Bistatic scattering from one-dimensional random rough homogeneous layers in the high-frequency limit with shadowing effect

Many fast asymptotic models of electromagnetic scattering from a single rough interface have been developed over the last few years, but only a few have been developed on stacks of rough interfaces. The specific case of very rough surfaces, compared to the incident wavelength, has not been treated before, which is the context of this paper. The model starts from the iteration of the Kirchhoff approximation to calculate the fields scattered by a rough layer, and is reduced to the high-frequency limit in order to rapidly obtain numerical results. The shadowing effect, important under grazing angles, is taken into account. The model can be applied to any given slope statistics. Then, the model is compared with a reference numerical method based on the method of moments, which validates the model in the high-frequency limit for lossless and lossy inner media.     

Rayleigh's hypothesis and the geometrical optics limit

The Rayleigh hypothesis (RH) is often invoked in the theoretical and numerical treatment of rough surface scattering in order to decouple the analytical form of the scattered field. The hypothesis stipulates that the scattered field away from the surface can be extended down onto the rough surface even though it is formed by solely up-going waves. Traditionally this hypothesis is systematically used to derive the Volterra series under the small perturbation method which is equivalent to the low-frequency limit. In this Letter we demonstrate that the RH also carries the high-frequency or the geometrical optics limit, at least to first order. This finding has never been explicitly derived in the literature. Our result comforts the idea that the RH might be an exact solution under some constraints in the general case of random rough surfaces and not only in the case of small-slope deterministic periodic gratings.     

时域混合算法在一维海面与舰船目标复合电磁散射中的应用

采用时域积分方程(TDIE)与时域基尔霍夫近似(TDKA)的混合算法研究粗糙海面与舰船目标的复合瞬态电磁散射.该方法将舰船目标及其近邻海面划分为TDIE区域,用TDIE方法精确求解;将剩余电大尺寸的粗糙海面划分为TDKA区域,采用高效的TDKA电流近似求解.通过混合算法和传统TDIE算法结果的对比,表明TDIE-TDKA混合算法能保证计算的精度,同时具有较高的计算效率.最后,讨论了海面上方有无目标、海面上方风速、电磁脉冲入射角、舰船目标尺寸、吃水深度对后向散射磁场的影响.     

Numerical and analytic study of rough surface morphology on the angular distribution of eroded impurity

The impact of rough surface morphology on the angular distribution of eroded impurities has been investigated with the three‐dimensional (3D ) rough surface code SURO and a newly developed analytic model. The property of the rough surface structure can be described by the shadow angle of the rough surface in SURO , which is defined as the ratio of the horizontal characteristic length to the initial surface roughness. The SURO simulation results show that the influence of the rough surface on the angular distribution of eroded impurities comes into play when the shadow angle is larger than a threshold value. The larger shadow angle of the rough surface leads to a stronger shift of the angular distribution of the eroded impurities. Different rough surface topographies have been used in the SURO code to check the angular distribution of the eroded impurities. It is found that the shift tendency of the angular distribution is similar for different structures of the rough surface. Based on the numerical modelling results, an analytical model has been developed to investigate the impact of the shadow angle on the angular distribution of the eroded impurities, which shows the consistent result as the SURO simulations.     

Application of the method of equivalent edge currents to composite scattering from the cone-cylinder above a dielectric rough sea surface

Compared with scattering from a rough surface only, composite scattering from a target above a rough surface has become so practical that it is a subject of great interest. At present, this problem has been solved by some numerical methods which will produce an enormous calculation amount. In order to overcome this shortcoming, the reciprocity theorem (RT) and the method of equivalent edge currents (MEC) are used in this paper. Due to the advantage of RT, the difficulty in computing the secondary scattered fields is reduced. Simultaneously, MEC, a high-frequency method with edge diffraction considered, is used to calculate the scattered field from the cone-cylinder target with a high accuracy and efficiency. The backscattered field and the polarization currents of the rough sea surface are evaluated by the Kirchhoff approximation (KA) method and physical optics (PO) method, respectively. The effects of the backscattering radar cross section (RCS) and the Doppler spectrum on the size of the target and the windspeed of the sea surface for different incident angles are analysed in detail.     

Developments in jet noise modelling—theoretical predictions and comparisons with measured data

Spectral information on the sound radiated from turbulent shock-free jets is now available over a wide range of Strouhal numbers, for jet densities ranging from 0·3 to 2 times the ambient density and jet velocities ranging from 0·3 to 2 times the ambient sound speed. In order to account for some of the trends observed, a jet noise model is developed which takes account of acoustic-mean flow interaction. The model is based on a shear flow analogy, for which the governing equation is Lilley's equation, and numerical solutions are obtained for sources representative of turbulent mixing noise. Analytic solutions developed for low- and high-frequency excitation show good agreement with the numerical results. Finally, the model predictions are compared with measurements on hot and isothermal jets.     

