Robust composite sine-trapezoidal phase-shifting algorithm for nonlinear intensity

Abstract

Phase-shifting profilometry (PSP) is an efficient three-dimensional (3D) measurement technique. The accuracy of the PSP based 3D measurement system is generally affected by the nonlinear intensity response of the projector. In general, nonlinear errors can be reduced by projecting more fringe patterns, but this approach significantly increases the measuring time. To improve the measurement accuracy and speed, a new composite sine-trapezoidal phase-shifting profilometry technique that suppresses nonlinear error is proposed in this study. The main idea of the proposed method is projecting a set of sinusoidal fringe patterns and two sets of composite sine-trapezoidal fringe patterns with different intensity ranges in sequence. Among these patterns, the sinusoidal fringe is used to encode the pixel position, and the order of the wrapping phase is determined by the region code of the composite fringe. The flat intensity parts of the composite fringe are used to encode the nonlinear intensity response of the measurement system. Through system identification, the response parameters of the pixels can be obtained, and the gray value of the pixels can be corrected to gain a better phase distribution. Compared to the straight edges of the trapezoidal fringe, the sinusoidal edges of the composite fringe are more robust to the projector defocus, which improves the accuracy of the identification of the system intensity response model. Simulation results show that the proposed method can achieve a higher phase retrieval accuracy than the trapezoidal PSP and the sine PSP. The experiment results indicate that the proposed method has a better measurement accuracy than those of the standard 3-step and 4-step sine PSP methods.