Table of contents

The papers that will appear in the second Topical Issue are listed below. They will be published in January 1998 as Volume 8, Issue 1 of Waves in Random Media, but will be available in the online edition (http://www.iop.org) several weeks earlier.

Methodological papers

Calculations of the Mueller matrix for scattering of light from two-dimensional surfaces

N C Bruce

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

S Mainguy and J-J Greffet

An iterative solution of the rough-surface scattering problem

S T McDaniel

An improved formulation of coherent forward scatter from random rough surfaces

D M Milder

Imaging of random surfaces and inverse scattering in the Kirchoff approximation

C J R Sheppard

Universal behaviour of scattering amplitudes for scattering from a plane in an average rough surface for small grazing angles

V I Tatarskii and M Charnotskii

Curvature effects in the composite model for low-grazing-angle rough-surface scatter

A G Voronovich and V U Zavorotny

Remote sensing papers

Rainfall effect on the microwave thermal emission of sea surface

M G Bulatov, Yu A Kravtsov, V G Pungin and E I Skvortsov

Two-polarization Ku-band radar imagery of sea surface in the presence of atmospheric boundary layer motions

M I Mityagina, V G Pungin and V V Yakovlev

Miscellaneous paper

`1001' correlations in random wave fields

I Freund

The field of rough surface scattering traces its beginnings to the work of Lord Rayleigh, who studied the scattering of a monochromatic plane wave incident onto a sinusoidal surface separating two different media [1]. Seventeen years later, Mandel'shtam [2] provided the first theoretical treatment of the scattering of an electromagnetic wave from a randomly rough surface in the context of the scattering of light from a liquid surface. In both of these works the angular distribution of the intensity of the scattered light was calculated by perturbation theory as an expansion in powers of the surface profile function. Beginning in the 1950s, the field of rough surface scattering began to expand. A perturbative vector theory of the scattering of electromagnetic waves from a two-dimensional, randomly rough, perfectly or finitely conducting surface was formulated by Rice [3], who used the approach introduced by Lord Rayleigh [1]. Subsequently, a simpler theory of the scattering of a scalar wave from a two-dimensional, random, perfectly conducting surface, modelling the ocean surface, was presented by Davies [4], which was then modified by Bennett and Porteus [5] to include the effects of the finite conductivity of optical surfaces. Much of the theoretical work during this period was restricted to single-scattering phenomena, either in its retention of only the leading non-zero contribution to the expansions of the intensities of specular and diffuse scattering in powers of the surface profile function, or in its use of the Kirchhoff approximation. That early work is well described in several by-now standard books dealing with rough surface scattering [6 - 9], and in chapters of other books devoted to the propagation and scattering of electromagnetic waves [10 - 16].

The last 15 years have seen many advances in this field. They include: improvements in analytic and computational approaches to rough surface scattering; the prediction and observation of interesting multiple-scattering phenomena; a developing interest in the study of higher moments of the scattered field than the second; the development of techniques for fabricating one- and two-dimensional random surfaces with specified statistical properties, and for the characterization of surface roughness; and the application of techniques of rough surface scattering theory to near-field optical microscopy. Some of these advances have been described in the proceedings of two workshops, one held in Madrid in September 1988 [17] and the other in Aix-en-Provence in September 1990 [18]. In view of the time that has elapsed since the latter workshop, and the intense activity in the field of rough surface scattering and related problems in the intervening years, it was thought to be desirable to publish a Topical Issue of Waves in Random Media devoted to this field. The response from the community to this project has been so enthusiastic that sufficient papers to fill two issues of this journal have been received. In this, the first such Topical Issue, we have gathered papers dealing with theories of rough surface scattering leading to new physical phenomena, and with correlations of amplitudes and intensities of electromagnetic fields scattered from random surfaces. In the second Topical Issue (to be published as Volume 8, Issue 1, in January 1998) we will present a collection of articles describing methodological advances and remote sensing.

We are grateful to all the authors whose contributions to these two Topical Issues of Waves in Random Media provide a good survey of the current status of the field of rough surface scattering, and in many cases indicate new directions it might take in the future.

Alexei A Maradudin Manuel Nieto-Vesperinas Guest Editors

References

[1] Rayleigh Lord 1896 The Theory of Sound vol II, 2nd edn (London: Macmillan) pp 89, 96

[2] Mandel'shtam L I 1913 Ann. Physik 41 609

[3] Rice S O 1951 Commun. Pure Appl. Math. 4 351

[4] Davies H 1954 Proc. IEE 101 209

[5] Bennett H E and Porteus J O 1961 J. Opt. Soc. Am. 51 123

[6] Beckmann P and Spizzichino A 1963 The Scattering of Electromagnetic Waves from Rough Surfaces (Oxford: Pergamon)

[7] Bass F G and Fuks I M 1979 Wave Scattering from Statistically Rough Surfaces (Oxford: Pergamon)

[8] Ogilvy J A 1991 Theory of Wave Scattering from Random Surfaces (Bristol: Hilger).

