Path independent demodulation method for single image interferograms with closed fringes within the function space C(2)

In the last few years, works have been published about demodulating Single Fringe Pattern Images (SFPI) with closed fringes. The two best known methods are the regularized phase tracker (RPT), and the two-dimensional Hilbert Transform method (2D-HT). In both cases, the demodulation success depends strongly on the path followed to obtain the expected estimation. Therefore, both RPT and 2D-HT are path dependent methods. In this paper, we show a novel method to demodulate SFPI with closed fringes which follow arbitrary sequential paths. Through the work presented here, we introduce a new technique to demodulate SFPI with estimations within the function space C(2); in other words, estimations where the phase curvature is continuous. The technique developed here, uses a frequency estimator which searches into a frequency discrete set. It uses a second order potential regularizer to force the demodulation system to look into the function space C(2). The obtained estimator is a fast demodulator system for normalized SFPI with closed fringes. Some tests to demodulate SFPI with closed fringes using this technique following arbitrary paths are presented. The results are compared to those from RPT technique. Finally, an experimental normalized interferogram is demodulated with the herein suggested technique.