X-ray scattering from a randomly rough surface

Abstract

On the basis of the method of reduced Rayleigh equations we present a simple and reciprocal theory of the coherent and incoherent scattering of x-rays from one- and two-dimensional randomly rough surfaces, that appears to be free from the limitations of earlier theories of such scattering based on the Born and distorted-wave Born approximations. In our approach, the reduced Rayleigh equation for the scattering amplitude(s) is solved perturbatively, with the small parameter of the theory η(ω) = 1 - ε(ω), where ε(ω) is the dielectric function of the scattering medium. The magnitude of η(ω) for x-rays is in the range from 10^?6 to 10^?3, depending on the wavelength of the x-rays. The contributions to the mean differential reflection coefficient from the coherent and incoherent components of the scattered x-rays are calculated through terms of second order in η(ω). The resulting expressions are valid to all orders in the surface profile function. The results for the incoherent scattering display a Yoneda peak when the scattering angle equals the critical angle for total internal reflection from the vacuum-scattering medium interface for a fixed angle of incidence, and when the angle of incidence equals the critical angle for total internal reflection for a fixed scattering angle. The approach used here may also be useful in theoretical studies of the scattering of electromagnetic waves from randomly rough dielectric-dielectric interfaces, when the difference between the dielectric constants on the two sides of the interface is small.     

Perturbation theory results for the diffuse scattering of light from two-dimensional randomly rough metal surfaces

Abstract

Using the unitarity and reciprocity preserving formulation of Brown et al a perturbation treatment, correct to fourth order in the surface profile function, is given for the scattering of electromagnetic waves from a weakly rough, two-dimensional, random metal surface. In this formulation the boundary conditions on the electromagnetic fields are satisfied using the extinction theorem in conjunction with the Rayleigh hypothesis and the vector equivalent of the Kirchhoff integral. The theory is applied to, and results are presented for, several different types of rough surfaces which are characterized by power spectra that are extensions to two-dimensional random surfaces of the power spectrum of some one-dimensional random surfaces recently fabricated by West and O'Donnell. These surfaces, which can be realized experimentally, favor coherent, interferent, multiple scattering of electromagnetic waves via surface plasmon polaritons in intermediate states, and clearly exhibit enhanced backscattering caused by the surface plasmon polariton mechanism. Theoretical results are presented for silver surfaces at optical wavelengths.     

Numerical simulation methods for rough surface scattering

Abstract

Numerical methods are of great importance in the study of electromagnetic scattering from random rough surfaces. This review provides an overview of rough surface scattering and application areas of current interest, and surveys research in numerical simulation methods for both one- and two-dimensional surfaces. Approaches considered include numerical methods based on analytical scattering approximations, differential equation methods and surface integral equation methods. Emphasis is placed on recent advances such as rapidly converging iterative solvers for rough surface problems and fast methods for increasing the computational efficiency of integral equation solvers.     

随机粗糙表面光散射场分布特性的机理研究

为了研究随机粗糙表面光散射分布特性机理,采用线性滤波法生成高斯分布随机粗糙表面,以基尔霍夫近似作为电磁场边界条件,采用蒙特卡罗方法数值计算了一组金属和一组电介质粗糙表面在S偏振光和P偏振光照射下的散射光强度空间分布。计算结果显示:金属表面与电介质表面的散射光分布宽度、散射峰值、散射峰位置三个散射特征存在显著差异,经过分析发现这种特征差异的产生机理是由表面面元的斜率分布和面元反射率共同因素导致,与数值计算结果对比,二者具有良好的一致性。     

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.     

Directional hemispherical radiative properties of random dielectric rough surfaces

In this paper the directional hemispherical reflectivity and transmissivity of one-dimensional, randomly rough, dielectric surfaces are determined by the use of the integral method. This method is derived from electromagnetic theory without any restrictive hypotheses. Since this exact approach is computationally very intensive, a geometric optics approximation method is also developed. Curves displaying radiative properties versus the correlation length for a constant mean square deviation of the surface from flatness are presented. In this respect, the influence on the validity of the approximate method of multiple scattering, the shadowing effect and the real index of refraction of the dielectric have been investigated. Transverse electric and transverse magnetic polarized incident plane waves are considered. For the latter, our interest is focused on the influence of roughness on the reflected and transmitted intensities for an angle of incidence close to the Brewster angle.     

