Phase-shifting shadow moiré using the Carré algorithm

The difficulty of implementing the phase shifting method in shadow moire lies in the fact that the phase shift due to the displacement of the light source, the imaging sensor, or the grating is non-uniform across the field of view. Typical phase shifting algorithms fail to produce accurate results. In the past few decades, various approximation methods have been developed to overcome this difficulty. In this paper, we describe an elegant solution that provides exact close-form result. In our proposed system, the grating is translated in equal steps to introduce phase shifts. The phase value at each point is determined by the Carre algorithm, which only requires uniform phase shifts for each point, instead of in the whole field of view. The 3-D shape of the object is then reconstructed from the phase map retrieved from the Carre algorithm. The simulation results demonstrate the effectiveness of the Carre algorithm for shadow moire.