为了从频域角度分析复Morlet小波、Fan小波和实Mexican hat小波等常用的小波频域特点,采用小波变换和基于结构光投影的3维面形测量方法重建被测物体,并进行了理论分析和实际实验.通过对比1维Morlet小波、1维Mexican hat小波、2维Morlet小波、2维Fan小波、2维Mexican hat小波抑制条纹非线性和噪声的能力,以及对具有不同形变特征的条纹图的相位解调精度,最终得到不同小波处理相同条纹时的重建精度.结果表明,2维小波比1维小波抑噪能力强;Mexican hat小波在恢复存在相位突变的条纹时精度较高.该研究工作为小波变换轮廓术的应用提供了理论参考.

In order to analyze the frequency features of commonly used wavelets,such as complex Morlet wavelet,Fan wavelet,real Mexican hat wavelet in frequency domain,wavelet transform and 3-D surface shape measurement method based on the structured light illumination were used in reconstruction of the object to be measured.Theoretical analysis and experimental verification were carried out.By comparing the capability of eliminating fringe nonlinearity and noise of 1-D and 2-D Morlet wavelets,1-D and 2-D Mexican hat wavelets and 2-D Fan wavelet,and comparing the demodulation accuracy of different fringe phases,the reconstructed accuracies of the same fringe based on different wavelet demodulations were obtained.The results show that the capability of eliminating the noise of 2-D wavelet is stronger than 1-D wavelet.Mexican hat wavelet is suitable for demodulating fringe pattern with phase mutation.The research provides the theoretical reference for the application of wavelet transform profilometry.