A statistical model of wave scattering from random rough surfaces

A rigorous three-dimensional (3-D) electromagnetic model is developed to analyze the scattering from anti-personnel (AP) nonmetallic mine-like target when it is buried near a clutter object under two-dimensional (2-D) random rough surfaces. The steepest descent fast multipole method (SDFMM) is implemented to solve for the unknown electric and magnetic surface currents on the ground surface, on the target and on the clutter object. A comprehensive numerical investigation of two clutter sources; the ground roughness and the nearby benign object, is presented based on using more than 800 random rough surface realizations which could not be achieved without using fast algorithms such as the SDFMM. The statistics of the scattered near-electric fields are computed using the Monte Carlo simulations for both polarizations. For the parameters used here, the results show that the average and the standard deviation of the target signature represent 5-7% and 3-3.5% of the total scattered signal, respectively, while they represent 16-20% and 7-12% of the signal for the clutter object, respectively. This study indicates the high possibility of a false alarm during the detection process when the target is located nearby a realistic object such as a piece of a tree root.

Full-wave solutions for the vertically and horizontally polarized diffuse single- and double-scatter cross sections of random rough surfaces are given in terms of multidimensional integral expressions. The one-dimensional random rough surface is characterized by joint probability-density functions for the surface heights and slopes, and we account for the correlations between the surface heights and slopes. The full-wave solutions are compared with experimental results. The sharp enhanced backscatter is due to the contributions associated with the quasi-antiparallel paths in the expression for the double-scatter cross section. We conduct a comprehensive parametric study to determine the dependence of the level and the angular width of the sharp enhanced backscatter on the rough-surface characteristics. The results for the diffuse double-scatter cross sections exhibit a distinct dependence on polarization. Full-wave, high-frequency approximations that are practically independent of polarization provide useful physical insights into the problem.

While recent studies have proven an unexpected liquid–vapor phase transition of adsorbed liquid films, a comprehensive description of the mechanisms of different types of phase change regimes over realistic representations of random rough surfaces is absent in the literature. The current comprehensive study investigates the effects of a gold random rough surface, liquid film thickness, and substrate temperature on the liquid–vapor phase change regime of an adsorbed sodium liquid film, considering the evaporator section of a wicked heat pipe (WHP) using a molecular dynamics (MD) simulation. At first, to generate a realistic random rough surface, a new and promising method is proposed that is entirely based on MD simulations. Then, to simulate the evaporator section of a WHP, a unique configuration for eliminating the vapor domain is developed. The simulation results reveal that three distinct regimes, namely, normal evaporation, cluster boiling, and film boiling, could be identified, which are presented on two-dimensional diagrams with the substrate temperature and liquid film thickness as coordinates for the ideally smooth and random rough surfaces. The results also manifest that even though using the random rough surface could lead to different phase transition regimes, the type of regime depends mainly on the substrate temperature and liquid film thickness. Furthermore, this study displays two different modes for normal evaporation. Also, it is shown that the impacts of the liquid film thickness and substrate temperature on the mode of normal evaporation are much more significant than the surface roughness.

The physical optics approach and Lorentz transformations are combined to formulate scatter from a random rough surface in uniform motion. The perfectly conducting scatterer is excited by an elliptically polarized plane electromagnetic wave and the analysis ends in the velocity‐dependent expressions for the scattering cross section per unit area, the depolarization factor and the radial tilt. The direction of motion is considered parallel as well as normal to the scatterer's mean plane. The combined effect of roughness and motion on scattering and depolarization is investigated through a numerical example. The calculations reveal that parallel motion modifies scatter through aberration while normal motion results in scatter amplification. The depolarization factor and/or radial tilt might be used for motion estimation.

Effects of random road surface roughness and long-term deflection of prestressed concrete girder and cable-stayed bridges on impact due to moving vehicles

Backscattering enhancement of electromagnetic wave scattering from a perfectly conducting two-dimensional random rough surface (three-dimensional scattering problem) is studied with Monte Carlo simulations. The magnetic-field integral equation formulation is used with the method of moments. The solution of the matrix equation is calculated exactly with an efficient method known as the sparse-matrix flat-surface iterative approach. Numerical examples are illustrated with 32,768 surface unknowns, surface areas between 256 and 1024 square wavelengths, rms heights of 0.5 and 1 wavelength, and as many as 1000 realizations. The bistatic scattering simulations show backscattering enhancement for both copolarized and cross-polarized components. Comparisons are made with controlled laboratory experimental data for which the random rough surfaces are fabricated with prescribed properties of a rms height of 1 wavelength and a correlation length equal to 2 wavelengths. Comparisons are made between simulations and experimental data for the absolute value of the bistatic scattering coefficient. The copolarized scattering coefficient is in good agreement, and the cross-polarized scattering coefficient is in excellent agreement.

In this paper, the model developed for predicting the scattering characteristics from statistically rough surfaces is based upon the integral-equation model with multiple scattering. Its objective is to examine the bistatic scattering characteristics from randomly rough surfaces along different azimuth angles. For a better understanding of the scattering behavior from randomly rough surfaces, information about scattering must be known omnidirectionally, not just in the specular or backscatter direction. Comparisons between the model prediction and the experimental measurements are made for both like and cross polarizations. This model prediction demonstrates good agreement with the experimental data. © 2000 John Wiley & Sons, Inc. Microwave Opt Technol Lett 25: 271–275, 2000.

