Gamma error correction algorithm for phase shift profilometry based on polar angle average

Phase errors caused by the gamma nonlinear response of the phase shift profilometry (PSP) severely affect 3D measurement accuracy. To tackle this, a simple phase error compensation technique based on polar angle average is presented in this paper to improve the accuracy. Wrapped phase values are regarded as polar angles, and a polar axis distribution map can be obtained in the polar coordinate. Practically, the polar axis distribution (PAD) of the undistorted wrapped phase is uniform. When there are nonlinear effects in an PSP, the polar axis is unevenly distributed. The difference between adjacent polar angles is computed and then rearranged with specifically labels. After that, the even PAD diagram is generated, and the smooth phase can be further recovered. Compared with conventional nonlinearity correction methods, the proposed method corrects the error without any auxiliary conditions. Its effectiveness and robustness are verified in simulations and experiments.