Scattering of a narrow wave beam by a randomly rough locally diffuse surface subject to pulse illumination

We consider the scattering of a narrow pulse wave beam by a randomly rough surface with a complex local scattering indicatrix. Analytical expressions are found for the mean received power for a normal distribution of heights and slopes of the surface in two cases: where the direction to the receiver is close to the direction of mirror reflection and where the direction to the receiver is very different from the direction of mirror reflection. It is shown that in these two cases the echo pulse is very different in shape and is controlled by the parameters of the source and receiver, the sounding scheme, and the variance of heights of a rough surface. The received power is strongly dependent on the width of the local scattering indicatrix, and the form of this dependence is determined by the angles of illumination and reception. The analytical expressions for the mean received power are in good agreement with the results of numerical calculations. Institute for Radioelectronics and Laser Engineering of the N. é. Bauman State Technical University of Moscow, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol.42, No.4, pp. 333–339, April 1999.     

Scattering of a Narrow Wave Beam on a Rough,Locally-Specular Surface in the Case of Pulsed Illumination

We consider scattering of a pulsed narrow wave beam on a rough surface with a locally-specular indicatrix. Analytical expressions for the average received power are obtained for normal distributions of heights and slopes of the rough surface in two cases in which the direction to the receiver is close to or strongly different from the direction of specular reflection. It is shown that in these cases, the received echo pulses have drastically different profiles determined by the source and receiver parameters, the scheme of sounding, and the variance of the heights and slopes of the rough surface. The obtained analytical expressions for the average received power agree well with the results of numerical simulations.     

Scattering of a Narrow Pulsed Wave Beam by a Randomly Rough,Locally Lambertian Surface under Conditions of Strong Shadowing

We consider the problem of scattering of a narrow pulsed wave beam irradiating a randomly rough surface in the atmosphere under conditions of strong shadowing of one surface element by another. Expressions for the average power recorded by a receiver are obtained for the case where a locally Lambertian surface with Gaussian distribution of heights and slopes is irradiated by a delta impulse. It is shown that the shadowing and the atmospheric turbulence give rise to a considerable distortion of the received optical signal. The obtained analytical expressions for the received power are in good agreement with the results of numerical calculations.     

Multifractal Structure of Intermittency in a Developed Ionospheric Turbulence

We present the results of studying the multifractal structure of intermittency in a developed ionospheric turbulence during special experiments on radio-raying of the midlatitude ionosphere by signals from orbital satellites in 2005–2006. It is shown, in particular, that the determination of multidimensional structural functions of the energy fluctuations of received signals permits one to obtain the necessary information on multifractal spectra of the studied process of radio-wave scattering in the ionosphere. Experimental data on multifractal spectra of slow fluctuations in the received-signal energy under conditions of a developed small-scale turbulence are compared with the existing concept of the radio-wave scattering within the framework of the statistical theory of radio-wave propagation in the ionosphere. It is inferred that under conditions of a developed ionospheric turbulence, the multifractal structure of the intermittency of slow fluctuations in the received-signal energy is a consequence of the intermittency of small-scale fluctuations in the electron number density of the ionospheric plasma on relatively large spatial scales of about several ten kilometers. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 6, pp. 485–493, June 2008.     

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.     

Scattering of a spherical wave by a statistically irregular dielectric surface

The scattering of a spherical wave by a static irregular dielectric surface, separating two subspaces with dielectric constant close to the permittivity of free space, is investigated by the Kirchhoff method. The irregularities of the surface — large-scale with small angles of inclination, and their heights are distributed according to a normal law. Self-shadowing and the set of spots associated with scattering on such a surface are taken into account. The polarization matrix of second moments of the components of the scattered field is calculated. The dependence of the matrix elements on the statistical parameters of a randomly irregular surface are discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 7–10, May, 1974.     

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.     

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

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.     

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.     

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

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.     

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

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.     

风浪因素对海洋波导雷达回波作用机理的研究

采用文氏谱模型描述近海海洋动力环境海面的粗糙特征, 并运用海浪谱理论得到风速和均方根高度偏差的关系. 进而应用修正的离散混合傅里叶变换方法和改进的雷达散射系数模型分别计算了电磁波传输损耗和雷达散射系数. 在此基础上, 通过数值计算分析了风浪因素对海洋波导环境雷达回波功率值的影响. 结果表明, 风浪因素对不同观测高度处的传输损耗的影响均不大; 风浪因素对雷达回波功率有显著影响, 并且相对于传输损耗, 雷达散射系数项受风浪因素影响较大因而导致较大的雷达回波功率的变化.     

Frequency dependence of the inversion layer conductivity in the metallic and localized regimes

Surface plasmons have been excited with the prism method at sinusoidally modulated silver surfaces. The scattered light intensity of the first diffraction order has been investigated for gratings with different modulation heights H. The scattered light intensity increases up to modulation heights H of ca. 70 Å with the square of H. We discuss the limits for applying first order scattering theories to surface plasmon scattering experiments.     

Study of the surface structure of Si(1 1 1)-6 × 1(3 × 1)-Ag using X-ray crystal truncation rod scattering

The structure of the Si(1 1 1)-6 × 1-Ag surface is investigated using crystal truncation rod (CTR) scattering along 00 rod. For the measurement, we developed a manipulator suitable for observing CTR scattering at large momentum transfer perpendicular to the surface. The heights of the silver and reconstructed silicon atoms from the substrate were determined. We also compared the obtained positions with those of the Si(1 1 1)-√3 × √3-Ag surface and found that the heights of those reconstructed atoms are almost the same.     

