Suppression of the nonlinear phase error in phase shifting profilometry: considering non-smooth reflectivity and fractional period.

Hilbert transform (HT) has been employed to compensate phase error arising from the nonlinear effect in phase shifting profilometry (PSP). However, in most common situations, pure HT may lead to a significant system error, which has a negative impact on subsequent phase error compensation. In this paper, system error from HT of non-stationary and non-continuous fringe is analyzed, and then a novel phase error suppression approach is presented. The cosine fringe without direct current (DC) component is reconstructed to eliminate the influence of non-smooth reflectivity, and the fractional periods at both ends of the reconstructed fringe are extended to generate fringe with integer number of periods. And then the HT is applied to the reconstructed and extended fringe. Finally, a revised phase-shifting algorithm is employed to calculate the phase with the fringe after HT. The proposed approach is suitable for PSP of the surface with non-smooth reflectivity (e.g. texture of complex colors), which is demonstrated in a series of experiments.