The Properties Of The Far Field Operator For The Conductive Inverse Scattering Problem

In this paper, We consider the conductive problem of finding such thatwhere r =|x| , uⁱ(x) = e^ikx-d, d is a vector on the unit sphere Ω and the radiationcondition (6) is assumed to hold uniformly for x = x /|x| on Ω. D is a bounded domain with connected complement R³\D and C2 boundary dD having unit outward normal v. For the sake of simplicity. We assume all the condition k, k₀ μ and λ to be positive. The u^s has an asymptotic behavioras r→∞, where u_∞ is the far field pattern of the scattered field u^s . We definethe far field operator F :L²(Ω) →Z²(Ω) by(8) (Fg)(x):=u(x,d)g(d)ds(d).We establish three basic results about the far field pattern and far field operator in the case of conductive problem: reciprocity for the far field pattern and the normality and injectivity properties of the far field operator.