.8). If the observation plane is near the Fourier transform plane, then Z~  0 and the Fraunhofer diffraction pattern of the object can be observed with the scaling factor of Zˆ depending on the distance zˆ  f  z1 . It means that by increasing the distance ẑ , the size of the diffraction pattern is greater until the object is directly behind the lens. If the distance ẑ decreases, the size of the pattern is reducing. Moreover, when the point light source is moved closer to the front focal plane of the transforming lens, then the illuminating beam converges less rapidly, and the Fourier transform plane moves away from the lens. Therefore, the scale changes of the observed diffraction patterns will be larger. In such optical system, the matrix size of the detectors may be smaller due to the possibility of adjusting an appropriate scale of the observed diffraction pattern. However, it should be pointed out, that results reported in [22] have shown that the bacterial colony is evolving over the time, and it can be considered as an optical element with the adaptive light focusing properties as the focusing properties are changing in time. This feature affects the use of Fraunhofer diffraction patterns for bacteria species identification, because the location of the Fourier plane due to the changing of the focal length of the colony, is continuously shifting along the optical axis over the time. Therefore, in the proposed optical method for bacteria species identification based on 182 Chapter 7. Advances in Label-Free Sensing of Bacteria by Light Diffraction Phenomenon diffraction patterns of bacterial colonies, the additional system of bacterial profile determination should be included. Moreover, also the use of Fresnel diffraction patterns of bacterial colonies for their species identification recorded in fixed collection distance is affected by the light focusing properties of bacterial colonies as well because the Fresnel patterns will be shifted along the optical axis for bacterial colonies incubated in different times. To omit this problem, it is necessary to additionally characterize the locations of Fresnel diffraction patterns observation plane for different times of bacterial colonies incubation or the time of incubation should be fixed [18]. This factor should be considered as standardized parameter limiting the efficiency of bacteria species identification by the methods based on analysis of bacterial colony diffraction patterns. Fig. 7.8. The experimental results of the change of the lateral size of Fresnel diffraction patterns in the case of Salmonella Enteritidis colony with decreasing the distance z1:(a) 28 cm; (b) 26.5 cm; (c) 25.3 cm, and (d) 24.5 cm (bacteria colony diameter: approx. 0.8 mm, beam diameter: approx. 1 mm) [13]. 7.3.2. The Configuration of the Experimental Optical System for Bacteria Identification The optical system for recording the Fresnel diffraction patterns of bacterial colonies presented in Fig. 7.9 includes: (1) the laser diode module (635 nm, 1 mW, collimated Thorlabs), (2) beam expander BE (1.5X, Thorlabs), (3) amplitude filters (OD: 0-4.0, Thorlabs) (4) iris diaphragm (diameter: 0-2, 5 cm, Thorlabs) (5) transforming lens L0 (f = 45 cm, Edmund Optics), (6) beam splitter (T:R = 50:50, Thorlabs), (7) holder with the sample of bacterial colonies in Petri Dish integrated with an automatic X-Y-Z translation stage, (8) beamsplitter (T:R = 50:50, Thorlabs), (9) CCD camera (EO-1312, Edmund Optics) with imaging objective (f = 3.5 cm, Edmund Optics) for diffraction patterns recording and (12) computer unit. 183 Advances in Optics: Reviews. Book Series, Vol. 3 The system also contains an additional channel for registration of image of all bacterial colonies on Petri dish and the automatic localization of bacterial colonies grown on the medium. It combines of (6) beam splitter, which enables recording of bacterial colonies on Petri dish in reflection mode, (10) the camera (CMOS, Basler ace) with imaging objective (f = 12 mm, Edmund Optics) and (11) the ring illuminator for uniform illumination of the Petri dish. Fig. 7.9. The experimental BISLD system configuration (description in text). 7.4. Bacteria Identification Based on Fresnel Diffraction Patterns of Bacterial Colonies 7.4.1. The Bacteria Sample Preparation The bacterial samples were prepared in the laboratory of the Department of Epizootiology and Veterinary Administration with Clinic of Infectious Diseases of the Wroclaw University of Environmental and Life Science. Bacteria suspensions of different bacteria species/ strains were first incubated for 18 hours at the temperature of 37 °C. The suspensions in respectively 10-5 and 10-6 dilutions were seeded on the surface of the solid nutrient medium in Petri dishes with Columbia agar (Oxoid), so as to obtain 12-20 colonies per plate, and were again incubated at 26 °C for the next 18 hours. The same solid nutrient medium was used for all bacterial species/strains to omit the initial differentiation and a priori information about their species/strains introduced by their metabolic properties. Fixing the parameters of the incubation process (nutrient medium, temperature and time of incubation etc.) and defined diameter of the colony, guarantees the proper comparison of the bacteria colonies diffraction patterns. Details of the sample preparation and incubation standardization can be found in [13, 17, 18]. 184 Chapter 7. Advances in Label-Free Sensing of Bacteria by Light Diffraction Phenomenon 7.4.2. The Experimental Fresnel Diffraction Patterns of Bacterial Colonies As it was mentioned above, the bacterial colonies exhibit the variety of the morphologies and optical properties among different bacteria species, but also among different strains of the same species. These factors are also influencing the optical wave field transformation on bacterial colonies, manifested by the spatial intensity distribution of the registered Fresnel diffraction patterns of these colonies (see Fig. 7.10). Fig. 7.10. The exemplary experimental Fresnel diffraction patterns of bacterial colonies. Under the visual inspection, it is possible to distinguish the unique features of the diffraction patterns of bacterial colonies among different species and strains, as a different number of the round-shaped intensity maxima or radial-spokes intensity maxima, as well as the presence of the round spot or disc and more complex spatial intensity modulations. The variety of colonies of different bacteria species/ strains exhibit unique properties and diffraction signature. Therefore it is hard to describe the light diffraction on bacterial colonies in details in each case. Therefore, this consideration will be limited to the case of the Staphylococcus aureus (ATCC43300) and Escherichia coli (ATCC35401) colonies (see Fig. 7.11). In case of the S.aureus colonies, the 2D transmission coefficient shows that the light transmission is limited in all regions of the colony with a slightly higher transmission near the colony edges, suggesting that it can be treated as the nearly opaque disc. 185 Advances in Optics: Reviews. Book Series, Vol. 3 Fig. 7.11. The comparison of (A) 2D transmission coefficients; (B) phase-contrast images, and (C) Fresnel diffraction of (I) Staphylococcus aureus and (II) Escherichia coli colonies. Moreover, the phase contrast image demonstrates regular and continuous changes of the intensity contrast, what suggests that it has a convex-shaped profile. In the region near the colony edges, the thickness of the colony is minimal, what is responsible for higher transmission coefficient in this region. In consequence, the diffraction pattern of this colony contains the set of the round-shaped intensity maxima with two strong maxima in the central region of the patterns and weaker maxima in the peripheral regions. This Fresnel pattern is similar to the diffraction patterns characteristic for opaque discs. However, the additional light focusing properties of the convex-shaped colony are affecting the distance between these intensity maxima. On the other hand, in case of the Escherichia coli colony, the two zones with different light transmission can be distinguished in the central and in the peripheral region. However, the central zone has irregular boundaries and contains the concentric spokes-like features, which are observed pointing outwards from the centre of the colony. Moreover, the phase-contrast image of the colony shows that around the central region of the colony with the lowest contrast the crescent-like structures are observed, what can be associated with the process of the colony forming and local inhomogeneity of the internal structure of the colony. The Fresnel pattern of this colony contains two round intensity maxima, but their shape is not as regular as in case of the S.aureus diffraction pattern. It can be associated with the irregular boundaries of the central zone with lower light transmission and irregular shape of the bacterial colony edges. Moreover, the Fresnel patterns include the radial spokeslike features, which presence can also be caused by shape irregularities of the central colony zone with the lowest light transmission or the crescent-like features observed on the phase-contrast image of the colony. It should be pointed out that the bacterial colonies are evolving in time, changing the morphology and the optical properties, and in consequence is also affecting the spatial distribution of the Fresnel diffraction patterns intensity (see Fig. 7.12). 186 Chapter 7. Advances in Label-Free Sensing of Bacteria by Light Diffraction Phenomenon Fig. 7.12. The representation of time-dependent changes in the Fresnel diffraction patterns of the Escherichia coli colony. For longer (36 and 40 hours) incubation times of the Escherichia coli colony, the second circular maximum occurs inside the region of the colony shadow and the diameter of the diffraction rings decreases. This effect can be caused by the change of the size of the bacterial colony, as well as the size of the zones with different 2D transmission coefficients inside the colony. According to the Eq. (7.30), the bacterial colony diffraction pattern can be treated as a Fourier transform of the colony amplitude transmittance function. According to the similarity theorem of the Fourier transform, when the diameter of bacterial colony and diameter of internal zones of the colony with different transmission properties increases with the incubation time, the diameter of the diffraction ring of Fresnel patterns decreases. However, it should be mentioned that some significant influence of the central thickness of bacterial colony on maximal diffraction angle and number of diffraction rings, is observed. Also, the different chemical compositions of the nutrient medium and temperature of incubation cause the changes of bacterial colony morphology, size and its transmission properties. However, after standardization of the bacterial colony incubation conditions: type of nutrient medium, the temperature of incubation and the time of incubation, it is possible to obtain high repeatability of the registered Fresnel diffraction patterns for different colonies of the same bacteria species/strains (see Fig. 7.13). Therefore, preservation of the above-indicated incubation conditions enables the use these optical signatures for bacteria species/strains differentiation. Fig. 7.13. The repeatability of the experimental Fresnel diffraction of Citrobacter freundii colonies. 187 Advances in Optics: Reviews. Book Series, Vol. 3 7.4.3. The Analysis of the Diffraction Patterns It was shown that the visual inspection of the Fresnel diffraction patterns of bacterial colonies enables the differentiation of different bacteria species or strains. However, from the clinical point of view in microbiological diagnosis, it is necessary to obtain quantitative indicators characterizing the accuracy of the bacteria species/strains identification based on the registered diffraction patterns. Evaluation of the system can be carried out using sectional analysis of the diffraction patterns was proposed. In this approach, the Fresnel diffraction patterns of bacterial colonies are partitioning by annularshaped limitation zones (partitioning ring) from which the quantitative and statistical features are extracted. The extraction of the new and interpretable features from the diffraction patterns was preceded using a dedicated macro written in the ImageJ free software (http://rsb.info.nih.gov/ij/) with human interaction for distinguishing the center and edges of the diffraction patterns [29]. Marking of the edges and the center was followed by partitioning each of Fresnel patterns into 10 disjoint rings of the equal thickness. Partitioning into 10 rings was shown to be the best of fixed splits [17, 20]. Then, the normalization process of the Fresnel patterns was performed with use of the standard algorithm for histogram stretching. For each partitioning ring of each pattern the values of the following features were calculated: mean and standard deviation denoting brightness and roughness of the regions of interest, respectively; skewness and kurtosis, relative smoothness, uniformity and entropy [17]. Additionally, the Fresnel diffraction pattern radius was calculated, as it is an important predictor. The selection of features, which are the best for building the classification models, was performed by the use of ANOVA (analysis of variance) [31] and Fisher divergence measure [32] to estimate the features separation possibilities measure. Fisher divergence is also called signal to noise ratio and thus further will be called SNR. The proposed measure denotes possibilities of the given feature to separate various classes (bacteria strains). In the study, several classification models were investigated: LDA (Linear Discriminant Analysis), QDA (Quadratic Discriminant Analysis) and SVM (Support Vector Machine). However, the best results of differentiating the bacteria on the strain level were obtained for QDA and SVM. The cross-validation (CV) was chosen as a classifier performance assessment method. The task of the performance assessment method is to estimate the unknown classification error that will occur after using the classification model on other, independent data sets. CV accomplishes the task by splitting the data set into two disjoint subsets (learning and test sets). The model is built with the application of given feature set (predictors) on the learning set, while its performance is tested on the test set. The procedure is repeated given a number of times, and upon the results, the classification error is estimated. The schema of the proposed Fresnel patterns of bacterial colonies was shown below (Fig. 7.14). The exemplary results of the classification assessment were performed on bacterial colonies of Escherichia coli (PCM O119), Staphylococcus aureus (PCM 2267), Proteus mirabilis (PCM 547), Salmonella Enteritidis (ATCC 13076) and Salmonella typhimurium (ATCC 14028) bacteria. The 250 Fresnel patterns of bacterial colonies were recorded at 188 Chapter 7. Advances in Label-Free Sensing of Bacteria by Light Diffraction Phenomenon the fixed distance from the colony for which the highest accuracy of identification on the bacteria strain level was achieved. The performed analysis (see Table 7.1) gives better results for SVM classification than for QDA, while there is the statistically non-significant difference between SNR and ANOVA feature selection methods on the same data. Fig. 7.14. The schematic of the proposed method of the bacteria identification based on Fresnel diffraction patterns. Table 7.1. Identification results of the optimized analysis. Two feature selection methods (ANOVA and SNR) were used for the features predictive properties ranking. The predictors used in the model building, identification error, multi-class sensitivity and specificity are depicted in the table. Most significant results are marked in bold. Number of features Error [%] Sensitivity Specificity SNR 18 3.7 0.9708 0.9626 QDA ANOVA 18 3.92 0.9791 0.9576 SNR 27 1.34 0.9759 0.9903 SVM ANOVA 27 1.38 0.9751 0.9900 The proposed method enables identification of the bacteria with an error as small as 1.34 %, sensitivity equal 0.9759 and specificity 0.9903. Obtained results indicate that the bacteria identification based on the Fresnel diffraction patterns of bacterial colonies can 189 Advances in Optics: Reviews. Book Series, Vol. 3 provide significant advances in the microbiological diagnosis, because its accuracy is comparable with conventional used biomolecular techniques, but can offer the costs limitation and facilitation of the measurements procedure. 7.5. The Use of the Fresnel Diffraction Patterns of Bacterial Colonies for Evaluation of the Efficiency of Antibacterial Factors The problem of bacteria identification and limitation of the bacteria contamination risk are the most important issues of the contemporary science in the context of increasing bacterial drug resistance. Therefore, there is a need to develop new, faster and more common methods of bacteria detection and identification, antibacterial agents and factors, as well as techniques to characterize their effectiveness against bacteria. Performed experiments have shown that it is possible to use also the Fresnel diffraction patterns of bacterial colonies for examination of the selected physicochemical factors with antimicrobial properties. The investigation was performed on the samples of Yersinia entercolitica (ATCC 23715) colonies, prepared as reported in the previous sections. Three physicochemical factors were used in the study: low temperature (4° C), UV radiation (340-390 nm) and chemical bactericide Skinsept® Pur (Ecolab). Skinsept® Pur in 100 g of active ingredient contains: 46.0 g ethanol (96 % denatured), 27.0 g of isopropyl alcohol; 1.0 g benzyl alcohol and excipients: hydrogen peroxide, purified water. Alcohols cause denaturation of proteins and dissolution of lipids of bacterial membrane, whose continuity can be interrupted, leading to cytoplasm leakage into the external environment and cell death. Skinsept® Pur containing a mixture of alcohols was used to investigate the effect of this agent. Approximately 0.09 g of the product was applied to the colonies. At the low temperature, there is a disturbance in the synthesis of essential compounds needed to carry out the life processes of the bacterial cell, which results in a slower metabolism. For this purpose, colonies of bacteria were placed at 4 ° C ± 0.5 °C for 55 minutes and then further incubated until the measurement. The ultraviolet radiation directly affects the structure of the deoxyribonucleic acid of the bacterial cell. It should be noted, that if UV irradiation does not destroy the bacteria in a way that will prevent them from continuing development, then the genes responsible for the reconstruction of bacterial cells will be activated and further microbial development will be possible. In the experiment, a UVA lamp emitting radiation at the wavelength of 340-390 nm was used. In the sample plane, the radiated power was 923.6 ± 1.99 μW, and the irradiance was 1175.96 ± 2.53 μW/cm2. Colonies of bacteria were illuminated for 40 minutes and then further incubated until the measurement was taken. Each of the applied antibacterial factors affects the morphology and size of the bacterial colonies, however with different efficiency (see Fig. 7.15). Compared to the colonies of the control sample, bacterial colonies treated with selected physicochemical agents have considerably smaller spatial sizes, indicating a slowdown or inhibition of colony development. To quantify the change in the diameter of the colonies treated with these factors to the control sample, the size of these colonies was determined using microscopic images. The obtained results show that, among all studied factors, the greatest reduction in colony diameter occurred with UV radiation. Colonies of bacteria 190 Chapter 7. Advances in Label-Free Sensing of Bacteria by Light Diffraction Phenomenon treated with UV radiation were 64 % smaller than the control colonies. For Skinsept® Pur and low temperature, the colony diameter decreased by 29 % and 9 %, respectively. The greatest inhibition of bacterial colonies has been obtained in samples irradiated with UV radiation. Slowing down the development of bacterial colonies leads not only to limiting their spatial sizes but also to diversify their internal structure. Changing the size of the colonies and their structure affects the spatial distribution of the Fresnel diffraction patterns generated by them, which are closely correlated with the morphological characteristics of the colonies. Based on the scalar diffraction theory, the Fresnel diffraction patterns can be expressed as a Fourier transform function of the amplitude transmittance function of the colony and an additional quadratic phase component strictly dependent on the distance of the observation plane from the objective plane. Therefore, given the properties of the Fourier transform, it is expected that the spatial dimensions of the diffraction spectra of bacterial colonies subjected to the physicochemical properties tested will also change as they change the size of the colonies. According to Fourier's similarity or scaling of the Fourier transform, the change in transverse dimensions of the object will lead to the inverse proportional change of Fourier spectra, of which the special case is the Fresnel spectra. In the case of bacterial colonies, this will be affected by changes in the diffraction patterns diameter, the distance between the outer and inner round-shaped intensity maxima and the width of these maxima. Fig. 7.15. The exemplary of microscopic images (objective: 4×) of Yersinia entercolitica bacterial colonies (incubation time 23h): (A) control sample and samples treated with: (B) low temperature - 4 °C, (C) Skinsept® Pur, (D) UV radiation. In case of the Fresnel pattern of the control colony shown in Fig. 7.16, two main diffraction rings are visible in the center and at the periphery of the Fresnel patterns. The interior of the diffraction patterns is characterized by a specific "reticular" modulation of intensity associated with the internal structure of the colony. On the other hand, in case of colony treated with physicochemical factors, the increasing effectiveness of their action 191 Advances in Optics: Reviews. Book Series, Vol. 3 leads to the inhibition of colonization and formation of colonies with significantly smaller diameter. In consequence, in their Fresnel patterns, the distance between the two major diffraction rings increases. It can be noted that the diameter of the central diffraction ring increases with the increase of the diameter of the colony, what means that its size depends on the stage of development of the colony. Comparing the Fresnel patterns of treated colonies with the pattern of the control colony, there is a gradual decline in the characteristic “reticular” modulation of the intensity of the diffraction patterns. It is worth emphasizing that this effect strengthens with increasing inhibitory effect of the factor under consideration. Fig. 7.16. The exemplary Fresnel diffraction patterns of Yersinia entercolitica bacterial colonies (incubation time 23 h): (A) control sample and samples treated: (B) at low temperature 4 °C, (C) Skinsept® Pur, (D) UV radiation (red dotted lines marked major intensity maxima). Obtained experimental results have shown that the Fresnel diffraction patterns, which spatial distributions are related to the morphology and optical properties of bacterial colonies, are highly sensitive to the induced changes in the colony development. The quantitative analysis of the mean and standard deviation of the pixels intensity in each diffraction pattern partitioning zone extracted in a similar way as in the case of features extraction for bacteria identification have shown that they can be used to characterize differences between diffraction patterns of colonies treated by different antimicrobial factors. These create perspectives on the future use the analysis of the Fresnel diffraction patterns of bacterial colonies for characterization of the minimal inhibitory concentration (MIC), which is the lowest concentration of a drug which prevents visible growth and development of the bacterial colonies, at which this drug has bacteriostatic activity. This examination is commonly used in microbiology for examination of the antimicrobial properties of different drugs or chemical agents and the light diffraction on the bacterial colonies can offer significant improvements and advantages in future microbiological diagnosis. 192 Chapter 7. Advances in Label-Free Sensing of Bacteria by Light Diffraction Phenomenon 7.6. The Perspectives for Exploiting of Light Diffraction on Bacterial Colonies Using Digital Holography Previously described results of the research have shown that diffraction patterns analysis enables the bacteria identification, however, are based on Fresnel patterns recorded in the specific observation plane. In analyzed case, the Fresnel diffraction takes place, the spatial distribution of diffraction patterns is significantly affected by the distance between the sample and detector. Described above technique utilizes light scattering/diffraction in one selected direction and at a fixed distance from the colony, although the spatial distribution of scattering/diffraction patterns is significantly affected by the observation distance. This dependence is characteristic for the Fresnel diffraction patterns, and it is caused by the presence of the quadratic phase factor in the Eq. (7.29). During the single measurement, only one diffraction/scattering pattern can be recorded. However, the diffraction patterns recorded at different distances from the sample can exhibit different unique features depending on this distance. Therefore, it is necessary to perform series of measurements of diffraction patterns in different distances from the colony, what is a time-consuming process. Moreover, the bacterial colony profile can be asymmetric and tilted respectively to the optical axis, and in consequence, the light diffracted on colony will not propagate in-line along the optical axis. Some of these disadvantages can be eliminated using digital holography, which enables reconstruction of the amplitude and phase properties of examined objects, as well as the amplitude and phase patterns of the optical field scattered/diffracted by the object in a chosen observation plane behind the object from one single digital hologram. The preliminary performed experiments by the use of point-source digital in-line holography have shown that digital holography can be used for the characterization of bacterial colonies and can find the potential use for microbiological investigation [21]. To the best of our knowledge, it was the first attempt at characterizing the species-dependent properties of bacterial colonies and their diffraction patterns by digital in-line holography. The performed analysis of the reconstructed amplitude and phase patterns of examined bacterial colonies (Escherichia coli and Staphylococcus intermedius) revealed unique species-dependent optical properties. Moreover, the single measurement digital hologram recording and its numerical reconstruction enabled obtaining a reference database of additional bacterial diffraction signatures from all observation space. In consequence, it allows for the extraction of additional differentiating features, in contrast to the already proposed methods based on single scattering/diffraction patterns recorded in a fixed observation plane. This method can provide new optical discriminators for bacterial species, which can extend the classification vector and improve the bacterial identification accuracy. The comparison of the reconstructed Fresnel patterns obtained with pointsource digital in-line holography microscopy with previously recorded Fresnel diffraction patterns of the same colonies demonstrated that both patterns are highly correlated. The potential of bacteria species differentiation by digital holographic signatures was also demonstrated by means of the Principle Components Analysis of examined optical signatures of bacterial colonies and it was demonstrated that these optical signatures obtained by digital holography exhibit unique species-dependent features. Future research 193 Advances in Optics: Reviews. Book Series, Vol. 3 will be focused on more extended investigation of potential application of digital holographic sensors for different bacteria species/strains characterization. 7.7. Conclusions The light diffraction on bacterial colonies being the macroscopic objects enables noncontact and nondestructive examination and offer significant facilities as no need for advanced and time-consuming sample preparation or the use of additional chemical reagents /fluorescence/immunological markers. Moreover, the bacteria samples can be used for further verification or investigation, what distinguishes this method from others conventionally used in microbiological diagnosis: biochemical or biomolecular. The phenomenon of light diffraction on bacterial colonies grew on solid nutrient media can be used for accurate bacteria identification using the examination of Fresnel diffraction patterns supported by statistical analysis as well as for characterization of the antimicrobial agents. The digital holography technique based on light diffraction phenomenon and numerical reconstruction algorithms also offers significant advantages which can enable the more complex and extended analysis of the optical signatures of bacterial colonies. Acknowledgements This work was partially supported by statutory funds of Wroclaw University of Science and Technology. I.B. is funded by a scholarship (No. 489/2014, Contract No. 0159/E366/STYP/9/2014) of the Polish Ministry of Science and Higher Education. References [1]. M. T. Madigan, J. M. Martinko, J. Parker, Biology of Microorganisms, Prentice Hall, 1997. [2]. National Instititute of Allergy and Infectious Diseases Report, https://www.niaid.nih.gov/sites/default/files/arstrategicplan2014.pdf [3]. S. J. Mechery, X. J. Zhao, L. Wang, L. R. Hilliard, A. Munteanu, W. Tan, Using bioconjugated nanoparticles to monitor E. coli in flow channel, Chemistry - An Asian Journal, Vol. 1, 2006, pp. 384-390. [4]. P. Leonard, S. Hearty, J. Quinn, R. 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Méndez-Vilas, Ed.), Formatex Research Center, 2013, pp. 711-721. [16]. A. Suchwalko, I. Buzalewicz, H. Podbielska, Identification of bacteria species by using morphological and textural properties of bacterial colonies diffraction patterns, Proceedings of SPIE, Vol. 8791, 2013, 87911M. [17]. A. Suchwałko, I. Buzalewicz, A. Wieliczko, H. Podbielska, Bacteria species identification by the statistical analysis of bacterial colonies Fresnel patterns, Optics Express, Vol. 21, Issue 9, 2013, pp. 11322-11337. [18]. A. Suchwałko, I. Buzalewicz, H. Podbielska, Bacteria identification in an optical system with optimized diffraction pattern registration condition supported by enhanced statistical analysis, Optics Express, Vol. 22, Issue 21, 2014, pp. 26312-26327. [19]. S. Nagai, Y. Nishizawa, M. Onodera, S. Aiba, Effect of dissolved oxygen on growth yield and aldolase activity in chemostat culture of azotobacter vinelandii, Journal of General Microbiology, Vol. 66, 1971, pp. 197-203. [20]. J. W. Goodman, Introduction to Fourier Optics, 3rd edition, Robert & Company Publishers, 2005. [21]. I. Buzalewicz, M. Kujawińska, W. Krauze, H. Podbielska, Novel perspectives on the characterization of species-dependent optical signatures of bacterial colonies by digital holography, PLoS ONE, Vol. 11, Issue 3, 2016, 0150449. [22]. I. Buzalewicz, K. Liżewski, M. Kujawińska, H. Podbielska, Degeneration of Fraunhofer diffraction on bacterial colonies due to their light focusing properties examined in digital holographic microscope system, Optics Express, Vol. 21, 2013, pp. 26493-26505. [23]. P. E. Bae, P. P. Banada, K. Huff, A. K. Bhunia, J. P. Robinson, E. D. Hirleman, Biophysical modelling of forward scattering from bacterial colonies using scalar diffraction theory, Applied Optics, Vol. 46, Issue 7, 2007, pp. 3639-3648. [24]. M. A. Bees, P. Andresen, E. Mosekilde, M. Givskov, The interaction of thin-film flow, bacterial swarming and cell differentiation in colonies of Serratia liquefaciens, Journal of Mathematical Biology, Vol. 40, Issue 1, 2000, pp. 27-63. 195 Advances in Optics: Reviews. Book Series, Vol. 3 [25]. H. Kim, A. K. Singh, A. K. Bhunia, E. Bae, Laser-induced speckle scatter patterns in Bacillus colonies, Frontiers in Microbiology, Vol. 5, 2014, 537. [26]. E. Bae, N. Bai, A. Aroonnual, J. P. Robinson, A. K. Bhunia, E. D. Hirleman, Modeling light propagation through bacterial colonies and its correlation with forward scattering, Journal of Biomedical Optics, Vol. 15, Issue 4, 2010, pp. 045001 (1-10). [27]. D. Joyeux, S. Lowenthal, Optical Fourier transform: What is the optimal setup?, Applied Optics, Vol. 21, 1982, pp. 4368-4372. [28]. J. D. Gaskill, Linear Systems, Fourier Transform and Optics, John Wiley & Sons, New York, 1978. [29]. M. D. Abràmoff, P. J. Magalhães, S. J. Ram, Image processing with ImageJ, Biophotonics International, Vol. 11, Issue 7, 2004, pp. 36-42. [30]. A. Suchwalko, I. Buzalewicz, H. Podbielska, Computer-based classification of bacteria species by analysis of their colonies Fresnel diffraction patterns, Proceedings of SPIE, Vol. 8212, 2012, 82120R. [31]. P. Dalgaard, Introductory Statistics with R, Springer New York, New York, 2008. [32]. Feature Extraction: Foundations and Applications (Studies in Fuzziness and Soft Computing) (I. Guyon, S. Gunn, M. Nikravesh, L. Zadeh, Eds.), Springer, 2006. 196 Chapter 8. Integrated Terahertz Planar Waveguides for Molecular Sensing Chapter 8 Integrated Terahertz Planar Waveguides for Molecular Sensing Borwen You and Ja-Yu Lu1 8.1. Introduction Terahertz (THz) waveguides have been developed and basically categorized as the dielectric and metal waveguides with simple media to guide THz waves [1]. For the further waveguide development of molecular sensing applications, the simple waveguide medium is not so efficient to detect the target molecules because of two sensing issues, the poor lateral-field overlap and the power-limited propagation length. Therefore, the waveguide structures composed of multiple layers of dielectrics and metals are critical to achieve the engineering purpose for sensing analytes in a waveguide medium. Eventually, the target analyte is sensitively detected by THz waves based on the efficient interaction in the optimal waveguide length and modal field. The porous dielectrics are commonly the low-loss waveguide media to deliver THz waves for the long-distance transmission because the high attenuation media reduces inside the modal field instead of the air space [2]. The solid-core dielectrics are operated as subwavelength-scaled waveguides to weakly guide THz waves inside the solid media, spreading most of the modal field outside the core, i.e., toward the surrounding air space [3]. Such dielectric waveguides based on large percentages of air space successfully realize the low-loss transmission in THz frequency region and can be applied as the important optical components for THz fiber communication. However, THz fiber mode intensity is so weak without strong interaction ability to detect analytes around the fiber cores. To achieve the sensing purpose, the evanescent field of a THz fiber sensor should be powerful or the sample amount should be large to identify analytes in power absorption [4]. The metal medium in THz waveguides mainly works as the reflective surface to confine THz waves and propagate along the hollow core space. The parallel-plate waveguide (PPWG) is the typical structure and simply assembled by two metal plates to efficiently Ja-Yu Lu Department of Photonics, National Cheng Kung University, Tainan, Taiwan 197 Advances in Optics: Reviews. Book Series, Vol. 3 deliver THz-broadband waves [5]. Although THz-PPWG is an enclosed waveguide structures, the open frame metal surface is also able to guide THz waves as SommerfeldZenneck surface waves [6]. Because THz wave frequencies are considerably lower than the metal plasmon frequencies, THz waves cannot penetrate metals to directly excite surface plasmon polaritons (SPPs). Hence, THz Sommerfeld-Zenneck surface waves propagate in the delocalized manner on metal surfaces, which are difficult to detect those analytes on the metal surfaces with very small across sections. Tightly confined and powerful surface waves in THz frequency are the solution, i.e., in the high field intensity, to achieve the sensitive detection purpose for analytes on a metal surface. However, surface-confined waves are commonly suffered from very strong attenuation at the waveguide medium without powerful interaction on the analytes. The metamaterial concept currently shows it is possible to flexibly tune THz wave confinement and the longest propagation length based on certain periodic metal structures, and the molecular sensing ability can be enhanced via the periodic metal structures due to the distinctly strong THz resonance or interference. In this chapter, integrated planar THz waveguides can be used for bio-chemical sensing applications when the composed metal and dielectric layers are engineered to control THz waves with the sufficient propagation lengths and the optimal lateral fields. The presented THz waveguide sensor basically contains three main parts, including the waveguide, superstrate, and analyte. In the chapter, the waveguide sensing mechanism is investigated form the waveguide transmission spectrum of the evanescent field. The detection sensitivity is significantly affected by the decay length of the evanescent waveguide mode, which is determined by the refractive indices or thicknesses of the waveguide and superstrate layers. Two kinds of THz waveguides are presented in this chapter, including the metal-grating and -rod-array structures, respectively, for THz-frequency- and -phasesensitive waveguide sensors. The detection sensitivity of a THz planar integrated waveguide sensor based on the periodical metal structures can be optimized by adjusting their geometrical parameters of metal, instead of modifying the refractive index of the waveguide/superstrate layers with various dielectric materials. 8.2. THz Frequency Sensitive Detection 8.2.1. Waveguide Configuration and Terahertz Spectral Characterization The waveguide configuration with THz-frequency sensitive response in molecular sensing is illustrated in Fig. 8.1 and demonstrated as a THz hybrid plasmonic waveguide [7, 8]. There are two planar constructions, containing a 220 mm-long dielectric ribbon and a 50 mm-long metal grating. The dielectric ribbon is made of the polyethylene (PE) material with a 15 mm width, a 220 mm length and a 20 m thickness. Because the ribbon thickness is smaller than the diffraction-limited-beam size of the guided THz waves (0.1-1 THz), the modal field range along the Y axis is not confined to propagate, resembling a THz plastic-wire waveguide with strong evanescent powers outside the core [3]. Such the weak-confined THz wave propagation is performed in the 17 cm-long PE ribbon after the input end, and then interacts the attached metal grating, performing as the 198 Chapter 8. Integrated Terahertz Planar Waveguides for Molecular Sensing hybrid THz plasmonic waveguide (Fig. 8.1). The metal grating is considered as a metallic diffraction grating because the structural sizes and an operated field wavelength are equivalent. The metal grating is prepared from periodically perforated slits on one brass sheet, where the structural period and slit width are, respectively, 1.5 and 1 mm. The brass gratings with three different thicknesses (100, 200 and 400 m), and two different slit widths (1 and 0.5 mm) are experimentally measured in THz spectroscopy to optimize the power transmission and field confinement (Y-axis) at the integrated waveguide section, i.e., the metal grating waveguide in Fig. 8.1. Contrarily, THz field along the waveguide width (X-axis) is ignored in the study because the width is sufficiently larger than that of input THz wave beam size, corresponding to a beam divergence along an unlimited axis without boundary. Fig. 8.1. A THz hybrid plasmonic waveguide (reprinted from [7]). THz wave polarization along the ribbon waveguide is consistent with that along the metal grating to smoothly deliver THz waves to perform a hybrid plasmonic waveguide at the overlapping section. Basically, a dielectric ribbon waveguide can support transverse magnetic (TM)-polarized THz waves while the electric field oscillation of the coupled waves is perpendicular to the ribbon surface [Fig. 8.1]. The proposed hybrid plasmonic waveguide consequently enables the THz wave transmission that are straightforwardly coupled from the PE ribbon. The TM-polarized modal field to enter the metal grating section are stabilized via the 170 mm-long propagation on a PE ribbon, where a large portion of waveguide mode is in the air cladding. When THz waves are illuminated on the metal grating from the air cladding of a ribbon waveguide, partial power transmits and reflects due to the mismatch in modal size or waveguide refractive index. The reflected THz waves from the meatal grating follows the momentum conservation relation,    K in  K   K R , (8.1) where the vectors of Kin, KR and Kare the propagation constants of the input, reflected THz waves and the wave vector of a metal grating respectively. The grating wave vector, K, equals 2m/ where m and  are, respectively, the Bragg diffraction order and a structural period. The directions of propagation constants, Kin and KR, are opposite but 199 Advances in Optics: Reviews. Book Series, Vol. 3 have the same value, 2neff/C where , C and neff are, respectively, THz wave frequency, the light speed in a vacuum and an effective waveguide refractive index. Therefore, the diffraction grating can reflect THz waves exactly at Bragg frequencies in different orders, derived as mC/2neff based on the momentum conservation relation. Fig. 8.2 (a) illustrates THz power transmittance of the 50 mm-long metal grating at different metal thicknesses. The transmittance is measured from the transmission power behind of the 220 mm-long ribbon waveguides with and without attaching the metal grating. The 100 m-thick grating waveguide has the largest transmission spectrum and highest transmittance, comparing to those of the 200 and 400 m-thick gratings. It means the wave transmittance along the 200 and 400 m-thick gratings are obviously restricted, only delivering low frequency waves, respectively, less than 0.285 and 0.250 THz. There are two transmission dips around 0.3 and 0.4 THz for all the three gratings. The low transmittance feature is caused from Bragg reflection among the periodical slits of the metal grating under the phase-matching condition, which are the 3rd- and 4th-order Bragg frequencies for the 1.5 mm structural period. For increasing the metal thickness, the power distinction at the spectral dip increases and the related dip frequency is also red shifted (Fig. 8.2 (a)). The measured results show the 3rd- and 4th-order transmission dips for the 100 m thick grating waveguide are, respectively, at 0.3 and 0.4 THz, exhibiting shallow spectral depths. For the 200 m-thick grating, the 3rd- and 4th-order transmission dips are shifted to 0.296 THz and 0.396 THz with lower transmittance, about 0.005 and 0.002, respectively. When the metal thickness is increased to 400 m, the 3rd- and 4th-order transmission dips are further red shifted to 0.280 THz and 0.380 THz, with the lowest transmittances about 0.003 and 5×10-5, respectively. The power-decrement and red-shift effects of the Bragg-reflection waves for the large-thickness gratings are both resulted from the raised scattering cross section [9] because the large slit depth (or the increased metal thickness) causes strong scattering and deflects the waves with THz frequency lower than the Bragg frequency. Fig. 8.2. Transmittance of different 50 mm-long metal gratings with a 1.5 mm structural period, having (a) the same slit width of 1 mm in different metal thicknesses; (b) the same metal thickness of 0.2 mm with different slit-widths (reprinted from [7]). 200 Chapter 8. Integrated Terahertz Planar Waveguides for Molecular Sensing Besides of the grating thickness to affect the waveguide spectrum, two different slit widths of a 200 m-thick grating are observed in the study. Fig. 8.2 (b) shows the grating waveguide transmittance for the slit widths of 1.0 and 0.5 mm based on the same structural period of 1.5 mm. The transmittances at 0.296 and 0.396 THz are clearly raised about one order of magnitude when the 1.0 mm-slit width reduces to 0.5 mm. This indicates that the wide slit width causes the large scattering cross section, resulting in the reduced transmittance. Such low transmittance also represents the large slit width of the grating waveguide makes high evanescent power transferred from the ribbon waveguide mode into the THz surface plasmon polariton (SPP) modes that are confined on the periodical metal structure. Therefore, suitably tailoring the geometrical parameters of the metal grating at the thickness and slit width enables the optimal coupling efficiency of the SP modes along this THz hybrid plasmonic waveguide. 8.2.2. Integration of a Superstrate and the Sensing Method THz waves generally cannot be confined to a general metal surface with the surface plasmons because THz frequency is much lower than that of the intrinsic plasmon frequency of a metal. Periodical structures on a metal surface, such as 2D hole arrays [10], periodic slits [11], and various patterns of metamaterials [12, 13], have been demonstrated as THz spoof surface plasmons (THz-SSPPs) and thus enhance lateral field confinement. The THz-SSPPs can be generated at the grating structure of the THz hybrid plasmonic waveguide and have the features of the tightly lateral confinement, long transmission lengths, and distinct spectral dips related to the refractive index of the analyte, which are the critical specifications of a sensitive waveguide sensor. Those THz propagation waves on the hybrid waveguide are generally called as THz surface plasmonic waves (SPW) because of the optical performances in wave guidance, local field resonance and surface field confinement. THz-SPWs are generated by transferring the plastic ribbon waveguide modes to THz-SSPPs by means of the integrated diffraction metal grating structure [14, 15]. The generated THz-SPWs can be subwavelength confined to propagate on a 50 mm-long grating metal surface, and resonantly reflected under the phase matching condition of Eq. (8.1). Fig. 8.3 schematically illustrates the side view of a hybrid plasmonic waveguide for THz wave sensing. The diffraction grating is made of a 200 m thick brass with a 1.5 mm structural period, including air and brass sections with lengths of 1.0 and 0.5 mm, respectively. The evanescent field of a THz-SPW can be sensitively modified by the attached analytes on a superstrate, covering the metal grating. Such sensing scheme enables THz-SPW interacting the analytes on the grating for a sufficiently long distance to generate obvious spectral response for sensing applications. To test the sensing capability of the hybrid plasmonic waveguide based on the THz-SPW resonance, PE-film superstrates with thicknesses of 20, 50, and 90 m are attached to the grating surface. Fig. 8.4(a) shows the transmitted spectrum of the hybrid plasmonic waveguide, attached with various superstrate thickness. The original spectral dip at 0.38 THz for the blank hybrid plasmonic waveguide obviously shifts to the low-frequency range while the superstrate is attached on the grating. However, the spectral shift of the 3rd-order SPW resonance at 0.296 THz does not occur because the 0.296 THz modal field is not efficiently coupled to the metal grating to form the THz-SSPPs. In the low Bragg 201 Advances in Optics: Reviews. Book Series, Vol. 3 resonance mode shown in Fig. 8.2(a) (i.e., 1st- and 2nd- Bragg order), the modal field is dominated by the TM modes of the ribbon waveguide to directly pass through the outer region of the metal grooves without being modulated by the metal grating. Thus, the surface wave of 0.296 THz directly propagates along the attached PE film with weak resonance reflection by the metal grating. Contrarily, a large portion of the modal field for the 4th-order Bragg resonance at 0.380 THz is confined as THz-SSPPs inside the metal grating, and a small portion of the modal field evanesces in the air cladding with a subwavelength modal tail strongly interacting with the covered superstrate. The Bragg resonance reflections of THz-SSPPs are greatly influenced by the effective refractive index of the covered thin film because of the waveguide lateral field matching to the superstrate thickness. Therefore, the frequency of the 4th-order SPW-Bragg resonance, 0.380 +/– 0.020 THz, can be completely modified when the effective refractive index of the waveguide is changed by the attached superstrate. Based on the phase matching condition, the resonant frequency is defined in Eq. (8.2) and inversely proportional to the effective refractive index of the waveguide. ν mC . 2  n eff  Λ (8.2) Fig. 8.3. Molecular sensing scheme of a THz hybrid planar plasmonic waveguide (reprinted from [8]). Fig. 8.4 (b) summarizes the spectral positions of THz-SPW resonance, responding from the 20, 50 and 90 m thick superstrates on the grating, respectively, at 0.318, 0.281, and 0.263 THz. These spectral positions show the effective refractive indices of waveguide increase due to the additional superstrate coverage. As shown in Fig. 8.4 (c), the effective refractive index of a blank grating is 1.05 and raises to 1.25, 1.42, and 1.51, respectively, for 20, 50 and 90 m thick superstrates. The effective waveguide index increment with the superstrate thickness is determined from the power-occupied ratio of the modal field inside each superstrate along the Y-axis. The effective index can thus be estimated by the formula, neff = (1 – ).nair + nPE, where nairandnPE represent the volume ratio of the waveguide field occupied in a superstrate, refractive indices of air and PE-film superstrate, respectively. The occupied ratios of the resonant THz-SPWs in the 2050and 90 m thick superstrates are estimated as 0.5, 0.8, and 1.0, respectively, as shown in Fig. 8.4(d). The overall power distribution along the Y-axis outside the grating can be 202 Chapter 8. Integrated Terahertz Planar Waveguides for Molecular Sensing clearly covered by the 90 m thick superstrate, which leads the effective waveguide index to approach the refractive index of a PE material in THz frequency range [16]. Furthermore, the knife-edge measurement of the waveguide modal field expresses the power distribution along the X-axis of the hybrid waveguide is about 2 mm whatever the PE film is attached or not, representing the superstrate attachment is critical to THz-TM modal field confinement along the lateral dimension of Y-axis, not the waveguide width dimension in X-axis. Fig. 8.4. (a) Power transmission spectra for various thicknesses of PE films integrated to the metal grating, showing the performed (b) resonant frequencies, (c) relating effective refractive indices of the waveguide, and (d) the occupied power ratios inside each PE thin film (reprinted from [8]). The evanescent field of the propagated THz-SPWs is significantly confined to interact the analytes on the superstrate based on the Bragg resonant dip in a transmission spectrum. The decay lengths of the 4th-order Bragg resonance for various PE-film superstrates on the metal grating can be estimated from the standard PE film thickness (d) and the occupied field ratio () inside the PE films as shown in Fig. 8.4 (d). The lateral decay length (Y) of waveguide field is defined in the inset of Fig. 8.5 (a) and can be calculated from the relation, Y = d/. Fig. 8.5 (a) shows the calculated decay lengths of the resonant THz-SPWs at 0.318, 0.281, and 0.263 THz are approximately 40 m (~/21), 60 m (~/16), and 90 m (~/12) apart from the metal-grating surface in the Y direction, respectively. The evanescent decay lengths of THz-SPWs can also be obtained from the waveguide transmittance (T) based on the relation, T = (ꞏ.e-L)+(1-), where L denote the absorption coefficient (~1 cm-1) [16] and the PE-film superstrate length of 50 mm, respectively. The occupied field ratio ()of the guided THz-SPWs is thus expressed as  = (1- T)/(1-e-L). The measured transmittance T of a PE film in 0.160 ~ 0.280 THz is obtained from the transmission power in Fig. 8.4(a) and the decay lengths are then estimated, as shown in Fig. 8.5 (b). The estimated minimal decay lengths of the delivered THz-SPWs for PE thicknesses of 20, 50, and 90 m are approximately 40, 60, and 90 m (Fig. 8.5 (b)), respectively, which are approximately consistent with the measured results in Fig. 8.5 (a). The spectral ranges of the best confined THz-SPWs with the minimal decay 203 Advances in Optics: Reviews. Book Series, Vol. 3 length at the 4th-order Bragg resonance are around 70 GHz within 0.250~0.318 THz, 0.210~0.281 THz and 0.190~0.263 THz for 2050and 90 m thick PE films, respectively. It means THz-SSPPs are excited within these spectrum ranges, performing the best field confinement and the sensitive response of spectral shift for the ambient index variation. Fig. 8.5. (a) The decay lengths of the 4th-order resonant THz-SPW for different thicknesses of PEfilm superstrate on the grating. (inset) The definition of the decay lengths of THz-SPWs; (b) Frequency-dependent decay lengths of guided THz-SPWs for different thicknesses of PE-film superstrate (reprinted from [8]). 8.3. Phase Sensitive Detection 8.3.1. Waveguide Configuration and Terahertz Spectral Characterization The waveguide configuration with THz-phase sensitive response in molecular sensing is illustrated in Fig. 8.6 and demonstrated as a metal-rod-array (MRA)-based THz plasmonic waveguide [17]. The MRA-structural planar waveguide medium is composed of the uniform metal rods with 2D periodic arrangement. The MRA structure period () is determined from a rod diameter (D) and an air gap size (G). The rod diameter and height are, individually, 160 µm and 1 mm, considered as the structural unit of a MRA. The 1 mm-thick MRAs have sufficiently large cross section for the input THz beam, and applicable in the edge-coupled configuration as one slab waveguide. The propagation length of the MRA-based waveguide is 30 rows of MRA along the Y-axis, and the polarization of the input THz waves is in the X-direction, as shown in Fig. 8.6 (a) and perpendicular to the rod axis [18]. The MRA width is approximately 9 mm along the X-axis and considerably larger than the 1 mm-long rod. For the MRA slab-waveguide, THz wave divergence in the Z-axis would be confined, but a metal blade should be placed ahead of the input end of the MRA to prevent the detection of leaky and scattered THz waves before the stabilized modal field (Fig. 8.6 (a)). 204 Chapter 8. Integrated Terahertz Planar Waveguides for Molecular Sensing Fig. 8.6. (a) MRA waveguide configuration. Microscopic photos in the top view for the (b) 420 µm-and (c) 620 µm- MRAs. Microscopic photos in the side view for the (d) 420 µm-and (e) 620 µm- MRAs (reprinted from [17]). The MRA is fabricated from the cylinder polymer rods with a periodical arrangement in a square array, which is constructed through bottom-up 3D micro-stereolithography using a UV curable photopolymer [19, 20]. The high aspect ratio of a MRA cannot be prepared from the traditional mechanical or 3D printing methods. After the micro-stereolithography process, a 100 nm-thick aluminum metal film is deposited on the surface of polymer rods based on the sputter coating method. The coated metal thickness is larger than that of the skin depth of the invasive THz waves in 0.1-1 THz [21]. Figs. 8.6 (b) and 8.6 (c) show the fabrication results of MRAs for the top-view photographs of the 420 and 620 µm- MRA, respectively. Obviously, this micro-stereolithography fabrication method makes the periods along the X- and Y-dimensions approximately equal. Figs. 8.6 (d) and 8.6 (e) illustrate the side-view photographs of the MRAs, showing the straightness and uniformity of each rod. Figs. 8.7 (a) and 8.7 (b), respectively, show the normalized transmission spectra of the 420 and 620 µm- MRA waveguides. There are two transmission bands for these two MRA structures in 0.1-0.6 THz. The transmittance of 620 µm- MRA is obviously higher than that of the 420 µm- MRA because of the higher air-filling ratio among the rods. The rejection bands in Fig. 8.7 are resulted from the destructive interference of multiple reflections among the metal rods while THz waves enter the 30 rows of MRA. The central frequency of the rejection band is consistent to the Bragg reflection principle based on the equation of c/2n,where c, n, and are the light speed in vacuum, an effective refractive index, and a MRA period, respectively. The rejection band of the 420 µm- MRA ranges from 0.284 THz to 0.425 THz with a 141 GHz bandwidth (Fig. 8.7 (a)). For the 620 µm- MRA, the rejection band shifts to the lower frequency range, comparing to that of 420 µm- MRA, and ranges from 0.24 THz to 0.27 THz (Fig. 8.7 (b)). The spectral performance of two different MRA periods is consistent to those calculated results, using the finite-difference time-domain (FDTD) method. 205 Advances in Optics: Reviews. Book Series, Vol. 3 Fig. 8.7. Measured transmittance of (a) 420 µm-, and (b) 620 µm- MRAs (reprinted from [17]). 8.3.2. Integration of a Superstrate and the Sensing Method To apply the THz plasmonic MRA waveguide for the molecular sensing applications, one superstrate is required to be attached on the top of the rods with the solid analytes. The PP superstrates are full covered on the top surfaces of the 420 and 620 µm-MRA structures. The superstrates have the same width of 9 mm but different lengths of 13 and 18 mm, respectively, for 420 and 620 µm-MRAs. PP superstrates integrated to 420 and 620 µm- MRAs are discussed in this section for different thicknesses, including 30, 50, 70, and 90 µm. Fig. 8.8 (a) illustrates the transmitted THz electric field oscillations (E) of the 420 µm-MRA waveguide integrated with various PP superstrate thicknesses. The waveform of the blank device is obviously changed when the PP-superstrate is top integrated on the waveguide. The waveform main peaks shift as the superstrate thickness increases from 30 to 90 µm, where the main peaks for the 30, 50, 70, and 90 µm-thick superstrates are located at 19.8, 24.3, 24.8, and 29.3 ps, respectively. Such apparent time-domain shift of the waveform originates from the phase retardation along the PP film superstrate. Fig. 8.8. THz waves propagate through a 420 µm- MRA waveguide with and without attaching PP superstrates with various thicknesses: (a) Electric field oscillations, and (b) Power spectra (reprinted from [17]). 206 Chapter 8. Integrated Terahertz Planar Waveguides for Molecular Sensing The corresponding transmission spectra (|E|2) of the electric field oscillation of the PP superstrate integrated 420 µm-MRA are illustrated in Fig. 8.8(b). The rejection band for each PP superstrate thickness is approximately in 0.284-0.425 THz without obviously change, but the transmission power of the rejection and transmission bands increases as the thickness of the PP superstrate increases. Fig. 8.9(a) summarizes the peak power (|Epeak|2) at the low- and high-frequency transmission bands, which are denoted as 1st and 2nd peaks, respectively, for different superstrate thicknesses. The peak power in the transmission band gradually increases with a slight sinusoidal fluctuation as the superstrate thickness increases. The proportionally increasing effect between the transmission peak power and the superstrate thickness implies that the partial THz power of the confined modal field at the MRA-air cladding interface is coupled toward the aircladding region via the PP superstrate and then the interference interaction inside the MRA structure decreases. It also means the partial transmitted power that originates from the constructive and deconstructive interference of MRA is guided in the air-cladding space when a PP superstrate is attached to the top of the MRA structure. Fig. 8.9(b) schematically illustrates the power distribution of THz plasmonic wave guided on the 420 µm-MRA waveguide with a PP superstrate thickness larger than 90 µm. A large fractional power is distributed in the air-cladding region with a decay length more extended than that of the blank device, thereby increasing the THz power transmission. Fig. 8.9. (a) The power transmission of the peak power at the low- and high-frequency bands, respectively, denoted as the 1st and 2nd peaks for different PP superstrate thicknesses on a 420 µm- MRA; (b) Schematic description about the Z-axial power distribution of a 420 µm- MRA, integrated by a PP superstrate thickness larger than 90 µm (reprinted from [17]). Figs. 8.10 (a) and 8.10 (b) respectively show the measured THz time-domain waveforms and the corresponding transmitted power spectra for the 620 µm- MRA waveguide integrated with different PP superstrate thicknesses. The measured waveforms in Fig. 8.10 (a) are quite similar, except of the broadening oscillations. A continuous timedelay shift can thus be observed, where the second electric field peak are taken as the example in observation and displayed in the dashed lines. The correlating power spectra of the electric field oscillations show the MRA rejection and transmission bands still exist 207 Advances in Optics: Reviews. Book Series, Vol. 3 at similar spectral positions for attaching all thickness conditions. Fig. 8.11 (a) summarizes the peak powers of the 1st and 2nd transmission bands for different thicknesses of superstrates to integrate the 620 µm- MRA waveguide. The peak power obviously decreases even with a slight sinusoidal fluctuation as the superstrate thickness increases, contrary to the result of the 420 µm- MRA waveguide. It represents the extended decay length of the blank 620 µm- MRA waveguide becomes more concentrated inside the MRA after integrating a thick superstrate. In other words, the superstrate top conjugated on the 620 µm- MRA waveguide can confine the extending power in the air-cladding region toward the MRA structure. This phenomenon results in a more fractional THz power both inside the PP superstrate and the MRA structure to attenuate the transmission power. Fig. 8.11(b) schematically shows the modal power distribution of the superstrate integrated the 620 µm- MRA waveguide. Most of the modal power immerses inside the 620 µm- MRA structure and only a small amount of the modal power evanesces to the air-cladding region. The strong interference interaction is eventually reserved inside the MRA structure, like the blank waveguide condition. The transmission peak power variations represent a certain thickness of a PP superstrate integrated on a MRA waveguide certainly changes Z-axial modal power distributions (Figs. 8.9 (a) and 8.11 (a)). Because the lateral power distributions are different between the two MRAs, their detection sensitivities to detect analytes on the superstrate are certainly different. Fig. 8.10. THz waves propagate through a 620 µm- MRA waveguide with and without attaching PP superstrates with various thicknesses: (a) Electric field oscillations; (b) Power spectra (reprinted from [17]). The waveform variations in Figs. 8.8 (a) and 8.10 (a) express that the phase retardations of THz electric field oscillations interacting the superstrates are approximately proportional to the thickness variation. Figs. 8.12 (a)-8.12 (d) summarize the phase retardations induced by the 30, 50, 70, and 90 µm-thick PP superstrates attached on the 420 and 620 µm- MRA waveguides at frequencies of 0.520, 0.424, 0.322, and 0.226 THz, respectively. The normalized phase retardation () is obtained by comparing the phases of the transmitted THz wave with and without attaching superstrates and divided by the waveguide lengths. All the phase retardations at the four THz frequencies and along the two different MRAs are approximately proportional to the PP film 208 Chapter 8. Integrated Terahertz Planar Waveguides for Molecular Sensing thicknesses. The slopes of linearly fitting curves represent the phase detection sensitivities of the two MRA waveguides at different frequencies. The phase retardation contributed by a PP-film superstrate per micrometer thickness can be estimated from the linearly fit slopes. Fig. 8.11. (a) The power transmission of the peak power at the low- and high-frequency bands, respectively, denoted as the 1st and 2nd peaks for different PP superstrate thicknesses on a 620 µm- MRA; (b) Schematic description about the Z-axial power distribution of a 620 µm- MRA, integrated by a PP superstrate thickness larger than 90 µm (reprinted from [17]). Fig. 8.12. PP superstrate induced phase retardations on the 420 and 620 µm- MRA waveguides at different THz frequencies: (a) 0.520 THz; (b) 0.424 THz; (c) 0.322 THz, and (d) 0.226 THz; (e) Sensitivities of phase change detection (reprinted from [17]). Fig. 8.12 (e) summarizes the phase detection sensitivities at different THz wave frequencies for the two MRA waveguides. The sensitivity is approximately proportional to THz frequency in 0.20-0.55 THz. Obviously, the phase detection sensitivity of the 620 µm-MRA waveguide for different superstrate thicknesses is superior to that of the 420 µm-waveguide above 0.226 THz. The difference in phase detection sensitivity between the 420 and 620 µm-MRAs are resulted from different lateral power 209 Advances in Optics: Reviews. Book Series, Vol. 3 distributions of the two superstrate-integrated MRA waveguides (Figs. 8.9 (b) and 8.11 (b)). For the superstrate-integrated 620 µm-MRA waveguide, the lateral modal field has a considerably longer optical path in the 30 rows of MRA because most of the waveguide power is guided inside the MRA structure. Thus, the increased optical-pathdifference (OPD) induced by the superstrate-thickness increment per micrometer (Fig. 8.12 (b)) on the 620 µm-MRA waveguide promotes the phase retardation. Contrarily, most of the modal power guided on the superstrate-integrated 420 µm-MRA waveguide extends toward the air-cladding region, thereby reducing the optical path in the 30 rows of MRA. Consequently, the superstrate-induced OPD per micrometer in the multiple reflections of the 420 µm-MRA is smaller than that of the 620 µm- MRA. 8.4. Conclusions THz planar waveguides are experimentally studied based on the metal grating and rodarray structures, and further integrated with dielectric superstrates for the molecular sensing purpose. The metal-grating-based THz planar waveguide performs the frequencysensitive response to detect analytes on the superstrate because the generated THz-SSPPs in THz-SPWs are not only subwavelength confined to the metal surface but also delivered over a long distance with resonant reflection by the periodic metal structure. THz-SPW resonance follows the Bragg principle, and the transmission spectrum depends on the ambient refractive index of the grating. For the MRA-based THz planar waveguide, analytes on the superstrate can be sensitively detected and monitored from wave phase change of a THz electric field oscillation, categorized as a phase-sensitive THz planar waveguide sensor. An MRA-based THz plasmonic waveguide can be engineered via the interspace for the suitable modal field to integrate a superstrate, which has a significantly large optical path to interact analytes and is highly sensitive to the phase variation of the surrounding analytes. The superstrate integrated in the MRA or metal grating THz waveguides can be applied for loading various molecules in the thin-film or particle states. Such analyte-loaded superstrates can also be considered as the biochips or lab-on-a-chip to be detected by THz waves. Such detectable OPDs are considerably smaller than THz coherent length and valuable to investigate intermolecular attraction, perturbed by THz electromagnetic waves. Acknowledgements This work was supported by the grants in Ministry of Science and Technology of Taiwan (MOST 104-2221-E-006-163-MY3) and Japan Society for the Promotion of Science (JSPS), Grants-in-aid for scientific research (KAKENHI, JP17K45678). References [1]. S. Atakaramians, S. Afshar V., T. M. Monro, D. Abbott, Terahertz dielectric waveguides, Adv. Opt. Photonics, Vol. 5, Issue 2, 2013, pp. 169-215. 210 Chapter 8. Integrated Terahertz Planar Waveguides for Molecular Sensing [2]. S. Atakaramians, S. Afshar V., H. Ebendorff-Heidepriem, M. Nagel, B. M. Fischer, D. Abbott, T. M. Monro, THz porous fibers: design, fabrication and experimental characterization, Opt. Express, Vol. 17, Issue 16, 2009, pp. 14053-14062. [3]. L.-J. Chen, H.-W. Chen, T.-F. Kao, J.-Y. Lu, C.-K. Sun, Low-loss subwavelength plastic fiber for terahertz waveguiding, Opt. Lett., Vol. 31, Issue 3, 2006, pp. 308-310. [4]. M. Walther, M. R. Freeman, F. A. Hegmann, Metal-wire terahertz time-domain spectroscopy, Appl. Phys. Lett., Vol. 87, Issue 26, 2005, 261107. [5]. R. Mendis, D. Grischkowsky, Undistorted guided-wave propagation of subpicosecond terahertz pulses, Opt. Lett., Vol. 26, Issue 11, 2001, pp. 846-848. [6]. T.-I. Jeona, D. Grischkowsky, THz Zenneck surface wave (THz surface plasmon) propagation on a metal sheet, Appl. Phys. Lett., Vol. 88, Issue 6, 2006, 061113. [7]. B. You, J.-Y. Lu, W.-L. Chang, C.-P. Yu, T.-A. Liu, J.-L. Peng, Subwavelength confined terahertz waves on planar waveguides using metallic gratings, Opt. Express, Vol. 21, Issue 5, 2013, pp. 6009-6019. [8]. B. You, J.-Y. Lu, T.-A. Liu, J.-L. Peng, Hybrid terahertz plasmonic waveguide for sensing applications, Opt. Express, Vol. 21, Issue 18, 2013, pp. 21087-21096. [9]. J. G. Rivas, M. Kuttge, P. H. Bolivar, H. Kurz, J. A. Sánchez-Gil, Propagation of surface plasmon polaritons on semiconductor gratings, Phys. Rev. Lett., Vol. 93, Issue 25, 2004, 256804. [10]. C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernandez-Dominguez, L. Martin-Moreno, F. J. Garcia-Vidal, Highly confined guiding of terahertz surface plasmon polaritons on structured metal surfaces, Nat. Photonics, Vol. 2, Issue 3, 2008, pp. 175-179. [11]. W. Zhu, A. Agrawal, A. Nahata, Planar plasmonic terahertz guided-wave devices, Opt. Express, Vol. 16, Issue 9, 2008, pp. 6216–6226. [12]. C. R. Williams, M. Misra, S. R. Andrews, S. A. Maier, S. Carretero-Palacios, S. G. Rodrigo, F. J. Garcia-Vidal, L. Martin-Moreno, Dual band terahertz waveguiding on a planar metal surface patterned with annular holes, Appl. Phys. Lett., Vol. 96, Issue 1, 2010, 011101. [13]. A. I. Fernández-Domínguez, E. Moreno, L. Martín-Moreno, F. J. García-Vidal, Terahertz wedge plasmon polaritons, Opt. Lett., Vol. 34, Issue 13, 2009, pp. 2063-2065. [14]. G. Nemova, R. Kashyap, Fiber-Bragg-grating-assisted surface plasmon-polariton sensor, Opt. Lett., Vol. 31, Issue 14, 2006, pp. 2118-2120. [15]. R. Kashyap, G. Nemova, Surface plasmon resonance-based fiber and planar waveguide sensors, J. Sens., Vol. 2009, 2009, 645162. [16]. J. W. Lamb, Miscellancous data on materials for millimetre and submillimetre optics, Int. J. Infrared Millim. Waves, Vol. 17, Issue 12, 1996, pp. 1997-2034. [17]. B. You, C.-C. Peng, J.-S. Jhang, H.-H. Chen, C.-P. Yu, W.-C. Lai, T.-A. Liu, J.-L. Peng, J.-Y. Lu, Terahertz plasmonic waveguide based on metal rod arrays for nanofilm sensing, Opt. Express, Vol. 22, Issue 9, 2014, pp. 11340-11350. [18]. A. Mazhorova, J. F. Gu, A. Dupuis, M. Peccianti, O. Tsuneyuki, R. Morandotti, H. Minamide, M. Tang, Y. Wang, H. Ito, M. Skorobogatiy, Composite THz materials using aligned metallic and semiconductor microwires, experiments and interpretation, Opt. Express, Vol. 18, Issue 24, 2010, pp. 24632-24647. [19]. J.-W. Choi, R. Wicker, S.-H. Lee, K.-H. Choi, C.-S. Ha, I. Chung, Fabrication of 3D biocompatible/biodegradable micro-scaffolds using dynamic mask projection microstereolithography, J. Mater. Process. Technol., Vol. 209, Issue 15-16, 2009, pp. 5494-5503. [20]. M. Farsari, F. Claret-Tournier, S. Huang, C. R. Chatwin, D. M. Budgett, P. M. Birch, R. C. D. Young, J. D. Richardson, A novel high-accuracy microstereolithography method employing an adaptive electro-optic mask, J. Mater. Process. Technol., Vol. 107, Issue 1-3, 2000, pp. 167-172. 211 Advances in Optics: Reviews. Book Series, Vol. 3 [21]. M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W. Alexander, C. A. Ward, Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared, Appl. Opt., Vol. 22, Issue 7, 1983, pp. 1099-1120. 212 Chapter 8. Integrated Terahertz Planar Waveguides for Molecular Sensing Chapter 9 Integrated-Optics Solutions for Biomedical Optical Imaging B. Imran Akca1 9.1. Introduction Several novel optical imaging techniques have been developed over the past years to be used in basic biological research and clinical applications. Flourescence, confocal, Raman, and Brillioun microscopy are just a few of these optical techniques that are actively investigated by many research groups. Optical coherence tomography (OCT) is also one of these hot research areas which is a non-invasive, three-dimensional imaging technique that offers close-to-histology-level image quality [1]. Based on broadband spectral interferometry, OCT has enabled clinical applications ranging from ophthalmology to cardiology that revolutionized in vivo medical diagnostics. There are currently two distinct OCT technologies commercially available: time domain (TD) and Fourier domain (FD) OCT technology. Integrated optics offers unique solutions for OCT systems. Integrating several complex optical devices as miniaturized components on a single microchip improves mechanical stability for maintenance-free operation and accesses lithographic high-volume fabrication for dramatic cost reduction and improved repeatability. Miniaturized OCT systems have recently garnered attention for mainly their high potential in overcoming the size and cost problems of the bulky OCT systems [2, 3]. One major advantage of integrated optics is that the operation of the existing optical components can be reconfigured by controlling the material properties using temperature, voltage, or pressure. Despite this unique feature, OCT based upon integrated optical components has as yet not utilized it properly. In this chapter, by exploiting the unique features of integrated optics, the design of a novel multiple-reference TD-OCT system, an akinetic beam scanner, and high-speed spectrometers with ultra-high resolution or broad bandwidth are presented. The TD-OCT system and the akinematic beam scanner are designed to work at 1300 nm wavelength range whereas spectrometers are designed for 800 nm range. In conventional TD-OCT B. Imran Akca Institute for Lasers, Life and Biophotonics Amsterdam, Department of Physics and Astronomy, VU University Amsterdam, Amsterdam, The Netherlands 213 Advances in Optics: Reviews. Book Series, Vol. 3 systems depth scanning is achieved by modifying the relative optical path length difference of the reference and the sample arms in a sequential way using mechanical scanners. Due to the speed limitations and accompanying significant sensitivity decrease, and motion artifacts conventional TD-OCT systems fall behind FD-OCT systems in many applications. Formation of 2D images in many imaging techniques requires precise lateral scanning of the incident light beam using mechanical scanners such as galvanometer actuated mirrors. These mechanical scanners cause some major problems such as image distortion, phase errors, beam jitter, and inaccuracies due to non-uniform scan pattern, etc. Spectrometers are the core of many optical imaging modalities, such as Brillioun microscopy, SD-OCT, Raman microscopy etc. Having high speed, broad bandwidth, high resolution, and small footprint are the main requirements of a spectrometer. The designs that are discussed in this chapter are all comprised of electro-optic switches and very compact delay lines. Firstly, the electro-optic switch design for the devices working at 1300 nm wavelength range will be discussed and later on the details of each device design will be given. Spectrometers that are designed at 800 nm wavelength range will be discussed separately in the following section. 9.2. Designs at 1300 nm 9.2.1. Material System The proposed sample arm configuration was simulated for the lithium niobate (LN)-onsilicon waveguide platform as it is being one of the most versatile and well-developed active optical materials [4]. The material system is 300-nm-thick ion-sliced lithium niobate film on oxidized silicon wafer. The oxide thickness is 3 μm. The refractive index of the LN layer is 2.22 at 1300 nm, and its electro-optic (EO) coefficient is (r33 ~ 30 pm/V) [4]. Single mode rib waveguides with 0.2 µm of slab height and 1 µm of waveguide width were designed. The effective refractive index of the rib waveguide was calculated to be 1.85 by using beam propagation method (BPM) simulations. The three-dimensional illustration of the waveguide structure as well as the optical mode profile are given in Fig. 9.1. The minimum bending radius of the curved waveguides was calculated to be R = 100 µm with a bending loss of 0.01 dB/cm. The propagation loss of the LN waveguides defined by the ion-implantation-assisted wet etching is around 0.23 dB/cm. Metallic electrodes can be defined using gold or chromium. A 500-nm-thick silicon dioxide (SiO2) top cladding will be used to prevent propagation losses induced by the electrodes. The fiber-to-chip coupling losses (~6 dB) can be reduced to < 0.5 dB by using a high numerical aperture fiber [5]. 9.2.2. Working Principle of the Electro-Optic Switch One of the main components of the proposed designs is an electro-optic switch which is a wavelength-insensitive Mach-Zehnder-type interferometric coupler as illustrated in Fig. 9.2 [6, 7]. 214 Chapter 8. Integrated Terahertz Planar Waveguides for Molecular Sensing Fig. 9.1. (a) Three-dimensional view of the waveguide stack with relevant design parameters. (b) Beam propagation method simulation of the optical mode. The blue outline shows the crosssectional profile of the waveguide geometry. Fig. 9.2. (a) The schematic of the wavelength-insensitive electro-optic switch. An electrode is placed on top of the right arm of the coupler which is drawn in gray. (b) Beam propagation method simulation of the switch; (Left) No phase difference between coupler arms, the input light will stay in the same arm (bar state). (Right) For a π phase difference between coupler arms, the input light will cross-couple to the other arm (cross state). L, D, Δx are the lengths of the straight sections of the directional couplers, and the delay section, and the separation between coupler arms, respectively. It is comprised of a pair of directional couplers connected by a delay section in which a phase shift is introduced. The second directional coupler cancels deviations introduced by the former, if these deviations are similar in both couplers. An electrode is placed on the right arm of the electro-optic switch as shown in gray in Fig. 9.2(a). When the voltage is off, the lights on both arms will be in phase and the input light will stay in the same arm, i.e. bar state as illustrated in the left part of Fig. 9.2(b). With the applied voltage, the effective refractive index of that arm is locally increased due to the electro-optic effect 215 Advances in Optics: Reviews. Book Series, Vol. 3 which induces a phase difference between two arms. At a certain voltage value corresponding to a π phase difference between arms, the sample beam cross-couples to the other arm, i.e. cross state (Fig. 9.2(c) right part). It is also possible to achieve switching operation using pressure-induced refractive index change by choosing the material technology accordingly. 