Combined far‐ield operators in electromagnetic inverse scattering theory

Abstract

SUMMARYWe consider the inverse scattering problem of determining the shape of a perfect conductor D from a knowledge of the scattered electromagnetic wave generated by a time-harmonic plane wave incident upon D. By using polarization e ects we establish the validity of the linear sampling method for solving this problem that is valid for all positive values of the wave number. We also show that it su ces to consider incident directions and observation angles that are restricted to a limited aperture.

A Qualitative Approach to Inverse Scattering Theory

“…For z ∈ D e and a given > 0 every function g z ∈ L 2 t (S 2 ) that satisfies F g z − E e,∞ (·, z, q) L 2 t (S 2 ) < is such that lim →0 E g z X(D,∂DI ) = ∞. Theorem 10.3 is also valid for the case of a perfect conductor (i.e., ∂D I = ∅) provided we modify the far-field operator F in an appropriate manner [16].…”

“…We now proceed to prove the foregoing approximation property [16]. Assuming that k 2 is not a Dirichlet eigenvalue for the disk Ω R (this is not a restriction since we can always find a disk containing D that has this property), by the trace theorem, it suffices to show that the set of functions…”

The Identification of Thin Dielectric Objects from Far Field or Near Field Scattering Data

“…The inverse scattering problem that we will consider in this section of our paper is to determine Γ and λ from a knowledge of u ∞ (x, d) forx and d on the unit circle S. Using [5], one can easily generalize the following analysis for the case of limited aperture data, i.e., forx, d ∈ S 0 ⊂ S. For the unique determination of Γ and λ from the above data, see [28] (see also [7], [10]). We will use the linear sampling method to solve this inverse problem [6].…”

The Determination of Anisotropic Surface Impedance in Electromagnetic Scattering

“…In the following investigation we assume, for simplicity, that E ∞ (x, d, p) is known for all d,x ∈ Ω. All theoretical results obtained here hold true for the case of limited aperture incident and observation directions due to the analyticity of the far field pattern (see Section 3.2 in [1]). We end this sections by introducing the main tools employed in our investigation…”