在光學影像中經常因為焦距不準確造成失焦，並且會使影像模糊不清，最近幾年失焦的改善逐漸被大眾所重視，本篇論文就是在探討失焦的改善與分析。

透鏡在光學影像系統中扮演著重要的角色，它可以把光聚集在一個點上，此點的距離稱為焦距，焦距是由物距和像距所決定的，光聚焦偏離焦點越遠，影像會越模糊，即稱為失焦。

一般處理失焦的方法是在失焦影像上做後製處理，在1995年由Dowski和Cathey首先提出波前編碼的理論，在透鏡前加上相位薄膜，並且強調事前處理，近年來越來越多學者在本領域發表研究。

本篇論文是在設計一個一環相位薄膜，調整相位差及半徑讓此薄膜的改善效果最佳。以往學者們研究波前編碼的目的是為了將讓不同程度的失焦得到近乎相同的光學轉移函數，本論文則是希望設計的薄膜能夠提供即時的改善效果，此想法可以做為即時影像監測的應用。

In optical imaging system, misfocus occurs because of a nonaccuate focal length. In recent years, the improvement for misfocus problem has caught much attention in researches. This thesis is aimed to explore the misfocus improvement and analysis.
Lens plays an important role in optical image system. It can focus light at one point. The distance between the focal point and the lens is called focal length. Focal length is determined by the object distance and the image distance. As light is focused farther out of the focal point, the image will blur. It is called misfocus.
The general method to improve misfocus image is done by post-processing. In 1995, wave-front coding was first proposed by Dowski and Cathey. They placed the phase mask in front of the lens, and then emphasized on the processing. In recent years, more and more researches work on this field.
In this thesis, a one ring phase mask is designed by modulating the phase difference in the ring to make the improvement better. Research before wave-front coding in order to achieve a closed optical transfer function for different degrees of misfocus, but we hope the phase mask can provide immediate improvement. This idea can be applied to real-time video monitoring.

論文審定書 i
致謝 ii
中文摘要 iii
Abstract iv
目錄 v
圖次 vii
表次 ix
第一章 引言 1
第二章 光學影像系統介紹 4
2.1 同調影像系統 4
2.2 非同調影像系統 6
2.3 同調轉移函數與光學轉移函數之間的關係 7
2.4 失焦原理 9
2.5 多重焦距下的光學轉移函數 11
第三章 波前編碼與薄膜設計 14
3.1 波前編碼 14
3.2 薄膜設計 15
3.3 遞迴型環狀薄膜 16
3.4 一環非遞迴型環狀薄膜 24
第四章 模擬結果與分析 31
4.1 以色列特拉維夫大學之研究 31
4.2 實驗室學長之研究 32
4.3 正失焦 32
4.4 負失焦 42
第五章 結論 45
參考文獻 47

