製作光學元件的過程當中，不管使用何種製造方法，必定需要量測經過加工後成品或半成品的元件之表面形狀。光學元件表面輪廓的檢驗及量測的方法，最常使用的光學方法，大致上可分類為雙波前的干涉方法以及在焦平面位置上橫向像差的量測方法，前者屬於波動光學領域的應用，後者則是屬於幾何光學領域的範疇。
本論文為屬於幾何光學的檢測方法，藉由梁博士最新發明的光柵-狹縫法，量取橫向像差。本實驗使用非同調光源照射液晶調制器，利用液晶調制器控制物體的亮暗程度，來達到光柵的功能，且配合十字形狀狹縫的調制，使得出瞳面上產生朗奇條紋，接著利用四步相移法，將橫向像差以數學方法計算出來，並重建波前，最後取得光學元件的表面的輪廓。
我們已經使用光柵十字狹縫法獲得待測鏡的波前及表面起伏輪廓，並經由和干涉儀量取結果做比較，發現兩者表面起伏擁有極相似的結果，驗證本實驗架構的可行性。

At a process of making the optics, no matter what manufacturing method we’ve chosen, we have to measure the surface profile of semi-finished goods or finished items. The most usual test method and measurement of optical element surface profile of optics roughly can be classified into two ways: the interferometry of two wavefronts; and the measurement of transverse ray aberration on the focal plane. The former belongs to the application of wave optics, and the latter belongs to the geometry optics.
Our dissertation belongs to the testing method of geometry optics. This experiment is by means of the grating-slit test invented by Dr. Liang to measure the transverse ray aberration. The experiment used incoherent light source to irradiate the liquid crystal modulator. And we used liquid crystal modulator to control the brightness of object and reached the function of grating. By using the cross-slit, we can get the Ronchigram on exit pupil plane. Then through four steps of phase-shifting method, we can mathematically calculate the amount of transverse ray aberration. Finally, we reconstruct the wavefront and get the information of surface profile of optics.
We already obtained the wavefront result of mirror’s surface profile by grating-cross slit method. Comparing it with the result measured by interferometry, we found the two surface profiles were very similar. By doing so, we can verify the feasibility of our experiment setup.

[1]V. Ronchi, "Forty years of history of a grating interferometer," Appl. Opt. 3, 437 (1964).
[2]B. J. Thompson, Studies in Optics, Technical Report, U.S. AFAL-TR-73-112, U.S. Government, Washington, D.C., (1973).
[3]T. Yatagai, "Fringe scanning Ronchi test for aspherical surfaces," Appl. Opt. 23, 3676 (1984).
[4]K. Omura, and T. Yatagai, "Phase measuring Ronchi test," Appl. Opt. 27, 523-528 (1988).
[5]K. Hibino, D. I. Farrant, B. K. Ward, and B. F. Oreb, "Dynamic range of Ronchi test with a phase-shifted sinusoidal grating," Appl. Opt. 36, 6178-6189 (1997).
[6]M. Mora-Gonzalez, and N. A. Ochoa, "Sinusoidal liquid crystal display grating in the Ronchi test," Optical Engineering 42, 1725-1729 (2003).
[7]C.-W. Liang, and J. Sasian, "Geometrical optics modeling of the grating-slit test," Opt. Express 15, 1738-1744 (2007).
[8]J. L. Rayces, "Exact Relation between Wave Aberration and Ray Aberration," Journal of Modern Optics 11, 85-88 (1964).
[9]D. Malacara, Optical Shop Testing (Wiley-Interscience, 1992).
[10]F. Zamkotsian, K. Dohlen, P. Lanzoni, S. P. Mazzanti, M.-L. Michel, V. Buat, and D. Burgarella, "Knife-edge test for characterization of subnanometer deformations in micro-optical surfaces," in Optical Manufacturing and Testing III(SPIE, Denver, CO, USA, 1999), pp. 328-336.