三维随机粗糙面与目标复合电磁散射的FDTD方法

用时域有限差分方法(FDTD)研究三维周期性延拓的随机粗糙面与上方目标复合电磁散射.用周期性延拓消除数值计算中截取有限大小粗糙面产生的边缘效应,讨论一个周期单元粗糙面的边长与其相关长度之间的关系.给出在FDTD方法中向粗糙面加载入射波的方法,建立了粗糙面上单个三维目标的复合散射FDTD计算模型.数值结果给出粗糙面与目标散射的近场分布,应用近远场变换得到全方位散射角的双站散射系数.比较了三维与二维散射模型的区别.结果显示当粗糙面上放置目标时,其后向散射显著增强.     

A new bistatic model for electromagnetic scattering from perfectly conducting random surfaces: numerical evaluation and comparison with SPM

This paper is a companion to our previous contribution deriving a new approximate bistatic model for electromagnetic scattering from perfectly conducting rough surfaces. We evaluate this model numerically and compare it with an 'exact' numerical solution of the scattering problem. This comparison shows good agreement between our approximation and numerical solution for a wide range of incident and scattering angles. However, for horizontal-incident horizontal-scattered polarization (HH-pol), the model exhibits strong deviation from the 'exact' solution for near-grazing scattering angles. The model shows a similar divergence at HH-pol when compared with the small-perturbation method (SPM). The cause of this divergence is explained. During the SPM comparison, we noticed that the integral equation method model also does not reproduce the SPM limit except for forward and backscatter geometries. We propose in this paper a simple modification of our model to ensure agreement with the bistatic SPM approximation when applicable, and show that the modified model also yields close agreement with numerical computations even when the surface roughness does not satisfy the SPM condition.     

Modeling of high-frequency scattering from objects using a hybrid Kirchhoff/diffraction approach

In this paper a numerical discretization and transformation into the time domain of a hybrid Kirchhoff/diffraction method is presented for the modeling of high-frequency pulse scattering from rigid bodies. A series of benchmark cases, for smooth and rough spheres and cylinders, is presented to establish the accuracy of the method in the time domain.     

Scattering on rough surfaces with alpha-stable non-Gaussian height distributions

We study the electromagnetic scattering problem on a random rough surface when the height distribution of the profile belongs to the family of alpha-stable laws. This allows us to model peaks of very large amplitude that are not accounted for by the classical Gaussian scheme. For such probability distributions with infinite variance the usual roughness parameters such as the RMS height, the correlation length or the correlation function are irrelevant. We show, however, that these notions can be extended to the alpha-stable case and introduce a set of adapted roughness parameters that coincide with the classical quantities in the Gaussian case. Then we study the scattering problem on a stationary alpha-stable surface and compute the scattering coefficient under the first-order Kirchhoff and small-slope approximations. An analytical formula is given in the high-frequency limit, which generalizes the well known geometrical optics approximation. Some numerical results are given and discussed.     

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...     

随机Gauss粗糙面上三维导体目标散射差场的随机泛函解析计算方法

提出一种解析的随机泛函方法(SFA),计算导体Gauss粗糙面上三维导体目标的复合电磁散射.推导粗糙面的随机Green函数,用一种新的四路径模型描述面体复合散射机理,用SFA求解双站差场雷达散射截面.以导体球目标为算例,与其他数值计算方法比较后验证了SFA的有效性与准确性,同时讨论了粗糙度、体目标尺寸以及距离粗糙面高度等参量变化对结果的影响,给出复杂形状体目标的双站差场雷达散射截面的空间角分布. 关键词： 随机泛函方法 粗糙面随机Green函数 差场雷达散射截面 面体复合散射     

Numerical solution for an inverse scattering problem of non-periodic rough surfaces

The paper presents the first results of a numerical study of inverse diffraction devoted to non-periodic rough surfaces in optics. Two kinds of rough surfaces are considered: first gratings with a finite number of grooves, and second random rough surfaces. For shallow surfaces, adequate Fourier theories have been employed with success. On the other hand, for deeper asperities, rigorous methods are needed and generally, the reconstruction of the profile is more difficult. For both Fourier and rigorous methods, the limit of resolution is studied numerically and numerous examples of reconstruction are given.Instituto Politecnico National, Escuela Superior de Fisica y Matematicas, Mexico, D.F., Mexico     

Kinetic modeling of a slow flow CW CO2 laser

A kinetic model for analysis of the slow-flow CW-discharge CO₂ laser with diffusion cooling has been developed in which the gas temperature is obtained from energy balance equations. The method is based on the numerical solution of a set of nonlinear differential equations for vibrational kinetics. The numerical predictions from the model are compared with some experimental results and a good agreement is obtained.     

