An illumination-invariant phase-shifting algorithm for three-dimensional profilometry

Uneven illumination is a common problem in real optical systems for machine vision applications, and it contributes significant errors when using phase-shifting algorithms (PSA) to reconstruct the surface of a moving object. Here, we propose an illumination-reflectivity-focus (IRF) model to characterize this uneven illumination effect on phase-measuring profilometry. With this model, we separate the illumination factor effectively, and then formulate the phase reconstruction as an optimization problem. To simplify the optimization process, we calibrate the uneven illumination distribution beforehand, and then use the calibrated illumination information during surface profilometry. After calibration, the degrees of freedom are reduced. Accordingly, we develop a novel illumination-invariant phase-shifting algorithm (II-PSA) to reconstruct the surface of a moving object under an uneven illumination environment. Experimental results show that the proposed algorithm can improve the reconstruction quality both visually and numerically. Therefore, using this IRF model and the corresponding II-PSA, not only can we handle uneven illumination in a real optical system with a large field of view (FOV), but we also develop a robust and efficient method for reconstructing the surface of a moving object.