[11]A. Ho, and K. Ehrmann, "Knife-edge system for evaluating contact lenses," in Ophthalmic Technologies X(SPIE, San Jose, CA, USA, 2000), pp. 102-107.
[12]J. Zhang, R.-z. Zhang, B.-w. Cai, and P. Liu, "Research on technology of digital knife-edge test," in 2nd International Symposium on Advanced Optical Manufacturing and Testing Technologies: Optical Test and Measurement Technology and Equipment(SPIE, 2006), pp. 61500M-61505.
[13]H. B. Cheng, Y. Yam, and H. Tong, "A Quantitative Knife-edge Testing Method for Local Deformation Evaluation in Optical Aspheric Fabrication," in Automation Science and Engineering, 2007. CASE 2007. IEEE International Conference on, Y. Yam, ed. (2007), pp. 818-822.
[14]H. Jing, B. Fan, S. Wu, F. Wu, and T. Fan, "Measurement of optical surfaces with knife edge method," in 3rd International Symposium on Advanced Optical Manufacturing and Testing Technologies: Optical Test and Measurement Technology and Equipment(SPIE, 2007), pp. 67235L-67235.
[15]J. Manuel, Alberto, S. Vergara-Limon, and J. Cuautle-Cortes, "Improved Ronchi Tester," Appl. Opt. 40, 501-505 (2001).
[16]A. Cordero-Davila, J. Diaz-Anzures, and V. Cabrera-Pelaez, "Algorithm for the Simulation of Ronchigrams of Arbitrary Optical Systems and Ronchi Grids in Generalized Coordinates," Appl. Opt. 41, 3866-3873 (2002).
[17]N. A. Ochoa, M. Mora-Gonzalez, and F. Santoyo, "Flatness measurement by a grazing Ronchi test," Opt. Express 11, 2177-2182 (2003).
[18]J. Salinas, E. Luna-Aguilar, L. Salas, A. Cornejo, I. C. Torres, and V. M. Garcia, "Classical Ronchi test for piston detection," in Large Ground-based Telescopes(SPIE, Waikoloa, HI, USA, 2003), pp. 758-763.
[19]Q. Xi, L. Chen, R. Zhu, Y. Li, and X. Bai, "Fast Ronchi test base on a liquid crystal display," in Optical Design and Testing II(SPIE, Beijing, China, 2005), pp. 682-687.
[20]B. Wang, H. Chen, X. Luo, C. Yu, and Z. Liu, "Surface measurement based on chessboard-shaped 2-D Ronchi grating method," Opt. Express 13, 5308-5314 (2005).
[21]C. L. Hou, and J. Bai, "Wavefront Measurement for Long Focal Large Aperture Lens Based on Talbot Effect of Ronchi Grating," (2006), p. 1037.
[22]S. Olivier, V. Laude, and J.-P. Huignard, "Liquid-Crystal Hartmann Wave-Front Scanner," Appl. Opt. 39, 3838-3846 (2000).
[23]J.-S. Lee, H.-S. Yang, and J.-W. Hahn, "Wavefront error measurement of high-numerical-aperture optics with a Shack-Hartmann sensor and a point source," Appl. Opt. 46, 1411-1415 (2007).
[24]http://www.thorlabs.com/NewGroupPage9.cfm?ObjectGroup_ID=884.
[25]M. Dubin, "Scatter, Color Science and Projector Illumination."
[26]http://www.thorlabs.com/thorProduct.cfm?partNumber=BP145B1.
[27]http://www.edmundoptics.com/onlinecatalog/displayproduct.cfm?productID=1912.
[28]http://www.theimagingsource.com/zh_tw/resources/whitepapers/download/fwcamspecwp.zh_tw.pdf.
[29]D. C. Ghiglia, and M. D.Pritt, Two-dimensional Phase Unwrapping: Theory, Algorithms, and Software (A Wiley-Interscience publication, 1998).