本文通过较严格的数学推导,得到一组由已知成像系统的两个平面上的光波强度分布去恢复相位的Gerchberg-Saxton算法和Misell算法方程。本文指出,只要成像系统的任何某两个平面上的波函数之间的变换是通过一个幺正算符实现的,那末,由已知它们的振幅,采用GS算法便可以实现相位复原。

In this paper, a set of equations for retrieving phase from two intensity distributions in the image plane or some other plane of an imaging system was obtained by the exactly mathematical derivation. The equations are completely analogous to the algorithm suggested by Gerchberg-Saxton[1,2,4] and Misell [3]. We point out that, if the transformation between two wave functions is performed by unitary operator and one of the wave functions is absolutely square integrable, the phase reconstruction from the known intensity distributions in any two planes of an imaging system can be achieved using OS algorithm.