Exponential Taylor Series Method to eliminate the gamma distortion in phase shifting profilometry

Abstract

Phase shifting profilometry (PSP) is widely applied in three-dimensional (3D) shape measurement because of its high precision and simple hardware configuration. However, the gamma effect of commercial digital projector usually causes nonlinear periodical phase error. In this paper, we propose an approach named as Exponential Taylor Series Method (ETSM) to eliminate the gamma distortion. The ETSM sets the input fringe pattern intensity as an exponential Taylor series function. Along with the decoding algorithm proposed, the nonlinear phase error caused by the gamma effect can be eliminated theoretically. Simulations and experiments are conducted to verify the ETSM’s performances by comparing with the conventional method of PSP and another method based on exponent. The results show that the ETSM greatly reduces the phase error caused by gamma distortion without any additional work or pre-process. The ETSM also performs better in resisting the noise due to its quasi-sinusoidal intensity distribution of the captured fringe patterns.