Scattering of electromagnetic radiation by surfaces with a fractal relief

The scattering indicatrix of electromagnetic waves for different types of rough surfaces and angles of incidence is calculated using the Kirchhoff scalar theory. The rough surfaces are modelled by a two dimensional Weierstrass function. The scattering index for a rough surface with a fractal relief is found to have a complicated structure with intensity bursts in directions quite far from the direction of mirror reflection.     

Scattering of Radiation of the Sun and the Sky from Two Dimensional Rough Sea Surfaces

The scattering of optical wave from two dimensional rough sea surfaces is studied first with method of facets. The sea surface is divided into many facets, and each facet is treated as a surface with small roughness instead of a smooth plane, therefore more practical and effective. In addition the shadowing function of sea surfaces for arbitrary incident and scattering angles is numerically calculated with the Z-BUFFER method, which applies to any kinks of rough surfaces compared with the methods available. Finally the spectral irradiance of the sun and the spectral radiance of the sky for different time at sea level with fine weather are obtained with the software of Lowtran7, and the scattering of the radiation of the sun and the sky from two dimensional rough sea surfaces for different time, waveband and wind speed is studied, which is of great reference value for reducing the interference to the infrared detector due to the scattering of the radiation of the sun and the sky from sea surfaces.     

Explicit results for wave scattering and transmission through a rough fluid-fluid interface

This paper describes an analysis of reflection and transmission of acoustic waves from an imperfectly reflecting, rough fluid-fluid interface within the Kirchhoff approximation. It presents the results of calculations of the coherent and diffuse field. This work is motivated by the fact that few explicit results of the characteristics of the scattered and transmitted wave field exist in the literature for this problem. For the problem of interest, the surface reflection coefficient depends at each point upon the local angle between the incident wave and the rough surface. For surfaces with statistically independent local surface position and gradient, coherent field calculations show that the correction to constant reflection coefficient analyses is simply a multiplicative factor that depends upon the statistical characteristics of the surface gradient, sound speed and density ratio across the surface. This multiplicative factor is interpreted as an average reflection or transmission coefficient, <R> and <T>, respectively. The principle differences between these results and constant reflection coefficient analyses occur when waves impinge upon regions with higher sound speeds, where total internal reflection may occur. While the wave characteristics of smooth or constant reflection coefficient surfaces change abruptly in the vicinity of the angle of total internal reflection, the average reflection coefficient exhibits a much smoother dependence upon angle of incidence or sound speed ratio for rough surfaces. It is also shown that the direction of maximum diffuse scattering moves relative to its value were the reflection coefficient constant.     

随机起伏冰面三维声散射的Kirchhoff近似数值计算模型

针对随机起伏冰面的声散射问题,建立了随机起伏冰面三维声散射的Kirchhoff近似数值计算模型.利用Delaunay三角剖分方法对随机起伏冰面进行三角面元剖分,然后采用Z-buffer算法进行面元的遮挡消隐,得到处于声波照射亮区的面元,最后采用Gordon面元积分的板块元方法计算得到随机起伏冰面的散射强度.数值计算模型...     

Numerical, analytical, and experimental studies of scattering from very rough surfaces and backscattering enhancement

This paper Presents numerical simulations, theoretical analysis, and millimeter wave experiments for scattering from one-dimensional very rough surfaces. First, numerical simulations are used to investigate the effects of roughness spectrum, height variation, interface medium, polarization, and incident angle on the backscattering enhancement. The enhanced backscattering due to rough surface scattering is divided into two cases; the RMS height close to a wavelength and RMS slope close to unity, and RMS height much smaller than a wavelength with surface wave contributions. Results also show that the enhancement is sensitive to the roughness spectrum. Next, a theory based on the first- and second-order Kirchhoff approximation modified with angular and propagation shadowing is developed. The theoretical solutions provide a physical explanation of backscattering enhancement and agree well with the numerical results. In addition to the scattering of a monochromatic wave, the analytical results of the broadening and lateral spreading of a pulsed beam wave scattering from rough surfaces are also discussed. Finally, the existence of backscattering enhancement from one-dimensional very rough conducting surfaces with exact Gaussian statistics and Gaussian roughness spectrum is verified by a millimeter-wave experiment. Experimental results which show enhanced backscattering for both TE and TM polarizations for different angles of incidence are presented.     

