Retrieving the instantaneous frequency from images by wavelet ridges

Instantaneous frequency (IF) is very important in signal communications and methods, such as Hilbert transform and more recently wavelet ridges, have been developed to extract them. The importance of IF for 2D images has often been ignored. For example, in moire interferometry, IF can directly provide strain contours, which usually is the desired parameter in experimental mechanics. In this paper, the method of wavelet ridges is first extended from a 1D signal to 2D images with carrier fringes. In cases where the carrier fringes is not available, the phase shift approach is proposed, to extract the instantaneous frequency (IF) using wavelet ridges. Both methodologies are introduced and applied to real fringe patterns.