9.2.3. Akinetic Beam Scanner Layout and Its Working Principle The akinetic scanner design is comprised of two main components; namely electro-optic switches and two-mode interference based beam splitters/combiners. Fig. 9.3(a) shows the akinetic scanner layout implemented in an integrated-OCT system centered at 1300 nm. For simplicity, only 4 arms of the scanner are shown in the figure. Input light is divided into two arms with an integrated 3 dB beam splitter; half of it towards the reference arm which is integrated on the same chip for further size reduction, the other half towards the sample arms. Each sample arm consists of an electro-optic switch (Fig. 9.3(b)) for beam steering and a beam splitter/combiner (Fig. 9.3(c)). The electrooptic switch changes the propagation direction of the sample beam from bar state to cross state by an applied voltage corresponding to π phase difference between coupler arms. By activating each switch sequentially, the sample beam can be steered from one imaging location to the next until whole imaging range is scanned. Fig. 9.3. (a) Akinetic beam scanner implemented in an integrated-OCT system. Light coming from the input waveguide is divided into two; half towards on-chip reference arm, half towards the sample arm where several electro-optic switches are placed. The end of each sample arm is divided into two branches with a constant length difference, i.e. ΔL, between each for simultaneous imaging. (b) Schematic of the electro-optic switch. (c) Schematic of the two-mode interference based beam splitter/combiner. The splitting ratio is 50/50. (d) Due to ΔL, signals from two different physical locations on the sample will be detected at two different depth locations which are separated by 2ΔL. 216 Chapter 8. Integrated Terahertz Planar Waveguides for Molecular Sensing In order to double the imaging speed, each sample arm is divided into two branches with a certain length difference, i.e. ΔL, between them. In this way, two physical locations on the sample can be simultaneously illuminated. When images are formed, signals from two different locations will be detected at two different depths separated by 2ΔL as depicted in Fig. 9.3(d). The number of branches can be increased further in accordance with the desired speed improvement. The separation between each branch is chosen to be d = 20 µm. For a scanning range of 1 mm, 24 electro-optic switches are used which results in a scanner size of around 1 mm × 9 mm (9 mm2). Using the central part of a focusing lens, light can be successfully delivered into the tissue and collected back through same path. Returned signal from different sample locations are combined at the 3 dB coupler and interfered with light from the reference arm. A single detector and a high-speed data acquisition card is utilized to record interference signal from all beams simultaneously. The switching time of an electro-optic coupler is only few nanoseconds, (<10 ns), therefore scanning of a 1 mm wide area on the sample would take approximately 200 nanoseconds. However, in order to avoid data acquisition related problems and increase the integration time for higher signal to noise ratio, it is necessary to apply some time delay between each imaging point. Even for a long time delay, e.g. 1 millisecond, a reasonably high scanning speed, i.e. ~1 kHz, can be achieved. 9.2.4. Multiple-Reference TD-OCT Layout and Its Working Principle Fig. 9.4 is the schematic of the integrated-optics-based multiple-reference TD-OCT system in which the micro-chip is outlined by the red dashed-rectangle. For ease of understanding the first two levels of the light tapping mechanism are demonstrated. Here, a central wavelength of 1300 nm, an axial resolution of 20 µm, and a depth range of 1 mm are aimed at. Light coming from a broadband light source will be divided into two arms with a 3 dB coupler; half towards the sample, half towards the reference arm. There will be several electro-optically-controlled directional couplers placed on both sample and reference arms at certain distances. Imaging of different depths will be controlled by the additional length increment between consecutive reference beams (i.e. a in Fig. 9.4). According to the Nyquist sampling theorem the step size of the beam scanning should not be more than half of the axial resolution, i.e. 10 µm, which defines the length difference between consecutive reference points. Consequently, a is calculated to be 14 μm for this design by reckoning in the round trip of the light inside the tissue as well as the effective refractive indices of tissue and waveguides (ne (tissue) × 10 μm × 2 = ne (waveguide) × a, where ne (tissue) = 1.4, ne (waveguide) = 2.01)). For larger bandwidths, the group refractive indices of the waveguide and tissue have to be used for calculating a. There is no restraint on the additional length between tapping sections, i.e. d, however smaller d is favorable for compact devices. 9.2.5. Design Parameters of the Electro-Optic Switch The design of the electro-optic switch was made in two steps. Firstly, lengths of the straight coupling sections of the directional coupler and the delay part were calculated to 217 Advances in Optics: Reviews. Book Series, Vol. 3 achieve full coupling using equations given in [7] as L = 95 µm and Δx = 0.28 µm, respectively. The separation between coupler arms was chosen as D = 1 µm in order to reduce the overall device length to 0.65 mm. Secondly, the coupler designed in the first step was used to simulate the required mode effective refractive index increment for a π phase difference by scanning the refractive index difference (Δn) between coupler arms from 0 to 5 × 10-3 with 10-4 step size (Fig. 9.5(a)). It was found to be Δn = 2 × 10-3. The required voltage value to induce such index difference was calculated to be 21 Volts by using below equation [8] 1 V n V   ne3 r33 Γ, 2 t (9.1) for an overlap factor of Г = 0.3, electro-optically active layer thickness of t = 0.3 μm, effective refractive index of ne = 1.85, and electro-optic coefficient of r33 = 30 pm/V. The coupling loss was simulated to be 0.04 dB. The simulated splitting ratio between two arms stays constant over 100 nm bandwidth, as shown in Fig. 9.5(b). The coupling ratio remains the same even after a certain voltage applied on one arm of the coupler (Fig. 9.5(b), bottom). Fig. 9.4. Schematic of the proposed multiple-reference arm TD-OCT system based on integrated optics. Electro-optically-controlled directional couplers act as optical switches, which keep it on the same arm when there is no voltage, and cross-couple the light when there is a π phase difference due to electro-optic effect. The cross-coupled light from reference and sample arms will be combined at the beam combiner and sent to a photodetector (PD). Imaging of different depths will be controlled by the additional length increment between consecutive reference beams, i.e. a. The micro-chip is outlined by the red dashed-rectangle. 218 Chapter 8. Integrated Terahertz Planar Waveguides for Molecular Sensing Fig. 9.5. Simulation results of the electro-optic switch (a) Refractive index difference between coupler arms versus power on the same arm (I2). For Δn = 2 × 10-3, 99 % of the input light is crosscoupled to the other arm. (b) The coupler is wavelength independent for a wavelength range of 100 nm, and its wavelength independency does not change after the voltage is turned on. The change in coupling ratio of the electro-optic switch due to the process non-uniformity and limitations in reproducibility has been investigated. The refractive index of the cladding layer can have non-uniformities of up to ± 3 × 10-4, and the core layer can show thickness variations up to ± 1 % over the wafer. The waveguide width can vary by ± 0.1 μm. The simulation results of the effects of these process-dependent deviations are summarized in Table 9.1. The wavelength-independent couplers used in electro-switches are relatively fabrication tolerant devices as indicated in Table 9.1. Variations in the refractive index of the cladding layer has the minimum effect on coupling ratio whereas the maximum variation in coupling ratio was calculated to be 0.2 % for ±1 % change in core thickness which is still insignificant. Table 9.1. The Effect of the Technological Tolerances on Electro-optic Switch Performance. Parameters Δw = ± 0.1 µm δdcore = ± 1 % Δncladding = ± 3×10-4 w = 1.1 µm w = 0.9 µm dcore = 303 nm dcore = 297 nm ncladding = 1.4488 ncladding = 1.4482 Effective index change (×10-3) 5.5 -6.5 2.6 -2.6 0.2 -0.1 Coupling ratio change (%) 0.09 -0.1 0.2 -0.2 0.01 -0.009 9.2.6. Two-Mode Interference Beam Splitter/Combiner Design The beam splitter/combiner used in the end of each arm of the TD-OCT system as well as in the akinetic scanner is based on two-mode interference (TMI). It is wavelength independent and compared to an optical Y junction it is more fabrication tolerant, and 219 Advances in Optics: Reviews. Book Series, Vol. 3 reproducible. Fig. 9.6(b) and Fig. 9.6(c) demonstrate the beam propagation simulation results of the TMI-based beam splitter and combiner, respectively. The separation between input waveguides, the width and the length of the slab region are h = 0.8 μm, w = 3 μm, and l = 9 μm, respectively. The splitting ratio is constant over 200 nm wavelength range as shown in Fig. 9.6(d). The overall loss of the beam combiner/splitter was simulated to be 0.18 dB. Fig. 9.6. (a) Schematic of the TMI-based beam splitter (b) and combiner (c). The loss of the splitter and combiner was simulated to be 0.18 dB. (d) The splitting ratio remains constant over 200 nm bandwidth range. 9.3. High-Speed Spectrometer Designs Optical spectroscopy is an essential tool in numerous areas including biochemical sensing, material analysis, optical communication, and medical applications [9]. The development of a high-resolution on-chip spectrometer could enable compact, low-cost spectroscopy for portable sensing and increase lab-on-a-chip functionality. Motivated by this demand, several integrated microspectrometers have been realized in different configurations [10-13]. Most of these spectrometers rely on dispersive components which are inevitably bulky because their spectral resolution scales inversely with optical path length. Fourier transform spectroscopy (FTS) is a technique that uses interference of light rather than dispersion to measure the spectrum of a sample [14]. It is basically a Michelson interferometer with a movable mirror. The basis of this technique is the Fourier-pair relationship between the interferogram of a sample and its spectrum. The primary advantages of FTS compared to dispersive spectrometers are high optical throughput thereby greater signal-to-noise ratio, compact size, and relatively easily attainable high resolution which is constant over the entire spectral region as determined by the mirror displacement from the origin. 220 Chapter 8. Integrated Terahertz Planar Waveguides for Molecular Sensing Although FTS can be more compact in size, its scanning interferometric configuration makes it slow for some applications where speed is a critical constraint [15]. Spatial heterodyne spectroscopy (SHS) is an interferometric Fourier-transform (FT) technique based on a modified Michelson interferometer with no moving parts and relying on analysis of stationary interference patterns [16]. The SHS concept was successfully implemented in bulk optics so far, and recently it has been proposed for planar waveguide implementation by Cheben et al. as a Fourier-transform arrayed waveguide grating (FT-AWG) microspectrometer [12]. Florjańczyk et al., have generalized the waveguide SHS FT concept into a waveguide Mach-Zehnder interferometer (MZI) array which was based on an array of independent MZIs with different phase delays [17]. Even though it is a promising technique, it is still challenging to place long delay lines on a single wafer to achieve ultrahigh resolution. As a follow-up, they have presented a spiral-based SHS FT design with a spectral resolution of 40 pm, and footprint of 12 mm2 [18]. However, besides being quite lossy, the spectrometer size will still be significant if ultrahigh resolution is aimed at. In this section, two novel FT spectrometer layouts are introduced; one with an ultrahighresolution of 500 MHZ (~ 1 pm) in a very small footprint of 1 cm2 and other one with larger bandwidth (40 nm). The ultrahigh-resolution spectrometer design is comprised of N = 60 MZIs whereas large-bandwidth spectrometer has N = 80 MZIs that are sequentially activated by voltage-controlled directional couplers. Compared to spiral-based FT spectrometer described in [18], the ultrahigh-resolution spectrometer layout will provide much smaller size for the same resolution in addition its N times larger throughput. The long optical delay between MZI arms is introduced by sequentially tapping the propagating light out at several locations on the light path which makes the overall device size very compact. The tapping operation is provided by electro-optically-controlled directional couplers that are placed on both interferometer arms with a certain length difference between consecutive tapping locations. Lithium niobate (LN)-on-silicon material technology was chosen for these specific designs, however it can be applied to other electro-optic materials. The proposed designs can be easily adjusted to realize spectrometers with different bandwidth and resolution combinations. The electro-optic switch and the waveguide geometry were redesigned in accordance with the new wavelength range, i.e. 800 nm. Since the bandwidth range of the spectrometers is not more than 40 nm, directional couplers are preferred in electro-optic switch design in contrary to 1300-nm designs as it has a shorter length which reduces the device size significantly. 9.3.1. Material System at 800 nm The proposed spectrometer ideas are simulated for the LN-on-silicon waveguide platform. The material system is 250-nm-thick ion-sliced lithium niobate film on oxidized silicon wafer. The oxide thickness is 3 μm. The refractive index of the LN layer is 2.25 at 800 nm. Single mode rib waveguides with 0.2 µm of slab height and 0.9 µm of waveguide width were designed. Fig. 9.7(b) demonstrates the cross-sectional beam profile of the mode obtained by using beam propagation method (BPM). The minimum bending radius 221 Advances in Optics: Reviews. Book Series, Vol. 3 of the curved waveguides was calculated to be R = 150 µm with a bending loss of -0.005 dB/cm. A 500-nm-thick silicon dioxide (SiO2) top cladding will be used to prevent propagation losses induced by the electrodes. The simulated beam profile and the relevant waveguide parameters are given in Fig. 9.7(b). 9.3.2. Electro-Optic Switch Design at 800 nm Directional couplers used in both layouts were designed to act as voltage-controlled electro-optic switches with nanosecond switch time. A metallic electrode was placed on top of one of the straight waveguides of the directional coupler as shown in Fig. 9.7(a). Fig. 9.7. (a) The schematic of the electro-optically-controlled integrated- optics-based directional coupler. Here I1 is the input light, I2 is the transmitted light, I3 is the cross-coupled light, Lc is the electrode length, and d is the separation between coupler arms. (b) Beam propagation method simulation of the optical mode. The blue outline shows the cross-sectional profile of the waveguide geometry. Relevant waveguide parameters are given. (c) The amount of cross-coupling of the input light at different voltage values for different electrode lengths. The most optimum combination was obtained for an electrode length of 300 μm and an applied voltage value of V = 18 Volts. (d), right Voltage is OFF, the light will be cross-coupled to the other channel. (d), left Voltage is ON, V = 18 Volts, a π phase difference will be generated between coupler arms and the input light will stay in the same arm. When there is no voltage on the electrodes, the lights on both arms will be in phase and the incoming light will be cross-coupled to the other arm. (Fig. 9.7(d) left side). At a 222 Chapter 8. Integrated Terahertz Planar Waveguides for Molecular Sensing certain voltage value (i.e. V = 18 Volts for this design), a π phase difference is generated between coupler arms which avoids cross-coupling of the light and forwards it to the next stage where a different spectral information is obtained (Fig. 9.7(d) right side). This operation will be performed in a sequential order by switching the directional couplers on and off until all range is scanned. It is assumed that the coupling ratios at each directional coupler does not vary substantially across the entire bandwidth which is relatively small for the example considered here (i.e. 15 GHz). However, the non-uniformity of light coupling among individual directional couplers can be calibrated out as described in [17].The effective refractive index of the waveguide stack was calculated to be 2.0 for TE polarization. The expected change in the mode effective refractive index due to applied voltage (Δn (V)) was calculated to be 12 × 10-5 × V using Eq. (9.1) for an overlap factor of Г = 0.25, electro-optically active layer thickness of t = 0.25 μm, effective refractive index of ne = 2.0, and electro-optic coefficient of r33 = 30 pm/V. BPM simulations were performed for designing and optimizing the optical components. The directional coupler was designed in two steps. Firstly, in-phase case was designed and the separation between waveguides was calculated to be d = 0.9 μm for full crosscoupling (Fig. 9.7(d) left). There is a trade-off between the length of the electro-optically defined part of the coupler (i.e. electrode length, Lc) and the applied voltage. For a π phase difference this length is defined as: Lc  0 2  n (V ) . (9.2) In the second stage, the electrode length was scanned from 250 μm to 350 μm with a 50 μm step size while applied voltage value was scanned from 0 to 25 Volts in 1 Volt steps as given in see Fig. 9.7(c). The most optimum case was obtained for an electrode length of 300 μm and an applied voltage value of 18 Volts to generate a π phase difference. At this voltage level, light will stay in the same arm and be directed to the next MZI section (Fig. 9.7(d) right). 9.3.3. Ultrahigh-Resolution Spectrometer Layout and Its Working Principle Fig. 9.8 is the schematic of the ultrahigh-resolution FT spectrometer layout. For ease of understanding the first two levels of the light tapping mechanism are demonstrated. Here a central wavelength of 800 nm is aimed at. There are several MZIs that are electrooptically-controlled in a sequential order. Input light will be divided into two arms with an integrated 3 dB directional coupler. Half of the light will travel through a multi-S-shaped path that is comprised of several curved waveguides and straight waveguide sections. This arm will be used for providing additional length difference between MZI arms. The other half of the light will be sent towards a straight waveguide section that can be considered as the reference arm of the interferometer. The end of the both arms can be a waveguide termination such as a matched load that decreases reflection. 223 Advances in Optics: Reviews. Book Series, Vol. 3 Fig. 9.8. Schematic of the ultrahigh-resolution FT spectrometer design. The input light is divided equally by an on-chip 3 dB coupler and sent towards two different paths; one has several S-shaped waveguides and the other has a straight waveguide. There are several electro-opticallycontrolled directional couplers on both arms that act as optical switches. They cross-couple the light when there is no voltage, and keep it on the same arm when there is a π phase difference due to electro-optic effect. The cross-coupled light from both arms will be combined at the beam combiner and sent to a photodetector (PD). Here Ls is the length of the straight sections; R is the radius of the curved waveguides on the S-shaped path. Each MZI consists of two electro-optically-controlled directional couplers one in each arm. The first MZI will have zero path length difference between its arms, therefore the length of segments |AB| and |DE| are equal. The length of the next segment on the multiS-shaped path is |BC| = (2 × π × R) + (2 × Ls) where Ls is the length of the straight parts, and R is the radius of the curved waveguide sections. The length difference between the arms of the next MZI (i.e. |BC| – |EF|) is chosen in accordance with the resolution requirements. The resolution of the spectrometer is defined by the maximum delay ∆Lmax, which also determines the spectrometer size. The calculation of ∆Lmax refers to the Littrow condition and can be expressed as [18]: Lmax  02 ,   ng (9.3) where δλ is the resolution of the spectrometer, ng is the group refractive index of the waveguide stack, and λ0 is the center wavelength. For a spectral resolution of 500 MHz a maximum delay of ∆Lmax ≅ 30 cm is needed which makes it very challenging to accommodate such a spectrometer on a standard 10-inch wafer using existing waveguide SHS designs. The proposed design solves the size problem by using light tapping approach. As the light travels through a waveguide, the optical length gets increased, and by tapping the propagating light out at certain locations on the waveguide, the required optical delay can be obtained for each MZI. The multi-S-shaped sections of this waveguide will keep the length of the device short while straight sections in between (with 224 Chapter 8. Integrated Terahertz Planar Waveguides for Molecular Sensing length Ls) will mainly provide the optical delay. As a constraint on proper operation of the spectrometer, each MZI path length must be an integer multiple of some fixed path length, i.e. ∆Lmax/N. The light coming from both MZI arms will get interfered on an on-chip beam combiner and sent to a matched photodetector. The output power distribution digitally processed by using a Fourier transform to retrieve the input spectrum. Photodetectors can be fabricated on the same chip or a commercial photodetector array can be externally buttcoupled to the chip. Based on the Nyquist sampling theorem, in order to scan 15 GHz of bandwidth with 500 MHz resolution, N = 60 directional couplers are needed which results in an overall device size of around 2 cm × 0.5 cm (1 cm2). The time needed for scanning 15 GHz bandwidth in 60 steps will be less than a millisecond. 9.3.4. Broadband Spectrometer Layout and Its Working Principle Some applications require high speed spectrometers working over a large bandwidth. The previously explained spectrometer design provides ultrahigh resolution over a very small bandwidth. By changing the spectrometer layout slightly, one can achieve large bandwidth and high speed over a small footprint. Fig. 9.9 demonstrates the FT spectrometer working over 40 nm bandwidth with a spectral resolution of 1 nm at the central wavelength of 800 nm. Such a spectrometer can be used in Raman spectroscopy which can outperform in terms of size and speed compared to existing bulky counterparts. By using Eq. (9.3) the required maximum length difference is calculated to be 372 μm. Assuming 80 MZIs (according to the Nyquist sampling theorem), the required length increment for each step is calculated to be ΔL = 4.7 μm which can be provided by applying a curved waveguide section to one side of the MZI parts. The working principle of this design is as follows; input light will be divided into two arms with an integrated 3 dB directional coupler. Half of the light will travel through a path that is comprised of several curved waveguides and straight waveguide sections. This arm will be used for providing additional length difference between MZI arms. The other half of the light will be sent towards a straight waveguide section (with small curved sections for avoiding coupling of light between straight sections) that can be considered as the reference arm of the interferometer. The end of the both arms can be a waveguide termination such as a matched load that decreases reflection. In the case of no voltage on the first couplers and a certain voltage (i.e. V = 18 Volts) on the rest of the couplers, the light will cross couple to the other branch and stay in the same branch until it reaches the detector. At this stage, there will be no path length difference between two arms. When a certain voltage is applied to the first couplers while there is no voltage on the rest of the couplers, there will be a ΔL path length difference between two arms. By increasing the number of couplers that are under a certain voltage, the path length difference will be increased by ΔL at every step until the maximum path length difference is reached. The overall device size will be around 2.5 cm × 0.5 cm. The time needed for scanning 40 nm bandwidth in 80 steps will be less than a millisecond. 225 Advances in Optics: Reviews. Book Series, Vol. 3 Fig. 9.9. Schematic of the broadband FT spectrometer design. The input light is divided equally by an on-chip 3 dB coupler and sent towards two different paths; one has several curved waveguides and the other has a straight waveguide. There are several electro-optically-controlled directional couplers on both arms that act as optical switches. They cross-couple the light when there is no voltage, and keep it on the same arm when there is a π phase difference due to electro-optic effect. The cross-coupled light from both arms will be interfered at the photodetector (PD). Here ΔL is the extra path length difference between curved and straight waveguide sections. 9.4. Conclusions In summary, a novel OCT beam scanner, a TD-OCT system and two high-speed FT spectrometer designs were presented to be used in various biomedical optical applications such as OCT, confocal and Brillioun microscopy, and Raman spectroscopy. The proposed designs are comprised of dynamic delay lines which are based on voltage-controlled directional couplers. The proposed ideas can be applied to other imaging modalities as well as other measurement techniques. Different switching mechanisms (e.g. pressurebased) can be applied in different material platforms, depending on the power consumption, and switching speed requirements. It is expected that the layouts described in here will evoke some experimental interest and will be followed up by several research groups and companies. Acknowledgements The author thanks Dr. Bob van Someren and Prof. Ton van Leeuwen for the fruitful discussions. 226 Chapter 8. Integrated Terahertz Planar Waveguides for Molecular Sensing References [1]. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, Optical coherence tomography, Science, Vol. 254, 1991, pp. 1178-1181. [2]. B. I. Akca, B. Považay, A. Alex, K. Wörhoff, R. M. de Ridder, W. Drexler, M. Pollnau, Miniature spectrometer and beam splitter for an optical coherence tomography on a silicon chip, Opt. Express, Vol. 21, 2013, pp. 16648-16656. [3]. G. Yurtsever, B. Považay, A. Alex, B. Zabihian, W. Drexler, R. Baets, Photonic integrated Mach-Zehnder interferometer with an on-chip reference arm for optical coherence tomography, Biomed. Opt. Express, Vol. 5, 2014, pp. 1050-1061. [4]. E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, D. E. Bossi, A review of lithium niobate modulators for fiber-optic communications systems, IEEE J. Sel. Top. Quantum Electron., Vol. 6, 2000, pp. 69-82. [5]. O. D. Herrera, K.-J. Kim, R. Voorakaranam, R. Himmelhuber, S. Wang, V. Demir, Q. Zhan, L. Li, R. A. Norwood, R. L. Nelson, J. Luo, A. K.-Y. Jen, N. Peyghambarian, Silica/electrooptic polymer optical modulator with integrated antenna for microwave receiving, J. Lightwave Technol., Vol. 32, Issue 20, 2014, pp. 3861-3867. [6]. B. I. Akca, C. R. Doerr, G. Sengo, K. Wörhoff, M. Pollnau, R. M. de Ridder, Broad-spectralrange synchronized flat-top arrayed-waveguide grating applied in a 225-channel cascaded spectrometer, Opt. Express, Vol. 20, Issue 16, 2012, pp. 18313-18318. [7]. B. E. Little, T. Murphy, Design rules for maximally flat wavelength-insensitive optical power dividers using Mach-Zehnder structures, IEEE Photon. Technol. Lett., Vol. 9, 1997, pp 1607-1609. [8]. B. Imran Akca, A. Dana, A. Aydinli, M. Rossetti, L. Li, A. Fiore, N. Dagli, Electro-optic and electro-absorption characterization of InAs quantum dot waveguides, Opt. Express, Vol. 16, 2008, pp. 3439-3444. [9]. N. V. Tkachenko, Optical Spectroscopy, Elsevier Science, 2006. [10]. E. Le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lerondel, G. Leblond, P. Kern, J. M. Fedeli, P. Royer, Wavelength-scale stationary-wave integrated Fourier-transform spectrometry, Nat. Photonics, Vol. 1, 2007, pp. 473-478. [11]. B. I. Akca, B. Považay, A. Alex, K. Wörhoff, R. M. de Ridder, W. Drexler, M. Pollnau, Miniature spectrometer and beam splitter for an optical coherence tomography on a silicon chip, Opt. Express, Vol. 21, Issue 14, 2013, pp. 16648-16656. [12]. P. Cheben, I. Powell, S. Janz, D.-X. Xu, Wavelength-dispersive device based on a Fouriertransform Michelson-type arrayed waveguide grating, Opt. Lett., Vol. 30, 2005, pp. 1824-1826. [13]. R. F. Wolffenbuttel, State-of-the-Art in integrated optical microspectrometers, IEEE Trans. Instrum. Meas., Vol. 53, 2004, pp. 197-202. [14]. M.-L. Junttila, J. Kauppinen, E. Ikonen, Performance limits of stationary Fourier spectrometers, J. Opt. Soc. Am. A, Vol. 8, 1991, pp. 1457-1462. [15]. G. Scarcelli, S. Hyun Yun, Confocal Brillouin microscopy for three-dimensional mechanical imaging, Nat. Photon., Vol. 2, 2008, pp. 39-43. [16]. J. Harlander, R. J. Reynolds, F. L. Roesler, Spatial heterodyne spectroscopy for the exploration of diffuse interstellar emission lines at far-ultraviolet wavelengths, Astrophys. J., Vol. 396, 1992, pp. 730-740. [17]. M. Florjańczyk, P. Cheben, S. Janz, A. Scott, B. Solheim, D.-X. Xu, Multiaperture planar waveguide spectrometer formed by arrayed Mach–Zehnder interferometers, Opt. Express, Vol. 15, Issue 26, 2007, pp. 18176-18189. 227 Advances in Optics: Reviews. Book Series, Vol. 3 [18]. V. Velasco, P. Cheben, P. J. Bock, A. Delâge, J. H. Schmid, J. Lapointe, S. Janz, M. L. Calvo, D. Xu, M. Florjańczyk, M. Vachon, High-resolution Fourier-transform spectrometer chip with microphotonic silicon spiral waveguides, Opt. Lett., Vol. 38, 2013, pp. 706-708. 228 Chapter 10. Video Based Heart Rate Estimation Using Facial Images from Video Sequences Chapter 10 Video Based Heart Rate Estimation Using Facial Images from Video Sequences Siong-Shi Ling, Yong-Poh Yu and Raveendran Paramesran1 10.1. Introduction Human heart rate is measured as the number of heart beats per minute (BPM). It is an important parameter used to reveal the health condition of an individual. The pattern of the measured heart rate can be used to indicate levels of fitness, the presence of disease, stress or fatigue and even blockages in the artery due to diabetes or high cholesterol level. Currently, the most common method used for human heart rate measurements is by using the Electrocardiography (ECG) machine. The electrodes are attached to the surface of the skin around the wrist and chest of the subject. The electrical activity of the human heart is captured through the attached electrodes. Heart rate measurements using ECG machine is a contact based method which might not be suitable for skin-burned patients and person with autistic disorder (sensitive to touch). Garbey et al. introduced a new approach for human cardiac pulse measurement based on thermal signal analysis of the major blood vessels near the skin surface (Garbey et al., 2007 [11]). The modulation of the temperature measured from these blood vessels is caused by the variations in blood flow. In the same year, Pavlidis et al. measured the human heart rate and breath rate through bio-heat modeling of facial imagery using a thermal camera (Pavlidis et al., 2007 [12]). The cardiac pulse detection at the forehead proposed by Gatto was extracted from the video infrared thermography (Gatto, 2009 [15]). This approach is based on the principle that the variations of blood flow during the cardiac cycle will cause the fluctuation of thermal energy released by the body tissue. Takano and Ohta developed a system to measure the human heart rate and respiratory rate based on the images from the Charge-Coupled Device camera (Takano & Ohta, 2007 S.-S. Ling Department of Electrical Engineering, Faculty of Engineering, University of Malaya, Kuala Lumpur, Malaysia 229 Advances in Optics: Reviews. Book Series, Vol. 3 [13]). The variations of the average brightness in the region of interest within the subject’s skin were recorded. These data were processed through a sequence of operations which involve interpolation, low pass filter and auto-regressive spectral analysis in order to obtain the heart rate and the respiratory rate. In the following year, Verkruysse et al. measured human respiration and heart rates through remote sensing of plethysmographic signals under ambient light using digital camera (Verkruysse et al., 2008 [14]). Jonathan and Leahy utilized the camera on the smartphone to capture a series of video frames of a human index finger (Jonathan & Leahy, 2010 [16]). The reflections of plethysmographic signals obtained from these video frames were used to compute the human heart rate. The engineering model created by Shi et al. was used for cardiac monitoring through reflection photoplethysmography (Shi et al., 2010 [18]). This noncontact model is made up of a light source that consists of a Vertical Cavity Surface Emitting Laser (VCSEL) and a photo-detector that consists of a high-speed silicon PiN photodiode. Photoplethysmography (PPG) is a non-invasive and inexpensive method to measure the variations of blood volume through the variations of light absorption or reflection (Kamshilin et al., 2011 [19]). The variations of blood volume in the blood vessels are due to the contraction and relaxation of heart muscles during each cardiac cycle. The relationship between the blood volume pulses and the light in reflection PPG has been investigated by some researchers (Hertzman, 1938 [1]; Weinman et al., 1977 [2]) since a few decades ago. The principle of PPG is based on the fact that body tissue is less opaque than the blood. Therefore, the increase in blood volume will reduce the intensity of the reflected light from the trans-illuminated tissue. The variations in blood volume will change the intensity of the reflectance accordingly. Therefore, the human heart rate which is the same as the frequency of cardiac cycle can be measured from the plethysmographic signals captured in the video. Heart rate measurement from video sequences is considered as low cost since the color can be captured using any available video recording device such as video camera, webcam or mobile phone. This remote and non-contact (without using any special device) heart rate measurement is very suitable for home-based health care applications and telemedicine. Poh et al. developed a non-contact technique to estimate the heart rate of a subject whose body was stationary (Poh et al., 2010 [17]; Poh et al., 2011 [20]). This contact-free approach is based on automatic face tracking and the use of blind source separation on color channels within the facial region. Besides that, their proposed method is robust to motion artifacts and able to extract the heart rate of multiple people at the same time. They showed that human heart rate can be measured from video recorder, such as webcam, under ambient light. However, the whole frontal face is used as the Region of Interest (ROI) which includes the regions with less or without blood vessels such as the eyes, hair and nostrils. Their model used a video with duration of 60 seconds that includes the entire facial region of a subject to compute the subject’s average heart rate variability for that duration. The Red, Green and Blue (RGB) pixel values of each video frame were used as the raw input signals. Blind source separation (BSS) method was utilized to extract the 230 Chapter 10. Video Based Heart Rate Estimation Using Facial Images from Video Sequences source signals (that contain the heart rate PPG signals) from the RGB input signals. The heart rate was calculated by using peak detection algorithm. The results obtained from their proposed method were compared to the ECG raw signals. Their results showed that BSS is able to extract the heart rate source signals from the facial images under stationary condition. Pursche et al. modified this technique by transforming the BSS source signals (the heart rate signals) into frequency domain (Pursche et al., 2012 [22]). They divided the facial region into three parts, and concluded that the area around eye and nose (center of the face region) provides better information compared to the other two parts. The time series signals were transformed into frequency domain using Fourier transform. They concluded that this method has higher correlation compared to the peak detection algorithm. On the other hand, Xu et al. showed a simplified mathematical model to obtain the BVP signals from images of human skin (Xu et al., 2014 [24]). They developed a model for pigment concentration in human skin, and used it to estimate the heart rate. They computed the heart rate readings from video recordings lasting from 45 s to 90 s. The subjects are required to keep still during the recording. Their heart rates did not vary much. Kumar et al. proposed a model, known as DistancePPG, to improve the signal-to-noise ratio of the camera-based PPG signal by combining the color change signals obtained from different regions of the face using a weighted average (Kumar et al., 2015 [25]). Additionally, they introduced a method to track different regions of the face separately to extract the PPG signals under motion. The method was evaluated on people having diverse skin tones, under various lighting conditions and natural motion scenarios. Kumar et al. concluded that the accuracy of heart rate estimation was significantly improved using the proposed method. Section 10.2 introduces the component analysis (both ICA and PCA). The way how component analysis (both ICA and PCA) can be used to estimate dynamic heart rate variation is discussed in Section 10.3. In Section 10.3, the experimental study consists of two experiments. The first experiment is on the dynamic heart rate estimation using facial images from video sequences. Although ICA can be used to separate the PPG signal from color components of a video clip, the amount of independence of the ICA sources may be decreased due to the short video duration. A method using ICA combined with mutual information is introduced to identify the minimum video duration needed to estimate the heart rate without compromising the accuracy of heart rate readings (Yu et al., 2015 [26]). In the second experiment we show that the PCA can be used to de-correlate the color components of the PPG signal to estimate the dynamic heart rates (Yu et al., 2015 [27]). This is possible because the color components in log-space are correlated to each other. Section 10.4 examines the impact of varying the distance between the subject and the video camera and also fixing the distance but varying the video duration. Section 10.5 concludes the study. 231 Advances in Optics: Reviews. Book Series, Vol. 3 10.2. Introduction to Component Analysis This section introduces both ICA and PCA. ICA is one of the blind source separation (BSS) methods. Generally, BSS is used to uncover the independent signals from a set of sensor observations that are linear mixtures of statistical independent sources. On the other hand, PCA is a way of identifying the patterns in a group of high dimensional data and expressing or analyzing the data by highlighting their similarities and differences (Lindsay, 2002 [9]). In other words, PCA is used to decorrelate the linearly dependent signals into uncorrelated signals. 10.2.1. Independent Component Analysis ICA is used to decorrelate the signals and reduce higher-order statistical dependencies (Lee et al., 2000 [6]). Assume that there are n linear mixtures (sensors) y1, …,yn of n independent components yj  mj1c1  mj 2c2 ... mjncn , for all j, (10.1) and each mixture yj as well as the independent component ck is the random variable, instead of a proper time signal. Let y denotes the mixture y, …,yn, c denotes c1, …,cn, and M denotes the mij, then (10.1) can be written as y = Mc (10.2) The statistical model in (10.2) is known as independent component analysis. It describes how the observed sensors yi are generated by a process of mixing the components si (Hyvärinen & Oja, 2000 [5]). The mixing matrix M is unknown but can be estimated. The independent components can be obtained by computing inverse of mixing matrix M, denoted by W. Hence, c = Wy (10.3) 10.2.2. Principal Component Analysis To utilize PCA, an important assumption has to be made, i.e. linearity (John, 2002 [8]). In other words, a new set of data can be formed as a linear combination of its basis vectors. Let A be the original data set, B be the representation of A and T be the linear transformation matrix that transforms A into B, then B = TA (10.4) Geometrically, T is a rotation and a translation matrix which transforms A into B. Considering both A and B are a m × n matrix, then the covariance matrix of A, CA can be defined as: 232 Chapter 10. Video Based Heart Rate Estimation Using Facial Images from Video Sequences CA = 1 AAT, n 1 (10.5) where AT is the transpose matrix of A. The respective eigenvectors and eigenvalues can be obtained from the covariance matrix. By sorting the eigenvalues in descending orders, the k eigenvectors that correspond to the k largest eigenvalues can be selected, where k is the number of dimensions of the new subspace. A new projection matrix T can be constructed from the selected k eigenvectors. Hence, the original dataset A can be transformed via T to obtain a k-dimensional feature subspace B, where the components of B are uncorrelated to each other. 10.3. Dynamic Heart Rate Estimation Using Component Analysis This section shows how dynamic heart rate measurements that are typically obtained from sensors mounted near to the heart can also be obtained from video sequences. A short video duration is needed for dynamic heart rate estimation. However, short video duration may decrease the amount of independence of ICA sources and may render to inaccurate readings. Hence, ICA is combined with mutual information to ensure accuracy is not compromised in the use of short video duration. Besides ICA, PCA may also be used to estimate the dynamic heart rates. It is found that the color components in log-space are correlated to each other. The color components in log-space can be de-correlated using PCA to recover the PPG signal. An important consideration for accuracy of the dynamic heart rate estimation is to determine the shortest video duration that realizes it. This video duration is chosen when the six principal components (PC) are least correlated amongst them. When this is achieved, the first PC is used to obtain the heart rate. 10.3.1. Experimental Setup All experiments were set up under constant office fluorescent light. A Sony camcorder (HDR-PJ260VE) was used for the video recording purposes. All videos were recorded and sampled at 50 frames per second. The camcorder was fixed at a position with a distance of about 0.60 m from the subject’s face. In both experiments, four subjects were selected and requested to carry out a cycling activity. All subjects were asked to cycle at different speeds for about two minutes. Then they were asked to stop for twenty seconds. The camcorder was used to capture their facial images during that time. Throughout the video recordings, all subjects were asked to remain stationary. For the first experiment, twenty heart rate readings (sampled at each second) were computed using ICA approach (Yu et al., 2015 [26]) for every subject. For the second experiment, another twenty heart rate readings (sampled at each second) were computed using PCA approach (Yu et al., 2015 [27]) for every subject. 233 Advances in Optics: Reviews. Book Series, Vol. 3 As reference, the instantaneous heart rates of each subject that obtained from the ICA and PCA methods were compared to the actual heart rate readings measured from Polar Heart Rate Monitor – Polar Team2 Pro (Schönfelder et al., 2011 [21]; Wallén et al., 2012 [23]). 10.3.2. Experimental Results Using ICA Method A total of 80 instantaneous heart rate readings were obtained for this experiment. In the experiment, the subjects’ heart rates were varying between 127 BPM and 153 BPM. Fig. 10.1 shows the detail workflow of the ICA method. The block diagram of the proposed model for dynamic heart rate measurement is illustrated in Fig. 10.1. Fig. 10.1. Workflow of ICA approach (Yu et al, 2015 [26]). After the ROI of each frame was identified, the mean of pixel values for red (R), green (G) and blue (B) components were computed separately, where  μR: the mean of all pixel values for R component;  μG: the mean of all pixel values for G component;  μB: the mean of all pixel values for B component. 234 Chapter 10. Video Based Heart Rate Estimation Using Facial Images from Video Sequences The respective μR, μG, and μB of all these 50 continuous frames were calculated. Therefore, at that instant, a set of three raw sensors R(n), G(n), B(n) were formed. Each raw sensor consists of 50 elements. The set of raw sensors were then detrended using algorithm developed by Tarvainen et al. (Tarvainen et al., 2002 [10]). ICA model developed by Cardoso and Souloumiac (Cardoso, 1999 [4]; Cardoso and Souloumiac, 1993 [3]) was then used to separate one set of 3 independent sources from the set of sensors. The set of ICA sources were bandpass filtered (128-point Hamming window, 0.6-4 Hz), and the mutual information was applied to obtain the independence of the ICA sources. The entire process was repeated by increasing the number of previous frames, one-by one until it fulfilled the criterion. The criterion was based on the convergence of the curve fitting coefficients. Table 10.1 summarizes the details of the computed heart rate readings of all subjects. The highest mean absolute error and the highest standard deviation of absolute errors are 1.48 and 1.19 BPM. Fig. 10.2 shows the scattered plot of all computed and actual heart rate readings. It shows that the computed heart rate readings are closely correlated to the actual heart rate readings. The correlation coefficient between the computed and actual heart rate readings is 0.97. The Bland Altman plot is shown in Fig. 10.3. It shows that only a small number of computed heart rate readings are located outside the 95 % limit of agreement interval. Table 10.1. Summary of heart rate readings results obtained from ICA approach. Subject 1 2 3 4 Heart Rate Readings (BPM) Highest Lowest 150 127 153 133 141 134 153 142 Mean absolute error (BPM) 1.29 1.37 1.38 1.48 Standard deviation of absolute errors (BPM) 1.06 1.09 1.19 0.81 Fig. 10.2. Comparison of all actual and estimated heart rate readings. 235 Advances in Optics: Reviews. Book Series, Vol. 3 Fig. 10.3. Bland-Altman plot for all estimated heart rate readings. 10.3.3. Experimental Results Using PCA A total of 80 instantaneous heart rate readings were obtained from this experiment. In the experiment, the subjects’ heart rates were varying between 129 BPM and 153 BPM. Fig. 10.4 shows the detail workflow of the PCA method. The face region was identified by using the model described in (Viola and Jones, 2001 [7]) and the region of interest (ROI) was fixed at the area below eyes and above the upper lip of mouth. For each frame, the spatially average of the RGB and YCbCr components, i.e.: μR, μG, μB, μY, μCb, and μCr are computed respectively. All six color components were projected into log-space. Therefore, at any time instant, a set of six input features log PR, log PG, log PB, log PY, log PCb and log PCr were formed. The set of input features were then detrended using the model developed by Tarvainen et al. (Tarvainen et al., 2002 [10]). PCA was then used to recover six PCs from these six input features. The set of PCs was bandpass filtered (128-point Hamming window, 0.8-4 Hz). The entire process was repeated by increasing the number of previous video frames, until the stopping criterion was met. At this point, the corresponding number of frames was chosen as the video duration needed to compute the instantaneous heart rate reading. The first PC was then chosen as the PPG signal. The corresponding frequency of this PPG signal was considered as the instantaneous heart rate reading for that particular instant. Table 10.2 summarizes the details of the computed heart rate readings of all subjects. The highest mean absolute error and the highest standard deviation of absolute errors are 1.94 and 1.21 BPM. Fig. 10.5 shows the scattered plot of all computed and actual heart rate readings. It shows that the computed heart rate readings are closely correlated to the actual heart rate readings. The correlation coefficient between the computed and actual heart rate readings is 0.93. The Bland Altman plot is shown in Fig. 10.6. It shows that only a small number of computed heart rate readings are located outside the 95 % limit of agreement interval. 236 Chapter 10. Video Based Heart Rate Estimation Using Facial Images from Video Sequences Fig. 10.4. Workflow of PCA approach (Yu et al, 2015 [27]). Table 10.2. Summary of heart rate readings results obtained from PCA approach. Subject Heart Rate Readings (BPM) Highest Lowest Mean absolute error (BPM) Standard deviation of absolute errors (BPM) 1 141 134 1.94 1.21 2 153 133 1.18 1.09 3 153 135 1.93 1.00 4 135 129 1.18 1.09 237 Advances in Optics: Reviews. Book Series, Vol. 3 Fig. 10.5. Comparison of all actual and estimated heart rate readings. Fig. 10.6. Bland-Altman plot for all estimated heart rate readings. 10.4. Distance between the Subject and Video Camera By increasing the distance between the subject and video camera, the high quality resolution is lost thereby affecting the accuracy of the heart rate estimation. In this study, two experiments were carried out to examine the impact of varying the distance between the subject and the video camera and to its heart rate estimation. In the first experiment, the distance between the subject and video camera was varied with fixed duration. The distance was varied between 30 cm and 200 cm with fixed durations of 5 and 8 seconds. In the second experiment, the duration was varied between 3 and 9 seconds with fixed distance of 50 cm and 100 cm. Four subjects took part in the experiments. The obtained data from both experiments were analyzed using an integrated method consisting of detrend, ICA, bandpass filters, and fast Fourier transform as shown in Fig. 10.7. 238 Chapter 10. Video Based Heart Rate Estimation Using Facial Images from Video Sequences Fig. 10.7. Flow chart of video-based heart rate estimation using ICA. 10.4.1. Varying Distance with Fixed Video Duration All experiments followed the setup described in Section 10.3.1. The subject was seated on a chair facing the video camera with an initial distance of 30 cm and was recorded for 60 seconds while his/her instantaneous heart rate reading was recorded simultaneously. The subject was requested to stay still with no motion. Viola et al model used to detect the face region (Viola et. al, 2001 [7]). The obtained data were processed and analyzed offline using MATLAB R2013a. The experiments were repeated by increasing the distance 10 cm for each case till the final distance reaches 200 cm. A total of 18 sets of videos and heart rate readings were captured for each subject. Four subjects’ heart rates were measured and they varied from 62 BPM to 90 BPM. The method as shown in Fig. 10.7 was used to estimate the heart rate readings from videos. A 5-second video clip was used in each case. The obtained results were compared to actual heart rate readings for each subject. This study also looks into the accuracy of the heart rate estimation when the duration is increased from 5-seconds to 8-seconds. Tables 10.3 and 10.4 show the Root Mean Square Error (RMSE) for all four subjects with distance varying from 30 cm to 200 cm for both fixed durations of 5-seconds and 8-seconds respectively. The error rates are much lower for 8-seconds duration when compared to 5-seconds duration. The results for both 5-seconds and 8-seconds duration gave the lowest scores when the distance was 50 cm. More details of the average error rates obtained from the differences between the estimated heart rates and actual heart rates for four subjects are shown using Box-Plot Graph in Fig. 10.8 and Fig. 10.9. Each box in the Figs. 10.8 and 10.9 indicate the average of the errors of the four subjects combined. More error rates are observed when the duration is for 5-seconds as shown in Fig. 10.8. 239 Advances in Optics: Reviews. Book Series, Vol. 3 Table 10.3. RMSE values for distance varying from 30 cm to 200 cm with 5-seconds duration. Distance (cm) 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 RMSE with 5-seconds duration S1 S2 S3 S4 1.056 9.331 3.090 0.841 2.282 2.388 7.002 5.187 1.238 2.075 2.757 0.850 1.609 4.047 4.610 1.785 2.183 12.597 2.680 1.585 1.724 2.750 2.493 2.219 2.677 5.006 7.723 1.887 2.473 5.473 7.231 2.664 2.408 4.929 31.580 1.648 1.762 3.897 8.979 5.590 4.378 4.714 8.968 1.492 4.594 4.270 25.483 2.493 18.463 9.818 9.672 3.109 16.995 4.787 34.688 1.536 4.431 3.453 32.981 2.081 2.003 39.025 30.779 22.533 2.906 7.923 7.501 5.807 36.442 30.142 61.079 7.240 Table 10.4. RMSE values for distance varying from 30 cm to 200 cm with 8-seconds duration. Distance (cm) 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 240 RMSE with 8-seconds duration S1 S2 S3 S4 1.048 3.202 2.859 0.896 1.304 1.792 6.252 0.768 1.368 1.300 2.675 0.646 0.984 2.448 2.917 0.836 0.746 3.635 2.644 0.566 1.381 2.560 1.341 1.304 1.476 1.230 5.505 1.285 1.843 4.942 1.913 1.808 1.650 3.448 5.958 0.722 1.105 2.450 0.920 4.462 1.663 6.173 3.078 1.860 7.831 3.299 25.008 1.400 21.131 1.475 8.664 1.565 1.985 2.684 15.970 0.779 0.969 2.514 4.136 1.391 1.485 0.858 10.929 1.923 1.739 9.385 8.417 6.115 22.674 29.222 44.849 11.181 Chapter 10. Video Based Heart Rate Estimation Using Facial Images from Video Sequences Fig. 10.8. Box-Plot Graph of error values for all subjects with duration time of 5 seconds. Fig. 10.9. Box-Plot Graph of error values for all subjects with duration time of 8 seconds. 10.4.2. Fixed Distance with Varying Video Duration The same four subjects from previous experiments were involved in this experiment. The same set-up as in the previous experiments was used except in this case the distance is fixed at 50 cm and 100 cm. The video frames used to analyze the data were varied from 3-seconds to 9-seconds. The same integrated ICA method shown in Fig. 10.7 was used to obtain the estimated heart rate readings. Tables 10.5 and 10.6 show the RMSE values for the four subjects with varying video duration for a fixed distance at 50 cm and 100 cm 241 Advances in Optics: Reviews. Book Series, Vol. 3 respectively. The results in Table 10.5 shows that beyond 5-second duration gave acceptable errors between the estimated and actual readings. Similar observations can be seen in Table 10.6 where in this case, the video duration beyond 6-second produces acceptable error rates. More details of the errors are shown using Box-Plot graph as shown in Fig. 10.10 and 10.11 for the distance 50 cm and 100 cm respectively. Table 10.5. RMSE values for varying duration time at distance of 50 cm. Time Duration (s) 3 4 5 6 7 8 9 RMSE at distance of 50 cm S1 S2 S3 S4 2.448 3.570 4.683 8.424 1.642 2.081 4.724 8.198 1.238 2.075 2.757 0.850 1.406 1.297 2.720 0.828 1.473 1.231 2.183 0.653 1.368 1.300 2.675 0.646 1.473 1.300 2.543 0.588 Table 10.6. RMSE values for varying duration time at distance of 100 cm. Time Duration (s) 3 4 5 6 7 8 9 RMSE at distance of 100 cm S1 S2 S3 S4 5.168 14.738 7.830 3.907 3.220 5.919 13.076 3.250 2.473 5.473 7.231 2.664 2.166 5.376 2.465 2.418 1.297 4.585 3.447 1.151 1.843 4.942 1.913 1.808 0.936 4.395 2.522 0.720 10.5. Conclusion This chapter presents the methods to estimate dynamic heart rates using both ICA and PCA approaches. A method using ICA combined with mutual information is introduced to identify the minimum video duration needed to estimate the heart rate without compromising the accuracy of heart rate readings. Four subjects took part in an experiment involving cycling activity. The obtained results were compared to the actual heart rate readings from the Polar Team2 Pro and acceptable errors were observed. In the next experiment, PCA is used to de-correlate the color components of the PPG signals to estimate the dynamic heart rates. Similar error rates were observed between the actual and the estimated heart rate. In addition to that, we also examine the impact of varying the distance between the subject and the video camera and also fixing the distance but varying the video duration. In the experiment where varying the distance up to 130 cm with fixed 242 Chapter 10. Video Based Heart Rate Estimation Using Facial Images from Video Sequences duration showed that acceptable error rates between the actual and computed method are observed. In the last experiment where the video duration is varied with fixed distance of 50 cm and 100 cm showed that beyond 6-second video duration gave acceptable error rates for both fixed distances. Fig. 10.10. Box-Plot Graph of error values for all subjects with distance of 50 cm. Fig. 10.11. Box-Plot Graph of error values for all subjects with distance of 100 cm. 243 Advances in Optics: Reviews. Book Series, Vol. 3 References [1]. A. B. Hertzman, The blood supply of various skin areas as estimated by the photoelectric plethysmograph, American Journal of Physiology, Vol. 124, Issue 2, 1938, pp. 328-340. [2]. J. Weinman, A. Hayat, G. Raviv, Reflection photoplethysmography of arterial-blood-volume pulses, Medical and Biological Engineering and Computing, Vol. 15, Issue 1, 1977, pp. 22-31. [3]. J. F. Cardoso, A. Souloumiac, Blind beamforming for non-Gaussian signals, IEE Proceedings F - Radar and Signal Processing, Vol. 140, No. 6, 1993, pp. 362-370. [4]. J. F. Cardoso, High-order contrasts for independent component analysis, Neural Computation, Vol. 11, Issue 1, 1999, pp. 157-192. [5]. A. Hyvärinen, E. Oja, Independent component analysis: algorithms and applications, Neural Networks, Vol. 13, Issue 4, 2000, pp. 411-430. [6]. T. W. Lee, M. S. Lewicki, T. J. Sejnowski, ICA mixture models for unsupervised classification of non-Gaussian classes and automatic context switching in blind signal separation, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 22, Issue 10, 2000, pp. 1078-1089. [7]. P. Viola, M. Jones, Rapid object detection using a boosted cascade of simple features, in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’01), Kauai, Hawaii, USA, 8-14 Dec. 2001, I511. [8]. S. John, A Tutorial on Principal Components Analysis, Princeton University, 2002, pp. 1-16. [9]. I. S. Lindsay, A Tutorial on Principal Components Analysis, University of Otago, 2002, pp. 1-27. [10]. M. P. Tarvainen, P. O. Ranta-Aho, P. A. Karjalainen, An advanced detrending method with application to HRV analysis, IEEE Transactions on Biomedical Engineering, Vol. 49, Issue 2, 2002, pp. 172-175. [11]. M. Garbey, N. Sun, A. Merla, I. Pavlidis, Contact-free measurement of cardiac pulse based on the analysis of thermal imagery, IEEE Transactions on Biomedical Engineering, Vol. 54, Issue 8, 2007, pp. 1418-1426. [12]. I. Pavlidis, J. Dowdall, N. Sun, C. Puri, J. Fei, M. Garbey, Interacting with human physiology, Computer Vision and Image Understanding, Vol. 108, Issue 1-2, 2007, pp. 150-170. [13]. C. Takano, Y. Ohta, Heart rate measurement based on a time-lapse image, Medical Engineering & Physics, Vol. 29, Issue 8, 2007, pp. 853-857. [14]. W. Verkruysse, L. O. Svaasand, J. S. Nelson, Remote plethysmographic imaging using ambient light, Optics Express, Vol. 16, Issue 26, 2008, pp. 21434-21445. [15]. R. G. Gatto, Estimation of instantaneous heart rate using video infrared thermography and ARMA models, PhD Thesis, University of Illinois, Chicago, 2009. [16]. E. Jonathan, M. Leahy, Investigating a smartphone imaging unit for photoplethysmography, Physiological Measurement, Vol. 31, Issue 11, 2010, pp. N79-N83. [17]. M. Z. Poh, D. J. McDuff, R. W. Picard, Non-contact, automated cardiac pulse measurements using video imaging and blind source separation, Optics Express, Vol. 18, Issue 10, 2010, pp. 10762-10774. [18]. P. Shi, V. A. Peris, A. Echiadis, J. Zheng, Y. S. Zhu, P. Y. S. Cheang, S. J. Hu, Non-contact reflection photoplethysmography towards effective human physiological monitoring, Journal of Medical and Biological Engineering, Vol. 30, Issue 3, 2010, pp. 161-167. [19]. A. A. Kamshilin, S. Miridonov, V. Teplov, R. Saarenheimo, E. Nippolainen, Photoplethysmographic imaging of high spatial resolution, Biomedical Optics Express, Vol. 2, Issue 4, 2011, pp. 996-1006. [20]. M. Z. Poh, D. J. McDuff, R. W. Picard, Advancements in noncontact, multiparameter physiological measurements using a webcam, IEEE Transactions on Biomedical Engineering, Vol. 58, Issue 1, 2011, pp. 7-11. 244 Chapter 10. Video Based Heart Rate Estimation Using Facial Images from Video Sequences [21]. M. Schönfelder, G. Hinterseher, P. Peter, P. Spitzenpfeil, Scientific comparison of different online heart rate monitoring systems, International Journal of Telemedicine and Applications, Vol. 2011, 2011, 631848. [22]. T. Pursche, J. Krajewski, R. Moeller, Video-based heart rate measurement from human faces, in Proceedings of the IEEE International Conference on Consumer Electronics (ICCE’12), Las Vegas, NV, USA, 2012, pp. 544-545. [23]. M. B. Wallen, D. Hasson, T. Theorell, B. Canlon, W. Osika, Possibilities and limitations of the polar RS800 in measuring heart rate variability at rest, European Journal of Applied Physiology, Vol. 112, Issue 3, 2012, pp. 1153-1165. [24]. S. C. Xu, L. Y. Sun, G. K. Rohde, Robust efficient estimation of heart rate pulse from video, Biomedical Optics Express, Vol. 5, Issue 4, 2014, pp. 1124-1135. [25]. M. Kumar, A. Veeraraghavan, A. Sabharwal, DistancePPG: Robust non-contact vital signs monitoring using a camera, Biomedical Optics Express, Vol. 6, Issue 5, 2015, pp. 1565-1588. [26]. Y. P. Yu, P. Raveendran, C. L. Lim, Dynamic heart rate measurements from video sequences, Biomedical Optics Express, Vol. 6, Issue 7, 2015, pp. 2466-2480. [27]. Y. P. Yu, P. Raveendran, C. L. Lim, B. H. Kwan, Dynamic heart rate estimation using principal component analysis, Biomedical Optics Express, Vol. 6, Issue 11, 2015, pp. 4610-4618. 245 Chapter 11. Implementing Differential Signalling in Free Space Optical Communication Link Chapter 11 Implementing Differential Signalling in Free Space Optical Communication Link Mojtaba Mansour Abadi1 11.1. Introduction to Free Space Optics One of the current challenges in wireless communications is to be able to provide a cost effective high speed data link in applications, where the radio frequency (RF) based technology cannot be used or is not suitable. For example, in highly populated indoor environments (train station, airports, etc.), and ‘the last mile access’ network, where the end users, using the RF based wireless technologies, do experience lower data rates and low quality services due to the spectrum congestion (i.e., bandwidth bottleneck). The high speed optical wireless connection is defined as a data link with a minimum speed of few Gbps, which is also known as gigabit data connection [1], in emergency situations such as flooding, earthquake, etc., and massive public events including concerts, festivals, as well as optical fibre networks maintenance and repair. Nowadays, using the internet and, in general, having access to the data network have become a typical daily task for everyone. With the rapid growth of smart devices, the RF spectrum, which is already being stretched too thinly, is experiencing congestion at a global level, which needs addressing. Nowadays, there are a growing number of applications as shown in Fig. 11.1, which require access quality to the data services anywhere, anytime and under all conditions. In a perfect scenario, all end users should have access to the optical fibre based backbone network with an ultra-high capacity, to benefit from truly high-speed data communications with a very low end-to-end transmission latency. Of course, for environment where deployment of optical fibre is not economical a combination of satellite communications and optical fibre communications technologies would be the most suitable option. However, this could also be quite costly and therefore may not be feasible in the long run. Mojtaba Mansour Abadi School of Engineering, University of Glasgow, Glasgow, Scotland 247 Advances in Optics: Reviews. Book Series, Vol. 3 Fig. 11.1. Variety of demands for high bit rate access to the data. Therefore, because of the limited bandwidth, and high cost of the RF technology [2], there is the need to consider alternative technologies. The cost and challenges associated with installation of optical fibre particularly in rural areas as well as maintenance of such a network is rather high, therefore is not considered for the last mile access network. Whereas bandwidth limited RF technologies are also not suitable, thus the need for the most attractive and relatively cost effective solution still exists. Free space optical (FSO) communications also known as optical wireless communications have been used to provide high speed data service for aforementioned applications [3]. The FSO technology is license free, easily deployable, secure and capable of offering low bit error rate (BER) as well as high speed link over a range of link span up to 10 km for civilian applications [4], which has been adopted in a number of applications including:  Broadband internet to rural areas [5] – FSO based link could replace optical fibre access technologies such as fibre to the home (FTTH) in order to provide connectivity between in-building networks and to broadband and backbone data networks;  Inter-building connectivity [4] and electronic commerce [6] – FSO provides highspeed, flexibility and high security;  Audio and video streaming [7] – FSO is an attractive solution for video surveillance and monitoring, as well as live broadcasting of sporting events, in emergency situation (e.g., the tsunami in Japan in 2011 that almost wiped out all the telecommunications infrastructure [11]) etc. Unmanned aerial vehicle (UAV) and high attitude platforms [4, 8] – UAVs and high attitude platforms have been used for military surveillance, monitoring traffic and disaster 248 Chapter 11. Implementing Differential Signalling in Free Space Optical Communication Link areas, or broadcasting vital data. UAVs generate a large volume of data, which needs downloading as quickly as possible. This can be achieved by employing the on-board FSO technology. 11.2. FSO Communications 11.2.1. Background Considering any information transmission via light as a form of optical communication; then the ancient Greeks and Romans around 800 B.C. who used fire beacons for signalling over a medium range distance were the first users of FSO links [9]. Since then, a growing interest in research, development and deployment in FSO is observed. The first modern system was developed by Alexander Graham Bell back in 1880 by inventing the “Photophone” that used sun rays to transfer voice over a distance of 200 m [10]. However, not much happened until the discovery of the laser in 1960s. In 1962 researchers from MIT Lincolns Laboratory demonstrated a television signal transmission over 48 km using a light emitting GaAs diode based FSO link [9]. For years FSO was used in military and deep space applications with very little commercial use. The reasons were that i) existing communication technologies were more than adequate to meet the demand; ii) lack of cost-efficient reliable optical components; and iii) impact of the atmospheric conditions on the performance of FSO links [10]. As mentioned before, the demand for higher data rate was the main motivation for researchers to reconsider FSO as a promising alternative and complementary technology to the RF. The growing number of research and development activities in FSO both within the academy and industry supported by a large number of scientific articles clearly demonstrate the potential of this emerging technology with optical fibre like capabilities. Currently, there are commercial FSO products available in the market offering data rates beyond gigabits per second [11, 12]. Research and development is going on to push the data rate to higher limits (e.g., 10 Gbps commercial FSO transceiver [13]) and improve the link quality (e.g., it is desirable to achieve ideal 100 % link availability in all weather conditions. In practice, using a hybrid link the availability of five nines (99.999 %) is reported [5]) as well as to reduce the cost of the complete system. The cost effectiveness of FSO system compared to the RF system is more obvious, when the RF system is supposed to deliver the same high data rate connection service [14-16]. To illustrate the comparison between existing technologies and FSO and to show the advantage of FSO one can refer to Fig. 11.2. [17, 18] In summary the key features of FSO systems for long range line-of-sight (LOS) high speed data connections are outlined as follow:  High data rate: At the moment RF provides 1 to 2 Mbps for unregulated 2.4 GHz ISM bands [19], 20 Mbps 875 Mbps at 5.7 GHz 4G mobile and 60 GHz millimetre wave technologies, respectively [20]. Potentially FSO can provide bandwidth as large 249 Advances in Optics: Reviews. Book Series, Vol. 3 as 2000 THz, which is far beyond the maximum data rate of RF technologies [21, 22], see Fig. 11.2 (a). (a) 180,000 160,000 Fibre RF FSO 140,000 Cost [$] 120,000 100,000 80,000 60,000 40,000 20,000 0 20 40 60 80 100 Data Rate [Mbps] 120 140 160 (b) Fig. 11.2. Comparison of communication technologies: (a) in terms of data rate and link coverage, figure taken from [17] with permission, and (b) in terms of cost and data rate (the figure is plotted using the data from [18]).  License free spectrum: FSO spectrum is not regulated therefore there are no license fees.  Power consumption: The global information and communications technology is responsible for 2 to 10 % of the global energy consumption according to the report 250 Chapter 11. Implementing Differential Signalling in Free Space Optical Communication Link smart 2020 [23]. The global warming and the existing concern to reduce the power consumption is a critical motivation to replace RF with FSO in LOS applications since FSO is potentially green in terms of energy consumption compared to RF.  Low cost: Covering installation, maintenance and license fees, see Fig. 11.2 (b).  High security: FSO links are inherently secure due to highly narrow, well confined and directional beam profile.  Back-bone network compatibility: FSO operating at all three optical transmission windows of 850, 1300 and 1550 nm are compatible with optical fibre based back bone networks. 11.2.2. FSO Structure Fig. 11.3 illustrates the general schematic system block diagram of a typical FSO communication link (Note that in the following chapters, the detailed block diagram will be presented for each case). Fig. 11.3. The fundamental system diagram of an FSO link. LD and PD are laser diode and photodetector, respectively. The modulated or unmodulated version of the transmit information, (i.e., a digital bit steam) is used for intensity modulation of the optical source. Note that, for much higher data rates (i.e., in excess of 10 Gbps) external modulation schemes should be used). As shown in Fig. 11.3, the modulation procedures are assumed to be performed in the transmitter (Tx) module. The optical source adopted could be a light emitting diode (LED) or a laser diode (LD). The latter is more widely used because of the LOS transmission requirement, longer transmission span and higher data rates in outdoor environments. Note that additional optics such as lens, beam splitters, beam polarizer, optical filter, optical fibre, etc. are also used as part of the Tx. Particularly, locating the LD at the focal length of a lens is a common practice used in beam forming and collimation of the laser output. The generated optical beam is launched into the free space channel and is captured at the receiver (Rx) using a combination of optics and an optical photodetector (PD). As in the Tx, typically a lens is used at the Rx to focus the received beam into the PD. The generated electrical signal at the output of the 251 Advances in Optics: Reviews. Book Series, Vol. 3 PD is then amplified, processed and converted back into the digital bit stream at the Rx, see Fig. 11.3. Depending on the application, the free space channel condition and the data rate, the aforementioned elements (i.e., LD, PD, and interface block) can be different. For instance, in a short range clear channel, a single Tx and Rx as well as a simple on-off-keying nonreturn-to-zero (NRZ-OOK) modulation scheme would be sufficient to meet the link requirements [17]. For most cost-effective typical systems, intensity-modulation/direct-detection (IM/DD) based FSO links are more adequate [7, 24-27]. In IM/DD technique, based on the information data, only the intensity of the light is modulated. Another technique to modulate and detect the light is the external modulation and the coherent detection, where in contrary to IM/DD, both intensity and phase/frequency of the light can be modulated [28]. Coherent systems require an external modulator such as Mach-Zehnder modulator to perform the modulation operation. Besides at the Rx, a light source synchronized with the one at the Tx is needed to down-convert the received optical beam [29]. Although coherent systems are shown to have impressive performance in terms of background noise rejection, atmospheric-induced fading mitigation and higher sensitivity of the Rx; the cost and complexity of practical implementation, in particular stability and synchronization of laser sources at the Tx and the Rx, make them less popular than IM/DD based systems [7]. Although the FSO technology has many benefits, it cannot provide 100 % link availability under all weather conditions as outlined below [8]: 1. Turbulence induced fading - This is due to the temperature gradient along the optical propagation path and the movement of air perpendicular to the propagating optical beam [30]. In Chapter 3, more detail is given about turbulence phenomena. 2. Atmospheric loss – This is mainly due to the fog, aerosol, haze, smoke particles [7], where the induced loss by fog/smoke is dominant [31]. The attenuation is the contribution of molecular absorption and light scattering [32]. Absorption occurs at the molecular level and is resulted from absorption of photon energy by molecules of gases in the atmosphere [33]. Since the dimension of fog particles varies between 0.5 m to 2 m, which is in the range of FSO wavelengths, therefore Mie scattering is the major cause of scattering attenuation [32, 33]. 3. Pointing errors induced fading - Is due to the vibration or small movements of both Tx and/or Rx [34]. In Chapter 4, more detail is given about this phenomena. 4. Link blockage - Mostly due to flying object or birds, which results in a burst error [17]. 5. Ambient noise – This can be considered as the main noise source in many scenarios [35]. The ambient noise is mostly due to sunlight or artificial lighting sources [35]. 252 Chapter 11. Implementing Differential Signalling in Free Space Optical Communication Link In particular, among these effects, the atmospheric loss can lead to attenuation as high as 50 dB∕km for <500 m visibility under the fog condition [40, 41]. As reported in [3] the fog attenuation in moderate continental fog environment (Graz, Austria) in winter season and in dense maritime fog environment (La Turbie, France) in summer months can lead to 120 dB/km and 480 dB/km, respectively [42]. Indeed, the FSO link undergoes a wide range of attenuation in presence of fog and smoke [3], which results in reduced link availability in a significant way so that it was shown in [2] that for the weather condition recorded in Graz, the link availability could drop to ∼67 %. The general FSO system block diagram with more detailed components is illustrated in Fig. 11.4. Note that the FSO link is based on IM/DD technique. The digital input bit stream or the information data is applied to the modulation block. Depending on the application, the modulation could be a simple OOK scheme or more complex multilevel amplitude, frequency and phase scheme [7]. y x S  0,1 Input Bit Stream Modulator w Driver LD Transmitter TIA Free Space Channel Circuit Receiver Aperture Transmitter Aperture Channel z Demodulator O  0,1 Output Bit Stream PD Receiver Fig. 11.4. The block diagram of an IM/DD FSO communication link. LD, PD, TIA are laser diode, photodetector, and transimpedance amplifier, respectively. In this work, the NRZ-OOK data format is adopted, which is the most widely used in commercial FSO systems [36]. NRZ-OOK is used because of its simplicity and a balanced power and spectral efficiency compared to other digital modulation schemes [37]. Note that the research main focus is on the design of the hybrid antenna and less on the modulation schemes. However, the system employing a hybrid antenna could readily be adopted for other modulation schemes. Then the output of the modulator (i.e., a bipolar NRZ-OOK signal in this case) with a bandwidth BW 1⁄ , where is the bit duration is DC-level shifted to convert it into a unipolar format prior to intensity-modulate the light source (i.e., LD in this case). The data rate of NRZ-OOK equals to BW [38]. , divergence angle The output of the LD (i.e., ) has four key parameters, wavelength , beam waist , and output power . The wavelength used in FSO is in the red to infrared range of the spectrum. In this work only two wavelengths of 670 nm and 830 nm have been adopted in the experimental investigation. The visible LD at 670 nm is also used for the alignment of the FSO link. The laser beam is collimated using a lens in order to reduce the geometrical loss [39]. This means that the divergence angle should be kept small, and will be the minimum radius of the propagating laser beam, which can be considered prior to the beam divergence [40]. However, the output power of the LD is subject to the eye and safety regulations. There are different standards for laser safety such as the international 253 Advances in Optics: Reviews. Book Series, Vol. 3 electrotechnical commission (IEC) [41], American national standards institute (ANSI) [42] and European committee of electrotechnical standardization (CENELEC) [43]. In this work one class 3R pointer laser with wavelength of 670 nm and 2 mW output power is used, which is considered to be safe if handled carefully. Also another class 3B pointer laser with wavelength of 830 nm and 10 mW output power which needs eyes protection is used. Note that class 3B lasers are only used for experimental proof of concept in laboratory and in an outdoor real scenario, safe lasers must be implemented [44]. In FSO systems with LOS configuration the link performance will be affected by blocking mostly due to flying objects (e.g., birds) and the atmospheric channel conditions (i.e., fog, smoke, turbulence, etc.). The channel affects are defined as the attenuation (loss) and a random fading. The attenuation is due to: 1. Geometrical loss - The real laser light is not an ideal collimated beam. With even a small divergence angle of , it experiences beam spreading and since the PD has a finite physical size, only a fraction of the laser power is captured and collected at the Rx. Therefore, the geometrical loss is defined by [45]: , 20 log √2 (11.1) where , , and denote the bear radius at transmitter, the link distance and the receiver aperture diameter. 2. Atmospheric attenuation - This loss is due to Rayleigh scattering and molecule absorption, with a typical value of 0.5 dB [39]. 3. Fog attenuation - This is the most important loss in FSO links. Generally speaking, fog and smoke, which are composed of small particles floating in the air, are the main cause of attenuation in FSO systems [32]. The optical beam interacting with fog and smoke particles results in both absorption and Mie scattering, which [46]. The fog attenuation is determined based on the channel's contribute to visibility (Vis) in km and is described by two well-known models of Kim and Kruse [45]. The visibility is define as [32]: Vis , (11.2) where is LD wavelength, and denote the maximum sensitive wavelength for human eye, which is normally set to 550 nm (i.e., the green colour). Based on Kim model is defined as [46]: q 254 1.6 1.6, Vis 50 1.3, 6 Vis 50 Vis 0.34, 1 Vis 6 . Vis 0.5, 0.5 Vis 0.1 0, Vis 0.1 (11.4) Chapter 11. Implementing Differential Signalling in Free Space Optical Communication Link The relation between the total attenuation due to the absorption and scattering of light is given by Beer-Lambert law as [46]: and . . (11.4) Depending on visibility ( Vis ), fog can be defined as thick ( Vis (0.1 Vis 1) or thin (Vis 1). 0.1 ), medium - This includes additional losses due to 4. Miscellaneous attenuation misalignment, devices or other unknown factors [39]. Rain also introduces a loss in FSO systems, which is not significant compared to fog, and smoke [2]. However, rain is a major source of attenuation in RF systems. The received power in terms of the transmit power and all losses is given by [47]: . (11.5) For a system point of view, knowing that the total noise variance at the Rx and the PD's responsivity are and , respectively, the link electrical signal-to-noise ratio (SNR) is defined as [47]: SNR . (11.6) In a clear channel with no fading the system BER is given by [47]: BER √SNR , where ∙ denotes the Gaussian -function defined as Thus in clear channel (i.e., no channel fading), to achieve BER SNR > +13.54 dB. (11.7) exp 10 ⁄2 . one needs In this research work, a channel with fading is considered as outlined below: 1. Scintillation/turbulence - In a clear channel with no turbulence the propagating optical beam only experiences attenuation. Whereas in turbulence channel the propagating beam will experience both attenuation and phase variation due to randomly varying refractive index of the air, thus leading to fading and link failure [7, 48]. Note that, turbulence is caused by the presence of temperature gradient along the laser propagation path and the air movement (wind) perpendicular to the laser beam [17]. Turbulence randomly changes the refractive index along the propagation path, which consequently causes the beam wandering [30]. Depending on the fading intensity, the turbulence can be classified as the weak, moderate, strong and saturated [17]. 