Application of window-optimized 2D S-transform in the optical 3D shape measurement

Abstract

Combing the merits of windowed Fourier transform and wavelet transform, 2D S-transform has been a popular method in optical 3D measurement. As an improvement of 1D S-transform, 2D S-transform has better features to reduce noises and non-linearity because it can analyze the whole fringe patterns in two directions. However, the window size of traditional 2D S-transform is related to local frequency of tested objects, therefore traditional 2D S-transform can not get accurate surface information when the tested surface is complicated. To overcome the problem, a window-optimized 2D S-transform with theory analysis and mathematical derivation is proposed with two parameters to control the width of Gauss window. Simulation verifies that the proposed method can extract more accurate wrapped phase. At last, simulation and experiments are carried out to show that the proposed method can get more accurate measurement results when the tested surface is complicated.