Summary: We consider the three dimensional electromagnetic inverse scattering problem of determining information about a target buried in a known inhomogeneous medium from a knowledge of the electric and magnetic fields corresponding to time harmonic electric dipoles as incident fields. The scattering object is assumed to be an anisotropic dielectric that is (possibly) partially coated by a thin layer of highly conducting material. The data is measured at a given surface containing the object in its interior. Our concern is to determine the shape of this scattering object and some information on the surface conductivity of the coating without any knowledge of the index of refraction of the inhomogeneity. No a priori assumption is made on the extent of the coating, i.e., the object can be fully coated, partially coated or not coated at all. Our method, introduced in [F. Cakoni, M. Fares
and H. Haddar
, Inverse Probl. 22, No. 3, 845–867 (2006; Zbl 1099.35167
); D. Colton
and H. Haddar
, Inverse Probl. 21, No. 1, 383–398 (2005; Zbl 1086.35129
)], is based on the linear sampling method and reciprocity gap functional for reconstructing the shape of the scattering object. The algorithm consists in solving a set of linear integral equations of the first kind for several sampling points and three linearly independent polarizations. The solution of these integral equations is also used to determine the surface conductivity.