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.     

Scattering and depolarization by rough surfaces near grazing angles--Full wave solutions

Using the full wave approach to rough surface scattering, the apparent singularity in the physical optics and perturbation expressions for the scattered fields is not encountered. The full wave expression for the far fields is shown to vanish in a continuous manner as the observer moves across a shadow boundary. Precise criteria are given for near grazing angles where uniform plane wave excitations cannot be assumed. Comparisons are made between the full wave and the physical optics and perturbation solutions. Since the full wave solution is shown to bridge the gap between the physical optics and perturbation solutions, it accounts for both specular and Bragg scattering. The full wave solutions satisfy reciprocity, duality, and realizability relationships in electromagnetic theory, and they are invariant to coordinate transformations.     

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 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.     

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     

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.     

Scattering cross sections for composite models of non-Gaussian rough surfaces for which decorrelation implies statistical independence

The full wave approach is used to determine the scattering cross sections for composite models of non-Gaussian rough surfaces. It is assumed in this work that the rough surface heights become statistically independent when they decorrelate, thus no delta function type specular term appears in the expressions for the scattered fields. The broad family of non-Gaussian surfaces considered range in the limit from exponential to Gaussian. It is seen that for small angles of incidence the like polarized cross sections have the same dependence on the specific form of the surface height joint probability density, but for large angles the scattering cross sections for the horizontally polarized waves are much more sensitive to the specific form of the joint probability density. On the other hand the shadow functions are rather insensitive to the specific form of the joint probability density.     

Unified full wave solutions to interpret Apollo lunar surface data

Bistatic radar experiments carried out by Tyler and Howard during the Apollo 14, 15, and 16 missions provide a very useful dataset with which to compare theoretical models and experimental data. Vesecky et al. (1988) report that their model for near grazing angles compares favorably to experimental data. However, for angles of incidence around 80°, all the analytical models considered by Vesecky et al. predict values for the quasi-specular cross sections that are about half the corresponding values taken from the Apollo 16 data. In this work, questions raised by this discrepancy between the reported analytical and experimental results are addressed. The unified full wave solutions are shown to be in good agreement with the bistatic radar data taken during Apollo 14 and 16 missions. Using the full wave approach, the quasi-specular contributions to the scattered field from the large scale surface roughness as well as the diffuse Bragg-like scattering from the small scale surface roughness are accounted for in a unified self-consistent manner. Since the full wave computer codes for the scattering cross sections contain ground truth data only, it is shown how it can be readily used to predict the rough surface parameters, based on the measured data     

Full wave physical models of nonspecular scattering in irregularstratified media

A physical interpretation is given of each term in the full-wave expansion of the vertically or horizontally polarized electromagnetic fields scattered by irregular stratified media. These solutions provide a basis for the construction of physical models of nonspecular scatter in complex, irregular, layered structures. The full wave solutions involve a pair of nonspecular reflection scattering coefficients and a pair of nonspecular transmission scattering coefficients that reduce to the familiar Fresnel reflection and transmission coefficients for the specular case. The full-wave solutions are shown to satisfy the reciprocity and duality relationships in electromagnetic theory, and they are invariant to coordinate transformations. The relationships between the full-wave solution, the high-frequency physical optics solution, and the low-frequency perturbation solution are demonstrated. The analysis is relevant to problems of communication in irregular stratified media and to problems of remote sensing     

Diffraction-limited laser excitation of a surface plasma wave andits scattering on a rippled metallic surface

A theory of excitation, reflection, and scattering of a surface plasma wave (SPW) over a metallic surface is presented by modeling a localized surface ripple by an electron density perturbation. The level of a laser excited SPW is significantly lowered by the diffraction effects. When an SPW is incident on a bump or a slot, it undergoes specular reflection. It also undergoes elastic scattering when encountering a surface defect, as observed in recent experiments     

Scattering from multiple conducting and dielectric bodies ofarbitrary shape

A simple moment-method solution is presented for the problem of electromagnetic scattering from structures consisting of multiple perfectly conducting and dielectric bodies of arbitrary shape. The system is excited by a plane wave. The surface equivalence principle is used to replace the bodies by equivalent electric and magnetic surface currents, radiating into an unbounded medium. A set of coupled integral equations, involving the surface currents, is obtained by enforcing the boundary conditions on the tangential components of the total electric and magnetic fields. The method of moments is used to solve the integral equations. The surfaces of the bodies are approximated by planar triangular patches, and linearly varying vector functions are used for both expansion and testing functions. Some of the limitations of the method are briefly discussed. Results for the scattering cross sections are presented. The computed results are in very good agreement with the exact solutions and with published data     

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     

The Contribution of Wedge Scattering to the Radar Cross Section of the Ocean Surface

This letter considers the contribution to the radar cross section of the ocean surface due to scattering from edges for which the local radius of curvature is small compared with the radar wavelength. An analytic expression based on the method of equivalent currents is given for such scattering and is evaluated for several assumed sets of parameters. This contribution is shown to augment the Bragg scattering cross section in regions where the latter underestimates the measured radar cross section, while remaining smaller than the Bragg component elsewhere.     

