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Keywords = grating linear displacement sensor

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11 pages, 5416 KiB  
Article
Design, Analysis, and Implementation of the Subdivision Interpolation Technique for the Grating Interferometric Micro-Displacement Sensor
by Jiuhui Tang, Haifeng Peng, Peng Yang, Shangzhou Guo, Wenqiang Sun, Li Jin, Kunyang Xie and Mengwei Li
Photonics 2025, 12(1), 64; https://doi.org/10.3390/photonics12010064 - 13 Jan 2025
Viewed by 215
Abstract
A high-resolution grating interferometric micro-displacement sensor utilizing the subdivision interpolation technique is proposed and experimentally demonstrated. As the interference laser intensity varies sinusoidally with displacement, subdivision interpolation is a promising technique to achieve micro-displacement detection with a high resolution and linearity. However, interpolation [...] Read more.
A high-resolution grating interferometric micro-displacement sensor utilizing the subdivision interpolation technique is proposed and experimentally demonstrated. As the interference laser intensity varies sinusoidally with displacement, subdivision interpolation is a promising technique to achieve micro-displacement detection with a high resolution and linearity. However, interpolation errors occur due to the phase imbalance, offset error, and amplitude mismatch between the orthogonal signals. To address these issues, a subdivision interpolation circuit, along with 90-degree phase-shifter and high-precision DC bias-voltage techniques, converts an analog sinusoidal signal into standard incremental digital signals. This novel methodology ensures that its performance is least affected by the nonidealities induced by fabrication and assembly errors. Detailed design, analysis, and experimentation studies have been conducted to validate the proposed methodology. The experimental results demonstrate that the micro-displacement sensor based on grating interferometry achieved a displacement resolution of less than 1.9 nm, an accuracy of 99.8%, and a subdivision interpolation factor of 208. This research provides a significant guide for achieving high-precision grating interferometric displacement measurements. Full article
(This article belongs to the Section Lasers, Light Sources and Sensors)
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10 pages, 3588 KiB  
Communication
Combined Displacement and Angle Sensor with Ultra-High Compactness Based on Self-Imaging Effect of Optical Microgratings
by Mengdi Zhang, Hao Yang, Qianqi Niu, Xuye Zhang, Jiaan Yang, Jiangbei Lai, Changjiang Fan, Mengwei Li and Chenguang Xin
Sensors 2024, 24(3), 908; https://doi.org/10.3390/s24030908 - 30 Jan 2024
Cited by 3 | Viewed by 1269
Abstract
In this paper, an ultracompact combined sensor for displacement and angle-synchronous measurement is proposed based on the self-imaging effect of optical microgratings. Using a two-grating structure, linear and angular displacement can be measured by detecting the change of phase and amplitude of the [...] Read more.
In this paper, an ultracompact combined sensor for displacement and angle-synchronous measurement is proposed based on the self-imaging effect of optical microgratings. Using a two-grating structure, linear and angular displacement can be measured by detecting the change of phase and amplitude of the optical transmission, respectively, within one single structure in the meantime. The optically transmitted properties of the two-grating structure are investigated in both theory and simulation. Simulated results indicate that optical transmission changes in a sinusoidal relationship to the input linear displacement. Meanwhile, the amplitude of the curve decreases with an input pitch angle, indicating the ability for synchronous measurement within one single compact structure. The synchronous measurement of the linear displacement and the angle is also demonstrated experimentally. The results show a resolution down to 4 nm for linear displacement measurement and a maximum sensitivity of 0.26 mV/arcsec within a range of ±1° for angle measurement. Benefiting from a simple common-path structure without using optical components, including reflectors and polarizers, the sensor shows ultra-high compactness for multiple-degrees-of-freedom measuring, indicating the great potential for this sensor in fields such as integrated mechanical positioning and semiconductor fabrication. Full article
(This article belongs to the Special Issue Imaging and Sensing in Optics and Photonics)
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13 pages, 2565 KiB  
Article
Optimizing Algorithm for Existing Fiber-Optic Displacement Sensor Performance
by Zeina Elrawashdeh, Christine Prelle, Frédéric Lamarque, Philippe Revel and Stéphane Galland
Sensors 2024, 24(2), 448; https://doi.org/10.3390/s24020448 - 11 Jan 2024
Viewed by 1553
Abstract
This paper describes the optimal design of a miniature fiber-optic linear displacement sensor. It is characterized by its ability to measure displacements along a millimetric range with sub-micrometric resolution. The sensor consists of a triangular reflective grating and two fiber-optic probes. The measurement [...] Read more.
