应用复Morlet小波变换分析条纹图相位

针对在使用干涉、Moiré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5×10-6g/cm4.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.

Phase extraction for fringe patterns based on complex Morlet wavelet transform

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 Moiré 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/cm4.It shows that the method can reduce the effect of invalid data on analysis precision effectively and can obtain reliable unwrapped phases.