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 for phase retrieval from a single-shot spatial carrier fringe pattern (SCFP), which combines the advantages of spatial carrier phase shift (SCPS) with two dimensional continuous wavelet transform (2D-CWT).•It doesn't require the spatial carrier to be constant as SCPS.•The subtraction operation in Step 2 of NTHA could considerably mitigate the edge errors of 2D-CWT, thus enhance its accuracy.•It is highly noise-tolerant, not only because CWT is noise-insensitive, but also because the noise in the FP doesn't take part in the phase reconstruction of Step 3 in NTHA.