Efficient phase error reduction in phase-shifting algorithm with unknown phase-shifts

Phase-shifting algorithms are widely employed in optical 3D measurement to extract phase distribution from multiple phase-shifted fringe patterns. Precise knowledge of phase-shifts is critical for accurate phase extraction, but these phase-shifts are often unknown or inaccurate due to various disturbances, leading to significant phase errors. To address this challenge, this paper presents an efficient method applicable to arbitrary phase-shifting algorithms with unknown phase-shifts. This method operates without requiring accurate phase-shifts estimation. Since the actual phase and the distorted phase increase monotonically, building a roughly monotonic mapping relationship. Our method corrects the distorted phase through sorting the phase values and mapping them into the linear phase. Simulations and experiments have been conducted, and their results demonstrate its efficiency of our method in reducing the phase errors resulting from unknown phase-shifts.