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.     

Fast iterative approach to the difference scattering from a dielectric target above a rough surface

The difference field RCS (d-RCS) has been defined to analyze the scattering from the target above a rough surface. The electric field integral equations (EFIEs) of the difference induced currentJ _sd on the rough surface, the induced electric currentJ _o and magnetic currentK _o on the dielectric target under a TE wave incidence are derived. A small portion of the rough surface towards the target along the specular direction is taken to compute the scattering contributionE _s0 from the rough surface towards the target, which improves the computation speed. A numerical iterative approach is developed to solve the EFIEs and bistatic d-RCS. The surface length for iterations is dependent on the scattering angle and discussed for comparison with Johnson’s method. Using the Monte-Carlo method to generate the Pierson-Morkowitz (P-M) ocean-like rough surface, bistatic d-RCS of the dielectric target, e.g. a cylinder or a square column, above the rough surface is numerically simulated. The induced electric and magnetic currents on the dielectric target and the difference induced current on the rough surface are numerically discussed.     

Multiple light scattering from metal and dielectric rough surfaces

Abstract

A numerical study is done on light scattering from one-dimensional random rough surfaces supporting both dielectrics and metals. The influence of the corrugation on the Brewster angle as well as on the angular distribution of transmitted intensity into the dielectric is investigated. The authors also obtain enhanced backscattering in the light reflected from metallic surfaces. Finally they discuss the influence of roughness on the drop of reflectance due to polariton absorption.     

Fast iterative approach to the difference scattering from a dielectric target above a rough surface

1 Introduction Electromagnetic scattering from the target above or beneath a rough surface has at- tracted much interest during recent years, because of extensive applications to radar surveillance, target detection, ground radar probing, and so on[1―3]. In order to numeri- cally simulate scattering from composite model of the target and underlying rough sur- face, some fast numerical methods, such as general forward backward method and spec- trum acceleration algorithm (GFBM/SAA)[4,5], fin…     

Scattering by an object above a randomly rough surface from a fast numerical method: Extended PILE method combined with FB-SA

In this paper, a fast exact numerical method, based on the method of moments, is developed to calculate the scattering by an object above a rough surface. N. Déchamps et al. have recently developed the PILE (Propagation-Inside-Layer Expansion) method for a stack of two one-dimensional rough interfaces separating homogeneous media. This method allows us to calculate separately and exactly the multiple scattering contributions inside the layer. This is done with a decomposition by block of the impedance matrix (the inverse of the impedance matrix of each interface and two coupling matrices are involved). The purpose of this paper is to extend the PILE method to the more general case of two illuminated surfaces and to apply it to an object located above a rough surface. In addition, to invert a matrix of large size, the Forward–Backward Spectral Acceleration (FB-SA) approach of complexity 𝒪(N) proposed by Chou and Johnson is applied. The new method, extended PILE combined with FB-SA, is tested on Perfectly Conducting (PC) circular and elliptic cylinders located above a rough surface (dielectric or PC) obeying a Gaussian process with Gaussian and exponential height autocorrelation functions.     

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.     

Gaussian beam scattering from arbitrarily shaped objects with rough surfaces

Abstract

The scattered field of Gaussian beam scattering from arbitrarily shaped dielectric objects with rough surfaces is investigated for optical and infrared frequencies by using the plane wave spectrum method and the Kirchhoff approximation, and the formulae for the coherent and incoherent scattering cross sections are obtained theoretically based on geometrical optics and tangent plane approximations. The infrared laser scattering cross sections of a rough sphere are calculated at 1.06 μm, and the influence of the beam size is analysed numerically. It is shown that when the beam size is much larger than the size of the object, the results in this paper will be close to those of an incident plane wave.     

