Two-dimensional continuous wavelet transform algorithm for phase extraction of two-step arbitrarily phase-shifted interferograms

•2D wavelet transform algorithm is used for analyzing phase-shifted interferograms.•The algorithm requires only two interferograms whose phase shift can be arbitrary.•The algorithm can handle interferograms with noise, defects, and complex fringes.•Validity and practicability have been verified by both simulation and experiment.

By virtue of the anti-noise and anti-defect abilities, in this paper, a two-dimensional continuous wavelet transform algorithm is proposed to analyze two-step arbitrarily phase-shifted interferograms with an orthonormalization process. The novel algorithm takes the advantages of the two existing ones, and it has a remarkable ability to accurately and automatically extract full-field phase distribution from two phase-shifted interferograms where they may contain arbitrary and unknown phase shift, complex fringes with phase ambiguity, large fringe-frequency variations, noise, defects and corrupted fringes. The validity of the algorithm is demonstrated by both computer simulation and real experiments.