Fast three selected frequencies phase unwrapping method in phase-shifting profilometry

Phase unwrapping is a key technique in phase-shifting profilometry (PSP). Among various phase unwrapping methods available, temporal phase unwrapping has received considerable attention due to its ability to handle discontinuous objects with high robustness. However, temporal phase unwrapping requires calculation of fringe patterns with multiple spatial frequencies, making this technique difficult to apply in online measurements. To reduce the number of fringe frequencies required for temporal phase unwrapping, three frequency-based phase unwrapping methods were proposed, including three selected frequency phase unwrapping (TSFPU) and heterodyne multiple frequency (HMF) methods. However, the TSFPU algorithm is computationally expensive and results in relatively long processing times, while the HMF algorithm lacks noise robustness. In this article, we propose an improved fast three selected frequency phase unwrapping algorithm to obtain absolute phase maps in PSP. Compared to existing TSFPU methods, our method relaxes the conditions for constructing the relationship between the wrapped phase and the unwrapped phase, making it simpler and faster. Compared to HMF, noise is not accumulated during the unwrapping process in our method. Simulation and experimental results demonstrate that the proposed method can effectively eliminate blurring and noise issues while being highly robust. Compared to TSFPU, our method has a processing speed that is 3.3 times faster and significantly reduces phase error.