[1]. E. R. Dowski, and W. T. Cathey, “Extended depth of field through wave-front coding”, Appl. Opt., Vol.34, No.11, 1859-1866, 1995
[2]. J. W. Goodman, “Introduction to Fourier Optics”, McGraw-Hill Book Co., New York, 1968
[3]. E. L. Key, E. N. Fowle, and R. D. Haggarty, ‘‘A method of dsigning signals of large time–bandwidth product,’’ IRE Int.Conv. Rec. 4, 146–155 119612.
[4]. E. N. Fowle, ‘‘The design of FM pulse compression signals,’’IEEE Trans. Inf. Theory IT-10, 61–67 119642.
[5]. M. Born and E. Wolf, Principles of Optics 1Pergamon, NewYork, 19892, App. III, pp. 747–754.
[6]. E. Ben-Eliezer, N. Konforti, B. Milgrom and E. Marom, “An optimal binary amplitude-phase mask for hybrid imaging systems that exhibit high resolution and extended depth of field”, Opt. Express, Vol.16, No.25, 20540-20561, 2008
[7]. E. Ben-Eliezer, E. Marom, N. Konforti, and Z. Zalevsky, “Radial mask for imaging systems that exhibit high resolution and extended depths of field” ,Appl. Opt. ,Vol.45, No.9, 2001-2013, 2006
[8]. A. Castro, and J. Ojeda-Castaneda, “Asymmetric phase masks for extended depth of field”, Appl. Opt., Vol.43, No.17, 3474-3479, 2004
[9]. M. Somayaji, and M. P. Christensen, “Frequency analysis of the wavefront-coding odd-symmetric quadratic phase mask”, Appl. Opt., Vol.46, No.2, 216-226, 2007
[10]. A. Castro, Y. Frauel, and B. Javidi, “Integral imaging with large depth of field using an asymmetric phase mask”, Opt. Lett., Vol.15, No.16, 10266-10273 2007
[11]. F. Zhou, G. Li, H. Zhang, and D. Wang, “Rational phase mask to extend the depth of field in optical-digital hybrid imaging systems”, Opt. Lett., Vol.34, No.3, 380-382, 2009
[12]. E. Ben-Eliezer, N. Konforti, B. Milgrom and E. Marom, “An optimal binary amplitude-phase mask for hybrid imaging systems that exhibit high resolution and extended depth of field”, Opt. Express, Vol.16, No.25, 20540-20561, 2008
[13]. S. Chen, Z. Fan, Z. Xu, B. Zuo, S. Wang, and H. Xiao, “Wavefront coding technique for controlling thermal defocus aberration in an infrared imaging system”, Opt. Lett., Vol.36, No.16, 3021-3023, 2011
[14]. H. Zhao, Y. Li, “Performance of an improved logarithmic phase mask with optimized parameters in a wavefront-coding system”, Appl. Opt., Vol.49, No.2, 229-238, 2010
[15]. M. Servin, J C Estrada,O. Medina, “Fourier transform demodulation of pixelated phase-masked interferograms”, Opt. Express, Vol.18, No.15, 16090-16095, 2010
[16]. M. Xutao, “Optimized annular phase masks to extend depth of field”, Opt. Lett., Vol. 37, No. 11, 1808-1810, 2012
[17]. T. Zhao, F. Yu, “Point spread function analysis of a cubic phase wavefront coding system with a circular pupil”, Opt. Express, Vol.37, No.11, 2408-2419, 2012
[18]. H. Lin, X. Chou, “Defocus blur parameters identification by histogram matching”, JOSA A, Vol. 29, No, 8, 1694-1706, 2012
[19]. Mahajan, N. Virendra, “Orthonormal aberration polynomials for anamorphic optical imaging systems with circular pupils”, Appl. Opt., Vol.51, No.18, 4087-4091, 2012
[20]. B. Zhang, S. Pechprasarn, J. Zhang, Somekh, G. Michael, “Confocal surface plasmon microscopy with pupil function engineering”, Opt. Express, Vol. 20, No.7, 7388-7397, 2012
[21]. A. B. Samokhin, A. N. Simonov, and M. C. Rombach, “Optical system invariant to second-order aberrations”, J. Opt. Soc. Am A,Vol.26, No.4, 977-984, 2009
[22]. W. Zhang, Z. Ye, T. Zhao, Y. Chen, and F. Yu, “Point spread function characteristics analysis of the wavefront coding system”,Opt. Express, Vol.15, No.4, 1543-1522, 2007
[23]. S. Bagheri, P. E. X. Silveira, R. Narayanswamy, and D. P. Farias, “Analytical optical solution of the extension of the depth of field using cubic-phase wavefront coding. Part I. Design and optimization of the cubic phase”, J. Opt. Soc. Am A, Vol.25, No.5, 1051-1063,2008
[24]. G. Muyo and A. R. Harvey, “Decomposition of the optical transfer function: wavefront coding imaging systems”, Opt. Express, Vol.30,No20, 2715-2717, 2005
[25]. W. T. Cathey, and E. R. Dowski, “New paradigm for imaging systems”, Appl.Opt., Vol.41, No.29, 6080-6092, 2002
[26]. C. Pan, J. Chen, R. Zhang, and S. Zhuang, “Extension ratio of depth of field by wavefront coding method”, Opt. Express, Vol.16, No.17,13364-13371, 2008
[27]. A. R. Harvey, T. Vettenburg, M. Demenikov, B. Lucotte, G. Muyo, A. Wood, N. Bustin, A. Singh, and E. Findlay, “Digital image processing as an integral component of optical design” , Proc. SPIE,Vol.7061, 706104, 2008
[28]. S. Bradburn, W. T. Cathey, and E. R. Dowski, “Realizations of focus invariance in optical–digital systems with wave-front coding”, Appl.Opt., Vol.36, No.35, 9157-9166, 1997
[29]. H. Lei, H. Feng, X. Tao, and Z. Xu, “Imaging characteristics of a wavefront coding system with off-axis aberrations”, Appl. Opt.,Vol.45, No.28, 7255-7263, 2006
[30]. E. R. Dowski, and G. E. Johnson, “Wavefront Coding: A modern method of achieving high performance and/or low cost imaging systems”, Proc. SPIE, Vol.3779, 137-145, 1999
[31]. S. Mezouari, G. Muyo, and A. R Harvey, “Amplitude and phase filters for mitigation of defocus and third-order aberrations”, Proc.SPIE, Vol.5249, 238-248, 2004
[32]. S. Mezouari, and A. R. Harvey, “Phase pupil functions for reduction of defocus and spherical aberrations”, Opt. Lett., Vol.28, No.10,771-773, 2003