A convenient analytical framework for electromagnetic scattering from composite targets

This paper furnishes a convenient theoretical framework for the analytical evaluation of the bistatic scattering coefficients, under the Kirchhoff approximation (KA) in electromagnetics. Starting from the KA, specific results under the geometrical optics and physical optics approximations are furnished, along with the backscattering geometry. The main aim is to provide closed-form expressions of the scattering matrix that are suited to scenarios where multiple-bounce scattering comes into play and/or surfaces with arbitrary unit normal are present. This is accomplished by addressing the following objectives: (1) to provide an explicit formulation of the scattering matrix under KA in terms of the incident and scattered unit wave vectors, (2) to provide a more generic derivation of the scattering matrix under the physical optics approximation by relaxing typical hypotheses regarding the geometry of the scattering problem, and (3) to highlight some important symmetries of the scattering matrix under KA. It is shown that the scattering matrix under KA can conveniently be expressed in terms of few variables, thus greatly reducing the complexity of the theoretical derivation of the scattering matrix. Some benefits of the proposed formalism are illustrated in two application examples, where the problem is the analysis of the electromagnetic scattering from canonical composite targets. The canonical study cases demonstrate the evaluation of the scattering matrix in complex scenarios, such as maritime and urban environments, where multiple-bounce contributions and/or contributions from tilted surfaces come into play. Finally, comparisons with literature results allow for validating the proposed derivation and assessing its validity limits in practical applications.