Accurate phase recovery algorithm in lateral shearing interferometry

LIU Xiao-jun; GAO Yong-sheng

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Accurate phase recovery algorithm in lateral shearing interferometry

更新时间：2020-08-12

- Accurate phase recovery algorithm in lateral shearing interferometry
- Optics and Precision Engineering Vol. 12, Issue 5, Pages: 471-479(2004)
- 作者机构：
  
  1. 香港科技大学, 机械工程系, 香港, 九龙, 清水湾
  2. 华中科技大学机械学院仪器系, 湖北, 武汉, 430074
- 作者简介：
- 基金信息：
- DOI：
  CLC： O241.2
- Received：21 July 2004，
  
  Revised：24 August 2004，
  
  Published Online：15 October 2004，
  
  Published：15 October 2004
- 稿件说明：
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刘晓军, 高咏生. 横向剪切干涉测量中准确的相位恢复算法[J]. 光学精密工程, 2004,(5): 471-479

LIU Xiao-jun, GAO Yong-sheng. Accurate phase recovery algorithm in lateral shearing interferometry[J]. Editorial Office of Optics and Precision Engineering, 2004,(5): 471-479
刘晓军, 高咏生. 横向剪切干涉测量中准确的相位恢复算法[J]. 光学精密工程, 2004,(5): 471-479 DOI：

LIU Xiao-jun, GAO Yong-sheng. Accurate phase recovery algorithm in lateral shearing interferometry[J]. Editorial Office of Optics and Precision Engineering, 2004,(5): 471-479 DOI：

摘要

提出一种剪切干涉测量中实现由相位差分准确高效恢复被测波前相位的算法.该算法是基于被测波前相位与其差分完全的点对点对应关系

及最小二乘算法原理.首先由被测波前相位与其差分完全的点对点对应关系及最小二乘原理

建立一特殊的线性等式

被测相位能通过解此等式直接获得.由于该线性等式的系数矩阵为稀疏矩阵

能转化为一新的小矩阵

以降低计算机存储空间和计算量;同时

由于该矩阵为正定矩阵

Choleski因式化分解方法能用来实现该线性等式方便的解.进行了计算机数值分析和相关试验测试

结果表明:该恢复算法可行

且计算精度高、计算复杂性低;可实现由相位差分准确恢复被测波前相位

同时具有良好的噪声误差传输特性.

Abstract

A phase recovery algorithm with improved accuracy and efficiency is proposed for test wavefront phase recovery from obtained phase differences in shearing interferometry. The algorithm is based on complete pixel by pixel mapping relationship between test phase and its differences

together with the least square principle. In the algorithm

a special linear equation set is firstly built

from which the test phase can be obtained directly by equation solving. Since the coefficient matrix of the equation is sparse

it is transferred to a small new matrix to reduce memory need and calculation amount. In the meantime

since the matrix is a positive-defined matrix

Choleski's factorzation is adopted for convenient equation solving. Reduced time cost and computer memory need and improved recovery accuracy and efficiency have been demonstrated by computational and experimental testing on the proposed algorithm and its comparison with others. Good noise suppression ability is proved by error propagation characteristic analysis.

关键词

Keywords

references

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DOUGLAS F J.Numerical methods, 2 nd edition [M] . Brooks/Cole Publishing Company, 1998.

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