Fast phase retrieval without unwrapping for 3D measurement based on digital phase difference

Phase unwrapping is still a tough task for fringe projection profilometry (FPP), due to the heavy computation burden and slow rate of the existing phase unwrapping algorithms. To speed up the retrieval of the absolute phase, a fast phase retrieval algorithm without unwrapping for 3D measurement based on digital phase difference is presented in this paper. Firstly, 4-step phase-shifting profilometry is utilized to retrieve a complex-valued map, who contains the complete phase information of the measurement object in its phase part. Instead of extracting the phase map from the complex-valued map directly, a novel complex-valued map containing the differential phase is obtained by the division between the complex-valued map and its pixel-shifted version. Then, the differential phase can be extracted from the novel complex-valued map by regular phase extraction operation easily. Finally, the absolute phase can be retrieved by integrating the differential phase along the inverse pixel-shifted direction. This proposed algorithm can retrieve the absolute phase easily and fast, while the measurement object has continuous surface with the phase variation in the range of (-pi, pi]. Simulated and experimental results were demonstrated to present that this algorithm has faster phase retrieval rate than existing algorithms and has no obvious jump error, which allows fast and high-quality phase retrieval.