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研究生:李鴻儒
研究生(外文):Hong-ru Li
論文名稱:利用Slanted-edge方法以及相位回復演算法量測光學系統的成像像差
論文名稱(外文):To measure the aberrations of optical system by Slanted-edge method and Phase retrieval algorithm
指導教授:梁肇文
指導教授(外文):Chao-wen Liang
學位類別:碩士
校院名稱:國立中央大學
系所名稱:光電科學與工程學系
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2014
畢業學年度:102
語文別:中文
論文頁數:128
中文關鍵詞:相位回復演算法成像像差
外文關鍵詞:Phase retrieval algorithmSlanted-edge methodLSFPSFMTF
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  • 被引用被引用:1
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本論文從傅氏光學來分析光學系統的相位函數,也就是成像像差。首先利用Slanted edge量測方法,並加以改進量測方法使得所獲取的量測資訊能夠更不受雜訊的影響。因為量測方法所得到的資訊就是線擴散函數(Line Spread Function,以下簡稱LSF)或者是點擴散函數(Point Spread Function,以下簡稱PSF),此兩函數在傅氏光學中對於透鏡的成像分析扮演著很重要的角色。在傅氏光學中光瞳函數(Pupil function)與剛剛所提到的LSF與PSF為傅立葉轉換的關係,因為存在著傅立葉轉換的關係,所以可以藉由相位回復演算法進行迭代運算出LSF和PSF所代表的相位函數,而此相位函數也代表著光學系統的成像像差。因此藉由改進後的Slanted edge量測方法以及相位回復演算法可以得到光學系統的成像像差。
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 I
ABSTRACT II
致謝 III
目錄 IV
圖目錄 VII
表目錄 X
第一章 緒論 1
1-1 研究動機 1
1-2 文獻回顧 1
第二章 基本原理 4
2-1 薄透鏡相位變化函數 4
2-2 薄透鏡的傅立葉轉換 7
2-3 光學成像系統的頻率響應分析 11
2-4 相位回復演算法 15
2-5 Slanted edge 量測法 17
2-6 Radon轉換以及Projection-slice理論 20
2-7 傅立葉轉換的單位分析 22
2-8 Zernike多項式與Seidel多項式之間的關係討論 23
第三章 實驗模擬 25
3-1 傅立葉轉換模擬以及Radon轉換模擬 25
3-1-1 傅立葉轉換模擬 25
3-1-2 Radon轉換模擬 26
3-2 二維相位回復演算法模擬 27
3-2-1 Error-reduction演算法 28
3-2-2 Hybrid input-output演算法 32
3-2-3 離軸像差Hybrid input-output演算法的模擬 37
3-3 一維相位回復演算法模擬 42
3-3-1 Error reduction演算法 43
3-3-2 Hybrid input-output演算法 45
3-3-3 非唯一性探討 49
第四章 實驗數據分析 52
4-1 Slanted edge量測實驗 52
4-1-1 實驗裝置 52
4-1-2 Slanted edge圖樣 53
4-1-3 Slanted line圖樣 57
4-2 Thorlabs LA1608鏡片的LSF量測 63
4-2-1 實驗裝置 63
4-2-2 Slanted line圖樣 65
4-2-3 Non-slanted line圖樣 68
4-2-4 相位回復演算法的分析 71
4-3 PSF量測及其相位回復演算法的分析 82
4-3-1 LA1608以及LA1433軸上PSF量測 82
4-3-2 LA1433軸上的相位回復演算法分析 87
4-3-3 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 109
5-1 實驗結論 109
5-2 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.
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[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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