255 Advances in Optics: Reviews. Book Series, Vol. 3 2. Pointing errors - This is due to the movement of building, mast, tower, and in general the structures on which the FSO units are mounted [34]. Pointing errors lead to the amplitude fluctuation (or oscillation) of the received optical signal in the transverse plan, thus contributing to deterioration of the link's performance [49]. More details on these fading effects will be given in the next sections. Also mitigation methods to overcome them will be introduced. As shown in Fig. 11.4 in the IM/DD system the received optical signal is captured using a lens and focused onto a PD the output of which is amplified using a transimpedance amplifier (TIA) prior to be demodulated in order to recover the transmitted information. 11.3. Turbulence If hypothetically the turbulent channel is frozen at 0, the channel can be considered as in Fig. 11.5. The input wavefront in this case is planar, which encounters random changes in the refractive index. The refractive index variation is a function of the atmospheric temperature, pressure, altitude and wind speed. The variation is modelled as small cells with different refractive index from the adjacent cells. These cells are called turbulence eddies. The size of eddies might change from a few millimetre to several metres [30, 50]. Turbulence is a slow varying fading channel and has the temporal coherence in the order of 1 to 10 ms [51]. Fig. 11.5. Turbulent channel frozen at t = 0. The turbulent channel consists of eddies with various sizes. A useful parameter is the channel correlation radius where correlation length 256 , which is defined as [52]: , (11.8) . (11.9) is given by [53]: Chapter 11. Implementing Differential Signalling in Free Space Optical Communication Link Also is spatial coherence radius and is defined as [52]: ⁄ 1.46 , (11.10) where 2 ⁄ is the wavenumber and is the index-of-refraction structure is an important parameter to choose the spacing between various parameter. independent Rxs in a system with multiple Rxs. The term ‘independent Rxs’ means that the correlation between the fading effects of two received signals from two independent Rxs is negligible. is a general use parameter and can be employed in different turbulence regimes, whereas correlation length ( ) is an approximation of for the weak turbulence regime [52]. For the index-of-refraction structure ( ) there are a number of models available but the most widely used is the altitude dependent model developed by Hufnagle-Valley, which is given by [54]: 2.7 0.00594 ⁄27 10 exp exp ⁄1000 10 ⁄1500 exp ⁄1000 , (11.11) where , , and represent the altitude (m), the root mean square (rms) wind speed (m/s), at 0 , respectively. Depending on the strength of and the nominal value of might be 1.7 10 m ⁄ during daytime for a 1 km link or turbulence 8.4 10 m ⁄ during night for the same link [54]. Provided that the received optical signal intensity is denoted by , a useful parameter to qualify the effect of turbulence is the scintillation index (SI) , which is defined as the normalized irradiance variance of the optical beam as given by [53]: , (11.12) where ∙ denotes the expected value. The variance of log-intensity signal fluctuation is given by [53]: defined by Rytov variance . 1.23 For the light beam with a spot size of diameter the weak turbulence condition are given by [30]: 1 and Λ (11.13) at the Rx, Rytov variance criteria for 1, (11.14) . Since in this research work Λ ≪ 1 , then only the condition where Λ 2 ⁄ 1 is applicable for weak turbulence. 257 Advances in Optics: Reviews. Book Series, Vol. 3 The distribution of fading coefficient for the weak turbulence regime can be modelled using Log-normal distribution, which is practically valid as long as 0.3. Log-normal probability distribution function (PDF) of the normalized irradiance with mean and is given as [15]: variance where ⁄ exp , (11.15) is the signal light intensity without turbulence. To normalize it is assumed that turbulence and are related as follow [30]: exp 4 [54]. Under the assumption of weak 1≅4 , (11.16) In the literature depending on the light propagation model different expressions are introduced for the variance of Log-normal distribution. For the plane wave propagation, [30]. one has Aperture averaging is a technique that reduces the variation of optical intensity according to the aperture diameter [55, 56]. To benefit from aperture averaging, the size of needs to be larger than in Eq. (11.9) [52, 54], which is valid for the weak turbulence regime. In fact, can be much larger in the moderate-to-strong turbulence regime [52, 56]. With defined as the scintillation index of the Rx with no 0 and aperture and with aperture of , respectively, the aperture averaging factor (AF) is given by [7, 56]: AF 1 ⁄ 1.6682 . (11.17) In the moderate-to-strong turbulence regime one has [30]: 1, for moderate regime, (11.18a) 1, for strong regime, (11.18b) and the received signal optical intensity is based the PDF of Gamma-Gamma (GG) distribution given by [57]: 2 , (11.19) where ≥ 0 and ≥ 0 are known as the effective numbers of large- and small-scale turbulence cells, respectively [58, 59]. Kn (∙), and Γ ∙ denote the modified Bessel function of 2nd kind and order n, and the Gamma function, respectively. 258 Chapter 11. Implementing Differential Signalling in Free Space Optical Communication Link The two parameters of and  that characterize the irradiance fluctuation PDF are related to the atmospheric conditions and , which are given by [30]: α , (11.20a) , (11.20b) 1, exp αβ (11.20c) where σ2lnX and σ2lnY represent the variances of large-scale and small-scale irradiance fluctuations, respectively. As mentioned above the presence of aperture at the Rx will reduce the effect of turbulence. For the plane wave propagation model and considering the aperture size the closed form expressions for σ2lnX and σ2lnY parameters are given by [30]: . . where ⁄4 . [30]. . . . . . ⁄ ⁄ ⁄ ⁄ ⁄ , (11.21a) , (11.21b) 11.4. Channel Model For a single-input single-output (SISO) FSO link with OOK employing a receive can be written as (see Fig. 11.6) [54]: apertures, the received signal at the aperture , (11.22) where ∈ 0,1 represents the information bit, is the optical-to-electrical conversion coefficient, denotes the irradiance received at the aperture, and is additive white . The AWGN can be Gaussian noise (AWGN) with zero mean and variance of considered as a combination of the thermal, shot, and dark noise sources of the Rx and the background ambient light [60]. The subscript m is denoting the fact that in general case an FSO system can consist of several SISO link with the given scheme in Fig. 11.6. It is assumed that the channel for Tx to each Rx is independent, which interprets to the fact that the transversal distance between the adjacent apertures is larger than in Eq. (11.8) [52]. In single-input multiple-output (SIMO), multiple-input single-output (MISO), and multiple-input multiple-output (MIMO), each FSO link (see Fig. 11.6) is equivalent to a 259 Advances in Optics: Reviews. Book Series, Vol. 3 SISO FSO link. For an IM/DD based link with AWGN and assuming an equiprobable data transmission ( 0 1 0.5 ), the probability of error conditioned on the |0 |1 . Note that |0 and |1 are received irradiance is BER 0.5 the conditional probabilities defined by averaging over the PDF of fading coefficient ∙ as [61]: |0 , |1 (11.23) 2 is the noise spectral density. Note that ∙ will depend on the channel where condition. Also note that Eq. (11.23) is only valid for SISO. To wrap up this section, a BER comparison of a SISO link in various turbulence situations with and without aperture averaging is presented to show both the effect of turbulence and using an optical lens at the receiver side, see Fig. 11.7. Fig. 11.6. A simplified illustration of m-th FSO link in a single-input multiple-output scheme. LD and PD are laser diode and photodetector, respectively. 10 10 BER 10 10 10 10 10 0 Clear Weak Weak+AF Mod Mod+AF Str Str+AF -1 -2 -3 -4 -5 -6 0 5 10 15 20 SNR (dB) 25 30 35 40 Fig. 11.7. Comparison of single-input single-output performance (BER versus SNR) over clear, weak, moderate and strong turbulence regimes with and without aperture averaging. ‘Weak’, ‘Mod’ and ‘Str’ refer to weak, moderate and strong regimes, respectively. ‘+AF’ denotes applying aperture averaging. 260 Chapter 11. Implementing Differential Signalling in Free Space Optical Communication Link Note that using Gauss-Hermite quadrature formula as in [79] Eq. (11.23) can be simplified to: √ ∑ , (11.24) where is the order of approximation, is the weight factor for the pth-order approximation, and is the zero of the pth-order Hermite polynomial. For values of and refer to mathematical handbooks such as [102]. 11.5. Differential Signalling The received signal in a FSO communication system is highly sensitive to the atmospheric effects such as fog, smoke, low clouds, snow, rain and the atmospheric turbulence [7, 17, 62, 63] that may result in severe power loss and channel fading. In NRZ-OOK IM/DD based systems, an optimal detection threshold level at the Rx can be used to distinguish the received ‘0’ and ‘1’ bits. However, under atmospheric turbulence the received optical signal will experience random intensity fluctuation as well as fading [64], which can result in the received signal power dropping below the Rx's threshold for a duration of milliseconds. For deep fading simply increasing the transmit power level and using a fixed optimal threshold level at the Rx are not the best options [63]. Most already-proposed detection methods rely on the knowledge of instantaneous or statistical channel state information (CSI). For instance, to resolve the fluctuation of threshold level, in [50] the maximum-likelihood sequence detection (MLSD) scheme was adopted, and it was shown that provided the temporal correlation of atmospheric turbulence is known MLSD outperforms the maximum-likelihood (ML) symbol-bysymbol detection technique. In practical applications ≅ 1 10 ms; then to maximize the link performance needs to be adjusted dynamically. In addition, MLSD suffers from high computational complexity. In [65] two sub-optimal MLSD schemes, based on the single-step Markov chain model, were proposed to reduce the Rx computational complexity; however they still require the CSI knowledge. Employing the pilot symbol (PS) assisted modulation (PSAM) scheme, and assuming that is known, CSI is acquired by inserting PS within the data stream [66]. However, obtaining an accurate-enough instantaneous CSI necessitates a non-negligible pilot overhead. In commercial FSO products, it is desirable to employ low complexity signal detection schemes with simple data framing and packetization structures in order to ensure infrastructure transparency [67]. In outdoor FSO links, a differential signalling scheme, also known as differential detection, was investigated in [35] to remove the effect of background noise. Also the same idea was adopted in [63] that used a pre-fixed optimal threshold level for various atmospheric channel conditions (rain, atmospheric turbulence, etc.). The detection technique did not rely on the CSI (with increased computational load at the Rx) and PS or 261 Advances in Optics: Reviews. Book Series, Vol. 3 a training sequence [63]. However, the simulation based investigation only considered narrow collimated beams without overlapping and with no experimental verification. To mitigate the fluctuation of pre-fixed optimal threshold level, the differential signalling scheme is preferred to AC-coupling (i.e., high pass filtering method) for a number of reasons including (i) no need to increase the transmit power to compensate for the filter attenuation; (ii) no baseline wander effect (i.e., disturbing the DC level of a signal); and (iii) removing the effects of the background noise. The basic concept of differential signalling is to send the signal and its inverted version simultaneously by using two pairs of Txs and Rxs over the same communication channel. Following reception of each signal by the corresponding Rxs and performing a subtraction operation at the final stage, the output signal is regenerated for further processing. With this scheme the challenges are to identify the received signals at the receiver and effectively exploit the potential of differential signalling method under various channel conditions. There are two main motivations for using the differential signalling method. First, it has been shown theoretically that provided Rxs are not saturated by the combined power of the received signal and the background noise level, the effect of ambient illumination can be cancelled out [35]. Second, in [63] a differential signalling scheme was adopted in an IM/DD OOK FSO links to overcome the variation of the threshold level caused by the channel fading. The benefit of differential signalling method in channels with large ambient illumination has been fully investigated in [35]. Therefore, in this research, only the performance of differential signalling in a fading channel is investigated. In addition to turbulence, pointing errors also results in threshold level fluctuations at the Rx, which can affect the link performance as well as making signal detection a challenging task [62, 68]. To mitigate signal degradation researchers have proposed a number of techniques including adaptive detection [62], more complex tracking systems [34], and spatial diversity [69]; also see [7] and the references therein. Adaptive detection techniques (ADT) either imposes computational load at the Rx or reduces the link throughput [65, 66]. When using ADT, the CSI or the temporal correlation of fading is required for data detection at the Rx [62]. FSO links with tracking systems requiring optics, monitoring and controlling circuits [70] are complex and costly to be used in commercial IM/DD NRZ-OOK FSO systems. Using spatial diversity with a number of Txs and Rxs will result in improved system performance for various channel conditions. However, there is still the need for a detection technique to extract the information bits from the combined signal [50]. The differential signalling technique can also be used to mitigate the fluctuation of threshold level due to the pointing errors. In this chapter, first the basic idea of differential signalling method is introduced. Then the challenges associated with the existing differential signalling methods are discussed and a solution is outlined. To the best of our knowledge no research work has been reported on the correlation between two channels in FSO systems with differential signalling. In this work theoretical, simulation and experimental investigation of the correlation are carried out. Correlation is shown to be an important key factor that needs 262 Chapter 11. Implementing Differential Signalling in Free Space Optical Communication Link considering. Also the theory of differential signalling method will be extended into channels with the pointing errors effect. 11.6. Differential Signalling Configuration The differential signalling system block diagram is depicted in Fig. 11.8. The NRZ-OOK signal and its inverted version ̅ are used to intensity-modulate two optical sources at wavelengths of and , respectively. By comparing with the optimal threshold level , where ∙ denotes expected value, the original data bit stream can be recovered (i.e., bit is 0 for and 1 elsewhere). Fig. 11.8. The system block diagram to implement differential signalling in correlated-channels conditions. T is the bit duration. OTx, BC, BS, ORx and TIA refer to optical transmitter, beam combiner, beam splitter, optical receiver, and transimpedance amplifier, respectively. Note that the optimal threshold level for ̅ is also of optical sources are given by: Γ 0 0 Γ . The output intensities Ii (i = 1,2) ̅, (11.25) where Γ denotes the electrical-to-optical conversion coefficient of optical sources. The outputs of optical sources are then passed through a beam combiner to ensure that both beams will be transmitted over the FSO channel of length . Note that the beam combiner is only used for alignment purposes and not for combining signals in the optical domain. The optical signals at the Rx end are given by: 0 0 Γ 0 0 Γ ̅, (11.26) where denotes the channel response including the effect of geometrical and atmospheric losses, pointing errors, and the turbulence. Here only the effect of turbulence is considered. 263 Advances in Optics: Reviews. Book Series, Vol. 3 At the Rx, the optical signal is passed through a 50/50 beam splitter and optical filters with the centre wavelengths of and , prior to being collected by an ORx. The generated photocurrents are amplified by TIA with outputs given by: 0 Γ 0 where is the PD responsivity, is gain of TIA, and variance , . The combined output Γ , ̅ Γ (11.27) is the AWGN with the zero mean is given by: ̅ Γ . (11.28) Note that in [35] it shown that for outdoor applications where the ambient noise effect is also embedded in , the impact of background noise is significantly reduced. 11.7. Differential Signalling and Turbulence 11.7.1. Optimal Detection Threshold Level A sampler with sampling at the centre of bit duration and a threshold detector are used to regenerate the transmit data. From Eq. (11.28), the optimal threshold level for is given by: Using [71] one obtains: Mean Var Mean 2 , . Γ Γ Var , Mean Var Var (11.30a) , 2 Var (11.29) (11.30b) where Mean ∙ denotes the average and Var ∙ introduces the variance. Here, , is correlation coefficient between the channels (i.e., and ). For simplicity, in 2⁄ and , are set. For the weak turbulence Eq. (11.30) Γ , regime follows Log-normal distribution with mean and variance , and , , respectively [71]. For Log-normal distribution one has [54]: 264 Var Mean exp 4 , exp 2 1 , 2 exp 4 , , , (11.31a) 4 , , (11.31b) Chapter 11. Implementing Differential Signalling in Free Space Optical Communication Link where : . Therefore, one has: , Var 2 , Mean exp 4 exp 4 , 0, exp 4 1 exp 4 , (11.32a) , , 1 2 2 . (11.32b) Since optical beams are in parallel and propagating very close to each other over the channel, then both beams will experience the same turbulence effects (i.e., , , ). Considering this approximation, one obtains: Var Mean 2 1 , 0, exp 4 (11.33a) , 1 2 . (11.33b) From Eq. (11.33a), it is seen that to recover the transmit bit stream, the optimal threshold level should be set to 0. This is similar to the work in [63] except for not considering the variance of the detection threshold in Eq. (11.33b) due to turbulence. The method proposed in [63] is effective only under constant fading conditions. However, for randomly varying fading scenario a Rx employing a fixed optimal threshold level is not the optimum and therefore alternative scheme should be considered to ensure improve FSO link performance. 11.7.2. Correlation between Channels From Eq. (11.33b), for 1 (i.e., the highly correlated channels), one has , Var 2 . In other words, turbulence does not affect signal detection provided the channels are highly correlated. According to [51], under the weak turbulence regime and , can be expressed in terms of the transversal distance between the Rx apertures the spatial coherence radius . Here, with parallel optical beams propagating over a LOS link, is in fact the distance between the propagation axes of beams. Thus the correlation coefficient between channels takes the form of [51]: , exp ⁄ , (11.34) where for a plane wave propagation model, the spatial coherence radius is given by ⁄ ⁄ 5 channels are considered uncorrelated Eq. (11.10). From Eq. (11.34), for 0.007 whilst for → 0 one can obtain , → 1. So, by adopting a small , one , can obtain highly correlated channels and, as a result, use an optimal threshold level independent of turbulence. This can be the challenging part of the differential signalling scheme; since the goal is to achieve the following features simultaneously: 265 Advances in Optics: Reviews. Book Series, Vol. 3 1. Both channels have to be highly correlated; 2. Signals are different, which necessitates minimum interference. In the next sections, it will be shown how these two challenges can be addressed by using the scheme illustrated in Fig. 11.8. 11.7.3. Channel Modelling In this section the differential signalling method in more details will be investigated and the effect of signal level, modulation extinction ratio, laser wavelengths, and correlation coefficient on the differential signalling performance will be described. Knowing that superscripts high and low denote corresponding high and low levels of the electrical signal , respectively, the electrical signals of LD in Fig. 11.8 are given by: ⁄2 ⁄2 bit 1 (11.35a) bit 1 (11.35b) Threshold, bit 0 Threshold. bit 0 Each bit in Eq. (11.35) is distinguished by the corresponding electrical signal level. Besides a constant threshold level, which is equivalent to the average signal level, is also included and one can regenerate the information bits by comparing signal to corresponding threshold level. In Section 11.6.1, this threshold level was defined as the optimal threshold level. and are used to internal-modulate two optical sources at and , respectively. The output of optical transmitter (OTx1) is wavelengths of given as: Due (11.36) equiprobable data transmission link the average power level ⁄2 ( 1, 2). By defining the extinction ratio , ⁄ 1 low and high power levels can be expressed as 2 and ⁄ 1 2 , respectively. Therefore, outputs of OTxs ( ) are expressed as: 266 to bit 1 Threshold. bit 0 Chapter 11. Implementing Differential Signalling in Free Space Optical Communication Link 1 1 bit 1 Threshold, bit 0 (11.37a) Threshold. bit 0 (11.37b) , where represents the atmospheric bit 1 The received optical power at the Rx turbulence. The outputs of ORxs are given by: bit 1 Threshold, 2 (11.38a) bit 0 bit 1 Threshold. 2 (11.38b) bit 0 As seen from Eq. (11.38) the threshold levels are affected by turbulence. If only a link with the wavelength is considered then the FSO link in Fig. 11.8 is simplified to a SISO link for which the average value and the variance of the received electrical signal are defined as [71]: Mean Mean Var where Φ , Var Φ bit 1 Threshold, Φ . Thus using Eq. (11.31) one has: (11.39a) bit 0 bit 1 Threshold, (11.39b) bit 0 267 Advances in Optics: Reviews. Book Series, Vol. 3 exp 4 , Threshold, Φ Mean Var bit 1 bit 0 1 , (11.40a) bit 1 Threshold. Φ (11.40b) bit 0 The expression in Eq. (11.40a) shows that the average of threshold level depends on Lognormal variances ( , ). Besides based on Eq. (11.40b), the threshold level fluctuates with the given order as predicted before. The combined output is given as: Φ bit 1 Threshold. Φ (11.41) bit 0 Mean ∙ and Var ∙ will be as given in Eq. (11.42). If laser beams are propagating very close to each other, then they experience the same turbulence strength and , , , therefore Eq. (11.42) leads to Eq. (11.43). Mean Mean Var Φ Var Φ Var Var 268 Var 2 2 Var 2 Var Φ , , , , , Φ , Var Φ Φ Var Var Var bit 1 Threshold, exp 4 bit 0 , (11.42a) bit 0 Mean , Var Mean Threshold, Φ Mean Φ Mean Mean bit 1 Mean 1 Var Var bit 1 Threshold, bit 0 (11.42b) (11.43a) Chapter 11. Implementing Differential Signalling in Free Space Optical Communication Link Φ 2 Φ 2 2 , , , bit 1 Threshold. Φ Φ (11.43b) bit 0 In Section 11.6.1, it is assumed that the links are the same. Here it is good to start with the same concept just to generalize the expressions derived before. Later on the general case where links are not the same be will discussed. By setting Φ Φ or equivalently the average of the threshold level is fixed to ~0 no matter how strong the turbulence is. On the other hand, the variance of the detection threshold under the same condition is defined as: Var 2 exp 4 , 1 Φ 1 , , , , (11.44) denotes the detection threshold level. The derived expression in Eq. (11.44) where is compatible with what was achieved in Eq. (11.33b). From Eq. (11.19), one can formulate the average and the variance of low level of the combined as: high level 2Φ Mean Mean 2Φ Var 4 exp 4 , 1 Φ Var 4 exp 4 , 1 Φ 2 , 2 , and , (11.45a) , (11.45b) , , , , , (11.45c) . (11.45d) Using Eq. (11.45) one can assess the quality of the signal using the Q-factor parameter as given by [72]: Q | | . (11.46) Eq. (11.46) will be used to study the effect of channel characteristics on the received signal in a differential signalling based FSO system in the following sections. 11.7.4. BER Expression For simplicity, the subtracted signal is assumed to be as: ̅ , (11.47) 269 Advances in Optics: Reviews. Book Series, Vol. 3 where is the total AWGN of the Rx. The fading of received intensities is exp 2 where denotes the average signal intensity without turbulence given as with Logand is a distributed normal random variable with mean and variance [54]. To ease the derivation two normal PDF [54]. Also for normalised PDF identical links meanings are considered as . Furthermore it is assumed that exp 2 , where is also a distributed normal random variable with and variance , . To normalize the condition is considered. mean , To obtain , , the following expression is used [71]: , , ln 1 (11.48) where is set to 1 for normalization and Var can be obtained the same as Eq. (11.32b). On the other hand, it can be shown that Var and Var are defined as [71]: Then Var 1 , E . (11.49) will be achieved by the following expression: , , ln 1 , 1 , 1 2 , , 1 , 1 . (11.50) Once equivalent Log-normal variance ( , ) is achieved it is possible to specify the PDF of a differential signalling FSO system by means of Eq. (11.15). Having PDF, one can calculate the average BER of the link using Eq. (11.23). 11.7.5. Numerical Analysis In this section, the effect of link parameters on the performance of differential signalling system will be analysed. The derived expressions will be used and wherever applicable will be supported with Monte-Carlo simulation. In previous section it was shown that by a constant threshold level of 0 can be used for different setting turbulent conditions. Also it was shown that for correlation coefficient ( , ) of 1 the fluctuation of the threshold level reaches its minimum value. In the analysis the adopted wavelengths were 830 and 850 nm and link was 1 km long. To calculate Mean and Var of SISO and differential signalling links, Eqs. (11.40) and (11.43) were used, respectively whereas Eq. (11.46) was used for calculation of the Q-factor. The given values of SNR denote the electrical SNR of the signal before the sampler block box as in Fig. 11.8. From Eqs. (11.40) and (11.43), it is deduced that the threshold level is dependent from extinction ratio ( ). To confirm this, Monte-Carlo simulation was used for both SISO and differential signalling systems for 5 and 10 with Φ Φ 5.7 mV, Φ 8.1 mV, , 1, and 0.5. To obtain each corresponding value, a 1 Mbits of data was transmitted with 270 Chapter 11. Implementing Differential Signalling in Free Space Optical Communication Link 10 independent iterations. The other parameters of the simulations were set according to Table 11.1. The obtained results are summarized in Table 11.2. Note that the fading varying frequency of the channel is in the order of 400 Hz [73], thus in both simulations and experiments, a low data rate was selected to avoid the need for storage of large number of samples. Table 11.1. The summary of FSO system properties used in the differential signalling simulation. Parameter Data rate Link length Turbulence strength Correlation coefficient , Received average optical power PD responsivity Noise spectral density Number of transmit bits Number of iterations Value 1 Mbps 1 km 1, 2.5, and 5 m ⁄ 10 0, 0.5, 0.8, and 1 20 dBm 0.4 102 dB/Hz 1 Mbits 10 Considering the theoretical and simulation results; it is seen that the proposed theory can predict the system behaviour accurately. Besides in agreement with Eqs. (11.40) and (11.43), for the same link condition but different extinction ratio ( ), mean value of threshold detection (Mean ) and standard deviation value of threshold detection ) are the same. ( Var Table 11.2. The theoretical analysis accompanied by simulation of mean of detection threshold (Mean) and standard deviation of detection threshold (√Var) of single-input single-output (SISO) and differential signalling (DS) links for different extinction ratios (ε) of 5 and 10 but fixed Ф1 = Ф2 = 5.7 mV, ФSISO = 8.1 mV, where channels are highly correlated 1,2 = 1, and Rytov variance (R2) is 0.5. SNR (dB) 5 12.2 10 14 Link SISO DS SISO DS a 7.6; [8.1, 0.5] 0.0; [0.0, 0.1] 7.6; [8.1, 0.6] 0.0; [0.0, 0.1] b √ 3.0; [3.3, 0.9] 1.9; [1.8, 0.1] 3.0; [3.4, 0.8] 1.9; [2.0, 0.1] For each case there is a pair of numbers separated by comma. The first number denotes theoretical analysis result while the pair shows the simulation outcome in form of expected value and standard deviation pair, respectively. a, b As discussed earlier for Φ Φ and , 1 , regardless of turbulence conditions, 0 and Var Mean , , . To prove this, another set of analysis 0 to was performed for a range of turbulence strength from almost a clear channel 1 . As shown before, the value of did not affect Mean and 271 Advances in Optics: Reviews. Book Series, Vol. 3 ; then for the simulation, the extinction ratio ( ) was set to 10 and SNR Var was changed by setting Φ . The results of the analysis are represented in Fig. 11.9. From Fig. 11.9 it is observed that for both SISO and differential signalling. For the theory can predict the Mean , there is a slight deviation between the theory and simulation, however Var both theory and simulation show the same trend. As predicted from Eq. (11.40) Mean and Var of SISO link are changing with the turbulence strength. Var of SISO link almost equals to the standard deviation of noise 1.32 mV for a clear channel condition (i.e., Rytov variance ( ) of ∼0) and it , values, which agrees well with Eq. (11.39b). Besides, increases for higher values of and Var of the SISO link. different SNRs results in various Mean Since in this analysis was fixed then SNR was changed by setting appropriately Φ . Thus, the gain of the TIA ( ), PD responsivity ( ), and LD output power ) can change the required threshold level whereas has no effect on it. On the other ( hand for the differential signalling link, Mean is constant for various turbulence conditions and different values of SNRs. This was expected because from Eq. (11.43a) when links have the same parameters (i.e., Φ Φ ) and the optical beams undergo the same turbulence effect; the required threshold level at the Rx is zero for various turbulence of the differential signalling link is also conditions and different SNRs. Var fixed for different turbulence conditions and various SNRs. From Eq. (11.43b) it is known ⁄ 1.9 mV, which agrees well with the simulation that Var , , results as in Fig. 11.9(b). In another set of analysis, the Q-factor for both SISO and differential signalling links are compared under different conditions. From Eqs. (11.40), (11.43), and (11.46) it is seen that in contrary to the Mean and Var , the Q-factor also depends on . Therefore, is set to 5 and 10 for SNRs of 10, 12, 14 dB and the same turbulence strength is used. The theoretical and simulation results are illustrated in Figs. 11.9(c) and 11.9(d). Figs. 11.9(c) and 11.9(d) confirm that the proposed theory predicts the Q -factor for both SISO and differential signalling links. In Fig. 11.9(c) 5, where is 10 for Fig. 11.9(d). For a clear channel ⁄ 10 and as increases, the Q-factor tends to reduce. Changing condition, Q from 5 to 10 has no effect on the Q-factor of the differential signalling link while the SISO 5 in a turbulent channel. link shows a lower Q-factor for So far it has been shown out that for , 1 and Φ Φ , both the Mean and of SISO and differential signalling links and the Q-factor of the differential Var signalling link are independent of and change with Φ . The results also showed that changing Φ has no effect on the Mean and Var of the differential 1. signalling link for , 272 Chapter 11. Implementing Differential Signalling in Free Space Optical Communication Link 12 8 6 p 4 Line+hollow marker Solid marker 2 SISO DS SNR = 10 dB SNR = 12 dB SNR = 14 dB 6 Var(Vthr esh ) mV M ean(Vthr esh ) mV 10 7 SISO DS SNR = 10 dB SNR = 12 dB SNR = 14 dB  i = 10 1,2 = 1 Theory Simulation 5  i = 10 1,2 = 1 Line+hollow marker Solid marker Theory Simulation 4 3 2 0 0 0.2 0.4 0.6 0.8 1 1 0 0.2 0.4 0.6 2 (a) 1 (b) 5.5 7 SISO DS SNR = 10 dB SNR = 12 dB SNR = 14 dB i = 5 1,2 = 1 6 5 Line+hollow marker Solid marker SISO DS SNR = 10 dB SNR = 12 dB SNR = 14 dB  i = 10 1,2 = 1 5 4.5 4 Theory Simulation Line+hollow marker Solid marker 3.5 4 Q Q 0.8 <2R <R Theory Simulation 3 2.5 3 2 1.5 2 1 1 0 0.1 0.2 0.3 0.4 0.5 <2R (c) 0.6 0.7 0.8 0.9 1 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 <2R (d) Fig. 11.9. Simulation results of: (a) mean of detection threshold Mean(Vthresh), (b) standard deviation of detection threshold √Var(Vthresh), and (c, d) Q-factor versus Rytov variance (R2). The comparison is performed for a range of turbulences and SNRs for: (a) and (b) εi = 10, (c) εi = 5, and (d) εi = 10. SISO and DS refer to single-input single-output and differential signalling, respectively. εi and 1,2 denote extinction ratio and correlation coefficient, respectively. Note that in (c) and (d) the error bars are too small to be seen. It is important to note that Eq. (11.13) gives different results for and , which results in different Log-normal variances (i.e., , , ). Therefore, the simplified expressions given in Eq. (11.34) are no longer valid. Also note that spatial coherence radius ( ) in Eq. (11.10) is a function of wavelength, which leads to different values of correlation coefficient ( , ) for the same FSO system. This issue necessitates us to define a constraint on how distinct the wavelengths can be and also to study the effect of correlation coefficient on the system performance. 273 Advances in Optics: Reviews. Book Series, Vol. 3 To define a constraint for the difference of two wavelengths, which still validates the use of Eqs. (11.10), (11.13), and (11.34), the derivatives of , , , and are taken with respect to . After a series of mathematical simplification, one has: ∆ where ∆ ⁄2 and ∆ , ∆ | , , 2 , ∆ ∆ , (11.51a) , ln (11.51b) , |. ∆ , (11.51c) Considering the rule of thumb that a 10 % tolerance relative to the absolute value is is extracted. This acceptable, from Eqs. (11.51a) and (11.51b) the criteria of ∆ ⁄ and ), means that for criteria, which is independent from the FSO channel (i.e., ∆ ⁄ , Eqs. (11.10) and (11.13) give approximately the results for both wavelengths with 10 % relative deviation. However, in Eq. (11.51c) a fixed constraint cannot be derived. It can be easily shown that assuming the same rule of thumb of ∆ , ⁄ , 0.1 the criteria based on Eq. (11.51c) is given by: ∆ ⁄ . (11.52) Fig. 11.10 shows ∆ ⁄ with respect to ⁄ , a characteristic, which is independent from wavelength, and the link distance or the turbulence strength. It is deduced from ⁄ → 0 the range of selecting and broadens Eq. (11.52) that for ⁄ (i.e., ∆ ⁄ → ∞), whereas for 0 0.26 the range of applicable wavelengths is reduced (i.e., ∆ ⁄ 0.47). Therefore, there is a trade-off between how close the beams have to be and how different the wavelengths can be. The two differential signalling link conditions (i.e., Φ Φ and , → 1) are ideal and in reality there are deviations from the ideal scenario. Thus, the mean value of threshold ), the variance value of threshold detection ( Var ) and detection (Mean the Q-factor are compared for SISO and differential signalling links for the same SNR but different values of Φ over a range of correlation coefficient ( , ). The SNR was set to 12 dB and extinction ratio ( ) was changed to 5, 10, and 20. The turbulence strength of 0.5 was considered and the results are depicted in Fig. 11.11. The value of , spans from uncorrelated channels conditions (i.e., , 0) to fully correlated channels 1). The accuracy of the proposed theory for , range is obvious condition (i.e., , from the good agreement between simulation and predicted results as depicted in Fig. 11.11. 274 Chapter 11. Implementing Differential Signalling in Free Space Optical Communication Link 10 0 " 6 =60 10 1 10 10 -1 -2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 dr =; 0 Fig. 11.10. Δλ/λ0 plotted with respect to dr/0. The graph shows the relation between the tolerable optical sources wavelengths and the distance between the optical receivers, while the channels are kept independent. The graph is obtained from Eq. (11.28). As expected from Eq. (11.39a) the mean value of the detection threshold (Mean ) of the SISO link in Fig. 11.11(a) depends on the link parameters. Mean of the SISO link decreases when extinction ratio of SISO link ( ) is higher. To keep SNR at 12 dB, the value of Φ was changed to 7.9, 6.4, and 5.8 mV. On the other hand, from Eq. (11.39a) it is observed that for higher Φ the resultant Mean is also higher. The variance value of the detection threshold (Var ) of the SISO link in Fig. 11.11(b) also is dependent on the link parameters and since for a fixed SNR higher requires lower Φ , then Var of the SISO link for higher is reduced. This deduction is in agreement with Eq. (11.39b). Fig. 11.11(c) illustrates the Q-factor for the SISO link, which are obtained from | in Eq. (11.46) is dependent on Mean Eq. (11.46). The numerator |Mean both and Φ , however the effects of Φ and are opposite, therefore for | value. On the same SNR, higher Mean results in the same |Mean the other hand, Var Var is increased for the same SNR and higher Φ . Therefore, the Q-factor of the SISO link is lower for lower values of . Mean of the differential signalling link in Fig. 11.11(a) is also dependent on the link parameters and since Φ Φ the value of Mean is non zero. But as discussed for the SISO link, for the same SNR and higher the value of Mean is reduced. and the Q-factor of the differential signalling link depend on not only the Var link parameters but also on correlation coefficient ( , ). As seen in Fig. 11.11(b) of the differential signalling link reaches the minimum value of total Var standard deviation of noise ( , , ⁄ 1.9 mV) for , 1. Also it can be seen 275 Advances in Optics: Reviews. Book Series, Vol. 3 that lower results in smaller Var . Fig. 11.11(c) shows the Q-factor of the 10 ⁄ at differential signalling link that achieves the maximum value of Q 1. As discussed for the SISO link, the same SNR and higher leads to higher , values of the Q-factor. SISO DS =5  = 10  = 20 SISO 9  = 10  = 20 3.2 Var(Vt hr esh ) mV 7 6 5 4 3 3 2.8 2.6 2.4 2.2 p M ean(Vthr esh ) mV =5 3.4 8 2 2 1 0 DS 1.8 0 0.2 0.4 ; 1;2 0.6 0.8 1.6 1 0 0.2 0.4 (a) ; 1;2 0.6 0.8 1 (b) SISO DS =5  = 10  = 20 2.4 2.2 Q 2 1.8 1.6 1.4 0 0.1 0.2 0.3 0.4 0.5 ; 1;2 0.6 0.7 0.8 0.9 1 (c) Fig. 11.11. Simulation results of: (a) mean of detection threshold Mean(Vthresh), (b) standard deviation of detection threshold √Var(Vthresh), and (c) Q-factor. The comparison is performed between single-input single-output (SISO) link and differential signalling (DS) and for different values of extinction ratios (εi) over a range of correlation coefficient (1,2). Based on the analysis, if achieving higher SNR in a differential signalling link is desirable, then increasing is the preferred option. Of course, increasing needs to be done with respect to the span of laser L-I curve linear region to avoid pulse shape distortion. 276 Chapter 11. Implementing Differential Signalling in Free Space Optical Communication Link To validate the work in Section 11.6.4, the BER results from Eq. (11.50) were compared with the simulation data. The parameters adopted for the FSO system investigated are given in Tabl. Fig. 11.12 shows the predicted and simulated BER versus SNR obtained from the theory as well as the performed simulation based on Eq. (11.50) for the FSO with 0 , and 0.8 and 1 10 and differential signalling for , ⁄ 2.5 10 m . The simulation results are presented by large markers for each case with the error bars to show the tolerance of the simulated values. To obtain each point, 10 iterations were carried out with 1 Mbps of transmit bit stream for each iteration. Note that for BER < 10-6, the simulation results were zero, and therefore are not shown in the graph. It is clear from the figure that the initial assumption that with a Log-normal distribution does indeed lead to a good approximation of PDF of the differential signalling method for the weak turbulence regime. 10 10 BER 10 10 10 10 10 0 -2 -4 -6 C2n =1.0x10-15 ,1,2 =0.0 C2n =2.5x10-15 ,1,2 =0.0 -8 C2n =1.0x10-15 ,1,2 =0.8 C2n =2.5x10-15 ,1,2 =0.8 -10 Line+hollow marker Solid marker -12 0 2 4 6 Theory Simulation 8 10 SNR (dB) 12 14 16 18 20 Fig. 11.12. BER versus SNR in dB of an FSO system with the differential signalling method. The comparison is carried out for various turbulence strengths (Cn2) and correlation coefficients (1,2). Solid lines marked with small markers are based on the derived equations whilst large markers are obtained from the simulation. It was discussed in Section 11.5 that when the channels are fully correlated (i.e., , 1) the effect of the turbulence has the minimum influence on the received signal. In the next 5 10 m ⁄ was considered and the correlation according was changed step based on Tabl. The results in Fig. 11.13 show that when the correlation coefficient increases, the performance of differential signalling method improves in term of 1 the FSO system mitigating the turbulence effect. As shown in Fig. 11.13, for , with the differential signalling scheme offers almost the same performance as in the clear 0 ) in Fig. 11.13, the simulation error channel. For the uncorrelated case (i.e., , increases so that the error bars shown are negative, which are not shown in the logarithmic scale. 277 Advances in Optics: Reviews. Book Series, Vol. 3 10 10 BER 10 10 10 10 10 0 -2 2 Cn = 5x10 -4 -15 Clear -6 1,2 = 0 1,2 = 0.5 -8 1,2 = 0.8 1,2 = 1 -10 Line+hollow marker Solid marker -12 0 2 4 6 Theory Simulation 8 10 SNR (dB) 12 14 16 18 20 Fig. 11.13. BER versus SNR in dB of an FSO system with the differential signalling method for Cn2 = 5×10-15 m-2/3 and a range of correlation conditions (1,2). Solid lines with small markers are based on theory whereas large markers are obtained from simulation. The plus maker denotes the clear channel condition. 11.7.6. Atmospheric Turbulence Experiment To prove the concept of differential signalling technique, the experimental work for the proposed system as given in Fig. 11.14 will be outlined. Chamber Length = 6 m OTx1 OTx2 Mirror BS ORx1 O F 2 Hot Air O F 1 ORx2 Fan Fig. 11.14. Block diagram of the atmospheric turbulence and differential signalling experiment. PATH1 and PATH2 are referring to uncorrelated and correlated paths, respectively. OTx, BS, OF, and ORx are optical transmitter, beam splitter, optical filter, and optical receiver, respectively. 278 Chapter 11. Implementing Differential Signalling in Free Space Optical Communication Link According to proposed scheme shown in Fig. 11.8, an experimental setup for the proposed 0) method was developed to evaluate its performance for both uncorrelated (i.e., , and correlated (i.e., , → 1) channels conditions as depicted in Fig. 11.14. Snapshots of the setup are also shown in Fig. 11.15. The laser beams (see Fig. 11.15(a)) were launched into a chamber of length 6 m, emulating an outdoor uncorrelated FSO channel (see Fig. 11.15(b)). The incident and reflected ray paths are labelled as PATH1 and PATH2, respectively (see Fig. 11.14). In PATH1 optical sources were spaced apart by a minimum ⁄ ⁄ 5 mm to ensure uncorrelated fading conditions (i.e., 5). distance of An adjustable mirror positioned at the other end of the chamber was used to increase the path length by reflecting back the beams. The reflected beams indicated by PATH2 in Fig. 11.14 were kept as close as possible to each other to ensure high correlation between the two paths (note that PATH2 in Fig. 11.14 corresponds to FSO channel in Fig. 11.8). (a) (b) Fig. 11.15. Experimental setup of atmospheric turbulence and differential signalling: (a) OTxs and ORxs at one end of the chamber, and (b) atmospheric camber with temperature sensors to measure temperature gradient, and a pipe to isolate either PATH1 or PATH2 from the turbulent condition of the chamber. OF, OTx, ORx, and BS are optical filter, optical transmitter, optical receiver, and beam splitter, respectively. Heater fans were used to generate turbulence in the chamber, see Fig. 11.14. To measure , the method of thermal structure parameter was used (based on temperature gradient measurement) as in [74]. The temperature gradient was measured using 20 temperature sensors positioned along the chamber, see Fig. 11.15(b). At the Rx end, the reflected beams passed through a 50/50 beam splitter and were applied to two identical PIN PDs after optical filters, see Fig. 11.14 and Fig. 11.15(a). The outputs of PDs were captured using a real-time digital storage oscilloscope for further processing in MATLAB®. First investigated was the effect of turbulence on the uncorrelated path within the chamber. The reflected beams (i.e., PATH2) were passed through a pipe positioned within the chamber. The pipe ensured that propagating beams inside it did not experience any turbulence, see Fig. 11.15(b). Similarly, the effect of turbulence on the correlated path was investigated by isolating the uncorrelated channels (i.e., optical beams in PATH1 279 Advances in Optics: Reviews. Book Series, Vol. 3 propagating through the pipe), see Fig. 11.14. The amplitude of and ̅ were then set in order to ensure that both received electrical signals and had the same amplitude of ~300 mV, which is equivalent to Γ Γ criterion. Fig. 11.16 illustrates the histogram of the detection threshold level obtained from the experiment. Note that due to the hardware dissimilarities, the average of the detection threshold is non-zero. However, since the offset levels are due to ORx1 and ORx2, then the problem can be resolved by adjusting the offset level of the output signal. Table 11.3 shows all the key parameters adopted in the experiment. The recorded data were processed and the detection threshold level was extracted from signals. Fig. 11.17 illustrates the sampled signal as well as the obtained detection threshold level of . The measured mean (indicated by Mean and √Var , respectively) for and standard deviation of correlated and uncorrelated channels are summarized in Table 11.4. 35 30 Uncorrelated Darkness 25 25 Number of Points Number of Points 20 15 10 20 15 10 5 0 -864.35 -864.3 -864.25 Uncorrelated Darkness 30 5 -864.2 -864.15 -864.1 -864.05 Threshold Level (mV) -864 -863.95 0 -887.15 -887.1 -887.05 -887 (a) -886.8 -886.75 (b) 35 35 Uncorrelated Darkness 30 Uncorrelated Darkness 30 25 Number of Points 25 Number of Points -886.95 -886.9 -886.85 Threshold Level (mV) 20 15 20 15 10 10 5 5 0 -915.74 -915.73 -915.72 -915.71 -915.7 -915.69 -915.68 -915.67 -915.66 -915.65 Threshold Level (mV) (c) 0 -949.92 -949.9 -949.88 -949.86 -949.84 Threshold Level (mV) -949.82 -949.8 (d) Fig. 11.16. Histograms of the detection threshold levels of the differential signal threshold (Vthresh) for atmospheric turbulence and differential signalling experiment: (a) uncorrelated channels in dark room; (b) uncorrelated channels in lit room; (c) correlated channels in dark room, and (d) correlated channels in lit room. 280 Chapter 11. Implementing Differential Signalling in Free Space Optical Communication Link Table 11.3. The setup parameters for atmospheric turbulence and differential signalling experimental. 1.05 1 1 0.95 0.95 0.9 0.9 0.85 0.85 0.8 v1 (V) v1(V) Link 2 Link 1 Parameter Data rate NRZ-OOK Chamber length Sampling rate Number of recorded points for each iteration Number of total iterations Optical transmit power Divergence angle PD responsivity Wavelength Optical transmit power Divergence angle PD responsivity Wavelength Optical receiver noise rms 0.8 Value 100 kbps 6m 2.5 M Sample/sec 1 M points 500 10 dBm 9.5 mDeg 0.3 A⁄W 830 nm 3 dBm 4.8 mDeg 0.4 A⁄W 670 nm 1.5 mV 0.75 0.75 0.7 0.7 0.65 0.65 0.6 1 2 3 4 5 Sample Point (a) 6 7 8 9 x 10 5 2.48 2.485 2.49 2.495 2.5 Sample Point 2.505 2.51 2.515 5 x 10 (b) Fig. 11.17. The sampled v1 signal with the estimated detection threshold during atmospheric turbulence experiment. The signal is in blue colour, where the dashed red line with circle markers refers to the estimated detection threshold. As predicted from Eq. (11.33a), for both uncorrelated and correlated conditions the measured mean value is zero. Fig. 11.18 shows an image taken from the oscilloscope screen illustrating how signals and for correlated channels are affected under the same turbulence conditions. Note that turbulence strength and the laser modulation index in Fig. 11.18 were deliberately set to relatively small values in order to better illustrate the correlation between and . 281 Advances in Optics: Reviews. Book Series, Vol. 3 Table 11.4. The summery of the experimental measurement results for turbulence effect on differential signalling. Mean (mv) and √Var (mv), denote the measured mean of detection threshold, variance of detection threshold of the differential signal. Cn2 and 1,2 denote obtained turbulence strength and correlation coefficient. Channels condition Uncorrelated (dark room) -864.2 Uncorrelated (lit room) -886.9 Correlated (dark room) -915.7 Correlated (lit room) -949.9 √ 43.4 45.5 12.9 12.9 ⁄ , 5.11 10 0.08 5.21 10 0.72 Fig. 11.18. Original (v1 in yellow and top) and inverted (v2 in green and bottom) signals captured on the oscilloscope during atmospheric turbulence experiment. It is expected to obtain √Var 2 from the measurements. However, given the rms noise of optical Rx in Table 11.3, the measured √Var in Table 11.4 is different from the predicted value of 2 2.1 mV. This difference might be due to imperfect correlation between channels in PATH2 and using two (not very close) wavelengths of 670 and 830 nm, which could lead to dissimilar . In the experiment 0.17, which corresponds to the weak turbulence regime [30]. Considering Eq. (11.51a) and using the 0.1, it is expected to have ∆ ⁄ 0.09. Note that in rule of thumb, to have ∆ ⁄ the experiment, the accuracy limit of Eq. (11.33b) does not apply perfectly (as 0.21, which corresponds to a maximum wavelength deviation of 160 nm around ∆ ⁄ the central wavelength of 750 nm). Using measured signals correlation coefficient ( , ) was estimated, which are presented in Table 11.4. The estimated , (for the correlated case) are relatively high but do not 282 Chapter 11. Implementing Differential Signalling in Free Space Optical Communication Link correspond to the ideal case of , 1. Other effects that could lead to inaccuracy of the measurement were the noise associated with the oscilloscope and the vibration of the whole setup. However, since it was intended to demonstrate only the difference between uncorrelated and correlated situations and during the entire measurement the same setup was used, these effects are not critical in the final conclusion. In addition to using two wavelengths and spatially closer beams from Eq. (11.10) it is evident that longer transmission spans will lead to larger values of , which in turn helps to achieve a highly correlated channels condition (i.e., , → 1) [75]. In [35], a similar differential signalling based technique was proposed to reduce the effect of background noise in the received signal. The above experiment was carried out in both dark and fully lit environments (with ambient light power level of 45 dBm and 18 dBm, respectively), see Table 11.4. A negligible difference between the standard deviation of detection threshold results in these two cases is noticed. This testifies that under the experimental conditions, the background noise was not dominant. Thus, the reduction in √Var values is due to the theory explained in Section 11.5 rather than the background noise level. Using the derived analytical expression of the variance of the detection threshold, it was shown that the fluctuation in the optimal threshold level highly depended on the correlation between the propagating optical beams. Thus the differential signalling technique is attractive when highly correlated FSO channels can be established. This deduction was validated by means of experimental investigations under uncorrelated and correlated conditions. Also note that to achieve a high correlated channel condition light sources with close wavelengths, spatially closer beams and longer transmission distance are critical to have. 11.8. Differential Signalling and Pointing Errors 11.8.1. Channel Modelling In the previous sections, the effect of differential signalling system in a turbulence channel was investigated and in this section the performance of the same system with the pointing errors is investigated. Considering Eq. (11.30), a clear weather condition and negligible atmospheric turbulence is assumed. Also it is assumed that channel coefficient ( ) includes the geometrical loss and pointing errors effects. The concept outlined in [76] is adopted to describe the pointing errors at Rxs, see Fig. 11.19. Rxs are assumed to have the same aperture diameter as well as the same electrical and optical characteristics. The aperture diameter is and the laser beam spot at the Rx transverse plane has a radius of . Besides the instantaneous radial displacement between the beam centroid and the aperture centre is denoted by . In terrestrial FSO communication systems the fading coefficient due to the geometrical loss and pointing errors is given by [76]: 283 Advances in Optics: Reviews. Book Series, Vol. 3 ; and , exp (11.53) correspond to the geometrical loss and equivalent beam-width, √ ⁄2 respectively. Note that erf and where where [76]. In most practical applications the beam divergence is ≪ 1 Rad), which leads to . Therefore, it is possible to set and . pointing errors , , by selecting the appropriate values for displacement has two components known as the boresight (displacement between beam centre and centre of the detector) and jitter (offset of the beam centre at detector plane) [49]. and erf small (i.e., √ y rb rj r 2wRX ds 2 x Beam Footprint Aperture Fig. 11.19. Rx aperture and a laser beam footprint at the Rx transverse plane. The boresight displacement ( ) represents a deviation originating from thermal expansion of the buildings [34] and determines the mean offset of pointing errors [77], whereas is a random variable originating from building sway and vibration [34]. From the statistics point of view the jitter corresponds to the random variation of the beam [77]. footprint around the boresight direction with the jitter variance of In terrestrial FSO links, the jitter consists of both vertical and horizontal components [34]. Thus, without loss of generality, here the focus will be on the deviation along either vertical or horizontal axis, which can be further extended to the other axis. It is shown in ) and the second moment [34] that has Rician PDF with the average (Mean ) given by: ( Mean 284 exp exp , , (11.54a) (11.54b) Chapter 11. Implementing Differential Signalling in Free Space Optical Communication Link where Var ⁄2 . Therefore the variance of will be: exp . exp (11.55) Since E E ̅ , where is an integer, thereafter by means of Eq. (11.54), the average and variance of Eq. (11.30) are derived as: Var Mean Var Var Mean 2 Mean Var , Var (11.56a) 2 , is the correlation coefficient between two channel coefficients of where 2⁄ . Note that to derive Eq. (11.56), it was assumed that Γ (11.56b) and . The dynamic response of a building with applied live loads depends on the directional stiffness, as well as the height, size and topology. The tip displacements of a tall building can be as large as tens of centimetres due to the normal wind loads. However, irrespective of the height and stiffness of the building, the relative displacement of Rx1 and Rx2 is almost zero. The segment of the Rx mast between the two Rxs can be reasonably assumed to be rigid if the mast is properly designed according to the building standards (i.e., earthquake or wind) and if the distance between the two Rxs is very small compared to in Fig. 11.20), then , . the overall height of the building ( ≅ , Considering the short distance between the two Rxs the relative displacement due to the thermal expansion, which results in , , , can be neglected. The same is true for the relative displacement between the Txs. In view of the above, it can be assumed , , and  ≅ 1. Fig. 11.20. Effect of building movement on FSO Rxs with exaggeration. On the left there is the Tx building hypothetically without movement and on the right the Rxs are installed on top of a building, which is influenced by the effect of building movement. 285 Advances in Optics: Reviews. Book Series, Vol. 3 Considering , , , Eq. (11.56) will be: Mean Var 2Var 1 0,  (11.57a) 2 . (11.57b) Therefore, regardless of the strength of pointing errors the detection threshold level can be set to zero but will experience fluctuation with the given variance. Considering 2 , thus leading to the elimination of  ≅ 1, Eq. (11.57b) simplify to Var pointing errors at the Rx. Therefore for the system shown in Fig. 11.8 provided links are identical, and Rxs are mounted on the same fixture structure, the threshold level could be set to zero for a range of pointing errors strength. To estimate the equivalent parameters of the differential signalling based link, a SISO link with a Rayleigh pointing errors PDF is used as the equivalent link. The pointing errors parameters of the equivalent SISO link is found so that SISO has the same pointing errors variance as differential signalling. For the simplified case where , 0, , Var assuming that and , and simplifying Var , the following equation is derived from which of the equivalent pointing errors PDF can be obtained: 2 1 ⁄ 2 1 2 1  ⁄ , (11.58) when , 0, Rician distribution becomes Rayleigh and it is assumed that PDF , of the equivalent pointing errors to perform comparison is also Rayleigh. 11.8.2. Pointing Errors Experiment To validate the proposed concept practically the experimental setup shown in Fig. 11.21 has been used. Both Txs and Rxs modules were located at one end of a 6 m long indoor atmospheric chamber. In order to double the link length a mirror was used at the other end of the chamber to reflect back the beams (note that the mirror is not shown in the figure). Since the optical beams were in parallel with no overlap at the Rx plane, no optical filters were used. The outputs of Rxs were recorded using a sampling oscilloscope for further analysis via MATLAB®. The amplitude of modulating signal was set such that the Rx output levels were at ~10 mV . Table 11.3 summarizes the key system parameters adopted. Note that in this experiment, the number of iterations was only 50 since the vibration had a fixed pattern rather than being random. To simulate pointing errors condition, both Rxs were positioned on a vibration stand vibrating at a frequency of 5 Hz with the deviation of ~2 mm in the vertical direction (a sinusoidal waveform was used to stimulate the vibrator). In practical scenarios FSO links will experience vibrations in both axes but here the vibration is generated only on the vertical axis. Note that it has the same effect as for vibrations on the horizontal axis. 286 Chapter 11. Implementing Differential Signalling in Free Space Optical Communication Link Fig. 11.22 depicts a captured image from the oscilloscope screen for two signals. Note that the laser modulation index in Fig. 11.22 was deliberately set to relatively small value in order to better illustrate correlation between and . As shown the effect of pointing errors on both signals are highly correlated. The recorded data were processed and the detection threshold level was extracted from signals. Fig. 11.22 illustrates the sampled signal as well as the detected signal . The histogram of the recorded threshold levels for the differentiated signal is illustrated in Fig. 11.23. As in the previous experiment, the dissimilarity of the offset levels added by ORxs results in a non-zero DC offset in the detection threshold level. Fig. 11.24 illustrates the histogram of the detection threshold level obtained from the experiment Fig. 11.21. The pointing errors and differential signalling experimental setup. OTx and ORx are optical transmitter and optical receiver, respectively. Fig. 11.22. An image taken from the oscilloscope screen during the pointing errors and differential signalling experiment. Top yellow signal is v1 whereas bottom green one is v2. 287 Advances in Optics: Reviews. Book Series, Vol. 3 Based on the covariance matrix of the received signals, the correlation coefficient ( ) of 0.92 was obtained from the measurements, which agrees well with the assumption of  → 1 made in the analysis. The measured standard deviation of , and are presented in Table 11.5. -9.846 -9.84 -9.848 -9.85 -9.852 -9.854 -9.86 v2(V) v2(V) -9.85 -9.856 -9.858 -9.87 -9.86 -9.862 -9.88 -9.864 -9.89 -9.866 1 2 3 4 5 Sample Point 6 7 (a) 8 9 4.07854.079 4.0795 4.08 4.08054.081 4.08154.0824.08254.083 4.0835 Sample Point 5 x 10 (b) 5 x 10 Fig. 11.23. The sampled v2 signal with the estimated detection threshold during pointing errors and differential signalling experiment. The signal is blue colour where the dashed red line with circle markers refers to the estimated detection threshold. Table 11.5. The summery of the measurements results for pointing errors and differential signalling experiment. Signal √Var mv 24.75 27.00 4.58 7 6 Number of Points 5 4 3 2 1 0 -9.914 -9.912 -9.91 -9.908 -9.906 -9.904 -9.902 -9.9 Threshold Level (V) -9.898 -9.896 -9.894 Fig. 11.24. Histogram of the detection threshold levels of the differential signal (Vthresh) for pointing errors and differential signalling experiment. 288 Chapter 11. Implementing Differential Signalling in Free Space Optical Communication Link As discussed before for the same pointing errors jitters (i.e., , , ), the variance of ) in Eq. (11.57b) results in almost the same range for both channel coefficient (Var signals. The close match between the measured values of standard deviation of and confirms the deduction. On the other hand, according to Eq. (11.57b), if the effects of pointing errors on both signals are highly correlated, then standard deviation will significantly be reduced by 2 . However the measured value of 4.58 mv slightly differs from the predicted value of 2 2.1 mV. This can be due to the small difference in the values Var and Var . Although the experiment was conducted over a 12 m long of Var FSO link, the investigation can be extended to longer spans. Using the same laser beam, but over a longer link span, the geometrical attenuation and the beam footprint at the Rx will be larger. Higher geometrical loss will reduces whereas larger optical footprints will lead to reduced and increased . However, as seen from Eq. (11.57b), for  → 1 these parameters will have no effect on the resultant variance. , (from Eq. (11.57)) the variance of equivalent differential Using the predicted signalling pointing errors ( , ) can be determined for a range of  . Fig. 11.25 depicts the jitter standard deviation against channel correlation (  ) for the SISO link and equivalent link of differential signalling for receiver aperture radius ( ) of 10 cm, laser beam radius at receiver ( ) of 100 cm , and the jitter variances of 10 cm (i.e., 10 cm ). It is observed that the pointing errors induced fading effect reduces , , with increasing value of  . Also from both Eq. (11.57) and Fig. 11.25 it is seen that for  0.5 one obtains . 14 12 <j (cm) 10 8 6 4 SISO DS PE = 0.5 2 0 0 0.1 0.2 0.3 0.4 0.5 ; PE 0.6 0.7 0.8 0.9 1 Fig. 11.25. Jitter standard deviation of the equivalent differential signalling (DS) pointing errors versus correlation coefficient (PE), for the single-input single-output (SISO) system with differential signalling and for receiver diameter (ds) of 20 cm, beam radius (wRx) of 100 cm, and jitter variances of 10 cm (i.e., j,1 = j,2 = 10 cm). 289 Advances in Optics: Reviews. Book Series, Vol. 3 11.9. Differential Signalling and Manchester Code 11.9.1. System Configuration To the best of our knowledge, Manchester code has not been used to mitigate the fading effect of the channel in a FSO link. In fact, Manchester code is used to achieve clock synchronization. It also can be used to remove the DC component of the signal and to avoid a long stream of logic ‘1’ or logic ‘0’ [78]. In this work Manchester code is adopted to remove the need for two parallel highly correlated links in a differential signalling system. Fig. 11.26(a) illustrates the proposed concept, where the input bit stream and its inverted version are applied to the encoder, which is fed directly to the optical source. The output of the encoder is the Manchester code (also known as phase encoding) word in which the encoding of each data bit has at least one transition at the centre of each bit period, and has a bandwidth twice that of the input signal [78]. Input Bit A Manchester Encoder 1 A 1 B 0 0 1 1 0 1 T Received Signal (a) B C r1 Sample Combiner r2 Received Bit D A 0 1 1 0 A Sampling at t T/4 Sampling at t 3 T/4 1 0 B Output Bit 1 t t+T/4 t+3× T/4 (b) Fig. 11.26. The required signal processing to perform differential signalling using one FSO link. The procedure is shown for a sequence of 01101 bits as an example: (a) the required signal shaping at the Tx, and (b) the required signal recovery at the Rx where two samples (i.e., r1 and r2) are taken at the presented intervals. In the proposed differential signalling scheme, the received raw signal is processed prior to quantization. At the Rx the regenerated bit stream is passed through sampler modules and a combiner, which simply subtracts the sampled outputs, to recover the NRZ data stream as shown in Fig. 11.26(b). As seen so far in the proposed technique the original and inverted versions of signal are transmitted by means of Manchester code and a single FSO link whereas in Section 11.6 and Section 11.7 this was done using two distinct FSO links. Thus, the proposed method ensures that the channels are highly correlated. Besides, it eliminates the need of optics for combining and separating two FSO links as in Section 11.6.3. 290 Chapter 11. Implementing Differential Signalling in Free Space Optical Communication Link 11.9.2. Manchester Code Experiment To prove the validity and benefit of the proposed method an experimental test bed for a SISO FSO link was developed to measure the variation of the threshold level and the Qfactor. The experiment was using the same indoor atmospheric chamber. The method (in unit of m ⁄ ), which is known described in Section 11.6.6 was used to estimate as refractive index structure coefficient and shows the strength of the turbulence strength. For each scenario 250 data sets were recorded. The summary of the experimental setup for the 830 nm wavelength is summarized in Table 11.3. (a) (b) Fig. 11.27. The experimental setup: (a) equipment at the Tx side, and (b) artificial atmospheric channel. AWG and OTx denote arbitrary waveform generator and the optical source, respectively. The experimental setup also is illustrated in Fig. 11.28. Measurements were taken for three different channel conditions, and were also repeated under dark (ambient light power 45 dBm) and bright (ambient light power 18 dBm) environments to ensure that the measurement were not influenced by any undesirable optical signal. Since the results taken under dark and bright room conditions were almost the same only measured data set for the bright room condition are presented, see Table 11.6. The results clearly show the advantage of the proposed method. For example, for 291 Advances in Optics: Reviews. Book Series, Vol. 3 6.06 10 m ⁄ where SISO link did not provide acceptable signal quality (the Q-factor is less than the required value of 4.75), the proposed method results in a Q-factor which is larger than SISO. Besides, compared to a SISO link, the proposed method effectively reduced the variation of detection threshold. The outcome of the experimental result agrees with the deduction in Section 11.6.3 and Section 11.8.1 in the way that in the proposed scheme the channels are highly correlated, therefore a high performance enhancement was expected. To conclude this section, the histogram of the recorded signals for a clear channel as well 6.06 10 m ⁄ are included in Fig. 11.28. In as a turbulent channel for contrast to the previous cases, the combination of Manchester code and differential signalling method results in a signal with a zero offset. 25 25 SISO Threshold Level Turbulence 20 Number of Points Number of Points 20 SISO Threshold Level Clear Channel 15 10 5 15 10 5 0 2853.9932853.9942853.9952853.996 2853.9972853.9982853.999 2854 Threshold Level (mV) 0 2854.001 2508.9 2508.95 2509 2509.05 2509.1 2509.15 2509.2 2509.25 2509.3 Threshold Level (mV) (a) (b) 18 14 12 DS Threshold Level Clear Channel 16 14 Number of Points 10 Number of Points DS Threshold Level Turbulence 8 6 4 12 10 8 6 4 2 0 -3 2 -2 -1 0 1 Threshold Level (mV) (c) 2 3 -3 x 10 0 -4 -3 -2 -1 0 1 Threshold Level (mV) 2 3 4 x 10 -3 (d) Fig. 11.28 (a-d). (a, b) histograms of the detection threshold levels of the single-input single-output link, (c, d) histograms of the detection threshold levels of the differential signalling (DS) link. 292 Chapter 11. Implementing Differential Signalling in Free Space Optical Communication Link 25 18 SISO Q-factor Clear Channel 14 Number of Points Number of Points 20 SISO Q-factor Turbulence 16 15 10 12 10 8 6 4 5 2 0 5 10 15 20 Q 25 30 35 0 0.5 40 1 1.5 2 (e) 3.5 4 DS Q-factor Turbulence 16 14 14 12 10 8 6 12 10 8 6 4 4 2 2 0 38 3 18 DS Q-factor Clear Channel Number of Points Number of Points 16 2.5 (f) 20 18 Q 40 42 44 46 Q 48 50 0 20 25 30 (g) 35 Q 40 45 50 (h) Fig. 11.28 (e-h). (e, f) histograms of the Q-factor of the SISO link, and (g, h) histograms of the Q-factor of the differential signalling link. (a, c, e, f) are for clear conditions whereas (b, d, f, h) are for turbulent channel with Cn2 = 6.06×10-11 m-2/3. Table 11.6. The summery of the measurement for single-input single-output (SISO) differential signalling (DS) link. These results are for DS and Manchester code scheme. SISO Clear 4.25 6.06 a, b ⁄ 10 10 √ DS a Q-factor 0.88 [33.0, 5.3] 40.77 [1.7, 0.6] 7.35 [7.9, 4.1] √ 0.89 0.91 1.09 Q-factorb [45.3, 1.4] [40.3, 2.1] [40.0, 4.1] The pair shows the simulation outcome in form of expected value and standard deviation pair, respectively. 293 Advances in Optics: Reviews. Book Series, Vol. 3 11.10. Summary Using theory, simulation and experiment, the benefits of differential signalling method in turbulence and pointing errors channels were described. Differential signalling has been known as an effective method to mitigate the impact of non-random fading channels (e.g., fog) and cancelling the ambient background noise. In this chapter it was shown that differential signalling also can mitigate the effects of turbulence and pointing errors. In conditions where threshold level of the received signal is varied by turbulence and pointing errors, it was shown that by using the differential signalling method threshold level variation is reduced and the reduction depends on how correlated the channels are. In one experiment the performance of differential signalling under turbulence of 0.17 was evaluated. The measurements showed that for differential signalling in uncorrelated channels condition (i.e., , 0 ) the threshold level had the standard deviation of 43 mV whereas for the same setup under correlated condition (i.e., 0.72 ) the standard deviation reduced to 13 mV . The appropriate conditions of , approaching high correlation were also discussed and it was shown that if the wavelength difference of differential signalling links relative to the central wavelength is less than 0.47, then the channels will have correlation higher than 0.9. In another experiment, the effect of differential signalling under pointing errors fading effect was investigated. The measurement showed that where the standard deviation of threshold level for both links of differential signalling scheme was 25 and 27 mV under the same conditions the threshold level of differential signalling system with correlation coefficient of 0.92 was 5 mV . Finally, an alternative scheme was introduced that in contrary to conventional differential signalling, it only needs one FSO link. The measurements showed that under 6.06 10 m ⁄ using the aforementioned the same turbulence condition of method the Q-factor of the received signal in the new differential signalling scheme was 40 while a SISO link under the same conditions delivers a Q-factor of 1.8. For the future work the following needs investigating: 1. In this chapter, only the performance of differential signalling under a weak turbulence regime was considered. As an extension to the current work, one can look at the behaviour of the FSO system using differential signalling under moderate and strong turbulence regimes. The outcome of such investigation can result in the closed-form expression for BER. Also it will be possible to compare the performance of the differential signalling technique with other existing methods; 2. In this work pointing errors without turbulence was investigated. This work can be extended by investigating the FSO link performance with both pointing errors and turbulence; 3. The differential signalling technique was only studied for a two-level signal (i.e., NRZ-OOK), and showed that in addition to the mean value of the received signal the signal levels were also affected. Therefore, the differential signalling technique should also investigated with higher order modulations such as M-order pulse amplitude modulation ( -PAM). 294 Chapter 11. 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Haddad, Inter-relay cooperation: a new paradigm for enhanced relayassisted FSO communications, IEEE Transactions on Communications, Vol. 62, 2014, pp. 1970-1982. [58]. N. D. Chatzidiamantis, G. K. Karagiannidis, On the distribution of the sum of GammaGamma variates and applications in RF and optical wireless communications, IEEE Transactions on Communications, Vol. 59, 2011, pp. 1298-1308. 297 Advances in Optics: Reviews. Book Series, Vol. 3 [59]. W. Zixiong, Z. Wen-De, F. Songnian, L. Chinlon, Performance comparison of different modulation formats over free-space optical (FSO) turbulence links with space diversity reception technique, IEEE Photonics Journal, Vol. 1, 2009, pp. 277-285. [60]. R. Paudel, Z. Ghassemlooy, H. Le Minh, S. Rajbhandari, E. Leitgeb, Lambertian source modelling of free space optical ground-to-train communications, in Proceedings of the 8th International Symposium on Communication Systems, Networks and Digital Signal Processing (CSNDSP’12), Poznan, Poland, 2012. [61]. M. A. Kashani, M. Uysal, M. Kavehrad, A novel statistical channel model for turbulenceinduced fading in free-space optical systems, Journal of Lightwave Technology, Vol. 33, 2015, pp. 2303-2312. [62]. I. S. Gradshtein, A. Jeffrey, I. M. Ryzhik, Table of Integrals, Series, and Products, 5th Ed., Academic Press, Boston, London, 1994. [63]. I. A. Stegun, M. Abramowitz, Handbook of Mathematical Functions: with Formulas, Graphs and Mathematical Tables, National Bureau of Standards, 1970. [64]. S. Tianyu, K. Pooi-Yuen, A robust GLRT receiver with Implicit channel estimation and automatic threshold adjustment for the free space optical channel with IM/DD, Journal of Lightwave Technology, Vol. 32, 2014, pp. 369-383. [65]. S. Hitam, M. Abdullah, M. Mahdi, H. Harun, A. Sali, M. Fauzi, Impact of increasing threshold level on higher bit rate in free space optical communications, Journal of Optical and Fiber Communications Research, Vol. 6, 2009, pp. 22-34. [66]. M. R. Bhatnagar, Z. Ghassemlooy, Performance evaluation of FSO MIMO links in GammaGamma fading with pointing errors, in Proceedings of the IEEE International Conference on Communications (ICC’15), 2015, pp. 5084-5090. [67]. X. Zhu, J. M. Kahn, Markov chain model in maximum-likelihood sequence detection for freespace optical communication through atmospheric turbulence channels, IEEE Transactions on Communications, Vol. 51, 2003, pp. 509-516. [68]. X. Zhu, J. M. Kahn, Pilot-symbol assisted modulation for correlated turbulent free-space optical channels, Proceedings of SPIE, Vol. 4489, 2002, pp. 138-145. [69]. M. L. B. Riediger, R. Schober, L. Lampe, Fast multiple-symbol detection for free-space optical communications, IEEE Transactions on Communications, Vol. 57, 2009, pp. 1119-1128. [70]. I. S. Ansari, M. S. Alouini, J. Cheng, Ergodic capacity analysis of free-space optical links with nonzero boresight pointing errors, IEEE Transactions on Wireless Communications, Vol. 14, 2015, pp. 4248-4264. [71]. H. Moradi, H. H. Refai, P. G. LoPresti, Spatial diversity for fiber-bundled FSO nodes with limited mobility, Journal of Lightwave Technology, Vol. 30, 2012, pp. 175-183. [72]. K. Yoshida, K. Tanaka, T. Tsujimura, Y. Azuma, Assisted focus adjustment for free space optics system coupling single-mode optical fibers, IEEE Transactions on Industrial Electronics, Vol. 60, 2013, pp. 5306-5314. [73]. A. Leon-Garcia, Probability and Random Processes for Electrical Engineering, AddisonWesley, 1989. [74]. G.976: Test Methods Applicable to Optical Fibre Submarine Cable Systems, ITU-T Recommendation G.976, ITU, 2004. [75]. D. P. Greenwood, Bandwidth specification for adaptive optics systems, Journal of the Optical Society of America, Vol. 67, 1977, pp. 390-393. [76]. Z. Ghassemlooy, H. Le Minh, S. Rajbhandari, J. Perez, M. Ijaz, Performance analysis of ethernet/fast-ethernet free space optical communications in a controlled weak turbulence condition, Journal of Lightwave Technology, Vol. 30, 2012, pp. 2188-2194. [77]. G. Yang, M. A. Khalighi, S. Bourennane, Z. Ghassemlooy, Fading correlation and analytical performance evaluation of the space-diversity free-space optical communications system, Journal of Optics, Vol. 16, 2014, 035403. 298 Chapter 11. Implementing Differential Signalling in Free Space Optical Communication Link [78]. A. A. Farid, S. Hranilovic, Outage capacity optimization for free-space optical links with pointing errors, Journal of Lightwave Technology, Vol. 25, 2007, pp. 1702-1710. [79]. D. K. Borah, D. Voelz, S. Basu, Maximum-likelihood estimation of a laser system pointing parameters by use of return photon counts, Applied Optics, Vol. 45, 2006, pp. 2504-2509. [80]. R. Forster, Manchester encoding: opposing definitions resolved, Engineering Science and Education Journal, Vol. 9, 2000, pp. 278-280. 