偏振双向衰减对光学成像系统像质影响的矢量平面波谱理论分析

Analysis of the influence of diattenuation on optical imaging system by using the theory of vector plane wave spectrum

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/λ),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/λ<v<0.8NA/λ),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/λ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 electroabsorption 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/A）.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/λ,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 √Dα should range respectively from 0.63 to 1.6（0.2NA/λ 〈v 〈0.8NA/λ） and from 0.9 to1.11（v 〉0.8NA/λ） 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 θn between the normal of optical interface n and the optical axis of imaging system z.If a polarization beam splitter is considered,√Dα→∞,θn/sin^-1 NA should be greater than 1-3.