HF ground wave propagation over a curved rough sea surface in the presence of islands

For a vertically polarized line source, in the context of HF (3–30?MHz) ground wave propagation over a curved rough sea surface in the presence of islands, this paper adapts the FB-SA (Forward–Backward Spectral Acceleration) method to compute the attenuation function over sea–land (island)–sea mixed paths for different shapes and heights of the islands. The rigorous FB-SA numerical method is based on the method of moments and was originally developed for scattering from rough surfaces and is especially efficient in solving a huge problem, which is required to predict the ground wave propagation over a long surface. In addition, for zero island height, this method is compared with an analytical approach expressed from a (residue) series, in which the roots of a differential equation, depending on the Airy function, must be calculated. In addition, from an intuitive approach and from the work of Barrick and Ishimaru, this analytical approach is extended to include the sea roughness and then validated from the FB-SA.     

Energy conservation of the scattering from one-dimensional random rough surfaces in the high-frequency limit

Energy conservation of the scattering from one-dimensional strongly rough dielectric surfaces is investigated using the Kirchhoff approximation with single reflection and by taking the shadowing phenomenon into account, both in reflection and transmission. In addition, because no shadowing function in transmission exists in the literature, this function is presented here in detail. The model is reduced to the high-frequency limit (or geometric optics). The energy conservation criterion is investigated versus the incidence angle, the permittivity of the lower medium, and the surface rms slope.     

Double-scatter Mueller matrices for vector electromagnetic scattering from single grooves and lines on a silicon surface

A recently developed numerical method is used to calculate the single- and double-scattered Mueller matrices for scattering of vector-electromagnetic waves from rough surfaces. Calculations are performed for the case of a single groove and a single rib on a silicon surface and results are compared to the published experimental results. The calculated results show good agreement with the experimental results for the groove case and poorer agreement with the rib case, probably due to errors in the experimental construction of the rib. It is found that, for the cases studied here, variations of the sign with scatter angle in individual Mueller matrix elements are associated with the presence of double- (or multiple-)scattered light, as has been found previously for scalar diffraction calculations in Gaussian randomly rough surfaces.     

Extended propagation-inside-layer expansion method combined with the forward-backward method to study the scattering from an object above a rough surface

In this Letter, a fast red rigorous numerical method, based on the method of moments, is developed to calculate the scattering from an object above a rough surface for three-dimensional problems (3D). G. Kubické has recently developed the extended propagation-inside-layer expansion (E-PILE) method to calculate the scattering from an object above a rough surface for two-dimensional problems. This method allows us to calculate separately and exactly the interactions between the object and the rough surface. The purpose of this paper is to extend the E-PILE method to a 3D problem. In addition, to invert a matrix of large size, the forward-backward (FB) method is applied to calculate the local interactions on the rough surface.     

杭州湾水体光谱高频观测及在悬浮物动态变化监测中的应用

现场光谱观测是水色遥感真实性检验的基础。传统基于航次站位观测获取的水体光谱数据少,难以满足快速变化的近岸水体遥感产品真实性检验的需求。为此,国际上开始发展水体光谱连续观测系统,但目前近岸水体光谱连续观测系统仍较少,特别是在高浊度、高动态的水体。针对该问题,在杭州湾建立了一套基于海上塔台的高浑浊水体光谱高频观测系统。该系统每3 min获取一次水体光谱数据,实现与过境卫星观测时间的匹配。本文重点开发了基于海上塔台特点的水体光谱高频观测数据的处理方法,实现了晴空、耀斑、阴影、弱光照等自动判别,并对处理结果进行了检验。结果表明,塔台观测获得的归一化离水辐亮度光谱与船测结果具有较高的一致性,相关系数大于0.99, 平均相对误差为9.96%。此外,对塔台水体高频观测系统的长期观测能力进行了评价,结果表明,尽管系统运行一年之久,系统与便携式地物光谱仪ASD同步观测获得的水体归一化离水辐亮度在谱形和数值上一致性均较好,相关系数大于0.90,平均相对误差为6.48%。同时,利用系统高频观测的水体光谱可有效监测悬浮物浓度随潮汐的快速动态变化。杭州湾塔台水体高频观测系统为进一步开展浑浊水体水色卫星遥感产品真实性检验提供了丰富的现场光谱数据,特别是高时间分辨率的静止轨道水色卫星遥感产品的真实性检验。     

Analysis of one-dimensional rough surface scattering based on bidirectional reflectance distribution function model

Through in-depth analysis of the scattering properties of a one-dimensional random rough surface, a method to calculate the spatial bidirectional reflectance distribution function (BRDF) characteristics of a randomly rough surface is proposed. The scattering characteristics of an electrically large rough surface can be substituted by combination of subsection electromagnetic fields. The radar cross-section (RCS), which is transformed from the BRDF, is compared with numerical results from the Method of Moment (MoM). The agreement of the results verifies that this method could calculate the electromagnetic scattering field efficiently and straightforwardly. Moreover, the resulting combined fields from the BRDF of subsections in the rough surface show a good match with the entire scattering field of a whole surface, which indicates that a large electrically rough surface could be feasibly and effectively substituted with the combination of scattering elements using the BRDF method and the statistical method.