299 Chapter 12. Fabrications of Holographic Optical Elements in Polycarbonate for Holographic Weapon Sight Application Chapter 12 Fabrications of Holographic Optical Elements in Polycarbonate for Holographic Weapon Sight Application V. Vadivelan and B. Chandar Shekar1 12.1. Introduction A new approach is reported for fabrication of transmission type phase holographic optical elements (HOE) especially for a holographic weapon sight (HWS) for small arms/riffles. Silver Halide (AgH) holographic emulsion has been used for the fabrication of transmission type hologram with reticle image [1-5]. The HWS is having advantages over other types of weapon sight in close quarters combat [6-10] and also it is used as crew optical alignment system [11]. The M/s L-3 EO-tech is pioneer in manufacturing HWS for small arms [12-16] and HWS recent developments and improvements are reported [17-18]. Here, we fabricated two different kinds of HOEs and two different methods for fabrication of HOEs in Polycarbonate [19]. The fabrications of two different types of HOEs are (1) Phase transmission HOE with reticle image and (2) High diffraction efficiency transmission phase holographic collimator. The two different type of fabrications are (1) Fabrication in Silver halide (AgH), conversion into photoresist by contact copying method and transfer to Polycarbonate by electroforming and recombination technique and (2) Direct fabrication of HOEs in photoresist and convert into polycarbonate by electroforming and recombination techniques. We fabricated HOE with reticle virtual image has diffraction efficiency of around 15-20 % in AgH holographic ultra fine grain commercially available photo material but less than 3 % diffraction efficiency of holograms are preferable in HWS due to its higher visible transmission. One of a main drawback of HOEs in AgH is final transmission hologram tends to darken by exposing under ambient light, known as print-out effect. It drastically reduces both the diffraction efficiency and transmission of HOEs. Hence, we V. Vadivelan R&D Department, Ignetta holographic (P) Ltd, Madukkari, Coimbatore, Tamilnadu, India 301 Advances in Optics: Reviews. Book Series, Vol. 3 try to avoid such darkening problem; we fabricated the same kind of HOE in transparent polycarbonate (PC) for HWS application. In our work, we fabricated fairly good diffraction efficiency reticle HOE of nearly 3 % with 80-85 % visible transmission (without antireflection coating) in Polycarbonate for HWS application. First we transferred the hologram from AgH into photoresist (PR) by copying method [20-25]. The crucial and controlled wet chemical process will result a high quality HOE in positive PR. The HOE in PR is once again transferred into PC by using electroforming and recombination techniques [26-29]. The poor transmission of HOE in PR is not suitable for HWS application. Hence, we fabricated HOE in high transmission PC to avoid this specific application. The diffraction efficiency comparison, visible transmission comparison and quality of the output beam of HOE in AgH, PR and PC are analyzed in detail. Our method of fabrication is simple, very fast and accurate in production. This method greatly reduces the cost in terms of mass production. Also we can keep constant diffraction efficiency and transmission for all the fabricated reticle HOE, which is impossible to achieve in conventional AgH emulsion. The HOE in PC can prevent environmental impact; no shatter problem, light weight, easy handling and long life are listed as a few added advantages of HOE in PC. Apart from these regular advantages, in our study we found that AgH transmission holograms have their peak diffraction efficiency by using the same writing wavelength and recorded angle due to Bragg condition [34]. But the holograms transferred into PR and PC shown some interesting results of keep on nearly constant diffraction efficiency with angular variation. Angular response of HOE in PC is much greater compare to the hologram in AgH leads to many applications especially for solar. The HOEs in PC for HWS application is first time reported by author [19]. The experimental method and deep analysis of reticle HOE in PC are reported here. 12.2. Material and Methods The PC received their name [30] because they are polymers containing carbonate groups (−O−(C=O) −O−). The inflexibility and the lack of mobility prevent PC from developing a significant crystalline structure. PC is produced by a polymerization reaction between bisphenol A, a volatile liquid derived from benzene, and phosgene, a highly reactive and toxic gas made by reacting carbon monoxide with chlorine. The resultant polymers (long, multiple-unit molecules) are made up of repeating units containing two aromatic (benzene) rings and connected by ester (CO-O) groups Tetrabromobisphenol A is used to enhance fire resistance. Tetramethylcyclobutanediol has been developed as a replacement for bisphenol A. The study of PC as a substrate for holographic emulsion coating instead of commonly using glass substrate was reported [31]. The PC is one of the strongest and safest materials on the market. Its applications are ranging from feeding bottles to helmet visors of astronauts and for space shuttle windshields. This amorphous nature of the polymer allows the light transmit ability nearly that of glass. Light weight, transparency, excellent toughness, thermal stability, high impact resistance and optical properties makes PC as one of the most widely used engineering thermoplastics [32-34]. There are certain 302 Chapter 12. Fabrications of Holographic Optical Elements in Polycarbonate for Holographic Weapon Sight Application constraints to the use of PC include limited chemical and scratch resistance, photo degradation, birefringence and thermal expansion. However, there are a number of solutions to solve these constraints. The birefringence and thermal expansion are significant problems in PC, but M. Toishi et al, are reported [29] that the PC having great potential in the substrate of a holographic recording medium. The photo degradation process is significantly reduced in the polycarbonate sheet because of the excellent protection offered by the UV co-extruded layer which incorporates UV stabilizers and UV absorbers. Over a prolonged period, a slight yellowing or hazing will be detected in a polycarbonate sheet. He-Ne laser of 25 mW and He-Cd laser of 100 mW are used. A few commercially available holographic materials [35-49] for comparisons are given in Table 12.1. Here, we have used AgH holographic emulsion supplied by M/s Ultimate holography’s ultra fine grain silver halide red sensitive emulsion specially coated for us, which is having spatial resolution of 20,000 lines/mm and the grain size are typical 4 nm. The thickness of the AgH emulsion is 10 µm, its spectral sensitivity is 633 nm and sensitivity is in the range of 150 µJ/cm2 - 200 µJ/cm2. The power of the beam is measured by using power meter from M/s Edmund Optics. The whole experimental setup is placed in vibration free isolation table supplied by M/s Holmarc. The exposed plates are developed in supplier developer of 6 ml mixed with 100 ml de-ionized water for 4 min; the developed HOEs are put into water for 3 min and the same plates were bleached by using R10 bleach [50] until clear. The chemicals combination of bleach formulation are 2 grams of potassium dichromate mixed with 10 ml of hydrochloric acid and added 35 grams of potassium bromide in distilled water to make 1 litre of bleach solution. Isopropyl bath of different concentration level will improve efficiency little more. The recording and chemical processes are done under dark room safe light condition. We have measured the diffraction efficiency of naturally dried HOEs and obtained desired diffraction efficiency. Table 12.1. A comparison of few holographic materials for HOEs. Material/Effect Silver Halide Dichromated gelatin Photopolymers Photoresist LiNbO3 LiTaO3 KNbO3 Sn2P2S6 Photochromics Bacteriorhodopsin gelatin matrix Spectral Range, nm Thickness μm Δn Range ˚C < 1100 Resolving power, lines/mm Up to 10000 7-10 0.02 < 100 < 700 > 5000 15-35 0.022 < 200 514-670 < 450 350-650 300-550 400-900 550-1100 400-700 > 5000 1000 > 2000 > 2000 > 2000 > 2000 > 1600 5-500 1.5-2.4 > 10000 > 10000 > 10000 > 10000 > 100 0.012 2×10-3 10-3 10-4 3×10-4 10-3 < 100 < 500 < 450 > 50 < 66 < 66 520-640 > 1000 30-40 3×10-3 20/40 303 Advances in Optics: Reviews. Book Series, Vol. 3 We have used 3-4 µm thickness blade coated positive PR supplied by M/s Shipley. We have used Microposit developer AZ303 as photoresist developing agent, diluted with deionized water in proportion 1:9. Developing time was 7-10 seconds. It is worth to note that photoresist plates also can be developed with 1.5 % KOH or NaOH solution. However, those chemicals remain in the developed relief and the thin layer of them is transparent. As a result, the holographic image looks great on photoresist, but as soon one will deposit silver on such a relief – silver enters into reaction with KOH or NaOH and the resulting silver relief is much shallower than the photoresist relief. Therefore we stuck with Microposit developer AZ303, which probably has some ingredients preventing developer's remains layer forming. 12.3. Experimental Arrangement 12.3.1. Fabrication Details of Reticle HOE in AgH He-Ne laser wavelength of 632.8 nm is used as a source for recording off- axis transmission type hologram. The unexpanded linear polarized laser beam is divided into two by density variable beam splitter BS, which is helpful to manage desired beam ratio at the holographic recording medium. The mirrors 1 and 2 are directed the laser beams and make them interfere at recording plate with decided angle of interference. The spatial filters SF1 and SF2 are used to expand and spatially clean the beams, the laser beam expanded by SF1 passing through the reticle mask and it is propagate through the imaging lens and referred as object beam, which is finally collected at the recording medium. The mirror 2 is directed the second unexpanded laser beam towards SF2 and it is expanded and spatially cleaned by SF2, which is collimated by collimating lens and referred as reference beam. The reference and object beams are interfered at 56° in AgH emulsion. The transmission hologram fabrication schematic representation is shown in Fig. 12.1. Fig. 12.1. Schematic representation of experimental set up of HOE fabrication. The M/s Uniblitz computer controlled electronic shutter ES is used for precise exposure at the recording plate. We have used ultra fine grain AgH holographic emulsions for this study. AgH supplier developer and bleach used for the fabrication of phase transmission hologram. We have achieved around 28 % diffraction efficiency in this emulsion. But for 304 Chapter 12. Fabrications of Holographic Optical Elements in Polycarbonate for Holographic Weapon Sight Application our study, we used only less than 5 % diffraction efficiency because of its higher transmission in visible spectrum. The final wash of chemically developed phase HOEs and finished HOEs light dispersions are shown in Fig. 12.2. Fig. 12.2. Photographs of Chemically processed HOEs. 12.3.2. Direct Fabrication of HOEs in Photoresist A 442 nm wavelength emitting He-Cd laser source of 100 mW power is used for the fabrication holographic grating recorded directly in photoresist. The exposure of two collimating laser beams interfered at the photoresist is controlled by computer controlled electronic shutter. The interfering angle is decided by two mirrors mentioned in the schematic representation; those are spatially cleaned by spatial filters 1 and 2. The laser beam splitted and intensity ratio is controlled by using variable density beam splitter. The method of fabrication is as same as in Fig. 12.1, only one change made is laser source. It is shown in Fig. 12.3. Fig. 12.3. Schematic representation of holographic reticle fabrication by using He-Cd laser. In Fig. 12.4, the schematic representation for the fabrication of holographic grating is shown. A laser beam is split into two and the beam ratio is adjusted by variable density beam splitter. The two mirrors are used to make desired interference angle at the 305 Advances in Optics: Reviews. Book Series, Vol. 3 holographic plate. Spatial filters 1 and 2 are used to expand and spatially clean the laser beams. Two achromatic doublet collimating lenses are used for collimation. Fig. 12.4. Schematic representation of holographic grating. 12.3.3. Transfer of HOE into PR and PC The HOE fabricated in AgH with 12 % diffraction efficiency is used for transfer process, the image transferred into positive PR by contact copying method by using He-Cd laser of 100 mW power is shown in Fig. 12.5. Fig. 12.5. Schematic representation of copying method. The fabricated HOE in AgH was placed as shown in figure. The gap between the HOE in AgH and HOE to be copy in positive PR is about 1 mm. The primary HOE in AgH diffracts light at an angle and interference takes place between originally separated by a distance. The total power at the recording copy plate is around 6 mW and the exposure time was 14 seconds is the best suitable recording condition for copying HOE in positive PR. When light photons observed by positive PR removed from the surface and unexposed portion will remains at the time of chemical process. Once again the hologram in PR is transferred into transparent PC by using electroforming and recombination technique and the photograph of the electroforming and recombination is shown in Fig. 12.6. The diffraction efficiency of the fabricated HOEs are calculated by general formula, the ratio of the diffracted beam intensity to the incident beam intensity is gives the diffraction efficiency of the HOE. 306 Chapter 12. Fabrications of Holographic Optical Elements in Polycarbonate for Holographic Weapon Sight Application Fig. 12.6. Photographs of electroforming and recombination unit. In electroforming there are two steps followed namely silver spray and electroforming bath. (1) Silver spray is a method of coating a surface with a thin film of pure metallic silver before electroplating. The two different solutions of Silver nitrate 10 grams mixed with Ammonia and Glucose added to Formaldehyde are used to reduce the silver nitrate into pure metallic silver as it falls on the surface of HOE in PR. (2) Silver coated HOE in PR is placed in the tank which is contains nickel sultanate and boric acid added into distilled water. Initially the current level is 5 amp and 5 amp stepwise incremental for every 5 seconds and kept for nearly 60 min. The result is thick layer of deposition of pure nickel on the surface of PR. This is used as a master shim for transfer of HOE into PC by recombination method. By using heat and pressure, the HOE transferred into PC. The study of angular response is very important aspect of this study; it is discussed later. 12.4. Result and Discussion The primary aim of this study is based on fabrication of HOE in PC in order to solve the print-out problem in AgH. We have fabricated phase transmission HOE in AgH holographic emulsion with required 5 % diffraction efficiency and around 90 % transmission at 150 µJ/cm2 exposure dose. It is noted from Fig. 12.7 that the visible transmission of HOE in AgH is comparable to HOE in PC; here we used all the primary visible wavelengths of 632.8 nm, 532 nm, and 442 nm. Higher visible transmission of HOEs is highly recommended for HCS. But the HOE fabricated in AgH have a drawback of became dark under Sun light exposure of few minutes. Here, we try to avoid such a problem by fabricating HOE in PC with the similar effect of HOE in AgH. For this, the HOE in AgH is transferred to positive PR, once again the transferred hologram in PR is replicated into PC by using thin silver coating, electroforming and recombination techniques. We have got the desired optimized diffraction efficiency of around 4 % in PR and around 3 % in PC. The fabricated HOEs in all the three material AgH, PR and PC are shown in Figs. 12.8 (a), (b) and (c) respectively. 307 Advances in Optics: Reviews. Book Series, Vol. 3 Fig. 12.7. Visible transmission comparison of all the three holograms at 90°. (a) (b) (c) Fig. 12.8. Fabricated phase transmission holograms in (a) AgH, (b) PR and (c) PC. The interfering angle between two beams is kept 56° and the reconstructed reticle image captured by CCD camera is shown in Fig. 12.9. The diffraction efficiency variation with angle is compared between AgH, PR and PC at three different wavelengths like 632.8 nm, 442 nm and 532 nm. Here it is important to note that holograms in AgH is angular sensitive and its peak diffraction efficiency is obtained at the exact reconstruction angle of 56 degree (Bragg Angle), but it is very interesting and surprise that the HOEs in photoresist and polycarbonate fabricated by 308 Chapter 12. Fabrications of Holographic Optical Elements in Polycarbonate for Holographic Weapon Sight Application copying method from AgH HOE are maintaining almost same diffraction efficiency and it is independent of its angle of incidence. The measurement values of angular variation with diffraction efficiency of AgH, PR and PC are plotted in Fig. 12.10. Fig. 12.9. Photograph of reconstructed reticle image of HOE in AgH. The HOE peak diffraction efficiency of 9.7 % in AgH was obtained in 442 nm at 45°, the same was 4.3 % for both 532 nm at 50° and 632.8 nm at 56°. But considering HOEs in both the PR and PC, the diffraction efficiency was almost has flat response of diffraction efficiency for all incident angles. The diffraction efficiency measuring method is shown in Fig. 12.11. The expanded collimated beam was incident on the hologram in perpendicular direction. The HOEs placed in precise stepper motor control angular rotational stage. The output diffracted beam is focused on power meter by using converging lens. The same setup is used for transmission measurements for all three kinds of holograms. To verify this flat response of diffraction efficiency independent of angular variation, we have fabricated holographic lens with focal length of about 8 cm in AgH and copied into PR. The diffraction efficiency measurement once again confirms the flat diffraction efficiency response and it is independent of angular variation. Hence, Copied HOE from AgH into PC leads to many useful applications. The result gives confidence to fabricate holographic solar concentrators in PC. The microscopic image of reticle HOE in PR and PC confirms the imitation of the same fringe patterns in both holograms and is shown in Fig. 12.12. The HOE in AgH is became fully dark after exposing under direct sunlight for 2 days, the diffraction efficiency reduced about 50 % and laser transmission reduced nearly 70 % but HOE in PC is almost have constant diffraction efficiency and transmission before and after exposure under Sun light for 6 months time. The advantages of PC holograms are easy production, fast and accurate replication, trouble-free handling, preventing from ambient light effect, cost effective, no need of wet chemical process, and better temperature withstand. Maintaining the same diffraction efficiency of all fabricated holograms is impossible in AgH but in PC, we shall keep the same diffraction efficiency for all HOEs to be fabricated. However, PC has few disadvantage, it requires scratch proof coating, UV stabilization need for long time Sun 309 Advances in Optics: Reviews. Book Series, Vol. 3 exposure. The reticle image of the reconstruction of HOE in PC is not sharp as like reticle image in AgH, further work is progressing for the quality improvement. DIFFRACTION EFFICIENCY VARIATION WITH ANGLE AT 632.8 nm 15 10 5 0 0 5 10 15 AgH Hologram 20 25 30 35 40 45 Polycarbonate Holograms 50 55 60 65 70 Photoresist Holograms (a) DIFFRACTION EFFICIENCY VARIATION WITH ANGLE AT 442 nm 20 10 0 0 5 10 15 20 25 30 35 AgH Hologram 40 45 50 55 60 65 70 Polycarbonate Holograms Photoresist Holograms (b) DIFFRACTION EFFICIENCY VARIATION WITH ANGLE AT 532 nm 5 0 0 5 10 15 20 25 30 35 AgH Hologram 40 45 50 55 60 65 70 Polycarbonate Holograms Photoresist Holograms (c) Fig. 12.10. Diffraction efficiency variation with angle at (a) 632.8 nm, (b) 442 nm, and (c) 532 nm. 310 Chapter 12. Fabrications of Holographic Optical Elements in Polycarbonate for Holographic Weapon Sight Application Fig. 12.11. Schematic of diffraction efficiency and transmission measurement set up. (a) (b) Fig. 12.12. Microscopic images of HOE in (a) Photoresist, and (b) Polycarbonate. 12.5. Conclusion We have fabricated desired diffraction efficiency of less than 5 % and visible transmission of more than 90 % in phase transmission HOEs with reticle image in red sensitive ultra fine grain AgH holographic emulsion. To avoid the print-out problem of HOE in AgH, we have transferred HOE from AgH into PR and again in PC, the transfering method was explained in detail. The more attention of the study is that we obtained almost flat response of diffraction efficiency of HOE fabricated in PC for all angle of incidence, which is due to conversion of volume hologram into plane hologram. Here, we compared the diffraction efficiency with angular variation for all the three prime colours of Blue, green and red. We have inspected HOEs in PC and AgH under direct Sun light exposure, The HOE in AgH became completely dark and useless. But HOE in PC was almost having constant value of diffraction efficiency and visible transmission before and after 3 months expousure under direct Sun light. The peculiar result of flat response of diffraction efficiency with variation of angle of PC shows the way to fabrication of HOEs in PC for holographic solar concentration application. Improvement of quality of the image is progessing for HCS and the diffraction efficiency enhancement of HOE in PC for solar applications is our future work plan. Acknowledgment I thank Mr. Thomas Rajan for his encouragement and thanks to Ignetta Holographic pvt Ltd for the use of their laboratory and equipment. 311 Advances in Optics: Reviews. Book Series, Vol. 3 References [1]. M. R. E. La, S. N. Koresheva, M. K. Shevtsov, Optical systems of holographic collimator sights, J. Opt. Technol., Vol. 82, Issue 9, 2015, pp. 592-597. [2]. S. N. Koreshev, G. B. 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Method for Design and Manufacturing of Optics for Holographic Sight, US Patent AG02B532FI, USA, 2015. [21]. G. Saxby, Chapter 21, in Practical Holography, 3rd Edition, 2004, IOP Publishing, pp. 328-332. [22]. P. Hariharan, Copying holograms, Chapter 9, in Basics of Holography, Cambridge University Press, 2002, pp. 78-81. [23]. F. S. Harris, G. C. Sherman, B. H. Billings, Copying holograms, Applied Optics, Vol. 5, Issue 4, 1966, pp. 665-666. [24]. D. B. Brumm, Copying holograms, Applied Optics, Vol. 5, Issue 12, 1966, pp. 1946-1947. 312 Chapter 12. Fabrications of Holographic Optical Elements in Polycarbonate for Holographic Weapon Sight Application [25]. M. J. Landry, The effect of two hologram copying parameters on the quality of copies, Applied Optics, Vol. 6, Issue 11, 1967, pp. 1947-1956. [26]. C. Puech, Copying holograms on photoresist, Applied Optics, Vol. 4, Issue 4, 1971, pp. 279-282. [27]. F. Iwata, J. Tsujiuchi, Characteristics of a photoresist hologram and its replica, Applied Optics, Vol. 13, 1994, pp. 1327-1336. [28]. G. Stojanoff, Review of the technology for the manufacturing of large format DCG-holo grams for technical applications, Proceedings of SPIE, Vol. 3011, 1997, pp. 267-278. [29]. M. T. Gale, Replication techniques for diffractive optical elements, Microelectron. Eng., Vol. 34, Issue 3-4, 1997, pp. 321-339. [30]. F. Iwata, K. Ohnuma, Brightness and contrast of a surface relief rainbow hologram for an embossing master, Proceedings of SPIE, Vol. 523, 1985, pp. 15-17. [31]. A. Fustin, C. Bailly, G. J. Clarkson, P. De Groot, T. H. Galow, D. A. Leigh, D. Robertson, Slawiin, A. M. Zoya, J. K. Wong, Mechanically linked polycarbonate, J. Am. Chem. Soc., Vol. 125, Issue 8, 2003, pp. 2200-2207. [32]. M. Toishi,, T. Tanaka, A. Fukumoto, M. Sugiki, K. Watanabe, Evaluation of polycarbonate substrate hologram recording medium regarding implication of birefringence and thermal expansion, Opt. Comm., Vol. 270, Issue 1, 2001, pp. 17-24. [33]. S. Chakraborty, S. Roy, Structural, dynamical, and thermo-dynamical properties of carbon nano tube polycarbonate composites: A molecular dynamics study, J. Phys. Chem. B, Vol. 116, Issue 10, 2012, pp. 3083-3091. [34]. W. Thaithae, C. Antonio, P. Wattanachai, Properties characterisation of polycarbonate and multi-walled carbon nanotubes composites prepared by solution technique, Asia-Pacific Journal of Chemical Engineering, Vol. 11, 2016, pp. 34-50. [35]. J. F. Lomax, J. J. Fontanella, C. A. Edmondson, M. C. Wintersgill, M. A. Wolak, M. A. Westgate, E. A. Lomax, P. Q. Lomax, X. Bogle, A. Rua, S. G. Greenbaum, Properties of Polycarbonate containing BaTio3 nanoparticles, J. Appl. Phys., Vol. 115, 2014, 104103. [36]. Y. N. Denisyuk, Photographic reconstruction of the optical properties of an object in its own scattered radiation field, Sov. Phys. Dokl., Vol. 7, Issue 158, 1962, pp. 543-545. [37]. P. B. Palacios, S. A. Alvarez, J. M. Saez, M. V. Collados, D. Chemisana, J. Atencia Broadband behavior of transmission volume holographic optical elements for solar concentration, Optics Express, Vol. 23, Issue 11, 2015, pp. A672-A681. [38]. A. Fimia, L. Carretero, A. BelIndez, Holographic optical elements recorded on spherical surfaces with photopolymers, Applied Optics, Vol. 33, Issue 17, 1994, pp. 3633-3634. [39]. A. Fimia, N. López, F. Mateos, R. Sastre, J. Pineda, F. Amat-Guerri, A new photopolymer useful as holographic recording material, Applied Optics, Vol. 32, 1993, pp. 3706-3707. [40]. V. Tigran, J. Galstyan, F. Viens, A. Villeneuve, K. Richardson, M. A. Duguay, Photoinduced self-developing relief gratings in thin film chalcogenide As2S3 glasses, Journal of Light Wave Technology, Vol. 15, Issue 8, 1997, pp. 1343-1347. [41]. G. Stojanoff, H. Schutte, P. Froning, Evaluation of holographic materials from applications point of view, Proceedings of SPIE, Vol. 3294, 1998, pp. 2-13. [42]. T. K. Gaylord, M. G. Moharam, Analysis and applications of optical diffraction by gratings, Proceedings of IEEE, Vol. 73, Issue 5, 1985, pp. 894-937. [43]. J. N. Cederquist, J. R. Fienup, Analytic design of optimum holographic optical elements, J. Opt. Soc. Am. A, Vol. 4, 1987, pp. 699-705. [44]. E. Hasman, A. A. Friesem, Analytic optimization for holographic optical elements, J. Opt. Soc. Am. A, Vol. 6, 1989, pp. 62-72. [45]. T. S. Yu, Effect of emulsion thickness variations on wavefront reconstruction, Applied Optics, Vol. 10, 1971, pp. 1324-1328. [46]. R. D. Rallison, Incoherent multifocus hololens design and fabrication, Proceedings of SPIE, Vol. 1183, 1989, pp. 663-668. 313 Advances in Optics: Reviews. Book Series, Vol. 3 [47]. M. Chang, N. George, Holographic dielectric grating: theory and practice, Applied Optics, Vol. 9, 1970, pp. 713-719. [48]. T. K. Gaylord, F. K. Tittel, Angular selectivity of lithium niobate volume holograms, J. App. Phys., Vol. 44, 1973, pp. 4771-4773. [49]. J. N. Latta, Computer-based analysis of hologram imagery and aberrations, Applied Optics, Vol. 10, 1971, pp. 599-618. [50]. D. H. Mcmahon, A. R. Franklin, Efficient, high quality, R-10 bleached holographic diffraction gratings, Applied Optics, Vol. 8, Issue 9, 1969, pp. 1927-1929. 314 Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators Chapter 13 Optical Methods for the Characterization of PV Solar Concentrators Antonio Parretta1 13.1. Introduction The concentration of solar radiation plays a key role in the field of renewable energies, as it can be effectively applied to thermal, thermodynamic, photovoltaic (PV) and even hybrid thermal/photovoltaic technologies [1-10]. In concentrating photovoltaic systems (CPV) the size of the photovoltaic receiver (solar cell) is reduced by a factor equal to the geometric concentration ratio, and this has a strong, positive impact on the cost of the total PV concentrator, opening perspectives for the use of more sophisticated and more efficient devices. The concentrating optics is one specific component of the photovoltaic concentrator. It must be designed to transfer the incident solar radiation to the receiver searching the maximal optical efficiency achievable within an angular range limited by physical constrains [11]. The concentrating optics should produce a concentrated flux with reduced non-uniformity on the receiver to minimize ohmic losses [12, 15], and should be designed with great attention on many aspects related to its final industrial application. These are: compactness, tolerance on assembling errors, low cost of manufacturing processes, optimal placement of the receiver for electrical and thermal issues, use of materials of high reliability, high durability and low cost, high efficiency at the module and array level. All the previously indicated characteristics must be considered in the design of photovoltaic concentrators; many optical configurations have been proposed during the last years [15]; a large spectrum of possible designs, with different levels of effectiveness, can be achieved by applying the “nonimaging” optics [16-20]. The fundamental quantities of a PV solar concentrating optics usually considered are, from one side, the geometric concentration ratio and the optical efficiency, giving the optical concentration ratio, and, from the other side, the spatial and angular flux distribution on the receiver. These quantities are defined based on the irradiation conditions that is on the angle-resolved radiance of the light source. At mid-high Antonio Parretta Physics and Earth Science Department, University of Ferrara, Italy 315 Advances in Optics: Reviews. Book Series, Vol. 3 concentration ratios that is at collecting angles of the order of few degree or less, only the direct component of solar radiation is effective, and the input flux can be approximated by a parallel beam of known spectral irradiance and direction. At low concentration ratios, it is useful to consider also the contribution from a portion of diffuse light, which can be modeled as a lambertian source with defined angular divergence. We have in this way introduced the concept of “optical characterization” of a solar concentrator [21-45]. Different approaches can be followed to perform it; here we will focus our attention on two of them, directly derived by our recent research on this subject: the “direct method” and the “inverse method”, distinguished by the modality in which the concentrator is irradiated, if from the input or the output aperture, respectively. In the “direct method” [21-35], the angle-resolved transmission efficiency is obtained irradiating the input aperture by a suitably oriented parallel beam, of known irradiance, and measuring the output flux; this must be repeated for all the significant directions of incidence, which are strictly dependent on the geometrical symmetry of the concentrator. From the transmission efficiency curve obtained for the different azimuthal directions the “acceptance angle” is derived; it is a parameter that defines the angular limit within which the incident radiation is collected. An alternative way to obtain the angle-resolved optical efficiency is the “inverse method” [36-45], a very effective method where the concentrator can be tested irradiating it from the output aperture, therefore reversing the light path which occurs during the normal operating conditions. It is characterized by a remarkable rapidity of measurements and by a very simple apparatus with respect to the direct method. The main features of this method are illustrated throughout the course of this work and compared with another inverse method, derived from a modification of the original one [36, 45]. The direct method and the two inverse methods are here applied to recently developed nonimaging photovoltaic concentrators of reflective and refractive optics nature. The reflective SCs were of the type CPC (Compound Parabolic Concentrator), developed by Winston [17, 18, 20] starting from his pioneering work [46]. As already discussed, solar concentrators (SC) are usually investigated to know their optical transmission properties when they are irradiated by a uniform, quasi-collimated light beam simulating the direct component of the solar radiation. The most important result of this study is the curve of optical transmission efficiency drawn as function of the angle of incidence of the collimated beam respect to the optical axis of the concentrator. For nonimaging CPC SCs, it has the aspect shown in Fig. 13.1. The transmission curve is 50 characterized by an acceptance angle,  acc , corresponding to 50 % of the efficiency measured at 0°, valid for generic applications, whereas, for photovoltaic (PV) 90 applications, an acceptance angle,  acc , corresponding to the 90 % of the efficiency measured at 0°, is usually adopted. The other important properties which are largely investigated in a solar concentrator are the spatial and angular distribution of the flux on the receiver, of minor importance in thermodynamic solar concentrators, but of crucial importance in photovoltaic solar concentrators [12-15, 47]. The optical transmission curve determines how efficient is the optical transmission and how accurate must be the pointing of the solar tracker, to keep always the efficiency on the top of the curve. The spatial and angular flux density distributions establish if the system is suitable for a photovoltaic receiver, or if a secondary optical element (SOE) must be added to it [48, 49]. These are 316 Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators the basic information which are generally pursued, both theoretically and experimentally, when working with photovoltaic solar concentrators. Fig. 13.1. Typical optical transmission curve of a nonimaging solar concentrator. In the next section, we will discuss about theoretical models of irradiation of the solar concentrator; these models are just simplifications of the real irradiation conditions which can be applied in practice with indoor experiments or outdoor expositions. For each model, we derive a specific method of characterization of the SC that can be applied by optical simulations at a computer or by experimental measurements. The acronym assigned to each model of irradiation is the same of that assigned to the corresponding characterization method. We distinguish, for example, between “direct irradiation” and “inverse irradiation” of the SC, depending on the direction of the incoming light, or between “local irradiation” and “integral irradiation”, depending if the irradiation is limited to a small area of the SC aperture, or if it is extended to the entire aperture area; we finally distinguish between a “quasi-collimated irradiation” by a far light source, in contrast to a “diffuse irradiation” by a lambertian source. In the last case, we speak about a “lambertian irradiation” that is an irradiation with constant radiance from all directions within a maximum value of solid angle. In the theoretical section of this work, we focus our attention to generic 3D solar concentrators, regardless if refractive or reflective, imaging or nonimaging, and they are studied as generic optical components for which reflection, absorption or transmission properties are defined respect to specific models of irradiation. In the further sections, instead, we discuss the practical application of the characterization methods, introducing real prototypes of nonimaging, 3D photovoltaic solar concentrators of the type CPC (Compound Parabolic Concentrator), which were realized and extensively studied at Ferrara University and other refractive PV concentrators realized at ENEA labs. In what follows, a generic PV SC is schematized as a device confined between an entrance aperture (ia) with area Ain and an exit aperture (oa) with area Aout, where Ain > Aout, as the definition of solar concentrator requires. A solar concentrator operates, in practice, under 317 Advances in Optics: Reviews. Book Series, Vol. 3 “direct irradiation”, that is under irradiation directed to the entrance aperture (ia) and with a receiver, the energy conversion device (the solar cell), at the exit aperture. In our models, however, when required, we replace the receiver by any detector suitable to measure the total output flux, or its spatial and angular distribution; we also use the exit aperture to put there any source of light for inverse irradiation. The same considerations are valid when we consider the input aperture of the SC; we can measure the total flux exiting from it, or its angular distribution, when operating in reverse direction, and we imagine also to use the entrance aperture to put there any source of light for direct irradiation. What is there between the two apertures depends on the specific fabrication technology, and will not be considered, discussing the theoretical models, because not relevant for a general discussion on its overall optical properties. The main question relative to the operation of a solar concentrator is its ability to transfer light to the output (here with light we intend the full spectrum of the sunlight or any portion of it). The simplest question to ask is: how an elementary beam, incident on (ia) at point P(x, y) from (, ) direction, is transmitted by the concentrator? This question introduces the first and simplest method of characterization of the solar concentrator: the “Direct Local Collimated Method” (DLCM) [31, 32]. To apply this method in the most general form we should consider also the polarization of the beam and its spectrum. In what follows, however, we simplify our discussion by considering always unpolarized and monochromatic light at input. The role played by unpolarized light, in fact, has a significant importance in this work. On the one hand, a solar concentrator works mainly with direct sunlight, which is strictly unpolarized, on the other one, in the following, all the presented methods of SC characterization require the use of unpolarized light. With DLCM irradiation, the elemental collimated beam impinging on the elementary area dAin of the entrance aperture is transmitted to output with an efficiency expressed by the quantity  ( P , dA ,  ,  ) , the local optical transmission efficiency. The beam can be dir in totally reflected backwards, or totally absorbed inside the concentrator: these are extreme cases in which we cannot draw a path for light from the entrance to the exit aperture or vice versa. In all the other cases, we can follow the beam from one aperture to the opposite one. We distinguish therefore between “connecting” and “not connecting” paths, when the paths connect or not the two apertures, respectively. The attenuation that an elementary beam experiments inside the SC is the result of all the interactions with the surfaces and the interfaces met during its travel. In the hypothesis that the beam undergoes only reversible processes [50], as reflections and/or refractions at planar surfaces, excluding surface diffusion or diffraction phenomena, the total attenuation of the beam can be derived by applying repeatedly the Fresnel equations. If  the incidence angle and ’ the transmission angle (by reflection or refraction), it can be found by Eqs. (13.1a) and (13.1b) that the transmission factors Trefl for reflection and Trefr for refraction do not change at exchanging  and ’ angles, that is inverting the direction of travel of the light path, establishing in this way a “reversibility principle”: “the attenuation undergone by an unpolarized beam on the same path, but at opposite direction, is the same” [51]. Trefl  318  cos 2 (   ' )  cos 2 (   ' )  1  sin 2 (   ' )   , 2 2 2  sin (   ' )  cos (   ' )  (13.1a) Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators   1  cos2 (  ' ) Trefr  2  sin  sin' cos  cos' 2 . 2  sin (  ' )  cos (  ' )  (13.1b) The identical connecting paths, as A→B and B→A between the two apertures of the SC, show the same transmission factor TAB = TBA when the starting beam is unpolarized. When the methods described in the following theoretical section are applied, the condition of depolarization of incident beam must be accurately satisfied, both for the “direct sources” and the “inverse sources”. If the irradiation of the SC by a collimated beam is extended to the entire area of input aperture, we talk about the “Direct Collimated Method” (DCM). Fig. 13.2 illustrates the basic scheme of DCM, where Edir is the input cross-section irradiance, in and out the corresponding input and output flux. Fig. 13.2. Basic scheme of the Direct Collimated Method (DCM). The condition TAB = TBA is the basis of the so called “Inverse Lambertian Method” (ILM) [36-45], initially named ILLUME (Inverse ILLUmination MEthod) and known as P-Method (Parretta-Method), to distinguish it from the PH-Method (Parretta-Herrero Method), which will be discussed later in this section. The ILM has been conceived for deriving the absolute transmission efficiency of DCM by analyzing, instead of the flux collected at the receiver (the output aperture) with direct irradiation, the flux collected at input aperture with the inverse irradiation. To apply this concept, it is necessary that the rays analyzed with the “direct irradiation” overlap those analyzed with the “inverse irradiation”, that is, that the respective optical paths be identical. Now, in the direct irradiation by DCM, the input beam should be varied in the 0°-90° range of polar angle. To deduce, therefore, the attenuation undergone by the direct rays inclined at any polar angle respect to the optical axis, it is necessary to analyze all the inverse rays emitted by the concentrator in any direction from the input aperture. The source of the inverse rays must be placed in correspondence of the receiver (the output aperture) and must be able to emit rays, from each point and in any direction inside the SC, at constant radiance, to not discriminate any direction. Only in this way it will be possible to produce, in the reverse mode, all the connecting paths which will overlap with those that are produced in direct mode by a collimated beam inclined at different polar 319 Advances in Optics: Reviews. Book Series, Vol. 3 angles between 0° and 90°. To apply the “inverse method” ILM in a correct way, therefore, we need to put a spatially uniform lambertian source at the output aperture, as shown in Fig. 13.3, where Linv is the constant radiance of the inverse lambertian source. Fig. 13.3. Scheme of the “Inverse Lambertian Method” (ILM). The limit polar angle, at exit aperture (oa), is m = 90°. As we will see, the direct transmission efficiency,  dir ( , ) , is obtained by ILM from the radiance of the inverse light, Ldir ( ,) . If we are interested in knowing the efficiency of light transmission from the input opening to a specific receiver area, dAin or Ain , around point P, we can apply the ILM method to this area, obtaining the quantity dir ( P, dAin , , ) or dir (P, Ain , , ) , introducing in this way the “Inverse Local Lambertian Method” (ILLM). Recent developments of the “inverse lambertian method” have been proposed by Herrero et al. [52, 53]. They modified the P-Method with the aim to test the real optical properties of a photovoltaic solar concentrator as a whole, that is as optical unit + receiver (the solar cell). In this approach, the electroluminescence (EL) light emitted by the forward biased solar cell (the receiver of concentrator) acts as reverse light. Here, the “generalized” Kirchhoff’s law must be applied, which was derived by Wurfel [54] by applying a thermodynamic treatment to both thermal and non-thermal radiation, and which is based on the concept of the chemical potential of the radiation. From the generalized Kirchhoff's law, the solar cell contributes to the reverse light with the same efficiency with which contributes to the absorption of light under direct irradiation [55]. The second change made by Herrero et al. to the P-Method was the use of a parabolic mirror to focus the EL light on the lambertian screen (see Fig. 13.4). This choice allows to get a linear polar distribution of the transmission efficiency directly on the screen, avoiding the need to keep the screen far from the concentrator. The peculiarity of the “luminescence” method is that it operates with “real” receivers (the solar cells), not the “ideal” lambertian ones (with unitary absorptivity); while this is a good feature for the characterization of specific CPV optics, it limits the method at the photovoltaic solar concentrators. To have general methods for testing any type of solar 320 Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators concentrator, independently from the nature of receiver (photovoltaic or thermodynamic), a source of lambertian properties for the reverse light is required. The use of a parabolic mirror to focus the reverse light on the screen is generally useful, so we have exploited the idea of adding a parabolic mirror to the optical path of reverse light in the original inverse method (ILM). The result is a method referred to as the “Parretta-Herrero method” (PH-Method), to keep memory of the two contributions [37, 45]. The schematic of PH-Method is reported in Fig. 13.4. Here, the raytracing of rays emerging parallel to the axis of the concentrator and focused on the origin of the x/y frame fixed on the screen is shown. The solar concentrator (sc) is not visible because it is much smaller of the parabolic mirror (pm) and of the planar screen (ps). In Fig. 13.4 the polar diagram built on the screen (ps) is also shown. The point of coordinates ( , ) is the target of any ray exiting from the concentrator at the same polar and azimuthal angles, independently from the starting position from the input aperture. In this way, it is solved the problem of angular resolution that ILM suffers when the planar screen on which is projected the inverse light is not far enough (see Section 13.5.2). Fig. 13.4. Schematic principle of the Parretta-Herrero (PH) method used for simulating the optical properties of a generic solar concentrator. Inverse rays exiting from different points of the solar concentrator (sc) input aperture at the same polar angle  and azimuthal angle , converge, thanks to the parabolic mirror (pm) on the same point on the screen (ps). If we want to analyze the SC, activating simultaneously all the connecting paths in direct mode, we should consider an infinity of beams impinging on the input aperture at different polar angles. This is achieved as well by using a spatially uniform lambertian source placed at the input aperture, as schematized in Fig. 13.5, where Ldir is the constant radiance of the direct lambertian source. We introduce in this way the “Direct Lambertian Method” (DLM). The DLM can be applied to simulate the SC when it is entirely irradiated by a diffused light. The DLM operates with Lambertian light with a divergence of 90°. If we reduce this divergence to an angle m, we talk about the “Direct Lambertian 321 Advances in Optics: Reviews. Book Series, Vol. 3 Methodm)”, DLM (m) (see Fig. 13.6). DLM (m) can be applied to simulate the SC partially irradiated by diffused light. If m is the angular divergence of the direct solar radiation, m = S = 0.27°, then DLM (S) simulates in a correct way the SC irradiated by the quasi-collimated direct component of solar radiation. The DLM (m) can simulate the irradiation of a SC by a near lambertian light source, as illustrated in Fig. 13.7. Fig. 13.5. Scheme of the “Direct Lambertian Method” (DLM). The limit polar angle, at input aperture (ia), is m = 90°. Fig. 13.6. Scheme of the “Direct Lambertian Method (m)”, DLM (m). Fig. 13.7. Irradiation of the SC by a nearby lambertian source (ls). 322 Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators If the concentrator is irradiated simultaneously in “direct” and “inverse” modes by lambertian sources, we talk about a mixed Lambertian irradiation and we can introduce the “Mixed Lambertian Method” (MLM) (see Fig. 13.8). In MLM all the connecting paths will overlap and, putting Ldir = Linv , also the elementary flux flowing through any connecting path will be the same along the two directions. Then, with Ldir = Linv , also the total flux flowing through the concentrator from one aperture to the other will be the same in the two directions. The application of MLM allows to look at the SC as a passive optical component with optical features which can be find an equivalence in the traditional electrical quantities. Fig. 13.8. Scheme of the irradiation of the SC by both “Direct Lambertian Method” (DLM) with radiance Ldir and “Inverse Lambertian Method” (ILM) with radiance Linv. 13.2. Theoretical Aspects of SC Irradiation and Definition of New Optical Quantities 13.2.1. Direct Collimated Irradiation An elementary beam, incident on the point P of (ia) and flowing inside the SC in the direct , ,  1. Alternatively, mode, will be transmitted to the output with an efficiency the elementary beam will be reflected backwards or totally absorbed inside SC. In practice, the DLCM is easily applied by utilizing a laser beam as it illustrated in [26, 31, 32, 42]. The DLCM method can be applied to a finite Ain area of input aperture; in this case we obtain the efficiency of direct transmission to this area dir ( P, dAin , , ) . If  dir ( P, ,  ) is averaged over a uniform distribution of points P on the input aperture, the transmission efficiency  dir ( , ) at collimated light of the SC can be approximately estimated. The precise estimation of  dir ( , ) , however, requires the full irradiation of input aperture by a collimated and uniform light beam, and this is obtained by the application of the “Direct Collimated Method” (DCM), the most appropriate method to simulate the behavior of a SC operating under the direct solar irradiation. As we have seen in the Introduction, the most important quantity summarizing the properties of light 323 Advances in Optics: Reviews. Book Series, Vol. 3 collection of a solar concentrator (SC) is its “absolute” transmission efficiency  dir ( , ) , expressed as function of the polar and azimuthal angles of direction of the collimated beam, characterized by a constant irradiance Edir on the wave front (see Fig. 13.1):  dir ( , )   out ( , )  out ( , )  ,  in ( , ) Edir  Ain ( , ) (13.2) where Ain ( ,  ) is the area of input aperture projected along (, ) direction. If the contour of input aperture is contained on a plane surface, Eq. (13.2) simplifies as: dir ( , )  out ( , ) . Edir  Ain  cos (13.3) The “absolute” transmission efficiency dir ( ,) can be expressed as:  dir ( ,  )   dir (0)  dir , rel ( ,  ) . (13.4) where  dir ,rel ( , ) is the “relative” transmission efficiency of the SC and  dir (0) is the transmission efficiency at 0° (see Fig. 13.1). It is clear that dir ( , ) is the average value of  dir ( P , ,  ) , the local, collimated optical efficiency, when  dir ( P, , ) is calculated for all the points of the entrance aperture. We have therefore for the output flux:  out ( , )   dS  E dir  cos  dir ( P, , )  ... Ain  ...  Edir  cos  dS   dir ( P, , )  Edir  cos  Ain  dir ( P, , ) , (13.5) Ain and for the transmission efficiency:  Edir  cos   dS  dir ( P, , )  dir ( , )  ...   Ain Edir  Ain  cos   ... dS  dir ( P, , ) Ain Ain (13.6)   dir ( P, , ). The basic scheme of the “direct collimated method” (DCM) is shown in Fig. 13.2. The representation of a perfectly parallel beam, as in Fig. 13.2, is purely ideal and cannot be achieved in practical experiments. The flux at input can be written in fact as: in  Edir  Ain  cos  Ldir ( ,)   Ain  cos . 324 (13.7) Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators To have a perfectly parallel beam, we should have  = 0, that is Ldir ( ,) should be infinite to have a finite flux at input, and this is impossible to reach in practice. In an ideal experiment, we could imagine collimating light from a dimensionless source placed in the focus of a parabolic mirror, or to collect light from a source of finite dimension placed at infinite distance: in both cases the radiance of the light source becomes infinite. So, we can write more precisely for the direct optical efficiency under a collimated beam: dir ( , )  d out ( , ) d ( , )   ... d in ( , ) din ( , ) lim d ( , ) 1  ...  , Ldir ( , )  Ain  cos d  0 d (13.8) where Ldir ( ,) is the radiance, from ( ,  ) direction, of a finite source at finite distance and the symbol  means “transmitted”. To explore the full properties of light collection of the SC, the collimated beam must be oriented respect to the optical (z) axis of concentrator varying  in the 0°-90° interval and  in the 0°-360° interval. If the SC has cylindrical symmetry, it is sufficient to fix a  value and to vary only . Generally, the SCs have squared or hexagonal input apertures, because these geometries allow to pack better them in a concentrating module, then the  angle can be limited, in these cases, to the 0°-90° or the 0°-60° interval, respectively. Despite this limitation, however, the number of measurements required by the application of DCM is very high, both for simulations and for experimental measurements. This is indeed the very strong limit of DCM applied to the determination of dir ( ,) . This limit can be overcome by using the “Inverse Lambertian Method” (ILM) of irradiation, as it will be demonstrated in the following section. Dealing with “nonimaging” SCs [16-20], whose transmission curve has a step-like profile (see Fig. 13.1), their characterization by DCM can be simplified; it is sufficient in fact to vary the input  angle from 0° to a little more than the acceptance angle at 50 % of 0° 50 50 efficiency,  acc . Rays incident at    acc , in fact, will be rejected back by the SC before reaching the output aperture. The quantity  dir ( , ) (see Fig. 13.1) represents the fraction of flux transferred to the output, and then it represents the “direct transmittance” at collimated light, or “direct collimated transmittance” of the SC, when it is viewed as a generic optical component. In like manner, we can speak of a “direct collimated reflectance”  dir ( ,  ) or of a “direct collimated absorptance”  dir ( , ) of the SC for the fraction back reflected or absorbed of the input flux, respectively: 325 Advances in Optics: Reviews. Book Series, Vol. 3  dir ( , )  d  ( , )  ... d in ( , ) lim d  ( , ) 1  ...  , Ldir ( ,  )  Ain  cos d  0 d  dir ( , )  d ( , )  ... d in ( , ) lim d ( ,  ) 1  ...  . Ldir ( , )  Ain  cos d  0 d (13.9) (13.10) We have for the conservation of energy:  dir ( , )   dir ( , )   dir ( , )  1 . (13.11) We observe that, while the fraction of transmitted flux at output is generally measured, the reflected or absorbed ones are not; only the total lost flux is deduced from Eq. (13.11). The measure of  dir ( , ) and  dir ( ,  ) is however possible and is a simple task by simulation. A typical curve of dir ( ) for a 3-D nonimaging concentrator like a CPC (Compound Parabolic Concentrator) is illustrated in Fig. 13.1 [16-20]. Here the  angle is not represented as the CPC has a cylindrical symmetry. We distinguish the 0° efficiency 50 dir (0) , the acceptance angle at 50 % of 0° efficiency  acc and the relative transmission 50 angle, as it can be easily demonstrated. curve  dir , rel ( ,  ) , characterized by the same  acc Respect to solar concentrators like the nonimaging CPCs, the “imaging” solar concentrators show a very different transmission curve, with a long tail and a short flat portion at small angles [17]. For these concentrators, the DCM must be applied by varying 50 . The transmission the polar angles from 0° to a limit  angle, m , well higher than  acc curves dir ( ) or  dir , rel ( ) are defined for a perfectly collimated light and can be drawn easily by simulations with an optical code. With experimental measurements, the beam will be quasi-collimated, with a divergence angle which can be easily controlled (see Section 13.3). In addition to transferring light from the entrance to the output, a concentrator also concentrates the light. The two functions, transfer and concentration, are closely linked, because there can be no concentration if there is no good light transfer, and the transfer of light is not significant in the absence of concentration. As we have seen, a 3D solar concentrator is characterized by an input aperture of area Ain , an output aperture of area Aout , then by a “geometric concentration ratio” given by: 326 Cgeo Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators Cgeo  Ain / Aout . (13.12) Cgeo cannot be chosen arbitrarily big, for example by reducing arbitrarily Aout , because that shouldn’t give any benefit in terms of the optical concentration, expressed by the dir “optical concentration ratio” Copt : dir Copt  Eout / Ein , (13.13) where Ein is the flux density (irradiance) at input and E out is the “average” irradiance at output of the concentrator. As we shall see soon, the maximum value of Cgeo depends on the geometry of the light source. To find the expression for the optical concentration ratio we start from the definition of the generalized Étendue, applied to 3D concentrators, which establishes the invariant quantity: n2  dx dy dL dM  const, (13.14) where L, M are the cosines directors of light rays respect to the x, y axes of the reference frame, and n is the index of refraction. Eq. (13.14) expresses the Liouville theorem [17] establishing the invariance of the volume occupied by the system in the phase space. By applying this invariance to the input and output apertures of the concentrators (see Fig. 13.9), we have, respectively: n 2  dx  dy  dL  dM  n'2  dx'  dy'  dL'  dM '. (13.15) Fig. 13.9. Irradiation of a generic optical system. The invariance expressed by Eq. (13.15) implies of course that there are no optical losses for the light beam during its path from the entrance to the exit. Integrating Eq. (13.15) we have: n 2  Ain  sin 2  in  n'2  Aout  sin 2  out , (13.16) 327 Advances in Optics: Reviews. Book Series, Vol. 3 Ain n '2  sin 2  out .  2 Aout n  sin 2  in (13.17) Eq. (13.17) represents the geometric concentration ratio C geo , but, having assumed the absence of optical losses inside the concentrator, it also represents the optical concentration ratio C opt , or better, the maximum optical concentration ratio achievable (see Appendix 13.A). We have in fact: Copt  Eout  out Ain out Ain     . Ein Aout in in Aout (13.18) The ratio  out  in represents the well-known “optical transmission efficiency” opt :  opt   out ,  in (13.19) that we have assumed equal to 1 when is valid the Eq. (13.15). We have therefore that, in the absence of optical losses, Eq. (13.17) expresses the ratio of both geometric and optical concentration. We can then write, when opt = 1, that: C opt  Ain n'2  sin 2  out .  2 Aout n  sin 2  in (13.17a) In general, however, opt < 1, and then Eq. (13.18) becomes: Copt  Eout  out Ain   opt  Cgeo ,  Ein in Aout (13.18a) and Eq. (13.17a) becomes: 3D C opt   opt  C geo   opt  Ain n '2  sin 2  out .   opt  2 Aout n  sin 2  in (13.17b) Of course, the same formulas, making the square root, can be adapted to the case of 2D concentrators: C geo  lin / lout , 2D  opt  Cgeo  opt  Copt 328 lin n' sin out  opt  , lout n  sinin (13.20) (13.21) Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators where lin and l out are, respectively, the widths of the input and of the output openings of the linear concentrator. The quantities n and n’ as the indices of refraction of the medium at the entrance and at the exit of the concentrator, respectively. In the practical case of a concentrator exposed to the Sun, we have n = 1, because the medium to which is exposed the input aperture is the air. The index of refractive n’ is that of the medium in which is placed the receiver (the solar cell) at the exit of the solar concentrator. 13.2.2. Direct Lambertian Irradiation The “Direct Lambertian Method” (DLM) [26, 29, 41, 42] allows to study the transmission efficiency of a concentrator when the irradiation at input is integrated over all the directions in space. DLM simulates the behavior of the concentrator under diffused light, for example the diffuse solar radiation in a totally covered sky. A clear sky, in fact, contrary to what one might think, is not a good example of isotropic light, because the polarization of solar light by Rayleigh scattering produces a radiance strongly dependent on the direction of diffuse light respect to the direction of Sun [56]. Fig. 13.4 shows the scheme of DLM applied to a 3D-CPC concentrator, with Ldir constant radiance of the diffused light source. The total incident flux is: 2  /2 0 0   indir  Ldir  Ain  d   d  sin   cos    A in  Ldir , (13.22) where   Ain is the Étendue. In the following, we will consider, for simplicity, only concentrators with cylindrical symmetry, then  dir ( , ) will be set equal to  dir ( ) . The equations can be easily extended, whenever necessary, to the general case by reintroducing the dependence on the azimuthal angle . The flux “transmitted” to the output aperture becomes:  out dir    dir  2  Ldir  Ain   /2  d  sin   cos  ). dir ( (13.23) 0  The optical losses due to the “reflected” flux  dir and to the “absorbed” flux  dir are expressed respectively as:   dir  2  Ldir  Ain   /2  d  sin   cos   ), (13.24) ). (13.25) dir ( 0 dir  2  Ldir  Ain   /2  d  sin   cos   dir ( 0 329 Advances in Optics: Reviews. Book Series, Vol. 3  In such a way that:  dir   dir   dir   indir . Here  dir ( ) is the “direct collimated reflectance” and  dir ( ) is the “direct collimated absorptance” of the concentrator, as previously defined. lamb DLM gives the “direct lambertian transmission efficiency”  dir , also called “direct lamb lambertian transmittance”  dir , defined as the ratio of output to input flux:  lamb dir  lamb dir   indir  2   dir ...  2   dir (0)   /2  d  sin   cos   dir ( )  ... 0  /2  d  sin   cos (13.26)   dir , rel ( ) . 0 In a similar way, we define the other two quantities related to DLM: the “direct lambertian lamb lamb reflectance”  dir and the “direct lambertian absorptance”  dir : lamb lamb  dir   dir  ...  2   dir (0)    dir  2  indir  /2  d  sin   cos   dir ( )  ... 0  /2  d  sin   cos (13.27)   dir , rel ( ) , 0  lamb dir  lamb dir   indir  2   dir ...  2   dir (0)   /2  d  sin   cos   dir ( )  ... 0  /2  d  sin   cos (13.28)   dir , rel ( ) . 0 The output radiance, in general, is not constant like the input radiance, so we speak about an average output radiance: out Ldir  2  Ldir  Ain dir   Aout   Aout ...  2  Ldir  C geo   /2  /2  d  sin   cos   dir ( )  ... 0  d  sin   cos (13.29)   dir ( ) , 0 where C geo is the geometric concentration ratio. Now we define a new quantity, lamb C opt , the ratio between average output and input radiance: 330 Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators lamb Copt  out Ldir  2  C geo  Ldir ...  2  C geo   /2  d  sin   cos    dir ( )  ... 0  /2  d  sin   cos  (13.30)  [1   dir ( )   dir ( )] . 0 From Eqs. (13.26), (13.30) we find the relationship: lamb  Copt out  Ldir A E A A E lamb   dir  C geo  indir  in  out out  in  out . Ldir Ein  Ain Aout Ein  dir Aout (13.31) Eq. (13.31) has the same form of the relationship defining the optical concentration ratio of a SC under collimated irradiation [17] (see also Eq. (13.18a)): coll  Copt Eout  A   dir  C geo  out  in . Ein  in Aout (13.32) lamb We define therefore the quantity Copt as the “optical concentration ratio under direct lambertian irradiation” or “direct lambertian concentration ratio”. The direct lambertian model can be applied also reducing the angular extension of the lambertian source from π/2 to a limit polar angle  m (see Fig. 13.5). The corresponding method, DLM ( m ) , is particularly useful when we analyze the behavior of nonimaging SCs. Because of the step-like profile of their optical efficiency (  dir ( )  const for 50 50 ;  dir ( )  0 for    acc ), in fact, the characterization of these SCs under direct   acc 50 lambertian irradiation can be limited to angles    m   acc , reducing in this way the time of computer elaboration or simplifying the experimental measurements. The theory of DLM ( m ) is just that developed until now for the DLM, modified in the limit polar angle of the diffuse irradiation. We have therefore for the input and output flux, respectively:   indir ( m ) 2 m 0 0    Ldir  Ain  d  d  sin   cos    Ain  Ldir  sin 2 m , (13.33) m  dir ( m )  2  Ldir  Ain  d  sin   cos  dir ( ) . (13.34) 0 The direct transmission efficiency of this method becomes: 331 Advances in Optics: Reviews. Book Series, Vol. 3 m lamb ( m )   dir dir ( m ) 2   d  sin   cos  dir ( ) . in  dir ( m ) sin 2  m 0  (13.35) The average output radiance becomes: m out Ldir ( m )  dir ( m )  2  Ldir  C geo  d  sin   cos  dir ( ),   Aout 0  (13.36) lamb and the optical concentration ratio C opt ( m ) is: m  lamb ( m) Copt out ( m ) Ldir   2  C geo  d  sin   cos  dir ( ). Ldir 0  (13.37) 13.2.3. Inverse Lambertian Irradiation We saw in the Introduction that, for the reversibility principle, the optical loss reported by a direct ray is the same as that shown by an inverse ray if the optical path is the same and if both starting rays are unpolarized. The attenuation factor for the radiance of the direct beam incident at point P in direction ( , ) represents the local direct transmission efficiency dir ( P, , ) , while the attenuation factor for the radiance of the ray emitted by the SC from point A in the reverse direction ( , ) represents the local inverse transmission efficiency inv ( P, , ) . We extend now these concepts to all points of Ain directly irradiated in direction ( , ) (DCM, see Fig. 13.2) and to the same points of Ain that emit light in the reverse direction ( , ) (ILM, see Fig. 13.3). If the inverse radiance at output aperture Linv (Fig. 13.3) is constant for all directions, that is, if the source at output aperture is Lambertian, then the inverse output radiance, Lout inv ( ,  ) , averaged over all points of Ain , must have the same angular distribution of the inverse transmission efficiency  inv ( , ) , averaged over all points of Ain . But the average inverse transmission efficiency  inv ( , ) must have the same angular distribution of the average direct transmission efficiency  dir ( , ) , because the transmission of the single connecting paths is invariant respect to the direction of travel of light. As consequence, we can affirm that the inverse radiance of the concentrator Lout inv ( ,  ) , irradiated on the output aperture with a uniform and non-polarized Lambertian source, is proportional to the efficiency of the direct transmission  dir ( ,  ) of a non-polarized collimated beam, that is the two corresponding relative quantities coincide. We have therefore that: Lout inv , rel ( ,  )  dir , rel ( ,  ), where: 332 (13.38) Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators Lout inv , rel ( ,  )  Lout inv ( ,  ) , Lout inv (0) (13.39)  dir , rel ( , )   dir ( , ) .  dir (0) (13.40) Eq. (13.38) establishes the equivalence between the “relative” inverse radiance and the “relative” direct transmission of the SC. The above discussion establishes therefore the suitability of the inverse lambertian method (ILM) to provide all information concerning the relative efficiency of transmission of the concentrator under direct irradiation,  dir , rel ( ,  ) (see Fig. 13.1). The simulated and experimental measurements of relative inverse radiance Lout inv,rel ( , ) of a solar concentrator is discussed in Sections 13.3, 13.5.2, 13.6. Here we recall that, to perform these measurements, it is sufficient to project the inverse light of concentrator towards a far planar screen and to record the image produced there; a simple elaboration of the image gives Lout , and so dir,rel ( ,) . Here we want to emphasize another inv , rel ( ,  ) fundamental aspect of ILM, that is the fact that it provides also the value of dir (0) , and so the “absolute” transmission efficiency dir ( , ) (see Eqs. (13.4), (13.40)), without recourse to any direct measure by DCM [36, 39, 41, 57], as it will be demonstrated by the following considerations. When the SC is irradiated in the reverse way (see Fig. 13.3), the exit aperture (oa) of area Aout becomes a Lambertian source with constant and uniform radiance Linv . The total flux, injected into the SC and function of radiance L inv , becomes: 2   ininv  Linv  Aout  d  0  /2  d  sin   cos    A out  Linv . (13.41) 0 The inverse flux transmitted to output, the input aperture (ia) of area Ain of the SC, supposed of cylindrical symmetry, is given by: out  inv  inv  2  Ain   /2  d  sin   cos  L  ), out inv ( (13.42) 0 where  is the direction and Lout inv ( ) is the radiance of inversely emitted light. We now define the inverse lambertian transmission efficiency, or “inverse lambertian lamb transmittance”,  inv , defined as the ratio of output to input flux: 333 Advances in Optics: Reviews. Book Series, Vol. 3      inv  ininv lamb inv ...  ...  2  C geo Linv 2  Ain   /2  d  sin   cos  L 0  /2  ...   Aout  Linv  d  sin   cos  L  ) out inv ( (13.43)  )  ... out inv ( 0 2  C geo Linv  Lout inv (0)   /2  d  sin   cos  L  ). out inv , rel ( 0 lamb Let us compare the inverse lambertian transmittance  inv of Eq. (13.43) with the direct lamb lambertian transmittance  dir of Eq. (13.26) by taking their ratio: 2  C geo   lamb inv lamb dir  Linv  Lout inv (0)   /2  /2  d  sin   cos  L 0  d  sin   cos  2   dir (0)  ) out inv , rel (  ... ) dir , rel ( (13.44) 0 ...  C geo  Lout inv (0) .  dir (0)  Linv This ratio is just a property of the SC and should not depend on radiance quantities as it lamb lamb appears in Eq. (13.44). To clarify this situation, we calculate the ratio  inv by  dir applying the simple condition Ldir = Linv , at which the total integral flux transmitted in the out “direct” and the “inverse” directions is the same:  out dir = inv , because such is the flux transmitted through the elementary connecting paths in the two directions. By putting out  out dir =  inv and using Eqs. (13.23) and (13.42) we find: 2  Ldir  Ain   /2  d  sin   cos   )  ... dir ( 0 ...  2  Ain   /2  d  sin   cos  (13.45a)  ). Lout inv ( 0 Putting Ldir = Linv and applying Eqs. (13.39), (13.40), we have: Linv   dir (0)   /2  d  sin   cos   )  ... rel dir ( 0 ...  Lout inv (0)   /2  d  sin   cos 0 334 (13.45b)  ).  Lout inv .rel ( Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators We finally find:  dir (0)  Lout inv (0) . Linv (13.45c) Eq. (13.45c) allows us to calculate  dir (0) by ILM measuring Lout , the average on-axis inv ( 0) inverse radiance of SC, and Linv , the radiance of the inverse lambertian source [39, 41]. From Eq.s (13.44), (13.45c) we find moreover that the ratio between the inverse and direct lambertian transmittances is equal to C geo , that is independent on radiance, as foreseen. out This could be also deduced by considering that, if  out dir =  inv , we have: lamb out  inv  indir  indir   Ldir  Ain  inv A    in   in  C geo , lamb in out  inv  dir  inv   Linv  Aout Aout  dir (13.46) that is: the “inverse lambertian transmittance” of a SC is C geo times its “direct lambertian transmittance”, or equivalently: the “input direct lambertian flux” needed to sustain an equal transmitted flux in the opposite directions is C geo times the “input inverse lambertian flux”. This result is not surprising; it is a direct consequence of the geometrical asymmetry of the concentrator and disappears when C geo = 1, that is Ain = Aout . It is interesting to note that this result does not require any information about the internal features of the SC, but is only dependent on the sizes of the lateral apertures. Eq. (13.46) tell us that the optical “transparency” of the SC to lambertian light is not symmetric. 13.2.4. Mixed Lambertian Irradiation Let us imagine now to irradiate both apertures of the SC by two different lambertian sources with Ldir  Linv (see Fig. 13.7). If  L  L dir  L inv is the difference of incidence radiance between input and output, then we have for the net flux through SC, in the direct direction: out out lamb in lamb in    net dir   dir   inv   dir   dir   inv   inv  ... lamb ...   dir  [ indir  C geo   ininv ]  ... lamb ...   dir  [  Ldir  Ain  C geo    Linv  Aout ]  ... (13.47) lamb ...  (  Ain   dir )  L. From Eq. (13.47) we deduce, for example, that a CPC immersed in an integrating sphere has no net flux flowing through it (the radiance is constant inside the integrating sphere, so  L = 0). Eq. (13.47) has a strong similarity with the Ohm’s law: I  G  V , where (W) has the role of current,  L (W/srꞏm2) the role of potential difference and  net dir 335 Advances in Optics: Reviews. Book Series, Vol. 3 lamb (  Ain   dir ) (srꞏm2) the role of conductance. The net flux inside the SC, indeed, is the natural optical partner of the electric current and the choice of the radiance as the optical partner of the electric potential is the only one which allows to put Eq. (13.47) in the form of the Ohm’s law. Attempts to assign the role of potential to the total input flux (  A L) or to the Étendue (  A) are in fact unsuccessful. From Eq. (13.47) we define the “direct conductance under lambertian irradiation” or “direct lambertian optical conductance” lamb : Gdir lamb lamb Gdir  (  Ain   dir ). (13.48) The surprising result is that, if we reverse the SC keeping fix the radiance gradient, now the flux flows in the inverse direction with the same conductance. We have in fact, changing the sign to both members of Eq. (13.47) and using Eq. (13.46): net out lamb in lamb in   inv  inv   out dir   inv   inv   dir   dir  ... lamb ...   inv  [  Linv  Aout    Ldir  Ain / Cgeo ]  ... ...  (  Aout   (13.49) lamb inv )  L, with L  Linv  Ldir . From Eq. (13.49) we define the “inverse conductance under lamb lambertian irradiation” or “inverse lambertian optical conductance” Ginv : lamb lamb Ginv  (  Aout   inv ). (13.50) From Eqs. (13.48), (13.50) we conclude that the two conductances are equal: lamb lamb Gdir  Ginv . (13.51) The result of Eq. (13.51) is surprising in the fact that the optical asymmetry of the SC has disappeared when the conductance of the SC is considered. Eqs. (13.48) and (13.50) show that the “optical conductance” can be put in the form: G lamb  (  A)   lamb , (13.52) that is: “conductance” = “Étendue” x “transmittance”. Now the equivalence between the two opposite conductances is direct consequence of the fact that the “direct étendue” is Cgeo times the “inverse étendue” and that the “inverse transmittance” is Cgeo times the “direct transmittance”. From Eq. (13.47) we derive the density of the net flux through the net input aperture J dir (the average net flux flowing through the unit area of the input aperture inside the SC in direct way): 336 Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators net J dir   net lamb dir  (   dir )  L , Ain (13.53) net where L  Ldir  Linv , and the density of the net flux through the output aperture J inv (the average net flux flowing through the unit area of the output aperture inside the SC in the reverse way) is: net J inv  net  inv lamb  (   inv )  L , Aout (13.54) where  L  Linv  Ldir . If l SC is the length of the SC, we can introduce the quantity  L / l SC , the average gradient of radiance through the concentrator, a quantity which cannot be measured in practice, but which can be imagined existing inside the concentrator from a theoretical point of view. Eq. (13.53) becomes net lamb J dir  (   dir  lsc )  L lamb  (   dir  lsc )  grad L. lsc (13.55) In Eq. (13.55) gradL is intended as the average gradient of L. Eq. (13.55) is optically net equivalent of the Ohm’s law expressed in local form: J    E , with J dir (W/m2) with the lamb role of current density, gradL (W/srꞏm3) with the role of electric field and (  dir  lsc ) (srꞏm) with the role of electrical conductivity. The equivalent expression for the inverse current density is given by: net lamb J inv  (   inv  lsc )  L lamb  (   inv  lsc )  grad L. lsc (13.56) lamb We can define therefore a “direct lambertian optical conductivity”  dir and an “inverse lambertian optical conductivity”  lamb inv of a solar concentrator as follows: lamb lamb  dir     dir  lsc , (13.57) lamb lamb  inv     inv  lsc . (13.58) From Eqs. (13.57), (13.58) and (13.46) we find that: lamb lamb  inv  C geo   dir . (13.59) 337 Advances in Optics: Reviews. Book Series, Vol. 3 Eq. (13.59) tell us that the “inverse optical conductivity” of a SC is Cgeo times its “direct optical conductivity”, so it restores the asymmetry of the concentrator, as we have found for the transmittance efficiency. As we have seen for the direct local collimated method (DLCM), which applies only to a portion of input opening, also the local inverse method can be applied fruitfully to small or large areas of the exit opening. We talk in this way of areas Aout , and of efficiency of direct transmission to these areas as:  dir ( P ,  Aout ,  ,  ) . The  dir ( P ,  Aout ,  ,  ) efficiency can be obtained by applying the ILLM method to measurements of , when the receiver is inversely irradiated by a lambertian source L out inv ( P ,  A out ,  ,  ) placed in the  A out area and centered on point P. The new situation is like that which would occur if the concentrator could be amended as follows: the new receiver is the selected area of the old receiver; the new concentrator is the old concentrator plus the excluded part of the receiver. This new way of looking at the receiver is very powerful. In this way, in fact, we can study the efficiency of collection of any portion of the optical receiver, and since the radiation on the receiver is generally not uniform when the concentrator is directly irradiated, it happens often to be wonder about the direction of the direct rays arriving in a certain area of the receiver. Through the ILLM method, therefore, we can know from which direction the rays in excess in a certain area of the receiver arrive, or from which direction they are failing to arrive in a certain area of it. In a forthcoming part of this work, the applications of the ILLM method to nonimaging CPCs will be shown. 13.3. Equivalence between DCM and ILM In the theoretical Section 13.2.3 we have discussed the ILM method, demonstrating that it can be very effectively used to find the optical transmission efficiency of a solar concentrator. We have shown that the transmission efficiency has the same angular profile of the inverse radiance measured looking at the entrance opening of the SC, which in this way acts as a light source. The only condition required is that the SC be illuminated by the side of the exit aperture that is where it is placed the receiver (solar cell), by a uniform and unpolarized Lambertian source. Here we demonstrate, by simulation, that DCM and ILM are equivalent in giving the transmission efficiency of the concentrator. At this purpose, we have chosen two concentrators. The first is an ideal 3D-CPC with the following characteristics (see Appendix 13.B): diameter of entrance aperture 50 = 5°; 2a = 114.8 mm; diameter of exit aperture 2a’ = 10 mm; length L = 712.9 mm; acc focal length f = 5.44 mm; wall reflectivity Rw = 1.0. The maximum divergence of output 50 is  out = 90°. The second concentrator is like the previous one after rays when in = acc halving its length from the entrance side, then it is called HT-CPC (Half-Truncated CPC). Its characteristics are: diameter of entrance aperture 2a = 104 mm; diameter of exit aperture 2a’ = 10 mm; length L = 356.4 mm; focal length f = 5.44 mm; wall reflectivity 50 is almost unchanged, as we shall see below and as Rw = 1.0. The acceptance angle acc discussed in (see Appendix 13.B). The optical simulations were carried out by using the software for opto-mechanical modelling TracePro of Lambda Research [58]. To apply the 338 Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators ILM method to the ideal 3D-CPC, we have irradiated the exit aperture by a uniform Lambertian source and projected the light onto a faraway ideal absorbing screen (with unitary absorptance). The screen was circular with D = 4 m diameter, placed at a distance d = 20 m. The use of large distances between CPC and screen is mandatory with the ILM method, because it is necessary to reduce as much as possible the polar angle resolution associated with each point on the screen (this aspect is discussed in detail in Section 13.5.2). Fig. 13.10 shows an example of raytracing with 500 k inverse rays. The CPC is hardly visible, being very small compared to the CPC-screen distance. These conditions assure an angular resolution better than 0.2° for all the points on the screen (see Eq. (13.63)). Fig. 13.10. Example of raytracing of the 3D-CPC with 500 k inverse rays. Fig. 13.11a shows the map of irradiance (W/cm2) produced on the screen, and Fig. 13.11b the irradiance profiles along x and y axes. The simulation of ILM at a PC requires long acquisition times, sometimes of the order of hours. Starting from the map of Fig. 13.11a, the following procedure was applied to get the transmission efficiency curve. Being the CPC a cylindrical symmetry concentrator, the irradiance map was first symmetrized with respect to the azimuthal angle, to get most of information from the raytracing data. Then we have converted the distance r into the polar angle :  = tan-1(r/d), and normalized the irradiance profile E() to the = 0° value, obtaining Erel ( ) ; the irradiance Erel ( ) was finally multiplied by the factor (cos)-4 to obtain the normalized radiance Lrel ( ) (see Eq. (13.C3) in Appendix 13.C). The normalized radiance profile Lrel ( ) is equal to the normalized transmission efficiency of the CPC, rel ( ) , obtained with DCM. The DCM simulations were carried out using the same TracePro software [58], by preparing a perfectly collimated beam at input of the 3D-CPC and an ideal absorber at the output aperture. The collimated beam was oriented at different polar angles respect to the optical axis, from 0° to 6° with 0.5° steps, and the flux absorbed by the receiver measured. The efficiency of transmission was simply the ratio between output and input flux (see Eq. (13.2)) and is reported in Fig. 13.12. Here, the transmission efficiency profiles obtained by the two methods, DCM and ILM, are reported. Without any doubt, the two methods are equivalent. The simulation of the second concentrator, HT-CPC, is here discussed (see Fig. 13.13a). The DCM and ILM were applied to HT-CPC as made for the ideal 3D-CPC. Fig. 13.13b shows an example of inverse raytracing. The map of irradiance on the screen is shown in Fig. 13.13c, whereas Fig. 13.13d shows its average cross section. Fig. 13.14a shows the 339 Advances in Optics: Reviews. Book Series, Vol. 3 curve of relative transmission efficiency measured with the DCM and the curve of relative inverse radiance measured with the ILM. As the wall reflectivity is unitary, the curve of relative transmission efficiency is equal to the curve of absolute transmission efficiency. The extreme coincidence between the two methods is clearly evident. Fig. 13.14b compares the DCM transmission efficiency of HT-CPC with that simulated for the original ideal 3D-CPC (with double length). The effect of halving an ideal CPC is clear: the acceptance angles remain quite constant, but a tail appears on the halved CPC just in correspondence of the 50 % acceptance angle (see Appendix 13.B for a discussion). (a) (b) Fig. 13.11. Map of irradiance distribution on the far screen (a) and cross section x/y profiles (b). Fig. 13.12. Comparison between the profiles of transmission efficiency and inverse radiance, simulated with DCM and ILM, respectively. 