High-precision 3D shape measurement of rigid moving objects based on the Hilbert transform

Accelerated Phase Deviation Elimination for Measuring Moving Object Shape with Phase-Shifting-Profilometry

Eliminating the phase deviation caused by object motion plays a vital role to obtain the precise phase map to recover the object shape with phase-shifting-profilometry. Pixel-by-pixel phase retrieval using the least-squares algorithm has been widely employed to eliminate the phase deviation caused by moving object. However, pixel-level operation can only eliminate phase deviation within a limited range, and will bring high computational burden. In this paper, we propose an image-level phase compensation method with stochastic gradient descent (SGD) algorithm to accelerate the phase deviation elimination. Since the iteration calculation is implemented at the image-level, the proposed method can accelerate the convergence significantly. Furthermore, since the proposed algorithm is able to correct the phase deviation within (−π,π), the algorithm can tolerate a greater motion range. In addition to simulation experiments, we consider 2-D motion of the object, and conduct a series of comparative experiments to validate the effectiveness of the proposed method in a larger motion range.