An effective near-field far-field transformation technique from truncated and inaccurate amplitude-only data

A general approach to the near-field far-field transformation from amplitude only near-field data is presented. The estimation of the far field is stated as an intersection finding problem and is solved by the minimization of a suitable functional. The difficulties related to the possible trapping of the algorithm by a false solution (common to any nonlinear inverse problem) are mitigated by setting the problem in the space of the squared field amplitudes (as already done in a number of existing papers) and by incorporating all the a priori knowledge concerning the system under test in the formulation of the problem. Accordingly, the a priori information concerning the far field, the near field outside the measurement region and the accuracy of the measurement setup and its dynamic range are properly taken into account in the objective functional. The intrinsic ill conditioning of the problem is managed by adopting a general, flexible, and nonredundant sampling representation of the field, which takes into account the geometrical characteristics of the source. As a consequence, the number of unknowns is minimized and a technique is obtained, which easily matches the available knowledge concerning the behavior of the field. The effectiveness of the approach is shown by reporting the main results of an extensive numerical analysis, as well as an experimental validation performed by using a very low cost near field facility available at the Electronic Engineering Department, University of Napoli, Italy