Determining the Refractive Index Distribution of an Optical Component Using Transmission Deflectometry with Liquids Shin, Sanghoon; Yu, Younghun;
Phase-measuring deflectometry is a full-field gradient measuring technique that lends itself very well to testing specular optical surfaces. We have measured the deformation of the surface of a lens by transmission deflectometry with liquids. In this study, a method is proposed for measuring the refractive index distribution of a transparent object component. The proposed method combines transmission deflectometry with liquids. The deformed fringe patterns of a sample immersed in different fluids are recorded, and then the three-dimensional phase information of the sample is reconstructed numerically. We have used phase-shifting and temporal phase-unwrapping methods to retrieve the phase from the measured deformed fringe pattern, and we have used a least-squares method to find the height information of the specular surface from the calculated slope. In particular, we have proposed a theoretical model for determining the refractive index of sample and planar convex lens are demonstrated experimentally.
A Study of Three-Dimensional Measurement By Transmission Deflectometry and Hilbert Transform, Korean Journal of Optics and Photonics, 2016, 27, 2, 61
S. Baumer, Handbook of Plastic Optics (Wiley-VCH Verlag GmBH, New York, 2005).
S. Baumer, L. Shulepova, J. Willemse, and K. Renkmena, "Integral optical system design of injection molded optics," Proc. SPIE 5173, 38 (2003).
W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. Dasari, and M. S. Feld, "Tomographic phase microscopy," Nature Methods 4, 717-719 (2007).
Y. Sung, W. Choi, C. Fang-Yen, K. Badizadegan, R. Dasari, and M. S. Feld, "Optical diffraction tomography for high resolution live cell imaging," Opt. Express 17, 266-277 (2009).
K. M. Yassien, "Comparative study on determining the refractive index profile of polypropylene fibres using fast Fourier transform and phase-shifting interferometry," J. Opt. A: Pure Appl. Opt. 11, 075701 (2009).
S. D. Nicola, P. Ferraro, A. Finizo, G. Pesce, and G. Pierattini, "Reflective grating interferometer for measuring the refractive index of transparent materials," Opt. Commun. 118, 491-494 (1995).
C. Y. Han, Z. Y. Lee, and Y. F. Chao, "Determining thickness of films on a curved substrate by use of ellipsometric measurements," Appl. Opt. 48, 3139-3143 (2009).
Y. F. Chao and K. Y. Lee, "Index profile of radial gradient index lens measured by imaging ellipsometric technique," Jpn. J. Appl. Phys. 44, 1111-1114 (2005).
M. C. Knauer, J. Kaminski, and G. Häusler, "Phase measuring deflectometry: A new approach to measure specular free-form surfaces," Proc. SPIE 5457, 366-376 (2004).
J. Horbach and T. Dang, "3D reconstruction of specular surfaces using a calibrated projector-camera setup," Mach. Vis. Appl. 21, 331-340 (2010).
Y. Tang, X. Su, Y. Liu, and H. Jing, "3D shape measurement of the aspheric mirror by advanced phase measuring deflectometry," Opt. Express 16, 15090-15096 (2008).
G. Hausler, C. Richter, K. H. Leitz, and M. C. Knauer, "Micro deflectometry a novel tool to acquire 3D micro topography with nanometer height resolution," J. Opt. Lett. 33, 396-398 (2008).
C. Quan, C. J. Tay, X. Kang, X. Y. He, H. M. Shang, "Shape measurement by use of liquid-crystal display fringe projection with two-step phase shifting," Appl. Opt. 42, 2329-2335 (2003).
M. Takeda and K. Mutoh, "Fourier transform profilometry for the automatic measurement of 3-D object shapes," Appl. Opt. 22, 3977-3982 (1983).
J. M. Huntley and H. O. Saldner, "Temporal phase unwrapping algorithm for automated interferogram analysis," Appl. Opt. 32, 3047-3052 (1993).
J. M. Huntley and H. O. Saldner, "Error reduction methods for shape measurement by temporal phase unwrapping," J. Opt. Soc. Am. A 14, 3188-3196 (1997).
J. Tian, X. Peng, and X. Zhao, "A generalized temporal phase unwrapping algorithm for three-dimensional profilometry," Optics and Lasers in Engineering 46, 336-342 (2008).
D. L. Fried, "Least-square fitting a wave-front distortion estimate to an array of phase-difference measurements," J. Opt. Soc. Am. 67, 370-375 (1977).
W. H. Southwell, "Wave-front estimation from wave-front slope measurements," J. Opt. Soc. Am. 70, 998-1006 (1980).
L. Huang and A. Asundi, "Improvement of least-squares integration method with iterative compensations in fringe reflectometry," Appl. Opt. 51, 7459-7465 (2012).
B. Rappaz, P. Marquet, E. Cuche, Y. Emery, C. Depeursinge, and P. J. Magistretti, "Measurement of the integral refractive index and dynamic cell morphometry of living cells with digital holographic microscopy," Opt. Express 13, 9361-9373 (2005).
L. A. Gerasimova, "Interferometric measurement of the refractive-index gradient distribution in gradient-index optical blanks," Appl. Opt. 35, 2997-3001 (1996).