Scattering cross sections for composite rough surfaces using the unified full wave approach

The full wave approach is used to derive a unified formulation for the like and cross polarized scattering cross sections of composite rough surfaces for all angles of incidence. Earlier solutions for electromagnetic scattering by composite random rough surfaces are based on two-scale models of the rough surface. Thus, on applying a hybrid approach physical optics theory is used to account for specular scattering associated with a filtered surface (consisting of the large sonic spectral components of the surface) while perturbation theory is used to account for Bragg scattering associated with the surface consisting of the small scale spectral components. Since the full wave approach accounts for both specular point scattering and Bragg scattering in a self-consistent manner, the two-scale model of the rough surface is not adopted in this work. These unified full wave solutions are compared with the earlier solutions and the simplifying assumptions that are common to all the earlier solutions are examined. It is shown that while the full wave solutions for the like polarized scattering cross sections based on the two-scale model are in reasonably good agreement with the unified full wave solutions, the two solutions for the cross polarized cross sections differ very significantly.     

A new unified full wave approach to evaluate the scatter crosssections of composite random rough surfaces

A new unified approach, based on the original full wave solutions, is presented to evaluate the like and cross polarized scattering cross sections of composite (multiple scale) random rough surfaces. The rough surfaces are assumed to be characterized by the Pieson-Moskowitz spectral density function. To account for the surface undulations, the incoherent radar cross sections are obtained by regarding the composite rough surface as an ensemble of pixels of arbitrary orientation     

Scattering by anisotropic models of composite rough surfaces--Full wave solution

Expressions for the scattering cross sections of anisotropic models of composite random rough surfaces are derived using the full wave approach that accounts for specular point scattering and Bragg scattering in a self-consistent manner. Backscatter cross sections are evaluated for vertically and horizontally polarized waves as a function of angle of incidence for cross wind, up wind, and down wind directions. The cross sections are most sensitive to wind direction for angles of incidence around40deg.     

Full wave analysis for rough surface diffuse, incoherent radarcross sections with height-slope correlations included

The bistatic scattering cross sections are derived for rough one-dimensional perfectly conducting surfaces using the full wave approach. The surfaces are characterized by four-dimensional Gaussian joint probability density functions for heights and slopes. Thus, correlations between the rough surface heights and slopes are accounted for in the analysis. Convergence of the formal series solution is considered. Self-shadowing effects are included. The full-wave solutions are compared with the small perturbation solutions, which are polarization dependent, and the specular point (physical optics) solutions, which are independent of polarization. Both the physical optics and the small perturbation solutions can be obtained from the full-wave solution     

Microwave backscatter from non-Gaussian seas

Rough-surface scattering theory is applied to study microwave backscattering from seas characterized by a non-Gaussian wave-height distribution. The relationship of the geometrical optics limit of rough-surface scattering theory to the probability density of surface slopes is used to relate the coefficients of Gram-Charlier expansions, describing measured slope statistics, to the wavenumber spectra of non-Gaussian surface components. Functional forms for the spectra consistent with measured slope statistics are assumed, and the backscatter predicted by rough-surface scattering theory is compared with measured cross sections. The predicted upwind-downwind asymmetry of scattering cross sections is comparable to that observed, and a measurable dependence of cross sections on atmospheric stability is predicted.     

Tilt modulation of high resolution radar backscatter crosssections: unified full wave approach

The unified full wave approach is used to determine the tilt modulation of the like- and cross-polarized (high-resolution) radar backscatter cross sections for the rough sea surface. Real or synthetic aperture radars (SARs) with small effective footprints (resolution cells) are considered. Since the unified full-wave approach accounts for Bragg scattering as well as specular point scattering in a self-consistent manner, it is not necessary to adopt a two-scale model for the rough sea surface. The sea surface slope probability density function is assumed to be Gaussian. The backscattering cross sections are evaluated for all angles of incidence (normal to grazing). For tilts in the plane of incidence, the modulation of all the cross sections is largest at angles of incidence of 10°. The cross-section modulation due to tilts perpendicular to the plane of incidence critically depends on the incident and scattered polarizations. The effective filtering of the large-scale spectral components of the rough sea surface by the high-resolution radar is accounted for, and the dependence of the cross-section tilt modulation on the size of the effective footprint is determined     

