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The solution to the problem of wave scattering from an object requires the calculation of the total field at the surface of the object. This task generally does not have an exact, explicit solution. In 1952, L. M. Brekhovskikh put forward an approximate solution, so-called the tangent-plane approximation (TPA), which is also referred to as the Kirchhoff approximation. In the TPA at each point of a smooth surface, the latter is approximated by a tangent plane at the point. Since in the case of reflection from a plane, the total field can be readily calculated by Fresnel-type formulas, the scattering problem acquires, in this case, an explicit, approximate solution. A natural generalization of the TPA in 2-D follows when the scattering surface at each point is approximated by a tangent cylinder [a tangent-cylinder approximation (TCA)]. The TCA is considered, in this communication, in the simplest case of convex surfaces, a scalar field, and an impedance boundary condition in 2-D. It is demonstrated that the TCA possesses significantly better accuracy and provides better treatment of the shadowing associated with scattering from rough surfaces being only slightly more demanding than TPA computationally. [ABSTRACT FROM AUTHOR]

The bistatic radar equation currently used for simulating surface-reflected waveforms or delay-Doppler maps (DDMs), produced by signals of opportunity from global navigation satellites system (GNSS) or communication satellites, was previously derived under some limiting assumptions. One of them was the use of the Kirchhoff approximation in a geometric optics limit that assumes strong diffuse (noncoherent) scattering typical for very rough surfaces. This equation would produce an incorrect result for the case of weak diffuse scattering, or in the presence of coherent reflection. In this paper, it is shown that the assumption of strong diffuse scattering is not necessary in deriving such an equation. The derivation of a generalized bistatic radar equation is now based only on the assumption of roughness statistics being spatially homogeneous, and thus this equation is applicable for a much wider range of surface conditions and scattering geometries. This approach allows to correctly describe the transition from partially coherent scattering to completely noncoherent, strong diffuse scattering. It is demonstrated for the case of the GNSS-R DDMs simulated for a wide range of surface winds, and their transitional behavior is discussed. [ABSTRACT FROM AUTHOR]

We propose stochastic solutions to the scattering of electromagnetic waves from penetrable randomly rough surfaces using the vector-based finite-element method (FEM). The random nature of the surface requires the computation to be performed on multiple surface instances. We propose a mesh deformation scheme, which allows the use of a single FEM mesh for computing ensemble averaged quantities. This scheme is used to perform Monte Carlo (MC) iterations, which is much faster than the conventional techniques where a different mesh is utilized for each surface instance. This scheme also allows for MC-free formulations of the problem; in the first kind, we expand the solution in a stochastic basis using the concept of generalized polynomial chaos obtaining ensemble averaged quantities. This results in a larger set of equations that need to be solved just once. In the second kind —the stochastic collocation method—we run the deterministic solver at certain specified points in the random domain corresponding to the rough surface description. We compare these results with those obtained by MC iterations, and outline the computational costs and convergence behavior. We find that stochastic methods are ideal for surfaces with large correlation lengths. For other parameters, the MC approach is preferable. [ABSTRACT FROM PUBLISHER]

We present an analytical, second-order perturbative solution to the problem of electromagnetic plane-wave scattering from a dielectric cylinder with a randomly rough surface. In contrast to previous integral equation-based approaches, we perturb the electromagnetic boundary conditions at the cylinder interface. Doing so affords us tractable expressions for the fields internal and external to the cylinder. We validate our results by comparing them with rigorous, but computationally intensive solutions obtained from the method of moments, and numerically estimate a region of validity for our results. We report this region as $h_0 < \lambda/20$ and $l> 4\,h_0$, where $h_0$ and $l$ are the root-mean-square surface roughness and surface correlation length, respectively, for scattering at a wavelength $\lambda$. [ABSTRACT FROM PUBLISHER]

The sub-domain decomposition iterative method (SDIM) is presented to solve efficiently a large linear system obtained by sampling the boundary integral equations from the method of moments. Then, this new technique is tested on the electromagnetic scattering problem from a large highly conducting one-dimensional rough sea surface. The diagonal blocks are the local impedance matrices corresponding to the geometry sub-domains while the off-diagonal blocks are the coupling matrices describing the interaction between two different sub-domains. The principle of SDIM is to invert the impedance matrix by blocks reducing significantly the complexity in comparison to a direct LU inversion of the whole impedance matrix. In addition, to accelerate the matrix-vector products and to reduce the memory requirement, the adaptive cross approximation (ACA) is applied to compress the sub-domain coupling matrices. For microwave frequencies, the results show that SDIM converges rapidly and faster for the TM polarization. Moreover, the mean compression ratio of ACA is of the order of 98%, which makes this method very efficient. [ABSTRACT FROM PUBLISHER]