修正反射系数的Kirchhoff近似方法计算高斯起伏冰面三维声散射

针对随机起伏冰面的声散射计算问题,利用修正反射系数的Kirchhoff近似方法计算了高斯起伏冰面的三维声散射。在计算模型中引入了冰面局部统计平均反射系数的概念,将二维高斯起伏冰面的散射分为相干散射和非相干散射,分别得到两类散射成分的散射系数公式,计算了高斯起伏冰面三维声散射的散射强度。分析了散射强度与随机起伏冰面的均方根高度、声波入射角度及频率的关系。通过实验室水池中高斯起伏冰面的散射强度测量实验,对理论模型的计算结果进行了验证。将实验结果分别与采用冰面局部统计平均反射系数的模型计算结果和文献中采用平整冰面镜反射系数的模型计算结果进行了对比,采用冰面局部统计平均反射系数的模型计算结果与实验测量值吻合较好。      

Numerical,analytical, and experimental studies of scattering from very rough surfaces and backscattering enhancement

Abstract

This paper Presents numerical simulations, theoretical analysis, and millimeter wave experiments for scattering from one-dimensional very rough surfaces. First, numerical simulations are used to investigate the effects of roughness spectrum, height variation, interface medium, polarization, and incident angle on the backscattering enhancement. The enhanced backscattering due to rough surface scattering is divided into two cases; the RMS height close to a wavelength and RMS slope close to unity, and RMS height much smaller than a wavelength with surface wave contributions. Results also show that the enhancement is sensitive to the roughness spectrum. Next, a theory based on the first- and second-order Kirchhoff approximation modified with angular and propagation shadowing is developed. The theoretical solutions provide a physical explanation of backscattering enhancement and agree well with the numerical results. In addition to the scattering of a monochromatic wave, the analytical results of the broadening and lateral spreading of a pulsed beam wave scattering from rough surfaces are also discussed. Finally, the existence of backscattering enhancement from one-dimensional very rough conducting surfaces with exact Gaussian statistics and Gaussian roughness spectrum is verified by a millimeter-wave experiment. Experimental results which show enhanced backscattering for both TE and TM polarizations for different angles of incidence are presented.     

Electromagnetic wave scattering in a semi-bounded plasma-molecular medium

The phenomenon of noncoherent wave reflection associated with scattering by electromagnetic fluctuations in a semibounded plasma-molecular medium is studied. The differential reflection coefficients are computed for scattering by collective bulk and surface fluctuations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 79–82, May, 1987.     

浅海起伏海面下气泡层对声传播的影响

分析了起伏海面下风浪引起的气泡层对海面反射损失和对声传播的影响.一方面,气泡层会改变原来水中的声速剖面;另一方面,气泡层会对声波产生散射和吸收作用.考虑以上两方面的因素,分析了不同风速下气泡层对海面反射损失和声传播损失的影响,仿真发现,在风速大于10 m/s时,对于2 k Hz以上频率时气泡层对小掠射角下海面反射损失的影响不可忽视.在给定的水声环境中,当声源深度和接收深度都为7 m时,风速为16 m/s的风浪下生成的气泡层,在10 km处对3 k Hz的声传播损失的影响达到8.1 d B.当声源深度和接收深度都为18 m时,风速为16 m/s的风浪下生成的气泡层,在10 km处对3 k Hz的声传播损失的影响达到4 d B.     

Streuung elektromagnetischer Oberflächen- und Volumenwellen an rauhen Oberflächen. Teil I. Allgemeine Grundlagen

Scattering of Electromagnetic Surface and Bulk Waves from Rough Surfaces. Part I. General Theory A classical theory of scattering of electromagnetic surface and bulk waves on rough surfaces (dielectrics or conductors) is given. The primary wave creates a surface polarization on the rough boundary presenting the source for the radiation of scattering. These roughness-caused polarization must be considered in the wave equations and in the boundary conditions of the fields, too. General expressions for the spectral power density of surface and bulk scattering waves will be given. The excitation of surface polarization can result from primary waves homogenously or inhomogenously.     

