Analyzing closed-fringe images using two-dimensional Fan wavelets

Abstract

In this paper, it will be shown how the use of two 2D Fan wavelets to analyze closed-fringe images can lead to a relatively fast and exceptionally noise-resistant algorithm capable of extracting not only local phase but also local frequency information. Our algorithm is up to 10 times faster than the current state-of-the-art in wavelet processing techniques and even up to 30 times faster than "windowed Fourier" transform programs, which achieve similar noise-resiliency figures. This improvement is mainly achieved by the use of Fan wavelets instead of Morlet wavelets, but a more efficient scale-space discretization strategy is also described, and three different alternatives are suggested capable of solving the phase sign-ambiguity problem in a quick and efficient manner. Finally, the application of the algorithm to real and numerically generated images shows that a precision of 1/30th of a fringe is achievable for noise levels going up to 1/5th of the input contrast.