Variable-frequency phase-shifting algorithm with least-squares iteration for hybrid errors reduction under structured-light illumination

In this paper, a novel variable-frequency phase-shifting algorithm is proposed to reduce hybrid errors under structured-light illumination, which combines a least-squares iteration with regularization processing. Theoretical formulas and related calculation techniques for the variable-frequency fringe model are respectively derived and proposed considering phase-shifting errors, temporal intensity fluctuations and Gamma distortion. From the perspective of theoretical model, it is successfully verified and implemented to establish a minimal and sufficient system of equations using a least number of fringe patterns. To tackle the challenge of solving numerous unknown parameters in the derived model caused by these sources, a grouped step-by-step strategy is adopted during the least-squares iteration process. Error point determination and compensation tricks are further developed to reduce the phase jump problem caused by underdetermined solution. A Gamma prediction technique based on bi-frequency single-frame fringe patterns is also put forward to enhance the accuracy of phase retrieval results. Corresponding simulation and experimental results have demonstrated that the proposed algorithm with attractive potentiality can achieve a significant enhancement in accuracy using the least number of phase-shifting fringe patterns (taking bi-frequency two-step as an example in this study) compared to other existing competitive techniques.