Adaptive windowed Fourier transform in 3-D shape measurement

TLDR: An adaptive windowed Fourier transform method in 3-D measurement based on a wavelet transform is proposed, in which, by applying aWavelet ridge, a series of scaling factors are calculated to determine the series of prime windows needed in the windowed Fresnel transform method.

Abstract: An adaptive windowed Fourier transform method in 3-D measurement based on a wavelet transform is proposed, in which, by applying a wavelet ridge, a series of scaling factors are calculated to determine the series of prime windows needed in the windowed Fourier transform method. Because the spectrum of each local fringe is simpler than that of the whole fringe, even though there is frequency aliasing as far as the whole fringe is concerned, the fundamental spectrum may separate into components in each local fringe. It is easy to filter out one of the fundamental frequency components from the local spectra. Adding these local fundamental components, the full fundamental component can be obtained correctly. The advantage of the method is that it not only eliminates the frequency aliasing, but also obtains the modulation distribution function to guide phase unwrapping.