A practical cross-section for scattering from rough surfaces at very low grazing angles in both the forward and backward directions

In this paper we develop an extension of the small slope approximation (SSA) for scattering from randomly rough Dirichlet surfaces, which includes some multiple scattering. This extension is designated by SSA+. We focus on scattering at very low grazing angles where multiple scattering of both the incident and scattered fields is of importance. Numerical results for the SSA+ bistatic scattering cross-section for very low forward grazing angles are presented using the Gaussian roughness spectrum and for both very low forward and very low backward grazing angles using the Pierson–Moskowitz and modified power law spectra. The results are restricted to an angle of incidence of 80°. It is shown that when the lowest-order SSA gives reasonably accurate results, the SSA+ increases the accuracy up to at least the final 0.2° of grazing in the forward direction. In the backward direction, the SSA+ gives good results for the Pierson–Moskowitz spectrum, but the results are less dramatic.     

Low-grazing angles scattering of electromagnetic waves from one-dimensional natural surfaces: Rigorous and approximate theories

We present a rigorous model, based on a specific boundary integral formalism for the wave scattering from rough, one-dimensional, dielectric or conducting surfaces at low-grazing incidence and scattering angles. Even though this so-called Grazing Method of Moment is, from a numerical cost point of view, independent of the incidence, it remains very numerically demanding. We thus propose an extrapolation technique for faster monostatic diagram computation, based on the theoretical behavior of the scattering amplitude at low-grazing angles. This technique is compared to the GMoM and to some approximate models, for surfaces with Gaussian spectrum as well as for sea surface.     

On the high-frequency limit of the second-order small-slope approximation

Abstract

Small-slope approximation (SSA) is a scattering theory that is supposed to unify both the small-perturbation model and the Kirchhoff approximation (KA). We study and compute the second-order small-slope approximation (SSA2) in a high-frequency approximation (SSA2-hf) that makes it proportional to the first-order term, with a roughness-independent factor. For the 3D electromagnetic problem we show analytically that SSA2-hf actually meets KA in the case of perfectly conducting surfaces. This no longer holds in the dielectric case but we give numerical evidence that the two methods remain extremely close to each other for moderate scattering angles. We discuss the potential applications of SSA2-hf and give some 2D numerical comparison with rigorous computations.     

Bistatic scattering and depolarization by randomly rough surfaces: application to the natural rough surfaces in X-band

Abstract

The scattering of waves by random rough surfaces has important applications in the remote sensing of oceans and land. The problem of developing a model for rough surfaces is very difficult since, at best, the scattering coefficient σ⁰ is dependent upon (at least) the radar frequency, geometrical and physical parameters, incident and observation angles, and polarization. The problem of electromagnetic scattering from a randomly rough surface is analysed using the Kirchhoff approximation (stationary phase, scalar approximation), the small-perturbation model and the two-scale models. A first major new consideration in this paper is the polarimetric signature calculations as a function of the transmitter location and receiver location for a bistatic radio-link. We calculate the like- and cross-polarized received power directly using the scattering coefficients, without calculating the Mueller matrix. Next, a study of the regions of validity of the Kirchhoff and small-perturbation rough surface scattering models (in the bistatic case) is presented. Comparisons between the numerical calculations and the models are made for various surface rms heights and correlation lengths both normalized to the incident wavenumber (denoted by σ and L, respectively). By using these two parameters to form a two-dimensional space, the approximate regions of validity are then established. The second major new consideration is the development of a theoretical two-scale model describing bistatic reflectivity as well as the numerical results computed for the bistatic radar cross section from rough surfaces especially from the sea and snow-covered surfaces. The results are used to show the Brewster angle effect on near-grazing angle scattering.     

