Phase Retrieval of Scalar Fields Radiated by Finite-dimensional Sources through Single-surface Measurements and a Crosswords-like Processing

We propose a new approach to the phase retrieval of 2-D radiated scalar fields. The technique takes advantage of existing knowledge and procedures for the recovery of a 1-D discrete complex signal from the intensity of its Fourier Transform and then uses an effective crosswords-like procedure for the solution of the corresponding 2-D problem. By exploiting only one measurement surface and without recurring to global-optimization algorithms the approach is able to find in a deterministic fashion all the different solutions of the problem.