Light scattering from rough surfaces with superimposed periodic structures

0 ), where K is the wave vector of the periodic structure and λ₀ is the correlation length for random roughness. The surface height h of the periodic structure plays a less important role in the suppression of the diffuse scattering, but it gives an oscillating term in grating scattering intensity that can produce the “rainbowing” (or coloration) effect for such a surface. In practice, this may result in increased visual brightness of textured metallic surfaces and also in a new and interesting method of surface coloration control. The rapid development of focused beam texturing technologies leaves no doubt that patterns with a given spatial frequency and amplitude can be easily produced in experiments. Received: 16 January 1997/Revised version: 19 June 1997     

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.     

求解水中加肋板声辐射特性的虚拟声源法*

发展一种利用虚拟声源离散声场的方法求解加肋板在水中的声振耦合问题。由波叠加原理和单元体积速度匹配的原则,根据离散的结构单元满足的动力方程和结构与介质的交界相容性条件,确定虚拟声源强度,计算结构的声辐射功率。本文以简支矩形加肋板为例,在不获得结构表面振速和声压的情况下,计算了结构在水中的声辐射功率,并与解析方法计算的结果进行了比较,表明了该方法具有较好的计算精度。     

Theoretical and computational aspects of scattering from periodic surfaces: one-dimensional transmission interface

Abstract

We consider the scattering from and transmission through a one-dimensional periodic surface. For this problem, the electromagnetic cases of TE and TM polarization reduce to the scalar acoustic examples. Three different theoretical and computational methods are described, all involving the solution of integral equations and their resulting discrete matrix system of equations for the boundary unknowns. They are characterized by two sample spaces for their discrete solution, coordinate space and spectral space, and labelled by the sampling of the rows and columns of the discretized matrices. They are coordinate-coordinate (CC), the usual coordinate-space method, spectral-coordinate (SC) where the matrix rows are discretized or sampled in spectral space and spectral-spectral (SS) where both rows and columns are sampled in spectral space. The SS method uses a new topological basis expansion for the boundary unknowns.

Equations are derived for infinite surfaces, then specialized and solved for periodic surfaces. Computational results are presented for the transmission problem as a function of roughness, near-grazing incidence as well as many other angles, density and wavenumber ratios. Matrix condition numbers and different sampling methods are considered. An error criterion is used to gauge the validity of the results.

The computational results indicated that the SC method was by far the fastest (by several orders of magnitude), but that it became ill-conditioned for very rough surfaces. The CC method was most reliable, but often required very large matrices and was consequently extremely slow. It is shown that the SS method is computationally efficient and accurate at near-grazing incidence and can be used to fill a gap in the literature. Extensive computational results indicate that both SC and SS are highly robust computational methods. Spectral-based methods thus provide viable computational schemes to study periodic surface scattering.     

Investigation of light scattering from rough periodic surfaces — numerical solutions

The Beckmann scalar scattering model based on the Kirchhoff approximation was used to investigate the scattering of light from periodic surfaces whose roughness amplitude is comparable to, and greater than, the illumination wavelength. Solutions by numerical integration were obtained for surfaces of different profiles and of different roughnesses. It was found that the scattering patterns from these surfaces were very different at large roughness amplitudes. As the incident angle was varied on a given surface, it was also observed that the intensity of any individual diffraction order oscillated and the degree of oscillation was directly related to roughness. By utilizing this property, a new procedure could be developed for surface roughness assessment.     

Theoretical and computational aspects of scattering from periodic surfaces: one-dimensional transmission interface

We consider the scattering from and transmission through a one-dimensional periodic surface. For this problem, the electromagnetic cases of TE and TM polarization reduce to the scalar acoustic examples. Three different theoretical and computational methods are described, all involving the solution of integral equations and their resulting discrete matrix system of equations for the boundary unknowns. They are characterized by two sample spaces for their discrete solution, coordinate space and spectral space, and labelled by the sampling of the rows and columns of the discretized matrices. They are coordinate-coordinate (CC), the usual coordinate-space method, spectral-coordinate (SC) where the matrix rows are discretized or sampled in spectral space and spectral-spectral (SS) where both rows and columns are sampled in spectral space. The SS method uses a new topological basis expansion for the boundary unknowns.

