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

Qian LIU; Dao-cheng YUAN; Jian-guo HE

doi:10.3788/OPE.20162410.2565

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

Information Sciences | 更新时间：2020-07-07

- Phase shift extraction algorithm with error estimation in phase-shifting interferometry
- Optics and Precision Engineering Vol. 24, Issue 10, Pages: 2565-2571(2016)
- 作者机构：
  
  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
- 作者简介：
- 基金信息：
- DOI：10.3788/OPE.20162410.2565
  CLC： TH744.3
- Received：06 May 2016，
  
  Accepted：22 June 2016，
  
  Published：2016-10
- 稿件说明：
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Qian LIU, Dao-cheng YUAN, Jian-guo HE. Phase shift extraction algorithm with error estimation in phase-shifting interferometry[J]. Optics and precision engineering, 2016, 24(10): 2565-2571.
DOI：

Qian LIU, Dao-cheng YUAN, Jian-guo HE. Phase shift extraction algorithm with error estimation in phase-shifting interferometry[J]. Optics and precision engineering, 2016, 24(10): 2565-2571. DOI： 10.3788/OPE.20162410.2565.

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0.7 nm。另外，利用本文方法得到的误差估计值为0.52 nm，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。

Abstract

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 error estimator 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 0.7 nm. 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

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references

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