Advanced iterative algorithm (AIA) is a flexible and effective phase-shifting algorithm (PSA) which can extract phase from fringe patterns with random unknown phase-shifts, making it attractive in the scenarios where phase-shifts are unknown or not accurate. However, accuracy of AIA degrades when intensity harmonics and/or phase-shift non-uniformity are presented. To solve this problem, multiple PSAs have been proposed, but they restrict their fringe model in one way or another, and thus sacrifice the immunity to certain error source(s). In this paper, a general iterative algorithm (GIA) which adopts a most general fringe model is proposed. In GIA, the many unknowns in the fringe pattern model are divided into three groups including: (i) the fringe amplitudes, (ii) the phase and (iii) the phase-shifts related parameters, and alternatively optimized through univariate search technique group by group to improve accuracy and convergence. The Levenberg-Marquart method is used for the optimization of each group of unknowns due to its excellent accuracy and robustness. GIA is shown to have better accuracies than all of its relevant competitors through both a large number of simulations as well as real experiments with a Fizeau interferometer. (C) 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
