应用复Morlet小波变换分析条纹图相位

张明照; 牟建华; 刘扬; 彭晓军; 王伯雄

doi:10.3788/OPE.20122003.0643

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应用复Morlet小波变换分析条纹图相位

信息科学 | 更新时间：2020-08-12

- 应用复Morlet小波变换分析条纹图相位
- Phase extraction for fringe patterns based on complex Morlet wavelet transform
- 光学精密工程 2012年20卷第3期页码：643-650
- 作者机构：
  
  1. 清华大学精密仪器与机械学系, 北京 100084
  2. 第二炮兵装备研究院北京,100085
- 作者简介：
- 基金信息：
  
  科技部中德科技合作重点项目(No. 2003DFB00028)()
- DOI：10.3788/OPE.20122003.0643
  中图分类号： TB937;TP391.4
- 收稿日期：2011-08-25，
  
  修回日期：2011-12-23，
  
  网络出版日期：2012-03-22，
  
  纸质出版日期：2012-03-22
- 稿件说明：
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张明照, 牟建华, 刘扬, 彭晓军, 王伯雄. 应用复Morlet小波变换分析条纹图相位[J]. 光学精密工程, 2012,(3): 643-650

ZHANG Ming-zhao, MOU Jian-hua, LIU Yang, PENG Xiao-jun, WANG Bo-xiong. Phase extraction for fringe patterns based on complex Morlet wavelet transform[J]. Editorial Office of Optics and Precision Engineering, 2012,(3): 643-650
张明照, 牟建华, 刘扬, 彭晓军, 王伯雄. 应用复Morlet小波变换分析条纹图相位[J]. 光学精密工程, 2012,(3): 643-650 DOI： 10.3788/OPE.20122003.0643.

ZHANG Ming-zhao, MOU Jian-hua, LIU Yang, PENG Xiao-jun, WANG Bo-xiong. Phase extraction for fringe patterns based on complex Morlet wavelet transform[J]. Editorial Office of Optics and Precision Engineering, 2012,(3): 643-650 DOI： 10.3788/OPE.20122003.0643.

摘要

针对在使用干涉、Moir偏折等方法进行流场高速动态测量时条纹图中大量无效数据对计算结果的影响

提出了一种基于连续小波变换的条纹图相位分析方法。利用小波变换的瞬时条纹频率分析能力

选用复Morlet小波及合适的小波参数

使得条纹图的小波变换模极大值与其调制度系数成正比

将其作为加权最小二乘法相位展开算法的权值

保证了相位有效展开。使用曲线拟合进行小波变换脊定位

缩短了定位时间并消除了噪声干扰。仿真实验显示

使用该方法得到的分析结果与实际相位值的相对误差小于0.01%;内波流场测量实验显示

使用该方法进行条纹图分析

密度梯度测量精度达到了510

-6

g/cm

。结果表明

用该方法进行条纹图相位分析可以有效消除无效数据对结果的不利影响

相位展开有效可靠

分析结果精度高。

Abstract

To reduce the effect of large number of invalid data in fringe patterns on calculation results in the measurement of high dynamic flows using interferometry or Moir? deflectometry

an effective phase extraction method was proposed based on the wavelet transform using complex Morlet wavelet. Through choosing proper parameters for the wavelet

the maximum modulus of the wavelet transform of a pattern was proportional to its modulation factor

then it was used as a weighting factor of a phase unwrapping algorithm based on weighted least squares to guarantee reliable phase unwrapping. In the process of wavelet ridge routing

a simple algorithm based on curve fitting was proposed to substantially reduce the routing time and the precision deterioration due to image noise. In simulation experiment

the relative error between calculated phase and actual phase is less than 0.01%. In internal wave measurement experiment

the method is used to analyze the fringe patterns

and the density gradient measurement precision has reached 5?10

-6

g/cm

. It shows that the method can reduce the effect of invalid data on analysis precision effectively and can obtain reliable unwrapped phases.

关键词

Keywords

references

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