Electromagnetic scattering from slightly rough surfaces with inhomogeneous dielectric profiles

Abstract

Abstract-Remote sensing of soil moisture using microwave sensors require 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 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. Closed-form analytical expressions for the induced polarization currents to any desired order are derived, which are then used to evaluate the bistatic scattered fields up to and including the third order. The analytical solutions for the scattered fields are used to derive the complete second-order expressions for the backscattering coefficients as well as the statistics of phase difference between the scattering matrix elements. The theoretical results are shown to agree well with the backscatter measurements of rough surfaces with known dielectric profiles and roughness statistics.

Multipath exploited Bayesian and Cramér-Rao bounds for single-sensor target localization

“…Typically in urban scenarios, to facilitate operational covertness large standoff distances maybe employed, which lead to large incident angles for most walls. EM intensive bistatic and backscattering models for rough walls are beyond the scope of analysis here, but could be seen in [21][22][23][24] and references therein.…”

“…It is noted that there are several other design criteria, however as stated in ( [8], p.153), D-optimal designs are practically relevant. A closed form solution to (22) is not possible, and the optimization will be performed numerically in Section 6. It is stressed that these computations may be performed offline, i.e., during the sensor deployment phase.…”

“…Our wall roughness model is based on using random perturbations to model roughness, as first pioneered by Rice [25], and used in for example [21][22][23] therein. That is, to emulate roughness/craters on the wall, we consider N subreflectors which form the length of the wall(s).…”

Electromagnetic scattering from short branching vegetation

“…Using ray optics, the propagation from the equi-phase plane [shown in Fig. 5(a)] directly to the scatterer is given by (17) where denotes the location at which the ray intersects the interface between the vegetation layer and free-space. Here, the effect of refraction is ignored assuming a diffuse boundary between the vegetation layer and free-space , and denotes the polarization of the wave.…”

“…In this paper, a second-order small perturbation model (SPM) [17] and a physical optic (PO) model [18] are incorporated to handle the backscatter from the rough surface.…”