基于凸壳理论圆域拟合的球面面型精度测量方法

许鑫; 王允; 王超峰; 张培杰

光学技术, 2019, 45 (4): 429, 网络出版: 2019-09-02

基于凸壳理论圆域拟合的球面面型精度测量方法

Spherical surface accuracy measurement method based on convex shell theory circular domain fitting

论文大纲

许鑫 ^*王允王超峰张培杰

作者单位

北京理工大学光电学院光学测量研究中心, 北京100081

光学测量 Zernike拟合凸壳理论最小覆盖圆 optical measurement Zernike fitting convex shell theory smallest enclosing disk random incremental method

摘要

针对干涉测量中采集到的波面数据是大量离散采样点不易寻找单位圆用于波面拟合的问题, 提出了一种凸壳理论圆域拟合的方法。方法对采集的波面数据寻找最小覆盖圆, 经归一化后以圆Zernike为基底进行波面拟合。利用Matlab仿真分析算法的性能, 对实测数据经过处理后与ZYGO测试数据进行对比分析得到面型PV值的绝对误差为0.0047λ, RMS值的绝对误差为0.0002λ。实验表明算法可对采集的大量离散波面数据进行高效准确的Zernike波面拟合, 为进一步光学元件面型像差的分析提供可靠依据。

Abstract

In order to solve the problem that a large number of discrete sampling points collected in the interferometry are not easy to find a unit circle for wavefront fitting. A method based on convex shell theory circular domain fitting is proposed. The method finds the minimum coverage circle for the acquired wavefront data, normalizes it to unit circle and perform Zernike wavefront fitting. Matlab is used to simulate the performance of the algorithm. After the measured data is processed and compared with the ZYGO test data, the absolute error of the PV value of the surface is 0.0047λ, and the absolute error of the RMS value is 0.0002λ. Experiments show that the algorithm can efficiently and accurately improve Zernike wavefront fitting on a large number of discrete wavefront data, which provides a reliable basis for the analysis of surface aberrations of optical components.

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许鑫, 王允, 王超峰, 张培杰. 基于凸壳理论圆域拟合的球面面型精度测量方法[J]. 光学技术, 2019, 45(4): 429. XU Xin, WANG Yun, WANG Chaofeng, ZHANG Peijie. Spherical surface accuracy measurement method based on convex shell theory circular domain fitting[J]. Optical Technique, 2019, 45(4): 429.

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