室内粗糙表面声散射体掠入射角度散射估计

针对经典边界元方法对掠入射角度下的散射估计精度较低的问题,发展了一种边界无网格模型.此模型将散射体视为具有无限延伸的形式,避免了经典边界元法中薄板形式所导致的声压差问题,而且更加符合实际房间中散射体的存在形式;模型利用无网格算法实现数值仿真,可对任意表面形状特别是曲面散射体具有更高的仿真精度。利用边界无网格模型计算了不同形状散射体的散射系数及散射声场,并将结果与解析方法、测量实验进行了对比.对比结果表明,边界无网格模型可以准确预测散射体的散射性质,特别是对掠入射角度的估计要优于经典边界元法.研究结论可应用于室内声学散射体特征预测及优化设计,对提高声场扩散及室内音质水平具有重要意义.      

Enhanced backscattering at grazing angles

Backscattering signals at small grazing angles are important for space vehicle atmospheric reentrance and subsurface radar sensing applications. They are also useful in Fourier-transform infrared grazing-angle microscopy. Recently we performed an experimental study of far-field scattering at small grazing angles, in particular, of enhanced backscattering at grazing angles. For a randomly weak rough dielectric film upon a reflecting metal substrate, a large enhanced backscattering peak was measured. Experimental results are compared with small perturbation theoretical predictions.     

Behaviour of scattering from a rough surface at small grazing angles

The particular problem of wave scattering at low grazing angles is of great interest because of its importance for the long-distance propagation of radio waves along the Earth's surface, radar observation of near surface objects, as well as solving many other fundamental and applied problems of remote sensing. One of the main questions is: how do the scattering amplitude and specific cross section behave for extremely small grazing angles? We consider the process of wave scattering by a statistically rough surface with the Neumann boundary condition. This model corresponds to sound scattering from a perfectly 'hard' surface (for example, the interface between air and the sea surface) or 'vertically' polarized electromagnetic waves scattered by a perfectly conducting one-dimensional (i.e. cylindrical) surface when the magnetic field vector is directed along the generating line of this cylindrical surface. We assume that the surface roughness is sufficiently small (in the sense of the Rayleigh parameter) and the surface is rigorously statistically homogeneous and therefore, infinite. We confine ourselves only to the first-order approximation of small perturbation theory and therefore consider every act of wave scattering in the Born approximation when the Bragg scattering process takes place. Only one resonant Fourier component of surface roughness is responsible for the scattering in a given direction. However, we take into account the attenuation of incident and scattered waves due to the multiple scattering processes on the path 'before' and 'after' a scattering event in a given direction. Also we consider every one of these multiple scattering events only in the Born approximation. The main result we have obtained is that for small grazing angles the scattering cross section of the diffuse component decreases as the second power of the grazing angles with respect to the incident and scattered directions, and as the fourth power of the grazing angle for the backscattering (radar) situation. Generalizing our results from plane-wave scattering to finite beams allows us to obtain the criterion on the beamwidth. For sufficiently narrow beams the multiple scattering processes do not play any role because of a short 'interaction path', and only single Bragg scattering determines the scattering amplitude (which does not tend to zero for small grazing angles). However, for sufficiently wide beams the result obtained for infinite plane waves becomes valid: due to the above-mentioned multiple scattering processes, the scattering amplitude tends to zero for small grazing angles. Consequently, the behaviour of the scattering cross section for small grazing angles depends on the radiation pattern width of the transmitting and receiving antennae: for sufficiently wide beams the scattering cross section decreases to zero at small grazing angles, but for narrow beams it tends to the finite non-zero value.     

On the high-frequency limit of the second-order small-slope approximation

Small-slope approximation (SSA) is a scattering theory that is supposed to unify both the small-perturbation model and the Kirchhoff approximation (KA). We study and compute the second-order small-slope approximation (SSA2) in a high-frequency approximation (SSA2-hf) that makes it proportional to the first-order term, with a roughness-independent factor. For the 3D electromagnetic problem we show analytically that SSA2-hf actually meets KA in the case of perfectly conducting surfaces. This no longer holds in the dielectric case but we give numerical evidence that the two methods remain extremely close to each other for moderate scattering angles. We discuss the potential applications of SSA2-hf and give some 2D numerical comparison with rigorous computations.     

