Wave diffraction by a concave statistically rough surface

Abstract

We consider a statistically rough impedance surface that is concave on average in contrast to a plane. Backscattering from such a surface is considered based on the small perturbation theory method. The diffraction problem is divided into two parts which are considered separately: the problem of scattering by small roughness (assumed to be local) and the propagation of incident and scattered fields over a smooth large-scale concave surface. In contrast to the ‘two-scale’ scattering model, the zero-order unperturbed wavefield is not assumed to be specularly reflected from the local tangent plane to the smooth surface, but it is a solution of a corresponding diffraction problem. Two particular cases of smooth surfaces are considered: first, the inner surface of a concave cylinder with a constant radius and finite angular pattern, and second, a compound surface that consists of a coupled half-plane and the cylindrical surface mentioned above. In a geometrical optics limit and with propagation at low grazing angles, the analytical results for a zero-order (unperturbed) field are obtained for these two cases in the form of a series over multiple specular reflected fields. It is shown that these non-local processes lead to the essential increase in the backscattering cross section in comparison with the two-scale model and tangent-plane approach.     

Physical optics theory of resistive surfaces

The physical optics current is obtained from the exact solution of the scattering problem of plane waves by a resistive surface. The edge point method is used for the determination of the physical optics surface current. The derived physical optics integral by considering the new surface current enables one to evaluate the scattering problems by various resistive surfaces with edge discontinuities. The method is applied to the diffraction problem of plane waves by a concave cylindrical reflector. The scattered fields are examined numerically.     

Scattering from a rough layer of a random medium

This paper deals with scattering from a random-medium layer with rough boundaries. The fluctuations of the surface heights and medium permittivity are assumed to be small and smooth. All random quantities are assumed to be stationary and independent of each other. After the introduction of approximate boundary conditions, the system of partial differential equations is transformed into an integral equation where the fluctuations of the problem are represented as a zero-mean random operator. Employing smoothing, integral equations for the coherent fields are obtained. Use of the Helmholtz operator leads to solution for the coherent propagation constant while the boundary operators lead to coherent Fresnel coefficients. The characteristics of the results are illustrated by considering several examples.     

Eliminate the influence of zero-order diffraction for wavefront reconstruction with selectable magnification in digital holographic

The objective surface is considered as the scattering plane; frequency spectrum of a digital hologram transmission light is studied when the reference light and reconstruction wave are spherical waves. The relation between relevant parameters and the object light, conjugate object light and zero-order diffraction wave frequency spectrum distribution. The research results show that: each frequency spectrum of the diffracted wave broadens to various degrees as the radius of the reconstruction wavefront decreases, and frequency aliasing is generated under certain conditions. Based on the research results, a new method that carries out high-pass filtering processing without zero-order diffraction interference upon digital hologram is proposed and the reconstruction experimental proof for eliminating the interferential changeable magnification wave is given.     

R-matrix method for a surface with one groove of arbitrary profile

The R-matrix propagation algorithm is applied to solve the problem of electromagnetic scattering from a perfectly conducting plane surface with one groove of arbitrary profile. Using the multilayer approximation, the fields inside each layer are written as modal expansions. The reflected intensity is obtained in both the fundamental cases of polarization, which are treated separately. Numerical examples are shown for several profiles of the groove, and comparisons with results known from physical optics are presented for the validation of the method.     

Small-slope expansion for electromagnetic-wave diffraction on a rough surface

The diffraction and absorption of the plane electromagnetic wave on a rough surface is considered to find the scattering and emissivity of the surface. For this purpose a system of integral equations for unknown surface fields is derived from Green's formula for the Helmholtz equation. The small-slope approach is used to find a solution, i.e. the solution is determined from an expansion over the roughness spectrum that, in the limit of the large-scale roughness, turns out to be the expansion over the slope spectrum.     

Small-slope expansion for electromagnetic-wave diffraction on a rough surface

Abstract

The diffraction and absorption of the plane electromagnetic wave on a rough surface is considered to find the scattering and emissivity of the surface. For this purpose a system of integral equations for unknown surface fields is derived from Green's formula for the Helmholtz equation. The small-slope approach is used to find a solution, i.e. the solution is determined from an expansion over the roughness spectrum that, in the limit of the large-scale roughness, turns out to be the expansion over the slope spectrum.     

Optical properties of an echelette grating in the short-wave approximation

The problem of plane-wave scattering by an echelette grating with a right angle is considered in the case of high-frequency approximation (the wavelength is assumed to be small compared with the period of grating). We present the results of short-wave asymptotic analysis for a ray optical solution to the problem that was derived on the basis of the method of summation of multiple diffracted fields that is well known in the geometric theory of diffraction. A new effect of perfect blazing for an echelette grating in the high-frequency approximation is also discussed.     

