PHASE RETRIEVAL OF RADIATED FIELDS

The problem of determining radiated electromagnetic fields from phasel ess distributions on one or more surfaces surrounding the source is co nsidered. We first examine the theoretical aspects and basic points of an appropriate formulation and show the advantage of tackling the pro blem as the inversion of the quadratic operator, which, by acting on t he real and imaginary parts of the field, provides square amplitude di stributions. Next, useful properties and representations of both field s and square amplitude distributions are introduced, thus making it po ssible to come to a convenient finite-dimensional model of the problem , to recognize its ill-posed nature and, finally, to define an appropr iate generalized solution. Novel uniqueness conditions for the solutio n of the problem and questions regarding the attainment of the general ized solution are discussed. The geometrical properties of the functio nal set corresponding to the range of the quadratic operator relating the unknowns to the data are examined. The question of avoiding local minima problems in the search for the generalized solution is carefull y discussed and the crucial role of the ratio between the dimension of the data representation space and that of the unknowns is emphasized.