Scattering from non-Gaussian randomly rough surfaces-cylindricalcase

A numerical method is developed to simulate electromagnetic wave scattering from computer-generated two-dimensional randomly rough surfaces. The rough surface generated for scattering simulation is specified only up to the second moment statistics, i.e. the height distribution and the autocorrelation function. The coherent and noncoherent scattering from four different types of random surfaces is examined. The four different types of surfaces are: Gaussian distributed heights and Gaussian correlation, Gaussian distributed height and non-Gaussian correlation, modified exponential distributed height and non-Gaussian correlation, modified exponential distributed height and Gaussian correlation, modified exponential distributed height and non-Gaussian correlation surfaces. It is shown by simulation that the dominating factor in coherent scattering is the surface height density and the autocorrelation can cause a higher order effect     

A numerical model for electromagnetic scattering from sea ice

A numerical model for scattering from sea ice based on the finite difference time domain (FDTD) technique is presented. The sea ice medium is modeled as consisting of randomly located spherical brine scatterers with a specified fractional volume, and the medium is modeled both with and without a randomly rough boundary to study the relative effects of volume and surface scattering. A Monte Carlo simulation is used to obtain numerical results for incoherent υυ backscattered normalized radar cross sections (RCSs) in the frequency range from 3 to 9 GHz and for incidence angles from 10° to 50° from normal incidence. The computational intensity of the study necessitates an effective permittivity approach to modeling brine pocket effects and a nonuniform grid for small scale surface roughness. However, comparisons with analytical models show that these approximations should introduce errors no larger than approximately 3 dB. Incoherent υυ cross sections backscattered from sea ice models with a smooth surface show only a small dependence on incidence angle, while results for sea ice models with slightly rough surfaces are found to be dominated by surface scattering at incidence angles less than 30° and by scattering from brine pockets at angles greater than 30°. As the surface roughness increases, surface scattering tends to dominate at all incidence angles. Initial comparisons with measurements taken with artificially grown sea ice are made, and even the simplified sea ice model used in the FDTD simulation is found to provide reasonable agreement with measured data trends. The numerical model developed ran be useful in interpreting measurements when parameters such as surface roughness and scatterer distributions lie outside ranges where analytical models are valid     

A Monte-Carlo FDTD Technique for Rough Surface Scattering

A Monte-Carlo finite-difference time-domain (FDTD) technique is developed for wave scattering from randomly rough, one-dimensional surfaces satisfying the Dirichlet boundary condition. Both single-scale Gaussian and multiscale Pierson-Moskowitz surface roughness spectra are considered. Bistatic radar cross sections are calculated as a function of scattering angle for incident angles of 0, 45, 70, and 80 degrees measured from the vertical. The contour path FDTD method is shown to improve accuracy for incident angles greater than 45 degrees. Results compare well with those obtained using a Monte-Carlo integral equation technique     

Full wave vertically polarized bistatic radar cross sections forrandom rough surfaces-comparison with experimental and numerical results

The one-dimensionally rough surfaces considered in this paper are characterized by four-dimensional Gaussian joint probability density functions for the surface heights and slopes at two points. The expressions for the diffuse scattered fields are used to obtain the random rough cross sections. The full wave solutions are compared with the corresponding small perturbation results and the physical optics results. They are also compared with experimental and numerical results based on Monte Carlo simulations of rough surfaces. The earlier assumption that the surface heights and slopes can be considered to be uncorrelated are examined, and the impact of self shadow is considered in detail. The impact of the commonly used assumption that the radii of curvature is very large compared to the wavelength is also examined in detail. These results are in agreement with the duality and reciprocity relationships in electromagnetic theory     

Depolarization and scattering of electromagnetic waves by irregular boundaries for arbitrary incident and scatter angles full-wave solutions