Radar backscattering coefficients for heterogeneous pixels are traditionally assumed to be the average of the coefficients for the constitutive homogeneous pixels. We investigate the validity of this assumption for bare rough surfaces by using the 2-D finite-element method to compute the ensemble averaged “true” coefficients for heterogeneous pixels and compare these values with the computed averages for a variety of surfaces. We quantify the impact of heterogeneity in both soil moisture and surface roughness on the averaging assumption. We find that the validity of the assumption rests crucially on the surface correlation type (exponential or Gaussian) and length. In particular, when considering pixels with either heterogeneous soil moisture or roughness, we find that for high-contrast pixels, the backscatter averaging assumption breaks down by as much as 11 dB for Gaussian correlated surfaces for the longest correlation lengths considered (regardless of the source of heterogeneity), whereas for exponentially correlated surfaces, it breaks down by 6 dB for pixels with heterogeneous roughness and 2 dB for pixels with heterogeneous moisture. We attribute this behavior to Gaussian correlated surfaces possessing higher cross-pixel coherent interactions. Furthermore, conditions of validity for the backscatter averaging assumption are identified. [ABSTRACT FROM PUBLISHER]

An efficient method for scattering analysis from slightly rough surfaces is introduced. This method can be used in ray tracing algorithm where the computational efficiency is important due to the complexity and size of problems. In this method, the Kirchhoff approach is used for a periodic extension of the finite surface, which is approximated by strong harmonics of its Fourier series. Typical asphalt surfaces are analyzed by this method in millimeter-wave band and validated with the method of moments. The dominant scattering angles and ray widths of the scattered field can be easily used in ray tracing algorithm. The computation time and accuracy of results show that this method can be used for rough surface scattering analysis in ray tracing algorithm efficiently. [ABSTRACT FROM AUTHOR]

A 2-D vector-element-based finite-element method (FEM) is used to calculate the radar backscatter from 1-D bare rough soil surfaces which can have an underlying heterogeneous substrate. Monte Carlo simulation results are presented for scattering at L-band (\lambda = 0.24\ \m). For homogeneous soils with rough surfaces, the results of FEM are compared with the predictions of the small perturbation method. In the case of heterogeneous substrates, soil moisture (and, hence, soil permittivity) is assumed to vary as a function of depth. In this case, the results of FEM are compared with those of the transfer matrix method for flat soil surfaces. In both cases, a good agreement is found. For homogeneous rough soils, it is found that polarimetric radar backscatter and copolarized phase difference have a nonlinear relationship with soil moisture. Finally, it is found that the nature of the soil moisture variation in the top few centimeters of the soil has a strong influence on the backscatter and, hence, on the inferred soil moisture content. [ABSTRACT FROM AUTHOR]

We evaluate a new 3-D numerical modeling approach for calculating the rough-surface scattering and emission of a soil layer. The approach relies on the use of Ansoft's numerical computation software High-Frequency Structure Simulator, which solves Maxwell's equations directly using the finite-element method. The interest of this approach is that it can be easily extended to studies of heterogeneous media. However, before being applied in this way, it must first be validated for the rough-surface case. In this letter, we perform this validation by comparing the results of rough-surface scattering and emission with the results of the method of moments (MoM) for a range of different roughness and permittivity conditions and with both Gaussian and exponential rough-surface autocorrelation functions. For the scattering case, we obtain results that are in agreement with the MoM to within approximately 1–3 dB for angles up to and including 40^\circ and 2–4 dB for angles from 50^\circ to 70 ^\circ. Agreement for emissivity is to within 3.2 and 3.6 K for low and high roughness conditions, respectively. We then illustrate the application of the new approach by calculating the emission of a two-layer system with rough surfaces, representing the soil-litter system in forests. [ABSTRACT FROM PUBLISHER]