Equations are derived for infinite surfaces, then specialized and solved for periodic surfaces. Computational results are presented for the transmission problem as a function of roughness, near-grazing incidence as well as many other angles, density and wavenumber ratios. Matrix condition numbers and different sampling methods are considered. An error criterion is used to gauge the validity of the results.

The computational results indicated that the SC method was by far the fastest (by several orders of magnitude), but that it became ill-conditioned for very rough surfaces. The CC method was most reliable, but often required very large matrices and was consequently extremely slow. It is shown that the SS method is computationally efficient and accurate at near-grazing incidence and can be used to fill a gap in the literature. Extensive computational results indicate that both SC and SS are highly robust computational methods. Spectral-based methods thus provide viable computational schemes to study periodic surface scattering.     

Propagation in an elastic wedge using the virtual source technique

The virtual source technique, which is based on the boundary integral method, provides the means to impose boundary conditions on arbitrarily shaped boundaries by replacing them by a collection of sources whose amplitudes are determined from the boundary conditions. In this paper the virtual source technique is used to model propagation of waves in a range-dependent ocean overlying an elastic bottom with arbitrarily shaped ocean-bottom interface. The method is applied to propagation in an elastic Pekeris waveguide, an acoustic wedge, and an elastic wedge. In the case of propagation in an elastic Pekeris waveguide, the results agree very well with those obtained from the wavenumber integral technique, as they do with the solution of the parabolic equation (PE) technique in the case of propagation in an acoustic wedge. The results for propagation in an elastic wedge qualitatively agree with those obtained from an elastic PE solution.     

A general method for analyzing em wave scattering from arbitrarily shaped two-dimensional periodic surfaces

In this paper the Method of Lines (MoL) is successfully extended to solve the EM wave scattering problems of periodic surfaces with arbitrary profile. As examples, the scattering coefficients of space harmonics of corrugated and sinusoidal surfaces are calculated. The results are in good agreement with available data from Wirgin and from A.K.Jordan et al. In addition, the results of comb structure are also calculated. The flexibility and less computation of this method make it eligible for analyzing various two-dimensional periodic structures.     

Performance analysis of source ranging by use of virtual receiver technique under different frequency bands

The traditional matched field processing localization need complicated computation to get the replica field and has high dependence on environment parameters and acoustic field model.To overcome the shortcoming,virtual receiver technique is used for source ranging.A virtual receiver is constructed by correlating the two signals of the guide source and the objective source received by a vertical line array.Then,the slope of the interference striation of the virtual field is estimated using relevant signal processing method.Combining with the waveguide invariant β,the range of the objective source is determined.Through the numerical simulations and data processing collected from the experiment carried out in the South China Sea in 2004,the virtual receiver technique for broadband source ranging under the slopebottom shallow water environment is discussed.As the frequency increases,the frequency bands should be broadened to obtain complete interference striation for good ranging results.In data processing,the receiving array spacing is too large to promise the orthogonality of the modes as the frequency increases and ranging results become worse.     

不同频段下利用虚拟接收方法的声源测距性能分析

考虑到传统的匹配场处理定位需要复杂的匹配声场计算,并对环境参数和声场模型有很高的依赖,为了克服这种缺点,采用虚拟接收方法对声源进行测距。首先对垂直阵接收到的引导声源和目标声源的信号进行相关处理,得到虚拟接收声场并估计虚拟接收声场干涉条纹的斜率,结合波导不变特征量β对目标声源进行测距。通过数值仿真和2004年南海实验数据处理,讨论了浅海斜坡海域环境中不同频段下利用虚拟接收方法对宽带声源测距的性能。随着频率升高,需要展宽频带以获得完整的干涉条纹和良好的测距结果。在实验数据处理中,选取频段较高的信号时,由于阵列间距偏大不能保证采样的简正波模式的正交归一特性,不能获得正确的测距结果。     