氢离子在固体表面掠角散射与能量损失的数值模拟

利用介电响应理论和镜像反射模型对氢离子在固体表面掠角散射和能量损失进行了数值模拟．离子在表面散射时同时受到表面上原子的库仑排斥作用和表面电子气的动力学相互作用,后者是表面电子受运动的正离子扰动所产生,用线性介电响应理论来确定．在高速和低速情况下,分别采用仅与频率有关的局域介电函数和局域场修正介电函数来确定表面电子气产生的动力学相互作用力．计算结果与实验结果作了比较．发现入射速度很低时能量损失随入射角度变化不太明显,而当速度很高时能量损失随入射角度的变大而有所增加. 关键词：     

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.     

Model of a Doppler Spectrum of Microwaves Backscattered from a Sea Surface at Small Grazing Angles

On the basis of known experimental data, we propose a model for a Doppler spectrum of a horizontally polarized 3-cm microwave signal backscattered from a sea surface at small grazing angles about 10^° for wind velocities 3-11 m/s. The model is represented as the superposition of Lorentz and Voight spectral lines with coefficients describing relative energy contributions of different scattering mechanisms as functions of the surface-wind velocity.     

In-beam orientation of low energy mass-separated radioactive beams: Development of the technique and first results

We report on the first results obtained with a system designed to polarize on-line mass-separated radioactive ion beams by scattering the beams from very flat single crystal surfaces at grazing incidence angles. Polarizations of 1 to 2% were already observed for deuterium.     

Specular propagation over rough surfaces: numerical assessment of Uscinski and Stanek's mean Green's function technique

The purpose of this paper is to numerically evaluate the effectiveness and accuracy of Uscinski and Stanek's mean Green's function technique for computing the mean field of a wave scattered by a rough surface. We present here a direct comparison of this technique with a rigorous numerical method, the forward scattering integral equation method, and another analytical method, the first-order smoothing approximation. Furthermore, we compare the roughness generated equivalent admittance using the three methods. Numerical computations reveal that the scattered field calculated by this technique is not accurate particularly for the equivalent admittance at low grazing angles, even though the mean surface current density is recovered when the wave has traversed several correlation lengths on the surface.     

Theoretical and computational aspects of scattering from periodic surfaces: two-dimensional perfectly reflecting surfaces using the spectral-coordinate method

We consider the scattering from a two-dimensional periodic surface. From our previous work on scattering from one-dimensional surfaces (1998 Waves Random Media 8 385) we have learned that the spectral-coordinate (SC) method was the fastest method we have available. Most computational studies of scattering from two-dimensional surfaces require a large memory and a long calculation time unless some approximations are used in the theoretical development. By using the SC method here we are able to solve exact theoretical equations with a minimum of calculation time.

We first derive in detail (part I) the SC equations for scattering from two-dimensional infinite surfaces. Equations for the boundary unknowns (surface field and/or its normal derivative) result as well as an equation to evaluate the scattered field once we have solved for the boundary unknowns. Special cases for the perfectly reflecting Dirichlet and Neumann boundary value problems are presented as is the flux-conservation relation.

The equations are reduced to those for a two-dimensional periodic surface in part II and we discuss the numerical methods for their solution. The two-dimensional coordinate and spectral samples are arranged in one-dimensional strings in order to define the matrix system to be solved.

The SC equations for the two-dimensional periodic surfaces are solved in part III. Computations are performed for both Dirichlet and Neumann problems for various periodic sinusoidal surface examples. The surfaces vary in roughness as well as period and are investigated when the incident field is far from grazing incidence ('no grazing') and when it is near-grazing. Extensive computations are included in terms of the maximum roughness slope which can be computed using the method with a fixed maximum error as a function of the azimuthal angle of incidence, the polar angle of incidence and the wavelength-to-period ratio.

