对于圆形孔径的光学系统,利用光强传播方程进行相位恢复时很难得到相位的边界径向斜率值,另外,要获得精确的圆域边界采样值也并非易事。为了克服上述困难,提出了一种相位恢复的改进方法,即改变了方程的表示形式、计算区域和边界条件,并用多重网格法进行求解获得重构相位,最后再将其修正。为了对重构相位进行修正,还得到了重构相位与原始相位之间泽尼克系数的传递矩阵。对均匀照明的情形进行了仿真,发现该方法不仅可以避免复杂的边界条件,减少运算时间,而且还能够较好地恢复出原始波前的泽尼克系数,即便在加噪的情况下,修正相位与原始相位的均方根误差也在可以接受的范围内。

For the optical system with circular apertures, it is difficult to get the boundary radical slope of phase and the accurate sampling value in the circular domain boundary when the intensity transport equation is used to recover the original phase. An improved method is put forward, in which the equation, computation domain and boundary condition are changed, and then the phase is reconstructed by the multigrid method and corrected at last. In order to correct the reconstructed phase, the transport matrix from the reconstructed phase to the original phase is also obtained. The case of uniform illumination is simulated and it is found that the method can recover Zernike coefficients of the original phase well while avoiding complicated boundary condition and reducing computation time, and furthermore the root-mean-square value between the corrected phase and the original phase is acceptable even when noise is added.