粗糙介质面对高斯波束的散射

该文研究了当入射场为光波束时粗糙介质面的散射问题。利用波束的平面波谱展开方法及基尔霍夫近似理论导出了散射场和非相干截面计算公式,并对后向非相干截面进行了数值计算,最后对其结果进行了分析讨论。     

二维粗糙面两束波束散射特性研究

基于Kirchhoff近似,推导两束波束散射强度相关系数的表达式,数值计算漫射强度及散射强度相关系数随角度差、相关长度及粗糙度变化情况。结果表明:散射角对粗糙表面相干散射强度与光滑表面相干散射强度的比值有影响,当两束波束的入射角、方位角均相等,意味着两束波束相互重合且散射强度比值为单波束比值的四倍;当两束波束的入射角、方位角中有一个角度不相等,由散射场干扰效应的影响,相干散射强度比值都会减小。相关长度的变化与漫射强度和散射强度相关系数均成正比;随着入射角度差增大,漫射强度的后向散射效应增强,且散射强度相关系数变小,说明两束波束的干扰越严重;随着散射角的增大,总散射强度受干扰项散射强度影响较大,则后向散射效应增强。     

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.     

二维带限分形粗糙面电磁散射的基尔霍夫近似

本文采用二维归一化带限Weierstrass分形函数来模拟二维分形粗糙面,主要利用基尔霍夫近似研究了该粗糙面的电磁散射,给出了散射场、平均散射强度系数和散射强度方差的计算公式,通过理论分析和数值计算讨论了散射场与分维及粗糙面其他有关参量间的关系.     

Fractal Characteristics Investigation on Light Scattering from Two Dimensional Rough Surface

A normalized two dimensional band-limited Weierstrass fractal function is used for modeling the rough surface. Based on Kirchhoff theory, an analytic solution of the average scattering field and the variance of scattering intensity are derived with emphasis on examining the relation of fractal dimension with the scattering pattern. The important conclusion is obtained that the diffracted envelope slopes of scattering pattern can be approximated to a slope of linear equation.     

二维分形粗糙面电磁散射的分形规律研究

采用二维归一化带限Brown分形函数来模拟二维分形粗糙面,利用基尔霍夫近似给出了该粗糙面的电磁散射场和散射强度方差的计算公式,主要讨论了散射场分布与分维的关系,获得了散射场波峰拟合线的斜率与分维D满足线性关系这一重要规律。     

Multiple scattering effects on wave propagation due to rain

At frequencies below 10 GHz, the scattering crosssection of raindrops is small compared with the absorption cross-section and the multiple scattering effect is negligibly small. At higher frequencies, however, the scattering cross-section becomes comparable to the absorption cross-section, and some multiple scattering effects may be observed. This paper presents a study of the multiple scattering effects, and the resulting incoherent intensity for a plane wave incident upon a plane-parallel rain region. General formulations of the equation of transfer using Stokes’parameters are given, and the extinction matrix is introduced which take into account the depolarization effects and the nonspherical shape of raindroplets. The calculations are made for the spherical droplet case. It is assumed that a circularly-polarized wave is normally incident upon a plane-parallel rain medium. The scattering characteristics are calculated using the Mie solution and the Laws-Parsons distributions. The calculation of the incoherent intensities are made using the matrix eigenvalue technique. The exact solutions are compared with the first-order scattering solution to estimate the range of validity of the first-order theory. The ratio of the incoherent to the coherent received powers are calculated at 30 GHz, for rain rates of 12.5, 50, 100, and 150 mm/h, rain thicknesses of 3 km and 10 km, and fields-of-view of 1, 5, and 15 deg.     

Coherent scattering of a spherical wave from an irregular surface

The scattering of a spherical wave from a rough surface using the Kirchhoff approximation is considered. An expression representing the measured coherent scattering coefficient is derived. It is shown that the sphericity of the wavefront and the antenna pattern can become an important factor in the interpretation of ground-based measurements. The condition under which the coherent scattering-coefficient expression reduces to that corresponding to a plane wave incidence is given. The condition under which the result reduces to the standard image solution is also derived. In general, the consideration of antenna pattern and sphericity is unimportant unless the surface-height standard deviation is small, i.e., unless the coherent scattering component is significant. An application of the derived coherent backscattering coefficient together with the existing incoherent scattering coefficient to interpret measurements from concrete and asphalt surfaces is shown.     

