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偏振双向衰减（diattenuation）是指偏振元件引入的光场传播过程中表征电矢量的两个正交偏振态的振幅变化特性. 在大部分有关偏振像差的讨论中，聚焦光场偏振态的振幅变化对其分布的影响较小而不被重视. 但在一些大相对孔径光学系统中，对于分束器、光调制器等有复杂平面介质结构的低透过率光学元件而言，引入的偏振相关的振幅调制相对大得多. 本文依据矢量平面波谱理论，建立了笛卡尔坐标系下的理想光学成像系统的矢量光学模型，验证了与德拜矢量衍射积分的一致性. 在线偏振光入射的条件下，对在汇聚光路中使用的光学元件的偏振双向衰减特性对成像质量的影响进行理论研究. 结果表明，在调制传递函数的低频率处（v 0.2NA/），这种影响是可以忽略的；随着空间频率的增加，光学元件的偏振双向衰减特性对成像系统调制传递函数的影响逐渐变大. 若要求调制传递函数的数值不低于衍射极限的90%，中频处（0.2NA/ v 0.8NA/），s光和p光的透射/反射系数之比至少需要控制在[0.63，1.6]的范围内；而当v 0.8NA/ 时，则需要控制在[0.9，1.11]的范围内. 随着光学系统光轴与光学分界面法向的倾角增加，容差范围有所放宽.In most of the researches of polarization aberration, the influence of diattenuation is not large enough to affect imaging quality evidently. However, the modulation transfer function decreases when optical elements with complex planar dielectric structures and low transmittance, such as beam-splitter and optical modulator, are introduced into an imaging system. In this paper, a vector optical model in Descartes coordinate system is proposed based on the concept of vector plane wave spectrum (VPWS). The results of calculation show that the VPWS model is consistent with Debye model. Compared with Debye vector diffraction integral, the VPWS method is more suitable to the description of the PA introduced by planar optical device with opaque mask, such as larger surface quantum-confined-stark-effect electro-absorption modulator, which is used to modulate the light collected by optical antenna of time-of-flight (TOF) depth system or modulating-retroreflector free-space-optical communication system. In order to simplify the calculation and obtain the conclusion of the change in imaging quality directly, the formula of optical transfer function is decomposed into three parts (TE component, TM component and the correlation of them) instead of polynomial expansion of pupil function. The influences of diattenuation on MTF is studied globally and locally in a range of cut-off frequency of optical imaging system (2NA/ ). Allowance of diattenuation is analysed by numerical calculation, and a mathematical expression is derived. The result shows that the change of diattenuation can be neglected when the spatial frequency v is less than 0.2NA/, and the range of allowance decreases with the increase of spatial frequency. According to numerical calculation shown in Fig.7 and the derived formulas (15) and (16), the ratios of reflection/transmission coefficient of s-light and p-light D should range respectively from 0.63 to 1.6(0.2NA/ v 0.8NA/) and from 0.9 to 1.11(v0.8NA/ ) when the MTF is required to be not less than 90% of the value in ideal diffraction-limited system. The range of allowance becomes larger gradually with the increase of angle n between the normal of optical interface n and the optical axis of imaging system z. If a polarization beam splitter is considered, D,n sin-1 NA should be greater than 1-3.
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Keywords:
- vector optics /
- polarization aberration /
- modulation transfer function
[1] Yu D Y, Dan H Y 2000 Engineering Optics (Beijing: China Machine Press) p176 (in Chinese) [郁道银, 淡恒英 2000 工程光学 (北京: 机械工业出版社) 第176页]
[2] Richards B, Wolf E 1959 Proc R. Soc. Lon. Ser. A 253 358
[3] Cooper1 I J, Royl M, Sheppard C J R 2005 Opt. Express 13 1066
[4] Lindlein N, Quabis S, Peschel U, Leuchs G 2007 Opt. Express 15 5827
[5] Pang W B, Cen Z F, Li X T, Qian W, Shang H B, Xu W C 2012 Acta Phys. Sin. 61 234202 (in Chinese) [庞武斌, 岑兆丰, 李晓彤, 钱炜, 尚红波, 徐伟才 2012 61 234202]
[6] Chipman R A 1989 Proc. SPIE 861 10
