The inverse problem of amplitude reconstruction on an inclined plane based on the values of amplitude or its module as recorded on semi-infinite plane orthogonal to the beam propagation direction is considered within the framework of 2D parabolic equation. It is demonstrated that this inverse problem, in case when the complex image plane amplitude is known, can be reduced to a singular Cauchy-type integral equation. The existence of its solutions requires that certain conditions be met but if a solution exists it is necessary unique. The obtained integral equation is then approximated piece-wisely and the resulting linear algebraic system is solved numerically while applying necessary regularization procedures to enhance the stability of its solutions. Finally, an iterative method of phase retrieval is developed and a set of numerical experiments is performed.

在二维抛物线方程的框架内，考虑了基于振幅值或其模块的，在正交于光束传播方向的半无限平面上记录的，在倾斜平面上的振幅重构的反问题。已经证明，在已知复像平面振幅的情况下，该反问题可以简化为奇异柯西型积分方程。其解决方案的存在要求满足某些条件，但如果存在解决方案，则必须是唯一的。然后将获得的积分方程分段近似，并对所得的线性代数系统进行数值求解，同时应用必要的正则化程序以增强其解的稳定性。最后，