This paper describes the optimal design of a miniature fiber-optic linear displacement sensor. It is characterized by its ability to measure displacements along a millimetric range with sub-micrometric resolution. The sensor consists of a triangular reflective grating and two fiber-optic probes. The measurement principle of the sensor is presented. The design of the sensor’s triangular grating has been geometrically optimized by considering the step angle of the grating to enhance the sensor’s resolution. The optimization method revealed a global optimum at which the highest resolution is obtained. Full article
(This article belongs to the Section Optical Sensors)
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20 pages, 6782 KiB  
Article
Research of a Fiber Sensor Based on Fiber Bragg Grating for Road Surface Monitoring
by Gulzhan Kashaganova, Ainur Kozbakova, Timur Kartbayev, Gani Balbayev, Kulzhan Togzhanova, Zhuldyz Alimseitova and Sandugash Orazaliyeva
Electronics 2023, 12(11), 2491; https://doi.org/10.3390/electronics12112491 - 31 May 2023
Cited by 15 | Viewed by 2223
Abstract
Road infrastructure is a key public asset because it benefits the social and economic development of any country. It plays an important role in the development of the industrial complex and the production sector, and the surfaces of transport roads should be of [...] Read more.
Road infrastructure is a key public asset because it benefits the social and economic development of any country. It plays an important role in the development of the industrial complex and the production sector, and the surfaces of transport roads should be of high quality and have a long service life. Road infrastructure, like all infrastructure, requires preservation, maintenance and repair. There are special requirements for roadways that must be observed during construction or repair. The uncertainty of the composition, temperature sensitivity and viscoelastic characteristics of road materials make the structural analysis of pavement very difficult compared to other civil structures, such as bridges, tunnels and buildings. For this reason, the question of how to improve fiber sensors based on fiber Bragg grating (FBG) arose. The novelty of this study is to modernize fiber sensors based on FBG so that they display deformation, stress and displacement, temperature and other parameters with much greater accuracy, which would provide a reliable scientific basis for modifying the theory, as well as the use of a fiber sensor based on FBG for simultaneous measurement of deformation and temperature when monitoring the road surface. This article is devoted to a detailed study of the use of fiber-optic sensors (FOS) based on fiber Bragg grating for road surface monitoring. Such a fiber sensor, consisting of a fiber Bragg grating and a pair of grids, can offer the possibility of simultaneous measurement of deformation and temperature for monitoring the pavement. Temperature and deformation measurements were carried out by installing a sensor on the surface of a made asphalt sample. The built-in fiber sensor based on FBG provides important information about how the pavement structure can withstand the load and subsidence of soil and implement road safety and stability measures in a timely manner to evaluate and predict the service life of the pavement. The results of the study showed that the synchronicity, repeatability and linearity of the characteristics of the fiber sensor are excellent. The difference between the experimental and theoretical results was about 7%. Thus, based on the results of the obtained data, the fiber sensor on the FBG can be used for monitoring and designing road surfaces and in general transport infrastructure. Full article
(This article belongs to the Section Optoelectronics)
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10 pages, 3886 KiB  
Communication
An Ultracompact Angular Displacement Sensor Based on the Talbot Effect of Optical Microgratings
by Zhiyong Yang, Xiaochen Ma, Daguo Yu, Bin Cao, Qianqi Niu, Mengwei Li and Chenguang Xin
Sensors 2023, 23(3), 1091; https://doi.org/10.3390/s23031091 - 17 Jan 2023
Cited by 6 | Viewed by 2116
Abstract
Here, we report an ultracompact angular displacement sensor based on the Talbot effect of optical microgratings. Periodic Talbot interference patterns were obtained behind an upper optical grating. By putting another grating within the Talbot region, the total transmission of the two-grating structure was [...] Read more.