340 Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators Fig. 13.13. Simulation of HT-CPC by ILM. (a) HT-CPC model; (b) Example of raytracing; (c) Irradiance map, and (d) Irradiance profile. (a) (b) Fig. 13.14. (a) Relative transmission efficiency measured vs. the incidence angle (DCM) and relative inverse radiance measured vs. the emission angle (ILM) of the HT-CPC concentrator; (b) The transmission efficiency of HT-CPC simulated by DCM is compared to that simulated for the original 3D-CPC. 341 Advances in Optics: Reviews. Book Series, Vol. 3 From the practical point of view, it is useful to repeat here that the great advantage of the ILM method with respect to DCM, when measuring the transmission efficiency, is that it requires only the recording of the reverse image produced on a screen by the SC, to obtain the angular profile of efficiency (the relative transmission efficiency), and the recording of the front image of the input aperture to calculate the efficiency on the optical axis, i.e. at 0 ° of polar angle (see Section 13.5.2). Conversely, the DCM method requires dozens of measures for different polar angle values in the case of SC with cylindrical symmetry, multiplied by the number of azimuthal angles of interest in the case of non-cylindrical symmetry. The ILM method contains, in two images, all the information of efficiency for all the polar and azimuthal angles, and this is really a great achievement. The ILM requires long acquisition times, but this is a problem for the computer and not for the operator. 13.4. Real Prototypes of Nonimaging Solar Concentrators Here we present some nonimaging SCs that we have used for the simulated and the experimental measurements. The first three SCs are of the type 3D-CPCs, but are not ideal (see Appendix 13.B), as they were obtained after a substantial change to their shape. An ideal 3D-CPC, in fact, although the many advantages mentioned in the Introduction, shows, as main drawback, to be too long respect to the linear dimensions of its input aperture. For example, an ideal 3D-CPC suitable for the use in PV, with a solar cell of around 1 cm diameter and a Cgeo  100x, has a length 7 times the diameter of the entrance aperture (see below). So, the first change to make on a CPC is to shorten it. This operation does not change too much its optical properties (see Appendix 13.B), so it’s a change that should be done. The second change to make on a CPC is the squaring of its input aperture, because this allows the efficient packing of the single optical units in a CPV module. This last operation produces four planar lateral walls which converge at the entrance opening. These walls are useless, then the last, very effective operation, is the removal of these walls. This was the ingenious idea of Antonini et al. [36, 37, 59-66], which led to the creation of a small, but efficient company (CPower), spin-off of Ferrara University, to produce medium concentration CPV modules made by nonimaging, very innovative optical units. The three modifications just discussed introduce three types of SC prototypes which we propose below. The last prototype we present is a nonimaging refracting concentrator realized at ENEA laboratories. The first prototype is the Truncated-CPC (T-CPC) that is an ideal CPC which was cut from the entrance side. The actual dimensional parameters are: 1-cm diameter exit aperture 2a’, 14-cm diameter input aperture 2a, 35.8-cm length L. Fig. 13.15a shows the CAD model of the T-CPC and Fig. 13.15b shows the T-CPC during an experiment with inverse light. As it can be seen, the inner wall surface was smooth, but deliberately left to the natural state after the forming process of a polyurethane prism, with the aim to study the effects of not mirroring. Fig. 13.16a shows the CAD model of the Truncated and Squared CPC (TS-CPC), the second presented prototype. The TS-CPC has a squared input aperture of 10-cm side, a circular output aperture of 1-cm diameter and a 35-cm length. Fig. 13.16b shows the prototype of TS-CPC during the characterization by a laser beam (DLCM). It was realized by forming a polyurethane prism and coating the internal walls 342 Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators by adhesive strips of the VM2002 Radiant Mirror Film of 3M (see Fig. 13.17a). The reflectance of the film resulted quite insensitive to incidence angle and equal to 951 % in the 400-110 nm spectral interval (see Fig. 13.17b). The mirroring of the internal wall determined some imperfections on the TS-CPC wall shape, which caused some loss of light by scattering, despite the high intrinsic reflectivity of the film (see Section 13.6.1.1). (a) (b) Fig. 13.15. (a) CAD of the truncated CPC (T-CPC); (b) Photo of the T-CPC during experiments with illumination by inverse light. (a) (b) Fig. 13.16. (a) CAD model of the truncated and squared CPC (TS-CPC); (b) Photo of the TS-CPC during an experiment with laser illumination. As anticipated, the “Rondine” SC [36, 37, 59-66] is an evolution of the TS-CPC, due to a further reduction of length, the removal of the four adjacent planar faces and, most important, the deformation of its surface, following a patented design. The concentrator length has been defined to obtain about only one reflection for the rays entering parallel to the optical axis of the concentrator and striking the surface, to reduce the optical losses 343 Advances in Optics: Reviews. Book Series, Vol. 3 due to multiple reflections. The elementary concentrator has a squared input window and lateral apertures; this gives to the “Rondine” a profile that resembles the swallows, hence the Italian name assigned to the concentrator. Due to the squared input window, many elementary units can be closely packed in a dense array, without losing active front surface. This approach gives the same angular tolerance as that from flat-mirrored surfaces placed on the cut lateral planes. The absence of a symmetrical rotational axis allows a quite uniform irradiance distribution on the solar cell, reducing in this way possible losses in FF. Two different designs of optical units were realized: Rondine-Gen1 and RondineGen2, differing in dimension and shape (see Fig. 13.18). Specular reflectance (%) 100 96 94 Unpolarized light  = 633 nm 92 90 (a) 3M Film on plastic 98 0 10 20 30 40 50 60 Incidence angle (°) 70 80 90 (b) Fig. 13.17. (a) Photo of the internal wall of the TS-CPC. It is visible the output aperture closed by a solar cell; (b) Data of specular reflectance of the 3M film/substrate sample at  = 633 nm as function of the incidence angle of the laser beam. The average reflectance is 95  1 %. Fig. 13.19 shows the CAD models, not the same scale, of the two “Rondine” concentrating units. As explained before, the two Rondine units work in practice with the four lateral apertures opened. When operating the simulation of these concentrators, therefore, the application of the DCM method required the reintroduction of the four walls (see Fig. 13.19) to properly set-up the parallel beam at input, because its entrance aperture has a non-planar profile. This arrangement was not necessary when working with the ILM method. In this case, in fact, the presence or absence of the four walls was indifferent, as verified by simulation. This result establishes another point in favor of the ILM method with respect to DCM, namely that ILM can be applied, without any modification, to concentrators in which the profile of the input opening is not contained in a plan, which often occurs in non-imaging concentrators. This is not possible with DCM. The last tested prototype is the “PhoCUS” concentrating unit, an optical element used in the CPV system PhoCUS (Photovoltaic Concentrators to Utility Scale), a project of ENEA laboratories [48]. The primary optics were manufactured as PMMA refractive elements. A secondary optical element (SOE) was included to minimize the optical losses due to module assembly and tracking inaccuracies. In this work, the tested optical unit is a rugged “Mock-up” containing the primary refractive optics, the secondary optical element (SOE) 344 Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators and a receiver. The “Mock-up” assembly is shown in Fig. 13.20. Two types of lenses were used: a “prismatic” lens and a “hybrid” lens (see Fig. 13.21). The SOE is a truncated inverted pyramid made of polycarbonate substrate coated by the VM2002 Radiant Mirror Film of 3M. This combination of materials assured a > 95 % reflectivity in the spectral range of the Silicon cell. x y (a) (b) Fig. 13.18. (a) Rondine-Gen1 single optical units based on NIO (Non-Imaging Optics); it is visible the exit aperture with its quasi-rectangular shape (the direction of x-axis is defined by the longer side); (b) Rondine-Gen2 single optical units; it is visible the exit aperture with its quasi-squared shape. Fig. 13.19. CAD models of Rondine-Gen1 (left) and Rondine-Gen2 (right) after the addition on the front aperture of four planar ideal mirrors. The two prototypes are shown with a different scale. 345 Advances in Optics: Reviews. Book Series, Vol. 3 (a) (b) Fig. 13.20. Schematic (a), and photo (b) of the Mock-up assembly comprising the primary lens, the secondary optics (SOE) and the solar cell. (a) (b) Fig. 13.21. Photos of the prismatic (a), and the hybrid (b) lens. 13.5. Practical Application of the SC Characterization Methods 13.5.1. Application of the DCM Method The application of the DCM method to the characterization of a SC would require, in principle, the use of a perfectly collimated light beam. This imply the use of a source with infinite radiance (see Eq. (13.7)), impossible to achieve in practice. On the other hand, the use of a perfectly parallel beam would be motivated by the need to draw a transmission efficiency curve with the maximum angular resolution possible. This need can only be justified if we want to have a perfect comparison between DCM and ILM, since ILM provides the transmission efficiency with an angular resolution practically of 0°. All this can be done through optical simulations on the computer. In practice, as a SC operates with the direct component of solar radiation, with a small angular divergence (±0.27°), the application of the DCM method can be made using a quasi-parallel beam having this angular divergence. To be precise, in this way we are applying the DLM(S) method, with S = 0.27° the angular divergence of the Sun, but since S is so small, we can consider the DLM(S) method practically equivalent to the DCM method. 346 Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators The basic experimental setup adopted for measurement of the optical efficiency of a light concentrator is schematically reported in Fig. 13.22. In Fig. 13.22a, the light source (ls) illuminates the integrating sphere (is1) which acts as a Lambertian source that is a source of diffuse light with constant radiance at its exit aperture, the window (w) with diameter D. A portion of light emerging from the sphere is collected by the parabolic mirror (pm1), placed slightly off-axis with respect to window (w) and at a distance d from it equal to the focal distance f of (pm1). The mirror (pm1) produces in this way a parallel beam whose maximum angular divergence can be controlled by varying the diameter D of (w). To obtain a beam with solar divergence (±0.27°), it is necessary to keep the ratio d /D equal to ~100, the same ratio between Sun-Earth distance and Sun diameter. The parallel beam, spatially filtered by the diaphragm (di), illuminates the solar concentrator (sc). The light at the exit aperture of concentrator (sc) is directed to a second integrating sphere (is2) and its flux measured, through the photodetector (pd), placed inside (is2), by the radiometric unit (ra). Fig. 13.22. (a) Schematic of the experimental setup used with the direct method for measuring the light collected by a solar concentrator (sc) at different incidence angles; (b) Reference setup used to measure the flux incident at input of the concentrator. 347 Advances in Optics: Reviews. Book Series, Vol. 3 To perform the angle resolved measurements required to draw the optical efficiency curve, the concentrator (sc) must be oriented with respect to the parallel beam at different angles (, ). The polar incident angle  is sufficient to define the orientation of the concentrator when it has a cylindrical symmetry; for other concentrators, it is necessary to consider also the azimuthal incident angle . If I ( , ) is the photodetector signal measured at the different incidence angles, the transmission efficiency of the SC relative to the on-axis direction (0° polar incidence angle) is obtained by the configuration of Fig. 13.22a and is given by: rel opt ( ,  )  I ( ,  ) . I (0) (13.60) rel To get the absolute optical efficiency, opt ( , )  opt (0) opt ( , ) , it is necessary to make a further measurement, that of the incident flux at entrance of the concentrator. This is done by removing the concentrator (sc), decoupling it from sphere (is2), and orienting the collimated beam from mirror (pm1) towards a second parabolic mirror (pm2) (see Fig. 13.22b), which will provide to re-focalise the beam inside the same integrating sphere (is2). For this measurement, it is required the knowledge of the spectral reflectance Rpm of (pm2). If I ref is the photodetector signal measured with the reference setup of Fig. 13.22b, the angle resolved absolute efficiency of the concentrator becomes: opt ( ,  )  I (0) I ( ,  ) I ( ,  )    R pm . I ref / R pm I (0) I ref (13.61) Fig. 13.23 shows the photos of the experimental set-up of Fig. 13.22, realized at ENEAPortici laboratories, applied to the characterization of the prismatic lens PhoCUS. (a) (b) Fig. 13.23. Photos of the experimental set-up of the direct method for measuring the optical efficiency of the prismatic lens PhoCUS, at ENEA-Portici laboratories. 348 Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators Alternative configurations of the experimental set-up are shown in Fig. 13.24 and Fig. 13.25. Here we use two integrated spheres instead of one to have a better integration of light inside the sphere used as source of diffused light. We distinguish between two different experimental configurations. In the first of Fig. 13.24a (configuration A), we have used a continuous light; in the second one of Fig. 13.24b, (configuration B), we have used a modulated light. In both configurations, the light source (ls) is a fluorescent lamp with a spectrum near to that of the Sun (T = 5500-6000 K), facing the inside of the integrating sphere (is1). In the configuration A, as detector for flux measurements, we have used a CCD camera, facing the inside of the integrating sphere (is3), operating like a normal photodetector; the collected flux is measured by averaging the intensity of the digital CCD image. Based on our experience, the CCD, due to its high sensitivity, is the only means of measuring the continuous, very low flux transmitted by the (sc) to the integrating sphere (is3). Fig. 13.24. Schematic principle of the direct method used for the measure of the output flux. (a) Configuration A: the source (ls) is a continuous light and the radiometer is a CCD. (b) Configuration B: the source (ls) is a chopped light and the radiometer is a lock-in amplifier. The diameter of window (w) is 5 mm and the focal length of (pm1) is 500 mm. 349 Advances in Optics: Reviews. Book Series, Vol. 3 Fig. 13.25. Schematic of the experimental configuration A applied to the measure of the flux at 0° incidence. A similar schematic applies for the experimental configuration B. In the configuration B, the light from the source (ls) is modulated by the chopper (ch). The Lambertian light from window (w) is then modulated and produces a modulated signal on the photodetector (pd), recorded by the lock-in amplifier (li). The use of the modulated-light configuration of Fig. 13.24b allows to increase the sensitivity of measurements made by using a photodetector (pd). Fig. 13.26 shows a photo of the experimental set-up used with configuration A. The parabolic mirror (pm1) was a low cost, commercial mirror with a focal length of 50 cm. Fig. 13.26. Photo of the apparatus for DCM measurements with configuration A. The tested sample is a nonimaging concentrator Rondine-Gen1. Photos of configuration B are shown in Fig. 13.27. Here a black wall separates the light source section from the receiver section. The mirror (pm1) is a high-quality, high-cost, Pyrex parabolic mirror of 1500 mm focal length. The use of a uniform quasi-collimated beam is very important in these measurements. The intensity distribution (irradiance) of light on the cross section of the collimated beam was measured by projecting the parallel 350 Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators beam on a lambertian diffuser [67] and recording the intensity distribution by means of a CCD. The intensity profile shows a flatness modulation of around ±8 % for the commercial parabolic mirror used for the configuration A of Fig. 13.26. This, as we shall see, will produce a small distortion of the efficiency curve and a small alteration of the acceptance angle (see Fig. 13.69). The projection on a lambertian diffuser of the parallel beam from the high-quality parabolic mirror is shown in Fig. 13.28a. The intensity map shows a flatness better than ±0.5 % within 100 mm width (Fig. 13.28b). ls+is1 sc fan is2 w ch sw pd li a) b) pm1 c) d) Fig. 13.27. Photos of the apparatus for DCM measurements with configuration B. Light source section with the separating wall (sw) (a). Receiver section with the lock-in amplifier (li) (b). L. Zampierolo is aligning the Rondine-Gen1 with the parabolic mirror (c). Parabolic mirror (d). The flux measurements at the exit aperture of the (sc) can be carried out in two modes. In the first one, that we have called SPHERE mode, we have coupled the exit aperture of the (sc) to the (is3) integrating sphere, provided with an internal photodiode (pd) (a high efficiency solar cell), as illustrated in Fig. 13.29a; in the second one, that we have called CELL mode, we have closed the (sc) exit aperture directly on a high efficiency solar cell, the same used in the CPV module (see Fig. 13.29b). 351 Advances in Optics: Reviews. Book Series, Vol. 3 (a) (b) Fig. 13.28. (a) Projection of the parallel beam on a lambertian diffuser after reflection from pm1. Plot of the intensity of light measured on a 100×100 mm2 square cross section of the parallel beam after reflection from pm1. solar cell a) b) Fig. 13.29. The Rondine-Gen1 solar concentrator is closed on the integrating sphere (is3) (SPHERE mode) (a); The Rondine-Gen1 solar concentrator is closed directly on the high efficiency solar cell (CELL mode) (b). In both cases, the photodiode (pd) inside (is3) and the high-efficiency solar cell were connected to the lock-in amplifier (li) shown in Fig. 13.27b. The reason why we adopted two different receivers for measuring the flux transmitted by the (sc) is the following: in the SPHERE mode, the integrating sphere behaves as an ideal receiver, because we haven’t losses for reflection at its exit window; then the measure gives the transmission efficiency of the (sc) itself, that is of the optical unit alone, regardless of the type of receiver used; in the CELL mode, on the other hand, the measure gives the transmission efficiency of the system (sc) + PV receiver, and then the more realistic angle-resolved optical performance of the PV solar concentrator when it is mounted on a CPV module. For a correct application of the CELL mode, however, we need to use a solar cell with the same optical and electrical characteristics of the true PV receiver used in practice. 352 Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators Fig. 13.30 shows some photos recorded during DCM measurements on the refractive, nonimaging concentrator PhoCUS. Fig. 13.30a shows the phase of assembly of the mockup with the prismatic lens. Fig. 13.30b shows the square shaped image of the focused light produced by the prismatic lens. The illuminated area corresponds to the area of the PV receiver, a high-efficiency SunPower cell. Fig. 13.30c shows the (sc) during measurements of the output flux by the integrating sphere coupled to a photodiode (SPHERE mode), and Fig. 13.30d shows the assembled mock-up with mounted the prismatic lens. (a) (b) (c) (d) Fig. 13.30. Experimental set-up of the DCM method applied to the PhoCUS concentrator. (a) F. Aldegheri is working on the assembly of the (sc) at the receiver section. (b) Square-shaped image of the focus produced by the prismatic lens. (c) DCM Flux measurements by the SPHERE mode. (d) Photo of the assembled PhoCUS mock-up. 13.5.2. Application of the ILM Method (Parretta-Method) The “inverse method”, initially known as ILLUME (Inverse Illumination Method) [44], was later revisited and improved, assigning the new name of “Inverse Lambertian Method” (ILM). The ILM was born as an alternative to the DCM just to obtain the relative 353 Advances in Optics: Reviews. Book Series, Vol. 3 (to 0°) or normalized transmission efficiency of the SC. We have demonstrated, in fact, in the theoretical Section 13.2.3, and by simulation in Section 13.3, that the two methods are equivalent. Subsequently, we could find the procedure to get also the “absolute” transmission efficiency. Later, we realized that ILM could become a powerful tool for analyzing other SC properties, by applying the ILLM (see Sections 13.6.1.3 and 13.6.2.1). ILM greatly simplifies the experimental apparatus for measuring the angle-resolved transmission efficiency, both relative and absolute, and drastically reduces the number of measurements. The method consists in irradiating the concentrator (sc) in a reverse way by placing a planar Lambertian light source (ls) of uniform radiance Linv at the exit aperture, and in measuring the radiance Linv () of the light emitted by the concentrator from the input aperture as function of the different orientations in space, characterized by the polar and the azimuthal emission angles  and  (see Fig. 13.31) (here we use for simplicity the same symbols for the angular direction of the rays incoming to and outcoming from the input aperture). When inversely illuminated, the concentrator becomes a light source whose radiance will no longer be constant, because the concentrator changes the angular distribution of the rays emitted by the lambertian source (ls) before they are emitted from the entrance opening. Fig. 13.31. Basic scheme of the inverse lambertian method (ILM). A Lambertian light source is applied at the exit aperture of the (sc). Differently from DCM, where measurement of output flux out (, ) every time requires changing the orientation of the concentrator with respect to the quasi-parallel beam, the measure of Linv () is now easy and immediate, because it can be obtained projecting the inverse light on a far planar screen, recording the intensity of its image and elaborating it at a computer (see Fig. 13.32). The processing procedure depends, however on the type of measurement, if simulated or experimental, and the details of this procedure are given in the Appendix 13.C. We summarize here this procedure. If the inverse method is simulated at a computer, the planar screen (ps) is assumed as an ideal absorber, and the irradiance E () of the absorbed light is easily measured and transformed into the inverse radiance Linv (). If the inverse method is applied experimentally, on the contrary, the planar screen must be a white diffuser with lambertian properties and a CCD, or a webcam, must be used to record the image on the screen. Still, from the intensity map of the image, the relative inverse radiance is calculated. In this case, the irradiance of incident light is measured 354 Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators indirectly, deriving it from the intensity of the CCD image, ICCD (). The only foresight to follow when applying the inverse method is that the planar screen, oriented perpendicular to the optical axis of the concentrator and illuminated by the inverse light, must be placed at a distance d from the concentrator much higher than the linear dimensions of the input aperture, to have an adequate angular resolution for the profile of optical efficiency (see Fig. 13.33a). Fig. 13.32. Schematic of the experimental ILM apparatus. For example, for a circular input aperture of diameter D, the angular resolution (uncertainty) res for all the points (in a circle) of the screen characterized by the polar emission angle  is given by:  res ( , D, d )  tg 1 [ D  cos2  (2d  D  sin   cos )]  ... ...  tg 1 [ D  cos2  2d ]. (13.62) The angular resolution is the worst on the optical axis:   res , max  tg 1 ( D 2 d ), (13.63) and improves at increasing  (see Fig. 13.33b) Fig. 13.33c shows, as an example, the angular resolution calculated for ILM applied to the TS-CPC when its distance from the screen is 360 cm. Since the angular range of light emission is generally small, we can assign to the points of the emission radiance the angular resolution obtained by Eq. (13.63). The need to have d >> D implies some limits to the practical application of the ILM in laboratory, where distance d is of the order of some meters. For example, a concentrator of 10-cm aperture size requires a screen at 5 m to have a resolution of at least ~0.5° on the optical axis. This is the only drawback of the ILM when applied experimentally. When ILM is simulated on the computer, on the other hand, it is easy to set a sufficiently high value of d /D to obtain the desired resolution, of course by using a ray-tracing with number of rays, and then with processing time, greater at greater resolution. The choice of d, then of the angular resolution, must be made mainly considering the expected value for the angle of acceptance. A resolution of ~0.5°, for example, cannot be tolerated for an acceptance angle (at 50 %) of about 1° or less, while it is acceptable for an acceptance angle of at least 5°. 355 Advances in Optics: Reviews. Book Series, Vol. 3 Fig. 13.33. (a) The drawing shows the effect of the SC-screen distance on the angular resolution at point P. (b) The drawing shows the effect on the angular resolution of the position on the screen of the point P. (c) Angular resolution as function of the emission angle, calculated for a TS-CPCscreen distance of 360 cm. 356 Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators Referring to the measurement of E ( ,  ) , it may happen that the optics of the CCD is not always adequate to capture the entire inverse image at the distance d between concentrator and screen. In this case, that we have effectively experienced, it is possible to double the optical path between the screen and the CCD interposing a mirror (mi) between the CCD and the screen, as shown in Fig. 13.34. Fig. 13.34. When the full inverse image on the screen cannot be captured by the CCD objective, a mirror (mi) can double the optical path between screen and CCD. With simulation measurements, the irradiance E (, ) on the planar screen is transformed into the radiance Linv (, ) of the concentrator by the following expression (see the Appendix 13.C): L inv ( ,  )  1 d2 E ( ,  )  , Ain cos 4  (13.64) where Ain is the input aperture area and d is the on-axis distance between the planar screen and the centre O of the input aperture of the concentrator. To obtain the relative profile of the inverse radiance, L rel inv ( ,  ) , that is the radiance normalized to the 0° value, it is sufficient to measure the normalized irradiance on the screen, E ( , ) : rel rel Lrel inv ( ,  )  E ( ,  )  1 . cos 4  (13.65) The factor (cos)-4 considers the fact that the screen is a flat surface rather than spherical, and this determines a (cos)-2 factor, and the points on the screen (ps) are not located at the same distance from the centre of the opening entrance, which is the point from which we measure the angles, and this determines another (cos)-2 factor. When the inverse method is applied experimentally, Eq. (13.64) modifies and becomes (see the Appendix 13.C): L inv ( ,  )    f 2 d2 R  Ain  I CCD ( ,  )  1 , cos 8  (13.64a) 357 Advances in Optics: Reviews. Book Series, Vol. 3 where f is the focal length of CCD and R the reflectivity of the lambertian screen. We emphasize here the fact that the screen must be a Lambertian reflector for the Eq. (13.64a) to be valid. The normalized radiance now becomes: rel Lrel inv ( ,  )  I CCD ( ,  )  1 . cos8  (13.65a) We have demonstrated on several occasions that the relative inverse radiance profile rel L rel inv ( ,  ) coincides with the relative optical efficiency profile  opt ( ,  ) of the concentrator operating in the direct mode (DCM) when the direct beam is parallel or quasi-parallel. When the direct beam is not strictly parallel, we should take account of its divergence and to put it as the uncertainty on the measured polar angle. We have therefore for the optical efficiency of the concentrator: rel dir ( , )  dir ( , ) dir (0)  L rel inv ( , )  dir (0), (13.66) where L rel inv ( ,  ) is obtained from Eq. (13.65) or (13.65a) depending if we are operating with a simulation program or with experimental measurements. We conclude this part highlighting the fact that the radiance L rel inv ( ,  ) summarizes all information relating to the light collection properties of the concentrator in relation to its orientation with respect to the solar disk. The inverse method as discussed until now seems to allow determining only the relative angle-resolved optical efficiency of the concentrator, by processing the intensity image produced on the planar screen by the concentrator irradiated in the inverse way. To obtain the absolute efficiency as indicated by Eq. (13.66), we should ask the direct method for help to measure the on-axis optical efficiency dir(0) . If it were so, we should need to setup, besides ILM, also the direct method apparatus just for one measurement, and the advantages of the inverse method in terms of simplicity of the experimental apparatus should be lost. Fortunately, new developments of the theory [22, 26, 36, 38, 57] provided a way of obtaining dir(0) also by the inverse method. It was shown in fact that the on-axis efficiency dir(0) can be obtained by the expression: dir (0)  L inv (0) , LREC (13.67) where Linv (0) and LREC are radiances measured on the image recorded by the CCD camera, or the web camera, oriented towards the input aperture of the concentrator irradiated in the inverse mode (ILM) (see the schematic of the apparatus in Fig. 13.35). Linv (0) is the average radiance of the whole input aperture, whereas LREC is the radiance of the receiver, the exit aperture, corresponding to the radiance of the Lambertian source. 358 Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators Fig. 13.35. Experimental set-up for determining the on-axis optical efficiency of the concentrator. The CCD camera is turned towards the concentrator irradiated in inverse mode and the image of the input aperture is recorded. It should be emphasized that Eq. (13.67) is easily applied to concentrators for which the exit aperture is visible from the input aperture, like any concentrator realized only by reflective optics, like the 3D-CPCs. For concentrators with refractive components in the front, like the PhoCUS, the measure of LREC becomes independent of that of Linv (0) and requires the removal of the primary lens for measuring the radiance of the lambertian source. As the optical efficiency dir (0)  1, we will always have Linv (0)  LREC . At its first appearance [44], the inverse method, at that time called ILLUME, was applied by illuminating, with a laser beam from the inside of the TS-CPC concentrator, a Lambertian white diffuser placed on the exit aperture (see Fig. 13.36a). This configuration, indeed, was the evolution of an accidental experiment that brought me to the discover of the ILLUME method (now ILM or P-Method (Parretta-Method)). On that occasion, the illumination of just the centre of the diffuser with a laser beam produced a back-reflected light which appeared as a well-defined image, with the same symmetry (square) of the concentrator input aperture (see Fig. 13.36b). Subsequently, I understood that the diffuser should be full illuminated to apply the ILLUME method in a correct way (see Fig. 13.36c), and this was made coupling the laser with a beam expander (see Fig. 13.36d). However, the laser beam was coming from the same side towards which the inverse light was reflected, so it was necessary to use a screen with a hole to allow the laser beam to pass and, at the same time, to allow the reflected light to be projected (see Fig. 13.37). Subsequently, another configuration was attempted to create a Lambertian source that is by applying a semi-transparent diffuser to the CPC exit aperture and illuminating it externally by means of a lamp (see Fig. 13.38). This configuration, however, did not work well, as a transmission diffuser never produces a Lambertian light, but a light where the most divergent rays are penalized. To produce the Lambertian source on the back of the concentrator (sc), therefore, the best solution remains the use of a lamp (lp) coupled to a pair of integrating spheres, (is1) and (is2) (see Fig. 13.39a). A Xenon arc lamp is the best choice to simulate the direct solar spectrum, whereas the integrating sphere is the best choice to obtain a lambertian light source [68-75]. The concentrator is grafted on to the output window of (is2) as shown in Fig. 13.39b, where it is also shown the “baffle” (ba) at the centre of the sphere. The baffle has the function to filter the light coming from sphere (is1) and to assure a lambertian distribution of light at the exit window of (is2). The planar screen is placed in laboratory at a proper distance from the source and there the 359 Advances in Optics: Reviews. Book Series, Vol. 3 characteristic light image, leaved by the inverse beam as a fingerprint, is produced (see Figs. 13.39c, d). Fig. 13.36. Application of ILM with a Laser beam. (a) Closing of exit aperture with a Lambertian diffuser. (b) Inverse light projected on a nearby screen. (c) The diffuser is fully illuminated. (d) The laser beam is expanded. Fig. 13.37. Schematic principle of the inverse illumination method (ILLUME), utilizing a laser and a Lambertian diffuser to produce the inverse Lambertian light. 360 Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators (a) (b) (c) Fig. 13.38. (a) Schematic principle of the inverse illumination method (ILLUME), utilizing a lamp (lp) and a semi-transparent diffuser (ld) to produce the inverse Lambertian light. (b) Back illumination of the diffuser (ld) by the lamp (lp). (c) Inverse illumination of the TS-CPC by a lamp (lp). The inverse image produced on the screen is then analysed by means of the software operating with the CCD camera (in our case the HiPic software operating with the Hamamatsu CCD camera). Fig. 13.40 shows, as an example, the intensity profiles recorded along the horizontal (x-axis) and vertical directions (y-axis) of the inverse image produced on the screen (ps). Some black dots are placed at known distances on the screen (ps) and used as reference points of a Cartesian frame for measuring the distances on the screen and then calibrating the polar and azimuthal angles associated to any point. During the calibration of distances, the horizontal and vertical profiles were traced in such a way to take in the dots, which appear in the profiles as thin peaks (see Fig. 13.40). To get the correct irradiance profile on the screen, it could be needed to adjust the intensity and shape of the image for possible effects of perspective; this depends on the actual position of the CCD camera respect to the optical axis and is not necessary when the camera is placed very close to concentrator. If necessary, the perspective correction can be applied by using a specific program [67, 76-79]. Once known the distances between the dots, the calculation of angles is straightforward. The photo of the front side of the Rondine irradiated in the inverse mode is shown in Fig. 13.41a. The CCD camera is placed very close to the concentrator and on the plane of its input aperture. 361 Advances in Optics: Reviews. Book Series, Vol. 3 Fig. 13.39. (a) Photo of the ILM (ex ILLUME) apparatus during characterization of the RondineGen1. (b) Photo of the Rondine-Gen1 "grafted "on the integrating sphere (is2). (c) The planar screen and the ILM image produced on it by the Rondine-Gen1. (d) ILM image produced on the screen by the TS-CPC. (a) (b) Fig. 13.40. Analysis by HiPic software (Hamamatsu) of the ILM image produced by the RondineGen1 concentrator. The irradiance profiles, traced along the horizontal (x-axis) (a) and the vertical (y-axis) (b) directions, are used to calibrate the polar angle of the points along the corresponding axis. 362 Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators Fig. 13.41. (a) Photo of the Rondine-Gen1 during ILM measurements. The CCD is placed just below at short distance. (b) Image of the front side (on-axis) input aperture of Rondine-Gen1. The blue frame surrounds the area of the receiver (REC), that is of the lambertian source; the red frame surrounds the total input area. Fig. 13.41b shows the detail of the entrance aperture sight in front, outlined by the red frame, with the central region REC, outlined by the blue frame, corresponding to the Lambertian source (the exit window of the integrating sphere). The central region is the most lit of the image, because it is the direct source of inverse light, which does not undergo attenuation inside the concentrator. If the lambertian source is made well, moreover, the image of REC is very uniform, as it represents the constant radiance of an integrating sphere. Following Eq. (13.67), the on-axis efficiency dir (0) is equal to the ratio between the average intensity of the red region and the uniform intensity of the blue region. Indeed, if we would take this measure at different CCD orientations, we would precisely get the absolute transmission efficiency: dir ( , )  Linv ( , ) . LREC (13.68) By doing so, however, we would fall back into the same drawbacks of direct method, because we would need again to carry out a measure for each orientation of the CCD. However, when the ILM method cannot be applied by projecting the reverse light on a screen, the use of a CCD which is oriented at different angles towards the concentrator becomes a very interesting alternative to the DCM method, because it is much cheaper (we have seen that the application of DCM involves the use of a quality parabolic mirror if we want to get a uniform parallel beam) (see Figs. 13.76 (b, c)). This application of ILM would require only a lamp, an integrating sphere and a webcam, all very economical components (the issue of integrating spheres is discussed apart in Appendix 13.D). If you consider Eq. (13.68), in fact, the use of the Lambertian screen is no longer necessary. 363 Advances in Optics: Reviews. Book Series, Vol. 3 Fig. 13.42a shows the input aperture of the refractive, nonimaging PhoCUS concentrator as it appears in the dark when irradiated in the inverse way, and Fig. 13.42b the corresponding image produced on the planar screen. The image is now smaller than that produced by the Rondine concentrator, because the acceptance angle is very low, 1°. In Fig. 13.42b are visible the black dots on the light image, used to calibrate the distances of the points on the screen, and then to assign the correct  and  angles to each point P. (a) (b) Fig. 13.42. In (a) the input aperture of the PhoCUS concentrator as it appears in the dark when irradiated in the inverse way; in (b) it is shown the corresponding image produced on the planar screen. To measure the absolute on-axis (0° incidence) optical efficiency of the Mock-up,  dir (0) , we had to use a different procedure respect to that used for the Rondine concentrator. In this case, in fact, we have a refractive concentrator, that needs the recording of two images for obtaining  dir (0) . We have oriented the CCD towards the concentrator, aligned with its optical axis, and we have taken one image of the full input aperture with the lens; after, we have taken a second image of the input aperture after removing the lens. In the first image, we have taken the mean radiance of the lens, Linv(0) ; in the second image, we have taken the mean radiance of the sphere cavity, LREC , corresponding to the lambertian source. The ratio between these two quantities has given the absolute on-axis optical efficiency of concentrator  dir (0) and, from Eq. (13.66), the absolute angle-resolved optical efficiency: dir (0)  Linv (0) / LREC . 13.5.3. The Application of DLCM Method As we have discussed in Section 13.2.1, the DLCM is a method that examines the local properties of the solar concentrator, then it can be effectively applied by using a laser for the irradiation of the input aperture. The method, even though constrained by lengthy measurements, gives nevertheless interesting information on local mirror surface defects or manufacturing defects, like internal wall shape inaccuracies. It is very useful to 364 Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators investigate CPC-like concentrators, which concentrate light through multiple reflections on their internal wall. The measurements with the laser can be supported by optical simulations with commercial codes. The method, simple to apply, requires just a laser to scan the CPC input aperture following a matrix-like path (see Fig. 13.43a), at a controlled orientation of the beam. For an electronically driven movement of the source, the laser can be fixed on a x/y table and moved following a matrix-like pattern of points (typically 25×25 points with 4 mm steps). In a simpler setup, the laser is moved manually along the vertical (y) direction on a column and translated horizontally along x direction on a rail (see Figs. 13.43b and 13.44). In this way, the square aperture of the concentrator is entirely scanned along x and y directions. Fig. 13.43. (a) Representation of the scanning process of the entrance aperture of a CPC with the laser beam; (b) Schematic experimental setup of the “laser method”. The output flux is measured directly by a photodetector (pd) coupled to a radiometric unit (ra), or through an integrating sphere (see box). (a) (b) Fig. 13.44. (a) The experimental DLCM apparatus with the manually driven laser. A photodiode is visible on the back of the TS-CPC; (b) Photo of the TS-CPC during the centering of the laser beam. 365 Advances in Optics: Reviews. Book Series, Vol. 3 Particularly important is the laser beam polarization state. It must be unpolarized, but in general the available laser beams are partially polarized. To overcome this, it is necessary to double the measurements, repeating them with the laser rotated of 90° respect to the previous ones, and making the average of the flux values. The light collected at output of the CPC can be measured by a photodetector (pd), controlled by a voltmeter (ra). The reference flux at input is obtained by a calibration step performed sending the laser beam to impinge directly on the (pd) surface. 13.5.3.1. Optical Efficiency Measurements The map of (pd) signals is then transformed in a map of optical efficiency of the CPC by the ratio between test signals and average reference signal. The photodetector (pd) plays an important role in the precision of efficiency data. Its response in fact must be as much as possible insensitive to variations of incidence angle of laser beam at the exit aperture of the concentrator. Regarding this, the results of previous investigations on the angleresolved absorbance of photovoltaic devices have been considered [47]. A preferred way to measure the flux at output of the CPC is to match it to an integrating sphere provided with a photodetector (pd) inside it (see the box in Fig. 13.43b), but it depends on the power of the laser in use, because the low integrating sphere sensitively reduces the irradiance on the photodetector compared to that of direct irradiation. If the entire CPC surface is scanned, the integration of the maps gives the value of transmission efficiency for a specific orientation of the laser, so a curve of optical transmission efficiency can be drawn, and the acceptance angle measured, after joining more maps of flux obtained at different polar angles. The analysis of the single maps allows to obtain interesting information on light collection by the different regions of CPC input area. It reveals, moreover, how the efficiency of light collection depends on several factors like surface reflectivity, number of reflections of the single beam, local angle of incidence, local surface defects, and so on. By comparing the simulated maps with the experimental ones, then is possible to emphasize the effects directly related to manufacturing defects. Fig. 13.44a shows a photo of the simple apparatus with a manually driven laser with = 633 nm wavelength and 5 mW power. The TS-CPC is positioned on a rotating support, provided with a goniometric scale [80], by which it is possible to fix the azimuthal angle of incidence of the laser beam. The incidence angle is adjusted by first aligning the laser beam with the TS-CPC, then projecting the beam on a far screen for adjusting the desired incidence angle. Fig. 13.44b shows a photo of the TS-CPC during the centering of the laser beam. 13.5.3.2. Beam Exit Angle Measurements The measurement of exit angles of the laser beam at the output aperture of a CPC, can be carried out by using the simple apparatus schematized in Fig. 13.45a and shown in Fig. 13.45b. A plastic hemispherical globe (hg), made from a garden lamp, is centered on the 366 Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators output aperture of the TS-CPC and drawn with parallels and meridians to indicate the polar and azimuthal angles of the laser beam spot. The opalescence of the globe, realized by sandblasting, allows to visualize the impact point of the laser beam and then, with a good approximation, its exiting direction. Fig. 13.45a shows how the two angles are measured: the polar angle  (0°-90°) on the parallels and the azimuthal angle  (0°-360°) on meridians, where  is measured starting from y axis and rotating towards x axis. Fig. 13.45. (a) Schematic of the experimental configuration for measurement of beam exit angle. It is illustrated a ray entering the TS-CPC and exiting at the polar angle . The azimuthal angle  is measured by rotating the y axis towards the x axis; (b) Photo of the apparatus with the hemispherical globe (hg) fixed to the TS-CPC and the laser. 13.5.4. The Application of the PH-Method (Parretta-Herrero Method) The schematic configuration of PH-Method is reported in Fig. 13.46a. In the figure, we have placed the Rondine concentrator deliberately enlarged to better show the path of the rays. The parabolic mirror (pm) has an aperture diameter D, a length L, a focal length f, and the square absorber (ps) has a side l. The solar concentrator (sc) coupled to the lambertian source (ls) is placed just below the screen, with its input aperture planar to the screen surface. The position of the concentrator must be accurately calculated placing it at a suitable distance from the optical axis to avoid any interference with rays reflected by the mirror (pm). This distance is found after fixing the maximum angular divergence, m (with m > 0) of inverse rays to be recorded along the x/y axes. Angle m must be chosen at a value where the optical efficiency is sufficiently low (  20 % of the maximum value) and the optical efficiency curve sufficiently well defined. Fig. 13.46a simulates red rays emerging from the concentrator with divergence m, which converge to the bottom of the screen y(m,), just at the upper edge of the Rondine, after being reflected by mirror (pm); this is highlighted in the enlarged detail of Fig. 13.46b. Fig. 13.46a shows also that all the rays (green) with direction parallel to the z axis are focused at the center of the screen. The y coordinate of rays emitted on the y/z plane at angle m can be expressed as: 367 Advances in Optics: Reviews. Book Series, Vol. 3 y ( m )  2 f (1  cos  m ) . sin  m (13.69) (a) (b) Fig. 13.46. (a) Schematic principle of the Parretta-Herrero (PH) method. (pm): parabolic mirror, (ps): planar screen, (sc): solar concentrator, (ls): lambertian source. D and f: diameter and focal length of (pm), respectively; l: side of the screen (ps). The concentrator lies below the coordinate y ( m ) in such a way to avoid any interference with the rays exiting at    m ; (b) It is shown a parallel beam emitted at    m on the y/z plane, which focuses at the bottom edge of the screen (ps). When the PH-Method is applied by simulation, it is necessary first to calibrate the angle coordinates in terms of x and y coordinates on the square screen (ps). This can be done by setting a uniform and parallel source of light exiting from the input aperture of the Rondine concentrator (see Fig. 13.46b) and oriented towards the mirror (pm) at some calibrated polar angles measured on the y/z incident plane, and on a plane parallel to the x/z plane and crossing the center of concentrator. Once a certain number of polar angles for the parallel beam are chosen, the x/y coordinates of the point on the screen, where the beam 368 Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators is focused, are recorded. The calibration provides the angle coordinate along x and y axes, as function of the pixel number npx (for example 128 for both axes covering the entire screen). We report here an example of the calibration made for the Rondine Gen1 concentrator [37, 45]:  X ()  14.94  0.232  n px , (13.70a) Y ()  14.75  0.226  n py . (13.70b) The calibration must provide an excellent linear, and pratically equal behavior for both axes. Fig. 13.47 shows, as an example, the calibration curve found for the Rondine Gen1. Fig. 13.47. Calibration curves of the emission angle vs. pixel number relative to the x and y axes of the screen. 13.6. Experimental Results 13.6.1 The Truncated and Squared CPC (TS-CPC) 13.6.1.1. Local Optical Efficiency by the Laser Method (DLCM) Fig. 13.48 shows some of a series of experimental local efficiency maps obtained at  = 0° azimuthal angle (input aperture edge horizontal), orienting the laser beam towards left (looking at the CPC input aperture), at different incidence angles  with respect to z optical axis. Besides the data of local absolute efficiency, each map brings also the information about average efficiency and standard deviation. Some of the  = 0° maps have been also simulated and are shown in Fig. 13.49. Other maps were obtained by measurements at  = 45° and are shown in Fig. 13.50. The summary of all the measured data for the total aperture, left-side aperture and right-side aperture, is reported in Table 13.1. 369 Advances in Optics: Reviews. Book Series, Vol. 3 =1° (>Left) ; Eff=73,4% (=11,6%) 10 1,100 0,9625 0,8250 0,6875 0,5500 0,4125 0,2750 0,1375 0 8 6 4 Y coordinate (a.u.) Y coordinate (a.u.) 10 2 2 4 6 8 X coordinate (a.u.) =0° ; =633nm; Eff= 78.9% (=7,4%) 1,100 0,9625 0,8250 0,6875 0,5500 0,4125 0,2750 0,1375 0 8 6 4 2 2 10 4 (a) 8 10 (b) =2°(>Left) ; Eff=56,4% (=23,6%) 10 1,200 1,050 0,9000 0,7500 0,6000 0,4500 0,3000 0,1500 0 8 6 4 Y coordinate (a.u.) Y coordinate (a.u.) 10 6 X coordinate (a.u.) =3°(>Left) ; Eff=35,4% (=31,9%) 1,200 1,050 0,9000 0,7500 0,6000 0,4500 0,3000 0,1500 0 8 6 4 2 2 2 4 6 X coordinate (a.u.) 8 2 10 (c) 4 6 8 10 X coordinate (a.u.) (d) Fig. 13.48. Some experimental maps of the local optical efficiency of the TS-CPC concentrator, obtained with the “laser method” (DLCM). Azimuthal angle: = 0°. Incidence angle: (a) = 0°; (b) = 1.0°; (c) = 2.0°; d) = 3.0°. (a) (b) (c) Fig. 13.49. Some simulated maps of the local optical efficiency of TS-CPC, obtained with the “laser method” (DLCM). Azimuthal angle: = 0°. Incidence angle: (a) = 0°; (b) = 1.5°; (c) = 2.5°. 370 Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators 10 10 1,200 1,200 1,050 0,9000 0,7500 6 0,6000 0,4500 4 0,3000 0,1500 2 4 6 X Coordinate (a) 8 0,9000 0,7500 6 0,6000 0,4500 4 0,3000 0,1500 2 0 2 1,050 8 Y Coordinate Y Coordinate 8 10 0 2 10 4 6 X Coordinate (b) 8 10 10 1,200 1,050 0,9000 0,7500 6 0,6000 0,4500 4 0,3000 0,1500 0 2 2 4 6 X Coordinate (c) 8 1,400 8 Y Coordinate Y Coordinate 8 1,225 1,050 0,8750 6 0,7000 0,5250 4 0,3500 0,1750 2 0 2 10 4 6 X Coordinate 8 10 (d) Fig. 13.50. Some experimental maps of the local optical efficiency of TS-CPC, obtained with the “laser method” (DLCM). Azimuthal angle: = 45°. Incidence angle: (a) = 0°; (b) = 1.0°; (c) = 2.0°; (d) = 3.0°. Table 13.1. All the experimental efficiency data of the TS-CPC, obtained with the “laser method” at = 0° and 45° azimuthal angles, after integration of the local efficiency maps. (°)  (°) Eff (%) sd (%) 0 0 0 0 0 0 0 45 45 45 45 45 0 0.5 1.0 1.5 2.0 3.0 4.0 0 1.0 2.0 3.0 4.0 78.4 75.2 73.4 63.9 56.3 35.4 25.3 75.8 72.9 45.7 29.9 22.3 21.3 19.3 21.3 28.7 32.7 37.3 32.8 23.1 27.6 39.2 36.7 33.3 Eff (%) (left) 75.6 71.8 68.0 49.9 55.6 11.7 12.5 sd (%) (left) 20.5 18.3 20.5 28.1 33,3 21.4 22.4 Eff (%) (right) 81.0 78.5 78.9 78.1 57.1 59.0 38.2 sd (%) (right) 21.7 19.6 20.9 21.2 32.1 35.2 36.3 371 Advances in Optics: Reviews. Book Series, Vol. 3 A look at the maps of Fig. 13.48 immediately gives a lot of information. Fig. 13.48a shows that the TS-CPC efficiency is not perfectly homogeneous, unlike what we would expect from Fig. 13.49a. The right side of the map is slightly more efficient than the left side, then the right-side mirror film was realized better. The central region of map is considerably inefficient. This is due to a wrong mechanical shaping of the prism surface near the bottom of the CPC, and to an overlapping of film strips near to the exit aperture. Is also visible the effect of joining the two portions of the prism by the less efficient vertical row at the center of the CPC. The average efficiency of the TS-CPC at  = 0° is 78.9 %, to be compared to the theoretical 94.9 % efficiency calculated by simulation the DCM with TracePro, with the assumption of a 95 % wall reflectivity (see Fig. 13.17b). The simulated results for  = 0° give an average number of reflections of light rays inside the TS-CPC of about one, as the loss of flux at each reflection is 5 % and ~5 % was the total calculated loss. The real prototype shows a real efficiency far smaller. This fact demonstrates the unsuitability of the manually surface coating process, despite the high reflectivity of 3M film. At increasing incidence angle at  = 0°, the development of optical maps is quite clear. Both left and right side of input aperture show a decreasing efficiency, but a remarkable loss of efficiency is observed on the left side of the input aperture map, because there the angle of impact of rays on the left side wall decreases (with respect to normal direction), with the consequent increase of the rejection probability for the rays (see Appendix 13.B). At  = 3° incidence, the loss of rays on left side aperture is remarkable, indicating that we are in the proximity of the acceptance angle. In practice, the left side is efficient only at  = 11.7 % (see Table 13.1). At 4° incidence, a large part of input window is not efficient at all. Due to the strong difference found for the efficiency between left side and right side, we have plotted separately the two integral efficiencies (see Fig. 13.51a). Relative efficiency (%) Relative Efficiency (%) 80 60 40 Right side Left side 20 0 TS-CPC, Incidence>Left, Azimuth = 0° 100 100 0,0 0,5 1,0 1,5 2,0 2,5 Angle of incidence (°) (a) 3,0 3,5 4,0 80 60 40 Absolute Relative 20 0 0 acc = 2.8° 1 2 3 Angle of incidence (°) 4 (b) Fig. 13.51. Experimental integral optical efficiency curves TS-CPC for 0° azimuthal angle. (a) Relative integral efficiency calculated separately for the left side and the right side of input aperture; (b) Absolute and relative integral efficiency for the entire input aperture. 372 Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators After 1° incidence, the two efficiency curves sensibly diverge. At  = 3.0°, near the acceptance angle, there is the maximum difference between them. We note incidentally a sort of on/off optical switch behavior for light entering in the TS-CPC at ~3° incidence: “on” for light impinging on the right side, “off” for light impinging on the left side. The integrated efficiency data of Table 13.1 give rise to the angle-resolved optical efficiency curves, absolute () and relative rel (), for = 0° azimuth and  = 633 nm wavelength 50 90 (see Fig. 13.51b). From them we derive the acceptance angles  acc = 2.8°, acc = 1.0°. The experimental efficiency is clearly affected by several factors: imperfections of TSCPC wall shape; imperfections of 3M coating surface and loss of light by scattering; wall reflectivity of dependent on incident angle of impinging rays, photodetector response dependent incidence angle of collected rays; laser characterization realized on a matrix of points of the input aperture (input aperture area not fully illuminated). The experimental local efficiency maps of TS-CPC obtained by measurements at the azimuthal angle  = 45° show a behavior like that of the  = 0° maps (see Fig. 13.50 and Table 13.1). By integrating these maps of local optical efficiency, we obtained a curve of efficiency with the following acceptance angles: acc ~ 2.3° at 50 % efficiency and acc ~ 1.2° at 90 % efficiency. 13.6.1.2. Beam Exit Angle Measurements The lengthy manual measurements suggested us to draw only maps of azimuthal and polar angle at = 0° incidence angle at the input of TS-CPC (laser beam parallel to the z optical axis) (see Fig. 13.45). Each point of the TS-CPC input aperture is represented by a value of the correspondent angle. The maps of Fig. 13.52 are very interesting for the beauty of the representation. Both have a well-defined symmetry. The polar angle map (see Fig. 13.52a) shows that rays incident on the periphery of input aperture (ia) exit from the TS-CPC with a small divergence. The divergence increases at decreasing the distance between impact point and center of (ia). The regularity of this result is assured by the fact that the number of reflections is virtually one for any point of (ia), as results also by simulations with TracePro. The central region of polar map is rather confused. Here the beam spot on the screen (hg) is very dispersed and so impossible to measure. The cause is the same affecting the efficiency maps at the central region (see Fig. 13.48a and 13.50a): the wrong shaping of the prism surface near the bottom of TS-CPC, and the pronounced overlapping of film strips near the exit aperture, which produce a strong scattering of the beam towards unpredictable directions. Fig. 13.52b shows that the azimuthal angle also varies very regularly with the coordinate of input beam. It is easy to note that at an entrance point on (ia) corresponds an exit direction opposite with respect to the center of aperture. Then, if we let the input ray move on a circle clockwise around the center, the exiting azimuth will regularly increase and the polar angle will remain constant. At the center of the map we note the same irregularities as for the polar angle map. 373 Advances in Optics: Reviews. Book Series, Vol. 3 Another way of describing the change of direction of the exit beam is to draw its path on a planar screen as function of the y coordinate of a line scanned on the input aperture. An example is shown in Fig. 13.53, where horizontal lines are scanned with a 1 mm diameter laser beam on the (ia) of the TS-CPC at different y coordinates, with steps of 4 mm. Only the upper half of TS-CPC has been explored, starting from y = 4.8 cm and going down to y = 0.4 cm. The path of exit beam is ring shaped, has an azimuthal excursion less than , and its divergence increases progressively when the y coordinate of scanned line approaches the center of input aperture. 10 400,0 350,0 300,0 250,0 200,0 150,0 100,0 50,00 0 8 6 4 2 2 4 6 8 X coordinate (a.u.) Y coordinate (a.u.) Y coordinate (a.u.) 10 10 80,00 8 70,00 60,00 50,00 6 40,00 30,00 4 20,00 10,00 2 0 2 (a) 4 6 8 X coordinate (a.u.) 10 (b) Fig. 13.52. Input aperture maps of polar (a) and azimuthal (b) angles of the laser beam exiting from the output aperture of the TS-CPC, at = 0° incidence angle. (a) (b) (c) Fig. 13.53 (a-c). Optical path of exit beam as obtained scanning different horizontal lines on the input aperture of the TS-CPC. (a) y = 4.8 cm; (b) y = 4.4 cm; (c) y = 4.0 cm. 374 Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators (d) (e) (f) (g) (h) (i) (l) (m) (n) Fig. 13.53 (d-n). Optical path of exit beam as obtained scanning different horizontal lines on the input aperture of the TS-CPC. (d) y = 3.6 cm; (e) y = 3.2 cm; (f) y = 2.8 cm; (g) y = 2.4 cm; (h) y = 2.0 cm; (i) y = 1.6 cm; (l) y = 1.2 cm; (m) y = 0.8 cm; (n) y = 0.4 cm. 375 Advances in Optics: Reviews. Book Series, Vol. 3 13.6.1.3. Optical Efficiency by DCM and ILM Fig. 13.54a shows the irradiance map on the planar screen, obtained by simulating the inverse method (at that time ILLUME, applied by illuminating by a laser beam a lambertian diffuser placed at the exit aperture of the concentrator) with a beam (ib) of 5-mm cross section radius. Fig. 13.54b shows the average x/y profile at the center of the screen. The HT-CPC was first investigated by simulating its relative transmission efficiency with the DCM and ILM methods. A wall reflectivity of 0.9 was used for both simulations. Fig. 13.54c shows the comparison between the results of relative efficiency (DCM) plotted as function of the polar angle of incidence of the collimated beam, and those of the relative radiance (ILM) plotted as function of the emission angle of inverse light (azimuthal angle  = 0°). Note that in Fig. 13.54c the DCM curve contains less points than the ILM curve, because DCM is a step-by-step process made manually at the computer, with intentionally smaller steps at around the acceptance angle, where the slope of the curve is higher. The number of points in the ILM curve, on the other hand, depends on the number of inversed rays used and then can be increased as desired. The two curves coincide almost perfectly, and give the following results: (a) (b) (c) Fig. 13.54. (a) Irradiance map of the TS-CPC concentrator, obtained by simulating the inverse method with a beam (ib) of 5-mm cross section radius. (b) Average x/y profile at the center of the screen. (c) Comparison between the angle-resolved relative efficiency (DCM) and relative radiance (ILM) of the TS-CPC. 376 Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators DCM: acc (90°) = 1.3°, acc (50°) = 1.9°; ILM: acc (90°) = 1.3°, acc (50°) = 1.8°. This result was obtained thanks to the fact that, in ILM simulations, we have placed the screen at a very high distance from the TS-CPC, obtaining an angular resolution   0°. The results of Fig. 13.54 confirm the equivalence of the DCM and ILM methods for what concerns getting the relative transmission efficiency. The experimental measurements were made by applying the ILM method. Fig. 13.55a shows the TS-CPC apparatus illuminated by the lambertian light from an integrating sphere, and Fig. 13.55b shows the inverse light projected on the screen 360 cm far apart. At this distance, we have an angular resolution on the screen at the optical axis   0.8°. Fig. 13.56a shows the obtained ILM experimental transmission efficiency curve. It is rather deformed, due to the poor angular resolution, and is like that of the laser method (see Fig. 13.56b), with the same acceptance angles. Fig. 13.56b shows, by comparison, the simulated ILM curve of Fig. 13.54, which surely represents the true transmission efficiency of the TS-CPC. (a) (b) Fig. 13.55. Photo of the ILM apparatus and image of the inverse light on the screen. (a) (b) Fig. 13.56. (a) Experimental efficiency curve (relative) obtained by ILM. (b) Comparison between the three simulated and experimental relative efficiency curves. 377 Advances in Optics: Reviews. Book Series, Vol. 3 13.6.1.4. Local Optical Efficiency by ILLM In the Introduction, we have seen that the ILM method becomes a powerful tool of investigation of the optical properties of a concentrator if the receiver is locally illuminated by inverse light, and this is the ILLM method [44]. In this way in fact we are able to derive the relative efficiency curve rel() specific of the illuminated region of the receiver, and to establish the range of incidence angles, in “direct irradiation”, at which that region collects light (is illuminated) by a beam at input with less or more efficiency. A demonstration of this procedure is given here simulating the inverse illumination of the center of the diffuser of the TS-CPC by a collimated beam with variable cross section (here we apply the old ILLUME method, where the inverse lambertian light is created by illuminating, by a parallel and centered beam, a lambertian diffuser placed close to the exit aperture of the CPC (see Fig. 13.57b)). The irradiance profiles, E ( d , x ) , E ( d , y ) , recorded on a squared screen of 2000-cm side placed very far from the TS-CPC (3000 cm), have been averaged and are reported in Fig. 13.58 for different values of the beam cross section radius. The x and y directions correspond to the TS-CPC input aperture edges (see Fig. 13.57a). The E (d ) profiles of Fig. 13.58 are shown at increasing beam cross section radius R. The higher radius (5 mm) is that required to illuminate the entire diffuser surface. In this case, we obtain the same irradiance profile from which the relative efficiency rel() of Fig. 13.54c was derived, by applying Eq. (13.C5). The angular interval spanned by the profiles is 18.4°. Fig. 13.57. (a) CAD model of the TS-CPC. (b) Example of raytracing by TracePro of the truncated and squared CPC (TS-CPC), illuminated in the inverse way by a collimated inverse beam (ib) of radius cross section R. The (ib) is evidenced in blue color. It is interesting to note that reducing the beam cross section the efficiency curve reduces in width and increases in height (about twice); as consequence, also the acceptance angle is reduced. This means that concentrating the inverse beam at exit aperture towards the center of the diffuser (of the CPC receiver) produces a direct beam at input aperture more aligned with the optical axis. This also means something well known from the science of nonimaging optics, that is a beam well collimated with the optical axis of the CPC (= 0°) produces an intense irradiation in the very center of the receiver [17]. This is demonstrated here by the simulation of Fig. 13.59, where it is shown the irradiance profile produced on the receiver of the TS-CPC by a plane wave aligned with the optical axis z (= 0°). 378 Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators (a) (b) (c) (d) (e) (f) Fig. 13.58. Irradiance profiles on the planar screen obtained by simulating (20k rays) the local inverse method (ILLM) for the TS-CPC concentrator. Input beam radius: (a) R = 0.05 mm (scale 10 W/m2); (b) R = 0.5 mm (scale 10 W/m2); (c) R = 1.0 mm (scale 10 W/m2); (d) R = 2.5 mm (scale 10 W/m2); (e) R = 3.5 mm (scale 7 W/m2); (f) R = 5.0 mm (scale 5 W/m2). (a) (b) Fig. 13.59. (a) Simulated irradiance map on the 1-cm diameter receiver of TS-CPC, illuminated by a plane wave aligned with the optical axis. (b) Irradiance profiles measured along x and y axes (see Fig. 13.57a). 379 Advances in Optics: Reviews. Book Series, Vol. 3 The thinning of the central profile in Fig. 13.58 is accompanied to an interesting result, that is the appearing of two satellite peaks at 7.2°. This angle corresponds to the angle  shown in Fig. 13.57b, made with z axis by a ray tangent to the upper edges of the TS-CPC exit and entrance apertures, along x or y directions. Angle  is also the minimum angle at which the square aperture starts to shadow the circular receiver respect to an incoming direct beam. To study the optical efficiency of regions of the receiver (diffuser) placed at different distance from the centre, we have simulated the inverse illumination of the TS-CPC diffuser with collimated beams having a constant cross section ( mm2), but the shape of annulus, with Rint and Rext internal and external radius, respectively. The irradiance profiles E ( d , x ) and E ( d , y ) have been recorded on the same squared screen of 2000 cm side at 3000 cm from the TS-CPC, as in the previous simulations. They have been averaged and are reported in Fig. 13.60 at increasing values of the internal radius Rint. (a) (b) (c) (d) (e) (f) Fig. 13.60. Irradiance profiles obtained by simulating (20k rays) the inverse local method ILLM for the TS-CPC concentrator. The profiles were taken along x and y axis directions, for different values of the internal radius Rint of the annulus (the external radius is in parenthesis) with constant area  mm2. (a) Rint = 0.5 (1.12) mm (scale 10 W/m2); (b) Rint = 1.0 (1.414) mm (scale 10 W/m2); (c) Rint = 2.0 (2.245) mm (scale 10 W/m2); (d) Rint = 3.0 (3.165) mm (scale 10 W/m2); (e) Rint = 4.0 (4.123) mm (scale 5 W/m2); (f) Rint = 4.9 (5.0) mm (scale 3 W/m2). The Rint = 0.0 (1.0) mm profile has not been shown as it corresponds to that with R = 1.0 mm of Fig. 13.58. 380 Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators The shape of the profiles in Fig. 13.60 changes quite noticeably at high values of Rint, when the illuminated region is more peripherical. Here we note the disappearing of a central peak and the formation of two strong satellite peaks near  = 0°. This is easily explained by the same argument used in occasion of the previous simulations, that is the direct illumination of the TS-CPC by a z axis aligned beam is not able to illuminate the periphery of the receiver, as the profile of Fig. 13.59b demonstrates. Then, if we illuminate the periphery of the receiver, we cannot extract from the input of the TS-CPC a beam aligned with the z axis. As consequence, the optical efficiency at near  = 0° for the peripheral region must be very small (see Fig. 13.60f). 13.6.2. The (Virtual) Half-Truncated CPC (HT-CPC) 13.6.2.1. Local Optical Efficiency by ILLM We describe here the optical properties of the Half-Truncated CPC (HT-CPC) virtual concentrator introduced in Section 13.3 [44]. The HT-CPC is similar to the TS-CPC in the dimensional parameters, but the different shape of entrance aperture, in particular the presence in TS-CPC of the four planar surfaces (see Fig. 13.57a), renders its response to inverse method very different. As for the TS-CPC, we have simulated the inverse illumination of the center of the diffuser, placed at the exit aperture of HT-CPC, by a beam with variable cross section (ILLUME method). The screen (ps) is of 1000-cm diameter at 3000-cm distance from the HT-CPC entrance window (ia). The irradiance profiles, E(d, x) and E(d, y), at the center of the planar screen (ps) have been averaged and reported in Fig. 13.61 for different values of the beam cross section radius R. They show the existence of satellite peaks similar to those obtained with the TS-CPC (see Fig. 13.58). The profiles of Fig. 13.61 span an angle of incidence of 9.5°, and the more pronounced satellite peaks are centered at 4.7°. Differently from those of the TS-CPC, they change drastically in shape at increasing the beam cross section radius, and the intensity decreases sevenfold. Increasing beam radius, the satellite peaks, well visible in Fig. 13.61 at R = 0.05 mm disappear at R ~ 0.25 mm, leaving a broad background; the central peak decreases progressively up to disappearing, and the broad peak transforms in the large and top-flat peak typical of ideal CPCs (see Fig. 13.12 and Fig. 13.14). This means that, even halved, an ideal CPC maintains quite unchanged its optical behavior. The simulation with R = 5 mm (see Fig. 13.62), gives the relative optical efficiency of the 90 50 =4.5° and acc =5.1°, practically the HT-CPC concentrator, with acceptance angles acc same value of the not halved CPC. The irradiance profiles on the planar screen (ps) relative to the inverse illumination of HT-CPC (ILLUME) with beams of constant cross section area (π mm2) and shape of annulus are reported in Fig. 13.63. These profiles differ strongly from the correspondent ones of TS-CPC concentrator. This demonstrates that, even though similar dimensionally, the TS-CPC and HT-CPC concentrators show a strong difference in optical behavior due to the different shape of the input aperture and of the internal wall. 381 Advances in Optics: Reviews. Book Series, Vol. 3 (a) (b) (c) (d) (e) (f) Fig. 13.61. Irradiance profiles obtained by simulating the inverse method for the HT-CPC. The profiles were taken at different cross sections of the input beam (ib), centered on the diffuser. (a) R = 0.05 mm (scale 0.4 W/m2); (b) R = 0.5 mm (scale 0.2 W/m2); (c) R = 1.0 mm (scale 0.12 W/m2); (d) R = 2.5 mm (scale 0.08 W/m2); (e) R = 3.5 mm (scale 0.06 W/m2) (f) R = 5.0 mm (scale 0.05 W/m2). (a) (b) Fig. 13.62. (a) Irradiance map obtained by applying the ILLUME method to the HT-CPC with a collimated beam of 5.0 mm radius incident on the center of the diffuser. The 1000-cm diameter and 3000 cm distant screen (ps) spans an angle of incidence of 9.5°; (b) The average x/y irradiance 50 = 5.1°. profile. The average value of acceptance angle is acc 382 Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators (a) (b) (c) (d) (e) (f) Fig. 13.63. Irradiance profiles obtained by simulating (50k rays) the inverse method (ILLUME) for the HT-CPC concentrator (50k rays). The profiles were obtained by averaging the profiles taken along x and y directions, for different values of the internal radius Rint of the annulus (the external radius is in parenthesis). (a) Rint = 0.5 (1.12) mm (scale 0.1 W/m2); (b) Rint = 1.0 (1.414) mm (scale 0.1 W/m2); (c) Rint = 2.0 (2.245) mm (scale 0.1 W/m2); (d) Rint = 3.0 (3.165) mm (scale 0.06 W/m2); (e) Rint = 4.0 (4.123) mm (scale 0.06 W/m2); (f) Rint = 4.9 (5.0) mm (scale 0.05 W/m2). 13.6.3. The Truncated CPC (T-CPC) 13.6.3.1. Optical Efficiency by ILM Fig. 13.64a shows T-CPC during measurements at inverse light with the ILM method. Distance T-CPC-screen: 360 cm. Fig. 13.64b shows the T-CPC in the dark. The image on the screen is viewed through the mirror (mi), used because the angle view of the CCD objective was too small. Fig. 13.65a and Fig. 13.65b show the use of the HiPic software (Hamamatsu) to trace the horizontal and vertical profiles of the irradiance map, respectively. The relative, horizontal and vertical, inverse radiance profiles are calculated by using Eq. (13.65) and are shown in Fig. 13.66a and Fig. 13.66b, respectively. We find 90 50 = 0.75°, acc = 1.47°. the following, average acceptance angles: acc 383 Advances in Optics: Reviews. Book Series, Vol. 3 Fig. 13.64. (a) Photo of the T-CPC concentrator during measurements with inverse light. It is visible the lamp (lp), the integrating sphere (is) and the planar screen (ps). (b) The T-CPC in the dark, with the CCD oriented towards the mirror (mi), reflecting the image on the screen and used to double the screen-CCD distance (see Fig. 13.34). The CCD is shown in the box. (a) (b) Fig. 13.65. Horizontal (a) and vertical (b) profiles of the irradiance map, taken by HiPic. (a) (b) Fig. 13.66. Horizontal (a) and vertical (b) profiles of the relative radiance. 384 Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators 13.6.4. The Rondine Concentrators 13.6.4.1. Optical Efficiency by DCM and ILM Fig. 13.67a shows the Rondine-Gen1 concentrator [59-66] during measurements at inverse light with the ILM method. Distance T-CPC-screen: 360 cm. Here we show the economical configuration of ILM experimental setup, where it is used a single sphere, a webcam to record the inverse image and the “ImageJ” software (free of charge from the web) for its elaboration. Later we used a CCD camera and the HiPic software of Hamamatsu (see Fig. 13.67b). The x-axis and y-axis irradiance profiles of the image of inverse light on the screen, taken by HiPic, can be found in Fig. 13.18a. Fig. 13.68a shows the irradiance ILM map and Fig. 13.68b shows the horizontal (y) and vertical (x) profiles of the relative inverse radiance of Rondine Gen1, calculated by using Eq. (13.65). The two profiles have a different trend due to the quasi-rectangular shape of the exit aperture (see Fig. 13.18a). We find the following average acceptance angles: x-axis profile, 90 50 90 50 = 4.3°, acc = 9.5°; y-axis profile, acc = 6.3°, acc = 9.5°. These values can be acc compared to that obtained by DCM (see Fig. 13.69). The corresponding average 90 50 90 = 4.4°, acc = 9.1°, y-axis profile acc = 6.5°, acceptance angles are: x-axis profile  acc 50 = 9.6°, practically the same found with ILM. For the orientation of the Rondine, refer acc to Fig. 13.18a. The horizontal or vertical orientations are not related to the x/y axes, but on the way the Rondine is mounted on its holder. We observe that the direction of longer side of exit aperture (x-axis) gives rise to a shorter acceptance angle at 90 % of maximum efficiency. Fig. 13.70a shows the irradiance ILM map and Fig. 13.70b shows the horizontal x/y profiles of the relative inverse radiance of Rondine-Gen2, calculated by using Eq. (13.65). The square symmetry of the exit aperture of Gen2 gives rise to the same 90 = 5.0°, profile for the x-axis and y-axis, with the following average acceptance angles: acc 50 = 8.0°. acc Fig. 13.67. (a) A single integrating sphere and a webcam were used in the first, economical, experimental setup of ILM applied to the Rondine-Gen1 concentrator. (b) Two integrating spheres and a CCD were used later in the more advanced experimental setup of ILM. 385 Advances in Optics: Reviews. Book Series, Vol. 3 1,1 rel rel LC () , opt () 1,0 0,9 acc=6.3° acc=-6.3° acc=-4.4° acc=+4.2° 0,8 0,7 acc=9.5° 0,6 acc=-9.5° 0,5 horizontal profile acc=6.3° 0,4 vertical profile 0,3 -10 (a) -5 0 acc=4.3° 5 Emission / incidence angle,  (°) 10 (b) Fig. 13.68. (a) Irradiance ILM map of the Rondine-Gen1; (b) Horizontal (y-axis) (black) and vertical (x-axis) (red) profiles of the relative inverse radiance. (a) (b) Fig. 13.69. (a) Relative efficiency of the Rondine Gen1 concentrator traced along the x-axis. (b) Relative efficiency of the Rondine Gen1 concentrator traced along the y-axis. A small distortion of the curves is observed, due to a not perfect uniformity of the parallel beam. We have already explained (see Section 13.4) that the application of DCM to the Rondine concentrators requires the adding of a box at the entrance side to recover the removed four planar walls (see Fig. 13.19), whereas the application of ILM can be made on the Rondine as it is. To demonstrate that the presence of the box do not alter the optical properties of the Rondine at inverse light, we have simulated by ILM also the Rondine-Gen2+box concentrator, with ideal mirror box walls. The measured relative inverse radiance is shown in Fig. 13.71a for the two configurations. The perfect overlap of the two curves demonstrates the non-influence of the box on the optical properties of the Rondine, so the idea of Antonini to remove the four walls proved to be very correct [59-66], because, also in the best real case, the four walls would never be equivalent to two ideal reflectors. 386 Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators 1,1 rel rel LC () , opt () 1,0 0,9 acc =+4.9° 0,7 0,6 0,5 0,4 50 0,2 acc =8.2° 50 acc =-7.8° horizontal profile vertical profile 0,3 (a) 90 90 acc =-5.1° 0,8 -8 -6 -4 -2 0 2 4 Emission / incidence angle,  (°) 6 8 (b) Fig. 13.70. (a) Irradiance ILM map of the Rondine-Gen-2. (b) Horizontal (black) and vertical (red) profiles of the relative inverse radiance. (a) (b) Fig. 13.71. (a) Simulated inverse radiances vs. emission angle of Rondine-Gen2, with and without box, averaged over the x and y directions, with the ILM method at d = 229 cm. Angular resolution =1.0°; (b) Average optical efficiency profile measured along x/y axes, compared to that measured along the diagonal of input aperture. Being the Rondine-Gen2 concentrator of non-cylindrical symmetry, we have proven to look at its transmission efficiency curve when the azimuthal angle is of  = 45°. Whereas this requires new simulations measurements when applying the DCM, the ILM immediately gives this information; it is sufficient in fact to take the map of irradiance (see Fig. 13.70a), to extract the data occupying the diagonal row of the map, to calculate the correct values for the polar angle, and finally to transform them in terms of relative radiance (efficiency) by applying Eq. (13.65). The result is shown in Fig. 13.71b and compared with the curve taken at  = 0°. 