[7] Totzeck M, Graupner P, Heil T, Gohnermeier, Dittmann O, Krahmer D, Kamenov V, Ruoff J, Flagello D 2005 Proc. SPIE 5754 23
[8] Xu X R, Huang W, Xu M F 2015 Opt. Express 23 27911
[9] Xu X R, Huang W, Xu M F 2016 Opt. Express 24 4906
[10] Tu Y Y, Wang X Z, Li S K, Cao Y T 2012 Opt. Lett. 37 2061
[11] Shen L N, Li S K, Wang X Z, Yan G Y 2015 Acta Opt. Sin. 35 0611003 (in Chinese) [沈丽娜, 李思坤, 王向朝, 闫观勇 2015 光学学报 35 0611003]
[12] Li Y H, Hao X, Shi Z Y, Shuai S J, Wang L 2015 Acta Phys. Sin. 64 154214 (in Chinese) [李旸晖, 郝翔, 史召邑, 帅少杰, 王乐 2015 64 154214]
[13] Park Y H, Cho Y C, You J W, Park C Y, Yoon H S, Lee S H, Kwon J O, Lee S W 2012 Proc. SPIE 8252 82520X
[14] Park Y H, Cho Y C, You J W, Park C Y, Yoon H S, Lee S H, Kwon J O, Lee S W 2013 J. Micro Nanolithogr. MEMS MOEMS 12 023011
[15] Rabinovich W S, Goetz P G, Mahon R, Swingen L, Murphy J, Ferraro M, Burris H R, Moore C I, Suite M, Gilbreath G C, Binari S 2007 Opt. Eng. 46 104001
[16] Yamanishi M, Suemune I 1984 Jpn. J. Appl. Phys. 23 35
[17] Guo H M, Chen J B, Zhuang S L 2006 Opt. Express 14 2095
[18] Melamed T 2011 J. Opt. Soc. Am. A 28 401
[19] Wood T H 1988 J. Lightwave Technol. 6 743
[20] Kan Y, Nagai H, Yamanishi M, Suemune I 1988 IEEE J. Quantum Electron. 23 2167
[21] Goodman 1968 Introduction to Fourier Optics (New York: McGraw-Hill) p98
[22] Na B H, Ju G W, Choi H J, Cho Chul Yong, Park Y H, Park C Y, Lee Y T 2012 Opt. Express 20 19511
[23] Na B H, Ju G W, Choi H J, Cho Y C, Park Y H, Lee Y T 2012 Opt. Express 20 6003
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[1] Yu D Y, Dan H Y 2000 Engineering Optics (Beijing: China Machine Press) p176 (in Chinese) [郁道银, 淡恒英 2000 工程光学 (北京: 机械工业出版社) 第176页]
[2] Richards B, Wolf E 1959 Proc R. Soc. Lon. Ser. A 253 358
[3] Cooper1 I J, Royl M, Sheppard C J R 2005 Opt. Express 13 1066
[4] Lindlein N, Quabis S, Peschel U, Leuchs G 2007 Opt. Express 15 5827
[5] Pang W B, Cen Z F, Li X T, Qian W, Shang H B, Xu W C 2012 Acta Phys. Sin. 61 234202 (in Chinese) [庞武斌, 岑兆丰, 李晓彤, 钱炜, 尚红波, 徐伟才 2012 61 234202]
[6] Chipman R A 1989 Proc. SPIE 861 10
[7] Totzeck M, Graupner P, Heil T, Gohnermeier, Dittmann O, Krahmer D, Kamenov V, Ruoff J, Flagello D 2005 Proc. SPIE 5754 23
[8] Xu X R, Huang W, Xu M F 2015 Opt. Express 23 27911
[9] Xu X R, Huang W, Xu M F 2016 Opt. Express 24 4906
[10] Tu Y Y, Wang X Z, Li S K, Cao Y T 2012 Opt. Lett. 37 2061
[11] Shen L N, Li S K, Wang X Z, Yan G Y 2015 Acta Opt. Sin. 35 0611003 (in Chinese) [沈丽娜, 李思坤, 王向朝, 闫观勇 2015 光学学报 35 0611003]
[12] Li Y H, Hao X, Shi Z Y, Shuai S J, Wang L 2015 Acta Phys. Sin. 64 154214 (in Chinese) [李旸晖, 郝翔, 史召邑, 帅少杰, 王乐 2015 64 154214]
[13] Park Y H, Cho Y C, You J W, Park C Y, Yoon H S, Lee S H, Kwon J O, Lee S W 2012 Proc. SPIE 8252 82520X
[14] Park Y H, Cho Y C, You J W, Park C Y, Yoon H S, Lee S H, Kwon J O, Lee S W 2013 J. Micro Nanolithogr. MEMS MOEMS 12 023011
[15] Rabinovich W S, Goetz P G, Mahon R, Swingen L, Murphy J, Ferraro M, Burris H R, Moore C I, Suite M, Gilbreath G C, Binari S 2007 Opt. Eng. 46 104001
[16] Yamanishi M, Suemune I 1984 Jpn. J. Appl. Phys. 23 35
[17] Guo H M, Chen J B, Zhuang S L 2006 Opt. Express 14 2095
[18] Melamed T 2011 J. Opt. Soc. Am. A 28 401
[19] Wood T H 1988 J. Lightwave Technol. 6 743
[20] Kan Y, Nagai H, Yamanishi M, Suemune I 1988 IEEE J. Quantum Electron. 23 2167
[21] Goodman 1968 Introduction to Fourier Optics (New York: McGraw-Hill) p98
[22] Na B H, Ju G W, Choi H J, Cho Chul Yong, Park Y H, Park C Y, Lee Y T 2012 Opt. Express 20 19511
[23] Na B H, Ju G W, Choi H J, Cho Y C, Park Y H, Lee Y T 2012 Opt. Express 20 6003
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