Highly noise-tolerant hybrid algorithm for phase retrieval from a single-shot spatial carrier fringe pattern

A highly noise-tolerant hybrid algorithm (NTHA) is proposed in this study for phase retrieval from a single-shot spatial carrier fringe pattern (SCFP), which effectively combines the merits of spatial carrier phase shift method and two dimensional continuous wavelet transform (2D-CWT). NTHA firstly extracts three phase-shifted fringe patterns from the SCFP with one pixel malposition; then calculates phase gradients by subtracting the reference phase from the other two target phases, which are retrieved respectively from three phase-shifted fringe patterns by 2D-CWT; finally, reconstructs the phase map by a least square gradient integration method. Its typical characters include but not limited to: (1) doesn't require the spatial carrier to be constant; (2) the subtraction mitigates edge errors of 2D-CWT; (3) highly noise-tolerant, because not only 2D-CWT is noise-insensitive, but also the noise in the fringe pattern doesn't directly take part in the phase reconstruction as in previous hybrid algorithm. Its feasibility and performances are validated extensively by simulations and contrastive experiments to temporal phase shift method, Fourier transform and 2D-CWT methods.