387 Advances in Optics: Reviews. Book Series, Vol. 3 Fig. 13.71b leads us to another consideration. The Rondine-Gen2 module is actually oriented in such a way to track the Sun disk along the x or y-axis (they are equivalent in Gen2). Angular misalignments between Gen2 and Sun are then expected along that direction. The curves of Fig. 13.71b, however, seem to favor the diagonal direction, instead of the x/y one. If we calculate the inverse radiance curve along the diagonal direction, indeed, we find that it is wider than that calculated along the x/y axis. We have 90 50 = 5.0±0.2°; acc = 8.4±0.2°; and in the diagonal direction: in fact in the x/y direction: acc 90 50 = 4.9±0.2°; acc = 9.9±0.2°. Then, to increase the collection capability of the acc Rondine-Gen2 along the direction of tracking, it could be convenient to have the tracking direction parallel to the diagonal of the opening entrance. This is valid for misalignments 90 50 90 , because, as it can be seen in Fig. 13.71b, acc is improved of ≈ 20 %, but acc > acc remains almost constant. 13.6.4.2. Optical Efficiency by Parretta-Method and Parretta-Herrero Method Here we compare the results of optical simulations carried out on the Rondine concentrators by applying two different inverse methods, the ILM, or Parretta Method, and the Parretta-Herrero Method. I remember that the first one is applied by projecting the inverse light on a far screen, as an ideal absorber, whereas the second is applied by interposing a parabolic mirror between the Rondine and the screen, which focus the inverse light on the ideal absorber screen, where, differently from ILM, the polar angle of a point is displayed linearly with the distance from the center. Here we demonstrate that the P-Method (ILM) and the Parretta-Herrero Method give the same results if both are applied correctly [37-45]. The flux distributions (irradiances in W/m2) recorded for the P-Method and the PHMethod applied to Rondine-Gen1 are shown in Figs. 13.72a and b, respectively. The map of Fig. 13.72b directly reproduces the radiance of the inversely irradiated concentrator, because of the reflection of the inverse light on the parabolic mirror surface. From the two flux distributions we derive the corresponding x-axis and y-axis profiles of the normalized transmission efficiency as follows: for the P-Method the normalized x/y-axes profiles of the intensity (irradiance) on the screen were multiplied by the (cosθ)−4 factor (see Eq. (13.65)); for the PH-Method, on the contrary, they were directly obtained from the normalized x/y-axes profiles of the intensity (irradiance) on the screen. The x-axis and y-axis profiles of the transmission efficiency, ηdir(θ), derived by the two methods, are shown in Figs. 13.73a and b, respectively. The maps of flux distribution recorded for the P-Method and the PH-Method applied to the Rondine-Gen2 are shown in Figs. 13.74a and b, respectively. The corresponding x-axis and y-axis profiles of the normalized transmission efficiency, ηdir(θ), are shown in Fig. 13.75a and b, respectively. Comparing the efficiency profiles of both concentrators (Figs. 13.73 and 13.75), the excellent overlap of the profiles obtained with the two methods appears evident, and hence the equivalence between P-Method and PH-Method. 388 Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators (a) (b) Fig. 13.72. Rondine-Gen1: (a) map of flux distribution recorded on the screen (ps) for the P-Method; (b) map of flux distribution recorded on the screen (ps) for the PH-Method. (a) (b) Fig. 13.73. Rondine-Gen1: x-axis (a) and y-axis (b) of the normalized optical efficiency profiles derived by the P-Method and the PH-Method. We are finally able to give a value to the on-axis absolute efficiency,  dir (0) , by experimental measurements of the radiance emitted frontally by the Rondine concentrators. Applying the Eq. (13.68) in Section 13.5.2: dir (0)  Linv (0) / LREC , where Linv (0) is the average radiance of the on-axis front image of input aperture, and LREC is the average radiance of the lambertian source (the integrating sphere). Fig. 13.76a shows the front image of the Rondine-Gen1 concentrator. It is visible the central, blue frame, region of the receiver (the window of the integrating sphere). The radiance LREC is slightly underestimated due to the presence of the baffle at the center (see Fig. 13.39b). By correcting this effect [A. Parretta, to be published], we obtain a better estimate of LREC , 389 Advances in Optics: Reviews. Book Series, Vol. 3 which, together with the average radiance of the red frame region, Linv (0) , gives: dir (0) = 84.0 ± 1.0 %. For the Rondine-Gen2 we obtain: dir (0) = 86.0 ± 1.0 %. The experimental values of dir (0) , together with those of  dir , rel ( ,  ) found so far by the DCM and ILM methods, give the final absolute transmission efficiency  dir ( ,  ) of the concentrators. The more advanced Rondine-Gen2 version proves therefore more efficient than the old Rondine-Gen1 version. (a) (b) Fig. 13.74. Rondine-Gen2: (a) map of flux distribution recorded on the screen (ps) for the P-Method; (b) map of flux distribution recorded on the screen (ps) for the PH-Method. (a) (b) Fig. 13.75. Rondine-Gen2: x-axis (a) and y-axis (b) of the normalized optical efficiency profiles derived by the P-Method and the PH-Method. 390 Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators (a) (b) (c) Fig. 13.76. Front image of the Rondine-Gen1 concentrator. The radiance LREC is obtained averaging the intensity of the blue frame region; the radiance Linv (0) is obtained averaging the intensity of the red frame region (a). On-axis image of the front aperture of the Rondine-Gen1 (b). Off-axis (right side) image of the front aperture of the Rondine-Gen1. The appearance of a darker zone on the left side means that the optical efficiency is reducing (c). 13.6.5. The PhoCUS Concentrator 13.6.5.1. Optical Simulations The focalization properties of the two lenses (prismatic and hybrid), without SOE, were simulated by TracePro with 100k rays. Fig. 13.77 shows the images produced at the focal distance of the two lenses [57]. Only the prismatic lens gives a uniform distribution of flux on the focal plane. To obtain a uniform flux on the receiver with both lenses, the distance lens-receiver was increased to 23 cm, greater than the focal length. 391 Advances in Optics: Reviews. Book Series, Vol. 3 (a) (b) Fig. 13.77. Simulated maps of irradiance at the focal plane of the prismatic (a) and hybrid (b) PhoCUS lenses, without SOE. The chromatic aberration introduced by the prismatic lens has been studied by simulating, with the direct method, the image produced on the receiver by blue light ( = 450 nm) and red light ( = 650 nm). The results are visible in Fig. 13.78. Being the receiver behind the focal plane, the short wavelengths are more expanded on the receiver surface. (a) (b) Fig. 13.78. Images of the flux on the receiver plane, at 23 cm from the lens, due to  = 450 nm light (a) and  = 650 nm light (b). The optical efficiency curves, simulated by DCM and ILM, of the two lenses (without SOE) are shown in Fig. 13.79a. First of all, we observe that the curves are typical of an “imaging” concentrator, with a monotonic decrease of efficiency, in contrast to “nonimaging” concentrators, characterized by a plateau followed by a rapid decrease at 50 90  1.5÷2.0° and acc  0.5°. We observe also that: the acceptance angle. We measure acc i) the two lenses have similar curves for the same method; ii) each method gives similar 392 Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators curves for the two lenses. The inverse method ILM has been also applied to simulate the PhoCUS mock-up, that is the lens + SOE, and the relative efficiency curves for the two types of lens are shown in Fig. 13.79b. The effect of SOE is positive, because it increases 50 90  2.4° and acc  1.0° for both lenses and equalizes the two the acceptance angles: acc curves. We now observe a behavior more similar to a nonimaging solar concentrator. (a) (b) Fig. 13.79. (a) Optical efficiency of the prismatic and hybrid lenses (no SOE), simulated by DCM and ILM. (b) Optical efficiency of the prismatic and hybrid lenses + SOE, simulated by ILM. 13.6.5.2. Experimental Measurements Some experimental results are shown in the following. (a) (b) Fig. 13.80. (a) Comparison between the experimental and simulated direct efficiency curves (DCM) of the prismatic lens without SOE; (b) Experimental direct efficiency curves of the hybrid lens without SOE, obtained by using a sphere or a solar cell as receiver. 393 Advances in Optics: Reviews. Book Series, Vol. 3 Fig. 13.80a shows that coupling the PhoCUS mock-up to the integrating sphere (see Fig. 13.30c), gives the optical properties of the concentrator alone, as obtained by simulations, confirming that the integrating sphere behaves as an ideal receiver. The use of the solar cell, on the contrary, gives a thinner curve, showing that the solar cell is not able to collect with the same efficiency all the incident light, particularly that incident at input at higher angles. The knowledge of difference between the sphere and the cell curve is important to establish how much the cell could be optimized to improve its light collection. Similar results were obtained with the hybrid lens, as shown in Fig. 13.80b. 13.7. Conclusions Purpose of this work has been to provide the experimentalist with all the theoretical and practical tools useful to investigate the main optical properties of individual units of a concentrated PV system, in order to confirm the overall characteristics of the original project. The subject of this work has been the description of methods for the optical characterization of solar concentrator prototypes, which involves the study of many properties, the most important of which are the optical transmission efficiency and the spatial and angular distribution of the flux on the receiver, the solar cell. However, to give this work a wider breath, the practical treatment of the characterization methods was preceded by a general theoretical discussion, which examines all the possible irradiation modes of a solar concentrator, schematized as a box with an entrance and an exit aperture, and a completely unknown interior. This discussion has allowed me to deepen theoretically the traditional "direct irradiation” model, that reflecting the solar concentrator operating mode in the field, and to consolidate the theory of innovative models, recently introduced, those based on the "inverse" (or "reverse") irradiation of the concentrator. I have proposed also new ones, though a bit bizarre, accompanied by the definition of new optical quantities, which could be useful in the future. The second part of this work has been devoted to the operating modes to follow in order to correctly apply two main characterization methods, namely the "direct" and the "inverse" ones. The optical quantity on which I have been most concerned was the optical transmission efficiency, which is represented by a curve that defines how efficient the light transmission is from the input to the output opening of the concentrator, as function on the orientation of the concentrator respect to a parallel light beam, simulating the direct sunlight component. In this part I have highlighted all the advantages of using the "reverse" method to derive the optical efficiency curve. The advantages are innumerable and they are both in optical simulation and in laboratory testing. During optical simulation, the method setting is simple and requires few operations. This is to set up a Lambertian source on the concentrator output opening, to place an absorbing screen on the side of the input opening, and sufficiently far from the concentrator, and to start raytracing, which can also last for hours, depending on the needed angular resolution on the curve. At the end of raytracing, the file of irradiance on the screen is converted to the reverse "radiance" file, which corresponds (this is the heart of the inverse method) to the "direct" optical efficiency file, containing all information for all possible polar and 394 Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators azimuth orientations. The simulated "direct" method, on the other hand, requires a great deal of operativeness at the computer, because an absorber must be positioned at the concentrator output, a parallel beam must be arranged at its input, oriented in a certain way, and the output flux measured. This operation must be repeated for a number (dozens) of polar incidence angles when the concentrator has cylindrical symmetry. If symmetry is not such, the previous sequence must be repeated for as many times as the azimuth angles of interest. Even in laboratory experimentation, the "inverse" method is very simple to accomplish. It is to illuminate the back of the concentrator with a lamp and one or two integrating spheres; the screen absorber is replaced by a white screen for projections and there is no need to wait. The image on the screen is recorded by a CCD and processed at the computer as before. The experimental "direct" method, on the other hand, requires the preparation, by means of a parabolic mirror, of a uniform parallel beam to be orientated towards the concentrator, and many flux measurements on the receiver by changing the orientation of the CPC from time to time. In addition to time and simplicity, the advantage of the "inverse" method is in its costeffectiveness. In fact, the CCD can be replaced by a webcam, while the "direct" method requires a very expensive parabolic mirror to obtain a uniform parallel beam of at least 1 %. The last part of this work has been devoted to the optical characterization of some solar concentrator prototypes, all nonimaging type. In particular, reflecting concentrators of the light cone type, or CPC, have been characterized, all obtained by transforming ideal CPC originals through subsequent modifications. The two characterization methods were applied and their respective results compared, highlighting the advantages and disadvantages of the two methods. The "reverse" method, however, remains the most profitable one. Among the concentrator prototypes, of great interest has been the Rondine® one, a very innovative concentrator of the light cones class, created by a spinoff company of the University of Ferrara (CPower), resulting from a sophisticated transformation of a classic CPC, which has shown remarkable results on the field. Acknowledgements This chapter of optics is the result of some years of work that I have been doing at the Physics Department of the University of Ferrara. The contribution I received from the students, the young researchers and the teaching staff of the Physics Department was decisive to get the described results. My thanks go to the late Prof. G. Martinelli, who trusted me and welcomed me to his lab, and to Ing. G. Palazzi, who promoted the fruitful collaboration between ENEA and Ferrara University. I am very grateful to Prof. F. Frontera for starting me on the didactic activity for PhD students, which was followed by the course of Applied Optics. The didactic commitment allowed me to deepen the theoretical issues encountered in the experimental work. I thank my young colleague 395 Advances in Optics: Reviews. Book Series, Vol. 3 A. Antonini for the long and fruitful collaboration, and the young researchers of the formidable CPower group, which brought to a high level the technology of nonimaging optics concentrators. I was introduced to this science by Prof. L. Vicari of Napoli University, who put the Welford and Winston's text "High collection of nonimaging optics" in my hand, obliging me to read it, and I was supported from then on by the uncontainable energy of Prof. C. Rubbia. I am finally very grateful to Prof. R. Calabrese, F. Petrucci and R. Tripiccione for the sharing of an exciting season of scientific and educational collaboration. References [1]. A. Luque, S. Hegedus, Handbook of Photovoltaic Science and Engineering, John Wiley & Sons Ltd., Chichester, UK, 2011. [2]. A. Luque, V. M. Andreev, Concentrator Photovoltaics, Springer-Verlag, Berlin, D, 2007. [3]. A. Martí, A. Luque, Next Generation Photovoltaics, Institute of Physics, Bristol, UK, 2004. [4]. V. M. Andreev, V. A. Grilikhes, V. D. Rumyantsev, Photovoltaic Conversion of Concentrated Sunlight, John Wiley & Sons, Chichester, UK, 1997. [5]. A. Luque, Solar Cells and Optics for Photovoltaic Concentrators, Institute of Physics, Bristol, UK, 1989. [6]. D. Barlev, R. Vidu, P. 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Antonini, Optics of solar concentrators. Part II: Models of light collection of 3D-CPCs under direct and collimated beams, International Journal of Optics and Applications, Vol. 3, Issue 5, 2013, pp. 72-102. [24]. A. Parretta, Optics of solar concentrators. Part III: Models of light collection of 3D-CPCs under direct and Lambertian irradiation, International Journal of Optics and Applications, Vol. 5, Issue 3, 2015, pp. 82-102. [25]. A. Parretta, A. Antonini, Optics of solar concentrators. Part IV: Maps of transmitted and reflected rays in 3D-CPCs, International Journal of Optics and Applications, Vol. 7, Issue 1, 2017, pp. 13-30. [26]. A. Parretta, A. Antonini, M. Butturi, E. Milan, P. Di Benedetto, D. Uderzo, P. Zurru, Optical methods for indoor characterization of small-size solar concentrators prototypes, Advances in Science and Technology, Vol. 74, 2010, pp. 196-204. [27]. A. Parretta, F. Aldegheri, D. Roncati, C. Cancro, R. Fucci, Optical efficiency of "PhoCUS" C-Module concentrators, in Proceedings of the 26th European Photovoltaic Solar Energy Conference (EU PVSEC’11), Hamburg, Germany, 5-9 Sept. 2011, pp. 658-663. [28]. A. Parretta, L. Zampierolo, G. Martinelli, A. Antonini, E. Milan, C. Privato, Methods of characterization of solar concentrators, in Proceedings of the 25th European Photovoltaic Solar Energy Conference (EU PVSEC’10), Feria Valencia, Valencia, Spain, 6-10 Sept. 2010. [29]. A. Parretta, L. Zampierolo, D. Roncati, Theoretical aspects of light collection in solar concentrators, in Proceedings of the Conference on Optics for Solar Energy (SOLAR), Advancing the Science and Technology of Light, The Westin La Paloma, Tucson, AZ, USA, 7-10 June 2010, p. STuE1. [30]. A. Parretta, A. Antonini, M. A. Butturi, P. Di Benedetto, E. Milan, M. Stefancich, D. Uderzo, P. Zurru, D. Roncati, G. Martinelli, M. Armani, How to "display" the angle-resolved transmission efficiency of a solar concentrator reversing the light path, in Proceedings of the 23rd European Photovoltaic Solar Energy Conference (EU PVSEC’08), Feria Valencia, Valencia, Spain, 1-5 Sept. 2008, pp. 95-98. [31]. A. Parretta, A. Antonini, M. Stefancich, V. Franceschini, G. Martinelli, M. Armani, Laser characterization of 3D-CPC solar concentrators, in Proceedings of the 22nd European Photovoltaic Solar Energy Conference (EU PVSEC’07), Fiera Milano, Milan, Italy, 3-7 September 2007. [32]. A. Parretta, A. Antonini, M. Stefancich, V. Franceschini, G. Martinelli, M. Armani, Characterization of CPC solar concentrators by a laser method, Proceedings of SPIE, Vol. 6652, 2007, 665207. [33]. E. Bonfiglioli, Sviluppo di metodi per la caratterizzazione ottica indoor di concentratori solari, Graduate Thesis in Physics and Astrophysics, Università degli Studi di Ferrara, Ferrara, Italy, 2007-2008. [34]. A. Antonini, M. Stefancich, J. Coventry, Modelling of compound parabolic concentrators for photovoltaic applications, International Journal of Optics and Applications, Vol. 3, Issue 4, 2013, pp. 40-52. 397 Advances in Optics: Reviews. Book Series, Vol. 3 [35]. A. Parretta, G. Martinelli, M. Stefancich, D. Vincenzi, R. Winston, Modelling of CPC-based photovoltaic concentrator, Proceedings of SPIE, Vol. 4829, 2003, pp. 1045-1047. [36]. A. Parretta, E. Bonfiglioli, L. Zampierolo, M. Butturi, A. Antonini, Optical characterization of Rondine® PV solar concentrators, International Journal of Optics and Applications, Vol. 4, Issue 4a, 2014, pp. 25-52. [37]. A. Parretta, A. Antonini, M. Butturi, P. Zurru, Optical simulation of Rondine® solar concentrators by two inverse characterization methods, Journal of Optics, Vol. 14, 2012, 125704. [38]. A. Parretta, A. Antonini, E. Bonfiglioli, M. Campa, D. Vincenzi, G. Martinelli, Il metodo inverso svela le proprietà dei concentratori solari, PV Technology, Vol. 3, Agosto/Settembre 2009, pp. 58-64 (in Italian). [39]. A. Parretta, A. Antonini, E. Milan, M. Stefancich, G. Martinelli, M. Armani, Optical efficiency of solar concentrators by a reverse optical path method, Optics Letters, Vol. 33, 2008, pp. 2044-2046. [40]. A. Parretta, L. Zampierolo, A. Antonini, E. Milan, D. Roncati, Theory of "inverse method" applied to characterization of solar concentrators, in Proceedings of the 25th European Photovoltaic Solar Energy Conference (EU PVSEC’10), Feria Valencia, Valencia, Spain, 6-10 September 2010. [41]. A. Parretta, D. Roncati, Theory of the "inverse method" for characterization of solar concentrators, in Proceedings of the Conference Optics for Solar Energy (SOLAR), Advancing the Science and Technology of Light, The Westin La Paloma, Tucson, AZ, USA, 7-10 June 2010, p. STuE2 [42]. A. Parretta, G. Martinelli, A. Antonini, D. Vincenzi, Direct and inverse methods of characterization of solar concentrators, in Proceedings of the Conference Optics for Solar Energy (SOLAR), Advancing the Science and Technology of Light, The Westin La Paloma, Tucson, AZ, USA, 7-10 June 2010, p. STuA1. [43]. A. Parretta, A. Antonini, M. Stefancich, G. Martinelli, M. Armani, Optical characterization of CPC concentrator by an inverse illumination method, in Proceedings of the 22nd European Photovoltaic Solar Energy Conference (EU PVSEC’07), Fiera Milano, Milan, Italy, 3–7 Sept. 2007. [44]. A. Parretta, A. Antonini, M. Stefancich, G. Martinelli, M. Armani, Inverse illumination method for characterization of CPC concentrators, Proceedings of SPIE, Vol. 6652, 2007, 665205. [45]. A. Parretta, F. Aldegheri, A. Antonini, M. Butturi, P. Zurru, Optical simulation of PV solar concentrators by two inverse characterization methods, International Journal of Optics and Applications, Vol. 2, Issue 5, 2012, pp. 62-71. [46]. R. Winston, Principles of solar concentrators of a novel design, Solar Energy, Vol. 16, 1974, pp. 89-95. [47]. A. Parretta, A. Sarno, P. Tortora, H. Yakubu, P. Maddalena, J. Zhao, A. Wang, Angledependent reflectance and transmittance measurements on photovoltaic materials and solar cells, Optics Communications, Vol. 172, 1999, pp. 139-151. [48]. C. Cancro, R. Fucci, G. Graditi, A. Romano, A. Antonini, M. Armani, Comparison between two different S.O.E. geometrical shape to increase the PhoCUS C-Module energy performances, in Proceedings of the 21st European Photovoltaic Solar Energy Conference (EU PVSEC’06), Dresden, Germany, 4-8 Sept. 2006. [49]. R. Leutz, L. Fu, H. P. Annen, Material choices and tolerance budget in the optical design of solar photovoltaic concentrators, in Proceedings of Optics for Solar Energy (SOLAR), Advancing the Science and Technology of Light, The Westin La Paloma, Tucson, AZ, USA, 7-10 June 2010, p. STuD4. [50]. R. C. Jones, On reversibility and irreversibility in optics, Journal of Optical Society of America, Vol. 43, 1953, pp. 138-144. 398 Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators [51]. M. Born, E. Wolf, Principles of Optics, Cambridge University Press, Cambridge, UK, 1999. [52]. R. Herrero, C. Domínguez, S. Askins, I. Antón, G. Sala, Two-dimensional angular transmission characterization of CPV modules, Optics Express, Vol. 18, 2010, pp. A499-A505. [53]. R. Herrero, C. Domínguez, I. Antón, S. Askins, G. Sala, Tools development for CPV characterization based on CCD camera measurements, in Proceedings of Optics for Solar Energy (SOLAR), Advancing the Science and Technology of Light, The Westin La Paloma, Tucson, AZ, USA, 7-10 June 2010, p. STuA4. [54]. P. Würfel, The chemical potential of radiation, Journal of Physics C: Solid State Physics, Vol. 15, 1982, pp. 3967-3985. [55]. L. Ferraioli, P. Maddalena, E. Massera, A. Parretta, M. A. Green, A. Wang, J. Zhao, Evidence for generalized Kirchhoff's law from angle-resolved electroluminescence of high efficiency silicon solar cells, Applied Physics Letters, Vol. 85, 2014, pp. 2484-2486. [56]. K. L. Coulson, Polarization and Intensity of Light in the Atmosphere, A. Deepak Publishing, Hampton, Virginia, USA, 1988. [57]. A. Parretta, F. Aldegheri, C. Cancro, R. Fucci, G. Graditi, R. Schioppo, Optical characterization of “PhoCUS” refractive solar concentrators, International Journal of Optics and Applications, Vol. 4, Issue 4A, 2014, pp. 12-24. [58]. Lambda Research Corporation, http://lambdares.com/ [59]. A. Antonini, M. A. Butturi, P. Di Benedetto, D. Uderzo, P. Zurru, E. Milan, M. Stefancich, M. Armani, A. Parretta, N. Baggio, Rondine® PV concentrators: Field results and developments, Progress in Photovoltaics, Vol. 17, 2009, pp. 451-459. [60]. A. Antonini, M. A. Butturi, P. Di Benedetto, D. Uderzo, P. Zurru, E. Milan, M. Stefancich, A. Parretta, N. Baggio, Rondine PV concentrators: Field results and innovations, in Proceedings of the 24th European Photovoltaic Solar Energy Conference (EU PVSEC’09), Hamburg, Germany, 21-25 Sept. 2009. [61]. A. Antonini, M. A. Butturi, P. Di Benedetto, D. Uderzo, P. Zurru, E. Milan, A. Parretta, N. Baggio, Rondine PV concentrators: Field results and progresses, in Proceedings of the 34th IEEE Photovoltaic Solar Energy Conference (PVSC’09), Philadelphia, US, 7-12 June 2009, pp. 001043-001047. [62]. A. Antonini, M. A. Butturi, P. Di Benedetto, E. Milan, D. Uderzo, P. Zurru, M. Stefancich, A. Parretta, M. Armani, N. Baggio, Field testing per la tecnologia di concentratori a disco e per moduli “Rondine”, in Proceedings of the “ZeroEmission Rome 2008” Conference, Rome, Italy, 1-4 October 2008. [63]. A. Antonini, M. A. Butturi, P. Di Benedetto, D. Uderzo, P. Zurru, E. Milan, M. Stefancich, M. Armani, A. Parretta, N. Baggio, Development of "Rondine" concentrating PV module field results and progresses, in Proceedings of the 23rd European Photovoltaic Solar Energy Conference (EU PVSEC’08), Valencia, Spain, 1-5 Sept. 2008. [64]. A. Antonini, M. Stefancich, P. Zurru, M. Butturi, P. Di Benedetto, D. Uderzo, E. Milan, G. Martinelli, M. Armani, A. Parretta, N. Baggio, L. Secco, Experimental results of a new PV concentrator system for silicon solar cells, in Proceedings of the 22nd European Photovoltaic Solar Energy Conference (EU PVSEC’07), Milan, Italy, 3-7 September 2007. [65]. A. Antonini, M. Butturi, P. Di Benedetto, P. Zurru, D. Sartore, In-Field performances of first commercial Rondine® PV concentrators, in Proceedings of the 26th European Photovoltaic Solar Energy Conference (EU PVSEC’11), Hamburg, Germany, 5-9 September 2011, pp. 640-643. [66]. A. Antonini, M. Butturi, P. Di Benedetto, E. Milan, D. Uderzo, P. Zurru, D. Sartore, GEN2 Rondine® PV concentrators, in Proceedings of the 25th European Photovoltaic Solar Energy Conference (EU PVSEC’10), Feria Valencia, Valencia, Spain, 6-10 September 2010, pp. 990-993. 399 Advances in Optics: Reviews. Book Series, Vol. 3 [67]. A. Parretta, M. L. Addonizio, Optical and structural characterization of diffuse reflectance standards, International Journal of Optics and Applications, Vol. 5, Issue 2, 2015, pp. 33-49. [68]. A. Parretta, G. Calabrese, About the definition of "multiplier" of an integrating sphere, International Journal of Optics and Applications, Vol. 3, Issue 6, 2013, pp. 119-124. [69]. A. Parretta, H. Yakubu, F. Ferrazza, P. P. Altermatt, M.A. Green, J. Zhao, Optical loss of photovoltaic modules under diffuse light, Solar Energy Materials and Solar Cells, Vol. 75, 2003, pp. 497-505. [70]. P. Maddalena, A. Parretta, P. Tortora, P. Altermatt, J. Zhao, Simultaneous optical losses and current measurements in photovoltaic devices at variable angle of the incident light, Solar Energy Materials and Solar Cells, Vol. 75, 2003, pp. 397-404. [71]. A. Parretta, P. P. Altermatt, J. Zhao, Transmittance from photovoltaic materials under diffuse light, Solar Energy Materials and Solar Cells, Vol. 75, 2003, pp. 387-395. [72]. P. Maddalena, A. Parretta, A. Sarno, P. Tortora, Novel techniques for the optical characterization of photovoltaic materials and devices, Optics and Lasers in Engineering, Vol. 39, 2003, pp. 165-177. [73]. A. Parretta, H. Yakubu, F. Ferrazza, Method for measurement of the hemispherical/hemispherical reflectance of photovoltaic devices, Optics Communications, Vol. 194, 2001, pp. 17-32. [74]. A. Parretta, P. Grillo, P. Tortora, P. Maddalena, Method for measurement of the directional/hemispherical reflectance of photovoltaic devices, Optics Communications, Vol. 186, 2000, pp. 1-14. [75]. A. Parretta, A. Sarno, H. Yakubu, Non-destructive optical characterization of photovoltaic modules by an integrating sphere. Part I: Mono-Si modules, Optics Communications, Vol. 161, 1999, pp. 297-309. [76]. A. Parretta, C. Privato, G. Nenna, A. Antonini, M. Stefancich, Monitoring of concentrated radiation beam for photovoltaic and thermal solar energy conversion applications, Applied Optics, Vol. 45, 2006, pp. 7885-7897. [77]. A. Parretta, M. Tucci, M. Izzi, Optical properties of light diffusers as targets for concentrated solar beams characterization, in Proceedings of the 30th European Photovoltaic Solar Energy Conference (EU PVSEC’15), CCH Congress Centre, Hamburg, Germany, 14-18 September 2015, pp. 1481-1486. [78]. A. Parretta, G. Nenna, A. Antonini, Monitoring of concentrated solar radiation beams by scattering from lambertian surface and CCD recording, in Proceedings of the Conference on Optical Diagnostics and Monitoring: from Advanced Components to Novel Devices (OpDiMon’04), Capo Miseno, Bacoli (Napoli), Italy, 22-26 March 2004. [79]. A. Parretta, A. Antonini, M. Stefancich, Codice di calcolo "LS-CCD" per l'analisi dell'immagine prodotta intercettando un fascio di luce con un diffusore, registrato presso la SIAE, Registro Pubblico Speciale per i Programmi per Elaboratore, Num. 007144, Ord. D006364, 15 Aprile 2009 (in Italian). [80]. Paolo Colombani Design, Ferrara, Italy, www.paolocolombani.com [81]. G. Kortum, Reflectance Spectroscopy, Principles, Methods, Applications, Springer, Berlin, Germany, 1969, p. 28. Appendix 13.A Note on the Optical Concentration Ratio Let us consider again Eq. (13.17) of Section 13.2.1: 400 Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators 3D  Copt n'2  sin 2  out . n 2  sin 2 in (13.A1) The meaning of in in Eq. (13.A1) must be correctly interpreted. In the case of an ideal SC, the angle below which all incident rays are transmitted and above which all incident 50 rays are back reflected is the acceptance angle acc . These SCs therefore have an optical response, i.e. a transmission efficiency curve, which has the shape of a descending step. The SCs that show the same response to the ideal are the 2D-CPCs [17]. Concentrators of the 3D-CPC type, on the other hand, show an almost ideal response, such as that of Fig. 13.1, if their form (canonical) is not altered by the effect of a truncation. The 50 , should not be confused with the angular acceptance angle of the concentrator,  acc 50 divergence S of the input light source. Let's imagine then to have a 3D-SC with acc acceptance angle. The actual and maximum optical concentration ratios will be given respectively by the following expressions: 3D  Copt n'2  sin 2  out , 50 n 2  sin 2  acc 3D Copt , max  n '2 . 50 n 2  sin 2  acc (13.A2) (13.A3) It is now clear that the optical concentration of such a concentrator will be determined by 50 , and not by the angular divergence of the incoming rays, in . its acceptance angle, acc 50 , its optical Although we illuminate the concentrator with a light beam with in < acc 3D 50 . If, however, we are concentration ratio Copt will always be determined by acc 3D considering the geometry of the incident beam and we want to know what values of Copt 3D and Copt , max we can realistically achieve with that beam by appropriately designing the SC, then the results will be: 3D  Copt n'2  sin 2  out , n 2  sin 2 in 3D Copt , max  n '2 . n 2  sin 2  in (13.A4) (13.A5) About out , the SC can be designed for different values of angular divergence, and in that 3D case Copt will be given by Eq. (13.A2) or (13.A4). The maximum out value is 90 °, and 3D then, at this value, the maximum value for Copt will be reached as indicated by Eq. 401 Advances in Optics: Reviews. Book Series, Vol. 3 2D (13.A3) or (13.A5) for a 3D-SC. Formulas for the optical concentration ratios Copt of a 2D concentrator can be obtained by Eqs. (13.A2)-(13.A5) after making the square root. Let us now consider a 3D-SC in the air, such as the 3D-CPC, and let us calculate the values of the optical concentration ratios for out  90 ° and out = 90: 3D Copt , max (out  90)  3D Copt , max ( out  n'2 sin2 out  n'2 sin2 out  46000, sin2 S (13.A6) n'2  90)  2  n'2 46000, sin S (13.A7) where  S is the angular divergence of solar radiation. For a SC with the receiver in air, like a 3D-CPC, at best we could focus the light 46,000 3D times. By immersing the receiver in a dielectric with n'  1.5, we could bring Copt to 3D values 100,000. Eqs. (13.A6) and (13.A7) establish that the limit values of Copt depend on the source-concentrator system geometry. By approaching the Sun, these limit values would decrease, while, moving away (for example on Mars), we would be able to reach higher optical concentration ratios. Appendix 13.B An Introduction to the 3D-CPC Concentrators Our interest on the 3D-CPCs (Three-Dimensional Compound Parabolic Concentrators) is that they allow to reach very high concentration levels, comparable to the theoretical ones, and that their optical transmission efficiency is quite constant within a defined angle of incidence of the collimated beam. A further advantage of these SC is that they operate with reflective surfaces, that do not induce the spectral dispersion of light. The 3D-CPC is a nonimaging concentrator developed by R. Winston to efficiently collect Cherenkov radiation in high energy experiments [46]. Since then, the nonimaging concentrators have been widely used to concentrate sunlight [16-20]. The CPC is a reflective concentrator with parabolic profile and is characterized by a quasi-step-like transmission efficiency (see Fig. 13.1) allowing the efficient collection of light from 0° to a maximum angle, called the acceptance angle acc . A 3D-CPC is characterized by the following parameters: a = radius of entrance aperture; a’ = radius of exit aperture; L = length; acc = acceptance (or tilt) angle; f = focal length of the parabolic profile. An ideal (canonical) 3D-CPC is completely determined by two of the above five parameters, related by the following basic relationships: 402 Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators f  a ' (1  sin  acc ), (13.B1) a'  a  sinacc, (13.B2) L  (a  a')  ctgacc, (13.B3) z p'1 acc p1 a' acc acc F1 O x F2 f Fig. 13.B1. Basic scheme of construction of an ideal 3D-CPC. The project of a 3D-CPC is very simple. We can start fixing, for example, the dimension of exit aperture, with radius a’, and the focal length, f; the acceptance angle acc is derived directly from Eq. (13.B1), but can be also obtained by the following geometric construction. We start drawing the longitudinal cross section of the 3D-CPC on the x/z plane (see Fig. 13.B1). On a Cartesian plane x/z the projected exit aperture of the CPC, with diameter F1F2, is aligned along the x-axis and centered on the origin O. Now we draw the parabola p1 with upward concavity, focal length f and focus on F1(-a’, 0) (see Fig. 13.B1). The parabola p1 is then rotated counter clockwise (CCW) around the axis perpendicular to the x/z plane and passing through F1, until it touches the point F2. The corresponding angle of rotation is the acceptance angle acc . The positive segment of the rotated parabola p'1 is the right profile of the CPC, intersected by the x/z plane. The left profile of the CPC is obtained starting from a second parabola with focus on F2 and rotating it clockwise (CW), and is the specular image of p'1 respect to the z axis. The analytical expression for the z’=z’(x’) coordinate of a profile of the CPC becomes: z '  d  w( x' )  e  w( x' )  g , (13.B4) where d, e and g are constant quantities: 403 Advances in Optics: Reviews. Book Series, Vol. 3 d cos acc , 16 f  sin 2  acc (13.B5) e a' cos acc 2b  cos acc 1   , 2 2 16 f  sin  acc 4 f  sin  acc (13.B6) g b 2  cos acc a'2  cos acc a' b  cos acc b  ...    2 16 f  sin 2  acc 4f 4 f  sin  acc (13.B7) ...  a' sin  acc  f  cos acc , where also b and c are constant quantities: b  4 f  cosacc  2a' sinacc, c  ( a ' ) 2  sin  acc  4 f 2  sin  acc  4 f a '(1  cos  acc ), (13.B8) (13.B9) and the function w (x’) is given by: w( x ' )  b 2  4  ( 4 f  x ' c )  sin  acc . (13.B10) Eqs. (13.B4)-(13.B10) allow to calculate the slope of the CPC curve at any point. In particular, we look for the point where the tangent is parallel to the z’ axis. This point defines the upper limit of the CPC profile, that is the maximum length L of the CPC, then it also defines the maximum value of the input opening radius, a (see Fig. 13.B2). By deriving Eq. (13.B4) we have: d z' d z' d w    ... d x ' d w d x'   e ...    d   (16 f  sin  acc ).  2 b 2  4  (4 f x'c)  sin  acc    (13.B11) The condition for a tangent to the curve parallel to z’ axis is: d z'  d x'  b 2  4  (4 f x'c)  sin  acc  0 f  a' sin  acc a'  x'  x'(L)    a. sin  acc sin  acc (13.B12) The profile of the CPC ends at the z’ = L, corresponding to the point A of Fig. 13.B2, where the tangent to the profile is parallel to the z’ axis. The surface of the 3D-CPC is finally constructed by turning the left and right profiles of the angle  around the z’ axis. Because of this construction, two extreme rays (1 and 2 in Fig. 13.B2) incident at acc and crossing the z’ axis (meridian rays), will be both collected at F1. 404 Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators acc acc z' a A 2 1 L acc acc x' F1 a' F2 Fig. 13.B2. Longitudinal cross section profile of the 3D-CPC. For the optical simulations (see Section 13.3), we have used an ideal (not truncated) 3D-CPCs with the following parameters: acc = 5°, L = 712.9 mm, a = 57.4 mm, a’ = 5.0 mm, f = 5.4 mm. All the optical simulations were carried out by using the TracePro ray-tracing software for opto-mechanical modeling of Lambda Research [58]. A brief note should be made here to clarify what happens when a 3D-CPC is halved. This discussion is not easy, because in a 3D-CPC the behavior is not the same for all rays; for example, meridians rays, i.e. those whose incidence plane contains the optical axis of the CPC, behave differently from the others, and in the same way as all rays behave in an ideal 2D-CPC concentrator. It is not easy to predict the overall behavior of rays in a 3D-CPC without a raytracing simulation, but we know that the response of optical efficiency in a 3D-CPC is much like that of a 2D-CPC, apart from the fact that the steplike optical efficiency curve is slightly rounded. So, our discussion with 3D-CPCs will take account of only meridians rays, knowing that this is an approximation that approaches enough the real behavior of the 3D-CPC. 50 Let's consider then an ideal 3D-CPC, which we call CPC1 with acceptance angle  acc 1, 50 having an ideal internal wall ( Rw = 1.0), designed to have a out = 90° at  in =  acc 1. Fig. 13.B3 shows the longitudinal section of the CPC1. An extreme ray (1), tilted of 50  in =  acc 1 , is transmitted and exits at 90° (edge ray principle), touching the point F1, 50 which is the focus of parabola p1. Also, the ray (2), inclined to  in =  acc 1 , is transmitted after touching point F1. This is because the axis of parabola p1 is parallel to the direction of rays (1) and (2), and the parabolic profile of the CPC1 has been designed to be inclined 50 at an angle equal to acc 1 . It is clear from Fig. 13.B3 that the rays entering the CPC1 at 50 50  in < acc 1 are all transmitted, by the definition of acc . 405 Advances in Optics: Reviews. Book Series, Vol. 3 Fig. 13.B3. Longitudinal cross section profile of the CPC1. Let’s try to slightly increase  in of the rays (1) and (2); it is easy to demonstrate, observing Fig. 13.B3, that in both cases, the rays (1') and (2') are reflected backwards. It 50 is also easy to convince that all rays with  in > acc 1 are back reflected. The CPC 50 transmission efficiency curve is then step-like shaped. For  in < acc 1 , we have therefore: Φout = Φin ; Eout  Aout  Ein  Ain ; A E out  C opt  in  C geo  Copt  Cgeo. Aout E in (13.B13) We now halve the CPC1 by removing the portion containing the input opening, building the CPC2 (see Fig. 13.B4). It is clear from Fig. 13.B4 that all rays incident on CPC2 with 50 50 50  in < acc 1 are transmitted, so we can already state that  acc 2 is at least equal to acc1 . 50 From Fig. 13.B4 it is also clear that rays entering the CPC2 with  in > acc 1 and hitting 50 the internal wall, such as radius (3), are rejected. However, rays with  in > acc 1 , entering the CPC2 through the annulus with OC inner radius and OB outer radius, without being impacted on the wall, are transmitted. Thus, the effect of halving the CPC1 is to extend a 50 , only little the optical efficiency curve, but it does not involve a significant increase in  acc 50 the appearance of a tail for  in > acc 1 , as it can be seen clearly from Fig. 13.14b. 406 Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators Although the CPC2 acceptance angle is almost equal to that of CPC1, it is a fact that its optical efficiency curve is extended to higher angles, and this must have a consequence on optical concentration ratio. It should be borne in mind, in fact, that the definition of angle of acceptance at 50 % of maximum efficiency is just a convention and works well when the curve is symmetrical around this angle, which is not the case for the halved CPC2. Fig. 13.B4. Longitudinal cross section profile of the CPC1 and its half CPC2. Fig. 13.B5. Longitudinal cross section profile of the CPC3 and its half CPC4. Let's see now what happens to the other CPC2 parameters after the halving operation. We have that Cgeo is decreased due to the decrease of Ain , but not too much, because the profile of parabola p1 is almost parallel to the optical axis in the truncated portion of the CPC1. Decreasing Cgeo , Copt must decrease, because we know that C geo is the insurmountable limit for Copt , being the optical efficiency always  1 (see Eq. (13.18a)). The decrease in Copt can also be evoked by Eq. (13.17a), as consequence of the increase of the  in denominator, while out remains unchanged and equal to 90°. It is interesting to continue this analysis by repeating it for a 3D-CPC concentrator that has been designed to have a maximum divergence at output out < 90°, CPC3 (see Fig. 13.B5). It’s clear that, for this 3D-CPC, the halving operation, which brings to CPC4, 407 Advances in Optics: Reviews. Book Series, Vol. 3 50 has different consequences. For example, rays incident at in >  acc 1 will all be transmitted until extreme rays such that of type (3) in Fig. 13.B5 will not reach 50 out = 90°. This condition defines the acceptance angle  acc 2 , which will be greater than 50  acc 1 and will result in an optical efficiency curve like that of CPC1, that is, step-like, but wider. Appendix 13.C How to Calculate the Inverse Radiance When the inverse method is simulated, the planar screen is configured as an ideal absorber and the profile of the measured incident irradiance E ( ,  ) (see Fig. 13.C1a) is converted into the profile of the radiance distribution function of the concentrator, Linv ( , ) , by the (cos)-4 factor. Indeed, if P ( ,  ) is a point on the screen, E ( ,  ) the corresponding incident irradiance and dS an elementary area around P ( ,  ) , the flux through area dS is d  E ( ,  )  dS and it is confined within the solid angle d  given by: d  dS  cos dS  cos dS   2  cos3  . 2 2 r ( ) d (d / cos ) (13.C1) The inverse radiance produced by the concentrator towards ( ,  ) direction will be therefore expressed by: Linv ( ,  )  d  ... d  Ain  cos  E ( ,  )  dS d 2 E ( ,  ) ...   , ( dS  cos 3  / d 2 )  Ain  cos  Ain cos 4  (13.C2) where Ain is the input aperture area of concentrator. The radiance can be normalized to the value at  = 0° giving: Lrel inv ( ,  )  E rel ( ,  ) Linv ( ,  ) E ( ,  )   . Linv (0) E (0)  cos 4  cos 4  (13.C3) The inverse radiance is related to the optical efficiency of the concentrator in the following way: 408 Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators Lrel inv ( ,  )   ( , ) Linv ( , ) rel ( ,  )  dir   dir . Linv (0)  dir (0) (a) (13.C4) (b) (c) Fig. 13.C1. (a) Schematic of the irradiation of the planar screen (ps) by the inverse light produced by the solar concentrator (sc); (b) Process of recording by the CCD of the image produced by the irradiance map produced on the planar screen. P( , ) is a point on the screen and E( ,) is the corresponding incident irradiance; (c) The CCD is schematized as a lens and a plane representing the image sensor of the CCD; Pccd ( ,  ) is a point and I ccd ( ,  ) is the intensity (irradiance) on the CCD sensor. We conclude that, when we simulate the inverse method, the normalized profile of the direct transmission efficiency of the concentrator is directly derived by the normalized irradiance incident on the ideal absorbing screen, by the expression: rel  dir ( ,  )  E rel ( ,  )  cos 4  . (13.C5) When the “inverse” method is applied experimentally, the screen is used to send back the diffuse, inverse light towards the CCD and must have a Lambertian character (reflectivity independent on the incidence angle, and constant radiance of the reflected light, as function of observation angle) in order to allow the reconstruction of the irradiance map on the screen from the intensity map produced on the CCD. 409 Advances in Optics: Reviews. Book Series, Vol. 3 If the CCD is aligned with the optical z axis and close to the concentrator (see Fig. 13.C1b), the intensity profile of CCD image must be corrected by a further (cos )-4 factor, as we demonstrate in the following (see also Fig. 13.C1c). The total flux reflected by the unitary area of (ps) centered in P ( ,  ) is: E R ( , )    LR ( , ), (13.C6) where R is the reflectance of (ps), ER ( , )  R  E ( , ) is the reflected irradiance, and L R ( ,  ) is the radiance of the screen. The flux reflected by the unitary area of (ps) and flowing inside the solid angle by which the unitary area is seen by point O ( ,  ) is:  R ( , )  LR ( , )  cos4  . d2 (13.C7) This flux is the same reaching the CCD sensor area (c / d)2 centered on point Pccd ( ,  ) . The intensity of the CCD image at point Pccd ( ,  ) , proportional to the irradiance incident at that point, is therefore: I ccd ( , )  k   R ( , )  ... (c / d ) 2 cos 4  cos 4  ( , )    k  E   ... R   c2 c2 cos 4  . k  R  E ( , )    c2 k  LR ( , )  (13.C8) By using Eq. (13.C2), we obtain: I ccd ( , )  k  R  Ain  Linv ( , )  cos8  . 2 2  c d (13.C9) From Eq. (13.C9) we finally obtain the inverse radiance of the concentrator from the intensity on the CCD: Linv ( ,  )    c2  d 2 k  R  Ain  I ccd ( ,  )  cos 8  . (13.C10) The normalized radiance becomes: rel 8 Lrel inv ( ,  )  I ccd ( ,  )  cos  . (13.C11) Finally, from Eq. (13.C4) we obtain the normalized transmission efficiency of the concentrator: 410 Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators rel rel inv ( , )  I ccd ( , )  cos8  . (13.C12) Appendix 13.D Realization of Lab-Made Integrating Spheres We have seen how it is important the use of integrating spheres in experimentation on the optical characterization of solar concentrators. We have made widespread use of integrating spheres both as Lambertian light sources, once they have been coupled to a lamp, either as light detectors or radiometers, once they have been coupled to photodetectors (or solar cells) inside it, in turn coupled to a voltmeter or to a lock-in amplifier. The problem of integrating spheres is that they must be built "ad hoc" for the specific application to which they are addressed. They are also made of aluminum and must be equipped with a series of windows for the entrance and exit of light, as well as for the measurement of the internal irradiation or light spectrum, depending on how sophisticated is desired the system [47, 68-75]. The inside of the spheres must be made with a highly reflective and highly diffusing white coating, so as to behave like a Lambertian diffuser [81]. I remember that a Lambertian diffuser is a diffuser that, when irradiated by a collimated light beam, emits reflected light of constant radiance in all directions, which depends on the cosine of the angle of incidence of light. Generally, the cost of these spheres is very high, in the order of thousands of euros, depending on the dimensions. Our main goal, before starting the work on SCs’ characterization, was therefore to organize ourselves to build in-the-lab low-cost integrating spheres. We took into consideration the use of plastic. Garden lamps with plastic transparent globes, of various sizes, are available in supermarkets at very low prices. They are made of polyethylene, robust and already equipped with a circular opening for the light bulb. Of course, the use of aluminum spheres has a very precise reason, i.e. to ensure mechanical stability to them, to be easily machined without any risk of fractures of the material, which can happen with plastic, but above all to ensure a good thermal stability to the sphere once illuminated by sources that can reach hundreds of watts of power. Of course, we were aware of this, but we considered that the power of the light sources we used was low enough to not produce any problems of thermal stability, deformation of the sphere, etc. To build a good integrating sphere [47, 68-75] it is necessary that the total surface of the openings present on it does not exceed 4-5 % of the total sphere area, limit most likely to be exceeded in small spheres. If the original sphere has already an opening exceeding these limits, then it is necessary to reduce it with a suitable flange. Before providing this, however, it is useful to work with a big opening at first, for example that of the original garden lamp (see Fig. 13.D1a), since it is easier to manually access it when going through all the surface treatments that we will discuss later. It should also be taken into account that these spheres do not always work alone, but sometimes they are paired with each other to better disperse the light inside them, so it is necessary to adapt the windows to one another. Finally, the spheres are not always empty; they can contain a lamp, when this is not simply faced to a window; for example, it can be used the original lamp holder to put inside the sphere an appropriate lamp. Inside the sphere, we can also insert some 411 Advances in Optics: Reviews. Book Series, Vol. 3 baffles, which serve to disperse the light, especially those particularly directional coming from a source. As for the size of the spheres, it must be big enough compared to the overall dimensions of the apertures, but not too much because the increase of dimensions reduces their sensitivity. So, a compromise must be found between these two requirements. Fig. 13.D1 shows some plastic globes used in the laboratory. (a) (b) Fig. 13.D1. Plastic globes made from garden lamps (a). Two spheres were optically coupled (b). In order to achieve a thick and well-adhering coating inside the sphere, it is necessary to properly prepare its surface. It must be abraded evenly using abrasive paper, or rather a sandblasting machine. Fig. 13.D2 shows an abraded sphere, during a temperature control in the interior. To make the openings on the sphere, we can engrave the surface using a common drawing compass after replacing the pencil lead with the blade of a cutter (see Fig. 13.D3a). After having sanded the inner and outer surfaces of the sphere, and before coating it with the diffusing coating, it is necessary to make the surface opaque, being originally transparent or semi-transparent. For this purpose, the outer and inner surfaces have been coated with a sprayed white paint (see Fig. 13.D3b), then the outer surface was coated with a chromium-plating spray paint (see Fig. 13.D3c). This ensures a perfect optical insulation between the inside and outside of the ball. Finally, to prevent spurious reflections from the outer surface of the sphere during the measurements, the outer surface was coated with an opaque black spray paint (see Fig. 13.D3d). The Lambertian inner coating can be prepared in different ways. We have chosen to use Barium Sulphate (BaSO4), which, besides being simple to apply, also shows the best optical properties. However, the preparation of the optimal suspension of Barium Sulphate requires a long work of study in which it is necessary to choose the correct components and their proportion, besides how to apply the solution on the inner surface of the sphere. Fig. 13.D4 shows some photos taken during the final coating phase. In Fig. 13.D5a it is shown a sphere coupled with the Rondine-Gen1 concentrator, and in Fig. 13.D5b it is shown a baffle for the optical decoupling of input and output windows. In order to decide how to prepare the BaSO4 suspension, many specimens were prepared by varying all possible parameters, including the substrate material (see Fig. 13.D6). Subsequently, spectral reflectance measurements were performed at the ENEA-Portici laboratories. 412 Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators Fig. 13.D7 shows the best results. It can be seen how the reflectance is over 90 % in the silicon range, whose technology is the base of all the devices we use, both photodetectors and solar cells. (a) (b) Fig. 13.D2. Example of plastic globe with abraded surface, with a lamp in the interior (a). In (b) a thermocouple, connected to a multimeter, has been inserted inside to reveal the temperature reached on the sphere surface. (a) (b) (c) (d) Fig. 13.D3. E. Bonfiglioli realizes the opening in a sphere (a). Preparation of the surfaces with different types of paints (b)-(d) before the application of the final BaSO4 coating. 413 Advances in Optics: Reviews. Book Series, Vol. 3 (a) (b) Fig. 13.D4. E. Bonfiglioli applies the BaSO4 suspension inside a sphere (a) and dries it with the hair-dryer (b). (a) (b) Fig. 13.D5. Photo of a sphere coupled to the Rondine-Gen1 concentrator (a). A baffle is visible inside the sphere (b). Fig. 13.D6. E. Bonfiglioli during the preparation of the Barium Sulphate specimens. 414 Chapter 13. Optical Methods for the Characterization of PV Solar Concentrators Fig. 13.D7. Results of the spectral analysis carried out on some samples in the spectral range 200-2500 nm (Silicon work range is between 300 and 1200 nm). 415 Chapter 14. Determination of the Heights of the Smoke-Plume Layering in the Vicinity of Wildfires and Prescribed Burns Chapter 14 Determination of the Heights of the SmokePlume Layering in the Vicinity of Wildfires and Prescribed Burns V. Kovalev, C. Wold, A. Petkov, S. Urbanski and W. M. Hao1 14.1. Introduction Recent decades have witnessed an increase in the frequency, duration, and severity of wildfires around the world. Fires are a major source of fine particulates (PM2.5), ozone (O3), and other pollutants that are detrimental to human health and degrade visibility. Heightened concerns about the impact of poor air quality on public health and the more strenuous regulatory established by the Environmental Protection Agency elevate the need for air regulatory and land management agencies to address the contribution of fires to air pollution. To comply with regulatory rules, land management agencies and air regulators need modeling tools to accurately predict the contribution of fire emissions to visibility impairment and PM2.5 and O3 pollution. Unfortunately, the ability of existing models to simulate smoke production and dispersion has not been thoroughly tested. The uncertainties and biases of these models and the limits of their applications are mostly unknown or poorly characterized, which is due mostly to the lack of adequate data for evaluation. The few smoke dispersion data sets available for model validation were from prescribed fires [1-3], which often differ significantly from wildfires in fuel conditions and meteorology, etc. To validate plume rise and high-resolution smoke dispersion models for a wide range of meteorological, fire behavior, fuel, and terrain conditions, smoke plume rise, dynamics, and transport in the near and far vicinities of wildfires and prescribed burns were investigated. This allowed for some evaluation of plume rise and high-resolution smoke dispersion models. Quantifying the plume heights under different meteorological conditions can potentially be achieved by remote sensing. Lidar profiling of the atmosphere is one of the most V. Kovalev Missoula Fire Sciences Laboratory, Missoula, Montana, USA 417 Advances in Optics: Reviews. Book Series, Vol. 3 suitable methods for this purpose. It allows extracting vertical profiles of the smoke plumes and probably is the best instrument for the investigation of smoke plume heights and downdrafts that transport the smoke particulates downward, worsening air quality at ground level. During the last decade, a number studies were published, in which the characterization of smoke plume behavior, including estimates of the plume injection height, were made using the information derived from satellite data, in particular, from the CALIPSO data [4-8]. However, the information derived from space data is limited to smoke plumes having discernable features. Satellite measurements are most effective when wildfires produce plumes that penetrate through the boundary layer and are transported downwind over great distances. However, they are much less effective for the investigation of smoke that remains within the boundary layer. Ground-based remote sensing instrumentation, in particular scanning lidar, is the most appropriate tool for monitoring of wildfire smoke-plume dynamics and heights within the boundary layer. The ground-based lidar is the only instrument capable of obtaining highly detailed, three-dimensional range and height-resolved information for smoke distributions and optical properties over ranges as long as 10+ km. It can operate from a position far outside the burning area with complete safety for the personnel involved. Lidar allows continuous monitoring of smoke-polluted atmospheres adjacent to both wildfires and prescribed burns, and for investigating temporal and spatial variation of aerosol properties, plume heights and dynamics, and direction and rate of smoke plume movement in near real-time. The lidar temporal data series can reveal strong downdrafts that transport smoke particulates downward, worsening air quality at ground level. An example of such a field experiment designed to obtain the data necessary to improve the air quality models used by agricultural smoke managers in the northwestern United States was performed in August of 2013. In that experiment, the ground-based mobile lidar, developed at the US Forest Service Missoula Fire Science Laboratory, was used to monitor plume rise heights for nine agricultural fires in the northwestern United States. The lidar measurements were compared with plume rise heights calculated with the Briggs equations, which are used in several smoke management tools. The preliminary evaluation results and recommendations regarding the application of the models to agricultural burning based on lidar measurements made in the vicinity of Walla Walla, Washington, on August 24, 2013 are published in [9]. Till recently, the basic issue with smoke measurements was the absence of a practical scanning lidar methodology for determining parameters of interest, that is, the methodology adapted to the specifics of smoke polluted atmosphere. In general, accumulated experience from investigations of the boundary layer is helpful. However, the structure and the temporal and spatial changes of smoke plumes in the vicinity of wildfires and prescribed burns differ dramatically from the features typically present in the entrainment zone of non-disturbed atmosphere. Temporal changes of the backscatter coefficient values in smoke plumes may be much larger or much less than those in the boundary layer. Spatial gradients in the backscattering at the smoke plume edge, which 418 Chapter 14. Determination of the Heights of the Smoke-Plume Layering in the Vicinity of Wildfires and Prescribed Burns must be determined to locate the smoke boundary, may have an extremely wide range of values. When determining the boundaries of the atmospheric aerosol formations, generally some relative rather than absolute characteristics of the lidar signal are used. For example, when using the most common gradient method, one can determine the aerosol boundary location as the range where the examined parameter (e.g., the derivative of the square-rangecorrected lidar signal) is a maximum; or where it decreases from the maximum value down to a fixed, user-defined level [10]. However, there is no unique way to establish standard values for this level which would be acceptable, at least for the most likely atmospheric situations. This issue is common for all such techniques; even the use of the modern wavelet technique requires an a priori selection of concrete parameters [11]. Recently in the studies [12-13], a new data processing method for determining the upper heights of the regions of intense backscatter was considered, which has significant advantages over the conventional technique of analyzing the derivative of the square range corrected signal. First, the method does not require separation of the square-range corrected backscatter signal from the recorded total signal, and accordingly, it does not require the estimation of the constant offset in the total signal. The second advantage of that method is that specific functions used in the data processing technique are generally significantly less noisy than the derivative of the range corrected signal, especially at distant ranges. Finally, the third advantage of this method is the possibility to use all information, which is present in the set of the multiangle signals of a scanning lidar. The differentiation technique, commonly used for the investigation of the atmospheric boundary layer, is generally applied to signals of one-directional, usually, zenith directed lidar; its application for multiangle profiling of the atmosphere, which would allow the investigation of the atmospheric layers close to ground level, is problematic. Below an advanced data processing methodology, based on principles proposed in [12] and [13] is considered. Its essence and specifics are cleared up by the analysis of real signals of a scanning lidar, obtained in August 2016 in the vicinity of wildfires near Missoula, Montana. 14.2. Determination of the Heights of the Smoke-Plume Layering in the Vicinity of Wildfires: Theory and Data Processing Methodology Let us consider the basic algorithms used for processing the lidar data. The lidar signal, P(r,), measured under elevation angle  and recorded at the range r, is the sum of the variable backscatter signal, P(r,) and the range-independent offset, B, P (r , )  P(r , )  B , (14.1) where the backscatter signal is defined as, 419 Advances in Optics: Reviews. Book Series, Vol. 3 P ( r , )    1 C   , m ( r )    , p ( r ) [Tm ( 0 , r )] 2 [T p ( 0 , r )] 2 , r2 (14.2) here C is the lidar constant, which includes also the transmitted light pulse energy; ,m(r) and , p(r) are the molecular and particulate backscatter coefficients; [Tm(0, r)]2 and [Tp(0, r)]2 are the molecular and particulate two-way transmission from the lidar to the slope range r, respectively. The total signal P(r,) is transformed in the auxiliary function Y(x,), defined as [13], Y ( x ,  )  [ P ( x ,  )  B ] x ( ), (14.3) where x() = r2 is the new independent variable. Using the method of finite differences, the sliding numerical derivative of this function, Y/x, is calculated, and the intercept point of the extrapolated slope fit with the vertical axis is found. The intercept function versus x() can be found as the difference of two terms, Y0* ( x)  Y ( x)  Y x, x (14.4) here for simplicity the function x() is written as single x. The retrieval technique is based on determining the range-weighted intercept function defined as, Y0 ( x)  Y0* ( x) Y ( x) dY   . x x dx (14.5) The absolute values of the function Y0(x), are transformed into the functions of height, Y0(h, ), where Y0(h, ) ≥ 0. Then the envelope of these positive functions, env[Y0(h)] for the all N elevation angles used during scanning is determined, envY0 (h)  maxY0 (h,1 )  Y0 (h, 2 )  ...  Y0 (h, N ) . (14.6) To reduce the influence of the high frequency spikes, the envelope is smoothed. The maximum value of the smoothed envelope, Y0,max  maxenvY0 (h) , (14.7) is found, and the function env[Y0(h)] is normalized to 1, that is, envY0 (h)norm  envY0 (h) . Y0. max (14.8) The data points of interest, Y0,(h) within the total height interval from hmin to hmax are found as, 420 Chapter 14. Determination of the Heights of the Smoke-Plume Layering in the Vicinity of Wildfires and Prescribed Burns Y0,  (h)  envY0 (h)norm . (14.9) The function, Y0,(h) is calculated using a selected set of fixed independent variables χ, which values may be chosen within the range 0 ≤ χ < 1. This function is then used for the determining the heights of interest, hmax(χ) for each selected χ. These heights are determined as the maximum heights, where Y0,(h) still differs from zero. An example of the functions Y0(h, ), obtained from real lidar signals, measured in a smoke polluted atmosphere, and their non-smoothed envelope, env[Y0(h)], are shown in Fig. 14.1. The lidar was scanning the atmosphere vertically within the angular sector from 10o to 80o. The functions Y0(h, ), measured under different elevation angles, , are shown as the colored curves; their non-smoothed envelope is shown as the thick black solid curve. Fig. 14.1. Set of functions Y0(h, ), measured by a scanning lidar in smoke polluted atmosphere (colored curves), and the initial non-smoothed envelope function, env[Y0(h)] (thick black curve). The dependence of the normalized function, env[Y0(h)]norm, on height is shown in Fig. 14.2. As can be seen in the figure, different  yield different hmax(). In our case, the selection  from 0.1 to 0.4 yields the values hmax() which are close to the actual maximum of the smoke plume, hmax, located close to height 1000 m. Meanwhile, the selection of the larger  = 0.5 yields hmax() ≈ 470 m, which significantly differ from the actual height hmax. Thus, the proper selection of , which provides hmax() close to the actual smokeplume height, hmax, may be a significant issue. The only sensible way to solve this issue is the examination of the behavior of hmax() in some range of the independent . The same as in [13], here the consecutive values of  with the fixed step  = 0.05 are used; that is, min = 0, 1 = 0.05, 2 = 0.1, etc. For each discrete , the corresponding height, hmax() is found. As shown in Fig. 14.2, the latter is determined as the maximum height where Y0,χ(h) still exceeds zero. 421 Advances in Optics: Reviews. Book Series, Vol. 3 Fig. 14.2. The solid curve is the smoothed and normalized envelope function env[Y0(h)]norm. The arrows illustrate the dependence of hmax() on selected . The dependence of the heights, hmax() on  for the case under consideration is shown in Fig. 14.3, where the discrete heights, hmax() versus χ are shown as black filled circles. Following the methodology in the study [13], the selection of the upper heights of smoke polluted layers is based on finding areas, where the differences between the adjacent heights hmax(k) and hmax(k+1) at k and k+1 are minimum. The second requirement in [13], used here, is that the differences between the previous adjacent heights hmax(k-1) and hmax(k) are maximum. Fig. 14.3. The black filled circles show the dependence of the heights hmax() on discrete  and the red horizontal dashes show the differences between the adjacent heights hmax(i) and hmax(j). Red arrows show the points where the differences between the adjacent heights are maximum. 422 Chapter 14. Determination of the Heights of the Smoke-Plume Layering in the Vicinity of Wildfires and Prescribed Burns In the figure, the differences, Δhi,j = hmax(i) - hmax(j), are shown as horizontal dashes. The corresponding upper heights, hup, of the layers of increased backscattering, determined in accordance with the above recommendations, are located at hup ≈ 1100 m and hup ≈ 480 m. 14.3. Some Results of Lidar Profiling of the Smoke-Polluted Atmosphere in the Vicinity of Spotted Wildfires The elements of the mobile Missoula Fire Sciences Laboratory (FSL) scanning lidar used in below investigation are given in [14]. As the light source, a short-pulsed Nd:YAG laser, attached to the top of a receiving telescope is used. The lidar receiver measures the backscatter signal at two wavelengths, 355 and 1064 nm, simultaneously. The laser beam is emitted parallel to the telescope after going through a periscope, so that the effective exit aperture is offset 0.41 m from the center of the telescope. The periscope increases the distance at which the laser beam overlaps the telescope field of view up to ~ 1000 m, simultaneously decreasing the dynamic range of the signals and increasing the total measurement range. The telescope-laser system is able to turn through 180 horizontally and 90 vertically. The schematic of determining the smoke plume heights in the vicinity of wildfire is shown in Fig. 14.4. The lidar, located generally at a distant range from a wildfire (or scattered wildfires), scans the plume under a number of elevation angles. The different colors in the figure show different intensity of the backscattering in relative units. The slant lines show the discrete directions of lidar scanning and the black filled dots mark the maximum heights of the smoke plume fixed under different elevation angles. Fig. 14.4. Schematic of determining the height of the smoke-plume layering with scanning lidar in a distant vicinity of wildfire. The schematic of the scanning lidar setup during lidar profiling of the smoky atmosphere polluted by three closely located wildfires is shown in Fig. 14.5. The Roaring Lion Fire [15], Observation Fire [16], and Cedar Fire [17] were located 28 miles, 33 miles, and 423 Advances in Optics: Reviews. Book Series, Vol. 3 35 miles from the lidar location, respectively. The lidar was oriented to scan east-west sectors to the south of its location; it operated making vertical scans in a wide azimuthal sector with the fixed azimuthal step 10o. In the morning of August 4, 2016 the Roaring Lion and Observation fires produced a well-defined column of smoke that flowed north along the east side of the Bitterroot Mountains, located on the west side of the Bitterroot Valley in Montana. In the afternoon, this column became diffused and spread eastward across the valley. The Cedar fire in Idaho contributed higher elevation smoke as smoke reaching the valley had to traverse the Bitterroot Range. Fig. 14.5. The relative locations of the three wildfires producing the majority of the smoke in the Bitterroot Valley during lidar scans made on 4 August 2016. Let us consider the spatial and temporal distribution of the smoke-plume upper boundaries, hup, and their dynamics during the day by analyzing simultaneously the temporal and spatial behavior of the discrete data points h(). Note that instead applying the whole set of , as was shown in Fig. 14.3, the data points shown in Figs. 14.6 and 14.7 are analyzed within the restricted range of , within the range, 0.05 ≤  ≤ 0.5. Our analysis revealed that the exclusion of the data points with  > 0.5 allowed better results in determining the height of interest, hup. 424 Chapter 14. Determination of the Heights of the Smoke-Plume Layering in the Vicinity of Wildfires and Prescribed Burns Fig. 14.6. Data points hmax() as a function of local time during the period from 11:40 to 14:00. The dashed arrows show the change of the upper heights of the areas of increased backscattering during the measurement interruptions. Fig. 14.7. The same as in Fig. 14.6 but for the period from 14:06 to 16:40. In Fig. 14.6, the set of the data points h() is shown obtained during the time period from 11:40 to 14:00 local time at the wavelength 1064 nm. The lidar operated in the multiangle mode, scanning the atmosphere vertically within the angular sector from 10o to 80o with the angular separation ~3o. The clusters of data points within the altitude range 400-1100 m, show the real layering dynamics. Initially at 11:40, two layers with increased backscattering were recorded, the upper at the height ~1000 m, and the bottom at and below 600 m. However, then the upper smoke-plume layering moved down, and after ~12:30 this dispersed layer can be seen at heights hup ~ 750 m and below, that is, two previously separated layers of increased backscattering merge. After ~13:00, an additional 425 Advances in Optics: Reviews. Book Series, Vol. 3 clusters with dispersed boundaries appears within the height interval 1300-1600 m, which have tendency of dispersing up and down. In Fig. 14.7, the next set of the data points h() is shown. These results were obtained during the period from 14:06 to 16:40. Note that after ~16:10, in addition to the areas of increased backscatter within the lower heights, below 1500 m, a small cluster of data points appears close to the height ~2500 m. Presumably it originated from the appearance of another smoke layering at this increased height. However, the absence of lidar data after 16:45 did not allow making trustworthy conclusions about the origin of these data points. 14.4. Determination of the Heights of the Smoke-Plume Layering in the Vicinity of Prescribed Burns The general schematic for determining the smoke plume heights in the vicinity of prescribed burns is shown in Fig. 14.8. The lidar, located close to the vicinity of a local scale fire, scans the plume under a number of elevation angles. The slant lines in the figure show the directions of lidar scanning and the filled dots mark the maximum height of the smoke plume fixed under different elevation angles. Fig. 14.8. Schematic of determining the height of the smoke plume column with scanning lidar. Let us consider experimental data obtained on August 25, 2013 in the area of the prescribed fires near Walla Walla, WA, USA [18]. These data were obtained with the same FSL scanning lidar which was used in the measurements discussed in Section 14.3. The vertical scans were performed in a fixed azimuthal direction. The vertical scans were made within the angular sector from 5o to 60o with the angle resolution 1o. Each recorded signal was the average of 30 shots, and each total scan was recorded for ~75 sec. Same as above, only the backscatter signals at 1064 nm were applied for the analysis. The typical optical situations met in August 25, 2014 are illustrated in Figs. 14.9 (a)-(d). Initially, when the prescribed fire is starting, the vertically stratified smoke-plume column without well-defined horizontal layering in its vicinity is observed (Fig. 14.9(a)). Then the smoke plume aerosols start accumulating in the vicinity of the maximum height of the 426 Chapter 14. Determination of the Heights of the Smoke-Plume Layering in the Vicinity of Wildfires and Prescribed Burns vertically stratified plume (Fig. 14.9(b)). The strong dispersing processes create the specific combination, in which the vertically stratified smoke plume and horizontal smoke-plume layering take place (Fig. 14.9(c)). Finally, when the fuel for the fire becomes exhausted, the vertical smoke-plume structure degrades. At that stage, the smoke plume particles create a horizontal (or close to horizontal) layer elevated over ground level (Fig. 14.9(d)). Fig. 14.9. (a) The white contour shows the two-dimensional image of the smoke plume boundaries determined on August 25, 2013, at 10:57 of local time; (b) The same as in (a) but at 11:03; (c) The same as in (a) but at 11:08; (d) The same as in (a) but at 11:23. Following the definition of plume injection height given in [4], we will define it as the maximum height of the vertical zone in which a buoyant plume begins to transport horizontally away from its origin source. In the case under consideration, the plume in in Fig. 14.9(a) is fixed at the initial moment of reaching the plume injection height, whereas Figs. 14.9(b)-(d) show the smoke plumes with well-developed horizontal layering. There is some inconsistency between the term “injection height” and the possibility of its accurate determination. In many cases, the lidar can reliably determine only top of such a zone. The bottom part of this zone is often extremely dispersed, moreover, it may have multilayering structure, or extend down to ground level, so that the definition of the lowest 427 Advances in Optics: Reviews. Book Series, Vol. 3 boundary of the injection height may often be an issue. However, just the top of this height determines the maximum distance over which the smoke plume may travel and impact its destination, for example, such as the Arctic ice. Keeping this observation in mind, we will focus here on the determination the maximum plume height when the smoke plume reveals well-developed horizontal layering, such as in Figs. 14.9(b)-(d). The general data processing methodology for determining the maximum plume heights in the case of prescribed burns are in principle the same as that used for the analysis lidar data obtained in the vicinity of wildfires. The only difference was some transformation of the intercept formula made to avoid increased values Y0(h, φ) over the heights, h < 500 m (see Fig. 14.1). The essence of this transformation is clarified in [12, 13]. In Figs. 14.10(a)-(d) the dependence of the heights h() on different  are shown for the same cases as shown in Figs. 14.9(a)-(d). One can see that the well-defined boundary of the smoke plume can be observed only in Fig. 14.10(d), whereas in other cases the smoke plumes are significantly dispersed, having multilayer structures (Figs. 14.10(b) and (c)). Figs. 14.10. (a)-(d). Dependence of the height, h() on  extracted from the scans given in Figs. 14.9 (a)-(d). An alternative way of determining the upper boundary of the smoke plume may be based on the straightforward usage of the signals of scanning lidar. In this variant, the simplest 428 Chapter 14. Determination of the Heights of the Smoke-Plume Layering in the Vicinity of Wildfires and Prescribed Burns function, the square-range-corrected signal, may be used as a basic function. The signal as the function of the slope  and the height, h, that is, 2 S ( , h)  P ( h)h sin   , (14.10) is calculated with the straightforward formula,   2 S ( , h )  P ( h,  )   B  h sin   , (14.11) where  B  is an estimate of the constant component, B, along the slope direction ; it may be found using the total lidar signals, P(h, ,), recorded over distant ranges, at which the backscatter signal presumably vanishes, that is, where P(h)  0. The maximum plume heights of interest, the envelope function, env[S(h)], should be calculated from the set of the functions, S(, h), as   env[ S ( h )]  max  S ( min , h), ... S ( j , h ), S ( j 1 , h), ... , S ( max , h)  ,   (14.12) and then normalized to unit, that is, Snorm (h)  env[ S (h)] . Smax,max (14.13) Here Smax,max is the maximum value of env[S(h)] within the altitude range from hmin = rmin sin  min to hmax = rmaxsinmax, where rmin and rmax are minimum and maximum points of the lidar operative range. The range of the normalized function, Snorm(h), may vary from zero to one, same as the range of the function env[Y0(h)]norm. In practice, the functions S(, h) are extremely scattered, it is sensible to average the function env[S(h)] before determining Smax,max and Snorm(h). The normalization of the square-range-corrected signal allows for determining the smoke plume maximum height using the selected levels,  < 1, same as was done above for the function, Y0,(h). In Fig. 14.11, typical normalized functions, Snorm(h), are shown. Here the filled circles show the smoke-plume maximum heights determined at the level,  = 0.1, whereas the filled squares show the heights where Snorm(h) reaches its maximum value equal to unit. As stated in [4], the surface smoke-particulate concentration, predicted by models, is sensitive to the amount of plume mass injected at various heights. The knowledge of the vertical structures of the smoke plumes may allow producing better smoke dispersion predictions. Assuming that the vertical structure of plume concentration and the shape of the lidar backscatter signal are uniquely related, the utilization of the normalized squarerange-corrected signals versus height allows obtaining some information about the 429 Advances in Optics: Reviews. Book Series, Vol. 3 investigated smoke plumes. Such a method can provide experimental data that allow some estimation of the temporal variations of the smoke-plume concentration at different heights and the height, at which the smoke-plume concentration is presumably at maximum. As shown in Fig. 14.6, these heights, symbolized as h(Smax,max), are different for different times, increasing from 385 m to 1143 m during the period from 10:57 to 11:23. Fig. 14.11. The normalized functions, Snorm(h), for lidar scans under consideration. The heights, h(Smax,max) for the different times shown in the legend are shown as filled squares. The filled dots show the maximum smoke-plume heights determined for the level,  = 0.1. The rate of heat release, which can be monitored by the behavior of the parameter Smax,max, is directly related to the rate of biomass consumption. In Fig. 14.12, the variations of the heights h(Smax,max), at which the maximum backscatter signals are located, are shown during the whole period of smoke-plume profiling. One can see that initially, at 10:57, the most intensive smoke particulates were located in the vicinity of the height h(Smax,max)  400 m; then the height increases, reaching its maximum, 1244 m at 11:20. After that it decreases down to the heights 900-1000 m. The maximum backscattering intensity, Smax,max, equal to 54.9 a. u., was fixed at 11:14, then it monotonically decreased, vanishing at the end of the prescribed burn period, at 11:47. Performing such analysis, one should keep in mind that there is no simple relationship between the smoke-plume concentration and the backscatter signal obtained in the process of profiling the smoke plume. Nevertheless, two assumptions used in the above analysis look sensible enough. First, in not too dense smoke, the heights of the maximum smoke430 Chapter 14. Determination of the Heights of the Smoke-Plume Layering in the Vicinity of Wildfires and Prescribed Burns plume concentration and the maximum backscatter signal are the same, or at least, are close to each other. Second, the temporal variations of the maximum smoke-plume concentration and the maximum backscatter signal are similar. However, one should keep in mind that in some cases these assumptions may be not satisfied and the vertical profiles of these parameters may be significantly different. Fig. 14.12. Variations of the maximum values of the square-range-corrected signals, Smax,max in arbitrary units, their heights h(Smax,max), and the heights, hmax, determined at the level,  = 0.1 on August 25, 2014 during the time period from 10:57 to 11:47. 