Statistical phase-shifting step estimation algorithm based on the continuous wavelet transform for high-resolution interferometry metrology

We propose a statistical phase-shifting estimation algorithm for temporal phase-shifting interferometry (PSI) based on the continuous wavelet transform (CWT). The proposed algorithm explores spatial information redundancy in the intraframe interferogram dataset using the phase recovery property on the power ridge of the CWT. Despite the errors introduced by the noise of the interferogram, the statistical part of the algorithm is utilized to give a sound estimation of the phase-shifting step. It also introduces the usage of directional statistics as the statistical model, which was validated, so as to offer a better estimation compared with other statistical models. The algorithm is implemented in computer codes, and the validations of the algorithm were performed on numerical simulated signals and actual phase-shifted moiré interferograms. The major advantage of the proposed algorithm is that it imposes weaker conditions on the presumptions in the temporal PSI, which, under most circumstances, requires uniform and precalibrated phase-shifting steps. Compared with other existing deterministic estimation algorithms, the proposed algorithm estimates the phase-shifting step statistically. The proposed algorithm allows the temporal PSI to operate under dynamic loading conditions and arbitrary phase steps and also without precalibration of the phase shifter. The proposed method can serve as a benchmark method for comparing the accuracy of the different phase-step estimation methods.