镜片面形误差与法珀标准具性能指标的关系

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关键词：面形误差；标准具；峰谷值；法布里-珀罗

中图分类号：TH74 文献标识码：A

doi：10.37188/OPE.20253314.2166 CSTR：32169.14.OPE.20253314.2166

Relationship between mirror surface figure errors and performance metrics ofFabry-Pérot etalons

YUHan，JIANGYi

（School ofOptics and Photonics，Beijing Institute of Technology，BeijinglOoo81， China） *Correspondingauthor， E -mail：bitjy@bit.edu.cn

Abstract：Toachieve deterministic control of surface figure errors in the fabrication of Fabry-Pérot etalon mirors，this study thoroughly investigated the relationship between mirror surface figure errors and the performance of etalons.A theoretical model was established to analyze the impact of surface figure errors on the transmission spectrum of the etalon，quantitatively revealing the effects of diferent surface profiles on key performance parameters，thereby optimizing manufacturing processes and surface control parameters.The research showed that the mean value of surface figure erors had a strong linear correlation with the central wavelength shift，with a sensitivity coefficient of 1.65pm/nm thatwas theoretically derived. The peak-to-valley value of surface figure errors affected the spectral linewidth broadening and peak transmittance attenuation. Within the region where the peak-to-valley value was less than λ/40 （ 15.8nm ）， both linewidth and peak transmitance gradually converged.To validate the theoretical model，a transmission spectrum test system with picometer-level acuracy was constructed. Through qualitative validation via clear aperture testing and quantitative analysis of surface figure errors，it was determined that the surface uniformity of the central plate exerted a greater influence on etalon performance than that of the edge plates. A critical surface figure error control threshold satisfying the performance specifications was established，guiding etalon fabrication experiments. Results demonstrate that for a 30mm -diameter etalon with the peak-tovalley value controlled within 10nm ，the peak transmittance reaches 98.63% ，achieving narrowband filtering with a bandwidth of 32.8pm at the central wavelength of 532.199 nm，which approaches the theoretical design limit. These conclusions hold significant application value for manufacturing high-precision etalons with high transmittance，narrow bandwidth，and picometer-level central wavelength stability.

Key words：surface figure error;etalon;peak-to-valley value;Fabry-Pérot

1引言

法布里-珀罗（Fabry-Pérot，F-P）标准具作为一种高精度的光学干涉仪，具有高光谱分辨率、高波长选择性和灵活可调性，广泛应用于天文光谱学[1-3]、激光与量子技术[4-5]、光通信[6-7]和精密测量89等领域，在其中发挥谱线分析、选模稳频、滤波等关键作用。（剩余13890字）