光学学报, 2009, 29 (1): 224, 网络出版: 2009-02-10
基于最小二乘迭代的多光束相移算法
Multiple-Beam Phase Shifting Algorithm Based on Least-Squares Iteration
测量与计量 干涉测量 最小二乘迭代 多光束干涉条纹 随机相移 measurement and metrology interferometry least-squares iteration multiple-beam interference fringe random phase shift
摘要
高阶谐波和随机相移误差是影响干涉测量精度的主要因素。为了同时解决这两问题, 提出了基于最小二乘迭代的多光束干涉条纹分析方法。该方法利用傅里叶级数将多光束干涉条纹展开为基波和各阶谐波之和。它只需要5帧随机相移的多光束干涉条纹, 即可通过最小二乘迭代准确地求得相移值和相位分布。模拟计算结果表明, 当测试面反射系数小于0.6、随机相移误差的均方根小于1时, 只需10次迭代运算即可将误差控制在0.005 (PV)和0.003(RMS)rad之下, 精度比传统的五步算法精度高。实验结果进一步验证了该算法的有效性, 并表明该算法比双光束相移算法优越。
Abstract
High-order harmonics and phase-shift miscalibration are the two main systematic error sources that affect the accuracy of interferometry. To deal with these problems simultaneously, a multiple-beam phase shifting algorithm based on least-squares iteration is proposed. The proposed algorithm decomposes multiple-beam fringes into fundamental wave and high-order harmonics by using the Fourier series expansion. Only five frames of multiple-bean interference fringes with random phase shifts are required to accurately determine the phase distribution and phase shifts. Simulations show that the proposed algorithm reaches the error less than 0.005 (peak-valley value, PV) and 0.003 rad (root-mean-square, RMS) with 10 iterations when the reflection coefficient and the RMS of random phase shifts are less than 0.6 and 1 respectively. It also shows that the proposed algorithm exhibits higher precision than the traditional five-bucket algorithm. Experiment demonstrates that the proposed algorithm is valid and superior to two-beam phase shifting algorithm.
徐建程, 陈建平, 许乔, 柴立群. 基于最小二乘迭代的多光束相移算法[J]. 光学学报, 2009, 29(1): 224. Xu Jiancheng, Chen Jianping, Xu Qiao, Chai Liqun. Multiple-Beam Phase Shifting Algorithm Based on Least-Squares Iteration[J]. Acta Optica Sinica, 2009, 29(1): 224.