Calibration method for fringe projection profilometry based on rational function lens distortion model

Abstract

The calibration of the fringe projection profilometry (FPP) system is susceptible to the camera lens distortion. This paper presents a calibration method based on the rational function lens distortion model. In this method, we integrate the rational function into the mathematical expression of the out-of-plane height to mitigate the impact of lens distortion. With arbitrarily arranged measurement components, we can flexibly measure the three-dimensional (3D) shape of objects with no expensive auxiliaries, high-precision setups, or complicated projector calibration. First, we project modulated sinusoidal fringe patterns with high frequency to the concentric circle grids calibration board to accurately estimate the unwrapped phase value, the pixel coordinate, and the out-of-plane height at each feature point. Then, the 3D coordinates can be recovered by determining the coefficients of the high order phase, coordinate, and height (PCH) mapping. Experiments on computer simulation and real data demonstrate that the modified calibration contributes to the flexibility and accuracy of the 3D shape measurement.