Phase-extraction algorithm for a single-shot spatial-carrier orthogonal fringe pattern with least squares method

In traditional phase measurement deflectometry (PMD), a number of sinusoidal fringe patterns are displayed on the screen in two orthogonal directions, which is time-consuming and not suitable for dynamic measurements. A phase-extraction algorithm based on the spatial-carrier phase-shifting technology for a single-shot spatial-carrier orthogonal fringe pattern is proposed. The phase increment of each pixel in two orthogonal directions is obtained by the least squares method and then the amount of spatial phase shift of all pixels relative to the probe pixel in the rectangular neighborhood centered on the probe pixel can be obtained. The number of fringe patterns required for the PMD is reduced to one by displaying a spatial-carrier orthogonal fringe pattern. Finally, the feasibility of the algorithm is verified by simulation and experiment.