Phaseless near field techniques: formulation of the problem and field properties

Abstract

In this series of two papers, we consider in its maximum generality the problem of determining radiated electromagnetic fields starting from phaseless distributions on one or more surfaces surrounding the source. In this first part, theoretical aspects of the problem and the basic point of an appropriate formulation are examined. The problem is conveniently tackled as the inversion of the nonlinear, in particular 'quadratic', operator mapping the set of radiated fields into square amplitude distributions over prescribed surfaces. Next, the compactness property of the set of the unknown field is exploited, leading to an introduction of the finite dimensional representations for it and the concept of its "essential dimension". Furthermore, for the square amplitude data distributions finite dimensional representations are introduced and their "essential dimension" considered, also for more than one observation domain. Finally, due to the ill-posed nature of the problem, a generalized solution is defined as the global minimum of an appropriate functional and its existence discussed.