A Phase Retrieval Method for 3D Shape Measurement of High-Reflectivity Surface Based on π Phase-Shifting Fringes

Fringe projection profilometry (FPP) has been widely used for 3D reconstruction, surface measurement, and reverse engineering. However, if the surface of an object has a high reflectivity, overexposure can easily occur. Image saturation caused by overexposure can lead to an incorrect intensity of the captured pattern images, resulting in phase and measurement errors of FPP. To address this issue, we propose a phase retrieval method for the 3D shape measurement of high-reflectivity surfaces based on π phase-shifting fringes. Our method only requires eight images to be projected, including three single-frequency three-step phase-shifting patterns and one pattern used to provide phase unwrapping constraints, called conventional patterns, as well as the π phase-shifting patterns corresponding to the four conventional patterns, called supplemental patterns. Saturated pixels of conventional fringes are replaced by unsaturated pixels in supplemental fringes to suppress phase retrieval errors. We analyzed all 16 replacement cases of fringe patterns and provided calculation methods for unwrapped phases. The main advantages of our method are as follows: (1) By combining the advantages of the stereo phase unwrapping (SPU) algorithm, the number of projected fringes is reduced. (2) By utilizing the phase unwrapping constraint provided by the fourth fringe pattern, the accuracy of SPU is improved. For highly reflective surfaces, the experimental results demonstrate the performance of the proposed method.