An Improved Super-Resolution Source Reconstruction Method

Abstract

The source reconstruction method (SRM) is a technique developed for antenna diagnostics and for carrying out near-field (NF) to far-field (FF) transformation. The SRM is based on the application of the electromagnetic equivalence principle, in which one establishes an equivalent current distribution that radiates the same fields as the actual currents induced in the antenna under test (AUT). The knowledge of the equivalent currents allows the determination of the antenna radiating elements, as well as the prediction of the AUT-radiated fields outside the equivalent currents domain. The unique feature of the novel methodology presented in this paper is that it can resolve equivalent currents that are smaller than half a wavelength in size, thus providing super-resolution. Furthermore, the measurement field samples can be taken at field spacings greater than half a wavelength, thus going beyond the classical sampling criteria. These two distinctive features are possible due to the choice of a model-based parameter estimation methodology where the unknowns are approximated by a continuous basis and, secondly, through the use of the analytic Green's function. The latter condition also guarantees the invertibility of the electric field operator and provides a stable solution for the currents even when evanescent waves are present in the measurements. In addition, the use of the singular value decomposition in the solution of the matrix equations provides the user with a quantitative tool to assess the quality and the quantity of the measured data. Alternatively, the use of the iterative conjugate gradient (CG) method in solving the ill-conditioned matrix equations can also be implemented. Two examples of an antenna diagnostics method are presented to illustrate the applicability and accuracy of the proposed methodology.