14.5. Summary The reliability of determining with lidar the smoke-plume boundaries in the vicinity of wild or prescribed fires depends on the concentration of smoke particulates injected in the atmosphere, on the presence of the multi-layering aerosol structures in it, and on the specifics of the lidar system used for atmospheric profiling. Because the lidar signal dramatically decreases with range, the level of random noise in the derived backscatter signals becomes a main factor which may significantly restrict the operative range of the lidar. The situation becomes much worse when the areas of increased backscattering has dispersed boundaries with decreased spatial gradients. This is why no commonly accepted methodology of such lidar measurements exists. The data-processing technique developed in the Fire Science Laboratory in Missoula, Montana, USA, is based on specific methodology of exposing and separating the data points of interest from noise, and on determination of the spatial and time locations of the data-point clusters. The thorough analysis of real experimental data shows that such 431 Advances in Optics: Reviews. Book Series, Vol. 3 technique can often yield significantly more reliable results. To illustrate the specifics of the inversion technique in the vicinity of wildfires, typical results of monitoring the temporal variations of the heights of the layers of increased backscattering in the smoke polluted atmosphere are presented. These measurements were performed with the scanning lidar on 4 August 2016 in the vicinity of three closely located wildfires, the Roaring Lion Fire, Observation Fire, and Cedar Fire near Missoula. This data processing methodology can be applied not only for examination of the smoke plumes originated by wildfires, but also for monitoring dust clouds, aerosol clouds created by volcano eruptions, etc. When measuring smoke plume propagation and dispersion, different situations can be encountered. Lidar monitoring of a smoke plume in vicinity of prescribed burns requires methodology significantly different from the one used for monitoring smoke plumes from wildfires. First, the prescribed burns are always spatially restricted, and the burning area is known beforehand. This allows selecting lidar measurement site quite close to the burning area. Second, stratification of the smoke plume, significantly changes during the burn. Initially the vertically stratified smoke-plume column without horizontal layering is observed. After that, dispersing processes create the specific combination of vertically stratified smoke plume and horizontal smoke-plume layering. On the last stage vertical smoke-plume structure degrades and the smoke plume particles create a horizontal (or close to horizontal) layer elevated over ground level. Accordingly, the lidar measurement methodology should follow these changes. References [1]. L. F. Radke, J. H. Lyons, P. V. Hobbs, D. A. Hegg, D. V. Sandberg, D. E. Ward, Airborne monitoring and smoke characterization of prescribed fires on forest lands in Western Washington and Oregon. Final Report, General Technical Report PNW-GTR-251, USDA Forest Service, 1990. [2]. P. V. Hobbs, J. S. Reid, J. A. Herring, J. D. Nance, R. E. Weiss, J. L. Ross, D. A. Hegg, R. D. Ottmar, C. Liousse, Particle and trace-gas measurements in the smoke from prescribed burns of forest products in the Pacific Northwest, in Biomass Burning and Global Change (J. S. Levine, Ed.), MIT Press, Cambridge, Mass., 1996, pp. 697-715. [3]. P. V. Hobbs, P. Sinha, R. J. Yokelson, T. J. Christian, D. R. Blake, S. Gao, T. W. Kirchstetter, T. Novakov, P. Pilewskie, Evolution of gases and particles from a savanna fire in South Africa, J. Geophys. Res., Vol. 108, 2003, 8485. [4]. S. M. Raffuse, K. J. Craig, N. K. Larkin, T. T. Strand, D. C. Sullivan, N. J. M. Wheeler, R. Solomon, An evaluation of modeled plume injection height with satellite-derived observed plume height, Atmosphere, Vol. 3, 2012, pp. 103-123. [5]. R. J. Dirksen, K. F. Boersma, J. de Laat, P. Stammes, G. R. van der Werf, M. V. Martin, H. M. Kelder, An aerosol boomerang: Rapid around-the-world transport of smoke from the December 2006 Australian forest fires observed from space, J. Geophys. Res., Vol. 114, 2009, D21201. [6]. V. Amiridis, E. Giannakaki, D. S. Balis, E. Gerasopoulos, I. Pytharoulis, P. Zanis, S. Kazadzis, D. Melas, C. Zerefos, Smoke injection heights from agricultural burning in Eastern Europe as seen by CALIPSO, Atmos. Chem. Phys., Vol. 10, 2010, pp. 11567-11576. 432 Chapter 14. Determination of the Heights of the Smoke-Plume Layering in the Vicinity of Wildfires and Prescribed Burns [7]. R. A. Kahn, Y. Chen, D. L. Nelson, F.-Y. Leung, Q. Li, D. J. Diner, J. A. Logan, Wildfire smoke injection heights: Two perspectives from space, Geophys. Res. Lett., vol. 35, 2008, L04809. [8]. A. J. Soja, T. D. Fairlie, D. J. Westberg, G. Pouliot, Biomass Burning Plume Injection Height Using CALIOP, MODIS and the NASA Langley Trajectory Model, http://www.epa.gov/ttnchie1/conference/ei20/session7/asoja.pdf [9]. S. Urbanski, V. Kovalev, A. Petkov, A. Scalise, C. Wold, W.M. Hao, Validation of smoke plume rise models using ground-based lidar, Proceedings of SPIE, Vol. 9239, 2014, 92391S. [10]. L. Menut, C. Flamant, J. Pelon, P. H. Flamant, Urban boundary-layer height determination from lidar measurements over the Paris area, Appl. Opt., Vol. 38, 1999, pp. 945-954. [11]. I. M. Brooks, Finding boundary layer top: Application of a wavelet covariance transform to lidar backscatter profiles, J. Atmos. and Oceanic Technol., Vol. 20, 2003, pp. 1092-1105. [12]. V. Kovalev, A. Petkov, C. Wold, S. Urbanski, W. M. Hao, Determination of smoke plume and layer heights using scanning lidar data, Appl. Opt., Vol. 48, 2009, pp. 5287-5294. [13]. V. Kovalev, A. Petkov, C. Wold, W. M. Hao, Lidar monitoring of the regions of intense backscatter with poorly defined boundaries, Appl. Opt., Vol. 50, 2011, pp.103-109. [14]. Fire Science Brief, Issue 103, http://www.firescience.gov/projects/briefs/04-1-104_FSBrief103.pdf [15]. InciWeb, Incident Information System, http://inciweb.nwcg.gov/incident/4913/ [16]. InciWeb, Incident Information System, http://inciweb.nwcg.gov/incident/4819/ [17]. InciWeb, Incident Information System, http://inciweb.nwcg.gov/incident/4874/ [18]. V. Kovalev, A. Petkov, C. Wold, S. Urbanski, W. M. Hao, Determination of the smoke-plume heights and their dynamics with ground-based scanning lidar, Appl. Opt., Vol. 54, 2015, pp. 2011-2017. 433 Chapter 15. Precision Glass Molding Chapter 15 Precision Glass Molding Weidong Liu and Liangchi Zhang1 15.1. Introduction Modern optical systems rely on advanced optical components [1-6]. The following are some examples. Precision aspherical optical lenses are critical to many consumer electronic systems such as digital cameras, mobile phones to assure image quality and reduce system weight [1, 7-9]. Micro-lens arrays are vital in the coupling of optical fibers in high-speed information transfer [10], wave-front sensors [11], high-resolution liquid crystal display panels [12], artificial compound eye structures [13], advanced laser systems [14-18] and 3D displaying systems [19]. Large-scale glass lenses are essential to space telescopes to explore the universe [20-23]. Diffractive optics with complicated surface microstructures are widely applied in diffraction gratings and advanced imaging systems [24]. Traditionally, macro glass optical components are manufactured by mechanical machining methods involving many steps such as grinding, polishing and lapping [25, 26]. In the last few decades, these machining methods have been significantly advanced owing to the development of computer numerical control (CNC) machines, single point diamond turning techniques, and multi-axial precision polishing centres [27-28]. It was these CNC machines that enable the production of aspherical and freeform glass optical components. However, the optics manufacturing using these methods is very time consuming and expensive [30]. As such, an aspheric optical lens can be some thousands of dollars [29, 30]. Moreover, Si-based optical glass can be easily damaged by severe cleavages and micro-chipping, and a diamond tool surface can quickly worn out [31-33]. Presently, micro optical components are mostly fabricated by physical and/or chemical methods such as photolithography [34, 35], wet/dry etching [36-38], and high energy beams [39-42]. However, these techniques are not cost-effective for large scale components and high-volume production. Mechanical machining methods have also been Weidong Liu Laboratory for Precision and Nano Processing Technologies, School of Mechanical and Manufacturing Engineering, University of New South Wales, Australia 435 Advances in Optics: Reviews. Book Series, Vol. 3 tried to make microstructures on optical glass surfaces using, e.g., cutting [43], grinding [44], micro-end milling [45] and sand blasting [46, 47]. However, it is very difficult to obtain damage-free optical surfaces due to the brittleness of glass materials. As a process to remove the barriers associated with mechanical machining processes outlined above, the technique of precision glass molding (PGM) has been developed [48-50]. The PGM makes use of the softening behavior of optical glass in its super-cooled liquid region (above glass transition temperature Tg) [29, 51], which enables the production of an optics in a single step. Once the surface of a mold cavity is made to have the designed features, a precision glass optical component can be thermally deformed to copy the features [29]. Hence, the PGM can significantly reduce the production time and cost. Fig. 15.1 compares schematically the PGM and machining processes, showing the convenience and efficiency of the PGM. Fig. 15.1. A comparison of PGM and machining processes [29]. The concept of PGM is straightforward and promising; but the molding of a precision macro/micro optical component is still challenging. This is because a successful PGM requires a suitable glass preform, a high quality mold with properly designed features, a well-controlled molding process, and a reliable method for quality inspection. In the last few decades, many studies have been carried out to improve the quality of optical components made by PGM [29, 52, 53]. A number of manufacturers have established technologies for making some specific optical components such as aspherical lenses, lens arrays, toroidal and ultra-micro lenses, for digital projectors, digital cameras and microscopes etc. [52, 54]. However, the production quality is still below that of the top optics fabricated by the precision machining methods [29]. This chapter will introduce the latest advancement of the PGM technology. Following the PGM production chain, the basic elements required in a typical PGM process will be introduce. Then the state-of-the-art progress and challenges of each element will be outlined, including glass material selection, preform preparation, mold fabrication, molding and quality characterization. Finally, the multi-objective optimization and digitalization of PGMs will be discussed for improving the quality of molded components. 436 Chapter 15. Precision Glass Molding 15.2. An Introduction to PGM PGM requires a suitable preform of glass, a precision mold and a controlled temperature and pressure environment, as illustrated in Fig. 15.2. A PGM process involves heating, soaking, molding, cooling, demolding and final cooling, as shown in Fig. 15.3. In the heating stage, the glass preform and mold are heated from room temperature to molding temperature, at which the glass viscosity should be low enough (normally in the range of 107 to 108 Pa·s) for copying the features of the mold cavity [29]. To avoid oxidationinduced deterioration of mold, the chamber of the PGM machine is normally filled with insert gas (e.g., nitrogen) before heating. The soaking stage provides additional time for the preform to achieve a uniform temperature distribution. Then the molding stage can be conducted either via a force-controlled process or a displacement-controlled process. Some PGM machines allow multi-step pressing in this stage to achieve a better molding quality. After molding, the optical component will usually be cooled down to glass transition temperature at a small cooling rate and pressure. The pressure will then be removed in the demolding stage, followed by a fast cooling stage for the sake of production efficiency [51, 55]. The last but most important step is the quality inspection of the molded component, to see if the PGM is successful or needs to be improved. The final quality of the molded optics is affected by many factors at different stages in the PGM process. These will be discussed in detail below. Fig. 15.2. A typical PGM process [29]. Fig. 15.3. A typical PGM processing cycle [29]. 437 Advances in Optics: Reviews. Book Series, Vol. 3 15.3. Selection of Glass and Preparation of Its Preform The index of refraction nd and Abbe number vd of optical glass are its two important properties used in the design of an optical component, although some other factors should also be considered for production efficiency and cost. The principle of PGM is that most optical glass materials become soft and moldable at high temperature above their Tg [30, 55]. Thus in general, optical glass with a lower Tg has a higher moldability. This is because a lower molding temperature generally means a smaller shape distortion at cooling, a less material property change during PGM, and a longer mold service life. Fig. 15.4 provides a summary of some moldable glass materials with their key optical properties [30]. Of those with similar optical properties, the one with a lower Tg is normally recommended for PGM. This figure also presents optical plastics with good transmission and very low Tg. As many of them are mainly used in the production by injection molding, they will not be discussed in this chapter. Fig. 15.4. Some moldable optical glass materials [1]. With the glass selected, the next step is to prepare a suitable preform for molding, and the preform quality would directly influence the final product quality. Generally, the surface quality of the final molded product cannot be better than that of the preform or the mold surface. For molding macro convex lenses, the spherical preform is usually used due to its following advantages: (1) A sphere can be easily deformed in PGM into many commonly used lens geometries; and (2) the cost-effective quality manufacture of 438 Chapter 15. Precision Glass Molding spherical preforms is already mature [29]. The diameter of a spherical preform is normally in the range of 1 mm to 8 mm [55]. Disk-shaped preforms are more suitable for molding macro concave or convex-concave lenses, micro/nano micro-lens arrays, V-groove arrays and other thin components [55]. To mold an optical component with a complex geometry or a large dimension, a near-net shape preform is often required to minimize the geometrical change in PGM, although producing such preforms is expensive [29]. 15.4. Precision Mold Fabrication The harsh environment in a PGM process calls for high performance mold materials. A mold should have excellent mechanical, physical and chemical properties at high temperature, and does not adhere with glass. Moreover, it should have acceptable machinability that allows the manufacture of precision cavity profiles and fine surface features of the mold. 15.4.1. Mold Materials in PGM According to the Tg of optical glass materials, a PGM process could be divided into three categories, i.e., ultra-low Tg PGM (Tg < 400 ˚C), low-Tg PGM (400 ˚C < Tg < 620 ˚C), and high Tg PGM (Tg > 620 ˚C) [55]. Table 15.1 lists some commonly used mold materials for each type of the PGM processes. Table 15.1. Selection of mold materials for different PGM processes [55]. Process Ultra-low Tg Low Tg Manufacturing process Cost < 400 ˚C Electroless nickelphosphor Single point diamond turning Low 400 ˚C <Tg < 620 ˚C Carbides or ceramics High Tg > 620 ˚C Carbides or ceramics Microgrinding Very high Tooling life Low Medium Very low Tg of glass Molds Micro-grinding High Tg Electroless nickel-phosphor (Ni-P) is a commonly used mold material for ultra-low Tg PGM, because of its good hardness, excellent corrosion resistance, anti-wear property, and excellent machinability using single-point diamond turning [29, 56-60]. This material was first produced by Brenner and Riddell in 1946 using electroless plating technique [61], and since then emerged as an outstanding hard coating material in industry applications. The mechanical behavior and machinability of Ni-P strongly depend on the phosphorus content. A recent work [62] reported that with the increase of phosphorus content, the structure of the electroless Ni-P coating changes from nanocrystalline to a mixture of nanocrystalline and amorphous phases, and finally to a pure amorphous phase. A record high hardness of 910 HV0.1 of as-deposited Ni-P coating was obtained at 439 Advances in Optics: Reviews. Book Series, Vol. 3 7.97 at. % phosphorus content [62]. However, the structure and properties of Ni-P is not stable at a temperature above 400 ˚C; after which its properties are deteriorated [63]. Therefore, the as-deposited Ni-P is suitable only to ultra-low Tg PGM processes. Some studies have tried to anneal it to raise its working temperature [53, 64]. Super-hard materials, such as tungsten carbide (WC) [65] and silicon carbide (SiC) [66, 67] are desirable mold materials in low-Tg PGM [29, 55]. Due to their strong covalent bonds, these materials have very high hardness, excellent thermal and corrosion resistance, and low thermal expansion. However, the machinability of these materials is normally poor because of the intrinsic brittleness. Significant efforts have been devoted to developing advanced precision machining techniques for these hard-brittle materials [68, 69]. To reduce significant workload in achieving the optical surface finish by precision grinding, a pre-shaped mold is normally needed [29, 55]. Glassy carbon and other hard carbon materials can work at a high temperature up to 1,500 °C, with good chemical stability, high hardness, wear resistance and gas impermeability [70, 71]. Therefore, they are suitable for molding high-Tg glass such as quartz glass (Tg = 1200 °C) [72]. Similar to carbide materials, glassy carbon is very brittle and thus is difficult to be machined. Some studies reported that complicated microstructures can be fabricated on the surface of glassy carbon by using high-energy beams [71, 72]. It should be noted that an inert environment is required to avoid the oxidization of glassy carbon. A recent investigation found that oxidation-induced property deterioration and surface cracking can occur at a low temperature of 500 °C [73]. To extend mold life and thus reduce cost, a mold surface is often coated. Three types of coatings have widely been used, which are noble metal coating (Re/Ir [74, 75] and Pt/Ir [76, 77]), ceramic coating (TiAlN, TiBCN, TiBC, and CrN,) [78], and hard carbon coating (diamond-like coating, amorphous carbon coating) [79]. Noble metal coatings, especially the Re/Ir coating, demonstrates very stable properties [74] and low wetting angle [75-77]. Ceramic coatings have widely been used in machining tools, and therefore are easily applicable to PGM molds [29]. However, some ceramic coatings are prone to adhesion with glass melts at high temperature [29, 76]. Hard carbons are promising coating materials for PGM; but they require an inert environment to avoid oxidation at high temperature [29, 79, 80]. The major factors that deteriorated the mold in a PGM process are: (1) the moldworkpiece mechanical interactions (pressure and friction), (2) significant thermal stress variations and adhesion during repeated heating-cooling cycles, and (3) the interface damages between the mold and coating. Therefore, in selecting mold/coating materials it is important to have an appropriate assessment or test involving all the above factors. A quick testing facility [81, 82] was proposed recently to assess the service life of mold coatings [29]. Three coatings (TiAlN, CrAlN, and Pt-Ir) on flat WC mold were studied for the molding of B270 glass. The images of the mold (pins) and glass imprints after 20 pressing steps are shown in Fig. 15.5 [82]. It is clear that the performance of the WC pin with the Pt-Ir coating is the best. 440 Chapter 15. Precision Glass Molding Fig. 15.5. Performance comparison of TiAlN, CrAlN and PtIr coatings after 20 pressing steps [82]. 15.4.2. Mold Fabrications Most mold materials are difficult to be machined. Various manufacturing techniques have been developed to reach the strict requirements of optical applications. It should be noted that the requirements for machining macro mold and micro mold (mold with micro features) are different. The former normally requires a high surface finish and form accuracy while the later has many complicated micro-scale features to be produced. 15.4.2.1. Macro Mold Fabrication Macro mold in PGM is normally fabricated by ultra-precision grinding and polishing [83]. Ultra-precision grinding is characterized by a low material removal rate with the depth of cut in the sub-micrometres range [83-85] and low feed rate [86]. Cross axis grinding is regarded as the most common grinding technique, and has been widely used in the grinding of large aspheric optical molds [88]. To allow the grinding wheel shaft to clear the mold, tilted grinding technique was developed through tilting the grinding wheel axis by an angle with respect to the normal of the workpiece spindle axis [87]. However, this grinding method requires extensive compensation to reach the required final form. Wheel grinding was developed to overcome the disadvantages of cross axis grinding and tilted grinding. Fig. 15.6 presents a typical set-up of wheel grinding, which can fabricate a variety of different tool geometries including aspheric concave cavities, aspheric convex surfaces, and microstructured surfaces [86, 87]. Freeform wheel normal grinding was also developed by functionally controlling the position of the work spindle. This technique can grind cylindrical, toric and lens array molds. However, it should be noted that the success of these grinding techniques relies on the ability to determine and compensate workpiece form errors caused by wheel wear and machine tool repeatable errors [86, 87]. Fig. 15.7 441 Advances in Optics: Reviews. Book Series, Vol. 3 presents a step-by-step procedure for achieving the required tolerance of the mold by ultraprecision grinding [86]. The performance of ultra-precision grinding is strongly influenced by the condition of grinding tools. Therefore, in-process tool dressing is required for stable, controllable, and optimal grinding processes [86]. Electrolytic inprocess dressing (ELID) grinding is widely used in ultra-precision mirror surface for hard brittle materials [52]. Fig. 15.6. Wheel normal grinding of precision molds [86, 87]. Fig. 15.7. Flow chart for grinding of optical glass molds [86]. 442 Chapter 15. Precision Glass Molding To make a mold for ultra-precision optical components, polishing/finishing of the mold surface is normally needed after grinding to remove the surface and sub-surface defects, to smooth the surface to ~1 nm rms, and to achieve a more accurate shape profile [88]. Commonly used polishing techniques include magnetorheological finishing (MRF) [89], fluid jet and bonnet polishing [90], and vibration-assisted polishing [91]. 15.4.2.2. Micro Mold Fabrication Ultra-precision milling and single point diamond turning can fabricate highly accurate surface features/textures on mold surfaces of hard materials [92]. The most successful case is machining complicated micro-features on the Ni-P surfaces by using the singlepoint diamond turning technique [63, 93, 94], which can achieve submicron form accuracy and <10 nm roughness [53]. Fig. 15.8 presents two typical miniaturised surfaces fabricated by V-shaped diamond tool and R-shaped diamond tool, respectively. In the machining process, burs, chips and some other defects could be generated. By properly making use of the material removal mechanism, such Ni-P mold surfaces with high form accuracy and low surface roughness can be fabricated through optimizing the cutting tool geometry and machining parameters, as shown in Fig. 15.9 [53]. Fig. 15.8. Single-point diamond cutting process: (a) Microgroove arrays; (b) Microlens arrays [53]. Electroless Ni-P can experience crystallization at 400 °C, which will cause mold surface deformation and thus will reduce the accuracy of PGM [53]. To avoid this problem, a heat treatment method prior to micro surface feature fabrication was proposed to eliminate the irregular concave deformation due to crystallization [53, 64]. That is, before the singlepoint machining, the amorphous Ni-P plating was heated to its annealing temperature (approximately 600 °C) to ensure the complete transformation into its crystalline state [53, 64], such that the crystallization effect in PGM above 400 °C could be avoided. Ultra-precision milling and turning can also be used for making micro-features on the surfaces of hard brittle materials such as WC and SiC. However, the cost for high-volume production is extremely high [53, 95]. As an alternative, micro-electrochemical machining and micro-electric discharge machining have been proposed for producing complex 3Dshapes on these material surfaces [53, 96]. High energy beams, such as laser and focused ion beams, have also been applied in the rapid fabrication of mold surface features [53]. 443 Advances in Optics: Reviews. Book Series, Vol. 3 However, these techniques are limited by poor surface finish. Indentation has also been used in producing microstructures on molds [53], but its accuracy and efficiency are low. Fig. 15.9. (a) Microgrooves, and (b) Micropyramids fabricated by single-point diamond turning [53]. 15.5. PGM Process After having the preform and mold manufactured, the PGM process can be done on a precision glass molding machine capable of a precise control of mold positioning, load application and temperature variation. The capability and flexibility of a molding machine in the design and implementation of customized load and temperature profiles are essential for the optimization of a PGM process. 15.5.1. Stages in a PGM Process The heating and soaking stages in a PGM process is to make the temperature distribute uniformly in the glass preform and mold. Thus a precision temperature control is central. The proportional-integral-derivative (PID) algorithm is the commonly used, which continuously calculates the difference between a desired temperature and a measured temperature and applies corrections based on the proportional, integral and derivative terms [97]. The determination of soaking time is important, because a too small soaking time cannot guarantee a uniform temperature distribution, but a too large soaking time increases the processing time and reduces the production efficiency. Finite element simulations can be used to provide a good estimation of soaking time. The molding stage can be conducted via two control modes: the displacement control mode and the force control mode. The former can provide an accurate final molding shape, while the later can achieve a stable force applied during the molding process. Molding temperature is vital in the molding stage, which should be carefully chosen for a good replication quality of optical features. If the molding temperature is too high, more profile derivation and residual stresses will be generated during the cooling process [29]. Moreover, glass is prone to adhere to a mold at a high temperature and in turn damage it. However, if the molding temperature is too low, a high pressing load is required, which would also increase the risk of mold damage. Thus molding temperature selection is a 444 Chapter 15. Precision Glass Molding particularly critical step in making complicated micro-optics such as Fresnel lenses and diffractive optical elements. Cooling is one of the most important steps in PGM. This is because (1) profile derivation, residual stresses and many defects initiate and grow in this stage, and (2) the cooling stage in a PGM process is the longest period of time which determines productivity [29]. Normally, cooling is in two-steps. In its first step, molded glass optics is cooled down to Tg at a small rate to minimise defects and residual stresses. The second step of cooling down to room temperature is faster to improve production rate. Therefore, optimizing the cooling rates is important to both the product quality and production efficiency. Demolding is normally conducted between the two cooling stages. Recently, a design of experiments (DOE) approach was used to characterize the effect of process parameters in PGM on the repeatability of the final thickness of molded N-BK7 and L-BAL35 glasses. The parameters include heating and cooling rates, soaking time, molding temperature and molding force [98]. It was found that the cooling rate has the largest impact on the repeatability of the final thickness of the molded components. However, it is still difficult to optimize a whole PGM process for a real optical product by the DOE approach because of the large combinations of processing parameters and quality inspection factors. 15.5.2. Finite Element Analysis In PGM, shape derivation and residual stresses are the major problems that influence the quality of molded optical components [29, 30, 51, 99-102]. Experimentally, however, one can only use a trail-and-error method to reduce their effects without knowing their exact details. Finite element (FE) simulations have been recognized as a useful tool for revealing the deformation mechanisms of workpiece materials and for minimizing the trial-anderror design effort [29, 51, 103-106]. Since a glass material in PGM experiences complicated thermo-mechanical deformation, a reliable constitutive description of optical glass is the basis of a reliable FE analysis. This is therefore discussed below. 15.5.2.1. Constitutive Modeling of Optical Glass A complete constitutive model of glass suitable for PGM should be able to reflect accurately the relationships of (1) the thermo-viscoelastic relationship of stress, strain, strain rate and temperature, and (2) the nonlinear temperature dependence of the material properties such as modulus, viscosity and coefficient of thermal expansion [29, 51]. Most constitutive models developed for glass were based on the classical viscoelastic models such as Maxwell model, Kelvin-Voigt model, standard linear solid model, and generalized Maxwell model. The temperature-dependent rheology was often modeled by the classical phenomenological Vogel-Fulcher-Tammann equation [51] or the thermosrheological simple assumption [107, 109]. A method was also proposed for identifying the shear relaxation modulus and the structural relaxation function by measuring the time variation of glass plate thickness [109]. The CTE variation was often described by the 445 Advances in Optics: Reviews. Book Series, Vol. 3 Tool-Narayanaswamy-Moynihan (TNM) model [109], with witch the parameterization needs structure relaxation tests and thermal expansion tests. Some studies obtained the viscoelastic properties of glass by using the relaxation data from a cylinder compression test, assuming that the material is incompressible [104]. Elasto-viscoplastic models have also been developed for glass to account for permanent plastic deformation [107]. Recently, a modulus-based constitutive model was developed for analyzing PGM processes numerically [51]. As summarized in Table 15.2, all the temperature-dependent material properties in this model are determined by the relationship between the elastic moduli and microstructure of a material. To do this, the strain and stress tensors are divided into their volumetric and deviatoric parts. The relationship between deviatoric stress and strain is regarded as a standard linear solid (SLS) [108], and the volumetric part is viewed as a thermal elastic relationship because the bulk viscosity of super-cooled glass can be considered to be infinite [51]. The material’s temperature-dependent moduli are measured by an impulse excitation method [109]. The temperature-dependent viscosity is directly linked to the shear modulus by using the shoving model [109, 110]. The CTE of glass is predicted through the Young’s modulus based on a phenomenological TNM model [105, 106], in which the parameters in TNM model can be determined by the temperature-dependent modulus changes in the impulse excitation method. The above constitutive model with the measured/derived parameters has been verified and numerically programmed [51], and has been used to reveal the formation mechanisms of profile derivation and residual stress in molding a macro glass lens. 15.5.2.2. Mechanisms of Profile Distortion Profile accuracy, including geometrical accuracy and surface finish quality, is critical to an optical component [29]. The shape derivation of a molded lens can be as high as 20 μm, about 20 times higher than the deviation allowed by the optical design specifications [29, 111]. Thus the quality of a molded optical component depends largely on the profile distortion during its PGM process [29]. The FE analysis is particularly useful to understand the mechanisms. Fig. 15.10a shows the evolution of a lens profile during a typical PGM process. In the molding stage, the preform was compressed to comply with the mold cavity. The subsequent demolding did not lead to a significant shape deviation [29]. In the cooling stage, however, a large shape deviation occurred near the center of the lens. The derivation kept increasing until the internal temperature reduced to below Tg [29]. Fig. 15.10b presents the evolution of profile derivation with respect to the mold in the radial direction. It was found that the large deviations near the center and the edge of the lens are due to the cooling-induced shrinkage and edge effect, respectively [51]. It should be noted that for a precision lens, the allowed center thickness change is about 25 μm [55], and the maximum deviation of overall surface shape should be within several micrometers or smaller [105, 106]. This analysis indicated that an ultra-precision mold is not enough for molding a high quality glass optical component. Compensation should be made in the model design stage [29]. 446 Chapter 15. Precision Glass Molding Table 15.2. Modulus-based constitutive model for optical glass [51]. Relationship Stress and strain Volumetric relationship Deviatoric relationship Equation  ij  eij  tr( ) ij 3 ,  ij  Sij  tr ( ) ij 3 tr ( ) / 3    T  tr ( ) / 9 K (1  Sij S ij G Gr )eij  r eij   G s 2G 2 s Viscosity variation s  0 exp(VcG (T ) / kBT ) Thermal expansion    G   L   G T f T T f  T  ((TT )) M p (   ' ) 0 Structure relaxation description dT d ' d ' t    1  p dt  0 M p ( )  exp[  (  pr )  ]  p   0 expxH / RT  (1  x)H / RT f  Variable definition εij - strain tensor, σij – stress tensor, eij - deviatoric strain, Sij - deviatoric stress, tr(ε) - the trace of the strain tensor, tr(σ) - the trace of the stress tensor, δij - Kronecker delta, K - bulk modulus, α - the coefficient of thermal expansion, T - temperature, Gr - the modulus in the elastic branch of the SLS model, G - the shear modulus in the Maxwell branch of the SLS model, ηs - shear viscosity, η0 - reference viscosity, kB - Boltzmann constant, Vc - characteristic temperature-independent microscopic volume, G∞(T) - instantaneous shear modulus, G - the reference CTE at low temperature glassy state, L - the reference CTE at high temperature liquid state, Tf - effective temperature, T0 - the reference temperature, Mp(ξ) - the structural relaxation function, ξ - reduced time, τp - structural relaxation time, ∆H - the active energy, R - the ideal gas constant, τ0, x, β – constants. 447 Advances in Optics: Reviews. Book Series, Vol. 3 (a) (b) Fig. 15.10. (a) The evolution of a lens shape in PGM, (b) the deviation with respect to the mold cavity [51]. Based on a parametric study [105, 106], it was found that the structural relaxation of glass in the supercooled liquid region was the primary cause for profile distortion in PGM. As aforementioned, the structural relaxation of glass in an FE analysis is normally described by the TNM model, in which the activation energy and relaxation time are the key parameters. A novel method has been developed recently [29, 109] to identify these parameters based on an impulse excitation technique. Some studies [105, 106] also suggested that the most critical stage to reduce lens distortion is the beginning of demolding, in which thermal expansion coefficients of the mold material and internal stresses of the lens play an important role. Other important factors include molding temperature, loading-unloading paths and cooling rates [105, 106]. 15.5.2.3. Residual Stresses Most glass preforms do not have significant internal residual stress because they have been well annealed by manufacturers. In a PGM process, however, a high cooling rate is often used to increase production efficiency, which can easily lead to internal residual stresses [29, 112-114]. Such residual stresses can severely alter the local density of optical glass, and lead to inhomogeneous refractive index in an optical lens [29, 112]. For example, a residual stress of 3 MPa in P-BK7 glass lens can bring about a variation of refractive index of 4×10-4, and thus produce unwanted changes in the light path, intensity, and deterioration of image quality [29, 115, 116]. Therefore, it is important to understand the formation mechanism of residual stresses in PGM and its effect on optical properties. A recent comprehensive investigation [51] revealed the formation mechanisms of residual stresses in molding a convex-convex optical lens. Fig. 15.11a shows a typical distribution of residual stress (von Mises stress) in a molded lens. Two minima of the von Mises stresses locate symmetrically close to the top and bottom subsurfaces [29, 51]. To reveal the formation mechanism of the residual stress, the stress evolution at the top, middle and bottom points of the lens during the PGM process were studied as shown in Fig. 15.11b 448 Chapter 15. Precision Glass Molding [29, 51]. It is clear that the internal stresses before 270 s were very small except in the initial pressing stage [29, 51]. At around 270 s (in cooling stage), however, the internal stresses increased to a plateau till the end of the PGM process to form residual stresses [29, 51]. To further reveal the stress distribution around 270 s, the internal stress distributions along the central line through the lens thickness were shown in Fig. 15.11d. It was found that both the magnitude and gradient of the internal stresses increase significantly from 279.5 s to 299.5 s. The stress increase was related to the heterogeneous evolution of CTE of the optical glass during PGM [51], as revealed in Fig. 15.11d. Due to the inhomogeneous temperature distribution in the lens, the changes of the CTE at different positions are asynchronous [29, 51]. The difference of CTEs reached the maximum at 280 s (see the insert of Fig. 15.11d), leading to the significant increase of the magnitude and gradient of the internal stresses. (a) (c) (b) (d) Fig. 15.11. (a) The distributions of residual von Mises stress; (b) Variations of the von Mises stresses with time at different points in the lens; (c) the stress distributions along the central line through the lens thickness, and (d) the variations of CTEs at different points with time [51]. Since residual stresses arise due to the sharp increase of internal stresses during cooling, controlling the cooling rate should be able to reduce residual stresses. Some studies proved that the duration of cooling from the molding temperature to Tg is important in minimizing residual stresses [103] and that the residual stresses in a molded lens can be controlled to a very small value if a proper cooling is applied [112]. A recent study [51] has explicitly 449 Advances in Optics: Reviews. Book Series, Vol. 3 shown that a good strategy of minimizing residual stress would be to use a small cooling rate in the first stage, and then a larger cooling rate in the second stage for the sake of production efficiency [51]. It is noted that residual stress could also be affected by changing the rheology behavior of glass at molding temperature, the friction at the glass/mold interface, and the time/temperature at which the demolding is applied [105, 106]. 15.6. Quality Inspection Techniques Quality inspection is the last but most important step in the production chain of PGM. Without a reliable and systematic quality characterization method, one cannot assess and improve a PGM process. Standard optical inspection methods have been established for machined macro optical components, and some can be utilized for assessing the quality of molded optical components. However, similar standard inspection methods for micro optical components are still under development. In addition, residual stress formed during the PGM process can significantly alter the optical properties and should be inspected as well. In the following sections, three quality inspection aspects for molded optical components will be introduced, i.e., surface characterization, internal residual stress characterization and the latest inspection methods for micro optical components. 15.6.1. Surface Characterization Surface quality is the key to the performance of optical components because the functional light refraction normally occurs in the surface. Surface roughness and profile derivation are two major factors that influence the surface quality and optical functions of a molded optical component. Therefore, they need to be accurately characterized and controlled within tolerance. Surface quality characterization methods can be divided into two categories, i.e. contact and non-contact types. At the microscopic scale, a contact type stylus profiler using electronic amplification is the most common tool [117]. However, its measurement accuracy can be significantly affected by the stylus size, scan area size, scan speed, etc. At a nanoscale, atomic force microscopy has been used [117]; but its scan area is limited to tens of micrometers. Non-contact measurements are normally achieved by optical methods, such as interferometric techniques and confocal microscopy [118]. The Fizeau configuration is the most commonly used interferometer because of its succinct set-up design [118, 119]. As shown in Fig. 15.12, the Fizeau interferometer consists of two plano-parallel glass plates aligned at an angle. Interference occurs between the beams reflected from the surfaces of the plates facing each other. Interferometric techniques can quickly characterize the entire surface in a single measurement with sub-nanometric resolution. In measuring aspherical or freeform optical components, however, a correction element such as a null lens or computer generated hologram are needed to generated a suitable reference wave front [119]. It is noted that the measurement of interferometer is very sensitive to 450 Chapter 15. Precision Glass Molding the environmental influences [119]. Moreover, certain surface structures such as high curvature area or steps in micro optics would lead to optical edge artefacts [120]. Fig. 15.12. A schematic setup of Fizeau interferometer [119]. 15.6.2. Residual Stress Characterization Internal residual stress after PGM can significantly affect the optical performance of molded optics [94, 121, 122]. It is noted that most transparent materials possess birefringence property, in which the difference of the principal refractive indexes is proportional to the difference of the principal stresses. Therefore, the measurement of internal residual stress can be converted to an optical problem [94, 122]. Some researchers [123] measured the optical retardation using a plane polariscope, and then compared the experimental results with numerical simulation as a validation of the modeling approach [123]. Some others [124] measured the whole field residual birefringence distribution of a molded P-SK57TM lens by a six step phase shifting technique. Fig. 15.13 presents the schematic of the experimental setup. To increase the measurement accuracy, the molded lens was placed in a tank with a glass bottom containing a liquid of matching refractive index. Fig. 15.14 shows the distribution of retardation in the P-SK57TM glasses lens molded with two different flow rates of N2 gas [124]. This technique can directly measure the retardation and the direction of the maximum principal residual stress. However, it is very difficult to work out the individual components of the residual stress, which needs an effective stress separation algorithm [125]. 15.6.3. Micro-Optics Characterization and Standardization All the techniques aforementioned can be used in characterizing micro-optics if the resolution is high enough. However, due to the small sizes and complicated structures of micro optics, the terminologies and definitions widely used for macro optics are no longer suitable for micro optics [126]. For example, in a microlens it is very difficult to find the principal plane and the optimum image plane to define the focal length. Therefore, effective focal length has been used instead, which is defined as the distance from the vertex of the microlens to the position of the focus given by locating the maximum of the power density distribution. Therefore, specific international standards need to be established to unify the terminology and characterization methods [126]. 451 Advances in Optics: Reviews. Book Series, Vol. 3 Fig. 15.13. Experimental setup for measuring the residual birefringence [124]. International standardization activities for microlenses were initialed in Japan in 1991. The first part of ISO standard of microlens arrays, ISO 14880-1 Microlens array Part 1 (Vocabulary), was published in 2001. After that, the test method standards were summarized in three different parts: ‘Part 2 Test methods for wavefront aberrations’, ‘Part 3 Test methods for optical properties other than wavefront aberrations’ and ‘Part 4 Test methods for geometrical Properties’. In 2006, a new part of the standard series was initiated to explain the different methods for testing microlenses and microlens arrays [126]. Fig. 15.15 shows the development road map of the microlens array standards. However, similar work has not been done for other micro optics. 452 Chapter 15. Precision Glass Molding Fig. 15.14. Experimentally measured retardation in a molded aspherical lens with two different flow rates of N2 gas [124]. Fig. 15.15. Development road map of microlens array standards [126]. 15.7. Optimization of PGM Process As have been discussed in previous sections, the quality of molded optical components is influenced by a series of factors [29], and their relationship is complex and highly nonlinear. Therefore, it is difficult to improve the PGM process by using a trial-and-error method. A process optimization with the aid of a reliable numerical simulation is a cost-effective way to minimize the problems in the manufacturing chain of lens production [29]. 15.7.1. Optimization Strategy To optimize a process, objective functions, optimization algorithms and criteria are required. The objective function for the lens PGM is not a simple equation but a FE numerical simulation (see Fig. 15.16) [99, 127, 128]. The FE analysis should be able to 453 Advances in Optics: Reviews. Book Series, Vol. 3 generate the parameters to be optimized from the optimization algorithms, and produce results to be assessed by the criteria. Some studies have carried out a single objective optimization process, such as reducing the shape deviation or minimizing the residual stresses. On the contrary, multi-objective optimization of PGM process is much more difficult. Fig. 15.16. A typical optimization process [131]. 15.7.2. Mold Shape Optimization Considering that the shape distortion of molded optical components is inevitable due to the thermal shrinkage in PGM process, the mold geometry and dimension must be optimized to compensate such effects in the initial design stage [99, 127, 128]. Different algorithms have been used for optimizing the mold shape, such as iterative algorithms [129, 130], sequential quadratic programming methods [128] and iterative deviation methods [99]. Based on the simplex method, a numerical platform was recently established for compensating aspherical molds [131]. A formulated aspherical lens surface was defined by Eq. (15.1), where X is the distance from the lens axis, Y is the Y-component of the distance from the vertex, R is the radius of curvature, k is the conic constant and a is the correction coefficient of high order terms [131]. X2 Y(X )  R (1  1  (1  k ) 2 X ) R2  aX 4 . (15.1) The profile-mean-square-deviation (PMSD) was selected as the optimization objective. PMSD can be calculated by Eq. (15.2), where N is the node number on the lens surface, yi  yˆ i represents the shape derivation at the ith node. Considering that a high-quality optical lens requires that the PMSD < 1 μm [132], the following optimization criterion in this optimization was applied [131]. PMSD  454 2  iN1 ( yi  yˆ i )  1 m . N (15.2) Chapter 15. Precision Glass Molding Fig. 15.17 shows the changes of the PMSD by optimizing R and k simultaneously. The value of a was set to zero during the optimization process [131]. The criterion was satisfied after 21 optimization cycles, and the optimized parameters were R = 11.819 mm and k = 2.0365 [131]. Fig. 15.17. (a) Variation of the PMSD during the optimization of R and k, and (b) the corresponding parameters [131]. To further reveal the compensation mechanism [131], the shape derivations of the molded lens along its radial direction with and without the mold optimization were compared as shown in Fig. 15.18a. It is clear that using the optimized mold could effectively reduce the large shape deviation near the edge. The evolutions of the PMSD during the molding process with and without the mold shape optimization were also compared as shown in Fig. 15.18b. It is clear that the deviation can be effectively reduced during cooling by using the optimized mold shape [131]. Fig. 15.18. (a) Comparison of the profile deviations of the molded lens along the radial direction with and without a die optimization, and (b) the evolution of the PMSD during the molding processes [131]. 455 Advances in Optics: Reviews. Book Series, Vol. 3 15.7.3. Residual Stress Optimization As revealed above, residual stresses in a molded optical component form in the cooling stage [51]. Therefore, it is reasonable to optimize the cooling curve for reducing the residual stress. An optimization trial [133] has been on the whole cooling stage in PGM. In this study, the cooling curve in the temperature region Tg -50 oC to Tg +100 oC was divided by 7 key points. Then the position of these points was optimized to reach the residual stress threshold. Fig. 15.19 shows the cooling curves before and after optimization for different stress threshold. Fig. 15.19. Initial and optimized cooling curves [133]. As have been clarified previously, lens cooling in PGM is in two stages. The first cooling stage influences the formation of residual stresses but the second stage does not. Thus the residual stress optimization can focus on the first cooling stage [131]. The division point between the first and the second cooling stages was selected as the optimization parameters (see Fig. 15.20a). The von Mises stress at the lens center (point N in Fig. 15.20b) was used as the optimization target with the threshold of 2.5 MPa [131]. Simplex method was used to optimize the position (t2, T2) to minimize the residual von Mises stress at point N. Figs. 15.21a and 15.21b present the evolution of the parameters during optimization and the corresponding residual stress changes. It can be seen that the optimization enables the residual stress reduction until reaching the criteria (<2.5 MPa). 15.7.4. Multi-Objective Optimization Multi-objective optimization is much more challenging than the single-objective optimization mentioned above [29]. With the progress of computational capability and 456 Chapter 15. Precision Glass Molding algorithm in recent years, multi-objective optimization approaches has been used in optimizing machining parameters. Non-dominated sorting genetic algorithm (NSGA-II) is the most popular multi-objective optimization tool [134], which has been applied in the design of injection molding processes [135], in getting good laser brazing parameters [136], in improving the hard turning performance of bearing steel [137], and in optimizing the process parameters of wire electrical discharge machine [138]. However, similar work on PGM is not available. (a) (b) Fig. 15.20. (a) Loading and temperature history of PGM, and (b) the distribution of residual von Mises stress in a molded glass [131]. (a) (b) Fig. 15.21. (a) Changes of parameters during optimization, and (b) the corresponding residual stresses [131]. 457 Advances in Optics: Reviews. Book Series, Vol. 3 To optimize a PGM production process, an effort has been place to digitize the whole manufacturing chain of PGM [94]. A web-based software for PGM was developed for all users to share the massive production data, including process developers and quality control inspectors. Based on these data, one can analyses the correlations between “input” preform, mold, processing parameters and “output” quality of molded optical components [29]. In this way, the optimization of the whole manufacturing chain could be achieved. However, how to effectively use this “Big Data” to make added value is still challenging. 15.8. Summary This chapter has introduced the specifications, challenges and latest progress of PGM, as a promising technique to manufacture better and lower-cost optical components. A brief summary and perspectives are given below: (1) PGM can produce glass optical components in a single-step process, and thus can significantly reduce the time and cost compared with traditional machining methods. (2) The quality of molded optical components strongly depends on the preform, mold and process control parameters. Defects in these preparatory elements will be transferred to the final products. Fabricating ultraprecision mold is one of the most important and difficult steps in the manufacturing chain of PMG. (3) FE-based numerical methods can simulate the PGM process and reveal the formation mechanism of shape distortion and residual stresses in molded optical components. However, a suitable constitutive model, which can describe the complicated thermomechanical deformation of glass over a wide range of temperature, should be developed and used. (4) Standard quality characterization methodologies should be developed, especially for micro optical components. They are the foundation to improve the PGM process. (5) Multi-objective optimization could be an effective way to improve the quality of molded optical components. Digitization of a real PGM process can provide massive insitu data to analyse the correlations between “input” preform, mold, processing parameters and “output” quality of molded optical components. Acknowledgements The work presented in this chapter was financially supported by the Australian Research Council. References [1]. R. E. Fischer, B. Tadic-Galeb, P. R. Yoder, Optical System Design, McGraw-Hill, New York, 2008. 458 Chapter 15. Precision Glass Molding [2]. M. U. Erdenebat, K. C. Kwon, E. Dashdavaa, Y. L. Piao, K. H. Yoo, G. Baasantseren, et al., Advanced 360-degree integral-floating display using a hidden point removal operator and a hexagonal lens array, Journal of the Optical Society of Korea, Vol. 18, Issue 6, 2014, pp. 706-713. [3]. J. L. Li, S. Hu, L. X. Zhao, Study of the influence of the shape of projection lens focal plane on the focus control of advanced lithography, Optik, Vol. 125, Issue 22, 2014, pp. 6775-6777. [4]. C. M. Tsai, Y. C. Fang, C. Z. 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Terrab, Hard turning behavior improvement using NSGA-II and PSO-NN hybrid model, International Journal of Advanced Manufacturing Technology, Vol. 86, Issue 9-12, 2016, pp. 3527-3546. [138]. G. J. Zhang, Z. Zhang, W. Y. Ming, J. W. Guo, Y. Huang, X. Y. Shao, The multi-objective optimization of medium-speed WEDM process parameters for machining SKD11 steel by the hybrid method of RSM and NSGA-II, International Journal of Advanced Manufacturing Technology, Vol. 70, Issue 9-12, 2014, pp. 2097-2109. 466 Chapter 16. Deterministic Loose Abrasive Wear in Conventional Grinding-Polishing Machines Chapter 16 Deterministic Loose Abrasive Wear in Conventional Grinding-Polishing Machines Luis C. Alvarez-Nuñez, Carolina Keiman and Oscar Chapa1 16.1. Introduction The processes of automation of manufacturing optical components are continually in development. Optical industry requires more precise components and low costs. Optical manufacturing automation is currently undergoing dynamic developments, and the search for higher precision at lower costs leads the market. However not all the optical components demand modern equipment for their manufacturing, most of the lens and mirrors continue and they will continue being spherical. The spatial frequency error is most difficult to control in CNC polishing machines due to small polishing pad given a mid-frequency errors. This means that conventional optical manufacturing machines can still be used in order to control low-medium and high spatial frequency errors [1]. The advantage of traditional grinding-polishing machines over numeric control machines is the facility and the capacity of mass production and most important the ability to control their figure in optical components adjusting strokes parameters [2-4]. This means that the optical manufacturing using traditional machines will be been able to continue using [2, 4], if we increase their efficiency and effectiveness. Traditionally, optical manufacturing processes are classified into three stages: generation, grinding and polishing. Luis C. Alvarez-Nuñez Universidad Nacional Autónoma de México, Instituto de Astronomía, Mexico City, Mexico 467 Advances in Optics: Reviews. Book Series, Vol. 3 Undoubtedly, grinding and polishing are of great importance, since it influences directly upon an optical element’s precision, through curvature radius, figure and roughness control. To minimize grinding and polishing time the technician should adjust the machines parameters like velocity, pressure defined in Preston’s theory [5] and most important adjust stroke parameter like amplitude and off-center machine [2-4] in order to control their figure (topography), thickness (waste material) and roughness (quality polishing) in optical components. To improve the processes of production of optical components is necessary to understand the mechanism of loose abrasive wear in traditional machines. The present work is a contribution in this sense, based in a mathematical model that optimizes the machine adjustment parameter. 16.2. Abrasive Wear Theory Abrasive wear is a stochastic-statistic process used in optical manufacturing process based in mechanical and chemical interaction between abrasive-glass. The Preston’s theory [5] predicts that the abrasive wear h in a point (x, y) is proportional to the pressure P (pressure applied on upper element) and the magnitude of the relative speed V (relative instantaneous speed among two interacting points) of the optical components concerning to the tool (Eq. 16.1). This representation, the first and simpler, uses an empirical constant proportionality KP that depends mainly of the physical properties of the materials that interact (as type of glass, tool and abrasive grain) and includes the effects without distinguishing the influence of each one of them, like the size of abrasive grain, workspace, the hardness of the tool, glass, and the abrasive, etc. t h  K P  P( x, y, t ) V ( x, y, t ) dt . (16.1) 0 Subsequent research, especially those headed by Kumanin [6], introduced a deterministic equation using physical parameters for KP representing loose abrasive wear. (Eq. 16.2) h  1 . 5 E  6 kQ  S t  P( x, y, t ) V ( x, y, t ) dt , (16.2) 0 where  is the glass relative wear rate (Unity = BK7), k is the tool hardness (сast iron = 1.2), Q is the abrasive particle diameter, S is the Area under abrasive wear action. In both equations P and V are functions of position (x, y) and time t. Besides P and V, the grinding wear and polishing with free abrasive, is proportional to the viscosity and pH of the liquid in that they are suspended, the abrasive particles, the 468 Chapter 16. Deterministic Loose Abrasive Wear in Conventional Grinding-Polishing Machines concentration of this suspension and the physical properties of the individual materials that participate in the abrasive process. W. Rupp [7, 8] investigated the effect of local pressure distribution. He demonstrated that the source of curvature change is non-uniform pressure distribution near lower disk’s edge. Along this line, Wagner and Shannon [9] suggested that the original wear model proposed by Preston and Kumanin [5, 6], should be improved to include non-uniform pressure distribution at tool edge. Following this reasoning, Cordero-Davila et al [10] introduced a new model to evaluate wear rate increase due to such edge pressure distribution. This model is based on the conditions of Force and Momentum equilibrium, that interacting disks must fulfill at all time. Following this research [10] Alvarez et al [4] introducing slight modifications to Cordero-Davila’s results, dictated by the differences between their theoretical model and world machine. The research leaded by Alvarez et al [2-4] confirm that the variable affecting the wear process is the relative velocity V(x, y, t) of displacement between point pairs (on the tool and on the work disk holding the optical components, interacting through slurry abrasive grains), within the instantaneous contact area among both disks. The relative velocity was calculated between disks and was estimated the wear in upper disk assumed that the tool (lower disk) is practically undeformable and unwearable, at least as compared to the material being worked (glass). It is also assumed that the tool’s surface is uniform. In real life, tool and work can be upper and/or lower disk depending of curvature glass and figure correction based in stroke adjustment. The purpose of this work is to complete the general relative velocity equations for upper and lower disk and based in Preston’s and Kumanin’s equations estimate the wear and figure in upper disk and lower disk for grinding and polishing stage, we confirm these results comparing the final figure with interferometric data. In Section 16.5 we present a brief summary of equations based in upper disk relative velocity condition [2], in Section 16.6 we present the relative velocity equations in lower disk condition, in Section 16.7 we present a boundary conditions based in non-contact pair of points in upper and lower disk, in Section 16.8 we presents a pressure model based in Cordero's ring, and finally in Section 16.9 we present two simulations for lower and upper disk and estimate the final topography (figure) based in tool-work configurations (lenspolishing tool) and compared with real data from interferometer using CaF2 and S-FTM16 glass for FRIDA astronomical instrument [11]. 16.3. Conventional Grinding-Polishing Machines In conventional grinding-polishing machines the lower disk is motorized (spindle), rotating at a constant angular velocity . Upper free disk undergoes a reciprocating movement sliding over the lower disk, led by an arm (length L0) which is driven by an eccentric pivot that rotates at  cycles per unit time. (Fig. 16.2). 469 Advances in Optics: Reviews. Book Series, Vol. 3 Upper disk rotates freely about its central pivot, at a variable angular velocity (t), driven by the resultant of the frictional forces arising from the abrasive process that takes place within both disks contact area. Almost all machine variables are under the technician’s direct control and only one of the relative velocity components (V2) arises as consequence of the interaction of the three factors of the abrasive wear process [2, 3]. The other two velocity components (V0 and V1) are under the machine operator’s total control, as will be described in detail below. Strassbaugh’s grinding-polishing machine, model 6UR-1 and modern 6DE-DC-2 machine employed in all experiments reported herein (Fig. 16.1) possess this configuration. Fig. 16.1. Strassbaugh Machines. Left. Model 6UR-1. Right. Model 6DE-DC-2. On this machine, the operator can adjust in continuous fashion three experimental variables: pressure P applied on the upper disk through the leading arm, spindle’s rotational speed  and the arm’s oscillating rate . Oscillating arm’s central position A0 (with respect to the spindle’s axis) and oscillating amplitude +A, can also be varied continuously within some ranges, but to do so the operator must stop the machine completely. The axis of the universal cylindrical polar coordinate system is defined by the straight line joining both machine fixed axes, the spindle (a) and the arm’s oscillation axis (d), see Fig. 16.2. Its origin is located at the oscillating axis (d). In this analysis, each disk possesses its own cylindrical polar coordinate system. Their origins are located at each disk’s rotational axis, see Fig. 16.2. 470 Chapter 16. Deterministic Loose Abrasive Wear in Conventional Grinding-Polishing Machines Fig. 16.2. (a) Grinding machine, upper view; (b) Simplified diagram, showing parameters. 16.4. Relative Velocities between an Arbitrary Pair of Points Velocity vector contributions arising from a conventional grinding machine’s operation are: V0, due to the arm’s oscillation leading upper disk, V1, due to the lower disk’s rotation  driven by machine’s spindle, and V2, due to upper disk’s rotation (t) driven by abrasive wear frictional forces (Fig. 16.2a). To keep track of the process at every point, it is necessary to know both disks’ coordinate axes orientations with respect to the machine’s universal axis. Let an arbitrary upper disk point coordinates be (2, ). Let W* be the integer of (t) (upper disk rotation) from an initial instant t0=0 to t, under the sole action of abrasive process frictional forces given by Eq. (16.3), similar manner let an arbitrary lower points coordinates be (1, ) and M* be integer of  (lower disk rotation). t W *    (t ) dt . (16.3) 0 During the same time interval, the lower disk rotated a total angle of M* =  t, driven by the machine’s spindle. These two angles (W*, M*), after subtracting complete rotations (modulo 2) are given in universal polar coordinates by Eqs. (16.4) and (16.5). W   2    (t ) dt  Int  0 t   (t) dt  , t 0 M   2  t  Int   t   . (16.4) (16.5) 471 Advances in Optics: Reviews. Book Series, Vol. 3 16.5. Upper Disk Relative Velocity 16.5.1. First Relative Velocity Contribution (V0) Approximate Calculation This contribution arises exclusively from upper disk translation across the lower disk’s surface (both disks assumed static) driven by the oscillating arm by means of a bar engaged to upper disk’s central pivot. At any small time interval t, it can be assumed that the upper disk undergoes a simple arc circle displacement. The driving arm’s oscillation can be approximated as Eq. (16.6), (Fig. 16.2a) and exact movement is given by 4 arms configuration [2]. A A  A 0  A sin ( 2  γ t ) , (16.6) where  is the eccentric rotational speed (RPM) driving the arm, A0 is the arm’s mean angular position (central), and A is the arm’s oscillation amplitude (Fig. 16.2a). It is assumed that during a small time interval t, at an arbitrary instant t, only the oscillating arm actuates ( = 0, (t) = 0), and that at that instant, the arm’s approximate angular position is given by Eq. (16.7), where T0 = 1/ is the eccentric period.  t  t    . A A  A 0  A sin 2    int   T T  0   0 (16.7) Time varying arm angular position AT can be represented either by Eq. (16.7) (AT = AA, Approximate value) or AT = AE = 7. Exact value, see [2]. At time t, the universal polar coordinates of the interacting pair of points combine to form their position vector: 0 = (0, 0) (Fig. 16.2a and Fig. 16.3a). Fig. 16.3. V0 computation. (a) Radial and auxiliary components; (b) angles. 472 Chapter 16. Deterministic Loose Abrasive Wear in Conventional Grinding-Polishing Machines The point pair radial coordinate will be given by Eq. (16.8),   0  L 0 2  2 L 0  2 cos(   W *  AT )   2 2  1/ 2 . (16.8) The angular coordinate 0 of the pair of points is given by Eq. (16.9), see Fig. 16.3b and [2],  ^  R0    0  AT    AT  arctan .  L0  R0    (16.9) Position vector 0 for the point pair always remains on the x, y plane Eq. (16.10) ^ . ^ ^ ^ 0  i 0x  j 0y  0  i sin 0  j cos 0  .   (16.10) The first relative velocity contribution V0 for the pair of points is given by the vector resulting of the arm’s instantaneous angular velocity  times the position vector 0 [2]. The relative velocity first contribution V0 (Fig. 16.3) is given by Eq. (16.11).  ^  i V0    ρ0   0   0 x  ^ j 0 0 y ^  k ^   α     0   ˆi cos  0  j sin  0  .    0  (16.11) 16.5.2. Second Relative Velocity Contribution (V1) Second relative velocity contribution originates exclusively from the lower disk rotation, as driven by the machine’s spindle at a constant rotational speed . For this calculation, are assumed static both arm and upper disk, during a small time interval t ((t) = 0 and  = 0). The only requirement to compute this velocity contribution is the radial distance between the interacting points and the spindle’s axis, i.e. their position vector in lower disk’s polar coordinate axis. The line 1 joining the interacting points and lower disk rotational axis, is given by Eq. (16.12)  2 ρ1  L1  2 L1 ρ2 cos(  W *  B)  ρ22  1/ 2 . (16.12) The previous results allow us to obtain the angular coordinate of a contacting pair of points in a universal polar coordinate system as 1 = B +  (Fig. 16.4b) is given by Eq. (16.13) 473 Advances in Optics: Reviews. Book Series, Vol. 3  ^  R1  1  B  arctan .  L1  R1    (16.13) Fig. 16.4. V1. Computation. (a) Radial and auxiliary line segments; (b) angles. Since point pair always remain on the x, y plane, its position vector is given by Eq. (16.14) ^ ^ ^ . ^  1  i  1 x  j  1 y   1 ( i sin  1  j cos  1 ) . (16.14) On the other hand, lower disk angular velocity vector remains constant, perpendicular to lower disk’s face and positive, it can be written:  = kM* ( k = 1 ). This means that the second relative velocity contribution vector is given by Eq. (16.15)  ^  i V1  Ω  ρ1   0    1x  ^ j 0  1y ^  k ^   ^      1   i cos  1  j sin  1  .    0  (16.15) Note that expression Eq. (16.15) correspond to lower disk point velocity, moving with respect to an upper disk’s point that remains instantaneously static. To compute the wear produced on the upper disk’s surface, this velocity contribution Eq. (16.15) must be taken as negative. This fact will be applied latter to the vector sum of all three relative velocity contributions. 16.5.3. Third Relative Velocity Contribution (V2) The third relative velocity vector contribution originates from the rotation of the upper disk, which spins under the action of frictional forces arising from the loose abrasive wear process taking place between disks [2, 3]. 474 Chapter 16. Deterministic Loose Abrasive Wear in Conventional Grinding-Polishing Machines Let us assume now that during a small time interval t this velocity is the only one acting upon the pair of points ( = 0,  = 0). The upper disk’s point polar coordinates are given by Eqs. (16.16) and (16.17), see Fig. 16.5. 2  W *   , ^ (16.16) . ^ 2  i 2 x  j 2 y ^ ^    2  i sin  2  j cos  2  .   (16.17) Fig. 16.5. V2. Computation. (a) Radial and auxiliary line segments, (b) angles. Due to machine setup, this velocity vector expression is given by Eq. (16.18)  ^  i ^ V 2  ω(t) k  ρ2   0   2 x  ^ j 0 2 y ^  k  ^ ^  (t)    (t )  2   i cos  2  j sin  2  .    0   (16.18) The only remaining unknown in Eq. (16.18) is (t). A number of theoretical and experimental contributions [3] have pointed at this variable’s importance. However, these results are difficult to calculate in real time, or apply only to particular cases. An approximate and exact (t) equation based on experimental results was tested, described in [2, 3]; it proved to be appropriate approximation simulations of the grinding and polishing process. Note: 2 and 2 is the arbitrary point position in upper disk that is evaluated and repeated N times for simulated total wear in upper disk. 475 Advances in Optics: Reviews. Book Series, Vol. 3 16.5.4. Vector Addition of Three Relative Velocity Contributions The relative velocity between upper disk-lower disk point pair is equal to V0, V1, and V2 vector addition, see Fig. 16.9. The upper disk point (Cartesian coordinates) relative velocity components are given by Eq. (16.19) VTx  V0 x  V1x  V2 x , VTy  V0 y  V1 y  V2 y . (16.19) The minus sign affecting V1 stands for the required opposite direction for this contribution to effect on the upper disk point, as pointed out above. The relative velocity magnitude in upper disk is given by Eq. (16.20), to be applied in Preston’s or Kumanin’s wear equations, Eqs. (16.1) and (16.2). VT  (VTx )2  (VTy )2 , (16.20) 16.6. Lower Disk Relative Velocity Lower disk velocity contribution can be calculated depending of tool-work configuration and is given for 3 velocities showing next. 16.6.1. Approximate Calculation of the First Relative Velocity Component (V0) At time t, the universal polar coordinates of the interacting pair of points combine to form their position vector: 0 = (0, 0) (Fig. 16.6). Fig. 16.6. V0. Computation. (a) Radial and auxiliary components. (b) angles. The point pair radial coordinate will be given by Eq. (16.21) ρ0  476 G  Ry , cos  0 (16.21) Chapter 16. Deterministic Loose Abrasive Wear in Conventional Grinding-Polishing Machines where the upper disk’s center position radial and tangential components are given by Eqs. (16.22) and (16.23) respectively, see also Fig. 16.3a, Rx  ρ1 sin( M *  ) Ry  ρ1 cos(M *  ) . , (16.22) The angular and radial coordinate 0 and 0 of the pair of points is given by Eq. (16.23), see Fig. 16.6b,  Rx  ,  Ry  G  (16.23)  0  arctan  ^ . ^ ^ ^ 0  i 0x  j 0y  0  i sin 0  j cos 0  .   (16.24) The first relative velocity contribution V0 for the pair of points is given by the vector resulting of the arm’s instantaneous angular velocity  times the position vector 0. The relative velocity first contribution V0 (Fig. 16.6) is given by Eq. (16.25)  ^  i V0    ρ0   0   0 x  ^ j 0 0 y ^  k ^   α     0   ˆi cos  0  j sin  0  .    0  (16.25) 16.6.2. Calculation of the Relative Velocity Second Component (V1) This relative velocity contribution is produced exclusively by the lower disk rotation at constant rotational speed . For the present calculation, consider static both the arm and the upper disk rotation, during a small time interval t. Lower disk point polar coordinates are given in Eq. (16.26) (Fig. 16.7) 1  M *   . (16.26) Since the angular velocity of the lower disk remains constant, perpendicular to lower disk´s face and takes place in a positive direction, we can write:  = kM* (| k | = 1 ). On the other hand, radial coordinates always remain in the x, y plane, we have in Eq. (16.27): ^ ^ ^ . ^ 1  i 1x  j 1 y  1 ( i sin 1  j cos 1 ) . (16.27) This means that the second relative velocity contribution vector expression is given in Eq. (16.28) 477 Advances in Optics: Reviews. Book Series, Vol. 3 Fig. 16.7. Auxiliary line segments, required for computation of V1.  ^  i V1    1   0   1x  ^ j 0 1 y ^  k ^  ^      1   i cos 1  j sin 1  .    0  (16.28) Note: 1 and 1 is the arbitrary point position in upper disk that is evaluated and repeated N times for simulated total wear in lower disk. 16.6.3. General Expression for the Third Relative Velocity Component (V2) Radial distance between the pair of contacting points referenced to upper disk 2 and its angle 2 referenced to universal coordinate axis and center of upper disk is our only unknown variable to compute this velocity contribution. The third vector contribution to the relative velocity among contacting point pairs, originates from the upper disk’s rotation, which spins under the action of frictional forces arising from the loose abrasive wear process taking place between disks. Let’s assume now that during a small time interval t this velocity component is the only one acting on the point pair. Due to arm’s oscillation, the distance between both disks rotation axes L1 is given by Eq. (16.29) (Fig. 16.8) L1   rx 2  ry  2 1/2 where radial components are given in Eq. (16.30) 478 , (16.29) Chapter 16. Deterministic Loose Abrasive Wear in Conventional Grinding-Polishing Machines rx  L0 sin( AT ) , ry  L0 cos( AT )  G . (16.30) Fig. 16.8. Auxiliary line segments, required for computation of V2. Angle B (Fig. 16.8) between L1 and universal polar coordinate axis is given in Eq. (16.31) r  B  arctan  x  . r   y  (16.31) Employing the radial and angular components of lower disk center position (L1, 1) we can obtain radial component of upper disk (Fig. 16.8) and Eq. (16.32).   2  L12  12  2 L1 1 cos( 3 )  1/ 2 , (16.32) where angular position 3 is given in Eq. (16.33)  3  1  B , (16.33) 1  M *   . (16.34) and 1 is given in Eq. (16.34) Angular coordinates 2 of the pair of points is given by Eq. (16.35) 2  B  4 , (16.35) where angular 4 coordinates is given in Eq. (16.36) 479 Advances in Optics: Reviews. Book Series, Vol. 3 ^  R1  4  tan   .  R1    (16.36) 1 ^ Auxiliary components R 2 , R2 are given by Eq. (16.37) R1  1 cos( 3 )  L1 , ^ R1  1 sin( 3 ) . (16.37) On the other hand, radial coordinates Eq. (16.38) always remain in the x, y plane, we have: ^ ^ ^ . ^  2  i  2 x  j  2 y   2 ( i sin  2  j cos  2 ) . (16.38) Due to machine setup, the angular velocity vector expression is: (t) = k (t), wherefrom is shown in Eq. (16.39):  ^  i V2   (t )   2   0   2 x  ^ j 0 2 y ^  k  ^ ^  (t )    (t )  2   i cos  2  j sin  2  .    0   (16.39) Note that these calculations correspond to the point on the upper disk, moving with respect to lower disk’s point, which remains instantaneously static. To compute wear produced on lower disk’s surface, this velocity contribution must take as the negative of the expression found. We’ll apply this fact latter, to the vector sum of all three relative velocity components. 16.6.4. Vector Addition of Three Relative Velocity Contributions The relative velocity among a given pair of points in contact, is the vector addition of the three contributions found, namely V0, V1, and V2, see Fig. 16.9. The lower disk point (Cartesian coordinates) relative velocity equations, are given by Eq. (16.40) V Tx  V 0 x  V 1 x  V 2 x , V Ty  V 0 y  V 1 y  V 2 y . (16.40) The minus sign affecting V2 stands for the required opposite sense for this contribution to effect on the lower disk point, as pointed out above. The relative velocity magnitude among arbitrary pair of points in lower disk is given by Eq. (16.41), to be applied in Preston’s or Kumanin’s wear equations, Eqs. (16.1) and (16.2). 