正弦型中频面形误差对光学传递函数的影响  

Effects of sinusoidal mid-spatial frequency surface errors on optical transfer function

作　　者：陈建军 王琳琳[1] 霍立民 匡翠方 毛磊[3] 郑驰 尹禄 CHEN Jian-jun;WANG Lin-lin;HUO Li-min;KUANG Cui-fang;MAO Lei;ZHENG Chi;YIN Lu(Qingdao University of Technology,Qingdao 266520,China;Zhejiang University,Hangzhou 310058,China;Ningbo Yongxin Optics Co.,Ltd.,Ningbo 315040,China;China Jiliang University,Hangzhou 310018,China)

机构地区：[1]青岛理工大学,山东青岛266520 [2]浙江大学,浙江杭州310058 [3]宁波永新光学股份有限公司,浙江宁波315040 [4]中国计量大学,浙江杭州310018

出　　处：《中国光学（中英文）》2024年第4期725-732,共8页Chinese Optics

基　　金：国家自然科学基金(No.62305320);山东省自然科学基金(No.ZR2021QF113,No.ZR2021MF081);山东省高等学校优秀青年创新团队(No.2022KJ162)。

摘　　要：中频面形误差(MSFSE)会导致光学系统发生小角度散射,影响系统性能。为了在光学设计和光学加工中制定合理的中频面形误差公差,就中频面形误差对光学系统调制传递函数(MTF)的影响进行了量化研究。在衍射受限条件下,推导出正弦型中频面形误差对光学系统MTF的影响的表达式并对其进行分析,然后通过光学设计软件仿真验证理论推导结果。假设光学系统光瞳上带有正弦型中频面形误差,对光瞳函数进行傅立叶变换,然后平方得到点扩散函数(PSF),再对PSF进行傅立叶变换得到光学系统的光学传递函数(OTF),对OTF取模,即可得到中频误差影响下的MTF表达式。将该式与衍射受限条件下无中频误差的光学系统MTF进行对比,得到中频误差对光学系统MTF的量化影响。理论计算结果表明:正弦型中频误差会使光学系统的MTF在不同空间频率处产生不同的损失,损失值随空间频率呈周期性变化;峰谷值(PV)分别为0.030μm、0.095μm、0.159μm和0.223μm的中频面形误差,导致的光学系统MTF的最大损失比例分别为0.89%、8.80%、23.48%和43.31%;随着中频误差PV的增加,MTF的损失值呈非线性快速增加。软件仿真结果与理论计算结果吻合。Mid-spatial frequency surface errors(MSFSE)can cause small angle scattering in optical systems.In order to determine a reasonable tolerance for MSFSE in optical design and processing,this paper conducts a quantitative study on the impact of MSFSE on the modulation transfer function(MTF)of optical systems.Under diffraction-limited conditions,we derived an expression for the influence of MSFSE on the MTF of optical systems and analyzed it.Then,we verified the theoretical derivation results through optical design software simulation.Assuming that the optical system has a sinusoidal MSFSE on the pupil,we performed the Fourier transform on the pupil function and squared it to obtain the point spread function(PSF),and then performed the Fourier transform on the PSF to obtain the optical transfer function(OTF)of the optical sys-tem.By taking the OTF mode,the expression of MTF under the influence of MSFSE can be obtained.By comparing this expression of MTF with the MTF of an optical system without MSFSE under diffraction-lim-ited conditions,the quantitative impact of MSFSE on the MTF of the optical system can be obtained.Theor-etical calculation results indicate that sinusoidal MSFSE can lead to different losses of MTF at different spatial frequencies and that the changes in MTF losses are periodic.The maximum loss ratios of MTF in op-tical systems caused by sinusoidal MSFSE with peak-to-valley(PV)of 0.030μm,0.095μm,0.159μm and 0.223μm are 0.89%,8.80%,23.48%and 43.31%,respectively.The loss of MTF will increase nonlinearly with the increase of PV of MSFSE.The theoretical calculation results are consistent with the software simu-lation results.

关 键 词：中频面形误差 光学传递函数 自由曲面 光学加工 光学设计 

分 类 号：TH741[机械工程—光学工程]