Phase-shifting techniques are extremely important in modern optical metrology. The advanced iterative algorithm (AIA) is an elegant, flexible and effective phase-shifting algorithm that can extract phase from fringe patterns with arbitrary unknown phase-shifts. However, comparing it with traditional phase-shifting algorithms, AIA has not been sufficiently investigated on (i) its applicability to different types of fringe patterns; (ii) its performance with respect to different phase-shifts, frame numbers and noise levels and thus the possibility of further improvement; and (iii) the predictability of its accuracy. To solve these problems, a series of innovations are proposed in this paper. First, condition numbers are introduced to characterize the least squares matrices used in AIA, and subsequently a fringe density requirement is suggested for the success of AIA. Second, the performance of AIA regarding different phase-shifts, frame numbers and noise levels is thoroughly evaluated by simulations, based on which, an overall phase error model is established. With such understanding, three individual improvements of AIA, i.e., controlling phase-shifts, controlling frame numbers and suppressing noise, are proposed for better performance of AIA. Third, practical methods for estimating the overall phase errors are developed to make the AIA performance predictable even before AIA is executed. We then integrate all these three innovations into an enhanced AIA (eAIA), which solves all the problems we mentioned earlier. The significant contributions of eAIA include the insurability of the convergence, the controllability of the performance, and achievability of a desired accuracy. An experiment is carried out to demonstrate the effectiveness of eAIA.
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