Efficient nonlinear correction method in fringe projection profilometry

In fringe projection profilometry (FPP), the nonlinear response of the projector is one of the key factors affecting the accuracy of three-dimensional (3D) measurement. The double <i>N</i>-step phase-shifting method (DNPSM) is an effective method for correcting nonlinear-induced phase errors. However, the DNPSM doubles the number of required fringe sequences, resulting in low 3D measurement efficiency. To enhance measurement efficiency, this paper proposes two efficient nonlinear-induced phase error correction (NIPEC) methods. First, we optimize the DNPSM by adding only a small number of additional fringe patterns in the high-frequency fringes, reducing the total number of fringe patterns from 18 to 12. Second, we introduce a Hilbert transform-based three-step phase-shifting algorithm (PSA) method, which does not require additional projected fringe patterns but instead constructs the phase-shifted fringe patterns through the Hilbert transform. Experimental results demonstrate that the proposed methods effectively suppress periodic ripple phase errors and improve measurement efficiency by 34% compared to the traditional DNPSM.