Development of a Mathematical Model for Light Scattering by statistically irregular particles

A mathematical model is described to predict Fraunhofer diffraction by statistically irregular particles. It is demonstrated that the particles are characterised by a probability distribution of radius and a correlation function in the surface. The results of calculation show that at angles not too far from the forward scattering direction and for irregularity heights within a limited range, the irregular particles may be represented approximately by spheres with a size distribution equal to the probability distribution of radius. However, the calculations are highly sensitive to the exact nature of the probability functions. Comparisons of the results with those of a simpler model are not satisfactory beyond the first forward scattering lobe.     

Small-slope simulation of acoustic backscatter from a physical model of an elastic ocean bottom

An underwater acoustic experiment with a two-dimensional rough interface, milled from a slab of PVC, was performed at a tank facility. The purpose was to verify the predictions of numerical models of acoustic rough surface scattering, using a manufactured physical model of an ocean bottom that featured shear effects, nonhomogeneous roughness statistics, and root-mean-square roughness amplitude on the order of the acoustic wavelength. Predictions of the received time series and interface scattering strength in the 100-300 kHz band were obtained from the Bottom Reverberation from Inhomogeneities and Surfaces-Small-Slope Approximation (BORIS-SSA) numerical scattering model. The predictions were made using direct measurements of scattering model inputs-specifically, the geoacoustic properties from laboratory analysis of material samples and the grid of surface heights from a touch-trigger probe. BORIS-SSA predictions for the amplitude of the received time series were shown to be accurate with a root-mean-square residual error of about 1 dB, while errors for the scattering strength prediction were higher (2-3.5 dB). The work is part of an ongoing effort to use physical models to examine a variety of acoustic scattering and propagation phenomena involving the ocean bottom.     

Scattering of an electromagnetic wave from a slightly random cylindrical surface: horizontal polarization

Abstract

The scattering of an electromagnetic wave from a random cylindrical surface ir studied for a plane-wave incidence with S-(TE) polarization, by means ofthe stochastic scattering theory developed by Nakayama, Ogura. Sakati et al. The theory is based on the Wiener-Ito stochastic functional calculus combined with the group-theoretic consideration concerning the homogeneity of the random surface. The random surface is assumed to be a homogeneous Gaussian random field on the cylinder C, homogeneous with respect to the group of motiolrs on C: translations along the axis and rotations around the axis. An operator D operating on a random field on C is introduced in such a way that D keeps the homogeneous random surface invariant This gives a reprerentation of the cylbdrical group and commutes with the boundary condition and the Maxwell equation. Thus, for an injection of the mth cylindrical TE or TM wave, which is a vector eigenfunction of the D operator, the scattered random wave field is an eigenfunctiou with the same eigenvalue: it satisfies the Maxwell equation and is a stoch-tic Iunctional of the Gaussian random surface, BO that it can be expressed in a vector form of the Wiener-Ito expansion in t e m of TE and TM waves and orthogonal functional. of the Gaussian random measures associated with the random cylindrical surface. In the analysis the random surface is modelled by an approximate boundaiy condition representing a perfectly conducting cylindrical surface with a slight roughness. The boundary condition on the random cylinder is transformed into a hierarchy of equations for the Wiener kernels which can be solved approximately. The random wave field for a plane-wave injection is obtained by summing these fields over m. From the stochastic representation of the electromagnetic field so obtained, various statistical characteristics can be calculated the coherent scattering amplitude. total coherent power flow, incoherent power flow, differential sections for coherent rcatlerhig and incoherent scattering, etc. The power conservation law is cast into a stochastic electromagnetic version of the optical theorem stating that the total scatteiing cross section is given by the imaginary part of the forward coherent scattering amplitude. Numerical calculations are made for a planewave injection with S-(TE) polarization. The case of p-(TM) polarization can be treated in a similar manner.     

Additional Nonreciprocity Effects in the Magneto-Optics of Asymmetric Layer Structures

The structure of the adsorbed layer of alkali ions on the surface of colloidal silica solutions with a particle size of 27 nm has been studied by reflectometry and diffuse scattering of synchrotron radiation with a photon energy of about 71 keV. Electron density profiles in the direction perpendicular to the surface have been reconstructed from experimental data and spectra of the correlation function of heights in the surface plane have been obtained. The revealed deviation of the integral and frequency characteristics of the roughness spectra of the silica sol surface from predictions of the capillary-wave theory is of a fundamental character. This deviation is due to the contribution from roughnesses with low spatial frequencies ν < 10^?4 nm^–1 and to the interference of diffuse scattering from different layer interfaces of the surface structure.     

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.     

Inverse scattering with far-field intensity data: random surfaces that belong to a well-defined statistical class

We consider the inverse scattering problem of retrieving the surface profile function from far-field angle-resolved intensity data. The problem is approached as a nonlinear constrained optimization problem. The surface, assumed one-dimensional and perfectly conducting, is also assumed to be a realization of a Gaussian random process with a Gaussian correlation function with known standard deviation of heights (δ) and correlation length (a). Starting from rigorously calculated far-field angle-resolved scattered data, we search for the optimum profile using evolutionary strategies. Examples that illustrate the proposed scheme are presented. Aspects of the convergence and lack of uniqueness of the solution are discussed.