Angular correlation function of wave scattering by a random rough surface and discrete scatterers and its application in the detection of a buried object

Abstract

The scattering of waves by a buried object is often obscured by the clutter around it. Such clutter can be attributed to the scattering by random rough surfaces and random discrete scatterers. Recent studies show that, because of the memory effect, the angular correlation function can suppress the effects of clutter and make the scattering by the buried object more conspicuous. In this paper, we study the angular correlation function of wave scattering by a buried object underneath a layer of random discrete scatterers and a non-Gaussian random rough surface. Such problems are common when the target is buried below a rough surface that is underneath a layer of vegetation. Numerical results are illustrated for various parameters of rough surfaces and discrete scatterers. The angular correlation function is calculated by frequency and angular averaging. It is shown that the use of the angular correlation function can enhance target detection in the presence of clutter.     

Theoretical study of the Kirchhoff integral from a two-dimensional randomly rough surface with shadowing effect: application to the backscattering coefficient for a perfectly-conducting surface

Abstract

In this paper, the backscattering coefficient of a two-dimensional randomly rough perfectly-conducting surface is investigated using the Kirchhoff approach with a shadowing function. The rough surface height/slope correlations assumed to be Gaussian are accounted for in this analysis. The scattering coefficient is then formulated in terms of a characteristic function for the integrations over the surface heights, in terms of expected values for the integrations over the surface slopes. Numerical comparisons of Kirchhoff's approach (KA) with the stationary-phase (SP) approximation are made with respect to the choice of the one-dimensional surface height autocorrelation function and the shadowing effect. For an isotropic surface the results show that SP underestimated the incoherent backscattering coefficient compared with KA. Moreover, when the correlation between the slopes and the heights is neglected, the shadowing effect may be ignored.     

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.     

Fourth moments of acoustic waves forward scattered by a rough ocean surface

Abstract

Three types of statistical fourth moments of acoustic waves forward scattered by a randomly rough ocean surface are derived and numerically evaluated. The first one is related to the scintillation index which characterizes intensity fluctuations. The second one is the two-position intensity correlation function which describes the spatial correlation of wave intensity. The third is the fourth-moment two-position coherence function which carries information on the phase fluctuations of the scattered wave. In the range of weak scattering, the ratio of the absolute value of the fourth-moment two-position coherence function over the two-position intensity correlation exactly describes the mean-square fluctuation of the relative phase between the two positions. The acoustic frequency is high so that the Kirchhoff approximation can be used. Two types of spectral functions for surface-height fluctuations are considered: a Gaussian spectrum and the Donelan-Pierson spectrum. The latter is obtained from a model for the fluctuations of the ocean surface height which are controlled by the wind speed at the ocean surface.     

Scattering of a scalar wave from a two-dimensional randomly rough Neumann surface

Abstract

We present a reciprocity and unitarity preserving formulation of the scattering of a scalar plane wave from a two-dimensional, randomly rough surface on which the Neumann boundary condition is satisfied. The theory is formulated on the basis of the Rayleigh hypothesis in terms of a single-particle Green's function G(q_‖|k_‖) for the surface electromagnetic waves that exist at the surface due to its roughness, where k_‖ and q_‖ are the projections on the mean scattering plane of the wave vectors of the incident and scattered waves, respectively. The specular scattering is expressed in terms of the average of this Green's function over the ensemble of realizations of the surface profile function (G(q_‖|k_‖)). The Dyson equation satisfied by (G(q_‖|k_‖)) is presented, and the properties of the solution are discussed, with particular attention to the proper self-energy in terms of which the averaged Green's function is expressed. The diffuse scattering is expressed in terms of the ensemble average of a two-particle Green's function, which is the product of two single-particle Green's functions. The Bethe-Salpeter equation satisfied by the averaged two-particle Green's function is presented, and properties of its solution are discussed. In the small roughness limit, and with the irreducible vertex function approximated by the sum of the contribution from the maximally-crossed diagrams, which represent the coherent interference between all time-reversed scattering sequences, the solution of the Bethe-Salpeter equation predicts the presence of enhanced backscattering in the angular dependence of the intensity of the waves scattered diffusely.     

Monostatic and bistatic statistical shadowing functions from a one-dimensional stationary randomly rough surface: II. Multiple scattering

Abstract

The integral equation model (IEM) has been developed over the last decade and it has become one of the most widely used theoretical models for rough-surface scattering in microwave remote sensing. In the IEM model the shadowing function is typically either omitted or a form based on geometric optics with single reflection is used. In this paper, a shadowing function for one-dimensional rough surfaces which incorporates multiple scattering, finite surface length and both monostatic and bistatic configurations is developed. For any uncorrelated process, the resulting equation can be expressed in terms of the monostatic statistical shadowing function with single reflection, derived in the preceding companion paper. The effect of correlation between the surface slopes and heights for a Gaussian surface is studied to illuminate the range over which such correlations can be ignored. It is found that while the correlation between surface slopes and heights in the monostatic statistical shadowing function with single reflection can be ignored, when calculating the average shadowing function with double reflection the correlation between slopes and heights between points must be incorporated.     