In a combined experimental and model study, we investigated the thermal L-band signatures of a sandy soil with periodic topography (furrows) with dimensions close to the observation wavelength of 21 cm. Measurements were carried out with a radiometer mounted on a tower and aimed at a soil box with an artificially prepared furrowed soil surface. Corresponding reflectivities were derived from brightness temperature measurements performed under dry and moist conditions, with the furrow direction either along or perpendicular to the plane of incidence. Results showed that the furrows had a pronounced effect on the reflectivity, depending on the polarization of the observed radiance, the direction of the furrows, and the soil moisture. A physical reflectivity model for dielectric periodic surfaces was used to explain the soil reflectivities measured for the different furrow directions and soil-water contents. Using this model improved the agreement between the measured and modeled reflectivities considerably compared to the Fresnel reflectivities. The observed dependence of soil reflectivity on furrow orientation and soil moisture could be reproduced by the reflectivity model. The quantitative agreement with the observed reflectivities was further improved by using a simple empirical approach to consider the small-scale heterogeneity of the top soil layer. [ABSTRACT FROM PUBLISHER]

A new hybrid numerical method is described for scattering from an electrically large perfectly-conducting object with dihedral effects above a very long one-dimensional rough surface (two-dimensional problem). Such a problem involves a large number of unknowns and cannot be solved easily with a conventional method of moments by using a direct LU inversion. Thus, to solve this issue, the Extended-PILE method is combined with the forward-backward spectral acceleration (FBSA) for the local interactions on the rough surface and with the second-order physical optics (PO2) approximation for the local interactions on the object. Classically objects under test do not present dihedral effects and in the high frequency domain the first-order PO (PO1) provides the main contribution. In opposite, in this paper since a cross is considered, the second-order inner reflections contribute significantly and the PO2 must be included. By assuming a Gaussian process with a Gaussian height spectrum, this new hybrid method, E-PILE+FBSA+PO2, is tested against the rigorous E-PILE+FBSA method (direct LU inversion on the object) as functions of the object inclination, the polarization and the incidence angle. [ABSTRACT FROM AUTHOR]

Fractal geometry is widely accepted as an efficient theory for the characterization of natural surfaces; the opportunity of describing irregularity of natural surfaces in terms of few fractal parameters makes its use in direct and inverse electromagnetic (EM) scattering theories highly desirable. In this paper, we present an innovative procedure for manufacturing fractal surfaces and for measuring their scattering properties. A cardboard-aluminum fractal surface was built as a representation of a Weiestrass--Mandelbrot fractal process; the EM field scattered from it was measured in an anechoic chamber. A monostatic radarlike configuration was employed. Measurement results were compared to Kirchhoff approximation and small perturbation method closed-form results that were analytically obtained by employing the fractional Brownian motion to model the surface shape. Matching and discrepancies between theories and measurements are then discussed. Finally, fractal and classical surface models are compared as far as their use in the EM scattering is concerned. [ABSTRACT FROM AUTHOR]

An asymptotic method is described for predicting the bistatic normalized radar cross section of a rough homogeneous layer made up of two rough surfaces. The model is based on iteration of the Kirchhoff approximation to calculate the fields scattered by the rough layer, and is reduced to the high-frequency limit in order to obtain numerical results rapidly. Shadowing effects, significant for large incidence or scattering angles, are taken into account through the use of shadowing functions. The model is applicable for moderate to large surface roughnesses having small to moderate slopes, and for both lossless and lossy inner media. It was validated for a rough layer with a rough surface over a perfectly flat surface in a preceding contribution. Here, the extension of the model to a rough layer with two rough surfaces is developed, and results are presented to validate the asymptotic model by comparison with a numerical reference method. [ABSTRACT FROM AUTHOR]

The emission of bare soils at microwave L-band (1-2 GHz) frequencies is known to be correlated with surface soil moisture. Roughness plays an important role in determining soil emissivity although it is not clear which roughness length scales are most relevant. Small-scale (i.e., smaller than the resolution limit) inhomogeneities across the soil surface and with soil depth caused by both spatially varying soil properties and topographic features may affect soil emissivity. In this paper, roughness effects were investigated by comparing measured brightness temperatures of well-characterized bare soil surfaces with the results from two reflectivity models. The selected models are the air-to-soil transition model and Shi's parameterization of the integral equation model (IEM). The experimental data taken from the Surface Monitoring of the Soil Reservoir Experiment (SMOSREX) consist of surface profiles, soil permittivities and temperatures, and brightness temperatures at 1.4 GHz with horizontal and vertical polarizations. The types of correlation functions of the rough surfaces were investigated as required to evaluate Shi's parameterization of the IEM. The correlation functions were found to be clearly more exponential than Gaussian. Over the experimental period, the diurnal mean root mean square (rms) height decreased, while the correlation length and the type of correlation function did not change. Comparing the reflectivity models with respect to their sensitivities to the surface rms height and correlation length revealed distinct differences. Modeled reflectivities were tested against reflectivities derived from measured brightness, which showed that the two models perform differently depending on the polarization and the observation angle. [ABSTRACT FROM AUTHOR]

