Wavelet ridge techniques in optical fringe pattern analysis.

Wavelet ridge techniques utilizing daughter wavelets under two different kinds of definitions in the optical fringe pattern analysis are theoretically clarified. The clarification reveals that the phase of the optical fringe pattern is equal to that of its wavelet transform coefficients on the ridge using both of the two wavelet definitions. The differences between the two definitions in the performance of wavelet transform algorithms are verified in theory. The strict relations between the instantaneous frequency of the fringe pattern and the scale parameter at the wavelet ridge position are also theoretically clarified for the phase gradient method. A simple method for selecting the scale vector is introduced. Computer simulations and experiments reveal the correctness of the clarification and the validity of the proposed method.