A New X-Words like Approach to Two Dimensional Phase Retrieval Problems

A new approach to Phase Retrieval (PR) problem, which is of interest in antenna testing and synthesis, is introduced and discussed. The proposed strategy can be interpreted as a proper combination of solutions of simpler problems, which are herein 1-D PR problems. In particular, the 2-D PR problem is split into a number of 1-D PR problems (along diameters and circumferences) solved through the Spectral Factorization technique, and a subsequent crosswords-like selection scheme. It is worth to note that in the possible applications to antenna testing, opposite to the most widespread existing techniques, the approach just requires a single measurement surface plus the knowledge of the source's support and of the field's phase in a couple of sampling points.