Optical 3D shape measurement profilometry based on 2D S-Transform filtering method

S transform combines the advantages of the windowed Fourier transform and the wavelet transform. In optical three-dimensional (3D) surface measurement based on the structured-light illumination, a two-dimensional S-Transform filtering (2DSTF) method is proposed to demodulate phase maps from fringe patterns. Unlike the two-dimensional S transform ridge (2DSTR) technique, in which the first-order approximation of Taylor expansion is introduced to express the phase information modulated in the fringe patterns, 2DSTF method reconstructs one of the fundamental components of the fringe pattern by adding the extracted local fundamental spectra of S-Transform, and the filtering operation and the inverse Fourier transform are used to calculate the phase maps. In this paper, a detailed theoretical analysis of 2DSTF method is given and its applicability is demonstrated on both simulations and experiments by comparing it with 2DSTR and the previous 1D ST (1DSTF and 1DSTR), which verify that the proposed method has a better performance than other methods in demodulating the phase of fringe patterns.