Electromagnetic scattering from slightly rough surfaces with inhomogeneous dielectric profile

Remote sensing of soil moisture using microwave sensors requires accurate and realistic scattering models for rough soil surfaces. In the past much effort has been devoted to the development of scattering models for either perfectly conducting or homogeneous rough surfaces. In practice, however, the permittivity of most soil surfaces is nonuniform, particularly in depth, for which an analytical solution does not exist. The variations in the permittivity of a soil medium can easily be related to its soil moisture profile and soil type using the existing empirical models. In this paper analytical expressions for the bistatic scattering coefficients of soil surfaces with slightly rough interface and stratified permittivity profile are derived. The scattering formulation is based on a new approach where the perturbation expansion of the volumetric polarization current instead of the tangential fields is used to obtain the scattered field. Basically, the top rough layer is replaced with an equivalent polarization current and using the volumetric integral equation in conjunction with the dyadic Green´s function of the remaining stratified half-space medium the scattering problem is formulated. All first-order scattering solutions and second-order scattering solutions for the cross-polarization fields are obtained. The theoretical results are compared with the backscatter measurements of rough surfaces with known dielectric profile and roughness statistics