An extension of the integral equation model IEM2M for rough surfaces of complex permittivity

The integral equation model (IEM) developed by A.K. Fung and co-workers has arguably been the most cited and implemented rough surface scattering model in the field of radar remote sensing. It was obtained as a second-order iteration of the incident electromagnetic field to the integral equations of the surface fields. Therefore, it is an extension of the first-order Born approximation of the corresponding Neumann series that produce the classical Kirchhoff approximation. The IEM was tuned many times over the last twenty years due to the imperfect introduction and handling of the Weyl representation of the spherical wave in its first version. The work presented here is a development of the contribution made by the same author in 2001 (IEM2M) and reported extensively in [1] (IEM2Mc). It has been the first version of IEM able to blend analytically both the Kirchhoff and the small-perturbation approximations for the bistatic case and dielectric surfaces. IEM2M was celebrated by those who found the original IEM not enough rigorous but also criticized by Fung and his co-workers. In this paper an extension of IEM2M is presented that extends it in two aspects: the inclusion of evanescent waves in the formulation of the model and the extension of the range of applicability of the second-order scattering terms to interfaces with complex permittivity scattering media. These two issues had only been addressed in the IEM version developed by Du. However, Du needed to make a mathematical assumption on the correlation function which was not explained from a physical point of view. In the work proposed here this assumption is not necessary. Although all these issues are dealt with extensively in [1], this paper focuses on the comparison of IEM2M, IEM2Mc, the Kirchhoff approximation (KA) and the Small Perturbation Method (SPM). account of them. Regarding IEM, Fung´s last update on his version of IEM is available in [2].