Algorithm for phase shifting shadow moiré with an unknown relative step

We report our experimental results of phase shifting shadow moiré with a constant but unknown phase step to estimate both the wavefront phases and the phase step. The method allows phase retrieval from phase shifting interferograms even though the calibration data of the phase shifter are unknown. Compared with the traditional shifting shadow moiré method, the proposed algorithm is insensitive to the height dependent effects, which is the main systematic source of error in phase shift shadow moiré when reconstructing surfaces from fringe patterns. Experiments show that the proposed method can effectively minimize the effects of the phase shifting errors and possesses a superior performance to existing typical phase shifting algorithms in the shifting shadow moiré technique.