A new wavelet transform for reliability-guided phase unwrapping of optical fringe patterns

A new daughter wavelet definition for reliability-guided phase unwrapping of the optical fringe pattern is introduced. The new daughter wavelet definition is given by normalized mother wavelet with a new factor including a Gaussian function. The modulus of the wavelet transform coefficients, obtained by using daughter wavelet under this new daughter wavelet definition, includes not only modulation information but also local frequency information of the deformed fringe pattern. Therefore, it can be treated as a good parameter which represents the reliability of the reconstructed phase data. Mathematical demonstration of this parameter is given. Both the computer simulation and experiment reveal the validity of the proposed method.