Frequency-guided windowed Fourier ridges technique for automatic demodulation of a single closed fringe pattern

A frequency-guided windowed Fourier ridges (FG-WFR) technique for phase extraction from a single closed fringe pattern is proposed. The algorithm begins with a selected seed point and is then guided by the local frequency of the computed pixels. For the seed point, the whole spectral range is examined with WFR to provide reliable local frequency and phase estimation. However, for the rest of the pixels, the WFR algorithm is performed in a more narrow spectral range centered at the determined frequency of its computed neighboring pixel, which not only enforces the continuity of the local frequency between adjacent pixels but also reduces computation consumption significantly. Besides, since phase unwrapping can be readily implemented after demodulation of each pixel, the algorithm directly offers a continuous phase map. The proposed FG-WFR algorithm is verified by successfully demodulating two computer simulated fringe patterns and one noisy experimental fringe pattern.