Windowed Fourier transform profilometry based on improved S-transform.

A novel method for windowed Fourier transform (WFT) profilometry is presented. This method is based on improved S-transform. The impact of the second order derivative of the phase (φ′′(b)) to the ridge of S-transform is derived, and how to estimate this deviation is discussed. An important conclusion that more accurate instantaneous frequency can be obtained after removing this deviation is shown. Thus, an accurate phase map of the fringe pattern is obtained by using the WFT based on the window size map, and this map is related to the instantaneous frequency. The method is compared with the WFT based on the wavelet transform. A numerical simulation and experimental example have shown its validity in practical applications.