Internal–External Layered Phase Shifting for Phase Retrieval

A new type of fringe projection profilometry (FPP) system can be constructed by using a MEMS micro-vibration mirror. However, the MEMS scanning speed generally surpasses the capture speed of an ordinary camera, making it challenging to take advantage of high-speed projection. In this paper, we propose a solution called the phase-shifting superimposition projection framework, which projects patterns with different phase shifts in one exposure. Using the phase-shifting superimposition projection framework as the algorithm core, we propose an internal-external layered phase-shifting method to extract phases accurately. The internal phase-shifting method superimposes multiple projection patterns with different phase shifts into a high-quality camera image. Subsequently, the external phase-shifting method uses camera images to extract wrapped phases. Furthermore, we establish a mathematical model to demonstrate the anti-harmonics ability of the proposed method. Finally, experimental results demonstrate that the proposed method can significantly improve the accuracy of phase retrieval without adding extra camera images. Due to the ability to generate anti-harmonics images, the phase-shifting superimposition projection framework also holds significant application potential for the DLP binary defocusing technique, the Fourier transform profilometry, and the construction of high-quality datasets.