Scattering from a slightly random, one-dimensional metal surface: 45° linearly polarized incidence, backscattering enhancement and degree of polarization

The scattering of an electromagnetic wave from a slightly random metal surface which supports the surface plasmon mode at optical frequencies is studied theoretically by means of a stochastic functional approach. In order to investigate the Stokes matrix or the state of polarizations, as well as the intensity of the scattered waves, the rough surface is assumed to be one dimensional, and is illuminated by a+45° linearly polarized plane electromagnetic (light) wave whose plane of incidence is perpendicular to the grooves of the surface. The stochastic wave fields are represented in terms of the Wiener-Hermite functionals, and the approximate solutions of the Wiener kernels are obtained for both TM- and TE-polarized components, from which the Stokes matrix elements can be determined. The dressed or perturbed plasmon mode in the presence of surface roughness is obtained by a mass operator involved in the solutions, and the enhanced backscattering closely related to the plasmon mode is studied in connection with the enhanced peak width and the mass operator for the dressed plasmon mode. The Stokes parameters and the degree of polarization are calculated numerically from various polarized components of the incoherent scattering distribution. To clarify the surface plasmon's association with the scattering characteristics, calculations are made for two kinds of random surfaces, a random surface with a centred Gaussian spectrum and a random grating with twin spectral peaks at the plasmon spatial frequency.     

雪层覆盖地面电磁散射的矩量法

为实现分层介质粗糙面电磁散射的矩量法研究,给出一种分层介质粗糙面电磁积分方程的区域分解方法.将格林定理应用于粗糙面所分的各子空间,结合波动方程和格林函数推导分层粗糙面的电磁积分方程,利用矩量法对其进行离散,数值计算得到雪层覆盖地面散射系数的角分布曲线,其中,粗糙表面由一维带限Weierstrass分形谱和Monte Carlo方法模拟.通过与时域有限差分法数值结果的比对,验证该方法的准确性,并分析散射系数随雪和地面参数、介质参数以及入射波参数的变化,获得了较完整的散射特征.     

Brewster's scattering angle in scattered waves from slightly rough metal surfaces

Brewster's scattering angle in electromagnetic wave scattering from slightly random metal surfaces is investigated by means of the stochastic functional approach. While there are dips due to Brewster's scattering angle in scattering profiles from dielectric surfaces, Brewster's scattering angle does not exist in scattering from metal surfaces. However, the dips can exist in scattering from rough metal surfaces with the optically denser medium to convert evanescent wave into radiative wave.     

Transmission scatter cross sections across two-dimensional random rough surfaces – full wave solutions and comparison with numerical results

Abstract

In this paper, the full wave expressions for the bistatic transmission scattering cross sections across two-dimensional random rough surfaces are obtained. The full wave analysis accounts for the surface height/slope correlations. Analytical and numerical comparisons of the full wave solutions with the small perturbation and physical optics solutions are made for isotropic random rough surfaces. The full wave results are also compared with the numerical results based on Monte Carlo simulations of one-dimensional random rough surfaces. Detailed consideration is given to illustrating the relationship between these full wave solutions and the original full wave solutions including the impact of accounting for the height/slope correlations in this analysis.     

随机粗糙面激光脉冲散射四阶统计特征

依据基尔霍夫近似,推导出一维高斯随机粗糙面四阶统计特性解析式,并获得脉冲波入射下粗糙面双点双频四阶矩互相关函数.数值计算不同入射角,不同高度起伏和相干长度,随机粗糙面双点双频四阶矩互相关函数随相干频谱带宽频差,散射角的变化情况.计算结果表明,高度起伏和相干长度对粗糙面散射四阶统计特的影响很大,粗糙面越光滑,在镜反射方向有最大的四阶矩散射峰值和小的相关带宽.随着粗糙度增加,随机粗糙面脉冲散射的四阶矩的相干分量减弱,展宽现象明显;而相干带宽频差越大,四阶矩衰减越快. 关键词： 四阶矩统计特征 双点双频互相关函数 随机粗糙面 脉冲波散射     

