A novel phase retrieval method in fringe projection based on phase-shifting algorithm

Abstract

In order to reduce nonlinear phase error in fringe projection based on phase-shifting algorithm, a novel phase retrieval method is proposed. Firstly, on the basis of expression for wrapped phase and corresponding phase in N-step phase-shifting algorithm, the nonlinear phase error and its simple expression is deduced. Secondly, based on the four-step phase-shifting algorithm, the wrapped phase expression of actual measured object is obtained. The corresponding nonlinear phase error is derived in a simple form, and then the new phase error value is obtained by offsetting π/4 from the nonlinear phase value. The mean of the new and original phase error values yields the final phase error; hence, the nonlinear phase errors are significantly reduced. Finally, the results of numerical simulations and experiments show that the proposed method is effective to reduce the nonlinear phase error due to system gamma nonlinearity in phase-shifting algorithm.