Predistorting Projected Fringes for High-Accuracy 3-D Phase Mapping in Fringe Projection Profilometry

A predistortion-based 3-D phase mapping method with linear epipolar constraints for fringe projection system calibration and measurement is reported. Hybrid system calibration methods have been developed recently to provide accurate measurement, high speed, and flexibility for fringe projection profilometry (FPP). However, these methods still have significant limitations. With projector distortion, for example, rigorous post-undistortion often results in low efficiency in computation. Conversely, simple, approximated undistortion is only effective for low levels of distortion. As a result, projector undistortion is usually not prioritized in practice. Aiming to achieve high-accuracy 3-D reconstruction with FPP, an easily implementable projector undistortion method is proposed in this article. Theoretical analyses and simulations confirm that the proposed method is rigorous. Experiments validate that the pixelwise root-mean-square reconstruction error is 0.042 mm, a 24% reduction from that of a simple post-undistortion method. The proposed method is also efficient computationally. Finally, a 3-D phase mapping lookup table is built. The results show that the proposed method is effective for achieving high accuracy and speed in 3-D surface measurement.