On inverse problem with phase retrieval for an inclined plane in the parabolic approximation

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