Accurate two-frame random phase retrieval: an integrated approach using quartic polynomial equation solving augmented by least squares method

To extract the phase distribution with higher accuracy in phase-shifting interferometry, a random two-step hybrid phase retrieval approach by combining the quartic polynomial equation solving method and the least squares iterative algorithm (Hybrid QPE+LSI) is proposed, which can be applied in the cases where different fluctuations and non-uniformity of background intensity and modulation amplitude exist. It can perform accurate and robust phase extraction compared with other methods under different noise conditions, showing an error reduction of 57% compared with the quartic polynomial equation (QPE) method with 30-dB white noise added. This method can retrieve the phase map with high precision that the average root mean square error is more than 23 times less than the QPE method and 13 times less than the principal component analysis and least squares iteration method when the fringe number of interferograms is <1. Moreover, it represents an 82% error reduction under fluctuating background and modulation.