  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.
