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CHEN Jian-jun, WANG Lin-lin, HUO Li-min, KUANG Cui-fang, MAO Lei, ZHENG Chi, YIN Lu. Effects of sinusoidal mid-spatial frequency surface errors on optical transfer function[J]. Chinese Optics. doi: 10.37188/CO.2023-0229
Citation: CHEN Jian-jun, WANG Lin-lin, HUO Li-min, KUANG Cui-fang, MAO Lei, ZHENG Chi, YIN Lu. Effects of sinusoidal mid-spatial frequency surface errors on optical transfer function[J]. Chinese Optics. doi: 10.37188/CO.2023-0229

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

doi: 10.37188/CO.2023-0229
Funds:  Natural Science Foundation of Shandong Province (No. ZR2021QF113, No. ZR2021MF081); Outstanding Youth Innovation Team in Shandong Higher Education Institutions (No. 2022KJ162); National Natural Science Foundation of China (No. 62305320)
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  • Objective 

    Mid-spatial frequency surface errors (MSFSE) can cause small angle scattering in optical systems, affecting system performance. In order to determine a reasonable tolerance for MSFSE in optical design and processing, a quantitative study is conducted on the impact of MSFSE on optical transfer function (MTF) of optical systems. Under diffraction-limited conditions, we derive an expression for the influence of MSFSE on the MTF of optical systems and analyze it. Then, we verify the theoretical derivation results through optical design software simulation.


    Assuming that the optical system has a sinusoidal MSFSE on the pupil, we perform Fourier transform on the pupil function and square it to obtain the point spread function (PSF), and then perform Fourier transform on the PSF to obtain the optical transfer function (OTF) of the optical system. By taking the mode of OTF, 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-limited conditions, the quantitative impact of MSFSE on the MTF of the optical system can be obtained.


    Theoretical calculation results indicate that sinusoidal MSFSE can lead to different losses of MTF at different spatial frequencies, and the changes in MTF losses are periodic. The maximum loss ratios of MTF in optical 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 simulation results.


    The research results can provide a theoretical basis for technical personnel in optical design and processing to determine the tolerance of MSFSE of optical elements in imaging systems.


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