两步相移法是均衡栅线投影技术的高速与高精度的重要方法。但是目前的求解算法的精度较低或算法复杂度较高。提出一种基于变量分组优化的两步相移求解方法。该方法将原始迭代变量分组为线性组变量和非线性组变量,针对确定的非线性组变量,通过最小二乘法获得线性组变量显式的最优解。通过对非线性组进行参数优化,获得全局的最优解。利用数值模拟与实验对本文方法进行了验证。结果表明本文方法有效地降低了多元非线性优化的相位值陷入局部最优的可能性,且降低了算法的复杂度。

The two-step phase-shifting method is an important method to balance high speed and high precision in fringe projection profilometry. However, the current solution algorithm has low accuracy or high algorithm complexity. This paper presents a two-step phase-shifting solution method based on variable grouping optimization. In this method, the original iterative variables are divided into linear group variables and nonlinear group variables. For the determined nonlinear group variables, the explicit optimal solution of linear group variables can be obtained by the least square method. By optimizing the parameters of the nonlinear group, the global optimal solution is obtained. The method in this paper is verified by the numerical simulation and experiment. The results show that the method in this paper effectively reduces the possibility of falling into the local optimum of the phase value obtained by the multivariate nonlinear optimization and reduces the complexity of the algorithm.