optical surfaces
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Optical surfaces are required to have high form accuracy and smoothness. The form accuracy must be below 50 nm. Form accuracy is currently on the order of several tens of nanometers or less; however, further improvement is required. To improve form accuracy, compensation grinding is performed based on form measurement results. However, when the form error is small, a small periodical waviness occurs on the ground surface, which is known as nano-topography. This waviness cannot be compensated for using conventional compensation methods because the nano-topography distributions are not reproducible. A previous study showed that grinding conditions affect the spatial frequency of nano-topography. Therefore, in this study, optimum grinding conditions are estimated from the view point of nano-topography distributions, and the grinding conditions are compensated to optimize these distributions.

In this paper, we demonstrate the use of the modified phase retrieval as a method for application in the measurement of small-slope free-form optical surfaces. This technique is a solution for the measurement of small-slope free-form optical surfaces, based on the modified phase retrieval algorithm, whose essence is that only two defocused images are needed to estimate the wave front with an accuracy similar to that of the traditional phase retrieval but with less image capturing and computation time. An experimental arrangement used to measure the small-slope free-form optical surfaces using the modified phase retrieval is described. The results of these experiments demonstrate that the modified phase retrieval method can achieve measurements comparable to those of the standard interferometer.

In digital holography recording as reconstruction of holograms are performed digitally by modern photonic devices to increase of optical non-contacting measurements of various kinds of surfaces including both specular and rough surfaces. In this article we discusses these features of digital holography using phase shifting techniques that has much extended its capabilities. Full Text: PDF ReferencesG. Bruning, D.R. Herriott, J.E. Gallagher, D.P. Rosenfeld, A.D. White, D.J. Brangaccio, "Digital Wavefront Measuring Interferometer for Testing Optical Surfaces and Lenses", Appl. Opt. 13, 2693 (1974). CrossRef I. Yamaguchi, T. Zhang, "Phase-shifting digital holography", Opt. Lett. 22, 1268 (1997). CrossRef F. Zhang, I. Yamaguchi, L.P. Yaroslavsky, "Algorithm for reconstruction of digital holograms with adjustable magnification", Opt. Lett. 29, 1668 (2004). CrossRef I. Yamaguchi, "Holography, speckle, and computers", Optics and Lasers in Engineering 39, 411 (2003). CrossRef I. Yamaguchi, M. Yokota, "Speckle noise suppression in measurement by phase-shifting digital holography", Opt. Eng. 48 085602 (2009). CrossRef I. Yamaguchi, J. Kato, S. Ohta, "Surface Shape Measurement by Phase-Shifting Digital Holography", Opt. Rev. 8, 85 (2001). CrossRef I. Yamaguchi, J. Kato, H. Matsuzaki, "Measurement of surface shape and deformation by phase-shifting image digital holography", Opt. Eng. 42, 1267 (2003). CrossRef F. Zhang, J.D.R. Valera, I. Yamaguchi, M. Yokota, G. Mills, "Vibration Analysis by Phase Shifting Digital Holography", Opt. Rev. 11, 5 (2004). CrossRef

The metrology of membrane structures, especially inflatable, curved, optical surfaces, remains challenging. Internal pressure, mechanical membrane properties, and circumferential boundary conditions imbue highly dynamic slopes to the final optic surface. Here, we present our method and experimental results for measuring a 1 m inflatable reflector’s shape response to dynamic perturbations in a thermal vacuum chamber. Our method uses phase-measuring deflectometry to track shape change in response to pressure change, thermal gradient, and controlled puncture. We use an initial measurement as a virtual null reference, allowing us to compare 500 mm of measurable aperture of the concave f/2, 1-meter diameter inflatable optic. We built a custom deflectometer that attaches to the TVAC window to make full use of its clear aperture, with kinematic references behind the test article for calibration. Our method produces 500 × 500 pixel resolution 3D surface maps with a repeatability of 150 nm RMS within a cryogenic vacuum environment (T = 140 K, P = 0.11 Pa).

Background: The equations of Monge–Ampère type which arise in geometric optics is used to design illumination lenses and mirrors. The optical design problem can be formulated as an inverse problem: determine an optical system consisting of reflector and/or refractor that converts a given light distribution of the source into a desired target light distribution. For two decades, the development of fast and reliable numerical design algorithms for the calculation of freeform surfaces for irradiance control in the geometrical optics limit is of great interest in current research. Objective: The objective of this paper is to summarize the types, algorithms and applications of Monge–Ampère equations. It helps scholars to grasp the research status of Monge–Ampère equations better and to explore the theory of Monge–Ampère equations further. Methods: This paper reviews the theory and applications of Monge–Ampère equations from four aspects. We first discuss the concept and development of Monge–Ampère equations. Then we derive two different cases of Monge–Ampère equations. We also list the numerical methods of Monge–Ampère equation in actual scenes. Finally, the paper gives a brief summary and an expectation. Results: The paper gives a brief introduction to the relevant papers and patents of the numerical solution of Monge–Ampère equations. There are quite a lot of literatures on the theoretical proofs and numerical calculations of Monge–Ampère equations. Conclusion: Monge–Ampère equation has been widely applied in geometric optics field since the predetermined energy distribution and the boundary condition creation can be well satisfied. Although the freeform surfaces designing by the Monge–Ampère equations is developing rapidly, there are still plenty of rooms for development in the design of the algorithms.