Phase error analysis and compensation for motion in high-speed phase measurement profilometry

Abstract

High-speed three-dimensional (3D) measurement is increasingly important in many fields. Phase measurement profilometry (PMP) based on the binary defocusing technique has been applied to the high-speed 3D measurement scene for its higher measurement resolution and precision, and breaking the speed limitations of projector. However, because the PMP needs three phase-shifting (3-PS) patterns, motion error is inevitable to measuring dynamic objects. In this research, we construct a complete high-speed 3-PS PMP system, and re-derive two clearer motion error models than those in Weise’s research [ Conference on Computer Vision and Pattern Recognition (CVPR) ( IEEE , 2007 ), pp. 1 10.1109/CVPR.2007.383291 ]. Then, we theoretically analyze the effects of the truncation error on the model accuracy, especially when the motion error is higher. To this end, a polynominal-based motion error model by fitting coefficient matrix of pre-simulation is proposed. Meanwhile, its corresponding error compensation method based on local domain estimation of the Nelder-Mead algorithm is developed. Finally, both simulations and quantitative and qualitative experiments verify the accuracy and effectiveness of the proposed method, as well as demonstrate the proposed method has improvements compared with the Weise’s research.