Scattering by random rough surfaces: Study of direct and inverse problem

In order to study the problems of scattering by rough metallic surfaces, we have used Maxwell’s equations in covariant form within the framework of a non-orthogonal coordinates system adapted to the geometry of the problem. Electromagnetic fields are written in Fourier’s integral form. The solution is found by using a perturbation method applied to the smooth surface problem; this is fully justified when the defects are of small magnitude.For the direct problem, the mean value of diffraction intensity is obtained for random rough surfaces of finite conductivity by computer simulation.In the case of the inverse problem, the reconstruction of the profile of the metal surface from values of the diffraction intensity, obtained by simulation, is found using an iterative algorithm.     

Radar backscattering from Gerstner's sea surface wave

In the framework of a two-scale scattering model, radar backscattering from the rough sea surface was considered. The sea surface was modelled as a superposition of a nonlinear, large-scale Gerstner's wave and small-scale resonant Bragg scattering ripples. The zero-order diffracted field was found by a geometrical optics approach, with shadowing taken into account, and by an 'exact' solution of the diffraction problem obtained numerically. For vertical and horizontal polarizations, the spatial distribution of specific scattering cross sections along the large-scale wave was obtained. The spatially averaged specific backscattering cross sections, as well as the mean Doppler frequency shifts at both polarizations, obtained by the geometrical optics approach are compared with those obtained by using the 'exact' solution of the large-scale diffraction problem. The roles of shadowing and multiple wave scattering processes are discussed, and qualitative explanations of the difference between these two approaches are given.     

衍射法测量低频液体表面波的衰减系数

提出了一种可用于几百赫兹低频液体表面声波研究的激光衍射法测量新技术。在实验上采用入射光掠入射到表面波上在远场得到了中间亮,两边暗的高反衬度的衍射条纹,实验中发现对频率为几百赫兹的低频衰减液体表面波,当移动振源改变激光入射点与振源间距离时发现零级条纹消失,这意味着此时的衍射效率接近100%。在理论上给出了衍射光强度与表面波振幅的解析关系,并利用所提出的新技术实现了对几百赫兹液体表面波的衰减系数的实时测量。     

Small-slope approximation for electromagnetic wave scattering at a rough interface of two dielectric half-spaces

Abstract

The small-slope approximation (SSA) for wave scattering at the rough interface of two homogeneous half-spaces is developed. This method bridges the gap between two classical approaches to the problem: the method of small perturbations and the Kirchhoff (or quasi-classical) approximation. In contrast to these theories, the SSA is applicable irrespective of the wavelength of radiation, provided that the slopes of roughness are small compared with the angles of incidence and scattering.

The resulting expressions for the SSA are given for the entries of an S-matrix that represents the scattering amplitudes of plane waves of different polarizations interacting with the rough boundary. These formulae are quite general and are valid, in fact, for waves of different origins. Apart from the shape of the boundary, some functions in these formulae are coefficients of the expansion of the S-matrix into a power series in terms of elevations. These roughness independent functions are determined by a specific scattering problem. In this paper they are calculated for the case of electromagnetic scattering at the interface of two dielectric half-spaces. In contrast to an earlier paper by the author, where only the formulae for the reflected field were presented, in this paper both reflected and transmitted fields are considered in detail.

The a priori symmetry relations that this scattering problem should obey (reciprocity and energy conservation) are formulated in terms of the S-matrix.

The statistical moments of scattering amplitudes are directly related to the mean-reflection coefficient and scattering cross sections, which are usually determined experimentally. The corresponding formulae are given here for the case of Gaussian space-homogeneous statistics of roughness.     

Radiative transfer in a layer of magnetized plasma with random irregularities

The problem of radio wave reflection from an optically thick plane uniform layer of magnetized plasma is considered in the present work. The plasma electron density irregularities are described by a spatial spectrum of arbitrary form. The small-angle scattering approximation in invariant ray coordinates is proposed as a technique for the analytical investigation of the radiation transfer equation. The approximate solution describing the spatial and angular distribution of radiation reflected from a plasma layer is obtained. The solution obtained is investigated numerically for the case of ionospheric radio wave propagation. Two effects occur as a consequence of multiple scattering: a change in the reflected signal intensity and an anomalous refraction.     

Distinctive features of a pulsed beam scattering on a plane surface (two-dimensional case)

A two-dimensional problem of scattering of pulsed beams having arbitrary time and spatial form on a plane surface of a lossy dielectric halfspace is solved. A pulsed beam has been modeled by letting an E- or H-polarized plane pulse with homogeneous front pass through a space filter. The reflected pulse is found using an expansion of the incident pulsed beam over time-harmonic plane waves.     

