Half-space Random Medium Research Articles

Wave propagation and scattering from a random medium with a random interface

This paper deals with the study of wave propagation and scattering in a half-space random medium with a random interface. The surface randomness and the volume randomness are treated with equal importance and a multiple scattering solution is sought. The random fluctuations of both the random medium and the surface are assumed to be small and obey Gaussian statistics. These assumptions enable us to use approximations and physically identify the various scattering processes. The Feynman diagram technique is used to derive the Dyson equation and the Bethe-Salpeter (B-S) equation for the first and second moments of Green's functions, respectively. Two approximations, viz., the bilocal approximation and the nonlinear approximation are applied to the Dyson equation. Proceeding along similar lines the ladder approximation is applied to the B-S equation. The Feynman diagram technique affords us to clearly identify the scattering interaction between the random surface and the random medium. These interactions which are usually ignored in a single scattering approximation become important in a multiple scattering solution.

Optimum polarizations in the bistatic scattering from layered random media

Investigates the polarimetric bistatic scattering characteristics of layered random media. On applying the Born approximation, the authors have calculated the bistatic Mueller matrix of a half-space random medium. The power received by a receiving antenna is the quantity chosen to optimize. The variables of the problem are the polarizations of the transmitting and receiving antennas. For the case when the polarizations of the transmitting and receiving antennas are identical, the authors have calculated the optimum polarizations and they have found that the optimum polarizations include both linear and elliptical polarizations. The conditions for maximum and minimum received power are also obtained. In the backscattering case, they have considered the situation when the transmitting and receiving antennas have independent polarizations. For a two-layer problem, they have observed the influence of the thickness of the layer in the classification of the optimum polarizations.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A high order renormalization method for radar backscatter from a random medium

The problem of radar backscattering from a half-space random medium is formulated in terms of a series solution to Dyson's equation for the mean field in the random medium. The renormalization method is applied to given an approximate solution through the use of Feynman diagrams. An improved approximation is then obtained by including two additional summations of infinite series of these diagrams. The results from this improved approximation are used to calculate the radar backscattering cross sections and compared with those of a previous paper (1980). For comparison with experimental data, a field of vegetation is modeled as a random medium with an average complex permittivity as well as fluctuations in the real and imaginary parts of the permittivity. The values of the average permittivity and the variance of the fluctuations are estimated by the use of dielectric mixture theory. >

A Monte Carlo method for radar backscatter from a half-space random medium

The problem of electromagnetic multiple scattering in a random medium is treated by a Monte Carlo method, in which an incident beam of photons is progressively scattered by scattering centers in the medium. The theory characterizes each scattering by functions describing the probability of the photon being scattered or absorbed, and the probability of its being scattered into certain directions. This process is tracked until the photon is finally absorbed or backscattered into the receiver. Variance reduction techniques are introduced to reduce the computation time required for acceptable ensemble averages of the backscattering cross sections. Ellipsoidal dielectric scatterers are used to model circular disk-shaped leaves, elliptical disk-shaped leaves, and needle-shaped leaves, which are randomly distributed in a half-space medium. The Monte Carlo simulations give good comparison with experimental data of backscattering cross sections from fields of wheat, corn, and milo. >

Mean wave solution: bounded medium—discrete scatterers

Multiple scattering technique has been employed in order to derive an eqaution for the mean wave which is propagating in a one dimensional half space random medium containing randomly distributed discrete scatterers with nonuniform background. The equation of the mean field is in the form of Dyson equation. Small and large scale variables have been defined, and the two variable expansion technique has been used in order to obtain the zero order solution to the mean field. In this solution it is assumed that the interparticulate spacing over the size of the particle is small compared to unity (sparse distribution of scatterers). In contrast to the one dimensional continuous random medium, only one effective propagation constant has been found. The zero order solution to the mean field can be used in order to derive the radiative transfer equation from the correlation equation, thus eliminating the gap between the multiple scattering and radiative transfer theory.

Active remote sensing of random media

Analytical results for the bistatic scattering coefficients and the backscattering cross sections have been derived for active remote sensing of earth terrain with the model of bounded random media which accounts for volume-scattering effects. It is found that as a result of the effect of the second boundary, the horizontally polarized return σhh can be greater than the vertically polarized return σvv, whereas for a half-space random medium σvv is always greater than σhh. We illustrate by matching the theoretical results with experimental data collected from vegetation field.

The mean Green's dyadic for a half-space random medium: A nonlinear approximation

The vector problem of a source embedded in a halfspace random medium is considered, and a zeroth-order solution for the mean Green's dyadic in the nonlinear approximation is derived. This is done by applying a two-variable expansion method to obtain a perturbation solution of the Dyson equation for the mean Green's dyadic. The final results of the dyadic are given in closed form as a corrected effective propagation constant, including terms of the order k_{a}^{2}\sigma^{2}l^{2} where k_{a} is the wavenumber in the average medium, l is the correlation length, and \sigma^{2} is the variance of the permittivity fluctuations. These results show a significant difference from those of the one-dimensional problem considered by Tsang and Kong [4]. Whereas the scalar solution gives different effective propagation constants for the component waves in the Green's function, the vector solution derived contains only a single propagation constant for all of the components in the Green's dyadic.