三维面形测量中小波变换和傅里叶变换的对比研究

傅里叶变换轮廓术（Fourier transform profilometry，简称FTP）进行三维面形测量时，若无频谱混叠，可以得到很好的测量效果。但由于FTP是全局变换，频域内丢失了空间信息。当被测物体形状复杂或被噪声严重污染时，频域中频谱分布展宽，可能发生频谱混叠，导致基频分量提取不完整，从而不能正确地恢复出被测物体。本文利用小波具有的局部分析能力和噪声抑制能力，采用小波变换的方法（Continuous Wavelet Transform，简称CWT）从混叠条纹和噪声条纹中提取出完整的基频分量。我们采用Morlet复小波函数对变形光栅条纹进行处理，详细研究了CWT和FTP两种方法在不同情况下的优缺点，并通过计算机模拟和实验证实理论分析的正确性。

The contrast analysis between FTP and CWT in 3D measurement

Fourier transform profilometry(FTP) is a popular method in 3-D measurement,which gives correct 3D shape information of the measured object in the case of no spectrum overlapping.But this method is full-field transform,tile spatial information of the deformed fringe pattern is lost in frequency domain.If the surface of measured object is complex or the pattern is seriously polluted by noise,the perfect foundational frequency is difficult to extract by filtering because of frequency aliasing,which results in incorrect 3D reconstruction of the object.This paper introduces wavelet analysis method(CWT) to extract completed foundational frequency,using its local properties and the ability of repress noise.We adopt complex Morlet wavelet to treat with deformed fringe pattern to retrieve surface of measured object.We also compare FTP and CWT in different Conditions.Simulation and experiment testify the validity of theoretical analysis.