Table of contents

In conventional approaches to the homogenization of random particulate composites, both the distribution and size of the component phase particles are often inadequately taken into account. Commonly, the spatial distributions are characterized by volume fraction alone, while the electromagnetic response of each component particle is represented as a vanishingly small depolarization volume. The strong-permittivity-fluctuation theory (SPFT) provides an alternative approach to homogenization wherein a comprehensive description of distributional statistics of the component phases is accommodated. The bilocally-approximated SPFT is presented here for the anisotropic homogenized composite which arises from component phases comprising ellipsoidal particles. The distribution of the component phases is characterized by a two-point correlation function and its associated correlation length. Each component phase particle is represented as an ellipsoidal depolarization region of nonzero volume. The effects of depolarization volume and correlation length are investigated through considering representative numerical examples. It is demonstrated that both the spatial extent of the component phase particles and their spatial distributions are important factors in estimating coherent scattering losses of the macroscopic field.

This paper presents a theory of the radar cross section (RCS) of objects in multiple scattering random media. The general formulation includes the fourth-order moments including the correlation between the forward and the backward waves. The fourth moments are reduced to the second-order moments by using the circular complex Gaussian assumption. The stochastic Green's functions are expressed in parabolic approximation, and the objects are assumed to be large in terms of wavelength; therefore, Kirchhoff approximations are applicable. This theory includes the backscattering enhancement and the shower curtain effects, which are not normally considered in conventional theory. Numerical examples of a conducting object in a random medium characterized by the Gaussian and Henyey–Greenstein phase functions are shown to highlight the difference between the multiple scattering RCS and the conventional RCS in terms of optical depth, medium location and angular dependence. It shows the enhanced backscattering due to multiple scattering and the increased RCS if a random medium is closer to the transmitter.

In this paper, we study the effects of turbulent atmosphere on the degree of polarization of a partially coherent electromagnetic beam, which propagates through it. The beam is described by a 2 × 2 cross-spectral density matrix and is assumed to be generated by a planar, secondary, electromagnetic Gaussian Schell-model source. The analysis is based on a recently formulated unified theory of coherence and polarization and on the extended Huygens–Fresnel principle. We study the behaviour of the degree of polarization in the intermediate zone, i.e. in the region of space where coherence properties of the beam and the atmospheric turbulence are competing. We illustrate the analysis by numerical examples.

Two new approximations for predicting the elastic scattering of plane acoustic waves by a weak scatterer are proposed. The approximations have been obtained by drawing an analogy between acoustic and light scattering problems. The validity of these approximations has been examined numerically for the exactly soluble case of scattering by a homogeneous sphere. Results show that for small angle scattering the proposed approximations have a considerably larger domain of validity in comparison to the extensively used Born approximation.

Precise measurements of the travel times of backscattered waves, and especially the travel times of the first (i.e., earliest) arrivals, underlie a number of geophysical remote sensing techniques. In this paper, statistical properties of the travel time and intensity of pulses backscattered by a two-dimensional rough surface are investigated within the geometric optics approximation by adopting a method originally developed in the theory of excursions of a stochastic process. We assume a wave source located sufficiently far from a rough surface with Gaussian statistics, and show that the probability distribution functions of the normalized deviation of the travel time of the first and second backscattered pulses from the travel time in the absence of roughness, are functions of a single dimensionless parameter, T = γ²₀H/(2πσ), where σ² and γ²₀ are the variances of the rough surface elevation and slope, and H is the source altitude. Signals from the rough surface return to the source location earlier than from the mean plane by O(2σ/c), where c is the velocity of wave propagation. On average, the travel times of the first and second arrivals decrease as parameter T increases, with the travel time shift being proportional to . The time delay between the first and the second arrivals is inversely proportional to . The joint probability density functions (PDF) of the travel times and the intensities of the first two backscattered pulses are derived. This allows us to obtain the travel time PDF for signals exceeding the given intensity threshold. It is shown that the travel time and the intensity are strongly correlated: on average, earlier arrivals have smaller amplitudes.

There are several nonlocal scattering models available in the literature. Most of them are given with little or no mention of their expected accuracy. Moreover, high- and low-frequency limits are rarely tested. The most important limits are the low-frequency or the small perturbation method (SPM) and the high-frequency Kirchhoff approximation (KA) or the geometric optics (GO). We are interested in providing some insight into two families of non-local scattering models. The first family of models is based on the Meecham–Lysanov ansatz (MLA). This ansatz includes the non-local small slope approximation (NLSSA) by Voronovich and the operator expansion method by Milder (OEM). A quick review of this first family of models is given along with a novel derivation of a series of kernels which extend the existing models to include some more fundamental properties and limits. The second family is derived from formal iterations of geometric optics which we call the ray tracing ansatz (RTA). For this family we consider two possible kernels. The first is obtained from iteration of the high-frequency Kirchhoff approximation, while the second is an iteration of the weighted curvature approximation (WCA). In the latter case we find that most of the required limits and fundamental conditions are fulfilled, including tilt invariance and reciprocity. A study of scattering from Dirichlet sinusoidal gratings is then provided to further illustrate the performance of the models considered.

The PDF file provided contains web links to all articles in this volume.

This review is intended to provide a critical and up-to-date survey of the analytical approximate methods that are encountered in scattering from random rough surfaces. The underlying principles of the different methods are evidenced and the functional form of the corresponding scattering amplitude or cross-section is given. The reader is referred to the original papers in order to obtain the explicit expressions of the coefficients and kernels. We have tried to identify the main strengths and weaknesses of the various theories. We provide synthetic tables of their respective performances, according to a dozen important requirements a valuable method should meet. Both scalar acoustic and vector electromagnetic theories are equally addressed.