Phase rectification for two-plus-one phase-shifting fringe projection technique via harmonic coefficient estimation

The two-plus-one phase-shifting fringe projection technique is a rapid measurement method owing to its requirement for very few fringe patterns; however, eliminating harmonic errors induced by luminance nonlinearities of the system remains a persistent challenge for its practical application. To address this issue, this paper proposes a phase rectification method integrating harmonic coefficient estimation and a nonlinear phase mapping process. First, the frequency response of the two-plus-one phase-shifting algorithm is analyzed. By reconstructing a complex fringe pattern from the results of the two-plus-one step algorithm, harmonic coefficients are estimated from the spectrum of this complex pattern based on the frequency response of the algorithm. Afterwards, the phase map is rectified by using a look-up table that maps an erroneous phase value to the true phase. Simulation and experimental results confirm that this method enables removal of harmonic-induced phase artifacts without a photometric calibration, and simultaneously preserving edges in the phase map from being blurred.