INVERSE SCATTERING OF AN ARBITRARILY SHAPED BURIED SCATTERER WITH CONDUCTIVE BOUNDARY CONDITION

In this study, an integral equation based method for arbitrarily shaped cylindrical objects that have conductive boundary condition on their surface and are buried in arbitrarily shaped cylindrical dielectrics is presented. The aim of the direct scattering problem is to obtain the far field in the case of time harmonic plane wave incidence. The inverse problem considered here is the reconstruction of the conductivity function of the buried scatterer from meausurements of the far field for one incident wave, assuming that the shapes of all scatterers are known. Both for the direct and the inverse problems potential approach is used to obtain a system of boundary integral equations which are numerically solved by Nystr¨ om method and Tikhonov regularization is applied to the first kind of integral equations. Let D0 ‰ IR 2 be a bounded medium closured by a smooth curve i0 and D1 denotes a doubly connected bounded medium with a smooth boundary @D1 consists of an interior boundary i0 and an exterior boundary i1 such that @D1 = i0 [i1 and i0 \i1 = ;. The unbounded domain D2 is connected with the boundary i1 to the domain D1. We shall denote by ”0 the unit normal of the boundary i0 directed into exterior of D0 and by ”1 the unit normal of the boundary i1 directed into exterior of D1. The direct scattering problem is to find the far field u1 where the total fields uj have to satisfy Helmholtz equations in the corresponding domains,