Application of the auxiliary sources method in the inverse problem of localization of a cylindrical impedance scatterer

In this article, based on the Method of Auxiliary Sources (MAS), an algorithm is proposed for localizing cylindrical scatterers filled with a medium characterized by a complex permittivity varying across a wide range of values. The cylinder was coaxially excited by a monochromatic electric current filament. The direct problem was solved using MAS with impedance boundary conditions applied to the surface of the cylinders. The method for solving the inverse problem is based on determining the amplitudes of auxiliary sources (AS), whose fields are expressed as the Green's function of the problem (specifically, Hankel and Bessel functions of zero order). The complex amplitudes of AS were determined from the boundary conditions matching the tangential components of the electromagnetic field in the air region along the spatial observation curve of the field scattered by the cylinder. The final amplitudes of AS were employed for numerically extending the wave fields from the observed scattered-field curve into the surrounding space. It is demonstrated that the proposed method enables reliable localization of cylindrical objects with variable surface impedance covering a broad range of values. Importantly, the distance between the field observation point and the localized cylinders must remain within 3–5 wavelengths.