Inverse scattering for an impedance cylinder buried in a dielectric cylinder

Abstract

An inverse scattering problem is considered for arbitrarily shaped cylindrical objects that have inhomogeneous impedance boundaries and are buried in arbitrarily shaped cylindrical dielectrics. Given the shapes of the impedance object and the dielectric, the inverse problem consists of reconstructing the inhomogeneous boundary impedance from a measured far field pattern for an incident time-harmonic plane wave. Extending the approach suggested by Akduman and Kress [Direct and inverse scattering problems for inhomogeneous impedance cylinders of arbitrary shape. Radio Sci. 38 (2003), pp. 1055-1064] for an impedance cylinder in an homogeneous background medium, both the direct and the inverse scattering problem are solved via boundary integral equations. For the inverse problem, representing the scattered field as a potential leads to severely ill-posed linear integral equations of the first kind for the densities. For their stable numerical solution Tikhonov regularization is employed. Knowing the scattered field, the boundary impedance function can be obtained from the boundary condition either by direct evaluation or by a least squares approach. We provide a mathematical foundation of the inverse method and illustrate its feasibility by numerical examples.

Inverse scattering for surface impedance from phase-less far field data

“…Then using the impedance boundary condition the impedance function can be reconstructed by a regularized least squares method. For a related reconstruction of the impedance function of a cylinder buried in another dielectric cylinder we refer to [16]. However, this direct method cannot be employed for the inverse problem IP2 without phase information.…”

Shape reconstruction of an inhomogeneous impedance cylinder via potential and neural network approach

“…Layer potentials are the solutions of the Helmholtz equation in D and in R 2 D and satisfy the Sommerfeld radiation condition [20]. Along this line to arrive at a uniquely solvable integral equation, we represent the scattered field via combined single-and doublelayer potential with a density , (4) where x ʦ R 2 ѨD. is the coupling parameter and it is chosen equal to the real part of the wave number, such as ϭ Re͕k͖.…”

“…In this context, Kress [1] described an effective method to reconstruct the shape of a sound-soft scatterer by solving boundary integral equations iteratively. This algorithm is extended to soundhard obstacles [2], to 3D geometries [3], to buried obstacles [4], and also to the second-order Newton method [5]. Moreover, methodologies reconstructing both the impedance function and the shape of the object have gained more attention due to the fact that one can distinguish the target from the environment if its impedance function has been already known.…”

“…Controlling the state of polarization (SOP) in optical fiber has been an active research topic in the last two decades because of the many important applications of automatic polarization controller (PC) in optical communications [1][2][3][4]. The aim of a PC is to transform an arbitrary input SOP into a desired output SOP.…”

Solutions of boundary detection problem for modified Helmholtz equation by Trefftz method

“…Many numerical schemes are recently proposed to deal with the inverse problems, such as the method of fundamental solutions, [1][2][3][4][5] the boundary element method (BEM), [6,7] the radial basis function collocation method, [8,9] the boundary particle method [10,11], the modified collocation Trefftz method (MCTM), [12][13][14] boundary integral equation, [15,16] etc. Most numerical schemes for inverse problems will result in illposed, inaccurate and unstable results.…”