Review of methods to suppress the impacts of polarization properties on optical systems
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摘要:
光学系统的偏振特性会改变入射光的偏振态，从而对成像质量、探测精度等产生影响。对于望远镜、光刻物镜等光学仪器，偏振特性是决定系统性能的重要因素之一。因此，抑制光学系统偏振特性的不利影响是实现高性能现代光学系统的关键之一。本文总结了光学系统偏振特性影响抑制方法的研究现状，并将已有方法归结为三类：偏振定标、偏振补偿和低偏振优化设计。介绍了上述三种方法的基本原理，并结合应用实例对各种方法进行了分类与讨论。最后，分析了三种方法的联系及其相互之间的协同应用，并对光学系统偏振特性影响抑制方法的未来发展进行了讨论与展望。
Abstract:The polarization properties of optical systems enable to change the polarization state of incident light, thus imaging quality and detection accuracy would be affected. For optical instruments such as telescopes and lithography lenses, polarization properties are important factors that determine the performance of these systems. Therefore, suppressing the unfavorable impacts of polarization properties on optical systems is key to achieve optical systems with good performance. This paper summarizes the current research status on methods to suppress the impacts of polarization properties on optical systems. The existing approaches are divided into three groups: polarization calibration, polarization compensation, and low polarization optimization design. The basic principles of these three methods are introduced, and the methods are classified and discussed with application examples. Finally, the relationship among the three methods and their cooperative applications is analyzed, and the future development of methods to suppress the impacts of polarization properties on optical systems is discussed.
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图 6 POSP星上定标器布局图，其中SD是太阳漫射板，SDSM是太阳漫射板稳定性监测器，DB代表黑体，SMA为扫描镜组件，LPC是线偏振定标器，NPC指非偏振定标器[37]
Figure 6. Layout diagram of the POSP onboard calibrators, where SD is the Solar Diffuser, SDSM is the Solar Diffuser Stability Monitor, DB represents the Dark Body, SMA is the Scanning Mirrors Assembly, LPC is the Linear Polarization Calibrator and NPC refers to the Non-Polarization Calibrator[37]
图 15 四点偏振定标原理示意图
Figure 15. Schematic diagram illustrating the principle of four-point polarization calibration
图 23 光刻物镜的透射图、二向衰减图、延迟图和标量相位图。(a1)-(d1)无涂层；(a2)-(d2)涂有LPC；(a3)-(d3)提高透过率的第一次优化结果；(a4)-(d4)降低透过率的第二次优化结果[100]
Figure 23. The transmission map, diattenuation map, retardance map and scalar phase map of the lithographic lens. (a1) - (d1) No coatings; (a2) - (d2) Coated with LPC; (a3) - (d3) First optimization results for improving transmittance; (a4) - (d4) Second optimization results for reducing transmittance[100]
图 24 对铝镀膜镜和带有负C板和AR膜层的铝镀膜镜进行了比较。原始未校正值用虚线表示，而校正值用实线绘制[103]
Figure 24. Comparison between an aluminum-coated mirror and an aluminum-coated mirror with a negative C-plate and AR coating. Original uncorrected values are presented with dashes lines, while corrected values are plotted with solid lines[103]
图 25 使用少量组件补偿DUV光刻系统中的相位延迟。(a)光学系统布局；(b)<011>-0°和<011>-90°方向累积延迟的相位延迟光瞳图和总延迟值[105]
Figure 25. Compensation of the phase retardation in a DUV lithographic system with small number of components. (a) Optical system layout; (b) Phase retardation pupil maps of cumulative retardation for <011>-0° and <011>-90° directions and total retardation value[105]
图 28 偏光显微镜示意图。ILLUM：照明灯；POL：线偏振片；COND：聚光镜、OBJ：物镜；SP：样本平面；RECT：偏振整流器；COMP：延迟补偿器；AN：线偏振片；IMG：中间像面[111]
Figure 28. Schematic diagram of polarizing microscope. ILLUM: illuminator; POL: linear polarizer; COND: condenser lenses; OBJ: objective lenses; SP: specimen plane; RECT: polarization rectifier; COMP: compensating retarder; AN: linear polarizer; IMG: intermediate image[111]
