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.     

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.     

A numerical evaluation of Rayleigh's theory applied to scattering by randomly rough dielectric surfaces

Abstract

We present a numerical simulation of scattering by one-dimensional randomly rough surfaces. It is based on the use of plane-wave expansions to describe the Melds on the surface (i.e. Rayleigh hypothesis). Accuracy and convergence properties of two different numerical implementations are studied. Some examples of results for a dielectric and a metallic Gaussian rough surface are shown to be in good agreement with calculations by a rigorous numerical method. The Rayleigh method appears to be a fast computation tool for dielectric surfaces with slopes of less than 0.2.     

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.     

The SSA+ for scattering from dielectric surfaces at very low grazing angles

Previously we developed a practical model for scattering from randomly-rough surfaces at very low grazing angles for the Dirichlet problem which was found to give good numerical results. In this paper, we derive the expression for the bistatic scattering cross-section for the non-local small slope approximation for dielectric interfaces. We then extend our practical model to dielectric surfaces based on this result. We discuss numerical results for scattering at low forward grazing angles for a Gaussian roughness spectrum with an angle of incidence of 80^○.     

A rapid boundary perturbation algorithm for scattering by families of rough surfaces

In this paper we describe a novel algorithm for the computation of scattering returns by families of rough surfaces. This algorithm makes explicit use of the fact that some scattering profiles of engineering interest (e.g., traveling ocean waves) come in branches parameterized analytically by a bifurcation quantity. Our approach delivers recursions which not only can be implemented to yield a rapid, robust and high-order numerical scheme, but also give a new proof of analyticity of scattering quantities with respect to the bifurcation parameter of the surface family. The real advantage of this new approach is that it computes, in one step, the scattered field for all possible members of the family of surfaces. By contrast, other state-of-the-art schemes must restart when the returns from a new surface are desired, so that the cost of our new approach is greatly advantaged when the number of samples of the family reaches even modest values. Numerical results which verify the accuracy of our approach and demonstrate their utility in computing grating efficiencies scattered by traveling surface ocean waves are presented.     

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.     

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.     

Wave diffraction by rough interfaces in an arbitrary plane-layered medium

Abstract

The problem of electromagnetic wave scattering by a slightly rough interface in an arbitrarily layered medium is solved by a small-perturbation method. The bistatic amplitude of scattering as well as the scattering cross sections for statistically rough surfaces are calculated for linear polarized waves. Along with scattering into up-going waves in a homogeneous medium and scattering cross sections in down-going waves into a layered medium, scattering amplitudes from a rough interface in the arbitrarily layered medium are obtained.     

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.     

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.     

Radar scatter cross sections for two-dimensional random rough surfaces – full wave solutions and comparisons with experiments

Abstract

In this paper, the full wave expressions for the radar scattering cross sections for two-dimensional random rough surfaces are obtained. The rough-surface height/slope correlations are accounted for in this analysis. Analytical and numerical comparisons of the full wave solution with the small perturbation and physical optics solutions are made for isotropic, homogeneous random rough surfaces with Gaussian probability density function. The full wave results are also compared with experimental results.     

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.     

On the high-frequency limit of the second-order small-slope approximation

Abstract

Small-slope approximation (SSA) is a scattering theory that is supposed to unify both the small-perturbation model and the Kirchhoff approximation (KA). We study and compute the second-order small-slope approximation (SSA2) in a high-frequency approximation (SSA2-hf) that makes it proportional to the first-order term, with a roughness-independent factor. For the 3D electromagnetic problem we show analytically that SSA2-hf actually meets KA in the case of perfectly conducting surfaces. This no longer holds in the dielectric case but we give numerical evidence that the two methods remain extremely close to each other for moderate scattering angles. We discuss the potential applications of SSA2-hf and give some 2D numerical comparison with rigorous computations.     

An improved operator expansion algorithm for direct and inverse scattering computations

Abstract

In the first part of the paper we present an implementation of Milder's operator expansion formalism for acoustic scattering from a rough non-periodic surface. Our main contribution to the forward-field calculation is the development of two accurate ways of computing the order-zero normal differentiation operator N ₀. The accuracy of our implementation is tested numerically. In the second part of our paper we apply this approach, combined with a continuation method, to an inverse scattering problem. The resulting scheme performs significantly better than the classical first-order methods.     

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.     

Pulse broadening of enhanced backscattering from rough surfaces

Abstract

Recently, we presented a study of pulse scattering by rough surfaces based on the first-order Kirchhoff approximation which is applicable to rough surfaces with RMS slope less than 0.5 and correlation distance l?λ. However, there has been an increased interest in enhanced backscattering from rough surfaces, study of which requires inclusion of the second-order Kirchhoff approximation with shadowing corrections. This paper presents a theory for the two-frequency mutual coherence function in this region and shows that the multiple scattering on the surface gives rise to an additional pulse tail in the direction of enhanced backscattering. The theory predicts pulse broadening approximately 20% greater than that caused by single scattering alone for a delta-function incident pulse and typical surface parameters. Analytical results are compared with Monte Carlo simulations and millimetre-wave experiments for the one-dimensional rough surface with RMS height 1λ and correlation distance 1λ, showing good agreement.     

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.