An analytical method is described for predicting the bistatic normalized radar cross section of a rough homogeneous layer made up of a rough surface over a flat surface. The model is based on iteration of the Kirchhoff approximation to calculate the fields scattered by the rough layer, and is reduced to the high- frequency limit in order to obtain numerical results rapidly. The shadowing effect, significant for larger incidence or scattering angles, is taken into account through the use of shadowing functions. The model is applicable for moderate to large upper surface roughnesses having small to moderate slopes, and for both lossless and lossy inner media. It was validated for a two-dimensional problem (with 1D surfaces) in a preceding contribution. Here, the extension of the model to 2D surfaces is developed, and results are presented to validate the asymptotic model by comparison with a numerical reference method. [ABSTRACT FROM AUTHOR]

We present a boundary integral method for the numerical solution of the rigorous problem of wave scattering from rough surfaces under grazing illumination. The model of a locally perturbated plane is adopted: a finite patch of rough surface has its roughness flattened at the edges. The boundary formulation unknowns are the tangential components of the scattered field, defined as the contribution from the rough area. This way, the numerical domain of study is correctly bounded, even with a plane wave as incident field, and the sampled area is made independent of the incidence. This rigorous approach, called the grazing method of moments, is implemented on two-dimensional perfectly conducting surfaces and validated by comparison with a reference numerical solution for surfaces with Gaussian correlation functions. Now, the validity of approximate models at low-grazing-angles can be investigated; the small perturbation method and the small slope approximation are addressed in this paper. Scattering diagrams show how the performances of these methods deteriorate drastically at backward scattering angles as the incidence goes to grazing. [ABSTRACT FROM PUBLISHER]

The well-known Rayleigh parameter, which characterizes the degree of roughness of a corrugated surface for the case of reflection on a rough surface, is extended to the reflection on a rough layer. An application to the forward radar propagation over oil slicks on sea surfaces, using the Ament model, is given. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 2285–2290, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22716 [ABSTRACT FROM AUTHOR]

Light detection and ranging (LIDAR) data acquired during the AMSR-Ice03 Arctic flights are used to observe and characterize the spectral behavior of sea ice roughness. Height distributions and roughness spectral densities are derived from surface profiles measured over a variety of sea ice types. The spectral densities are fit to Lorentzian curves to obtain the correlation length and root-mean-square height of roughness within the sampling bandpass of the LIDAR profiler. The utilization of these spectral parameters outside of their bandpass is also discussed. [ABSTRACT FROM AUTHOR]

The low-grazing-angle (high incidence angle) microwave back scattering from three-dimensional (3-D) surfaces approximating the crests of plunging-breaker water waves has been numerically found using the multilevel fast multipole algorithm. The test profiles were synthesized from a series of two-dimensional (2-D) profiles that represent the time evolution of a breaker. The results show that the strong cancellation of the vertically polarized backscattering (VV) midway through breaking that was previously identified with the 2-D profiles is maintained when the azimuthal variation of the 3-D wave is included. An optical-based model confirms that this is due to interference between back reflection from points on the forming jet and cavity of the wave. This is matched by constructive interference at horizontal polarization (HH), leading to HH-to-VV backscattering ratios that are much larger than unity. This effect remains when the azimuthal look angle is moved from directly upwave. When looking upwave, the interference disappears later in breaking when the fully formed jet shadows the cavity region. However, it returns when looking sufficiently away from directly upwave so that the cavity again becomes visible. The HH-to-VV ratios are typically greater than unity at this time, although HH cancellation can appear very late in the breaking when the round-trip distances to the jet and cavity specular points are sufficiently different. [ABSTRACT FROM AUTHOR]

In this article, the influence of Rayleigh and Mie scattering, which are the main causes of mode mixing in polymer optical fibers (POFs), is investigated. Measurement results obtained from a variety of different POF types ranging from standard POF, high-temperature POF, up to custom-made POF are presented. These measurements are compared to theoretical results obtained from a simplified scattering model. By comparing both results, the contribution of the different scattering sources and mechanisms is characterized independently [ABSTRACT FROM PUBLISHER]

