为了提高小波变换轮廓术中小波的空域局部化能力, 提出了一种基于Mexican hat小波变换的条纹图处理方法。基于希尔伯特变换得到条纹对应的解析信号, 用Mexican hat小波计算解析信号的连续小波变换, 从小波变换的脊上提取相位信息, 恢复物体高度信息。模拟结果表明, Mexican hat小波变换法在相位快变或突变的区域有更高的相位提取精度, 测量误差可减小0.1～0.5 rad。以人脸石膏像为例, 进行了实验测量。实验结果表明, 在高度不连续或变化剧烈的区域, Mexican hat小波变换法较Morlet小波方法误差传播更小, 精度更高。

A method handling fringe patterns based on Mexican hat wavelet transform is presented to improve the ability of spatial localization in wavelet transformation profilometry. Mexican hat wavelet is chosen to perform continuous wavelet transform of the fringe pattern after converting original signal into the analytic form by Hilbert transform. The phase distribution is recovered from the coefficients on the ridge of the transform and the height distribution is retrieved. The simulated results show Mexican hat wavelet transform method has good performance in spatial localization and high accuracy both in the neighborhood of the height-discontinuous points and in the areas with sharply varying height, and the errors can be reduced by 0.1 rad～0.5 rad. The experiment for the fringe image of a plaster face shows Mexican wavelet transform method has smaller error propagation and higher precision than Morlet wavelet method in the areas with incontinuous or sharply varying height.