Here, we report an ultracompact angular displacement sensor based on the Talbot effect of optical microgratings. Periodic Talbot interference patterns were obtained behind an upper optical grating. By putting another grating within the Talbot region, the total transmission of the two-grating structure was found to be approximatively in a linear relationship with the relative pitch angle between the two gratings, which was explained by a transversal shift of the Talbot interference patterns. The influence of the grating parameters (e.g., the grating period, the number of grating lines and the gap between the two gratings) was also studied in both a simulation and an experiment, showing a tunable sensitivity and range by simply changing the grating parameters. A sensitivity of 0.19 mV/arcsec was experimentally obtained, leading to a relative sensitivity of 0.27%/arcsec within a linear range of ±396 arcsec with the 2 μm-period optical gratings. Benefitting from tunable properties and an ultracompact structure, we believe that the proposed sensor shows great potential in applications such as aviation, navigation, robotics and manufacturing engineering. Full article
(This article belongs to the Topic Advances in Optical Sensors)
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12 pages, 5949 KiB  
Article
A Double FBGs Temperature Self-Compensating Displacement Sensor and Its Application in Subway Monitoring
by Hongli Li, Gang Xu, Xin Gui and Lei Liang
Materials 2022, 15(19), 6831; https://doi.org/10.3390/ma15196831 - 1 Oct 2022
Cited by 3 | Viewed by 1821
Abstract
In order to ensure the effective vibration–reduction and vibration–isolation of the steel spring floating plate rail and meet the safe operation requirements of the subway, a Fiber Bragg Grating (FBG) displacement sensor for the deformation monitoring of the subway floating plate is proposed. [...] Read more.
In order to ensure the effective vibration–reduction and vibration–isolation of the steel spring floating plate rail and meet the safe operation requirements of the subway, a Fiber Bragg Grating (FBG) displacement sensor for the deformation monitoring of the subway floating plate is proposed. The sensor adopts double FBGs to realize temperature self-compensation. The elastic ring is used as the elastic conversion structure after the fiber grating is pre-stretched; the two ends are pasted and fixed in the groove in the diameter direction of the ring, which avoids the waveform distortion caused by the full pasting of the fiber grating. The combination of linear bearing and displacement probe rods can increase stability and reduce friction loss so that the sensor has the advantages of high sensitivity and accurate measurement results. The test results and error analysis show that in the range of 0~20 mm, the sensitivity of the sensor is 164.2 pm/mm, the accuracy reaches 0.09% F.S, and the repeatability error and hysteresis error are only 1.86% and 0.99%, respectively. The thermal displacement coupling experiment proves that the sensor has good temperature self-compensation performance. It provides a new technical scheme for the effective monitoring and condition assessment of the built-in steel spring floating plate rail. Full article
(This article belongs to the Special Issue Fiber Bragg Gratings and Its Applications)
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13 pages, 4401 KiB  
Article
Force-Displacement Analysis in Diaphragm-Embedded Fiber Bragg Grating Sensors
by Arnaldo Leal-Junior, Vitorino Biazi, Carlos Marques and Anselmo Frizera
Sensors 2022, 22(14), 5355; https://doi.org/10.3390/s22145355 - 18 Jul 2022
Cited by 7 | Viewed by 2082
Abstract
This paper presented the force and displacement analyses of a diaphragm-embedded fiber Bragg grating (FBG) sensor. In the first step, a numerical analysis (via finite element method) was performed considering linear elastic materials, where there is a linear variation on the strain in [...] Read more.
This paper presented the force and displacement analyses of a diaphragm-embedded fiber Bragg grating (FBG) sensor. In the first step, a numerical analysis (via finite element method) was performed considering linear elastic materials, where there is a linear variation on the strain in the optical fiber for both displacement and force (or pressure). In the second step, the experimental analysis was performed using two approaches: (i) controlling the displacement applied in the diaphragm-embedded FBG (while the force is also measured). (ii) Controlling the force applied in the sensor (also with the measurement of the displacement). Results showed reflected optical power variations and wavelength shift following the application of displacement and force. The sensitivities of both wavelength shift and optical power were different (and non-proportional) when displacement and force were compared. However, a higher correlation, determination coefficient (R2) of 0.998, was obtained in the analysis of the wavelength shift as a function of the displacement, which indicated that the strain transmission in the optical fiber is directly related to the strain in the diaphragm, whereas the force has an indirect relation with the strain and depends on the material features. Then, the possibility of simultaneous estimation of force and displacement was investigated, where the linear relation of both parameters (displacement and force) with the wavelength shift and the optical power were obtained in a limited range of displacement and force. In this range, root mean squared errors of 0.37 N and 0.05 mm were obtained for force and displacement, respectively. In addition, the force variation with a step displacement input also shows the possibility of using the proposed FBG device for the characterization of the materials’ viscoelastic features such as phase delay, creep, and stress relaxation, which can be employed for in situ characterization of different viscoelastic materials. Full article
(This article belongs to the Special Issue Recent Advances in Liquid Level Sensors)
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16 pages, 7477 KiB  
Article
A New Image Grating Sensor for Linear Displacement Measurement and Its Error Analysis
by Fang Cheng, Dongfang Zhou, Qing Yu and Tegoeh Tjahjowidodo
Sensors 2022, 22(12), 4361; https://doi.org/10.3390/s22124361 - 9 Jun 2022
Cited by 3 | Viewed by 2621
Abstract
To improve the accuracy of the current vision-based linear displacement measurement in a large range, a new type of linear displacement sensing system, namely, image grating, is proposed in this paper. The proposed system included a patterned glass plate attached to the moving [...] Read more.
