Theory and Applications of Universal Phase-shifting algorithm

Abstract

Phase shifting technique provides a fully automatic analysis for fringe pattern or interferogram processing. In practice, due to the imperfections of phase shifter, optical elements, experimental setup and other various reasons, typical phase-shifted interferograms generally contain nonlinear phase shifting errors, variations and fluctuations of background intensities and modulation amplitudes, optical nonlinearities between intensities and phases, and so on. These errors in practice severely violate the assumptions in the principles of the existing phase shifting algorithms. To cope with these problems in applications, this paper presents a simple, rigorous, precise yet unveiled universal phase-shifting algorithm for retrieving desired phase distributions with ultrahigh accuracies from actual interferograms. The algorithm is based on a least-squares approach and a generic governing equation for the description of practical interferograms. Computer simulation shows a perfect performance of the universal algorithm, and applications to selected experiments demonstrate its validity and practicability.