  The inverse problem of amplitude reconstruction on an inclined line based on
the values of amplitude or its module as recorded on semi-infinite line
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.
