PHASELESS NEAR-FIELD TECHNIQUES - FORMULATION OF THE PROBLEM AND FIELD PROPERTIES

In this series of two papers, we consider in its maximum generality th e problem of determining radiated electromagnetic fields starting from phaseless distributions on one or more surfaces surrounding the sourc e. In this first part, theoretical aspects of the problem and the basi c point of an appropriate formulation are examined. The problem is con veniently tackled as the inversion of the nonlinear, in particular 'qu adratic', operator mapping the set of radiated fields into square ampl itude distributions over prescribed surfaces. Next, the compactness pr operty of the set of the unknown field is exploited, leading to an int roduction of the finite dimensional representations for it and the con cept of its ''essential dimension''. Furthermore, for the square ampli tude data distributions finite dimensional representations are introdu ced and their ''essential dimension considered, also for more than one observation domain. Finally, due to the ill-posed nature of the probl em, a generalized solution is defined as the global minimum of an appr opriate functional and its existence discussed.