中国光学（中英文）2024，Vol.17Issue(4)：725-732,8.DOI:10.37188/CO.2023-0229
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
摘要
Abstract
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 0.030 μm,0.095 μm,0.159 μm and 0.223 μm 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Key words
mid-spatial frequency surface errors/optical transfer function/freeform surface/optical pro-cessing/optical Design分类
机械工程引用本文复制引用
陈建军,王琳琳,霍立民,匡翠方,毛磊,郑驰,尹禄..正弦型中频面形误差对光学传递函数的影响[J].中国光学（中英文）,2024,17(4):725-732,8.基金项目
国家自然科学基金(No.62305320) （No.62305320）
山东省自然科学基金(No.ZR2021QF113,No.ZR2021MF081) （No.ZR2021QF113,No.ZR2021MF081）
山东省高等学校优秀青年创新团队(No.2022KJ162)Supported by National Natural Science Foundation of China(No.62305320) （No.2022KJ162）
Natural Science Foundation of Shandong Province(No.ZR2021QF113,No.ZR2021MF081) （No.ZR2021QF113,No.ZR2021MF081）
Outstanding Youth Innovation Team in Shan-dong Higher Education Institutions(No.2022KJ162) （No.2022KJ162）
