Field and Source Equivalence in Source Reconstruction on 3d Surfaces

Abstract

Abstract-This paper describes in detail different formulations of the inverse-source problem, whereby equivalent sources and/or fields are to be computed on an arbitrary 3-D closed surface from the knowledge of complex vector electric field data at a specified (exterior) surface. The starting point is the analysis of the formulation in terms of the Equivalence Principle, of the possible choices for the internal fields, and of their practical impact. Love's (zero interior field) equivalence is the only equivalence form that yields currents directly related to the fields on the reconstruction surface; its enforcement results in a pair of coupled integral equations. Formulations resulting in a single integral equation are also analyzed. The first is the single-equation, two-current formulation which is most common in current literature, in which no interior field condition is enforced. The single-current (electric or magnetic) formulation deriving from continuity enforcement of one field is also introduced and analyzed. Single-equation formulations result in a simpler implementation and a lower computational load than the dual-equation formulation, but numerical tests with synthetic data support the benefits of the latter. The spectrum of the involved (discretized) operators clearly shows a relation with the theoretical Degrees of Freedom (DoF) of the measured field for the dual-equation formulation that guarantees extraction of these DoF; this is absent in the single-equation formulation. Examples confirm that singleequation formulations do not yield Love's currents, as observed both with comparison with reference data and via energetic considerations. The presentation is concluded with a test on measured data which shows the stability and usefulness of the dual-equation formulation in a situation of practical relevance.

Fast Antenna Characterization Using the Sources Reconstruction Method on Graphics Processors

“…However, as indicated in previous works [5,14,21,24], the SRM seeks a least-mean-square solution, that is, the minimum energy solution. The issue of solution uniqueness of the inverse problem for antenna characterization has been widely discussed in [13,24,25], as well as the different ways of Equivalence Principle application depending whether the zero internal field condition is enforced or not.…”

“…In [24] the accuracy of the SRM is improved by means of a formulation based on a dual integral equation. The accuracy of the most common formulation based on a single integral equation is compared to the one of the dual integral equation in [25].…”

Molecular Em Fields and Dynamical Responses in Solids With Magnetic Charges

“…These equivalent field sources are constituted of superficial electric and magnetic currents located in the closed surface. The consideration of the currents of magnetic charges can be an excellent and effective mathematical procedure for calculating complex electromagnetic problems [16][17][18]. However, these procedures are developed in order to obtain more accuracy in the solutions of the Maxwell equations in very complex electromagnetic systems and do not try to assign independent phenomenology to these magnetic charges and currents.…”

“…Other lines of research of magnetic charges and magnetic currents have been developed for the calculation of the fields in the wave scattering of diffraction in the aperture antennas [16], in the studies on the memristors [17] and in the study of equivalent sources in the reconstruction of 3D surfaces [18]. These equivalent field sources are constituted of superficial electric and magnetic currents located in the closed surface.…”

A Semi-Analytical Method to Calculate the Entries of the Method of Moments Matrix for the Mixed Potential Integral Equation of a Source Reconstruction Problem

“…The dual-integral equation formulation is demonstrated to provide robust field reconstruction in the close vicinity of actual radiators for a wide range of signal to noise ratio in the measured field data. In [28], different formulations of the source reconstruction problem on an arbitrary 3-D closed surface are examined in detail. The dual-integral formulation is derived using the Love's equivalence principle.…”