[9] Voronovich A G 1994 Wave Scattering from Rough Surfaces (Berlin: Springer)

[10] Feinberg E L 1967 The Propagation of Radio Waves Along the Surface of the Earth (Foreign Tech. Div., Air Force Systems Command, Wright-Patterson Air Force Base, Ohio) ch 8

[11] Ishimaru A 1978 Wave Propagation and Scattering in Random Media vol II (New York: Academic) ch 21

[12] Ulaby F T, Moore R K and Fung A K 1982 Microwave Remote Sensing: Active and Passive Vol II Radar Remote Sensing and Surface Scattering and Emission Theory (Reading, MA: Addison-Wesley) ch 12

[13] Tsang L, Kong J A and Shin R T 1985 Theory of Microwave Remote Sensing (New York: Wiley-Interscience) ch 2.6

[14] Lekner J 1987 Theory of Reflection of Electromagnetic and Particle Waves (Dordrecht: Martinus Nijhoff) ch 11

[15] Kong J A 1990 Electromagnetic Wave Theory (New York: Wiley-Interscience) ch VI

[16] Nieto-Vesperinas M 1991 Scattering and Diffraction in Physical Optics (New York: Wiley-Interscience) ch 7

[17] Nieto-Vesperinas M C and Dainty J C (ed) 1990 Scattering in Volumes and Surfaces (Madrid, September 1988) (Amsterdam: North-Holland)

[18] Ishimaru A (ed) 1991 Modern Analysis of Scattering Phenomena (Aix-en-Provence, September 1990) Conference issue Waves in Random Media 1 (issue 3) S1 - S190

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.

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 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 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.

Using a first-order vector perturbation theory, we calculate some scattering characteristics of surfaces which have both surface roughness and subsurface permittivity variations. These variations are treated as random variables where the roughness yields phase perturbations and the permittivity variations yield reflectance perturbations. Numerical results are given for both types of scattering.

The scattered field in the far-field region for two small metallic particles on a conducting substrate is analysed as a function of both their separation and the angle of incidence. Special attention is paid to multiple scattering, which appears when the particles are very close, as well as to its related effects such as its influence on the enhanced backscattering phenomenon and depolarization of the incident beam in the plane of incidence.

It is shown that the wavelet correlation dimension is a very relevant quantity for the characterization of rough surfaces by remote sensing means. First, the concept of correlation length is generalized to surfaces with wide power spectrum. Second, it is demonstrated that, in the framework of the small-perturbation theory, the wavelet correlation dimension can be retrieved from a knowledge of the backscattered cross section for a discrete set of frequencies. Rigorous numerical experiments confirm these predictions, and in the last section an experimental scheme for a straightforward derivation of the wavelet correlation dimension is proposed.

The scattering of an electromagnetic wave from a two-dimensional, slightly rough dielectric surface is studied based on the stochastic functional approach. It is shown that in the case of TM(p)-polarized incidence there exists a zero in the incoherent scattering at the angle we call the `Brewster scattering angle', which depends on the incident angle in contrast to the Brewster angle of coherent reflection which is independent of the incident angle, that a `quasi-anomalous scattering' can generally occur in the optically denser medium at the critical angle of total reflection in both TE(s)- and TM(p)-polarized incidence, regardless of which side of the random surface is illuminated, and that the Yoneda peak in the x-ray scattering can be interpreted as a special case of the quasi-anomalous scattering which becomes sharper when the relative refractive index becomes closer to unity as in the x-ray region. Cross-polarized scattering and enhanced backscattering due to the second-order effect are also calculated.

Reflection and scattering of waves from plane and statistically rough interfaces between nonlinear media are studied theoretically. New hysteresis-type dependences of the reflection and transmission coefficients on the amplitude of the incident wave and on the angle of incidence are predicted. Scattering diagrams for diffusely reflected and transmitted fields are calculated. It is found that when the dielectric constant is a steep function of the incident amplitude, nonlinearity suppresses the Bragg resonant scattering mechanism. Smooth roughness of the boundary is shown to enhance the penetration of evanescent waves into nonlinear media.

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 , where is the dielectric function of the scattering medium. The magnitude of for x-rays is in the range from to , 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 . 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.

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.

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.

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.

Diagrammatic perturbation theory and computer simulation methods are used to compute the angular intensity correlation function for p-polarized light scattered from a weakly rough, one-dimensional random metal surface. is the squared modulus of the scattering matrix for the system, and and are the projections on the mean scattering surface of the wavevectors of the scattered and incident light, respectively. Contributions to C include: (a) short-range memory effect and time-reversed memory effect terms, ; (b) an additional short-range term of comparable magnitude ; (c) a long-range term ; (d) an infinite-range term ; and (e) a term that along with displays peaks associated with the excitation of surface plasmon polaritons. The diagrammatic methods are also extended to treat the angular intensity correlation function for the scattering of p to p, p to s, s to p, and s to s polarizations of light from a two-dimensional randomly rough surface. These correlations are again described in terms of , and contributions to C for the two-dimensional surfaces. Short-range memory and time-reversed memory effects are observed in the two-dimensional correlations, and peaks associated with the excitation of surface polaritons are observed in the two-dimensional and correlations. Most of the results for the one- and two-dimensional systems are presented for incident electromagnetic plane waves. In addition, results for one-dimensional systems are presented for incident electromagnetic beams of finite width. Some of the results for one-dimensional surfaces are corroborated by means of computer simulation techniques.