一般多重网格算法求解光强度传播方程是从精细网格层开始计算, 精细网格层的初值选择影响算法的收敛速度和求解精度。提出了一种完全多重网格方法求解光强度传播方程的相位恢复方法。基于限制法将最细网格上的方程转化为最粗网格上的方程, 求解该方程得到最粗网格上的解; 然后对此解用延拓法得到上一层细网格上的解, 以得到的解作为此层网格上的初解, 利用Ⅴ循环解此层上的方程, 得到此层网格的精确解。依次, 直到得到最细网格上的精确解。模拟相位恢复实验结果表明, 本文方法具有较快的收敛速度, 能够恢复复杂相位分布。

The computation of the basic multigrid method is started with an arbitrary approximation on the finest grid. When the basic multigrid method is used to solve the transport of intensity equation(TIE) for phase retrieval, the retrieved phase distribution is sensitive to the initial values on the finest grid. To mitigate the above-mentioned problem, a full multigrid method (FMG) solving the TIE for phase retrieval is presented. Instead of starting with an arbitrary approximation on the finest grid, the first approximation is obtained by interpolating from a coarse grid solution. The coarsest grid is created based on the finest grid using the restrain operators, and the solution on the coarsest grid is gotten. Then the initial value of the fine grid can be obtained through prolongation operator, and the Ⅴ-cycle is adopted to solve the equation on this fine grid. Based on this nested iteration technique, the exact solution to the TIE is obtained. The simulation experiments show that this method can retrieve the complicated phase distributions with high accuracy, and has fast convergence speed.