Rough surface scattering using specular point theory

The expression for the average scattering cross section for a random surface is derived using the stationary phase approximation for the scattered field due to specular points on a finitely conducting rough surface. A previous error in the literature is corrected by showing that the proper result is proportional to the average value of the product of the number of specular points per unit area and the principal radii of curvature at the specular point, rather than the product of the average value of the number of specular points and the average value of the radii of curvature. When the correct expression for the average value of the product is inserted in the expression for the scattering cross section, the result is in total agreement with the answers obtained when the averaging and stationary phase processes are interchanged. This analysis explicitly accounts for shadowing.     

Measurement and classification of low-grazing-angle radar seaspikes

High-resolution dual-polarization X-band images of the ocean surface were obtained at a grazing angle of about 3°. Area extensive imaging allowed us to study the backscatter properties of sea spikes and to compare radar measurements with visual surface features evident from video recordings. The vertically polarized radar images consist of distributed scatter whose amplitude and Doppler velocity are modulated by larger scale gravity waves consistent with Bragg scattering and composite surface theory (CST). The horizontally polarized radar images are dominated by spatially discrete scattering centers (or sea spikes) moving at velocities comparable to the phase velocities of gravity waves beyond the spectral peak. These sea spikes also exist in the corresponding V-pol radar images, but are less prominent due to the dominant Bragg backscatter. Sea spikes are characterized by polarization ratios H/V that often exceed unity, typically by about 5 dB. Comparison of the larger spikes with simultaneous co-registered video recording of the surface indicates that approximately 30% of observed sea spikes are associated with actively breaking waves (whitecaps) while the remainder are identified with “steep” wave features. By classifying the larger sea spikes according to their corresponding surface features, we find hat the Doppler velocities for sea spikes due to whitecaps are noticeably faster (about 50%) than other sea spikes, though the distributions for both overlap significantly. We also find little measurable difference in the polarization ratios of the two classes of sea spikes as observed on the open ocean     

A new model for sea clutter

First-order (small roughness amplitude) scattering theory is applied to obtain sea clutter cross sections in terms of mean-squared height spectrum of the sea surface. The results are in remarkably good agreement with observations for vertical polarization atP-, L-, C-, andX-bands. Modification of the calculation to take into account the larger scale structure of the sea surface yields reasonable agreement for horizontal polarization atP- andL-bands but is less successful for the cross-polarized and horizontal cross sections atC- andX-bands.     

Backscattering from a Gaussian-distributed perfectly conducting rough surface

An analytical approach to the problem of scattering by composite random surfaces is presented. The surface is assumed to be Gaussian so that the surface height can be split (in the mean-square sense) into large (zeta_{l}) and small (zeta_{s}) scale components relative to the electromagnetic wavelength. A first-order perturbation approach developed by Burrows is used wherein the scattering solution for the large-scale structure is perturbed by the small-scale diffraction effects. The scattering from the large-scale structure (the zeroth-order perturbation solution) is treated via geometrical optics since4k_{0}^{2}bar{zeta_{l}^{2}} gg 1. The first-order perturbation result comprises a convolution in wavenumber space of the height spectrum, the shadowing function, a polarization dependent factor, the joint density function for the large-scale slopes, and a truncation function which restricts the convolution to the domain corresponding to the small-scale height spectrum. The only "free" parameter is the surface wavenumber separating the large and small height contributions. For a given surface height spectrum, this wavenumber can be determined by a combination of mathematical and physical arguments.     

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     

On the theory of Δk radar observations of ocean surface waves

We consider the theory of waves scattered from a moving, rough, and dispersive surface in the small perturbation limit. The first-order scattered field for a time-dependent surface is obtained in the far zone of scattering in terms of the two-dimensional spectral amplitude of the surface and its dispersion relation. We develop a rigorous Δk radar theory and show that the nonzero output of a Δk radar occurs only when the Bragg condition for each signal component is satisfied separately. The frequency correlation function of the scattered field is then proportional to the mean value of the product of the spectral amplitudes of the surface at the corresponding Bragg wavenumbers. The mean value of this product is nonzero only for surfaces that have a locally varying spectrum and is proportional to the Fourier transform (with the argument Δk) of the variation of the local spectrum with respect to the pattern position. Such variations may be caused by either amplitude or phase modulation of the surface structure. In the former case, our results are similar to the results of existing theory. The latter case of phase modulation of the surface (for example, internal waves interacting with capillary waves) cannot be explained by previous theory