FDTD Investigation on Electromagnetic Scattering from Two-Layered Rough Surfaces under UPML Absorbing Condition

Electromagnetic scattering from one-dimensional two-layered rough surfaces is investigated by using finite-difference time-domain algorithm （FDTD）. The uniaxial perfectly matched layer （UPML） medium is adopted for truncation of FDTD lattices, in which the finite-difference equations can be used for the total computation domain by properly choosing the uniaxial parameters. The rough surfaces are characterized with Gaussian statistics for the height and the autocorrelation function. The angular distribution of bistatic scattering coefficient from single-layered perfect electric conducting and dielectric rough surface is calculated and it is in good agreement with the numerical result with the conventional method of moments. The influence of the relative permittivity, the incident angle, and the correlative length of two-layered rough surfaces on the bistatic scattering coefficient with different polarizations are presented and discussed in detail.     

A heuristic model approximation for scattering from perfectly conducting one-dimensional random rough surfaces

Abstract

We propose a model for scattering from one-dimensional, perfectly conducting, slightly rough surfaces. A possible method for solving the scattering equations is examined which, with some assumptions, suggests the final result. The approximation is relatively simple and is comparable in computational effort with most first-order theories. We compare the bistatic scattering cross section for TE waves predicted by the present model for Gaussian randomly rough surfaces with numerical simulations and with some first-order theories. The comparison shows that the model is remarkably accurate for slightly rough surfaces and TE polarization.     

Enhanced backscattering and blazing effect from gratings,quasi-gratings and randomly rough surfaces

Abstract

The blazing effect is probably the most important property of diffraction gratings used for spectroscopic purposes. On the other hand, the enhanced backscattering phenomenon has been generally studied in the framework of scattering from randomly rough surfaces. Using numerical results from rigorous theories, it will be shown that these phenomena, which have very different origins, should have more precise definitions. In a special case of a randomly rough surface formed by random corners, it will be shown that the effects of these phenomena are sometimes very difficult to distinguish.     

An iterative solution of the rough-surface scattering problem

Abstract

An iterative solution to the problem of scattering from a one-dimensional rough surface is obtained for the Dirichlet boundary condition. The advantages of this method are that bounds for convergence of the solution can be established and that the solution may readily be iterated to sufficiently high order in the interaction to examine the rate at which it converges. Absolute convergence of the iterative solution is also a sufficient condition for the convergence of the operator expansion method for surfaces on which the slope is everywhere less than unity. A numerical example of scattering from an echelette grating is considered, and bounds for convergence established. It is found that for scattering from such surfaces the rate at which the iterative solution converges decreases as the surface slope is increased. Corresponding results are found for the operator expansion method.     

An iterative method for scattering from rough dielectric or conducting interfaces

Abstract

We introduces an iterative method for scattering a two-dimensional scalar wave from a rough interface between two media. The method is applicable to the case of electromagnetic scattering from a rough metallic or dielectric surface that varies only in one dimension. The first iteration is equivalent to the Kirchhoff approximation, and the series converges in one step for a flat surface. We discuss the conditions for convergence, and find that they are similar to those which Meecham showed to be necessary in the Dirichlet case.     

An improved formulation of coherent forward scatter from random rough surfaces

Abstract

The operator expansion method is known to give accurate numerical results for scattering from individual surfaces that are too complicated for other methods. It is less widely appreciated that the method can be applied to random surfaces as well. The simplest application is the modelling of mean forward scatter from a homogeneous Gaussian ensemble of surfaces. To leading order in the admittance operator, the formula for the scalar Dirichlet boundary includes an exponential form in the roughness correlation function. The scalar Neumann boundary adds terms involving the gradients of the exponential form. These factors modestly alter the magnitude and advance the phase of the coherent scatter relative to the conventional one-point (Kirchhoff) approximation when the significant surface correlation scales are comparable to the radiation wavelength. Narrow troughs in the surface undulations ‘repel’ the radiation and effectively elevate and flatten the mean surface. These results are reliable over a wide range of surface amplitudes and correlation scales, provided the slope times Rayleigh height (Dirichlet problem) and slope (Neumann problem) are not large.