A linearized inverse scattering problem for the polarized waves and anisotropic targets

We analyze the scattering of a plane transverse linearly polarized electromagnetic wave off a plane interface between the vacuum and a given material. For a variety of predominantly dielectric materials, from isotropic to anisotropic and weakly conductive, we show that when the scattering is weak, the first Born approximation predicts the correct scattered field in the vacuum region. We also formulate and solve the corresponding linearized inverse scattering problem. Specifically, we provide a necessary and sufficient condition under which interpreting the target material as a weakly conductive uniaxial crystal allows one to reconstruct all the degrees of freedom contained in the complex 2× 2 Sinclair scattering matrix. This development can help construct a full-fledged radar ambiguity theory for polarimetric imaging by means of a synthetic aperture radar (SAR), which is in contrast to the approach that currently dominates the SAR literature and exploits a fully phenomenological scattering matrix. Moreover, the linearized scattering off a material half-space naturally gives rise to the ground reflectivity function in the form of a single layer (i.e. a δ-layer) at the interface. A ground reflectivity function of this type is often introduced in the SAR literature without a rigorous justification. Besides the conventional SAR analysis, we expect that the proposed approach may appear useful for the material identification SAR (miSAR) purposes. (Some figures may appear in colour only in the online journal)