Alternate Iterative Least-Squares Algorithm Based on Nonuniform Phase Shifting for Suppressing Nonlinearity Errors in Fringe Projection Profilometry

Abstract

In fringe projection technique, nonlinearities of used devices are recognized as major factors inducing phase errors, especially when the used camera and projector simultaneously have nonlinear features. In this case, ripple artifacts appear to be unevenly distributed over the reconstructed surface depending on the local reflectivity. For suppressing these errors, this paper suggests a phase-measuring technique which is characterized by two critical steps including anti-aliasing phase-shifting and iterative least-squares phase estimation. Anti-aliasing phase-shifting requires the selected phase shifts to be nonuniform and to have no common divisors. It provides a possibility of accurately recovering phases from few to four fringe patterns and eliminating influence of high order harmonics on the measurement results. By expanding the fringe signals from projector into harmonics and modeling the camera response as a polynomial, we derive a least-squares algorithm based on alternate iterations to calculate the fringe phase map and the related nonlinearity coefficients simultaneously. Through practical experiments, it has been demonstrated that this technique allows us to decrease artifacts caused by the simultaneous nonlinearities of the camera and the projector, thus improving measurement accuracy significantly.