PAA-RLME: a robust online adaptive algorithm for nonlinear error suppression in phase-shifting profilometry

Abstract This study proposes an online blind estimation method for nonlinear distortion parameters in structured light measurement systems, addressing key limitations in three-step phase-shifting profilometry. The method overcomes the challenges of nonlinear intensity response from projection devices, which affects measurement accuracy. Current solutions, such as traditional pre-calibration and blind nonlinear compensation approaches, either require cumbersome procedures or have limited adaptability and accuracy due to dependence on the surface profile of the measured object. The proposed polar angle average (PAA)—robust LM parameter estimation algorithm uses PAA and robust 3 σ screening to estimate nonlinear parameters, eliminating the need for time-consuming calibration. It integrates parameter estimation with measurement, enhancing accuracy, simplifying device design, and maintaining efficiency. Compared to existing online nonlinear error correction methods, the approach is based on parameter estimation, improving both compensation accuracy and robustness. Validation through theoretical analysis, simulations, and experiments shows the method’s effectiveness. It reduces absolute mean phase error by up to 57% under real-world conditions, with compensation accuracy decoupled from the object’s surface, demonstrating improved stability over previous methods.