离轴非球面干涉测量中标记点最优排布求解与畸变误差校正方法(特邀)  

Solution for Optimal Arrangement of Marking Points and Method of Distortion Correction in Off-Axis Aspheric Interferometry(Invited)

作　　者：闫烁 万嵩林 李瀚捷 韩宜池 牛振岐 吴珍 路晴 江国昌 沈鹏程 魏朝阳[1] Yan Shuo;Wan Songlin;Li Hanjie;Han Yichi;Niu Zhenqi;Wu Zhen;Lu Qing;Jiang Guochang;Shen Pengcheng;Wei Chaoyang(High Power Laser Element Technology and Engineering Department,Shanghai Institute of Optics and Fine Mechanics,Chinese Academy of Sciences,Shanghai 201800,China)

机构地区：[1]中国科学院上海光学精密机械研究所高功率激光元件技术与工程部,上海201800

出　　处：《光学学报(网络版)》2024年第3期33-42,共10页Acta Optica Sinica(Online)

基　　金：国家重点研发计划(2022YFB3403403);国家自然科学基金青年科学基金项目(62205352,62305356,62305351);上海市自然科学基金(21ZR1472000,22YF1454800);中国科学院青年创新促进会项目(2022246)

摘　　要：为了在有限标记点数量下实现更高精度的畸变校正,提出一种基于泽尼克多项式的标记点最优排布求解与逆向拟合畸变校正方法。校正过程不直接依据测量结果中标记点位置误差拟合得到的畸变分布,而是先基于标记点在元件真实位置下的畸变误差进行拟合,再逆向求解恢复畸变分布,可有效避免畸变引入的高阶误差;同时,建立基于矩阵条件数最小化的标记点分布求解算法,得到以泽尼克多项式为基函数的标记点最优排布坐标。在更少的标记点数量需求下,所提方法的校正精度相比传统方法提升了7倍以上。该方法成功应用于有效口径为150 mm双曲率椭球镜(非球面度为8.86 mm,最大畸变量为79 mm)的检测及加工过程中,平均校正精度可达0.252 mm,最终面形精度(RMS)达到0.029λ,有力支撑了相关重要元件的制造。To achieve higher accuracy in distortion correction with a limited number of marking points,we propose a method for optimal arrangement of marking points and reverse fitting distortion correction based on Zernike polynomials.In this method,we do not directly obtain the distortion distribution by fitting the position errors of marking points in the measurement results.Instead,we first fit the distortion errors based on the true positions of the components and then recover the distortion distribution through a reverse solution,which effectively avoids high-order errors introduced by the distortion itself.Additionally,we establish an algorithm for solving the marking point distribution by minimizing the matrix condition number and obtain the optimal arrangement coordinates for marking points based on Zernike polynomials.Compared with traditional methods,our proposed method improves the correction accuracy by more than 7 times with fewer marking points.This method has been successfully applied in the testing and processing of aΦ150 mm doublecurvature elliptical mirror(asphericity of 8.86 mm,maximum distortion of 79 mm),achieving an average correction accuracy of 0.252 mm.The final surface accuracy,represented by the root mean square(RMS)error,reaches 0.029λ,which strongly supports the manufacturing of important optical components.

关 键 词：干涉检测 畸变校正 条件数 泽尼克多项式 

分 类 号：O436.1[机械工程—光学工程]