Inverse scattering problem for the tensor fields in a coordinate-free representation

Abstract

The inverse scattering problem is to reconstruct or recover some physical and/or geometric properties of an object from the measured scattered field in the process of illumination by an incident wave. The probing radiation can be an electromagnetic wave (e.g., microwave, optical wave, and X-ray), an acoustic wave, or some other waves. The inverse scattering problem is important when detailed information about the structure and composition of an object is required, but it cannot be obtained directly from the measurements. The paper is devoted to the electromagnetic inverse scattering problem for a dielectric anisotropic and magnetically isotropic media. The properties of an anisotropic medium with respect to electromagnetic waves are defined by the tensors, which give the relation between the inductions and the fields. The tensor Fourier diffraction theorem derived in the paper can be considered as a useful tool for studying tensor fields in inverse problems of electromagnetic scattering. The Fourier diffraction theorem is obtained in a coordinate-free representation by the use of tensor (dyadic) analysis techniques. The method of inversion is based on the first Born approximation.