Backscattering from a randomly rough dielectric surface

A backscattering model for scattering from a randomly rough dielectric surface is developed. Both like- and cross-polarized scattering coefficients are obtained. The like-polarized scattering coefficients contain single scattering terms and multiple scattering terms. The single scattering terms are shown to reduce to the first-order solutions derived from the small perturbation method when the roughness parameters satisfy the slightly rough conditions. When surface roughnesses are large but the surface slope is small, only a single scattering term corresponding to the standard Kirchhoff model is significant. If the surface slope is large, the multiple scattering term will also be significant. The cross-polarized backscattering coefficients satisfy reciprocity and contain only multiple scattering terms. The difference between vertical and horizontal scattering coefficients increases with the dielectric constant and is generally smaller than that predicted by the first-order small perturbation model. Good agreements are obtained between this model and measurements from statistically known surfaces     

Backscattering coefficient of a perturbed sinusoidal surface

A coherent model for scattering from a randomly perturbed periodic surface is developed using the Kirchhoff approximation. It is intended to model wave scattering from ground surfaces with row directions. Results are illustrated and compared with an incoherent scatter model and measured backscattering angular curves from ploughed fields.     

Transport of the mutual coherence functions and the intensity of a backscattered pulse in a random medium

Starting with a Helmholtz wave equation, the transport equations for the coherent and incoherent parts of the two-frequency two-position mutual coherence function in the transform domain can be derived. These equations have their respective analogs in the conventional radiative transfer theory. By solving the equations for the coherent part and the incoherent part, the incoherent scattered intensity is expressed as an infinite series, each term of which can be interpreted as an "nth order" scattered contribution. A procedure is given to compute the effective wavenumber and the total cross section, starting from a proper form of the mean Green's function. The intensity of a backscattered pulse is next investigated. A series expression is obtained. In order to be able to localize the position of pulse returns, "higher order" scattering terms must not be important when compared with the "single" scattered pulse. Numerical examples, applicable to the microwave scattering, show that the backscattered intensity is reduced when it is compared with the Booker-Gordon formula, even when the mean-square dielectric fluctuation is very small. This reduction is attributed to the multiple scattering effects, especially the multiple large-angle scatterings.     

Application of the integral equation method of smoothing to random surface scattering

The integral equation method of smoothing (IEMS) is applied to the magnetic field integral equation (MFIE) weighted by the exponentialexp (jk_{1}zeta)wherezetais the stochastic surface height. An integral equation in coordinate space for the average of the product of the surface current and the exponential factor is developed. The exact closed-form solution of this integral equation is obtained based on the specularity of the average scattered field. The complex amplitude of the average scattered field is thus determined by an algebraic equation which clearly shows the effects of multiple scattering on the surface. In addition, it is shown how the incoherent scattered power can be obtained using this method. Comparisons with the Kirchhoff approximation and the dishonest approach are presented, and the first-order smoothing result is shown to be superior to both.     

Effects of a Rough Boundary Surface on Polarization of the Scattered Field from an Inhomogeneous Medium

The effect of surface roughness on the polarization of the scattered field is studied by combining the standard Kirchhoff method for rough surface scattering with the radiative transfer method for volume scattering using the Rayleigh phase function. Corresponding cases of pure surface scattering from a homogeneous layer and volume scattering from a plane inhomogeneous layer are also computed to serve as points of reference. In each case the degree of polarization DP, polarization ratio PR, locations on the Poincaré sphere of copolarization nulls CN, and cross-polarization nulls XN are computed. It is found that for pure surface scattering PR between 0-20° incidence angles is quite sensitive to change in surface roughness. However, when both surface and volume scattering are present, CN by colatitude or DP between 0-15° incidence angles and CN or XN by longitude at large incidence angles (>60°) are better indicators of change in surface roughness. Since XN changes insignificantly in pure surface scattering, it appears that a significant change in it can serve as an indicator for the presence of volume scattering. Also, in pure surface or volume scattering, the variations of DP and CN by colatitude are monotone with the incidence angle, while in the combined surface and volume scattering DP has a minimum and CN by colatitude has a maximum. This character offers the possibility of separating combined surface and volume scattering from pure surface or volume scattering.     

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.     

