A Forward Scattering Model in Two-Dimensional Half-Space for Scatterers’ Size Estimation Using Linear Inversion

Abstract

Analytic expressions of scattered electric fields for different categories of cylindrical targets buried in the half-space have been developed. In all the cases, investigation domains have been considered two-dimensional and are infinitely long in the remaining dimension. The investigation domains have been excited by the fields generated by a z-directed line source of constant amplitude, operating in the microwave frequencies. The usefulness and validity of these scattering models have been examined by inversion of the scattered electric field generated by the same. The inversion is based on the fact that the scattered field is mapped by a linear operator containing the induced current density and Green’s function of the investigation domain. On application of the incident field, the presence of a discontinuity in half-space induces the current density. By using the information retrieved from the reconstruction of current density by inversion and analytical expressions of the scattered electric field, information about the diameter and the type of the scatterer have been obtained. In addition, the performance of the linear sampling method for shape reconstruction of the scatterer in half-space is also explored.

Keywords

• Current density
• green’s function
• half-space
• inversion
• microwave
• scattered fields