Nonlinear error active coding optimal estimation correction method for fringe projection

Stripe projection technology is widely used in 3D measurement and surface morphology reconstruction, where phase quality is a critical determinant of measurement accuracy. However, the nonlinear relationship between input and output light intensity is a major source of phase error. To address this issue, this paper introduces a novel system nonlinear active correction method. This method captures the variation pattern between input and output light intensity by projecting a small number of uniform gray-scale images onto a standard plane. This pattern is then integrated with active system nonlinear correction to construct a system nonlinear model based on the input-output light intensity variation. Genetic algorithms are used to optimize the coding values, which are then used to actively correct the projected fringes via fringe coding. The corrected fringes effectively reduce the influence of nonlinear effects, thereby significantly improving the quality of phase acquisition. To validate the proposed method, computer simulations were performed using three-step phase shifting. The results showed an 88% reduction in the standard error and an 85.5% reduction in the maximum error. In actual standard plane experiments, the corrected standard phase error decreased from 0.0706 rad to 0.0168 rad, and the maximum phase error decreased from 0.4129 rad to 0.0960 rad. In the face plaster model experiments, the corrected standard phase error decreased from 0.0472 rad to 0.0102 rad, and the maximum phase error decreased from 0.2990 rad to 0.2408 rad. In 3D reconstruction of complex morphology plaster models of human faces, the surface quality was significantly improved, and the water ripple effect, which affects the phase quality, was significantly reduced. Compared with existing large-step phase-shifting methods, the proposed method not only achieves high-quality phase acquisition accuracy, but also offers clear advantages in terms of required data volume and operational convenience, demonstrating broad application potential.