Explicit expressions are presented for the radiation fields scattered by rough surfaces. Both electric and magnetic dipole sources are assumed, thus excitations of both vertically and horizontally polarized waves are considered. The solutions are based on a full-wave approach which employs complete field expansions and exact boundary conditions at the irregular boundary. The scattering and depolarization coefficients axe derived for arbitrary incident and scatter angles. When the observation point is at the source these scattering coefficients are related to the backscatter cross section per unit area. Solutions based on the approximate impedance boundary condition are also given, and the suitability of these approximations are examined. The solutions are presented in a form that is suitable for use by engineers who may not be familiar with the analytical techniques and they may be readily compared with earlier solutions to the problem. The full-wave solutions are shown to satisfy the reciprocity relationships in electromagnetic theory, and they can be applied directly to problems of scattering and depolarization by periodic and random rough surfaces.     

A comparison of scattering model results for two-dimensionalrandomly rough surfaces

Bistatic radar cross sections are calculated using two modern scattering models: the small slope approximation (both first- and second-order), and the phase perturbation technique. The problem is limited to scalar-wave scattering from two-dimensional, randomly rough Dirichlet surfaces with a Gaussian roughness spectrum. Numerical results for the cross sections are compared to those found using the classical Kirchhoff, or physical optics, approximation and perturbation theory. Over a wide range of scattering angles, the new results agree well with the classical results when the latter are considered to be accurate. A comparison between the new results shows that the phase perturbation method gives better results in the backscattering region for correlation lengths greater than approximately one wavelength, while both the first- and second-order small slope approximations yield greater accuracy in the forward scattering direction at low grazing angles     

Wave diffraction by a rough boundary of an arbitrary plane-layeredmedium

The problem of electromagnetic (EM) wave scattering by a slightly rough boundary of an arbitrary layered medium is solved by a small perturbation method. The bistatic amplitude of scattering as well as scattering cross sections for a statistically rough surface are calculated for linear and circular polarized waves. Along with the scattering into the upgoing waves in the homogeneous medium, the scattering cross sections in the downgoing waves into a layered medium are obtained. Analytical results are applied to the modeling of natural layered media (ice and sand layers) remote sensing problems employing global positioning system (GPS) technics     

Non-Gaussian surface generation

An approach has been found to generate two-dimensional non-Gaussian surfaces with known height densities and surfaces with known height densities and surface correlation functions. Four types of surfaces with various combinations of Gaussian and non-Gaussian height densities and correlation functions are generated. Statistical properties of the generated surfaces are computed and shown to agree with the specified properties. The surface height density function of the generated surface is found to depend upon the number of filter weights chosen and the density function of input random numbers. The results are pertinent to the study of electromagnetic-wave scattering by rough surfaces     

Bistatic scattering by arbitrarily shaped objects with rough surface at optical and infrared frequencies

The scattering cross sections for arbitrarily shaped dielectric objects with rough surface are determined for optical and infrared frequencies using the Kirchhoff approximation. The formula of the coherent scattering cross section is derived, and numerical method of incoherent scattering cross section is given. As a specific example, the infrared laser scattering cross sections of rough spheres are calculated at 1.06 μm.     

Computations of scattering cross sections for composite surfaces and the specification of the wavenumber where spectral splitting occurs

The scattering cross sections for composite random rough surfaces are evaluated using the full wave approach. They are compared with earlier solutions based on a combination of perturbation theory which accounts for Bragg scattering, and physical optics which accounts for specular point theory. The full wave solutions which account for both Bragg scattering and specular point scattering in a self-consistent manner are expressed as a weighted sum of two cross sections. The first is associated with a filtered surface, consisting of the larger scale spectral components, and the second is associated with the surface consisting of the smaller scale spectral components. The specification of the surface wavenumber that separates the surface with the larger spectral components from the surface with the smaller spectral components is dealt with in detail. Since the full wave approach is not restricted by the limitations of perturbation theory, it is possible to examine the sensitivity of the computed values for the backscatter cross sections to large variations in the value of the wavenumber where spectral splitting is assumed to occur.     

