Phase unwrapping error reduction framework for a multiple-wavelength phase-shifting algorithm

We address a framework to reduce the unwrapping errors of the measurement system using a digital multiple-wavelength phase-shifting algorithm. In particular, the following framework is proposed: (1) smooth the raw phase by smoothing the sine and cosine images of the phase computation of the inverse tangent function; (2) locate and remove the incorrectly unwrapped points by the monotonicity condition of the phase map; (3) obtain the unwrapped phase map for the shortest wavelength without smoothing; (4) detect holes and fill them to preserve as much useful information as possible. Experiments demonstrated that the proposed framework significantly alleviated the measurement errors caused by the phase noise.