The weighted curvature approximation in scattering from sea surfaces

A family of unified models in scattering from rough surfaces is based on local corrections of the tangent plane approximation through higher-order derivatives of the surface. We revisit these methods in a common framework when the correction is limited to the curvature, that is essentially the second-order derivative. The resulting expression is formally identical to the weighted curvature approximation, with several admissible kernels, however. For sea surfaces under the Gaussian assumption, we show that the weighted curvature approximation reduces to a universal and simple expression for the off-specular normalized radar cross-section (NRCS), regardless of the chosen kernel. The formula involves merely the sum of the NRCS in the classical Kirchhoff approximation and the NRCS in the small perturbation method, except that the Bragg kernel in the latter has to be replaced by the difference of a Bragg and a Kirchhoff kernel. This result is consistently compared with the resonant curvature approximation. Some numerical comparisons with the method of moments and other classical approximate methods are performed at various bands and sea states. For the copolarized components, the weighted curvature approximation is found numerically very close to the cut-off invariant two-scale model, while bringing substantial improvement to both the Kirchhoff and small-slope approximation. However, the model is unable to predict cross-polarization in the plane of incidence. The simplicity of the formulation opens new perspectives in sea state inversion from remote sensing data.     

并行时域电场积分方程方法在动态海面二维电磁散射中的应用

采用并行时域电场积分方程方法对动态海面的二维瞬态散射特性进行研究。为了保证该方法的后期稳定性,时间基函数和空间基函数采用二阶B样条基函数和三角基函数,矩阵元素采用时间维度精确解析、空间奇异部分精确解析进行计算;为了减少对无限海面进行截断带来的边缘效应,入射波采用锥形调制高斯脉冲;结合信息传递接口（MPI）技术和稀疏矩阵压缩存储技术,对不同时刻的海面进行瞬态散射分析。大量的数值算例证明了该方法在计算动态海面的二维瞬态散射问题时的正确性,还可以保证后期的稳定性,提高计算效率,减少对计算机内存需求。     

The effect of curvature variation on the scattering from rough surfaces

The general high-frequency, rough-surface reflection process is treated by the method of stationary phase. In particular, the principle of stationary phase is applied to each of the local reflection events, which appear to depend on surface curvature as well as slope. However, we show that the number of reflecting highlights also depends on curvature and cancels the curvature dependence. These results agree fully with those obtained by Beckmann and Spizzichino for the special case of the Gaussian process.     

虚拟接收目标定位技术中引导声源对目标声源的信噪比补偿

目标声源的低信噪比是目标定位技术中的瓶颈。在浅海近似均匀环境中,利用虚拟接收方法对声源测距的目标定位方法相比于传统的匹配场定位方法可以避免对环境参数和声场模型的依赖,同时省去生成拷贝场时的大量计算。通过数值模拟和实验数据处理,比较了在虚拟接收方法声源测距中不同信噪比的引导声源对目标声源测距的结果。提高引导声源的信噪比,可以一定程度上提高于涉条纹清晰度,从而提高测距准确度。提高引导声源的信噪比可作为目标声源的信噪比补偿是利用虚拟接收方法的目标定位技术的又一个优点。     

A puzzle in the inelastic scattering of atoms from surfaces

The insensitivity of helium atoms to possible inelastic scattering involving bulk phonons that terminate at the surface is explained in terms of the experimental parameters that need to be incorporated into the scattering theory.     

Factors influencing electromagnetic scattering from the dielectric periodic surface

The scattering characteristics of the periodic surface of infinite and finite media are investigated in detail.The Fourier expression of the scattering field of the periodic surface is obtained in terms of Huygens' s principle and Floquet's theorem.Using the extended boundary condition method(EBCM) and T-matrix method, the scattering amplitude factor is solved,and the correctness of the algorithm is verified by use of the law of conservation of energy.The scattering cross section of the periodic surface in the infinitely long region is derived by improving the scattering cross section of the finite period surface.Furthermore, the effects of the incident wave parameters and the geometric structure parameters on the scattering of the periodic surface are analyzed and discussed.By reasonable approximation, the scattering calculation methods of infinite and finite long surfaces are unified.Besides, numerical results show that the dielectric constant of the periodic dielectric surface has a significant effect on the scattering rate and transmittance.The period and amplitude of the surface determine the number of scattering intensity peaks, and, together with the incident angle, influence the scattering intensity distribution.     

Theory of charge exchange scattering from surfaces

We present a simple model calculation of the charge exchange probability for ions scattering from solid surfaces, including interactions with both broad band delocalized electrons and with localized core electrons within an Anderson type Hamiltonian with time dependent parameters. The results exhibit some of the major observed experimental features, including characteristic oscillations as a function of incident velocity (from quasi-resonant electron interchange with the core levels) and overall exponential decay $\text{～exp}\text{(?A}\text{v)}$, with v the incident ion velocity, from interactions with the broad band electrons.