A theory of wave scattering from an inhomogeneous layer with an irregular interface

Bistatic wave scattering from a layer of Rayleigh scatterers with an irregular interface is investigated by combining the doubling method in volume scattering with the Kirchhoff method in rough surface scattering. Theoretical results are shown illustrating the effect of the rough interface. It is found that for scattered and incident angles near the vertical, the rough interface causes a substantial increase relative to the plane interface in both the like and cross-scattering coefficients over all azimuth angles. However, for large scattered and incident angles, the reverse is true except for azimuth angles around the specular direction. It is interesting to note that while one dominant peak of the like polarized scattering coefficient occurs along the specular direction, two dominant peaks of the cross-polarized scattering coefficient may appear symmetrically with respect to the specular direction. In backscattering, the surface roughness causes a peak to appear in both the like and cross-scattering coefficients at near vertical incidence and also a decrease of these coefficients at large incidence angles.     

Analysis of scattering from rough surfaces at large incidenceangles using a periodic-surface moment method

The moment method is used to calculate electromagnetic backscattering from one-dimensionally rough surfaces at near-grazing incidence (angles of incidence up to 89°). A periodic representation of the scattering surface is used to prevent edge effects in the calculated scattering without the use of an artificial illumination weighting function. A set of universal series common to all elements of the moment interaction matrix are derived that allow the efficient application of the moment method to the periodic surface. Comparison with other moment method implementations demonstrates the efficiency of this approach. The scattering from surfaces with Gaussian roughness spectra is calculated at both horizontal and vertical polarizations, and the results are compared with the theoretical predictions of the small-perturbation method (SPM) and Kirchhoff approximation (KA). SPM shows the expected loss of accuracy in predicting the vertically polarized backscattering from small-roughness, short-correlation-length surfaces at large incidence angles. SPM accurately predicts the backscattering from the same type of surface at incidence up to 89° at horizontal polarization, KA provides accurate estimates of the scattering from long correlation-length surfaces as long as the incidence angle is small enough that surface self-shadowing does not occur. When shadowing occurs, KA severely underpredicts vertically polarized backscattering and less severely overpredicts backscattering at horizontal polarization     

On the use of finite surfaces in the numerical prediction of roughsurface scattering

Method of moments (MOM)-based Monte Carlo calculations are widely used in determining the average radar cross section of randomly rough surfaces. It is desirable in these numerical calculations to truncate the scattering surface into as short a length as possible to minimize the solution time. However, truncating the surface tends to change the solution for the surface fields near the truncation points and may alter the scattered far fields. In this paper, these end effect errors are examined for one-dimensional (i.e., grooved or corduroy) surfaces which are Gaussian distributed in height and have either a Gaussian or a Pierson-Moskowitz spectra. In the case of the Pierson-Moskowitz type surface, it is shown that a relatively short surface of 80-120 wavelengths can be used to obtain the average backscattered radar cross section for backscattering angles as large as 60° from normal. For a comparatively smooth Gaussian surface, on the other hand, its is shown that the truncation effects can be very significant at moderate backscattering angles. Also, great care should be taken when examining the scattering from Gaussian surfaces which are dominated by specular scattering. It is shown that in this situation, a very large number of calculations may be needed to obtain a good numerical average     

A Monte Carlo study of the rough-sea-surface influence on the radarscattering from two-dimensional ships

The generalized forward-backward (GFB) method was introduced in Pino et al. (1999) for computing the electromagnetic scattering from two-dimensional targets on a rough surface. The GFB method is used in this article to generate numerical data for a Monte Carlo simulation of the horizontally polarized radar cross section (RCS) of two-dimensional ship-like targets on random rough sea surfaces. The RCS is computed as a function of the incidence angle and wind speed for a large number of surface realizations. It is found that the mean RCS of a given target on a rough surface is generally lower than or equal to the RCS of the same target on a flat surface, while the maximum RCS is usually greater than or equal to the flat-surface case. It is also observed that the variations in the RCS introduced by the rough surface become less significant as the elevation angle approaches grazing