To improve the accuracy of the current vision-based linear displacement measurement in a large range, a new type of linear displacement sensing system, namely, image grating, is proposed in this paper. The proposed system included a patterned glass plate attached to the moving object and an ultra-low distortion lens for high-accuracy image matching. A DFT local up-sampling phase correlation method was adopted to obtain the sub-pixel translation of the patterns onto the target plate. Multiple sets of stripe patterns with different designs were located on the glass plate to expand the measurement range, based on the principle of phase correlation. In order to improve the measurement accuracy, the main errors of the image grating system were analyzed, and the nonlinear error compensation was completed based on the dynamic calibration of the pixel equivalent. The measurement results, after the error compensation, showed that the total error of the proposed system was less than 2.5 μm in the range of 60 mm, and the repeatability was within 0.16 μm, as quantified by standard deviation. Full article
(This article belongs to the Topic Manufacturing Metrology)
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27 pages, 9566 KiB  
Review
Modern Displacement Measuring Systems Used in Geotechnical Laboratories: Advantages and Disadvantages
by Małgorzata Jastrzębska
Sensors 2021, 21(12), 4139; https://doi.org/10.3390/s21124139 - 16 Jun 2021
Cited by 5 | Viewed by 5507
Abstract
The paper presents the contemporary displacement measurement systems used in geotechnical laboratories during the determination of soil precise mechanical parameters, e.g., the shear modules G: initial and in the range of small and very small strains. In the laboratory, researchers use standard sensors [...] Read more.
The paper presents the contemporary displacement measurement systems used in geotechnical laboratories during the determination of soil precise mechanical parameters, e.g., the shear modules G: initial and in the range of small and very small strains. In the laboratory, researchers use standard sensors for measuring deformation, pressure, and force as well as modern measuring systems such as linear variable differential transformers (LVDT), proximity transducers (PT), magnetic encoder sensors with fiber Bragg grating (FBG), or methods based on laser or X-ray measurement. None of the measurements are universal and their use depends on the type of soil (cohesive, non-cohesive), its condition (loose or dense, stiff or very soft), and its characteristic properties (e.g., organic soil, swelling soil). This study points out the interesting equipment solutions and presents the guidelines for selecting appropriate methods of deformation measurement. Full article
(This article belongs to the Special Issue Sensors and Measurements in Geotechnical Engineering)
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12 pages, 2633 KiB  
Article
Phase Imbalance Optimization in Interference Linear Displacement Sensor with Surface Gratings
by Sergey Odinokov, Maria Shishova, Michael Kovalev, Alexander Zherdev and Dmitrii Lushnikov
Sensors 2020, 20(5), 1453; https://doi.org/10.3390/s20051453 - 6 Mar 2020
Cited by 7 | Viewed by 3369
Abstract
In interferential linear displacement sensors, accurate information about the position of the reading head is calculated out of a pair of quadrature (sine and cosine) signals. In double grating interference schemes, diffraction gratings combine the function of beam splitters and phase retardation devices. [...] Read more.