Fractal geometry provides reliable models to describe geometrical properties of natural surfaces. Therefore, their use in the electromagnetic scattering methods deserves careful research. In order to have complete insight into the phenomenon, a measurement campaign on a fractal surface in a controlled environment is a key step. In this paper, we propose a technique for building a fractal surface that can be used for electromagnetic scattering evaluation purposes. The surface characteristics are imposed by computer synthesizing a bandlimited Weierstrass-Mandelbrot function, whose actual shape is constructed by means of a cheap innovative technique: the synthesized surface is made from cardboard covered with aluminum foil, which gives a conducting surface and creates the micro-scale conditions, useful to represent manufacturing errors. Statistics of the overall surface shape are then measured, analyzed and compared with the imposed ones, providing and verifying the rationale for a fully controlled surface to be applied in any kind of experiment on natural surfaces. [ABSTRACT FROM AUTHOR]

In order to reliably predict long-range radar coverage within an ocean environment, one must accurately account for the effects of ocean roughness on radar propagation. The method known as the Miller-Brown approximation is a widely used technique for computing the coherent field reflected by a rough sea surface and it is often incorporated into sophisticated numerical propagation models such as the Fourier split step algorithm of the parabolic wave equation. Nevertheless, the accuracy of the Miller-Brown approximation has not been systematically or rigorously assessed for realistic scenarios of interest to shipboard radars. We present here a first step toward this assessment by using a method of moments solution to compute the propagation factor, η, for an ensemble of one-dimensional (1-D) rough sea surface realizations having dielectric properties and roughness profiles that are consistent with a wind roughened ocean surface. The particular method of moments (MoM) technique used combines an accelerated spectral method and a multigrid iterative approach (MGIA). The MGIA results for the propagation factor ηMGIA are compared to the corresponding predictions ηMB obtained via the Miller-Brown approximation. In addition, the well-known Ament approximation is used to compute results for the propagation factor, ηA and the results predicted by ηA are compared with those of ηMB. A heuristic numerical fitting scheme is also presented that improves the agreement between ηMGIA and ηMB and is used to facilitate the comparison between ηMB and ηA. [ABSTRACT FROM AUTHOR]

Several techniques are considered for the analysis of electromagnetic scattering from rough ocean surfaces. A rigorous Multi-Level Fast Multipole Method (MLFMM) is employed, as well as a high-frequency ray-based solution. The MLFMM analysis is implemented in scalable form, allowing consideration of scattering from very large surfaces (in excess of 1002 × 1002, where A represents the electromagnetic wavelength). Plane-wave incidence is assumed, and a key aspect of the MLFMM study involves investigating techniques for rough-surface truncation. The rough surface is modeled as a target placed in the presence of an infinite half-space background; to minimize edge effects, the surface is smoothly tapered into the planar half space. We also consider the technique of employing a resistive taper on the edges of the rough surface. These two truncation techniques are compared in accuracy, memory requirements (RAM), and in computational time (CPU). The MLFMM results are used to validate an approximate ray-based high-frequency model that allows rapid analysis of large surfaces. The computational results are compared to measured forward-scattering data from scaled laboratory measurements, used to simulate scattering from an ocean surface. [ABSTRACT FROM AUTHOR]

Random rough surfaces with slowly decaying power spectral density can have infinite slope variance. Such surfaces do not satisfy the classical curvature criterion for validity of the physical optics (P0) approximation, and the infinite frequency geometrical optics limit or specular point scattering model breaks down. We show for two-dimensional surfaces with infinite slope variance that the Gaussian form of the classical geometrical limit generalizes to a stable distribution function. We also show that the PO integral is insensitive to surface components with spatial frequency above a cutoff wavenumber, which explains past observations that PO can be accurate for surfaces with power law spectra. This result leads to a general validity condition for the PO approximation in the backscattering direction for power-law surfaces, which in the case of a κ-4 spectrum requires that the significant slope of the surface be less than 0.03. [ABSTRACT FROM AUTHOR]

The microwave backscattering from a three-dimensional (3-D) target approximating the rough crest of a gently spilling water wave at low grazing angle illumination has been numerically examined. The target surfaces were synthesized from the direct two-dimensional (2-D) measurement of the time evolution of the upwave-downwave cross-section of a wave-tank breaker. The reference scattering was found using the multilevel fast multipole algorithm implemented with impedance boundary conditions and resistive surface loading to suppress nonphysical edge diffraction. The scattering was compared with the predictions of the two-scale model and a synthesis of the 3-D backscattering from individual 2-D calculations. Specular reflection from a bulge feature that appeared on the crest prior to breaking dominated the backscattering at both polarizations, overwhelming even the strong vertical polarization Bragg scattering that appeared in the corresponding scattering from the individual 2-D profiles used to synthesize the 3-D target. The scattering from the surface including the bulge could be accurately modeled using a coherent addition of the scattering from the 2-D profiles. The two-scale model performed poorly whenever there are steep sections on the surface that provide significant quasi-specular back-reflection. Accuracy improved when the specular points were eliminated and the dominant scattering roughness was fully illuminated, but was still sensitive to the surface-roughness scale-separation threshold used in its application. [ABSTRACT FROM AUTHOR]

