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本文利用稳相法从本质上分析了三次相位波前编码系统的点扩散函数特性.通过分析三次相位板任意位置掩膜带和点扩散函数的关系,指出点扩散函数和稳相点的关系:两个稳相点引起点扩散函数的振荡,一个稳相点则只会造成点扩散函数的平稳变化.相位掩膜带或相位掩膜对的对称结构是同一区域内存在两个稳相点的必要条件,对称结构的不同位置对应于点扩散函数的不同部分.这种对应关系同时解释了对焦点扩散函数只存在振荡,而离焦点扩散函数却还存在平缓变化区域的本质原因,这是由离焦时光学对称轴和几何对称轴不重合引起的.本文建立了点扩散函数和对称相位掩膜对之间的对应关系,可以有效地指导相位掩膜的加工和检验.Wavefront coding system with a cubic phase mask is one of important methods to extend depth of the field. This paper analyzes the characteristics of the system based on stationary phase method in space domain. By analyzing the point spread function of an arbitrary strip of the cubic phase mask, this paper points out that two stationary phase points lead to oscillations in point spread function while one stationary phase point causes a smooth curve in point spread function. Theoretical analysis illustrates that the oscillations exist in point spread function if and only if there are symmetrical components about the optical symmetrical axis. Furthermore, different areas of the point spread function correspond to different positions of symmetrical components of the mask, which is useful in the manufacture and test of the cubic phase mask. In addition, the optical symmetrical axis does not coincide with the geometrical symmetrical axis in the defocused system, causing smooth curve in defocused point spread function. As a contrast, smooth curve can not be observed in focused point spread function because of the coincidence of the symmetrical axis and the geometrical symmetrical axis.
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Keywords:
- wavefront coding /
- cubic phase mask /
- stationary phase method
[1] Dowski E R,Cathey W T 1995 Appl.Opt.34 1859
[2] Zhao T Y,Ye Z,Zhang W Z,Yu F H 2008 Acta Phys.Sin.57 200 (in Chinese)[赵廷玉,叶子,张文字,余飞鸿 2008 57 200]
[3] Yun M J,Wan Y,KongWJ,Wang M,Liu J H,Liang W2008 Acta Phys.Sin.57 194 (in Chinese)[云茂金,万勇,孔伟金,王美,刘均海,梁伟 2008 57 194]
[4] Wang W,Zhou C H,Yu J J 2011 Acta Phys.Sin.60 024201 (in Chinese)[王伟,周常河,余俊杰 2011 60 024201]
[5] Zhao H,Li Y C 2010 Opt.Lett.35 267
[6] Zhao H,Li Y C 2010 Opt.Lett.35 2630
[7] Zhou F,Ye R,Li G W,Zhang H T,Wang D S 2009 J.Opt.Soc.Am.A 26 1889
[8] Yang Q G,Liu L R,Sun J F 2007 Opt.Commun.272 56
[9] Muyo G,Harvey A R 2005 Opt.Lett.30 2715
[10] Bagheri S,Silveria P E X,Farias D 2008 J.Opt.Am.A 25 1051
[11] Zhang W Z,Ye Z,Zhao T Y,Chen Y P,Yu F H 2007 Opt.Exp.15 1543
[12] Zhuang S L,Qian Z B 1981 Optical Transfer Function (Beijing:China Manchine Press)p276 (in Chinese)[庄松林,钱振邦 1981 光学传递函数 (北京:机械工业出版社)第276页]
[13] Born M,Wolf E 1980 Principles of Optics (Oxford:Pergamon)p747
[14] Mandel L,Wolf E 1995 Optical Coherence and Quantum Optics (Cambridge:Cambridge University Press)p128
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[1] Dowski E R,Cathey W T 1995 Appl.Opt.34 1859
[2] Zhao T Y,Ye Z,Zhang W Z,Yu F H 2008 Acta Phys.Sin.57 200 (in Chinese)[赵廷玉,叶子,张文字,余飞鸿 2008 57 200]
[3] Yun M J,Wan Y,KongWJ,Wang M,Liu J H,Liang W2008 Acta Phys.Sin.57 194 (in Chinese)[云茂金,万勇,孔伟金,王美,刘均海,梁伟 2008 57 194]
[4] Wang W,Zhou C H,Yu J J 2011 Acta Phys.Sin.60 024201 (in Chinese)[王伟,周常河,余俊杰 2011 60 024201]
[5] Zhao H,Li Y C 2010 Opt.Lett.35 267
[6] Zhao H,Li Y C 2010 Opt.Lett.35 2630
[7] Zhou F,Ye R,Li G W,Zhang H T,Wang D S 2009 J.Opt.Soc.Am.A 26 1889
[8] Yang Q G,Liu L R,Sun J F 2007 Opt.Commun.272 56
[9] Muyo G,Harvey A R 2005 Opt.Lett.30 2715
[10] Bagheri S,Silveria P E X,Farias D 2008 J.Opt.Am.A 25 1051
[11] Zhang W Z,Ye Z,Zhao T Y,Chen Y P,Yu F H 2007 Opt.Exp.15 1543
[12] Zhuang S L,Qian Z B 1981 Optical Transfer Function (Beijing:China Manchine Press)p276 (in Chinese)[庄松林,钱振邦 1981 光学传递函数 (北京:机械工业出版社)第276页]
[13] Born M,Wolf E 1980 Principles of Optics (Oxford:Pergamon)p747
[14] Mandel L,Wolf E 1995 Optical Coherence and Quantum Optics (Cambridge:Cambridge University Press)p128
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