# 臺灣博碩士論文加值系統

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 This thesis discusses the analysis of phase function of optical system in the field of Fourier optics and this phase function is also called the imaging aberrations. Firstly, the experiment is by means of the Slanted-edge method and then improved the method so that the measured information can be obtained free from the impact of noise. The information which is obtained from the experiment is the Line spread function or the Point spread function. These two functions play the important role in the analysis of lens in the Fourier optics. In the Fourier optics, the Fourier transform of the pupil function are the Point spread function. Because there are the Fourier transform between the pupil function and Point spread function, we can utilize the phase retrieval algorithm to carry out the phase function of the Point spread function or the Line spread function. At the beginning, the phase function is the imaging aberrations of the optical system. Therefore, the thesis can discusses the imaging aberration of the optical system by the improved Slanted edge method and the phase retrieval algorithm.
 摘要 IABSTRACT II致謝 III目錄 IV圖目錄 VII表目錄 X第一章 緒論 11-1 研究動機 11-2 文獻回顧 1第二章 基本原理 42-1 薄透鏡相位變化函數 42-2 薄透鏡的傅立葉轉換 72-3 光學成像系統的頻率響應分析 112-4 相位回復演算法 152-5 Slanted edge 量測法 172-6 Radon轉換以及Projection-slice理論 202-7 傅立葉轉換的單位分析 222-8 Zernike多項式與Seidel多項式之間的關係討論 23第三章 實驗模擬 253-1 傅立葉轉換模擬以及Radon轉換模擬 253-1-1 傅立葉轉換模擬 253-1-2 Radon轉換模擬 263-2 二維相位回復演算法模擬 273-2-1 Error-reduction演算法 283-2-2 Hybrid input-output演算法 323-2-3 離軸像差Hybrid input-output演算法的模擬 373-3 一維相位回復演算法模擬 423-3-1 Error reduction演算法 433-3-2 Hybrid input-output演算法 453-3-3 非唯一性探討 49第四章 實驗數據分析 524-1 Slanted edge量測實驗 524-1-1 實驗裝置 524-1-2 Slanted edge圖樣 534-1-3 Slanted line圖樣 574-2 Thorlabs LA1608鏡片的LSF量測 634-2-1 實驗裝置 634-2-2 Slanted line圖樣 654-2-3 Non-slanted line圖樣 684-2-4 相位回復演算法的分析 714-3 PSF量測及其相位回復演算法的分析 824-3-1 LA1608以及LA1433軸上PSF量測 824-3-2 LA1433軸上的相位回復演算法分析 874-3-3 LA1433離軸的PSF量測以及其相位回復演算法的分析 95第五章 結論與未來展望 1095-1 實驗結論 1095-2 未來展望 110第六章 參考文獻 111
 [1] D. Gabor, “A New Microscopic Principle”, Nature 161(4098), pp. 777-778, 1948.[2] W. Hoppe, “Principles of electron structure research at atomic resolution using conventional electron microscope for the measurement of amplitudes and phases”, Acta Cryst, A26, pp, 414-429, 1970.[3] H. Erickson and A. Klug, “The Fourier transform of an electron micrograph: effect of defocusing and aberrations, and implications for the use of underfocus contrast enhancement”, Beritchte der Bunsen-Gesellschaft, 74, pp. 1129-1137, 1970.[4] R. W. Gerchberg, W. O. Saxton, “A Practical Algorithm for the Determination of Phase from Image and Diffraction Plane Pictures” OPTIK, 35(2), pp. 237-246, 1972.[5] J. R. Fienup, “Phase retrieval algorithm: a comparison”, Applied O　ptics, 21(15), 1982.[6] J. R. Fienup, “Phase retrieval with continuous version of hybrid input-output”, OSA, 2003.[7] J. W, Goodman, Introduction to Fourier Optics, 2nded, Mc Graw-Hill.[8] P. D. Burns, E. Kodak Company, Rochester, NY USA, “Slanted-Edge MTF for Digital Camera and Scanner Analysis”, Proc. IS&;T 2000 PICS Conference, pp. 135-138, 2000.[9] S. E. Reichenbach, S. K. Park, R. Narayanswamy, “Characterizing digital image acquisition devices”, Opt. Eng., 30(2), pp. 170-177, February 1991.[10] M. Estribeau, P. Magnan, “Fast MTF measure of CMOS imagers using ISO 12233 slanted-edge methodology”, SPIE, 5251, 2004.[11] F. W. Marchand, “Derivation of the Point Spread Function from the Line Spread Function”, OSA, 54(7), July 1964.[12] E. W. Marchand, “From Line to Point Spread Function : The General Case”, OSA, 55(4), April 1965.[13] J. R. Fienup, “Reconstruction of an object from the modulus of its Fourier transform”, OSA, 3(1), July 1978.[14] B. Osgood, Lecture Notes for EE 261 The Fourier Transform and its Application, Electrical Engineering Department Stanford University.[15] J. C. Wyant, K. Creath, “Basic Wavefront Aberration Theory for Optical Metrology”, in Applied Optics and Optical Engineering, R. R. Shannon, J.C. Wyant, eds. (Academic, New York, 1992), 6, pp. 1-53[16] J. R. Fienup, “Phase retrieval algorithm: a personal tour [Invited]”, Applied Optics, 52(1), January 2013.[17] E. Wolf, “Is a complete determination of the energy spectrum of light possible from measurements of the degree of coherence?”, Proc. Phys. Soc. London 80, pp. 1269-1272, 1962.[18] A. Walther, “The question of phase retrieval in optics”, Opt. Acta 10, pp. 41-49, 1963.
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 1 光學成像系統之調變轉換函數理論 2 微型音圈馬達自動對焦致動器的設計與其光學性能分析 3 屋脊稜鏡量測與公差的制定

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