图 39 两层薄膜（a）和六层薄膜（b）的透射率和透射相移。实线表示两种薄膜的透射特性，虚线表示两种薄膜引起的相移[137]
Figure 39. Transmittance and phase shift on transmission for the two-layer coating (a) and the six-layer coating (b). The solid lines represent the transmission properties of the two coatings, and the dotted ones represent the phase shifts induced by the two coatings[137]
图 43 设计参数与光学指标关联图
Figure 43. Correlation diagram between design parameters and optical indexes
图 48 光学系统偏振特性影响抑制方法的联系
Figure 48. The relationship among methods for suppressing the impact of polarization properties in optical systems
图 49 三种抑制方法协同应用的流程图
Figure 49. Flow chart of collaborative application of the three suppression methods
表 1 定标光源分类
Table 1. Classification of calibration light sources
光源类型 定标光源 定标对象 人工定标光源 积分球（非偏振光） (a)起偏度[32] (b)相对透过率[21]，[23]，[25]，[28] (c)增益比[41] 积分球+偏振片 (a)偏振器件方位角[21]，[22]，[23]，[24]，[25]，[26]，[27] (b)起偏度[23]，[31] (c)二向衰减[59] (d)穆勒矩阵第一行前3个元素[62] 可调偏振度光源 (a)偏振度[48]，[49]，[50]，[51]，[54] (b)偏振器件方位角[28] (c)二向衰减[61] 积分球等人造光源+定标单元 穆勒矩阵[71]，[72]，[76]，[77]，[78]，[80]，[81]，[84] 自然景物定标光源 水云(非偏振光) (a)起偏度[33]，[34]，[35]，[36] (b)相对透过率[33]，[35]，[36] 太阳光 (a)增益比[39] (b)二向衰减[60] 海洋(水面)场景太阳耀光(强偏振光) (a)消光比[33] (b)偏振度[47]，[56]，[57]，[58] 地球反照光+（线/非）偏振定标器 消光比/增益比[37] 白天天空背景光 穆勒矩阵[70] 太阳光、非偏振标准星、太阳黑子等自然偏振源+定标单元 穆勒矩阵[64]，[65]，[66]，[67]，[68]，[69]，[74]，[75]，[79]， 
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Method Field 1
Retardation
(nm)Field 2
Retardation
(nm)Field 3
Retardation
(nm)Max
Coefficients
(nm)Time
(s)Origin 4.53 4.84 5.1 3.71 - PSO 1.95 1.85 1.96 1.87 27416.78 NLS 0.89 0.9 1.28 −1.17 64.45935
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表 3 四种偏振补偿方法的总结
Table 3. Summary of four polarization compensation methods
补偿方法 主要方案 优势 局限 结构补偿 1、交叉折轴镜结构；
2、反射元件与折射元件结合；1、基于光学结构设计，有较高的灵活性；
2、补偿效果较好；1、会改变光学系统结构；
2、方案1只能完美消除单点偏振像差；
3、方案2会产生色差；薄膜补偿 1、常规薄膜补偿设计；
2、双折射材料薄膜补偿；1、对光学系统的结构影响较小；
2、补偿效果较好；1、低偏振要求下的薄膜补偿设计难度大；
2、难以兼顾波像差、光学效率等指标；旋转补偿 旋转光学元件 1、不改变光学系统的结构；
2、补偿手段相对便捷；
3、不改变波像差、光学效率等指标；1、仅对含双折射光学元件的系统
具有较好的补偿效果；
2、最优旋转角度的计算难度大；偏振器件
补偿1、添加常规偏振补偿器件；
2、利用液晶等微纳手段进行调控；1、方案1相对便捷；
2、方案2的补偿精度高；1、容易对波像差、光学效率等指标产生影响；
2、系统的复杂性增加；
3、目前方案2的制造难度较大；
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表 4 偏振相关参数的总结
Table 4. Summary of polarization-related parameters
参数名称 定义 计算公式 备注 仪器偏振 因光学仪器导致出射光相对于入射光的偏振态变化 — — 偏振像差 光学元件/系统的偏振特性随波长、入射角和位置变化的函数 二向衰减和相位延迟是其主要表现形式，具体计算公可见下方 — 二向衰减 偏振相关的振幅变化 $D = \dfrac{{{T_{\max }} - {T_{\min }}}}{{{T_{\max }} + {T_{\min }}}}$ Tmax，Tmin分别表示最大透过率和最小透过率（最大和最小透过率对应的偏振态定义为元件的本征偏振态） 相位延迟 偏振相关的相位变化 $\delta = {\delta _{\max }} - {\delta _{\min }}$ δmax，δmin分别表示本征偏振态的相位 退偏 偏振度的随机降低，可通过退偏指数（DI）描述穆勒矩阵对入射态的退偏程度 $ DI = \dfrac{{\sqrt {\left(\displaystyle\sum\limits_{i,j} {M_{ij}^2} \right) - M_{00}^2} }}{{\sqrt 3 {M_{00}}}} $ Mij为穆勒矩阵元素 偏振串扰 由主偏振光在正交偏振方向的衍生光 — — 偏振度 以非偏振光入射时出射光的偏振化程度 $DoP = \dfrac{{\sqrt {S_1^2 + S_2^2 + S_3^2} }}{{{S_0}}} = \dfrac{{\sqrt {M_{10}^2 + M_{20}^2 + M_{30}^2} }}{{{M_{00}}}}$ Si为斯托克斯参量；Mij为穆勒矩阵元素 起偏度 光学系统产生偏振光的能力 二向衰减的一种表现形式 — 增益比 不同偏振探测通道增益系数的差异，包含了光学和电子学的综合效应 $G = \dfrac{{{I_2}}}{{{I_1}}}$ I1，I2表示不同偏振通道的探测器响应 相对透过率 描述了同一波段、不同偏振通道的光学透过率差异 $T = \dfrac{{{T_2}}}{{{T_1}}}$ T1，T2表示不同偏振通道的透过率 消光比 偏振光学元件最大透过率Tmax与最小透过率Tmin之比，是衡量偏振片性能的关键指标 $E = \dfrac{{{T_{\max }}}}{{{T_{\min }}}}$ 对于理想的偏振片E=∞ 退偏比 大气后向散射系数的垂直与平行分量之比 $\rho = \dfrac{{{\beta _ \bot }}}{{{\beta _\parallel }}}$ 适用偏振激光雷达领域
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