We investigate the transport of intensity equation (TIE) and the transport of phase equation (TPE) for solving the phase retrieval problem. Both the TIE and the TPE are derived from the paraxial Helmholtz equation and relate phase information to the intensity. The TIE is usually favored since the TPE is nonlinear. The main contribution of this paper is a discussion of preferential use of either one of the two equations or potential benefits of a hybrid use. Moreover, we discuss the solution of the TPE with the method of characteristics and with viscosity methods. Both the TIE and the viscosity method are numerically implemented with finite element methods.

翻译：本文研究了强度传输方程（TIE）与相位传输方程（TPE）在求解相位恢复问题中的应用。TIE与TPE均从傍轴亥姆霍兹方程推导而来，并将相位信息与强度分布相关联。由于TPE具有非线性特性，通常更倾向于使用TIE。本文的主要贡献在于探讨了优先选用其中任一方程的依据，以及混合使用二者可能带来的优势。此外，我们讨论了利用特征线法和粘性法求解TPE的方法。文中采用有限元方法对TIE和粘性法进行了数值实现。