In interferential linear displacement sensors, accurate information about the position of the reading head is calculated out of a pair of quadrature (sine and cosine) signals. In double grating interference schemes, diffraction gratings combine the function of beam splitters and phase retardation devices. Specifically, the reference diffraction grating is located in the reading head and regulates the phase shifts in diffraction orders. Measurement diffraction grating moves along with the object and provides correspondence to the displacement coordinate. To stabilize the phase imbalance in the output quadrature signals of the sensor, we propose to calculate and optimize the parameters of these gratings, based not only on the energetic analysis, but along with phase relationships in diffraction orders. The optimization method is based on rigorous coupled-wave analysis simulation of the phase shifts of light in diffraction orders in the optical system. The phase properties of the reference diffraction grating in the interferential sensor are studied. It is confirmed that the possibility of quadrature modulation depends on parameters of static reference scale. The implemented optimization criteria are formulated in accordance with the signal generation process in the optical branch. Phase imbalance and amplification coefficients are derived from Heydemann elliptic correction and expressed through the diffraction efficiencies and phase retardations of the reference scale. The phase imbalance of the obtained quadrature signals is estimated in ellipticity correction terms depending on the uncertainties of influencing parameters. Full article
(This article belongs to the Section Optical Sensors)
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33 pages, 14144 KiB  
Review
Optical Sensors for Multi-Axis Angle and Displacement Measurement Using Grating Reflectors
by Yuki Shimizu, Hiraku Matsukuma and Wei Gao
Sensors 2019, 19(23), 5289; https://doi.org/10.3390/s19235289 - 1 Dec 2019
Cited by 45 | Viewed by 9502
Abstract
In dimensional metrology it is necessary to carry out multi-axis angle and displacement measurement for high-precision positioning. Although the state-of-the-art linear displacement sensors have sub-nanometric measurement resolution, it is not easy to suppress the increase of measurement uncertainty when being applied for multi-axis [...] Read more.
In dimensional metrology it is necessary to carry out multi-axis angle and displacement measurement for high-precision positioning. Although the state-of-the-art linear displacement sensors have sub-nanometric measurement resolution, it is not easy to suppress the increase of measurement uncertainty when being applied for multi-axis angle and displacement measurement due to the Abbe errors and the influences of sensor misalignment. In this review article, the state-of-the-art multi-axis optical sensors, such as the three-axis autocollimator, the three-axis planar encoder, and the six-degree-of-freedom planar encoder based on a planar scale grating are introduced. With the employment of grating reflectors, measurement of multi-axis translational and angular displacement can be carried out while employing a single laser beam. Fabrication methods of a large-area planar scale grating based on a single-point diamond cutting with the fast tool servo technique and the interference lithography are also presented, followed by the description of the evaluation method of the large-area planar scale grating based on the Fizeau interferometer. Full article
(This article belongs to the Special Issue Sensors for Precision Dimensional Metrology)
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22 pages, 6482 KiB  
Article
Development of a 3-PRR Precision Tracking System with Full Closed-Loop Measurement and Control
by Ling-bo Xie, Zhi-cheng Qiu and Xian-min Zhang
Sensors 2019, 19(8), 1756; https://doi.org/10.3390/s19081756 - 12 Apr 2019
Cited by 12 | Viewed by 4399
Abstract
A 3-PRR (three links with each link consisting of a prismatic pair and two rotating pairs) parallel platform was designed for application in a vacuum environment. To meet the requirement of high tracking accuracy of the 3-PRR parallel platform, a full closed-loop control [...] Read more.
A 3-PRR (three links with each link consisting of a prismatic pair and two rotating pairs) parallel platform was designed for application in a vacuum environment. To meet the requirement of high tracking accuracy of the 3-PRR parallel platform, a full closed-loop control precision tracking system with laser displacement sensors and linear grating encoders was analysed and implemented. Equally-spaced laser displacement sensors and linear grating encoders were adopted not only for measurement but also for feedback control. A feed-forward control method was applied for comparison before conducting the closed-loop feedback control experiments. The closed-loop control experiments were conducted by adopting the PI (proportion and integration) feedback control and RBF (radial basis function) neural network control algorithms. The experimental results demonstrate that the feed-forward control, PI feedback control, and RBF neural-network control algorithms all have a better control effect than that of semi-closed-loop control, which proves the validity of the designed full closed-loop control system based on the combination of laser displacement sensors and linear grating encoders. Full article
(This article belongs to the Special Issue Laser Sensors for Displacement, Distance and Position)
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11 pages, 5014 KiB  
Article
A High Precision Capacitive Linear Displacement Sensor with Time-Grating that Provides Absolute Positioning Capability Based on a Vernier-Type Structure
by Xiaokang Liu, Hui Zhang, Kai Peng, Qifu Tang and Ziran Chen
Appl. Sci. 2018, 8(12), 2419; https://doi.org/10.3390/app8122419 - 28 Nov 2018
Cited by 16 | Viewed by 7871
Abstract
Nanometer-scale measurement devices with high accuracy and absolute long-range positioning capability are increasingly demanded in the field of computer numerical control machining. To meet this demand, the present report proposes a capacitive absolute linear displacement sensor with time-grating that employs a vernier-type structure [...] Read more.