The results show that the SC method is highly robust. This is demonstrated with extensive computations. Furthermore, the SC method is found to be computationally efficient and accurate for near-grazing incidence. Computations are presented for grazing angles as low as 0.01°. In general, we conclude that the SC method is a very fast, reliable and robust computational method to describe scattering from two-dimensional periodic surfaces. Its major limiting factor is high slopes and we quantify this limitation.     

A numerical evaluation of Rayleigh's theory applied to scattering by randomly rough dielectric surfaces

Abstract

We present a numerical simulation of scattering by one-dimensional randomly rough surfaces. It is based on the use of plane-wave expansions to describe the Melds on the surface (i.e. Rayleigh hypothesis). Accuracy and convergence properties of two different numerical implementations are studied. Some examples of results for a dielectric and a metallic Gaussian rough surface are shown to be in good agreement with calculations by a rigorous numerical method. The Rayleigh method appears to be a fast computation tool for dielectric surfaces with slopes of less than 0.2.     

Subcritical penetration of acoustic waves into inhomogenous seafloors

A generalized model is applied to estimate the incoherent penetration ratio caused by volume scattering at grazing angles below the critical grazing angle. The factors that affect volume scattering have been discussed using experimental data in literature. A two-layered model that refers to sound scattering in two-layered media is used to evaluate the incoherent penetration ratio for most typical sediments. But for special cases, such as the experiment, SAX04, a three-layered model is necessary to describe scattering features especially for grazing angles θ<30°. It is shown that subcritical penetration is enhanced when the scale of volume fluctuations is comparable with the acoustic wavelength, and the scattered waves into the seafloor dominate over evanescent waves at depths larger than a few wavelengths.     

Doppler spectrum of polarimetric scattering field from two-dimensional time-varying nonlinear sea surfaces

Polarimetric scattering model of second-order small-slope approxi-mation combined with “choppy wave" model (CWM) for describing nonlinear hydrodynamic interactions between ocean waves is utilized in this paper to investigate the influence of sea surface nonlinearities on backscattering coefficient as well as Doppler spectrum signatures including Doppler shift and spectral bandwidth. Simulation results show that at moderate to large incidence angles the Doppler shift and spectral bandwidth of the CWM nonlinear sea surfaces are significantly larger than those of linear sea surfaces, in particular at low grazing angles. In addition, Doppler signatures show distinct polarization dependence, and most importantly the cross-polarized Doppler signatures significantly differ from the co-polarized ones. It is also indicated that co-polarized Doppler shift increases obviously with wind speed increasing, whereas the cross-polarized Doppler shift looks less sensitive to wind speed variations. The difference of Doppler signatures between co- and cross-polarization is potentially valuable for ocean remote sensing applications, especially for observing very high winds.     

Topical Issue on Wave Scattering from Rough Surfaces and Related Phenomena (Part 1)

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.     

Investigation of EM scattering from electrically large sea surface with breaking wave at low grazing angles

According to the high-resolution radar data, backscattering scattering from sea surfaces may give rise to super events of strong scattering and large Doppler offsets for horizontal (HH) polarization at low grazing angles (LGA), which are usually considered to be caused by breaking waves. In this paper, the mesoscale breaking wave model is introduced to account for the contribution of breaking waves, which can be responsible for sea spikes and high Doppler shift. The backscattering radar cross-section (RCS) from a single breaking wave is computed and the scattering from sea surfaces is analyzed by a composite surface scattering model, in which the phase factor of every facet is modified by the capillary waves. By using the slope criterion, the spatial distribution of the breaking waves is obtained. At the same time, the RCS of sea surfaces with breaking waves is calculated and the results agree with measured data well at LGA for HH polarization. Considering the Bragg phase velocity, orbital motion of facets and wind drift, the Doppler spectrum of sea surface with breaking wave is simulated, and when compared with the result without breaking wave, there is a good improvement for HH polarization, and for the vertical polarization, the revision is little, which are agreeable with the results of recent researches.