Steady-state coherent Raman beam combining with multiaxial mode lasers

Forward-stimulated Raman scattering can be used to combine multiple broad-band pump beams into a single coherent Stokes wave. In this paper, the equations of motion for the Stokes electric field are derived in the presence of multiple pump waves propagating at slightly different angles with respect to the Stokes propagation direction. The solutions with pump depletion are presented for fully coherent pump waves. It is shown that the Raman gain is lower for incoherent pump waves than for coherent pump waves. Stokes field solutions are used to evaluate the far-field intensity of the Stokes output from a saturated Raman beam combiner. It is shown that the condition for coherent combination depends on the beam diameter, pump coherence length, and the angle between the pump and the Stokes. It is also shown that multiaxial mode Raman shifting can generate Stokes waves with higher beam quality than the pump waves, both with phase perturbed or highly distorted pump beams.     

Effect of incoherent scattering on attenuation and cross-polarization of millimeter waves due to rain: preliminary calculations at 34.8 and 82 GHz for spherical raindrops

A numerical solution of the radiative transport equation is given for a plane-parallel rain medium in connection with the estimation of the incoherent effect on attenuation and cross-polarization of a millimeter wave due to rain. The method of solution consists of an extension of the spherical harmonics method. An assembly of spherical raindrops is considered. From the analysis, it is found that the exact expression of Mie scattering can be incorporated into the integral term of the transport equation, thus allowing the integral to be evaluated without approximation. Preliminary calculations are performed at 34.8 and 82 GHz. Circular polarizations are considered. The results include the directional patterns of reflected and transmitted incoherent intensity, both for left-hand and right-hand circular polarizations, the effect of drop size on the directional patterns, the incoherent signal intensities within the rain medium, and so on.     

Multiple scattering and depolarization by a randomly rough Kirchhoff surface

A matrix approach has been developed to compute bistatic scattering coefficients which include shadowing and multiple scattering effects for a randomly rough Kirchhoff surface. The method permits the computation of these coefficients in terms of the existing single-scatter bistatic scattering coefficients. Thus the effects of multiple scattering are readily recognized from the expressions obtained. The bistatic scattering coefficients are shown to satisfy energy conservation to at least two significant figures. It is observed that while polarized backscattering is dominated by the single-scattering process, the depolarized backscattering is due to multiple scattering. Unlike depolarization by slightly rough surfaces or volume scattering, the angular behavior of the depolarized backscattering is similar to that of the polarized backscattering. The transitional behavior of the relative dominance between single and multiple scattering for the polarized and depolarized scattering coefficient as a function of the azimuth angle is illustrated.     

On the far-field approximation for scattering from randomly rough surfaces

Various authors have justified the far-fields approximation for rough surface scattering using one of the classical approximations for the scattered fields, usually considering either the coherent scattered field or the incoherent scattered intensity. An exact expression for the field scattered from a perfectly conducting rough surface is considered. The expression for the incoherent scattered intensity is formally derived, and a condition under which the far-field approximation is valid is found, independent of specific approximations for the surface or scattered fields or for the surface height statistics. The condition so derived is, under many circumstances, substantially less restrictive than that derived before in the general case. Furthermore, the previous results may be easily recovered by further specialization of our result.     

Bistatic specular scattering from rough dielectric surfaces

An experimental investigation was conducted to determine the nature of bistatic scattering from rough dielectric surfaces at 10 GHz. This paper focusses specifically on the dependence of coherent and incoherent scattered fields on surface roughness for the specular direction. The measurements, which were conducted for a smooth surface with ks<0.2 (where k=2π/λ and s is the RMS surface height) and for three rough surfaces with ks=0.5, 1.39, and 1.94, included observations over the range of incidence angles from 20° to 65° for both horizontal and vertical polarizations. For the coherent component, the reflectivity was found to behave in accordance with the prediction of the physical optics model, although it was observed that the Brewster angle exhibited a small negative shift with increasing roughness. The first-order solution of physical optics also provided good agreement with observations for hh-polarized incoherent scattering coefficient, but it failed to predict the behavior of the vv-polarized scattering coefficient in the angular range around the Brewster angle. A second-order solution is proposed which appears to partially address the deficiency of the physical optics model     

二维fBm随机分形界面的电磁散射特性

应用二维fBm（分形布朗运动）模拟了这种既非完全周期的也非完全随机的实际粗糙界面，用Kirchhoff方法计算了电磁波在随机分形界面的散射特性。数值结果表明随着分形维数的增加，散射场中非相关分量逐渐增大，旁瓣增多并在镜面方向周围不断展宽。