Universal N-step phase-differencing profilometry with robustness optimal design based on dual-frequency phase...

A universal N-step phase-differencing profilometry (PDP) is proposed. Different from N-step phase shifting profilometry (PSP), by capturing N (N ≥ 3) phase-shifting deformed patterns and establishing what we believe to be a brand-new mathematical model, the phase difference between phase caused by the measured object on the reference plane and phase just caused by the reference plane rather than the above phases themselves can be directly extracted, so the proposed PDP plays much lower time consumption than PSP. Though phase difference is also wrapped within (-π, π], the phase difference unwrapping instead of phase unwrapping as in PSP may play much more robust due to the differencing operation. Taking the dual-frequency temporal phase unwrapping (DF-TPU) as a tool, the robustness optimal design is also proposed to further improve the robustness of the proposed PDP. Theoretical and experimental results demonstrate that the proposed PDP outperforms PSP in both time consumption and robustness while ensuring same level of high accuracy, thus showing its promising prospects in three-dimensional (3D) imaging.