New possibilities for phaseless microwave diagnostics. Part2: The uniqueness problem and half plane imaging

The ambiguity of the phase-retrieval problem has been investigated. Theoretical studies have concentrated on the asymptotic properties of the Fourier-transform integral to investigate the band-limiting function of the aperture in determining the zeros of the transform. For one-dimensional functions, the phase-ambiguity problem is identified as finite permutations of zero conjugation, which, although modifying the existing phase, leave the intensity unperturbed. Based on these studies a new practical algorithm for halfplane imaging is proposed for one-dimensional functions. The relevance of the proposed technique has been discussed, with a theoretical analysis which studies the distribution of transform zeros for two-dimensional functions.