Measurements of light scattering by a characterized random rough surface

Abstract

Measurements are presented of the angular distribution of four wavelengths of light scattered by a one-dimensional random rough surface, whose probability density function is Gaussian with a standard deviation σ=1.22±0.02 μm and whose lateral correlation function is also Gaussian with 1/e width τ=3.17±0.07 μm. The wavelengths used are 0.63, 1.15, 3.39 and 10.6 μm. The surface is used in two forms: coated with gold and as an almost lossless dielectric. The results are compared to those predicted by a double scattering form of the Kirchhoff formulation. Agreement is good at small angles of incidence but less good at larger angles of incidence.     

Pulse broadening and two-frequency mutual coherence function of the scattered wave from rough surfaces

Abstract

Analytical expressions for the two-frequency mutual coherence function and angular correlation function of the scattered wave from rough surfaces based on the Kirchhoff approximation are presented. The coherence bandwidth depends on the illumination area as well as on the incident and scattered angles and the surface characteristics. Scattered pulse shapes are calculated as the Fourier transform of the two-frequency mutual coherence function. Calculations based on analytical solutions are compared with millimetre wave experimental data and Monte Carlo simulations showing good agreement.     

Dispersion and damping of a surface plasmon polariton on a one-dimensional randomly rough metal surface

Abstract

By the use of the reduced Rayleigh equation for the amplitude of a surface plasmon polariton on a one-dimensional randomly rough metal surface that is in contact with vacuum, we calculate the dispersion and damping of the surface electromagnetic wave to the lowest nonzero order in the rms height of the surface. It is found that the frequency of the surface plasmon polariton is depressed by the surface roughness. The attenuation of the surface plasmon polariton in the long wavelength limit is due primarily to its scattering into other surface plasmon polaritons, while in the short wavelength limit it is due primarily to its roughness-induced scattering into volume electromagnetic waves in the vacuum. The energy mean free path of the surface plasmon polariton is shorter on a randomly rough metal surface than it is on a lossy planar metal surface, and the surface plasmon polariton is more tightly bound to a rough surface than to a planar one.     

Calculation of the scattering of electromagnetic waves from a two-dimensional perfectly conducting surface using the method of ordered multiple interaction

Abstract

Calculations, using the method of ordered multiple interaction (MOMI), of the scattering of electromagnetic waves from a two-dimensional, randomly rough, perfectly conducting surface with a ratio of RMS height [sgrave] to correlation length a of 1.0 or smaller are presented which demonstrate the robustness of the method. Convergence is achieved in six iterations or less. Some surfaces with [sgrave] = a = 1.0λ and certain topological features exhibited slow convergence. The MOMI inherently will show slow convergence when there are multiple back and forth scatterings. Since resonant scattering is characterized by this type of scattering, this suggests the presence of surface resonances on these surfaces.     

Two-frequency mutual coherence function for electromagnetic pulse propagation over rough surfaces

The propagation of a transient electromagnetic pulse over irregular terrain is considered. We model the wave propagation using the parabolic wave equation, which is valid for near-horizontal propagation. We model the effect of scattering from the rough terrain by introducing a surface-flattening coordinate transform. This coordinate transform simplifies the boundary condition of our problem, and introduces an effective refractive index into our wave equation. As a result, the problem of propagation over an irregular surface becomes equivalent to the problem of propagation through random media. The parabolic equation is solved analytically using the path integral method. Both vertically polarized and horizontally polarized signals are treated. Cumulant expansion is introduced to obtain an approximate expression for the two-frequency mutual coherence function. From the mutual coherence function, spatial and temporal dependence of the propagating signal can be determined. It can be shown that scattering from the irregular surface can cause broadening of the transient signal. This can have a significant impact on the performance of radio communication systems.     

Experimental study of the angular correlation function in the double passage of waves through a one-dimensional random phase screen

Abstract

Experimental results are presented for the angular correlation function of far-field speckle patterns scattered in the double passage of waves through a one-dimensional random phase screen. The experiment for the correlation measurement was set up to use a CCD camera to obtain the image of the speckle patterns in the scattering directions for each given angle of incidence; the cross-correlation function is then calculated from the digitized images. The theoretical analysis of the motion of the speckle as the source is moved, as given by Escamilla, is verified experimentally. It is found that in contrast with the memory effect line of speckle motion, the speckle pattern produced in the region of observation tracks the backscattering direction.     

Subsurface detection of a buried object using angular correlation function measurement

Abstract

A new technique is proposed for subsurface detection of buried objects using the angular correlation function (ACF) measurement of scattered waves. Compared with the traditional detection technique which relies on radar cross section (intensity) measurement, this new ACF-based technique results in better signal-to-clutter ratio and thus higher target visibility. Laboratory experiments were conducted at millimetre-wave (80–105 GHz) and X-band (7–13 GHz) frequencies to illustrate the potential effectiveness of this new correlation approach over the traditional cross section approach.     

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.     

