光学精密工程2026，Vol.34Issue(9)：1400-1410,11.DOI:10.37188/OPE.20263409.1400
基于灵敏度矩阵的高阶非球面自动干涉检测
Automatic null testing of high-order aspheric surfaces based on sensitivity matrix
摘要
Abstract
High-precision interferometric testing of high-order aspheric surfaces is a critical step in ultrapre-cision optical fabrication.Conventional manual interferometric testing relies heavily on expert experience,suffers from low efficiency,and fails to meet the requirements of batch inspection.To address these limita-tions,exact five-degree-of-freedom sensitivity functions for rotationally symmetric surfaces are derived based on rigid-body kinematics and Fringe Zernike aberration theory.For high-order aspherics,Zernike projection integrals are evaluated using numerical quadrature,thereby avoiding the low-order truncation in-herent in conventional analytical approaches.The proposed model requires only sag equation parameters as input and eliminates the need for empirical calibration or complete optical system modeling.To resolve the coupling between surface figure errors and misalignment-induced aberrations that cannot be effectively separated by standard least-squares methods,a weighted least-squares inversion strategy is introduced.In this approach,weight factors are applied to dynamically regulate the contributions of critical modes,there-by suppressing the influence of inherent figure errors on pose estimation and improving overall testing accu-racy.Experimental results demonstrate that,in known-misalignment verification,correction errors for all five degrees of freedom remain within 3.5%.In unknown-misalignment verification,the conventional method fails to converge,yielding a misalignment-induced residual of RMS=0.113λ,whereas the pro-posed weighted least-squares method converges within two iterations and reduces the residual to RMS=0.004λ(λ=632.8 nm).The proposed method provides an efficient and reliable solution for batch interfer-ometric testing of high-order aspheric surfaces.关键词
非球面检测/灵敏度矩阵/加权最小二乘/自动对准Key words
aspheric testing/sensitivity matrix/weighted least-squares/automatic alignment分类
信息技术与安全科学引用本文复制引用
郭乃泉,周满,张鑫,李明茁,胡海翔,薛栋林..基于灵敏度矩阵的高阶非球面自动干涉检测[J].光学精密工程,2026,34(9):1400-1410,11.基金项目
国家自然科学基金资助项目(No.62127901,No.62305333) （No.62127901,No.62305333）