Nanometer-scale measurement devices with high accuracy and absolute long-range positioning capability are increasingly demanded in the field of computer numerical control machining. To meet this demand, the present report proposes a capacitive absolute linear displacement sensor with time-grating that employs a vernier-type structure based on a previously proposed single-row capacitive sensing structure. The novel proposed vernier-type absolute time-grating (VATG) sensor employs two capacitor rows, each with an equivalent measurement range. The first capacitor row is designed with n periods to realize fine measurement, while the second capacitor row is designed with n − 1 periods, and the phase difference between the second row and the first row is employed to obtain absolute positioning information. A prototype VATG sensor with a total measurement range of 600 mm and n = 150 is fabricated using printed circuit board manufacturing technology, and its measurement performance is evaluated experimentally. Harmonic analysis demonstrates that the measurement error mainly consists of first-harmonic error, which is mostly caused by signal crosstalk. Accordingly, an optimized prototype VATG sensor is fabricated by adding a shielding layer between the two capacitor rows and designing a differential induction structure. Experimental results demonstrate that the measurement error of the optimized prototype sensor is ±1.25 μm over the full 600 mm range and ±0.25 μm over a single 4 mm period. Full article
(This article belongs to the Special Issue Precision Dimensional Measurements)
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16 pages, 7570 KiB  
Article
Quasi-Distributed Active-Mode-Locking Laser Interrogation with Multiple Partially Reflecting Segment Sensors
by Chang Hyun Park, Gyeong Hun Kim, Suck Won Hong, Hwi Don Lee and Chang-Seok Kim
Sensors 2018, 18(12), 4128; https://doi.org/10.3390/s18124128 - 25 Nov 2018
Viewed by 3043
Abstract
A new type of quasi-distributed sensor system is implemented using an active mode locking (AML) laser cavity with multiple partially reflecting segments. The mode locking frequency of the AML laser is linearly proportional to the overall lasing cavity length. To implement multiple resonators [...] Read more.
A new type of quasi-distributed sensor system is implemented using an active mode locking (AML) laser cavity with multiple partially reflecting segments. The mode locking frequency of the AML laser is linearly proportional to the overall lasing cavity length. To implement multiple resonators having multiple reflection points installed in a sensing fiber, two types of partial reflectors (PRs) are implemented for an in-line configuration, one with fiber Bragg grating and the other with a fiber Fabry–Perot interferometer. Since the laser has oscillated only when the modulation frequencies for the mode locking frequency match with the corresponding resonator lengths, it is possible to read the multiple partially reflecting segments along the sensing fiber. The difference between two corresponding mode locking frequencies is changing proportionally with the segment length variation between two PRs upon strain application. The segment length change caused by the applied strain can be successfully measured with a linear sensitivity between mode locking frequency and displacement, linearity over 0.99, and spatial position resolution below meter order. Full article
(This article belongs to the Section Physical Sensors)
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14 pages, 4589 KiB  
Article
Alignment Method for Linear-Scale Projection Lithography Based on CCD Image Analysis
by Dongxu Ren, Zexiang Zhao, Jianpu Xi, Bin Li, Zhengfeng Li, Huiying Zhao, Lujun Cui and Hang Xu
Sensors 2018, 18(8), 2442; https://doi.org/10.3390/s18082442 - 27 Jul 2018
Cited by 3 | Viewed by 5178
Abstract
This paper presents a method to improve the alignment accuracy of a mask in linear scale projection lithography, in which the adjacent pixel gray square variance method is applied to a charge-coupled device (CCD) image to obtain the best position of the focal [...] Read more.
This paper presents a method to improve the alignment accuracy of a mask in linear scale projection lithography, in which the adjacent pixel gray square variance method is applied to a charge-coupled device (CCD) image to obtain the best position of the focal length of the motherboard and then realize the alignment of the focal plane. Two image positions in the focal plane of the CCD are compared with the traits overlap according to the image splicing principle, and four typical errors are corrected on the basis of the total grating errors. Simultaneously, the rotation error of the mask is used to summarize the grayscale variation function of the CCD image. Threshold functions are employed to express the factors including the wave crests of the amplitude, period error, and phase error, which govern the rotation accuracy and weight alignment accuracy expression of the established four error factors. Finally, in the experiment, the slope of the mask is corrected and adjusted to the same direction as the slide plate with the assistance of a dual-frequency laser interferometer. The effect of the alignment error on the lithography accuracy is discussed and verified in the static case, and it is found that the CCD maximum resolution pixel is 0.1 μm and accuracy of the scale is 0.79 μm in only a 200-mm-measurement range. Full article
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