Phaseless near field techniques: uniqueness conditions and attainment of the solution

Abstract

In this series of two papers we consider in its maximum generality the problem of determining electromagnetic fields starting from phaseless distributions on one or more surfaces. In this second part, novel uniqueness conditions for the solution of the problem, requiring in principle a single scanning surface, are introduced. Then, all questions related to the attainment of the generalized solution are discussed. The geometrical properties of the functional set corresponding to the range of the quadratic operator relating the unknowns to the data are examined. It is shown how to avoid both contingent local minima problems and ill-conditioning questions. The crucial role of the dimension of the data representation space is emphasized. The main benefits of the proposed approach are in the numerical search for the solution, that is the exact, closed form line search step in the minimization procedure and the introduction of a proper metric change in the functional, are stressed. A critical review of the results already obtained is performed with a particular care to the key points of the method.