Nonlinear error reduction for phase-shifting profilometry considering periodicity and symmetry of a phase histogram

Phase-shifting profilometry is extensively utilized for three-dimensional (3D) measurement. However, because of gamma nonlinearity, the image intensities of the captured fringe patterns are regrettably distorted. An effective nonlinear error reduction method without requiring parameter estimation is presented in this paper. Differing from the traditional whole-period phase histogram equalization (PHE) method, our method takes into account not only the periodicity but also the symmetry of the phase histogram. Taking a three-step phase-shifting algorithm as an example, the phase error frequency triples the fringe frequency; thus, we first propose a 1/3-period PHE method. Moreover, since the phase error distribution is sinusoidal with symmetry, we further propose a 1/6-period PHE method. Simulations and experiments both indicate that the 1/6-period PHE method, compared with the whole-period PHE and 1/3-period PHE methods, can further reduce the nonlinear error.