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

In this article, the mixed potential integral equation is discretized using the Rao-Wilton- Glisson basis functions in order to obtain a method of moments matrix equation for a source reconstruction problem. The weighting functions used in the setup of the moments equation are Dirac delta functions. The entries of the moments matrix are computed using a semi-analytical method which is applicable to any method of moments problem with point matching. The analytical calculation is made possible by employing a differentiation property of the scalar Green function and the properties of the mesh elements of the source plane. The semi-analytical method makes it easier to increase the accuracy of the moments matrix elements. The accuracy of the method is shown by comparing the results obtained using the semi-analytical method to those obtained by a fully numerical procedure. The source reconstruction for a specific electromagnetic field distribution is the procedure of either setting up equivalent electromagnetic problems in order to determine equivalent sources or determining the actual sources by solving the related integral equations. The source reconstruction method is used in several areas which can be mentioned as near-field to far-field (NF-FF) transformation, microwave imaging, antenna design, antenna characterization, antenna diagnostics, electromagnetic interference estimation in electronic circuits, corrections in antenna measurements, radome defect localization. The most important aspect of the source reconstruction method is that it takes the electromagnetic problem into consideration just as it is, with all of the real world factors included through the electromagnetic field measurement results. The literature on the source reconstruction method can be divided into two parts with respect to the type of the integral equation formulation for the problem. In the first group, a single integral equation formulation is done whereas in the second group, a dual-integral equation formulation is preferred. In the single equation formulation, the equivalent sources obtained using the equivalence principle are related to the field measurement results using the radiation integrals. In the dual equation formulation, an extra equation is set up using the Love's equivalence principle at the measurement surface. Some of the articles in the single equation formulation group are to be cited now. In (7-30), several NF-FF transformation formulations using the source reconstruction method and the related applications are studied. In (7), equivalent magnetic currents are constructed on a plane including the aperture of an antenna using the near electric field data on a plane. These currents are then used to calculate the far-field. In (8), equivalent magnetic currents are built on a plane including the aperture of an antenna again. However, the near electric field data is not necessarily to be obtained on a plane and can be gotten from a surface with an arbitrary geometry. In (9), an equivalent electric current is set up on a