散射光彩色数字全息光学系统及波面重建算法研究

令物体表面为散射面,参考光及重建光为球面波,详细研究了离轴数字全息物光场重建平面的光波场.导出物光、共轭物光及零级衍射光分布与光学系统参数的关系.根据彩色数字全息的特点,提出抑制零级衍射干扰的光学系统设计方法,并且对一种能够避免插值误差的波面重建算法进行了优化研究,给出了相应的实验证明.     

Rigorous and approximate methods for modeling wave scattering from a locally perturbed perfectly conducting surface

Rigorous and approximate methods are considered for solving the problem of harmonic plane wave scattering from a plane surface arbitrarily perturbed along one dimension on a finite interval. This problem is treated using the Fredholm integral equations of the second kind and the Kirchhoff and Rayleigh approximations. The estimates of the computational efficiency of the integral equation method and the Rayleigh approximation are compared by calculating fields scattered from random rough surfaces in the resonance region (i.e., when the roughness height is comparable to or smaller than the incident wavelength) for an arbitrary incidence of a plane wave. Scattering patterns calculated using the integral equations and the Kirchhoff approximation are discussed in the case of large-scale random rough surface scattering. Particular attention is paid to scattering at near-grazing incidence.     

Diffraction of a convergent sound wave by an elastic cylindrical shell with a longitudinal fixation

The problem of the diffraction of a zero-order convergent cylindrical wave by a cylindrical shell with a longitudinal fixation along one of its generatrices is considered. The problem is solved on the basis of using the so-called helical waves, which are aperiodic eigensolutions to the equations of the shell motion. The diffraction field is represented in the form of a convergent series in cylindrical harmonics. The method of the solution allows for a generalization to several cases of longitudinal fixation with conditions of different forms. The calculation of the scattering amplitude of the diffraction field is carried out for various frequencies and shell parameters.     

High-frequency wave diffraction by an impedance segment at oblique incidence

The plane problem of high-frequency acoustic wave diffraction by a segment with impedance boundary conditions is considered. The angle of incidence of waves is assumed to be small (oblique). The paper generalizes the method previously developed by the authors for an ideal segment (with Dirichlet or Neumann boundary conditions). An expression for the directional pattern of the scattered field is derived. The optical theorem is proved for the case of the parabolic equation. The surface wave amplitude is calculated, and the results are numerically verified by the integral equation method.     

Low-frequency scattering of acoustic waves by a bounded rough surface in a half-plane

The problem of the scattering of harmonic plane waves by a rough half-plane is studied here. The surface roughness is finite. The slope of the irregularity is taken as arbitrary. Two boundary conditions are considered, those of Dirichlet and Neumann. An asymptotic solution is obtained, when the wavelength lambda of the incident wave is much larger than the characteristic length of the roughness iota, by means of the method of matched asymptotic expansions in terms of the small parameter epsilon= 2piiota/lambda. For the Dirichlet problem, the solution of the near and far fields is obtained up to O(epsilon2). The far field solution is given in terms of a coefficient that have a simple explicit expression, which also appears in the corresponding solution to the Neumann problem, already solved. Also the scattering cross section is given by simple formulas to O(epsilon3). It is noted that, for the Dirichlet problem, the leading term is of order epsilon3 which, by contrast, is different from that of the circular cylinder in full space, that is, of order epsilon(-1) (log epsilon)(-2). Some examples display the simplicity of the general results based on conformal mapping, which involve arcs of circle, polygonal lines, surface cracks and the like.     

Acoustic scattering by a three-dimensional elastic object near a rough surface

The ensemble-averaged field scattered by a smooth, bounded, elastic object near a penetrable surface with small-scale random roughness is formulated. The formulation consists of combining a perturbative solution for modeling propagation through the rough surface with a transition (T-) matrix solution for scattering by the object near a planar surface. All media bounding the rough surface are assumed to be fluids. By applying the results to a spherical steel shell buried within a rough sediment bottom, it is demonstrated that the ensemble-averaged "incoherent" intensity backscattered by buried objects illuminated with shallow-grazing-angle acoustic sources can be well enhanced at high frequencies over field predictions based on scattering models where all environmental surfaces are planar. However, this intensity must compete with the incoherent intensity scattered back from the interface itself, which can defeat detection attempts. The averaged "coherent" component of the field maintains the strong evanescent spectral decay exhibited by flat interface predictions of shallow-angle measurements but with small deviations. Nevertheless, bistatic calculations of the coherent field suggest useful strategies for improving long-range detection and identification of buried objects.