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 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.     

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 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.     

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     

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.     

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     

Low-grazing-angle microwave scattering from a three-dimensional spilling breaker crest: a numerical investigation

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.     

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.     

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     

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     

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.     

Modeling of wind direction signals in polarimetric sea surfacebrightness temperatures

There has been an increasing interest in the applications of polarimetric microwave radiometers for ocean wind remote sensing. Aircraft and spaceborne radiometers have found a few Kelvins wind direction signals in sea surface brightness temperatures, in addition to their sensitivities to wind speeds. However, it was not clear what physical scattering mechanisms produced the observed brightness dependence on wind direction. To this end, polarimetric microwave emissions from wind-generated sea surfaces are investigated with a polarimetric two-scale scattering model, which relates the directional wind-wave spectrum to passive microwave signatures of sea surfaces. Theoretical azimuthal modulations are found to agree well with experimental observations for all Stokes parameters from near nadir to 65° incidence angles. The upwind and downwind asymmetries of brightness temperatures were interpreted using the hydrodynamic modulation. The contributions of Bragg scattering by short waves, geometric optics scattering by long waves and sea foam are examined. The geometric optics scattering mechanism underestimates the directional signals in the first three Stokes parameters, and predicts no signals in the fourth Stokes parameter (V). In contrast, the Bragg scattering was found to dominate the wind direction signals from the two-scale model and correctly predicted the phase changes of the upwind and crosswind asymmetries in T_υ and U from middle to high incidence angles. The phase changes predicted by the Bragg scattering theory for radiometric emission from water ripples is corroborated by the numerical Monte Carlo simulation of rough surface scattering. This theoretical interpretation indicates the potential use of polarimetric brightness temperatures for retrieving the directional wave spectrum of short gravity and capillary waves     

Effect of shadowing on electromagnetic scattering from rough oceanwavelike surfaces at small grazing angles

A hybrid moment-method/geometrical-theory-of-diffraction technique (MM/GTD) has been implemented to numerically calculate the electromagnetic scattering from one-dimensionally rough surfaces at extreme illumination angles (down to 0° grazing). The hybrid approach allows the extension of the modeled scattering surface to infinity, avoiding the artificial edge diffraction that prevents use of the standard moment method at the smallest grazing angles, Numerical calculation of the backscattering from slightly rough large-scale surfaces approximating ocean wave features shows that roughness in strongly shadowed regions can contribute significantly to the total backscatter at vertical polarization. This is observed when the shadowing obstacle is several wavelengths high, and the magnitude of the shadow-region contribution does not depend on the radius-of-curvature of the shadowing feature. Strongly shadowed roughness does not significantly contribute to the backscatter at horizontal polarization, although weakly shadowed roughness near the incidence shadow boundary does. The calculations indicate that a shadowing-corrected two-scale model may be able to predict the distributed-surface portion of the sea-surface scattering from the ocean surface at grazing angles down to about 15°, but at lower grazing the shadowing and large-scale curvature of the surface prevent the establishment of a Bragg resonance and invalidate the model     

Comparison of modeled backscatter from slightly rough curvedsurfaces with numerical predictions

The slightly rough facet model has often been used to describe radar scattering from two-scale rough surfaces. Moment method scattering calculations are used to investigate the validity of a theoretical method for determining the maximum allowable facet sizes. The method is shown to give accurate facet sizes for rough surfaces with large-scale curvatures comparable to that expected on the ocean surface at angles of incidence where the traditional two-scale scattering model has proved to be valid     

脉冲波入射时分形粗糙海面的双频散射截面和脉冲展宽

根据粗糙面基尔霍夫小斜率近似研究了脉冲波入射时实际海谱分布的一维分形海面的电磁散射。分析了毫米波入射时不同分维、入射角和入射中心频率下双频散射截面的散射角分布。结果表明分形海面的双频散射截面在镜反射方向有最大的相关带宽，随着海面分维的减小、入射中心频率和入射角的增加，该相关带宽是增大的。对于入射功率为δ函数时的散射波功率是一个具有一定脉冲展宽的散射脉冲，且脉冲展宽与相关带宽成反比关系。     

海面掠入射散射特性及布儒斯特效应研究

海面掠入射散射特性对海洋遥感等问题有着重要应用,海面对雷达波束的镜面反射对海上超低空目标与海面的耦合场有着重要影响,利用海面的布儒斯特效应将有效削弱镜面反射。以西太平洋和东南沿海盐度场与温度场的卫星数据为基础,根据双Debye方程建立修正海水介电模型计算不同海域介电常数;基于Elfouhaily海谱模型,采用修正双尺度模型并考虑不同风速及频率下的截断波数,仿真分析了风速、频率、海水温度与盐度等因素对海面掠入射散射特性及布儒斯特效应的影响,总结归纳了海面布儒斯特效应产生机理和变化规律。分析表明:风速、频率及海水温度均会对海面布儒斯特效应产生影响。该研究为海洋环境的遥感探测及海上超低空目标的监测与跟踪提供了理论支撑。     

Electromagnetic modeling of multipath scattering from breakingwater waves with rough faces

The low-grazing-angle (LGA) backscattering from one-dimensionally rough surface profiles approximating breaking water waves with roughened front faces has been numerically examined. The added front-face roughness approximates that expected from wind generation. The reference "exact" backscattering was found using a numerical technique based on the moment method. A model-based approach to predict the backscattering was also implemented. In this, the crest scattering was found directly using the moment method, the multipath scattering was modeled using physical optics, and the distributed-surface scattering from the small-scale roughness was found from the two-scale model. The calculations show that the roughness adds incoherent components to both the vertically (VV) and horizontally (HH) polarized scattering cross sections. At VV, this is due to the random scattering from the small-scale roughness, while at HH it results from random changes in the multipath interference due to the large-scale roughness. As the mechanisms for the incoherent scattering are independent, it is difficult to predict the magnitude of the HH-to-VV backscattering ratio that will occur with specific realizations of the roughness from the underlying breaking-wave shape alone, particularly with large rms roughness added. Overall, the model-based calculations give a good prediction of both the coherent and incoherent scattering coefficients