Phase Retrieval of 2-D Radiated Fields from Phaseless Data: A new Crossword Approach

We tackle the problem of recovering 2-D complex fields starting from the spectral amplitude data, the support of the source, and a few additional information. In particular, we further elaborate on our 'crosswords-solution like' approach where the solution is found by solving 1D problems and congruence arguments. Its argued that intersecating lines and circles (rather than just lines) is more effective, and we show how the resulting approach, initially developed for the case of continuos (aperture) sources, is also effective in determining the excitations of discrete (array) sources.