利用小波“脊”处的小波系数来提取变形条纹中的相位信息可以在很大程度上抑制条纹图中有用的基频分量与零频和其它谐波频率分量的混叠,弥补了傅里叶变换轮廓术的不足。从离散信号频域分析角度,推导了变形条纹小波变换的频谱描述形式,讨论了其测量范围,包括结构条件和抽样条件。结果表明,只有在无周期内瞬时频谱混叠,即任意位置处物体瞬时高度变化满足h/xx=b<1/3条件时,和不存在抽样引起的周期间瞬时频谱混叠的抽样条件下(即一个周期内的抽样点数m≥4时),小波变换轮廓术才能正确恢复被测物体的三维面型。计算机模拟和实验验证了该结论。

By the wavelet transform profilometry, the height distribution of an object can be obtained by calculating the wavelet coefficient of the deformed fringe pattern at the “ridge” position even there are some frequency overlaps between the fundamental frequency and the higher-order spectra. It provides a way to overcome the shortcoming of Fourier transform profilometry. But by now the discussion of the measurement range of wavelet transform profilometry has not been done yet. The frequency-domain description of wavelet coefficient is deduced from the point of view of the frequency analysis. And the measurement range of the wavelet transform profilometry is discussed, including the structure condition of the measurement system and the sampling condition introduced by digitizing the deformed fringe. A conclusion has been made that as long as there aren't any instantaneous frequency overlapping, both within a frequency island and between the adjacent periods, the correct reconstruction can be obtained by wavelet transform profilometry. In another word, under conditions that the instantaneous height variation of the test object in the fringe pattern at any position satisfies h/xx=b<1/3 and the number m of sampling points in one period must be greater or equal to 3, the correct phase included in the deformed fringe pattern can be retrieved by this method.