刻线误差与面型误差对平面光栅光谱性能影响的二维快速傅里叶变换分析方法

李晓天; 巴音贺希格; 齐向东; 于海利; 唐玉国

doi:doi:10.3788/aos201232.1105001

光学学报, 2012, 32 (11): 1105001, 网络出版: 2012-08-17

刻线误差与面型误差对平面光栅光谱性能影响的二维快速傅里叶变换分析方法

Two-Dimensional Fast Fourier Transform Method of Analyzing the Influence of Plane Grating′s Line Error and Surface Error on Grating′s Spectral Performance

论文大纲

李晓天 ^1,2,*巴音贺希格 ¹齐向东 ¹于海利 ¹唐玉国 ¹

作者单位

¹ 中国科学院长春光学精密机械与物理研究所, 吉林长春 130033

² 中国科学院研究生院, 北京 100049

光栅快速傅里叶变换衍射波前光栅指标光栅刻线误差 gratings fast Fourier transform diffraction wavefront grating specification grating line error

摘要

光栅刻线误差与基底面型误差影响平面光栅衍射波前、分辨本领、鬼线、卫线及杂散光等光谱性能，研究光栅性能指标与光栅刻线误差及基底加工误差之间的因果关系，对提高光栅质量极为重要。根据光栅衍射中产生的源于刻线误差与面型误差的光程差，推导出了在光栅锥面衍射情况下的光栅刻线误差、基底面型误差、入射角θ、衍射级次m与衍射波前关系的数学表达式，得到构建非理想光栅衍射波前的理论模型。以理论模型为依据，采用干涉仪测量光栅对称级次衍射波前，实现在测量结果中对光栅刻线误差与基底面型误差的分离，并基于二维快速傅里叶变换分析光栅衍射波前，考察了刻线误差与面型误差对光栅性能指标的影响。借助此方法通过重构的光栅衍射波前，分析光栅分辨本领、鬼线等光谱性能，还可以反演光栅全表面刻线误差与面型误差的大小，为光栅基底加工、光栅制造和使用技术提供理论依据。

Abstract

Plane grating′s line error and surface error of substrate influence grating′s spectral performance, such as diffraction wavefronts, resolving power, ghost lines, satellites, scattered light etc. It is extremely important to study the relationship among grating performance, line error and substrate′s surface error. According to optical path difference caused by grating′s line error and surface error, math equations, which contain the relationship among line error, surface error, angle of incidence θ, diffraction order m and diffraction wavefront under condition of cone diffraction, are deduced and mathematical model of reconstructing the diffraction wavefronts of non-ideal grating is acquired. Based on above model, grating′s diffraction wavefronts of symmetric orders are measured by interferometer and the separation of grating line error and surface error of substrate are realized from measured results. Grating′s diffraction wavefronts are analyzed by two-dimensional fast Fourier transform method and the influence of grating line error and surface error on grating performance is discussed. With the aid of aforesaid method, grating′s resolving power, ghost lines, satellites, scattered light can be analyzed by reconstructing grating′s diffraction wavefront, and grating′s line error and surface error on the whole surface of grating can be deduced, both of which can provide a theoretical basis for grating′s substrate processing, grating manufacture and application.

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李晓天, 巴音贺希格, 齐向东, 于海利, 唐玉国. 刻线误差与面型误差对平面光栅光谱性能影响的二维快速傅里叶变换分析方法[J]. 光学学报, 2012, 32(11): 1105001. Li Xiaotian, Bayanheshig, Qi Xiangdong, Yu Haili, Tang Yuguo. Two-Dimensional Fast Fourier Transform Method of Analyzing the Influence of Plane Grating′s Line Error and Surface Error on Grating′s Spectral Performance[J]. Acta Optica Sinica, 2012, 32(11): 1105001.

刻线误差与面型误差对平面光栅光谱性能影响的二维快速傅里叶变换分析方法

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