Channeling phenomenon is a type of forward scattering and multipath that occasionally occurs when a well formed sea wave briefly reflects or focuses the out-of-plane energy toward the receiver, yielding a higher than expected, broadband power gain. A series of X-band, forward-scattering measurements in a large wave tank observed multiple channeling events at low grazing angles. The wave tank simulated a one-dimensional, 1/10th-scale Pierson-Moskowitz surface at sea states 0, 3, and S. During the measurements, channeling events were observed under crosswind wave conditions when a properly constructed wave trough, coinciding with the radar's line of sight, channeled or focused the out-of-plane, forward-scattered energy toward the receiver. Presented is a summary of the channeling events observed and a physical model of the channeling phenomenon based on experimental observations and numerical simulations. [ABSTRACT FROM AUTHOR]

A series of low-angle radar measurements were conducted over a large wave pool capable of producing a wide range of scaled sea conditions. The X-band (8-12 GHz) measurements were performed for 1°, 3°, and 5° look down angles (LDAs) for the HH and VV polarizations. The roughened water simulated a one-dimensional 1/10th-scale Pierson-Moskowitz surface at sea states 0, 3, and 5. The wave profiles were detailed using both ultrasonic point detectors and a laser sheeting technique capable of measuring a cross section of the sea. The compiled data represent the first forward-scattering measurement 1) preformed under a variety of controlled conditions for low grazing angles and 2) with detail profiling of the wave structure syncronized with the radar. Presented are the experimental setup with calibration methodology, measurement conditions, and selected radio-frequency forward-scattering (HH polarization) results for the 5° LDA for sea state 0, 3, and 5 sea conditions. [ABSTRACT FROM AUTHOR]

As wirelessly connected embedded systems become ubiquitous, previously undocumented propagation environments must be explored to support their design. This paper describes the results of a study of such an environment: short-range wireless propagation outdoors, near the ground. In the study, frequencies were considered within three industrial, scientific, and medical (ISM) bands: 902–928 MHz, 2400–2426 MHz, and 5725–5752 MHz. Experimental propagation loss was summarized based on measurements in eighteen environments, at varying heights, distances, and polarizations. Based on the data collected, the appropriateness of a simple design guideline, based on a two-ray propagation model, is discussed. Summaries of the path loss, fading, and the influences of antenna height, antenna separation, and surrounding clutter in highly variable environments are given. Additionally, limited numerical modeling of the impact of surface roughness is provided. Particular focus was given in the study to heights and distances appropriate for randomly deployed wireless sensor networks, such as autonomous unattended ground-sensor systems. [ABSTRACT FROM AUTHOR]

The far-field theory of Beckmann and Spizzichino is modified to produce a theory for diffuse scatter in the near field which can be applied to the analysis of multipath effects over a rough sea. [ABSTRACT FROM AUTHOR]

The forward-backward (FR) method is an efficient technique for numerical evaluation of electromagnetic scattering from rough surfaces. In its usual formulation, this technique can be only applied to perfectly or highly conducting surfaces. In addition, up to now FB has been employed to compute scattering from surfaces modeled by Gaussian stochastic processes with Gaussian or Pierson-Moscowitz spectra. Accordingly, this technique can be fruitfully used for numerical simulations of scattering from sea surfaces. However, in order to properly deal with natural soil surfaces, extension to the dielectric interface case and to fractal surface models is needed. Extension of the FB method to the dielectric interface case has been recently presented, whereas application to fractal surface models is presented here. Original contribution of the present paper is twofold. First of all, the FB method for dielectric profiles is framed within the theory of iterative methods for the solution of linear systems. In addition, application of the EB method to dielectric band-limited fractional Brownian motion (fBm) fractal one-dimensional surfaces is explored. Numerical experiments show that, for most of realistic values of dielectric constant and fractal parameters actually encountered for natural soil profiles, the FB method is very rapidly convergent, and its results are in perfect agreement with "exact" ones (i.e., with results of method of moments solved via a direct method). [ABSTRACT FROM AUTHOR]