Surface reverberation spectrum of underwater sound

A general formulation is derived for the power spectrum of fluctuations in the signal received by way of reflection from a rough sea surface, in terms of an arbitrary wavenumber-frequency spectrum of the surface waves and an arbitrary source directivity function. The formulation is then applied to the specific case of backscatter for which the extreme cases of acoustically slightly rough and very rough sea surfaces are examined in detail. The results of the analysis are compared with experiments, and with the somewhat more restricted results of other theoretical work.     

Anomalous sea surface reverberation scale model experiments

Low frequency sea surface sound backscattering from approximately 100 Hz to a few kHz observed from the 1960s broadband measurements using explosive charges to the Critical Sea Test measurements conducted in the 1990 s is substantially higher than explained by rough sea surface scattering theory. Alternative theories for explaining this difference range from scattering by bubble plumes/clouds formed by breaking waves to stochastic scattering from fluctuating bubble layers near the sea surface. In each case, theories focus on reverberation in the absence of the large-scale surface wave height fluctuations that are characteristic of a sea that produces bubble clouds and plumes. At shallow grazing angles, shadowing of bubble plumes and clouds caused by surface wave height fluctuations may induce first order changes in the backscattered signal strength. To understand the magnitude of shadowing effects under controlled and repeatable conditions, scale model experiments were performed in a 3 m x 1.5 m x 1.5 m tank at the Technical University of Denmark. The experiments used a 1 MHz transducer as the source and receiver, a computer controlled data acquisition system, a scale model target, and a surface wave generator. The scattered signal strength fluctuations observed at shallow angles are characteristic of the predicted ocean environment. These experiments demonstrate that shadowing has a first order impact on bubble plume and cloud scattering strength and emphasize the usefulness of model scale experiments for studying underwater acoustic events under controlled conditions.     

Angular correlation function of wave scattering by a random rough surface and discrete scatterers and its application in the detection of a buried object

Abstract

The scattering of waves by a buried object is often obscured by the clutter around it. Such clutter can be attributed to the scattering by random rough surfaces and random discrete scatterers. Recent studies show that, because of the memory effect, the angular correlation function can suppress the effects of clutter and make the scattering by the buried object more conspicuous. In this paper, we study the angular correlation function of wave scattering by a buried object underneath a layer of random discrete scatterers and a non-Gaussian random rough surface. Such problems are common when the target is buried below a rough surface that is underneath a layer of vegetation. Numerical results are illustrated for various parameters of rough surfaces and discrete scatterers. The angular correlation function is calculated by frequency and angular averaging. It is shown that the use of the angular correlation function can enhance target detection in the presence of clutter.     

Bistatic electromagnetic scattering from a three-dimensional perfect electric conducting object above a Gaussian rough surface based on the Kirchhoff–Helmholtz and electric field integral equation

A hybrid integral equation is developed to solve the problem of electromagnetic (EM) scattering from a three-dimensional (3D) perfect electric conducting (PEC) object above a two-dimensional (2D) PEC or dielectric Gaussian rough surface. Firstly, the Kirchhoff–Helmholtz (KH) equation is adopted to describe the wave reflection on the rough surface; only one integral operation on the rough surface is needed, and the scattering from the object can be described by solving the electric field integral equation (EFIE) on the surface of the object. Moreover, according to scattering theory, the KH equation and the EFIE are coupled together (KH-EFIE) to describe wave propagation between the object and the rough surface. Then method of moments (MoM) is adopted to solve the KH-EFIE, and the current is obtained to calculate the scattering field. Finally, compared with other methods, the accuracy of the proposed approach is validated, and its efficiency is proved to be much higher than numerical solutions. Furthermore, by calculating the statistic composite radar cross-section (RCS) of the object/surface and the difference radar cross-section (DRCS) of the object, the influence of the rough surface root mean square (rms) height, the correlation length, the medium permittivity, the shape of the object, and the altitude of the object on the scattering characteristic is investigated.