Efficient 3-D Measurement Method Based on Nonlinear Error Correction

Shuo Shan, Ze Li, Wen Zhang, Peng Xu, Jianhua Wang

Abstract: Fringe projection profilometry (FPP) is a widely used technique for 3-D measurements, but the nonlinear response of the instrument often introduces errors that compromise measurement accuracy. Furthermore, traditional nonlinear error correction methods typically require a large number of fringes, leading to reduced measurement efficiency. To address these issues, this study integrates the error model of the two-step phase-shifting algorithm (PSA), the Hilbert transform, and a newly discovered phase unwrapping order to propose three innovative algorithms: the hierarchical $222+2$ algorithm and the heterodyne $222+2$ algorithm, both utilizing eight fringes, as well as the heterodyne $121+2$ algorithm, which requires only six fringes. The steps and theoretical measurement capabilities of these algorithms were demonstrated through simulations, and their actual performance was validated via experiments. Compared to classical error correction algorithms, the proposed methods not only reduce the number of required fringes but also significantly enhance measurement accuracy.

External IDs:dblp:journals/tim/ShanLZXW25