可实现误差估计的移相量计算方法  

Phase shift extraction algorithm with error estimation in phase-shifting interferometry

作　　者：刘乾[1] 袁道成[1,2] 何建国[1] LIU Qian YUAN Dao-cheng HE Jian-guo(Institute of Machinery Manufacturing Technology, China Academy of Engineering Physics, Mianyang 621999, China School of Mechanical Engineering ,Xi＇an Jiaotong University, Xi＇ an 710049,China)

机构地区：[1]中国工程物理研究院机械制造工艺研究所,四川绵阳621999 [2]西安交通大学机械工程学院,陕西西安710049

出　　处：《光学精密工程》2016年第10期2565-2571,共7页Optics and Precision Engineering

基　　金：中国工程物理研究院超精密加工技术重点实验室基金资助项目(No.ZZ15008);能力提升课题资助项(No.2015B0405)

摘　　要：针对移相干涉仪中移相器的标定,提出了一种基于干涉图计算移相量的迭代方法。该方法分为两步:首先假设移相量已知,构建三元最小二乘方程计算位相;然后假设位相已知,构建二元最小二乘方程计算移相量,同时依据三角函数关系和遍历原则,建立估算移相量计算误差的参数。利用计算机仿真和实验验证了提出方法的有效性。计算机仿真显示:提出的方法比已有算法计算精度更高,而且误差估计值与实际计算误差偏离小于15%。在Fizeau干涉仪上开展了验证实验,利用两个电容位移传感器测量了镜架的位移。计算结果与电容传感器测量结果非常吻合,最大偏差仅为0.7nm。另外,利用本文方法得到的误差估计值为0.52nm,显示测量结果和计算结果的偏差在误差估计值范围内。所提出的方法可以高精度地提取移相量,且能给出移相量计算误差,是一种简单可靠的移相器标定方法。For calibration of the phase shifter in a phase-shifting interferometer,an iterative algorithm was proposed to extract phase shift from a set of interference patterns.In each iteration cycle,the wavefront phase and phase shifts were calculated in two individual steps.Firsly,the phase shifts were assumed knowns and the calibration wavefront phase was retrieved from tri-variate equations.Then,the wavefront phase was assumed knowns and the phase shifts were extracted from bi-variate equations.Meanwhile,an error estimator to indicate the maximum calculation error of phase shifts was established based on the basic trigonometry and ergodic principles.The proposed algorithm was verified with computer simulations and experiments.The simulation results indicate that the proposed algorithm achieves higher accuracy,lightens the calculation burden,and the deviation between the errorestimator and actual error is less than 15%.Validation experiments were carried out on a Fizeau interferometer.Two capacitive displacement sensors were employed in experiment to measure the actual phase increment.The results show that the extracted phase shifts are identical that from the proposed algorithm well and the maximum deviation is 0.7nm.Moreover,the error estimator is 0.52 nm,which covers the deviation between calculation and measurement.It concludes that the proposed algorithm achieves higher accuracy and is more advantageous on that the calculation error can be given simultaneously,showing a convenient and reliable way to calibrate the phase shift for phase-shifting interferometers.

关 键 词：移相干涉仪 移相器 标定 误差估计 迭代算法 

分 类 号：TH744.3[机械工程—光学工程]