480 Chapter 16. Deterministic Loose Abrasive Wear in Conventional Grinding-Polishing Machines VT  (V Tx ) 2  (V Ty ) 2 . (16.41) Fig. 16.9. Final relative velocity vector contributions. 16.7. Boundary Conditions in Abrasive Wear Process Depending upon both disk sizes, arm’s length L0, oscillation amplitude A and central position A0, there can be moments when an upper disk fraction slides beyond the lower one’s edge. At these time intervals, an upper disk and lower disk region will not experience abrasive wear whatsoever. The upper disk no-wear condition takes place when the magnitude of the upper disk point position vector becomes larger than the lower disk radius i.e. 2 > R1 and for lower disk no-wear condition when 1 > R2 upper disk radius (Fig. 16.9). 16.8. Pressure Distribution within Disks Contact Area Instantaneous pressure among point pairs is not uniformly distributed, neither is constant, but changes continuously as a function of upper disk’s position over the lower one assuming contacting surfaces match each other. Applying the results of Cordero-Davila [10] and modify the notation for to use in our system is possible to determine the pressure in any point of contact in upper disk and lower disk [4]. 481 Advances in Optics: Reviews. Book Series, Vol. 3 16.9. Arm Stroke Adjustments (Controlling Curvature Radius and Figure) Three of the arm stroke adjustments most frequently employed in optical fabrication, to drive the curvature towards a desired value, are described here [4]. The tendency followed by the upper disk surface curvature or lower disk curvature is a direct consequence of the abrasive wear induced in each case and depends of relative velocities and pressure distribution due to machine adjustments. Labels in parenthesis (Fig. 16.10) indicate upperdisk’s surface change tendencies as grinded and polishing against lower disk. Fig. 16.10. Stroke settings and upper disk surface change tendency (in parenthesis). Lower disk’s surface changes in a complementary manner. <1/(3-4) Diameter (Convex), =1/(3-4) Diameter (Flat), >1/(3-4) (Concave). The relationship 1/(3-4) (upper disk diameter) < eccentric position > 1/(3-4) (upper disk diameter) is based in technician experience and can be modify slightly depending of curvature control and tool-work diameter configuration. The purpose of this arm stroke adjustment is for grinding process maintain and/or correct curvature radius to nominal value and reduce the internal fracture, and for polishing stage is correct the figure (maintaining the curvature radius) and reduce the roughness in glass. 16.10. Simulation and Real Optical Manufacturing In order to apply the wear equations in real world (using Kumanin’s equation), were computed the theoretical results presented in this research to the lens surface from FRIDA project [11]. One lens surface using S-FTM16 glass was polished and controlling their figure using normal stroke to achieve /4 P-V quality surface, the lens (work) was located in lower disk and tool (pitch) in upper disk position, the adjustments machines was established in normal stroke see Fig. 16.11, the results are shown in Fig. 16.11a and simulation results in Fig. 16.11b. Simulations results can be compared with figure and P-V quality, the results between real and simulated results in figure and P-V are closer (P-V 158 nm (simulation) real 0.239 waves = 151 nm (real)). Same conditions, one lens surface using CaF2 glass was polished in upper disk position and tool (pitch) was placed in lower disk position, the adjustments machines was 482 Chapter 16. Deterministic Loose Abrasive Wear in Conventional Grinding-Polishing Machines established in normal stroke see Fig. 16.12, the results are shown in Fig. 16.12a and simulation results in Fig. 16.12b. (a) Interferometric data’s surface (b) Simulations (lower disk) Fig. 16.11. Computed wear and figure over lower disk. (a) Normal Stroke A0 = 4.5˚, A = +3˚, (Sampling interval: t = 0.1 seg Load = 1 kgf,  = 33  = 20), 40 mm diameter work-tool. (b) 100×100 simulated points. (a) Interferometric data’s surface; (b) Simulations (upper disk) Fig. 16.12. Computed wear and figure over upper disk: (a) Normal Stroke A0 = 6.5, A = +4.5˚, (Sampling interval: t = 0.1 seg Load = 1 kgf  = 30  = 24), 40 mm diameter work-tool. (b) 100×100 simulated points. 483 Advances in Optics: Reviews. Book Series, Vol. 3 Results in figure and P-V are closer with real and simulation (P-V 125 nm (simulation); 0.189 waves = 119.5 nm (real)). Note the good agreement between simulated and real results for figure estimation. 16.11. Concluding Remarks The advantage of numerical simulations in optical fabrication will allow one to compute the most suitable machine settings for each desired curvature. In optical manufacturing processes, curvature control accuracy during grinding-polishing stages depends upon the type of work performed. For average and low quality large scale industrial production, quality control seeks only to maintain surface curvatures within relatively wide tolerance limits. For precision optics, constant curvature value for each surface must be controlled during the whole process, frequently adjusting machine parameters. Employing relative velocity equations given in this research, it will be feasible to simulate both trajectory and relative velocity for any upper disk point as upper disk slides over the lower disk and vice versa, lower disk point as upper disk slides. Knowing relative velocity and pressure distribution now is possible to calculate abrasive wear and figure for arbitrary lower and upper disk points as well using Kumanin’s wear equations, results can be applied with good results in both grinding and polishing stage in special this numerical simulation can be useful due to can estimate and avoid if the machine parameters are in resonance 1x Ω (spindle velocity) = 1x  (eccentric velocity), this resonances are the principal cause of errors in manufacturing due to produce surface aberration like astigmatism, ashtray, trefoil etc. For grinding stage is possible to estimate and control curvature radius and wear (waste material) and optimize the optical production process. For polishing stage we can estimate the final figure estimating the best machines parameters in consequence to save time especially using soft materials like CaF2 and improve optical quality surface. For future works we will motorize upper disk and simulate several velocities and conditions in order to control high precision optical manufacturing process and obtain a general wear equation (grinding and polishing) based in machine parameters and toolwork properties (glass-abrasive) based in theoretical and experimental results. Acknowledgment Valuable support from the administrative staff at the IA-UNAM. Special thanks to Dr. Jesus Gonzalez and Lic. Angelina Salmeron. Valuable support to FRIDA’s Engineering Team at IA-UNAM to provide optical lenses in special to Beatriz Sanchez, Salvador Cuevas and Carlos Espejo. 484 Chapter 16. Deterministic Loose Abrasive Wear in Conventional Grinding-Polishing Machines References [1]. S. Li, Y. Dai, Large and Middle-Scale Aperture Aspheric Surfaces, John Wiley & Sons, 2017. [2]. L. C. Álvarez-Nuñez, R. B. Flores-Hernández, Relative velocity and loose abrasive wear in conventional grinding machines, Optik, Vol. 120, Issue 16, 2009, pp. 845-854. [3]. L. C. Álvarez-Nuñez, R. B. Flores-Hernández, Free upper-disk rotational speed under loose abrasive grinding in conventional machines, Optik, Vol. 121, Issue 2, 2010, pp. 195-205. [4]. L. C. Álvarez-Nuñez, R. B. Flores-Hernández, Loose abrasive edge wear effects and final surface topography in conventional grinding machines, Optik, Vol. 121, Issue 3, 2010, pp. 217-229. [5]. F. W. Preston, The theory and design of plate glass finishing machines, J. Glass Tech., Vol. 11, 1927, pp. 214-256. [6]. K. G. Kumanin, Generation of Optical Surfaces, Focal Library, New York, 1962. [7]. W. Rupp, Loose abrasive grinding of optical surfaces, Appl. Opt., Vol. 11, Issue 12, 1972, pp. 2797-2810. [8]. V. Rupp, The development of optical surface during grinding process, Appl. Opt., Vol. 4, Issue 6, 1965, pp. 743-748. [9]. R. E. Wagner, R. R. Shannon, Fabrication of aspheric using a mathematical model for material removal, Appl. Opt., Vol. 13, Issue 7, 1974, pp. 1683-1689. [10]. A. Cordero-Davila, J. Gonzalez-Garcia, M. Pedrayes-Lopez, L. A. Aguilar-Chiu, J. CuautleCortes, C. Robledo-Sanchez, Edge effects with the Preston equation for a circular tool and workpiece, Appl. Opt., Vol. 43, Issue 6, 2004, pp. 1250-1254. [11]. B. Sánchez, C. Keiman, C. Espejo, S. Cuevas, L. C. Álvarez, O. Chapa, R. Flores-Meza, J. Fuentes, L. Garcés, G. Lara, J. A. López, R. Rodríguez, A. Watson, V. Bringas, A. Corrales, D. Lucero, A. Rodríguez, B. Rodríguez, D. Torres, J. Uribe, FRIDA diffraction limited NIR Instrument, the challenges of its verification processes, Proceedings of SPIE, Vol. 9150, 2014, 91501. 485 Chapter 17. Quantitative Phase Microscopy and Tomography with Spatially Incoherent Light Chapter 17 Quantitative Phase Microscopy and Tomography with Spatially Incoherent Light Azeem Ahmad and Dalip Singh Mehta1 17.1. Introduction Coherence properties of light sources play a crucial role in various optical techniques such as profilometry, digital holography (DH), quantitative phase microscopy (QPM) and optical coherence tomography (OCT) [1-5]. Coherence is broadly classified into two categories: temporal and spatial coherence [6-8]. The spatial coherence is further divided into two sub-categories: lateral and longitudinal spatial coherence [6-8]. Most of the offaxis DH and QPM techniques so far employed a highly temporally and spatially coherent (i.e., laser) light source to obtain the interference pattern easily throughout the field of view (FOV) of camera [9]. The QPM techniques provide the measurement of different parameters associated with biological objects, such as cell dynamics (i.e., thickness and refractive index fluctuations) and a cell’s dry mass density (i.e., nonaqueous content) [3]. For the quantification of these parameters off-axis digital interference microscopy is widely preferred as it can recover information related to specimen from a single interferogram [9-11]. This makes it suitable to study dynamical behaviour of biological cells or tissues, which could be a good indicator of various cell’s diseases like malaria, sickle cell anemia etc. [3]. However, high temporal and spatial coherence properties of laser light source degrade the image quality due to coherent noise and parasitic fringe formation due to multiple reflections from surfaces of the optical components [12]. As a consequence, it reduces phase and height measurement accuracy of the specimens. To improve the measurement accuracy, broadband light sources like white light (halogen lamp) and light emitting diodes (LEDs) have been used extensively in the field of QPM, DH and profilometry of biological and industrial objects [13-15]. The spatial phase sensitivity of such types of light sources comparative to lasers is very high due to their low temporal coherence length [16]. It is well known that the interference pattern occurs only when the optical path length difference between object and reference beam is within the coherence length of the light source [16]. Therefore, it is difficult to obtain interference Azeem Ahmad Department of Physics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, India 487 Advances in Optics: Reviews. Book Series, Vol. 3 pattern quickly while employing low coherent light sources (coherence length ~ 2-6 µm). Moreover, obtaining high fringe density of the interference signal and exploitation of whole camera FOV cannot be done simultaneously in case of low coherence based interferometric techniques [17]. To overcome this limitation, on-axis interferometric configurations attracted strong attention of many researchers, which can utilize whole FOV of camera at the cost of low fringe density of the modulated signal [13, 18]. Fourier transform based single-shot phase recovery of the specimens is difficult to implement with such low fringe density [19]. Therefore, on-axis interferometric configurations generally require multi-shot phase retrieval algorithms for noise (DC and twin image) free recovery of complex field related to specimens at full detector’s resolution [20]. This limits the ability to study the live cell dynamics of the biological cells and adds complexity to the system. In addition, use of the spectrally broad band light sources in DH and QPM systems require chromatic aberration corrected optical components. Further, most of the OCT systems exploit the low temporal coherence properties of light source to perform non-contact, non-invasive optical sectioning of biological cells or tissues [4, 5]. According to Wiener-Khinchin Theorem, temporal coherence function and source spectrum form Fourier transform pairs [6, 7]. In other words, larger the bandwidth of source temporal frequency spectrum, smaller will be the coherence length of light source or vice versa. Therefore, broadband temporal frequency spectrum light sources such as super-luminescent diodes (SLD), tungsten halogen lamps, and broadband Ti: Sapphire lasers are used for obtaining high-axial resolution sectioning in OCT imaging [4, 5]. However, the main disadvantages while using these broad band light sources in OCT is the requirement of dispersion-compensation mechanism for dispersion correction, and inhomogeneous spectral response of highly absorbing specimen or medium [4, 8, 21]. These limitations compel us to devise a straightforward and cost effective method to overcome aforementioned issues related to various OCT and QPM techniques. The use of a spectrally narrow, i.e., monochromatic (temporally highly coherent) and spatially extended, i.e., spatially incoherent (pseudo-thermal) light source may have advantages over all commercially available light sources [8, 22]. To date, there have been made several attempts to use spatial coherence properties of light sources in the field of profilometry and OCT [1, 8, 22-24]. Safrani and Abdulhalim used broad band thermal light source in conjunction with a narrow bandpass filter (spectral bandwidth ~10 nm) but it is still a large bandwidth compared to laser [25]. Takeda and Rosen have demonstrated surface profilometry from a synthesized pseudo-thermal source generated from a direct laser using spatial light modulator [1]. These types of light sources do not require any dispersion compensation mechanism for dispersion corrections while imaging biological specimens, which have strong dispersion or inhomogeneous spectral response [1]. The light sources having high temporal coherence (spectrally narrow) and low spatial coherence (wide angular spectrum) have been synthesized by many authors just by passing the laser light through the rotating diffuser [1, 2, 26] or stationary diffuser, followed by vibrating a multiple multimode fiber bundle (MMFB) [12, 23, 27]. The spatially low-coherent light sources generated by employing aforementioned procedures or illuminating a speckle field [28] can also be helpful for the reduction of speckle noise 488 Chapter 17. Quantitative Phase Microscopy and Tomography with Spatially Incoherent Light significantly as in case of broadband light sources. A significant number of works have been reported previously for investigating coherence properties of such light sources [26, 29-33]. This chapter, first, provides a brief introduction about different types of coherence and their use in different optical systems (Section 17.2). Here, we will focus on the mathematical formulation of temporal and spatial coherence properties of light sources. In Section 17.3 a highly efficient method to synthesize a low spatial and high temporal coherent (pseudo thermal) light source is presented. In Section 17.4 two different phase retrieval algorithms such as five step and Fourier transform methods are described. In Section 17.5 characterization of system parameters like spatial phase sensitivity and transverse as well as axial resolution of QPM and OCT techniques is studied. In Section 17.6 influence of coherence on the spatial phase sensitivity of QPM is presented. Finally in Sections 17.7 and 17.8 successful implementation of pseudo thermal light source to perform quantitative phase imaging (QPI) and OCT of various industrial and biological cells is demonstrated. 17.2. Concepts of Coherence The coherence properties of the light sources have a significant role in various optical techniques. In the coherence theory of optical fields, Wiener–Khintchin theorem is used for the determination of temporal coherence (TC) function [6, 7]. For determination lateral spatial coherence (SC) function the van-Cittert–Zernike theorem is used [34]. The longitudinal spatial coherence (LSC), which is different from the lateral SC, can be determined from the more generalized form of van-Cittert–Zernike theorem [8, 30]. The distinction among all types of coherence and their role in the microscopic systems are briefly discussed below. 17.2.1. Temporal Coherence Temporal coherence describes fixed or constant phase relationship, i.e., correlation between light vibrations at two different moments of time. According to WienerKhintchin theorem, autocorrelation or temporal coherence function Γ ∆ ∗ 〈 ∆ 〉 and source power spectral density forms Fourier transform pairs and given by the following relation [7, 8]. Γ ∆ exp 2 ∆ , (17.1) is the source spectral distributaion where Γ ∆ is the temporal coherence function, and ∗ ∆ . function, and ∆ is the temporal delay between optical fields The full width half maximum (FWHM) of temporal coherence function provides information about the coherence length. It can be seen from Eq. (17.1), larger spectral bandwidth of the light source leads to smaller coherence length or vice versa. Michelson interferometer with a collimated light beam is generally used to realize temporal 489 Advances in Optics: Reviews. Book Series, Vol. 3 coherence function experimentally as shown in Fig. 17.1(a) [35]. The light beams reflected from mirrors M1 and M2 generate interference pattern in the camera FOV, only if the optical path difference (OPD) between them is within the temporal coherence length of light source. The scanning of either mirror M1 or M2 provides temporal coherence function related to the light source. If one replaces say mirror M2 with a multilayered biological specimen then only those layers of the sample produce interference signal which come under the temporal coherence gate of the light source. Therefore, conventional OCT systems utilize low temporal coherent light sources to perform high axial resolution optical sectioning of biological cells or tissues [4]. In addition, the use of low coherent light source in DH and QPM reduces the problems of coherent noise, speckle noise, and parasitic fringe formation from the captured interferometric images [13, 16]. Michelson Interferometer Young’s Interferometer Screen CCD L BS Scan Extended source S1 M1 Point source S2 M2 (a) (b) Fig. 17.1. Schematic diagrams of Michelson and Young interferometer. L:Lens, BS: Beam splitter, : Path lengths, CCD: Charge coupled device, is spatial extent M1 – 2: Mirrors, of the light source, and S1 – 2: double slits. 17.2.2. Spatial Coherence Spatial coherence describes the correlation of optical fields at two different spatial locations, situated either transverse or longitudinal direction of the beam propagation, at the same moment of time [7, 8]. It can be seen from the previous section, the spectral bandwidth of the light source controls the temporal coherence function. In contrast, spatial coherence function is decided by angular frequency spectrum, i.e., number of spatial frequency contained in the light source [7, 8].In other words, source size controls the spatial coherence function. Fig. 17.2 is the manifestation to determine tranverse and longitudinal spatial coherence function of an extended source. 490 Chapter 17. Quantitative Phase Microscopy and Tomography with Spatially Incoherent Light (a) (b) Fig. 17.2. (a) Manifestation to determine tranverse and longitudinal spatial coherence function of an extended source. , : is an extended light source; (b) Spatial periods and spatial frequencies of a plane wave propagating along the direction [7]. 17.2.2.1. Transverse Spatial Coherence For transverse (lateral) spatial coherence, the correlation function Γ , , ∆ 0 ∗ 〈 , , 〉 between the light fieldsoriginated from source , at two different spatial points , and , located in , plane (Fig. 17.2) is considered [7, 8]. Van-Cittert-Zernike theorem relates the correlation or transverse spatial 0 ’ to the spatial frequency spectrum of the source as coherence function ‘Γ , , ∆ follows [7, 8]: Γ , ,∆ 0 , exp , (17.2) , is the spatial frequency spectrum of the light source, and are the where position vectors of points and located in , plane, and are the spatial frequencies of the light field along and directions, respectively. The spatial frequencies and for a plane wave propagating along the direction cos , cos can be written as (Fig. 17.2(b)) [7] cos cos cos cos , , (17.3) (17.4) where , are the spatial periods of the propagating field along and directions, , are the angles between the direction of propagating field and and axes respectively, and is the wavelength of optical field.The transverse spatial coherence lengths can be defined as follows: 491 Advances in Optics: Reviews. Book Series, Vol. 3 where ∆ and ∆ ∆ , (17.5) , ∆ are the transverse spatial frequency range. Finally, the expressions for tranverse (lateral) spatial coherence lengths of the optical field along and directions, in terms of and , can be defined as follows: , (17.6) . The details about the mathematical description to achieve the above relationships can be found elsewhere [7]. Young’s interferometer is the most commonly used experimental technique to determine the transverse spatial coherence function associated with the light source [35]. The experimental scheme of Young’s interferometer is illustrated in Fig. 17.1(b). 17.2.2.2. Longitudinal Spatial Coherence The generalized Van-Cittert–Zernike theorem [8], relates LSC to the spatial structure (i.e., angular frequency spectrum) of the quasi monochromatic extended light source, analogous to the Wiener-Khintchine theorem [6, 35], which states that temporal coherence function and the source spectrum form Fourier transform pairs. According to the generalized Van-Cittert–Zernike theorem [7, 8, 30], correlation or LSC function 0 ’ is defined as follows: ‘Γ δ , ∆ Γ δ ,∆ 0 exp , (17.7) 0 is the longitudinal spatial coherence function and is the where Γ δ , ∆ angular frequency spectrum of the light source, ( is the separation between spatial points and situated in two different observation planes, and is the longitudinal spatial frequency [7]. cos cos , (17.8) is the spatial period along the z-direction. is the angle between the direction where of propagating field and axis and is the wavelength of light source. The longitudinal coherence length is defined as: where ∆ ∆ , (17.9) is the longitudinal spatial frequency range. The general expression of the longitudinal coherence length ( ) which depends on both the angular frequency and temporal frequency spectrum of the light source, as follows [7]: 492 Chapter 17. Quantitative Phase Microscopy and Tomography with Spatially Incoherent Light ∆ 2 , (17.10) where is a half of the angular spectrum width, is the central wavelength, and ∆ is related to the temporal spectrum width of the source. If the size of the light source is small (i.e. a point source) then the coherence length or the coherence time or simply the longitudinal coherence properties of the light vibrations can be purely determined by the temporal frequency spectrum (spectral distribution) of the light source [7]. On the other hand, if the size of the light source is large (extended) and then the temporal frequency spectrum is narrow (Quasi-monochromatic, ∆ ≪ longitudinal spatial coherence properties of the light source can be purely determined by the angular frequency spectrum of the light source [7, 29, 33]. Thus, for sufficiently narrow temporal frequency spectrum width, second term in the above expression can be neglected and is determined by the angular frequency spectrum only: 2 2 . (17.11) In this case, the axial resolution (i.e., 2) is dominated by LSC rather than temporal coherence length of the source. In this chapter, this phenomenon is experimentally demonstrated and applied for QPI and high-resolution spatial coherence gated optical sectioning of biological cells. 17.3. Synthesis of Low Spatial and High Temporal Coherent light Source To synthesize a low spatial and high temporal coherent (pseudo thermal) light source, an effective speckle reduction scheme, i.e., combined effect of spatial, angular and temporal diversity is adopted [23, 36]. First, a green laser (temporal coherence length ~10 cm) was made incident onto the beam splitter BS1, which splits the beam into two beams as shown in Fig. 17.3. One of the beams is passed through a microscope objective MO1 to get a diverging beam and the other one is coupled into a 50/50 fiber based beam splitter using microscope objective MO2. The three diverging beams thus achieved are projected onto a common area (spot size ~6 mm) of the stationary diffuser. All the beams are made incident on the diffuser at angles – 40°, 0°, and 40°, called as angular diversity. The diffuser scattered all three beams and generates uncorrelated speckle patterns, which are coupled into MMFB (hundreds of fibers, each fiber having core diameter 0.1 mm), by a condenser lens (focal length ~17.5 mm). The direct laser beam and the two other beams coming from the fiber coupler are not travelled equal optical path length; therefore, uncorrelated speckle patterns will be present at the output of the diffuser. At least two of them add on the intensity basis and subsequently reduced speckle contrast is observed [36]. In other words, the output of the diffuser contained wide range of spatial frequency components, which leads to the short LSC length. The source 493 Advances in Optics: Reviews. Book Series, Vol. 3 spatial frequency spectrum can also be modified by employing other speckle reduction schemes such as wavelength and polarization diversity [36]. The output spatial frequency spectrum after the diffuser is further modified by vibrating MMFB having each fiber of equal length. The modification of output angular spectrum of MMFB can be achieved either by changing the length of each fiber in bundle or by changing the illumination strategy [36, 37]. As it is difficult to fabricate a fiber bundle having each fiber of different length, therefore angular illumination strategy is preferred. All modes propagated inside each fiber of the bundle will experience different phase delays depending upon the entrance angles of light beams at the input of MMFB. Therefore, a large number of independent point sources are generated at the output of MMFB, thus generating M independent speckle patterns which add on an intensity basis. Further, vibration to MMFB scrambles all the modes and produce uniform intensity at the output port of MMFB. The combined effects of all aforementioned strategies modify the spatial frequency spectrum and thus generate a pseudo thermal light source having very short LSC length from a high temporally coherent laser. The effective LSC length is reduced due to the combined effects: (1) superposition of the three angular beams at the diffuser plane, (2) various path lengths within the MMFB, (3) mode coupling within the multimode fiber, and (4) numerical aperture (NA) of the imaging lens as utilized in next section. Obtaining such a short LSC length leads to the elimination of parasitic/spurious fringes and speckle contrast in the laser based optical setups. Similar procedure is adopted for He-Ne laser (temporal coherence length ~ 15 cm) to obtain short LSC length pseudo thermal light source. Therefore, with these achievements a laser source can be used for the QPI and OCT of delicate biological samples, which are demonstrated in this chapter. Fig. 17.3. Synthesis of low spatial and high temporal coherent light source with the combined effect of spatial, angular, and temporal diversity. BS1: beam splitter, MO1 – 2: microscope objectives, 50/50: fiber coupler, MMFB: multiple multi-mode fiber bundle. 494 Chapter 17. Quantitative Phase Microscopy and Tomography with Spatially Incoherent Light 17.3.1. Experimental Details To perform QPI and OCT of biological cells, the scattered light at the output of MMFB is coupled into the NIKON microscope (Nikon Eclipse 50i) as shown in Fig. 17.4. The lens L2 nearly collimated the scattered light beam and made incident onto a beam splitter BS2 which directed the beam towards the attached Mirau interferometer objective lens. Mirau interferometer is a highly compact interferometer in the form of an objective lens, which has the capability to produce interferometric signal very quickly even with a very short coherence length light sources such as halogen lamp and LEDs. It contains inbuilt beam splitter which splits the input beam into two beams. Fig. 17.4. Schematic diagram of the experimental set-up; BS1 – 2: beam splitters, MO1 – 2: microscope objectives, 50/50: fiber coupler, MMFB: multiple multi-mode fiber bundle and CCD: charge coupled device [27]. One of the beams goes towards inbuilt reference mirror to produce reference beam and the other one goes towards the sample to generate object beam. Both the beams recombine at the same beam splitter and generate interference pattern, which is finally projected onto a CCD camera plane. The interference pattern is recorded by a CCD camera [Lumenera Infinity 2, 1392×1024 pixels, pixel size: 4∶65×4∶65 μm2]. In order to record five phase shifted interferograms, the Mirau interferometric objective lens is attached with a piezoelectric transducer (PZT) (Piezo, Jena, MIPOS 3), which is driven by an amplifier as shown in Fig. 17.4. PZT moves the inbuilt reference mirror, as well as the imaging lens vertically to introduce a constant phase shift between consecutive interferograms. The five π∕2 phase-shifted interferograms are then recorded by a CCD camera (~10 fps) within 1 s and stored in a personal computer for further processing. During the recording of all frames, samples were within the depth of field of the objective lens. Subsequently, five frame phase shifting algorithm is utilized to extract phase information related to the specimen [38]. The image post processing took ∼50-60 s. 495 Advances in Optics: Reviews. Book Series, Vol. 3 17.4. Phase Retrieval Algorithm 17.4.1. Five Step Algorithm Different QPM techniques work on the principle of interferometry in order to measure the phase shift produced by the biological sample. For quantitative phase recovery, five frame phase shifting algorithm is widely preferred over the other phase shifting interferometry because of moderate phase error and acquisition time [38]. There is trade-off between phase shift error and acquisition time, i.e., if one tries to decrease the phase shift error by increasing the number of frames, the acquisition time gets increased or vice versa. Hariharan proposed a five frame phase shifting algorithm for the phase measurement with acceptable phase measurement error [38].The two-dimensional intensity modulation produced by the superposition of object and reference waves can be written as follows [27, 38]: , 2 , , , cos ∆ , , 3 , (17.12) . (17.13) , and I , are the intensities of the reference and sample beam, where I respectively, n (n = 1-5) corresponds to the different phase shifted interferograms, ∆ϕ , is the phase difference between the sample and reference arm, α is the phase shift between the consecutive phase shifted interference patterns for wavelength λ. Phase difference between the sample (cells + medium) and reference arm can be given by the following expression [38]: ∆ , , , , , , The phase map of the sample (cells + outside medium) ‘φ , ’ can be obtained by subtracting the phase of the reference field from ‘∆ϕ , ’. The reconstructed phase maps can be utilized to determine the refractive index profiles or height map of sample for individual wavelengths using the following expression [27]: , , , ∗2 , , (17.14) where n x, y and n x, y are the refractive indices of cell and medium. h(x, y) is the cell thickness. The Eq. (17.14) can be rewritten into the following form: , ∆ , . (17.15) This expression can be further utilized to quantify corresponding height maps of biological cells. 496 Chapter 17. Quantitative Phase Microscopy and Tomography with Spatially Incoherent Light 17.4.2. Fourier Transform Algorithm Fourier transform algorithm has the capability to recover phase information related to specimen from a single interferometric image. The 2D intensity variation of an interferogram can be expressed as follows [19]: , , ,  cos 2 , (17.16) , , and , are the background (DC) and the modulation terms, where respectively. Spatially-varying phase  , contains information about the specimen. , are the spatial carrier frequencies of interferogram along , axes. In practical , , , and  , are slowly varying functions applications, it is envisaged that compared to the variation introduced by the spatial carrier frequencies , and . The above intensity modulation can be rewritten in the following form for convenience , where ∗ , , , , exp exp 2 2 , exp , The Fourier transform of Eq. 17.17 is given as follows: , , , (17.17) . (17.18) ∗ , , . (17.19) The term , is simply a background (DC) term at the origin in the Fourier plane. The term , corresponds to +1 order term contains information about , . Similarly, ∗ , is –1 order term the object and situated at , which carry complex conjugate information about of the specimen. situated at After applying Fourier filtering of zero and –1 order terms, Eq. (17.19) can be reduced into the following form: , , . (17.20) The filtered spectrum is, first, shifted at the origin and then inverse Fourier transformed , , subsequently the wrapped phase map from the to retrieve the complex signal following expression [19]: , tan , , , (17.21) where and are the imaginary and real part of the complex signal. The reconstructed wrapped phase map lies between – to . These discontinuities are then corrected by 497 Advances in Optics: Reviews. Book Series, Vol. 3 minimum LP–norm two dimensional (2D) phase unwrapping algorithm [39].The retrieved unwrapped phase map can be further used to calculate corresponding height map by employing Eq. (17.15). 17.5. Characterization of System Parameters 17.5.1. Temporal and Spatial Phase Noise High temporal and spatial phase sensitivity is a primary requirement of any QPM setup. The temporal phase sensitivity provides information about the stability of an interferometer, which further leads to measure membrane fluctuations/stiffness of various biological cells [3]. Accurate measurement of membrane fluctuations could be a good indicator of various diseases like sickle cell anemia and cancer etc. However, spatial phase sensitivity of QPM is a measure of spatial phase variation in the reconstructed phase map, which can be measured by imaging a standard flat mirror [3]. Ideally, for a standard flat object, the measured phase variation subsequently the height variation should be equal to zero. The major source of spatial phase variation could be due to the high coherent nature of light source being used to image the specimen [12]. In other words, interference between multiple reflections from the optical surfaces and light scattering from the dust particles etc. degrade the image quality and finally reflect in the phase images. Eventually, spatially phase sensitivity limits the phase measurement accuracy of QPM systems. To measure the temporal and spatial phase sensitivity of the present QPM, we imaged a standard flat mirror, subsequently, a 1 min time lapse interferometric movie was recorded under the stable environmental condition. Fourier transform method, as described in Section 17.4.2, is further utilized to retrieve phase maps corresponding to whole interferometric movie. The variation of phase value of a given pixel as a function of time is a measure of temporal phase sensitivity of the system. Temporal phase noise of the setup is measured in all three different cases (single, double, and triple beam). Since, temporal phase noise of the setup does not depend on the coherence length of the light source, i.e., angular multiplexing of the beam. It only depends on the stability of the interferometer. Therefore, temporal phase noise of the system is found to be almost same in all three cases. The temporal phase noise of the setup is obtained less than 5 mrad, which corresponds to the 0.2 nm sensitivity in the measurement of temporal height variation, for example, cell’s membrane fluctuations, as shown in Fig. 17.5(a). To measure the spatial phase noise of the system, one of the interferogram of flat mirror is utilized [12]. The corresponding recovered phase map is depicted in Fig. 17.5(b). It can be seen from Fig. 17.5(b), recovered phase values are not same at each spatial location of the phase image. The spatial phase noise, i.e., root mean square (RMS) standard deviation, of the system is measured to be ~10 mrad and found to be quite less than that for coherent laser. 498 Chapter 17. Quantitative Phase Microscopy and Tomography with Spatially Incoherent Light Phase (mrad.) Temporal phase sensitivity Spatial phase sensitivity 8 0 6 50 4 100 2 0 0 Phase (mrad.) 20 0 150 -20 20 40 Time (Sec) 60 (a) 200 0 100 200 (b) Fig. 17.5. Phase sensitivity of the present setup. (a) Temporal phase sensitivity. (b) Spatial phase sensitivity. Color bar represents phase in mrad. Reproduced from [27], with the permission of OSA Publishing, © 2016 OSA. 17.5.2. Transverse Resolution For the measurement of transverse resolution of the system, we captured an image of a standard USAF test target using an objective lens of NA 0.3 (10×) and wavelength 532 nm (Fig. 17.6(a)). The field of view of our experimental setup was 2.0×1.5 mm2 for 10×, objective lens. Fig. 17.6(b) represents the line profile of resolution target along the red line enclosed in blue color box. It is clear from Figs. 17.6(a) and (b) that we are able to resolve the 6th element of 7th group. The measured lateral resolution was obtained to be 2.19 µm, and calculated value is found to be 1.09 µm using the formula (0.61× )/NA. Fig. 17.6. Characterization of the transverse resolution of the microscope. (a) Standard USAF resolution chart image recorded by employing objective lens having NA 0.3 (10×) at 532 nm wavelength. (b) Normalized line profile of 5th and 6th element in 7th group enclosed in blue color box. Reproduced from [23], with the permission of AIP Publishing, © 2015 AIP. 17.5.3. Axial Resolution The axial resolution determined from short LSC length rather than TC length plays an important role in high-resolution topography and tomography of industrial and biological objects. As already discussed in the introduction section, the use of pseudo thermal light 499 Advances in Optics: Reviews. Book Series, Vol. 3 source does not require any dispersion compensation and chromatic aberration corrected optics, which are otherwise mandatory in case of broadband light sources [40]. For the measurement of axial resolution, a flat mirror as a test sample is placed under the microscope and scanned vertically. The sequential interferograms are then recorded as a function of vertical scanning of the sample mirror. The sample mirror is translated vertically in a step of 1 µm for the measurement of LSC function of the light source. It is observed that the fringe visibility reduces as the sample mirror go away from the zero OPD position. Further, fringe visibility is plotted as a function of sample mirror vertical position for the measurement of LSC length. The FWHM of the fringe visibility curve thus obtained provides information about the LSC length of synthesized light source. Once the information about coherence envelope is obtained, the axial resolution (half of LSC length) of the microscope can be determined. For the determination of axial resolution as a function of wavelength, two Mirau interferometric objective lenses having NA 0.3 (10×) and NA 0.4 (20×) were used in the experimental setup. Here, two different temporally high coherent lasers: DPSS laser ) and He-Ne laser ( ~15 ) are utilized for measurement. Figs. 17.7(a) and ( ~6 (b) depict the LSC functions for NA 0.3 (10×) and 0.4 (20×) Mirau interferometric objective lenses at 532 nm wavelength respectively. Similarly, the LSC functions for NA 0.3 (10×) and 0.4 (20×) objective lenses at 632 nm wavelength are illustrated in Figs. 17.7(c) and (d) respectively. Fig. 17.7. Measurement of the LSC length of setup. The LSC length is measured for the objective lens (a) NA 0.3 (10×), and (b) NA 0.4 (20×) at 532 nm wavelength; (c) NA 0.3 (10×), and (b) NA 0.4 (20×) at 632 nm wavelength. Reproduced from [23], with the permission of AIP Publishing, © 2015 AIP. 500 Chapter 17. Quantitative Phase Microscopy and Tomography with Spatially Incoherent Light For 532 nm wavelength, axial resolution is measured of the order of 9.5 µm and 4 µm for objective lenses of NA 0.3(10×) and 0.4 (20×), respectively, as shown in Figs. 17.7(a) and (b).The calculated values are found to be 5.77 µm and 3.18 µm, for NA 0.3 and 0.4, respectively, using Eq. (17.11), at the central wavelength of 532 nm. Similarly, the measured axial resolution for red wavelength (632 nm) is found to be 11 µm and 5 µm for objective lenses of NA 0.3 (10×) and 0.4 (20×), respectively, as shown in Figs. 17.7(c) and (d) and the calculated values are found to be equal to 6.86 µm and 3.78 µm, respectively, using Eq. (17.11) at the central wavelength 632 nm. The short LSC length thus achieved may find potential application in QPM and high resolution optical sectioning of multilayered biological specimens. 17.6. Spatial Phase Noise Comparison in Case of Direct Laser and Synthesized Light Source 17.6.1. Standard Flat Mirror For the comparison of spatial phase sensitivity of the phase microscope while using two different light sources such as direct laser (type ‘A’) and synthesized source(type ‘B’), a standard flat mirror is placed under the microscope and corresponding interferometric images are acquired by the CCD camera. These interferometric images are further postprocessed for the phase recovery using Fourier transform based phase retrieval algorithm Eq. (17.21). Figs. 17.8(a) and (d) illustrate the interferometric images of the standard flat mirror for type ‘A’ and type ‘B’ light sources, respectively. Fig. 17.8. Spatial phase noise comparison of QPM generated due to direct laser and synthesized light source. (a, d) interferogram of the standard flat mirror, (b, e) recovered phase map (the color bar is in rad.), and (c, f) corresponding height map (the color bar is in nm) for two different light sources: He-Ne laser and synthesized light source, respectively [12]. 501 Advances in Optics: Reviews. Book Series, Vol. 3 The corresponding reconstructed phase and height maps of the standard flat mirror are shown in Figs. 17.8 (b, e) and (c, f) respectively. The spatial phase sensitivity of the microscope using type ‘A’ and type ‘B’ light sources are found to be approximately equal to 112 mrad and 8.3 mrad, respectively. The corresponding sensitivities in the height measurements are found to be 5.62 nm and 0.42 nm. It is quite evident from Figs. 17.8(b, e) that the coherence property of the light source plays an important role in generation of spatial phase noise. It further leads to introduce an unwanted error in the phase measurement of specimen. Approximately 90 % enhancement in the spatial phase sensitivity is observed while using synthesized light source rather than direct laser [12]. The synthesized light source is further used to perform QPM and OCT of some industrial as well as biological objects. 17.6.2. Human Red Blood Cells The effect of coherence properties of light sources: direct laser and synthesized light, are further studied on the QPI of RBCs. As mentioned earlier that synthesized light source does not generate coherent noise in the images. It is depicted from Fig. 17.9(a), strong non-uniform intensity distribution is observed in case of direct laser due to high coherent nature of the light source. In contrast, synthesized light source produces quite uniform intensity distribution throughout the image (Fig. 17.9(d)). Figs. 17.9(b) and (e) present the interferometric images of RBCs, which are recorded using direct laser and synthesized light source respectively. Fig. 17.9. QPI of RBCs using direct laser and synthesized light source and comparison. (a, d) noninterferometric, (b, e) interferometric images, and (d, f) recovered phase maps of human RBCs for two different light sources: He-Ne laser and synthesized light source respectively. The color bars represent phase in rad. 502 Chapter 17. Quantitative Phase Microscopy and Tomography with Spatially Incoherent Light The insets of Figs. 17.9 (b) and (e) clearly depict the fringe quality difference in the interferometric images generated from highly coherent and low spatial coherent light source. The synthesized low spatial coherent light source produces quite smooth interferometric fringes. These recorded interferometric images are further processed to generate corresponding phase maps of human RBCs. The recovered phase maps of RBCs corresponding to highly coherent and pseudo thermal light sources are illustrated in Figs. 17.9 (c) and (f). It is observed from the phase images that high coherent light source produces unwanted spatial phase variation in the reconstruction, which is almost negligible in case of synthesized pseudo thermal light source. 17.7. Quantitative Phase Imaging of Industrial and Biological Cells Using Pseudo Thermal Light Source 17.7.1. QPI of Standard Waveguide To quantify the phase measurement accuracy of the present technique, experiment is performed on a standard strip waveguide chip of known height. The core layer of strip waveguide chip (height ~220 10 nm) is made of tantalum pentoxide (Ta2O5). Ta2O5 has refractive index value around 2.1359 at an operating wavelength 632 nm. The height profile of the waveguide chip is first measured from a standard surface profilometer (P-7 stylus profiler). The height of Ta2O5 layer was found to be equal to 224.8 nm as shown in Fig. 17.10(a). Further, the experiment is performed on the same waveguide chip using the proposed technique shown in Fig 17.4. Fig. 17.10(b) shows one of the interferogram selected from a set of five phase shifted interferograms, which are recorded using 50× (NA 0.55) Mirau interferometric objective lens. These five phase shifted interferograms are further utilized to measure the phase as well as the height profile of waveguide chip. The phase and height map of the chip are calculated using Eqs. (17.14) and (17.15), as shown in Figs. 17.10(c) and (d), respectively. The height of the chip is found to be equal to 225.5 nm, which is very close to the value obtained using surface profilometer. 17.7.2. QPI of Human RBCs Next, the experiment was performed for the QPI of RBCs using a Mirau-interferometric objective of magnifications 50× (NA = 0.55). The 50× objective provides a sufficient field-of-view and required transverse resolution for imaging of Human RBCs. A set of five phase shifted interferograms are recorded with and without vibrating the MMFB for the reconstruction of RBCs phase map as shown in Fig. 17.11. Figs. 17.11(a) and (b) clearly depict the difference in the interferometric image quality of RBCs without and with vibrating MMFB. It can be seen that the image quality is quite bad in case of static MMFB, i.e., RBCs are not visible in FOV of camera. Whereas, vibrating MMFB significantly improves the image as well as fringe contrast as shown in Fig. 17.11(b). In order to reduce the speckle contrast, MMFB is vibrated at a constant frequency ~15 Hz. 503 Advances in Optics: Reviews. Book Series, Vol. 3 Fig. 17.10. (a) Height map of waveguide chip measured from surface profilometer, (b) interferogram, (c) unwrapped phase map, and (d) height map of the same chip using present setup at 632 nm wavelength. Reproduced from [27], with the permission of OSA Publishing, © 2016 OSA. Fig. 17.11. Effect of non-vibrating and vibrating MMFB on the QPI of RBCs. (a, b) Interferograms, and (c, d) corresponding phase map of Human RBCs, without and with vibrating MMFB respectively. Reproduced from [27], with the permission of OSA Publishing, © 2016 OSA. 504 Chapter 17. Quantitative Phase Microscopy and Tomography with Spatially Incoherent Light To reconstruct the phase map of RBCs five equally π/2 phase shifted interferograms were recorded by the CCD camera. The exactly π/2 phase shift is introduced between the reference and sample arm with the help of PZT. Figs. 17.11(a) and (b) show one of the interferogram from five phase shifted interferograms without and with vibrating MMFB, respectively. The five phase shifted interferograms are then utilized to calculate wrapped phase maps using five step phase retrieval algorithm given in Eq. (17.14). The Minimum LP-norm two-dimensional phase unwrapping algorithm [39] is used to remove the discontinuities from the wrapped phase map of sample. Figs. 17.11(c) and (d) shows the unwrapped phase maps of RBCs (image size ~48 μm × 60 μm) at 632 nm wavelength corresponding to vibrating and non-vibrating MMFB respectively. In Fig. 17.11(d), the artifacts present in the reconstructed phase image of RBCs could arise due to the phase shift error between consecutive data frames. The major sources of these errors are the uncalibrated phase shifter and environmental fluctuations. Ideally, phase shift between the two consecutive frames must be equal to π/2 or a constant number ‘α’ for the artifacts free phase images. If somehow PZT does not introduce exact phase shift between the frames then such artifacts can be present in the reconstructed phase images. It can be visualized from Fig. 17.11(c), it is difficult to retrieve phase information related to biological cells in case of static MMFB, which is completely filled with the speckle noise. There are various computational approaches present in the literature which have the capability to recover phase information from speckle images [41, 42]. But this is not the scope of this chapter. The speckle noise is effectively reduced with vibrating MMFB due to the temporal averaging of the speckle patterns (Fig. 17.11(b)). Therefore, vibrating MMFB is a smart choice for the speckle free phase imaging of biological cells with high spatial phase sensitivity. The maximum phase value of the RBCs is found to be 3.042 rad. with vibrating MMFB. 17.7.3. QPI of Onion Cells Similarly, the experiment was performed for the QPI of onion cells at 632 nm wavelength with vibrating MMFB. This time 10× (NA = 0.33) Mirau objective lens is preferred to image onion cells as the size of onion cells are bigger than RBCs. The 10× objective lens provides a sufficient field of view and required transverse resolution for imaging onion cells. Fig. 17.12(a) shows one of the interferogram selected from a set of five phase shifted interferograms recorded at 632 nm wavelength. The unwrapped phase map for onion layer is obtained by following the similar procedure opted for RBCs (Fig. 17.12(b)). It is clear from the phase map; onion skin is not uniform due to different thicknesses of the cells at different positions. Therefore, the OPD is also different at each position. The height map of onion cells is obtained by using the value of ∆n equal to 0.3345 in Eq. (17.15) at red wavelength. This value is obtained by using refractive index values of onion layer and outside medium equal to 1.3345 and 1.0 at red wavelength, respectively [43]. Figs. 17.12(c) and (d) show height map and corresponding line profile of onion cells marked with blue box, respectively. The maximum height of the cell is found to be ~3 μm at the center of the cell. 505 Advances in Optics: Reviews. Book Series, Vol. 3 Fig. 17.12. QPI of onion cells. (a) Interferogram of onion cells, (b) unwrapped phase map, (c) height maps of few onion cells, and (d) corresponding line profile at red wavelength. Reproduced from [27], with the permission of OSA Publishing, © 2016 OSA. 17.8. Profilometry and Optical Coherence Tomography 17.8.1. Profilometry of Standard Gauge Block and Indian Five Rupee Coin To demonstrate tomographic capability of the setup, the experiment is performed on standard gauge blocks. Two standard gauge blocks with height difference (i.e., step height) of 5 µm are placed under the microscope. It is clear from Figs. 17.13 (a) and (b), that initially high contrast fringe is formed on the left gauge block while the right side gauge block is out of LSC length of the light source. As the sample stage is moved upward by ~5 µm, the high contrast fringes sifted from left to right side gauge block (Fig. 17.13 (b)). The reconstructed height map of the gauge blocks obtained from these two interference patterns is shown in Fig. 17.13 (c). The feasibility of present setup is demonstrated by measuring the height of letter ‘R’ imprinted on a five rupee Indian coin. A 20× Mirau interferometric objective lens is used to generate interferogram, which occurs due to superposition of scattered light from the coin and the reference beam. The field of view 20× objective lens is 910×680 µm2 (1392×1040 pixels). For height measurement of the coin, the sample stage is translated vertically in a step size of 1 µm and a series of corresponding interferograms are captured. For phase recovery, five equal phase shifted interferograms are then recorded and analyzed using Eq. (17.13) at each vertical position of the sample stage. The phase shift between data frames is introduced with the help of PZT attached to the objective lens. Subsequently, the phase ambiguities are corrected using Minimum LP-norm 2D phase 506 Chapter 17. Quantitative Phase Microscopy and Tomography with Spatially Incoherent Light unwrapping algorithm[39].In order to acquire en-face OCT images of the feature on coin, the sample platform is scanned vertically, until the depth of 19 µm. Since, the LSC lengths obtained for DPSS and He-Ne laser are 8 µm and 10 µm respectively. Therefore, high contrast interference fringes are observed only when the condition of zero OPD is satisfied. In other words, foreground and background of letter ‘R’ will not produce interference pattern simultaneously. As the sample stage is translated vertically, the fringe contrast shifted from the foreground to background of letter ‘R’. In this way, height of letter ‘R’ is measured to be 19 µm. The 3D volumetric images with dimensions (X) 557 × (Y) 437 × (Z) 19 µm3 of the letter ‘R’ for green and red wavelengths are shown in Figs. 17.13(d) and (e) respectively. Fig. 17.13. Profilometry of industrial objects. (a, b) interference pattern on the standard gauge block, and (c) reconstructed height map, Volumetric image of letter ‘R’ of the coin using 20× microscope objective at (d) 532 nm, and (e) 632 nm wavelength. Reproduced from [23], with the permission of AIP Publishing, © 2015 AIP. 17.8.2. OCT of Multilayered Onion Sample To demonstrate the feasibility of setup, we performed experiment on the multilayered onion sample. For the sample preparations, two onion slices are placed one over the other on a reflecting mirror. The onion layers are placed one over the other in a way that the upper and bottom layers are oriented perpendicular to each other as shown in Figs. 17.14(a) and (d). The interferometric images of each onion layer are recorded using 20× (NA 0.4)interferometric objective lens at wavelength 532 nm as depicted in Figs. 17.14 (a) and (b). It is clear from Fig. 17.14 (a), the interference fringes are formed only for the light reflected from top layer due to short LSC length of the light source. As 507 Advances in Optics: Reviews. Book Series, Vol. 3 the sample stage is moved vertically, the interference pattern is shifted from the upper layer to the bottom layer of the onion sample (Fig. 17.14 (b)). Phase (rad.) 0 0 (a) 100 Phase (rad.) 0 (b) 2 100 (c) 40 100 30 0 200 200 300 0 300 0 20 200 10 -2 200 400 200 300 0 400 200 400 Phase (rad.) 0 0 (d) 100 100 200 200 Phase (rad.) 0 (e) 2 40 (f) 30 100 0 20 200 10 -2 300 0 200 400 300 0 200 400 300 0 200 400 0 Fig. 17.14. Optical sectioning of multilayered onion sample. (a, d) Interferograms of top and bottom layer of onion sample, (b, e) corresponding wrapped phase map, and (c, f) unwrapped phase maps of the top and bottom layers respectively. The color bars represent phase in rad. Reproduced from [23], with the permission of AIP Publishing, © 2015 AIP. For phase recovery, five phase shifted interferograms corresponding to each onion layers are recorded. The calculated wrapped phase maps are illustrated in Figs. 17.14(b) and (e). The wrapped phase maps of top and bottom layers are then corrected using 2D phase unwrapping algorithm as depicted in Figs. 17.14(c) and (f) respectively. Finally, it can be seen from the recovered phase images, short LSC length instead of TC length can be utilized for the optical sectioning of multilayered biological specimens. 17.9. Conclusions This chapter provides an overview about the coherence properties of the light sources and further their role in QPM and OCT techniques is studied. Most of the OCT techniques generally utilized broadband light sources to obtain high axial-resolution and speckle free imaging. However, broadband light sources require dispersion compensation mechanism for dispersion correction which adds complexity to the system. In addition, chromatic aberration corrected optical components are also mandatory for the noise free images. To overcome these limitations, a narrowband light source like laser could be a possible solution. But these light sources also suffer from the problem of poor axial resolution due to high temporal coherence length and coherent or speckle noise, which reduces sensitivity of the system. 508 Chapter 17. Quantitative Phase Microscopy and Tomography with Spatially Incoherent Light To avoid these problems associated with broadband and narrowband light sources both, a spatially low and temporally high coherent source with the combined effect of spatial, angular and temporal diversity is synthesized. To exhibit potential of the technique, QPI of biological cells (RBCs and onion cells) using such light source is demonstrated. The spatial phase sensitivity of the synthesized light source is found to be quite high compared to direct laser. Moreover, it significantly reduces the problem of parasitic/spurious fringe formation and speckle noise from the images. Further, LSC length of synthesized pseudo thermal light source is found to be equal to ~8 µm with 20× objective lens at 532 nm wavelength. The short LSC length instead of TC length is further utilized to perform high axial-resolution sectioning of multilayered objects. The present system does not require any dispersion compensation optical system for biological samples as a highly monochromatic light source is used. In addition, it is useful for obtaining morphological information about the cells and tissues with good accuracy and precision. Acknowledgements The authors are thankful to Department of Atomic Energy (DAE), Board of Research in Nuclear Sciences (BRNS) for financial grant no. 34/14/07/BRNS and DST, Govt. of India, Project No.: SB/S2/LOP-026/2013. References [1]. J. Rosen, M. Takeda, Longitudinal spatial coherence applied for surface profilometry, Applied Optics, Vol. 39, 2000, pp. 4107-4111. [2]. F. Dubois, M.-L. N. Requena, C. Minetti, O. Monnom, E. Istasse, Partial spatial coherence effects in digital holographic microscopy with a laser source, Applied Optics, Vol. 43, 2004, pp. 1131-1139. [3]. G. Popescu, Quantitative Phase Imaging of Cells and Tissues, McGraw Hill Professional, 2011. [4]. W. Drexler, J. G. Fujimoto, Optical Coherence Tomography: Technology and Applications, Springer, 2015. [5]. H. M. Subhash, Full-field and single-shot full-field optical coherence tomography: A novel technique for biomedical imaging applications, Advances in Optical Technologies, Vol. 2012, 2012, 435408. [6]. L. Mandel, E. Wolf, Optical Coherence and Quantum Optics, Cambridge University Press, 1995. [7]. V. Ryabukho, D. Lyakin, A. Grebenyuk, S. Klykov, Wiener–Khintchin theorem for spatial coherence of optical wave field, Journal of Optics, Vol. 15, 2013, 025405. [8]. I. Abdulhalim, Spatial and temporal coherence effects in interference microscopy and full‐ field optical coherence tomography, Annalen der Physik, Vol. 524, 2012, pp. 787-804. [9]. M. K. Kim, Digital Holographic Microscopy: Principles, Techniques, and Applications, Springer, New York, 2011. [10]. T. Colomb, F. Montfort, J. Kühn, N. Aspert, E. Cuche, A. Marian, F. Charrière, S. Bourquin, P. Marquet, C. Depeursinge, Numerical parametric lens for shifting, magnification, and complete aberration compensation in digital holographic microscopy, J. Opt. Soc. Am. A, Vol. 23, 2006, pp. 3177-3190. 509 Advances in Optics: Reviews. Book Series, Vol. 3 [11]. K. Lee, K. Kim, J. Jung, J. Heo, S. Cho, S. Lee, G. Chang, Y. Jo, H. Park, Y. Park, Quantitative phase imaging techniques for the study of cell pathophysiology: from principles to applications, Sensors, Vol. 13, 2013, pp. 4170-4191. [12]. A. Ahmad, V. Dubey, V. Singh, A. Butola, T. Joshi, D. S. Mehta, Reduction of spatial phase noise in the laser based digital holographic microscopy for the quantitative phase measurement of biological cells, Proceedings of SPIE, Vol. 10414, 2017, 104140H. [13]. D. Singh Mehta, V. Srivastava, Quantitative phase imaging of human red blood cells using phase-shifting white light interference microscopy with colour fringe analysis, Appl. Phys. Lett., Vol. 101, 2012, 203701. [14]. V. Dubey, G. Singh, V. Singh, A. Ahmad, D. S. Mehta, Multispectral quantitative phase imaging of human red blood cells using inexpensive narrowband multicolor LEDs, Applied Optics, Vol. 55, 2016, pp. 2521-2525. [15]. R. Guo, B. Yao, J. Min, M. Zhou, X. Yu, M. Lei, S. Yan, Y. Yang, D. Dan, LED-based digital holographic microscopy with slightly off-axis interferometry, Journal of Optics, Vol. 16, 2014, 125408. [16]. B. Bhaduri, H. Pham, M. Mir, G. Popescu, Diffraction phase microscopy with white light, Optics Letters, Vol. 37, 2012, pp. 1094-1096. [17]. P. Girshovitz, N. T. Shaked, Doubling the field of view in off-axis low-coherence interferometric imaging, Light: Science and Applications, Vol. 3, 2014, p. e151. [18]. V. Dubey, V. Singh, A. Ahmad, G. Singh, D. S. Mehta, White light phase shifting interferometry and color fringe analysis for the detection of contaminants in water, Proceedings of SPIE, Vol. 9718, 2016, 97181F. [19]. M. Takeda, H. Ina, S. Kobayashi, Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry, J. Opt. Soc. Am. A, Vol. 72, 1982, pp. 156-160. [20]. H. Schreiber, J. H. Bruning, Phase shifting interferometry, Chapter 14, in Optical Shop Testing (D. Malacara, Ed.), 3rd Edition, John Wiley & Sons Inc., Hoboken, NJ, USA, 2006, pp. 547-666. [21]. L. Vabre, A. Dubois, A. C. Boccara, Thermal-light full-field optical coherence tomography, Optics Letters, Vol. 27, 2002, pp. 530-532. [22]. D. S. Mehta, V. Srivastava, S. Nandy, A. Ahmad, V. Dubey, Full-field optical coherence tomography and microscopy using spatially incoherent monochromatic light, Chapter 10, in Handbook of Full-Field Optical Coherence Microscopy, Pan Stanford Publishing Pte. Ltd., 2016, pp. 357-392. [23]. A. Ahmad, V. Srivastava, V. Dubey, D. Mehta, Ultra-short longitudinal spatial coherence length of laser light with the combined effect of spatial, angular, and temporal diversity, Appl. Phys. Lett., Vol. 106, 2015, 093701. [24]. P. Pavliček, M. Halouzka, Z. Duan, M. Takeda, Spatial coherence profilometry on tilted surfaces, Applied Optics, Vol. 48, 2009, pp. H40-H47. [25]. A. Safrani, I. Abdulhalim, Ultrahigh-resolution full-field optical coherence tomography using spatial coherence gating and quasi-monochromatic illumination, Optics Letters, Vol. 37, 2012, pp. 458-460. [26]. M. Gokhler, J. Rosen, General configuration for using the longitudinal spatial coherence effect, Optics Communications, Vol. 252, 2005, pp. 22-28. [27]. A. Ahmad, V. Dubey, G. Singh, V. Singh, D. S. Mehta, Quantitative phase imaging of biological cells using spatially low and temporally high coherent light source, Opt. Lett., Vol. 41, 2016, pp. 1554-1557. [28]. Y. Park, W. Choi, Z. Yaqoob, R. Dasari, K. Badizadegan, M. S. Feld, Speckle-field digital holographic microscopy, Optics Express, Vol. 17, 2009, pp. 12285-12292. [29]. V. Ryabukho, D. Lyakin, M. Lobachev, Longitudinal pure spatial coherence of a light field with wide frequency and angular spectra, Optics Letters, Vol. 30, 2005, pp. 224-226. 510 Chapter 17. Quantitative Phase Microscopy and Tomography with Spatially Incoherent Light [30]. I. Abdulhalim, Competence between spatial and temporal coherence in full field optical coherence tomography and interference microscopy, Journal of Optics A: Pure and Applied Optics, Vol. 8, 2006, pp. 952-958. [31]. V. Ryabukho, D. Lyakin, V. Lychagov, Longitudinal coherence length of an optical field, Optics and Spectroscopy, Vol. 107, 2009, pp. 282-287. [32]. V. Ryabukho, A. Kal’yanov, D. Lyakin, V. Lychagov, Influence of the frequency spectrum width on the transverse coherence of optical field, Optics and Spectroscopy, Vol. 108, 2010, pp. 979-984. [33]. V. Ryabukho, D. Lyakin, The effects of longitudinal spatial coherence of light in interference experiments, Optics and Spectroscopy, Vol. 98, 2005, pp. 273-283. [34]. C. McCutchen, Generalized source and the Van Cittert–Zernike theorem: a study of the spatial coherence required for interferometry, Journal of the Optical Society of America, Vol. 56, 1966, pp. 727-733. [35]. J. W. Goodman, Statistical Optics, John Wiley & Sons, 2015. [36]. J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications, Roberts and Company Publishers, 2007. [37]. D. S. Mehta, D. N. Naik, R. K. Singh, M. Takeda, Laser speckle reduction by multimode optical fiber bundle with combined temporal, spatial, and angular diversity, Applied Optics, Vol. 51, 2012, pp. 1894-1904. [38]. P. Hariharan, B. Oreb, T. Eiju, Digital phase-shifting interferometry: a simple errorcompensating phase calculation algorithm, Appl. Opt., Vol. 26, 1987, pp. 2504-2506. [39]. D. C. Ghiglia, L. A. Romero, Minimum Lp-norm two-dimensional phase unwrapping, J. Opt. Soc. Am. A, Vol. 13, 1996, pp. 1999-2013. [40]. J. Wang, J.-F. Léger, J. Binding, A. C. Boccara, S. Gigan, L. Bourdieu, Measuring aberrations in the rat brain by coherence-gated wavefront sensing using a Linnik interferometer, Biomedical Optics Express, Vol. 3, 2012, pp. 2510-2525. [41]. M. Trusiak, K. Patorski, M. Wielgus, Adaptive enhancement of optical fringe patterns by selective reconstruction using FABEMD algorithm and Hilbert spiral transform, Optics Express, Vol. 20, 2012, pp. 23463-23479. [42]. M. B. Bernini, A. Federico, G. H. Kaufmann, Normalization of fringe patterns using the bidimensional empirical mode decomposition and the Hilbert transform, Applied Optics, Vol. 48, 2009, pp. 6862-6869. [43]. W. Wang, C. Li, Measurement of the light absorption and scattering properties of onion skin and flesh at 633 nm, Postharvest Biology and Technology, Vol. 86, 2013, pp. 494-501. 511 Index Index 3D micro-stereolithography, 205 A Abbe number, 438 Abrasive Wear, 467, 468, 481 Acceptance angle, 316, 325, 326, 338, 340, 351, 355, 364, 366, 372, 373, 376, 378, 382, 385, 392, 401-403, 405, 407, 408 active optical materials, 214 Additive white Gaussian noise. See AWGN adjacent heights, 422 Adults module, 40 aerosol structures multi-layering, 431 akinetic beam scanner, 213 Akinetic Beam Scanner, 216 AliveCor, 27 altitude range, 425, 429 Analysis Linear Discriminant, 188 of variance, 188 Quadratic Discriminant, 188 Angular distribution, 316, 318, 332, 354, 394 divergence, 316, 322, 346, 347, 367, 401, 402 resolution, 321, 339, 346, 355, 356, 377, 394 sector, 421, 425, 426 arm stroke, 482 aspherical optical lenses, 435 AWGN, 259 Axial Resolution, 499 B Baby's cradle module, 40 backscatter signal, 419, 423, 429, 430 bacteria identification, 21–20 resistant, 169 band-pass filtering, 145 basic algorithms, 419 beam propagation method, 117 splitter/combiner, 219 beat length, 108 BER, 248, 255, 260, 261, 269 biosensors optical, 169 bit error rate. See BER BodyMedia’s, 27 Bragg condition, 302 frequency, 200 resonant dip, 203 Bragg-reflection waves, 200 burning agricultural, 418 area, 418, 432 C CCD camera, 349, 358, 359, 361, 385 CellNovo, 27 cells bacterial, 171 Chromatic aberration, 392 Cisco’s Connected Factory, 28 classification, 188 Cloud, 24, 25, 28, 38 CMOS fabrication, 104 CNC machines, 435 coefficient 2D transmission, 173 Coherence, 489 coherent gradient sensor, 129 colony bacterial, 170 Communication Models, 24 component analysis, 231 Component Analysis, 232, 233 independent component analysis, 232 Independent Component Analysis, 232 Principal Component Analysis, 232 Concentration ratio geometric, 315, 326, 328, 330 optical, 315, 328, 331, 332, 401, 407 Concentrator 513 Advances in Optics: Reviews. Book Series, Vol. 3 2D, 328, 401, 402, 405 3D, 317, 326, 327, 329, 338-342, 359, 401-405, 407 characterization, 316-318, 320, 325, 331, 342, 346, 348, 362, 373, 394, 395, 411 CPC, 316, 317, 326, 329, 335, 338-344, 355, 356, 359, 361, 362, 365-367, 369-385, 395, 401-407 direct collimated absorptance, 325 reflectance, 325 transmittance, 325 direct Lambertian absorptance, 330 concentration ratio, 331 optical conductance, 336 optical conductivity, 337 reflectance, 330 transmittance, 330 inverse irradiation, 317, 318, 319 inverse Lambertian optical conductance, 336 optical conductivity, 337 transmittance, 333 optical losses, 327-329, 343, 344 PhoCUS, 344, 348, 353, 359, 364, 391394 photovoltaic, 315-317, 320 reflective, 316, 317, 359, 402 refractive, 317, 353, 364 Rondine, 343-345, 350-352, 361-364, 367-369, 385-391, 395, 412, 414 thermodynamic, 315, 316, 321 transmission efficiency, 316, 318-320, 323, 324, 328-333, 338-342, 346, 348, 352, 354, 363, 366, 376, 377, 387, 388, 390, 394, 401, 402, 406, 409, 410 transmission properties, 316, 317 confocal microscopy, 450 constitutive model, 445-447, 458 Contrast. Véase Visibility Cost, 315, 350, 395, 411 coupling coefficients, 106 CPC squared, 342, 343, 369, 378 truncated, 338, 342, 343, 381, 383 cross-sensitivity, 86 Cryogenic Medium, 134 514 Cryogenic Vacuum Chamber, 138 curvature radius, 468, 482, 484 curvatures, 133 D data CALIPSO, 418 data points clusters of, 425 delay phase, 175 detection limit, 113 Threshold Level, 264 developer AZ303, 304 DHL’s IoT Tracking and Monitoring, 28 Differential signalling Channel modelling, 266, 283 Diffraction efficiency, 301 Diffractive optics, 435 Disabled and elderly module, 40 distance, 231, 233, 238-243 dynamic heart rate estimation, 231, 233 E effective refraction index, 92 electroforming. See Silver spray Electroless nickel-phosphor, 439 electro-optic coupler, 217 switch, 214, 216, 217, 222 envelope function, 421, 422, 429 Ericsson Maritime ICT, 28 etching, 435 Étendue, 327, 329, 336 ethanol, 104 extrinsic FP fiber temperature sensors, 93 F factors antibacterial, 190 features extraction, 188 FFT method, 141 Fiber Bragg Grating, 35, 36 optic interferometers, 34 Optic Sensors, 21, 28, 30, 33 optical, 173 Index finite difference method, 111 element, 444, 445 Fire Cedar, 423 Observation, 423 Roaring Lion, 423, 432 Fitbit Flex, 27 Five Step Algorithm, 496 Fizeau interferometer, 450, 451 Flux distribution, 315, 388-390 Focal length, 338, 349, 350, 358, 367, 368, 391, 402, 403 focused ion beams, 443 Fourier Transform Algorithm, 497 spectroscopy, 220 four-wave mixing (FWM), 52 Free space optical. See FSO spectral range, 70, 120 frequency domain, 145 Fresnel equations, 318 lenses, 445 reflection, 85, 95 FSO, 248 Aperture averaging factor, 258 Atmospheric attenuation, 254 Differential signalling, 261 Fog attenuation, 254 Geometrical loss, 254 Miscellaneous attenuation, 255 Pointing errors, 256 Scintillation/turbulence, 255 System diagram, 251, 253 Turbulence, 256 G Generalized Van-Cittert–Zernike theorem, 492 glass, 436-440, 444-446, 448, 450, 451, 457, 458, 468, 469, 482, 484 Glassy carbon, 440 glucose, 104 grinding, 435, 436, 439-443, 467-471, 475, 482, 484 H health and well-being applications, 29 Health and wellness, 21, 26 Health and Wellness Application, 28 heat treatment, 443 He-Cd laser, 305 height interval, 420, 426 He-Ne laser, 304 hetero-core fiber, 33 High energy beams, 443 holographic optical elements HOE, 301 solar concentration, 311 weapon sight, 301 holography digital, 193 homogeneous broadening, 49, 60 homogeneous mechanism, 111 horizontal layering smoke-plume, 427, 432 well-defined, 426 well-developed, 427, 428 I iHealth, 27 impulse excitation method, 446 increased backscattering layers of, 423, 425, 432 index of refraction, 438 inhomogeneous broadening, 50 injection height, 427 plume, 427 integrated optics, 213 intensity-modulated sensor, 30 intercept function, 420 interference mechanisms, 104 interferometric techniques, 450 Internet of Things, 21, 22, 24, 41 intrinsic FP fiber sensors, 99 Inverse method, 316, 320, 321, 338, 353355, 357-359, 376, 379, 381-383, 393, 394, 408, 409 ion-sliced lithium niobate film, 214 IoT Systems for the Family, 38 iRobot’s Roomba, 28 Irradiation diffuse, 317, 331 direct, 317-320, 333, 366, 378, 394 515 Advances in Optics: Reviews. Book Series, Vol. 3 lambertian, 316, 317, 320, 321, 331, 333, 336 K Kumanin, 468, 469, 476, 480, 482, 484 L L-3 EO-tech, 301 Lambertian diffuser, 351, 352, 376, 378 light, 321, 350, 354, 359-361, 411 source, 316, 317, 320-322, 331, 335, 338, 354, 359, 363, 364, 367, 368, 389 lapping, 435 Laser, 360, 364, 366, 367 beam, 323, 342, 344, 359, 360, 365-367, 369, 373, 374, 376 method, 365, 370, 371, 377 lens arrays, 436, 439 surface, 482 lidar ground-based, 418 scanning, 418, 419, 421, 423, 426, 428, 432 backscatter signal, 429 profiling, 417 light diffraction on bacterial colonies, 169, 178 LN-on-silicon waveguide platform, 221 Longitudinal Spatial Coherence, 492 function, 492 loss factor, 106 M Machine Support Vector, 188 Mach-Zehnder interferometer, 221 Manchester code, 290 maximum fringe contrast, 90 measurement interruptions, 425 Medtronic’s, 27 metal waveguides, 197 metal-rod-array, 204 method data processing, 419 516 gradient, 419 Method direct, 316, 347-349, 358, 363, 392, 395 direct collimated, 319, 323, 324 direct Lambertian, 321-323, 329 direct local collimated, 318, 338 inverse Lambertian, 319, 320, 323, 325, 333, 353 inverse local Lambertian, 320 mixed Lambertian, 323 Parretta, 359, 388 Parretta-Herrero, 319, 321, 367, 368, 388 PH-Method, 319, 321, 367, 368, 388390 P-Method, 319, 320, 359, 388-390 methodology advanced data processing, 419 Michelson interferometer, 221, 490 Micro and macrobending, 31 Micro-lens arrays, 435 microring resonators, 104 microscope transmission, 173 microspectrometer, 221 milling, 436, 443 Mirau interferometer, 495 Mirror film, 343, 345 parabolic, 320, 321, 325, 347, 348, 350, 351, 363, 367, 368, 388, 395, 402, 405 Radiant, 343, 345 surface, 364, 388 MMI, 104 modal field, 197 model classification, 188 modeling biophysical, 170 models smoke dispersion, 417 modified factor, 141 molecular sensing, 197, 204, 206 multi-beam interference, 92 multichannel sensors, 104 multicore fibers, 37 multilayer mediums, 139 structures, 428 multimode interference, 106 multi-objective optimization, 454, 457 multiplied fringe, 144 mutual information, 231, 233, 235, 242 Index N Nest, 28 Nonimaging optics, 378, 396 normalized functions, 429, 430 NRZ-OOK, 253 numerical platform, 454 simulations, 484 Nyquiest sampling theorem, 217, 225 O objective functions, 453 Optical axis, 316, 319, 339, 342, 343, 355, 361, 364, 367, 369, 373, 377-379, 405, 407 channel Channel correlation radius, 256 Correlation length, 256 Spatial coherence radius, 257 coherence tomography, 213 Coherence Tomography, 506, 507 communication, 220 efficiency, 315, 316, 324, 325, 331, 347, 348, 355, 358, 359, 364, 366, 367, 370373, 380, 381, 387, 389-392, 394, 405408 glass, 435, 436, 438, 439, 442, 445, 447449 imaging techniques, 213 manufacturing, 467, 468, 484 path, 321, 332, 357 length, 92 sensors, 103 simulations, 317, 338, 346, 365, 388, 405 spectroscopy, 220 Optics primary, 344, 346, 359 refractive, 316, 329, 344, 359, 364 secondary, 316, 344, 346 optimization, 436, 444, 453-458 oxidation-induced deterioration, 437 oxidized silicon wafer, 214 P Gamma-Gamma, 258 Log-normal, 258 phase error, 146 imaging, 502, 503 Retrieval Algorithm, 496 unwrapping, 145 Philips’ Hue Light Bulbs and Bridge, 27 Photodetector, 347-350, 365, 366, 373 photoelasticity experiment, 146 Photo-emf effect, 155, 156, 158 sensor, 158, 160-164, 166 signal, 158, 161, 162, 163 photolithography, 435 Photoplethysmography, 230 Photoresist Positive photoressit, 302 photoresist (PR), 302 pigment concentration, 231 plume concentration vertical structure of, 429 heights quantifying, 417 injection height, 418 Pointing errors. See FSO Pointing errors polishing, 435, 441, 443, 467, 468-470, 475, 482, 484 Polycarbonate, 301 Tetrabromobisphenol A, 302 polynomial fitting function, 149 prescribed fires, 417, 426, 431 pressure distribution, 469, 482, 484 Preston, 468, 469, 476, 480 Print-out effect, 301 darkening problem, 301 profile derivation, 444-446, 450 profiles bacterial colony, 175 Profilometry, 506 propagation constants, 199 proportional-integral-derivative, 444 Q Qualcomm Life’s, 27 quality factor, 120 parallel-plate waveguide, 197 PDF 517 Advances in Optics: Reviews. Book Series, Vol. 3 R Radiometer, 349 Ralph Lauren’s Polo Tech Shirt, 28 Ray-tracing, 355, 405 Reflection, 317, 318, 343, 352, 372, 388 light intensity, 92 Reflections, 318, 344, 365, 366, 372, 373, 412 Refraction, 318, 327, 329 refractive index, 198, 223 sensing Method of Measuring Fluid RI in FP Cavity, 84, 88 residual stresses, 444, 445, 448, 449, 454, 456-458 resonance wavelength, 112 shift, 113 Reticle image, 301 Ring, 27 Ronchi grating, 154 roughness, 468, 482 S Samsung SmartThings, 28 scanning lidar setup schematics of, 423 scans vertical, 426 sensitivity, 110 enhancement, 111 sensor application, 29 shoving model, 446 signal square range-corrected, 429 Silicon, 345, 415 waveguide, 104 Silver Halide AgH, 301 SIMO, 259 simplex method, 454 simulated image, 147 Single-input multiple-output. See SIMO single-output. See SISO SISO, 259 smoke plume actual height, 421 518 boundaries, 431 column, 426 concentration, 430 vertically stratified, 427, 432 smooth filtering method, 148 soaking, 437, 444, 445 Solar cell, 315, 318, 320, 329, 338, 342, 344, 346, 351, 352, 393, 394 Sparse Interferometric Fringes, 144 Spatial Coherence, 490 heterodyne spectroscopy, 221 Phase Noise Comparison, 501 spherical mirror, 141 spindle, 469-471, 473, 484 stereolithography, 205 Strain sensing Cylindrical FP Cavity Strain Sensor, 76 Prolate Spheroidal FP Cavity Strain Sensor, 71 Spherical FP Cavity Strain Sensor, 75 Strassbaugh, 470 stress-optical law, 149 structural relaxation, 445, 447, 448 surface finish quality, 446 plasmon polaritons, 198 Symmetry, 316, 325, 326, 329, 333, 339, 342, 348, 359, 385, 387, 395 absolute error limits, 137 relative error limit, 137 T Talbot distance, 153, 154, 160, 164, 166 effect, 153-155, 163, 165, 166 self images, 154 temperature fluctuations, 114 sensing Coating Type FP Fiber Optic Sensor, 97 Splicing Type FP Fiber Optic Sensor, 93 Temperature Sensitivity for the Fiber FP Strain Sensor, 83 Temporal and Spatial Phase Noise, 498 Temporal Coherence, 489 The intensity of the interference fringe, 70 Index The interference fringe contrast of the reflecting spectrum, 70 The last mile access, 247 the minimum interference intensity, 70 thermal drift, 114 expansion coefficient, 83, 84, 85, 93 shrinkage, 454 thermal-expansion effect, 95 thermo-optic coefficient, 84 THz fiber sensor, 197 hybrid plasmonic waveguide, 198 spectroscopy, 199 spoof surface plasmons, 201 surface plasmonic waves, 201 wave polarization, 199 waveguides, 197 THz-phase sensitive response, 204 tilt of the transparent window, 138 TNM model, 446, 448 transfer matrix, 105, 115 Transmission curve, 316, 317, 325, 326 transmittance amplitude, 172 Transverse Resolution, 499 Spatial Coherence, 491 spatial coherence function, 491 tungsten carbide, 440 two-way transmission, 420 U UV curable photopolymer, 205 V Van-Cittert-Zernike theorem, 491 variation of refractive index, 134 vertical scans, 424 video sequences, 230, 231, 233 viscosity, 437, 445-447 Vitality, 27 Vogel-Fulcher-Tammann, 445 W wave length, 143 waveguide sensitivity, 110 factor, 118 wheel grinding, 441 Wiener Khintchin theorem, 489 wildfires, 417-419, 423, 428, 432 locations of, 424 wrapped phase, 145 Y Young interferometer, 490 519