3-D Shape Measurement Technique Using Wavelet Transform: Wavelet Transform Profilometry

The application of 3-D shape measurement is more and more important in the domain of industrial inspection, quality controlling, machine vision, and medical science, etc. And because of its high precision, nondestructive feature san also fastness of data acquisition, the method of non-contact optical measurement becomes very popular. Take the limitation of Fourier transform profilometry as the beginning, wavelet transform profilometry is brought forward as a new measurement method. The theoretical analysis, simulation and experimental results are presented.Firstly, the Gauss window is introduced to Fourier transform, i.e. Gabor transform, and applied to the fringe analysis. By introducing dilating transformation to the Gauss window function on the space scale, dilating Gabor transform is got. The theoretical analysis, simulation and experimental results are presented that demonstrate the limitation of them.Furthermore, wavelet transform(WT) is applied to analyze the spatial carrier-fringes, that is, wavelet transform profilometry. The theoretical analysis, simulation and experimental results presented demonstrate the validity of the principle. And the key technique of WT, such as the selection of the mother wavelet, the scale function, and the ridge of the wavelet transform are studied.Finally, the spatial bi-frequency grating pattern, the ratio of the two frequencies of that is an irrational number, is introduced. By using the wavelet transform profilometry, the wrapped modulated phase distributions corresponding to the two frequencies respectively are got in one bi-frequency grating pattern. And then applying the phase unwrapping by a lookup table method for unwrapping, the determinate phases corresponding to the two frequencies are got. Such technique can be applied to the analysis of the nonstationary and transient signals.