Harmonics suppression in frequency domain for fringe projection profilometry with arbitrary phase shifts

Abstract

In phase-shifting fringe projection profilometry, nonlinearities of the used devices affect measurement accuracy by induing harmonics in fringe signals. The resulting errors are manifested as ripple artifacts in the measured phase maps. Especially when phase shifts are not uniform, the error artifacts have unpredictable profiles and complicated frequency components thus being not easy to eliminate. To solve this problem, this paper suggests a method for suppressing effects of fringe harmonics when using arbitrary phase shifts. For doing it, this paper derives the frequency transfer function that explicitly represents the response of the phase-shifting algorithm to each order of fringe harmonics, and then uses this function to deduce a method that allows one to estimate the coefficients of harmonics from spectrum of the calculated complex fringe pattern. By iteratively subtracting off the estimated harmonics from the calculated complex fringe pattern, fringe phases are calculated accurately. Simulation and experimental results demonstrate that this method significantly suppresses the influence of fringe harmonics on measurement results and, simultaneously, it preserves edges and details of the measured object from being blurred.