Multiple reflections in backscattering by a single scatterer near a perfectly reflecting surface

The scattering of a plane electromagnetic wave by a solitary scatterer randomly positioned near a perfectly reflecting surface is investigated in the dipole approximation taking into account infinite multiplicity of scattering. It is shown that the presence of multiply reflected waves increases the “effective” polarizability of the particle and adds another component of the dipole moment along the normal to the surface. As a result, the backscattering enhancement effect becomes stronger, and the angle of incidence at which amplification of the p-polarized wave vanishes becomes smaller. The influence of multiply scattered waves increases as the particle approaches the boundary in this case. Zh. Tekh. Fiz. 67, 72–75 (September 1997)     

Reflection and scattering of spin waves by surface roughness of a ferromagnet

Abstract

A detailed theory of volume spin wave reflection from the randomly rough surface of a ferromagnet is presented. The contribution to damping of the reflected wave is calculated. This contribution is due to the scattering of the initial volume wave into secondary surface and volume spin waves. The value of damping is proportional to the correlation length and the square of the roughness amplitude. Numerical calculations of the attenuation rate as a function of the angle of incidence and the ratio between the surface anisotropy and the wavenumber are provided. They yield the angle of incidence where the attenuation has a maximum. In analogy to optics, this angle is similar to the Brewster angle. Numerical estimations of damping and a comparison of its value with the ferromagnetic resonance linewidth are also made. Finally, the results of the calculation of the scattering of surface exchange spin waves by surface roughness are presented and discussed.     

Bistatic scattering coefficient from one- and two-dimensional random surfaces using the stationary phase and scalar approximation with shadowing effect: comparisons with experiments and application to the sea surface

Abstract

In this paper, the bistatic scattering coefficient from one- and two-dimensional random surfaces using the stationary phase method and scalar approximation with shadowing effect is investigated. Both of these approaches use the Kirchhoff integral. With the stationary phase, the bistatic cross section is formulated in terms of the surface height joint characteristic function where the shadowing effect is investigated. In the case of the scalar approximation, the scattering function is computed from the previous characteristic function and in terms of expected values for the integrations over the slopes, where the shadowing effect is analysed analytically. Both of these formulations are compared with experimental data obtained from a Gaussian one-dimensional randomly rough perfectly-conducting surface. With the stationary-phase method, the results are applied to a two-dimensional sea surface.     

Far-field intensity of electromagnetic waves scattered from random,self-affine fractal metal surfaces

Abstract

By means of the rigorous Green theorem integral equation formulation, we study the far-field intensity of linearly polarized, monochromatic electromagnetic waves scattered from a one-dimensionally rough silver surface characterized by a self-affine fractal structure. These surface fractal properties are ensured for the entire range of relevant length scales, from the illuminated spot size down to a sufficiently small (in terms of the wavelength) lower cut-off length. A peak in the specular direction is found in the angular distribution of the diffuse component of the mean scattered intensity, which becomes broader and smaller with increasing fractal dimension. For large fractal dimensions, enhanced backscattering in the case of p-polarization is observed owing to the roughness-induced excitation of surface plasmon polaritons. The interplay of different length scales of the fractal surface in the scattering process is analysed for an intermediate fractal dimension.     

Application of the finite element method to Monte Carlo simulations of scattering of waves by random rough surfaces: penetrable case

Abstract

The finite element method (FEM) of Monte Carlo simulations of random rough surface scattering is extended to penetrable rough surface scattering. The attraction of the method is the banded nature of the resulting matrix equation. The method yields a system of linear algebraic equations which is solved by a direct sparse symmetric matrix inversion. Convergence and accuracy of the method is demonstrated and established by varying various input parameters such as the number of evanescent waves, the number of sampling points and the surface lengths. Results with incident plane wave TE polarization are presented for both the mean reflected scattered intensity and the mean transmitted scattered intensity as a function of surface parameters such as RMS surface heights and correlation lengths. The numerical results are compared against the tapered wave integral equation (TWIE) method. The results of a tapered wave solution of the integral equation averaging over many realizations are in good numerical agreement with FEM if large surface lengths are used in the integral equation method. It is found that a large surface length is required in the TWIE method to have a narrow incident angular spectlum to accurateiy predict the transmitted scattered intensity, whereas a relatively small surface length is sufficient in the FEM. The total CPU time and memory storage requirements for the FEM are much less than that of the TWIE method for eases when the number of horizontal sampling points is much larger than the number of vertical sampling points in the region of discretization. The percentage error in conservation of energy for the FEM is shown to be less than 0.4% for all the examples presented. The total CPU time, memory storage requirements and the percentage error comparisons between the FEM and the TWIE are presented.     

Travel-time statistics for signals scattered at a rough surface

Abstract

The travel time of signals reflected or refracted by a rough surface is investigated in the geometrical optics approximation. It is shown that surface roughness typically decreases the mean travel time in the case of large-scale roughness, when only one specularly reflecting point moves randomly around its unperturbed position, resulting in a negative travel-time bias (toward early echoes). In the opposite limiting case of multipath propagation, when many specular points exist on a random surface, the travel-time bias is always positive. General results are illustrated by two examples related to ocean remote sensing which involve sound scattering from the ocean surface and bottom.