Near Field Approximation by Successive Scattering from Finite Cylinders for Random Media

This research investigates successive scattering of electromagnetic waves from tree branches by introducing an efficient approach to determine the scattered field from one branch to another when the branches are near to each other. This sort of higher-order scattering mechanism within a vegetative canopy is of increasing interest to the Earth science remote sensing community. The purpose of the present work is to verify the accuracy and computational efficiency of an analytic scattering model suitable for use in creating higher fidelity canopy simulations. Such applications require these types of calculations for a large number of scatterers, making solutions by numerical methods unacceptably slow. The approach offers faster results relative to traditional moment methods.;A physical arrangement is considered where the branches may be arbitrarily oriented and in the near-field of each other for microwave frequencies of interest (L- through X-Band). First, a successive scattering methodology is used to derive the second-order scattered field for the case of two generic scatterers in proximity to each other. Such a two-body system represents the simplest arrangement to address near-field volume scattering. Next, the general formula is applied to find the second-order bistatic scattering amplitude for a pair of tree branches modeled as finite length thin cylinders. To improve computational efficiency, the solution is then specialized to the Fresnel region and results compared with both an exact Green's function solution and the far field approximation over the Fresnel range of interaction distances. Finally, beginning with the general successive scattering expression, an analytical spectral formulation is applied to the finite cylinder scatter problem. Fourier transform methods are applied to transform the spatial three-dimensional vector integral to the wave vector domain in spectral spherical variables. The vector integral is evaluated by first employing Cauchy's theorem to the integral over the magnitude variable, leaving a two-dimensional integral over the spectral angular variables between the cylinders. Care must be taken in evaluating the remaining integral, as poles lead to singularities in the integration domain. Results are first presented for a single cylinder vector field problem to illustrate the technique and verify the approach. Results and conclusions are then presented for the case of a two-cylinder arrangement assuming a thin cylinder approximation.;To assess performance of the proposed Fresnel and spectral approximation models, representative bistatic scattering results are compared to a benchmark "exact" model and aspects of computational efficiency are addressed.