改进的多重网格法重建含遮拦物的干涉波前

Wave Front Reconstruction from Opaque Object Containing Interferogram Using Modified Multigrid Algorithm

阐述了由单张干涉图求取相位主值图像及最小二乘相位恢复。推导出基于梯度拟合的泊松方程及其离散化形成后，详细讨论了多重网格法对此方程求解的原理和过程。结合路径无关与路径相关算法的优点，设计了自适应最优路径法作为多重网格法的预处理，改进迭代的初始条件，提高了重建精度，同时大大加快了收敛速度。实验结果证明改进的多重网格法对含遮挡物的干涉图能获得很好的波前重建效果。

Abstract An adaptive optimum path method and least mean square (LMS) phase unwrapping as a typical path independent method are discussed. In the latter case Poisson equation and its discrete formulation are derived. The multigrid algorithm for solving this equation is given in detail. Especially a weighted multigrid algorithm aimed at cases with boundary and blockage is presented. Then a modified multigrid algorithm which combines the advantages of two classes of phase unwrapping algorithms is developed. It takes the results of the adaptive optimum path method as initial guess of the iteration of multigrid and a high accuracy is reached within a considerably faster convergence speed. In the simulation experiment an interferogram of a flow field containing opaque objects and the related results are given. The method is applied to a real interferogram and is proved that it is effective and practical for reconstructing wave front containing opaque object.