Polarization aberration analysis of catadioptric anamorphic optical systems and its effect on the point spread function
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摘要:目的
变形光学系统是一种具有双平面对称性的相对特殊的光学系统，其结构引起了非旋转对称的偏振像差。本论文构建一个折反式变形光学系统，并对该系统的偏振像差及其对点扩散函数的影响进行系统分析，为后续变形光学系统的设计提供参考。
方法基于三维偏振光线追迹对折反式变形光学系统进行仿真计算，获得偏振像差的详细数据，并计算各个表面的二向衰减、相位延迟分布特性以及系统的琼斯瞳、振幅响应矩阵、点扩散函数和偏振串扰对比度。
结果最大二向衰减为0.145，最大相位延迟为1.46×10−2 rad，均出现在次镜位置。2∶1变形比的光学系统的振幅响应函数在长焦端和短焦端方向偏振串扰项存在40.6%的差异，偏振串扰对于该变形光学系统对比度限制在10−6量级。
结论高精度变形光学系统中的偏振像差不可忽略，可采用膜层设计和折反式结构等方法降低偏振像差影响。该研究结论可为变形光学系统在深空探测、相干通信系统等领域的设计提供参考。
Abstract:ObjectiveThe anamorphic optical system is a relatively special optical system with bi-planar symmetry, whose structure gives rise to non-rotationally symmetric polarization aberrations. This thesis constructs a foldback anamorphic optical system. It also systematically analyzes the polarization aberration of this system and its effect on the point spread function, with the aim of providing a reference for the design of subsequent anamorphic optical systems.
MethodSimulations of a folded-reversal anamorphic optical system based on a three-dimensional polarized light trace were performed to obtain detailed data on the polarization aberration and to compute the two-way attenuation and phase delay distribution characteristics of individual surfaces, as well as the Jones pupil, the amplitude response matrix, the point spread function, and the polarization crosstalk contrast of the system.
ResultThe maximum two-way attenuation is 0.145, and the maximum phase delay is 1.46×10−2 rad, both occurring at the secondary mirror position. The amplitude response function of the optical system with a 2∶1 anamorphic ratio has a 40.6% difference between the polarization crosstalk term in the long and short focal end directions, and the polarization crosstalk is limited by an order of magnitude of 10-6 for this anamorphic optical system contrast.
ConclusionPolarization aberration in high-precision anamorphic optical systems is not negligible. The effects of polarization aberration can be reduced by film layer design and folded-back structure. The conclusions of this study can serve as a reference for designing anamorphic optical systems in deep space exploration and coherent communication systems.
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图 1 铝反射膜 (a)rs、rp 反射系数随入射角变化曲线、(b)Φs、Φp 相位随入射角变化曲线
Figure 1. (a) Variations of amplitude reflection for rs rp with incident angle (b) Variations of phase reflection for rs rp with incident angle
图 2 增透膜 (a) ts、tp 透射系数随入射角的变化曲线、(b) Φs、Φp 相位随入射角的变化曲线
Figure 2. AR coating (a) Variations of amplitude transmission for ts tp with incident angle (b) Variations of phase transmission for ts tp with incident angle
图 8 折返式变形光学系统各个光学表面的中心二向衰减分布图。线段长度代表二向衰减值，线段方向代表最大透过率轴方向。(a) M1；(b) M2；(c) L1前表面；(d) L1后表面；(e) L2前表面；(f) L2后表面。
Figure 8. Diattenuation maps for each mirror and lens element in the designed catadioptric anamorphic optical system. (a) M1; (2) M2; (c) L1 front; (d) L1 rear; (e) L2 front; (f) L2 rear
图 9 折反式变形光学系统各个光学表面的中心视场相位延迟分布图。线段长度代表相位延迟值，线段方向代表快轴方向。(a) M1；(b) M2；(c) L1前表面；(d) L1后表面；(e) L2前表面；(f) L2后表面。
Figure 9. Retardance maps for each mirror and lens element in the designed catadioptric anamorphic optical system. (a) M1; (2) M2; (c) L1 front; (d) L1 rear; (e) L2 front; (f) L2 rear
图 5 （a）系统1，主镜与次镜间距80 mm；（b）系统2，主镜和次镜间距90 mm；（c）系统3，主镜和次镜间距100 mm。
Figure 5. (a) System1, the length of the primary and secondary mirror 80 mm; (b)the length of the primary and secondary mirror 90 mm; (c)the length of the primary and secondary mirror 100 mm.
图 6 （a）不同主镜与次镜间距长度对应的最大二向衰减；（b）不同主镜与次镜间距长度对应的最大相位延迟；
Figure 6. (a) Maximum diattenuation corresponding to the length of the primary and secondary mirror; (b) Maximum retardance corresponding to the length of the primary and secondary mirror
图 7 出瞳面零视场（a）二向衰减图；（b）相位延迟图，单位为度。
Figure 7. Exit Pupil Zero-Field (a) Diattenuation Map; (b) Retardance map, the unit is degree.
图 10 琼斯光瞳图。 Axx 、Axy、Ayx、Ayy伪色图的值表示透过率；Φxx、Φxy、Φyx、Φyy伪色图的值表示相位变化量单位为π rad。
Figure 10. Jones pupil. The values of Axx, Axy, Ayx, Ayy denote the transmittance; the values of Φxx, Φxy, Φyx, Φyy denote the phase change in units of π rad.
图 12 （a）Ixx点扩散函数；（b）Iyx点扩散函数；（c）Iyy点扩散函数；（d）Iyx点扩散函数。
Figure 12. (a) Ixx PSF; (b) Iyx PSF; (c) Iyy PSF; (d) Iyx PSF.
图 13 （a）沿着Ixx和Iyx的PSF图像对角线方向做截面。实线和虚线分别表示Ixx和Iyx。（b）沿着Iyy和Ixy的PSF图像对角线方向做截面。实线和虚线分别表示Iyy和Ixy。
Figure 13. (a)cross-sections along the diagonal direction of the PSF images for Ixx and Iyx. The solid and dashed curves show Ixx and Iyx.. (b)cross-sections along the diagonal direction of the PSF images for Iyy and Ixy. The solid and dashed curves show Iyy and Ixy.
图 14 沿着Ixy和Iyx的PSF图像对角线方向做截面，实线和虚线分别表示Ixy和Iyx。
Figure 14. cross-sections along the diagonal direction of the PSF images for Ixy and Iyx. The solid and dashed curves show Ixy and Iyx.
表 1 光学系统参数
Table 1. Parameters of optical system
参数 数值 波长/μm 0.48-0.65 F数 10 X方向视场角/(°) 1 Y方向视场角/(°) 0.5 X方向焦距/mm 1000 Y方向焦距/mm 500 X方向系统孔径/mm 50 Y方向系统孔径/mm 100 Detector array size /pixel 2160×2160 Detector array size /μm 6.61 
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