Presents results for full three-dimensional simulations of numerical solutions of Maxwell equations for random rough surfaces. Emissivities and back-scattering coefficients are calculated for soil surfaces and ocean surfaces at microwave frequencies. This is unlike analytical methods or empirical models in that different roughness parameters are used for different microwave frequencies and for active and passive remote sensing. With advances in computational electromagnetics and available computer resources, we calculate 3-dimensional Maxwell equation solutions with a 2-D rough surface for practical remote sensing applications. Highlights of our numerical approach are: (i) the sparse-matrix canonical grid method (SMCG) and the physics-based two-grid method (PBTG) are used. (ii) An algorithm has been implemented for parallel computing. Dense discretization of the surfaces is used because of high permittivity and the energy conservation check is verified. We present results for soil surfaces in L- and C-bands, and for ocean surfaces at 19 GHz.

We study the electromagnetic scattering problem on a random rough surface when the height distribution of the profile belongs to the family of alpha-stable laws. This allows us to model peaks of very large amplitude that are not accounted for by the classical Gaussian scheme. For such probability distributions with infinite variance the usual roughness parameters such as the RMS height, the correlation length or the correlation function are irrelevant. We show, however, that these notions can be extended to the alpha-stable case and introduce a set of adapted roughness parameters that coincide with the classical quantities in the Gaussian case. Then we study the scattering problem on a stationary alpha-stable surface and compute the scattering coefficient under the first-order Kirchhoff and small-slope approximations. An analytical formula is given in the high-frequency limit, which generalizes the well known geometrical optics approximation. Some numerical results are given and discussed.

This paper is concerned with a numerical procedure to estimate two parameters, amplitude modification factor α and propagation order of distance β, for electromagnetic (EM) propagation in complicated natural environments such as random rough surface (RRS). These two parameters are key parameters when we simulate field distributions along various types of RRS based on 1-ray model. We assume that the former parameter α can be evaluated by the visual planar angles of illuminated lines in case of 1D RRS and by the visual solid angles of illuminated planes in case of 2D RRS. We also assume that the latter parameter β can be estimated not only by base station (BS) antenna height, similar to Okumura-Hata model simulating EM propagation in urban and suburban areas, but also by mobile station (MS) antenna height. In order to demonstrate validity of the proposed parameter estimation, we compare the numerical field distributions obtained by the 1-ray model using estimated two parameters with those computed by discrete ray tracing method (DRTM) which is an effective EM field solver. It is shown that both numerical results are in good agreement.

This article describes the development of a suite of programs that is capable of simulating the radiation properties of a random rough surface (RRS). The fundamental approach involves the generation, by fast Fourier transform (FFT) built with rigorous finite difference time domain (FDTD), as the theoretical basis for the simulation of a bidirectional reflectance distribution function (BRDF) of the RRS. The results are compared with the measurements and modeling of existing work to verify the feasibility of customized programming. It was found that the results of this study were a better match to the measurement data than those achieved in other modeling work.

When a random rough surface is illuminated by light or high-frequency radio waves, the specular reflected points make an ensemble, the statistical properties of which are of great interest not only for a general theory of scattering, but also for many practical applications, ranging from real-time monitoring of man-made surface roughness to sea roughness parameter measurements using sunlight flares at the surface. Apparently, M.S. Longuet-Higgins (see J. Opt. Soc. Am., vol.50, p.838-56, 1960) was the first to employ the theory of random functions for solving this problem. In particular, the explicit equations for the spatial density of extrema and saddle points were derived for Gaussian surfaces, and the fundamental relations between them were established. We use the general theory of random field excursions (Adler, R.J., 1981; Stoyan, D. et al., 1995) to obtain the statistical characteristics of specular points arising on random surfaces at normal incidence.

Estimates are obtained for the pressure field reflected from random rough surfaces when the surfaces are insonified by a high‐frequency, omnidirectional point source. A geometric acoustics or ray‐tracing approach is taken together with the assumptions that there is no shadowing of the surface and that each ray undergoes a single reflection. A stationary phase approximation of the Helmholtz integral is used to estimate the field associated with each ray. The emphasis of the paper is on accounting for the phase differences, that is, the interference effects, between the possibly very many geometric rays from source to surface to receiver.Subject Classification: 20.30.

Simulation of 3-D random rough surface by 2-D digital filter and fourier analysis

To study wave scattering from random lossy dielectric rough surfaces with large permittivities using the method of moments, a dense grid is needed for accurate results. A dense grid requires more CPU and memory. The physics‐based two‐grid (PBTG) method can reduce both CPU and memory requirements. In this paper, the PBTG is used in conjunction with the multilevel fast multipole method (FMM) to solve wave scattering from one‐dimensional random lossy dielectric rough surfaces. The proposed algorithm has the computational complexities of O(Ndg) for near‐field interactions and O(Ncg) for nonnear‐field interactions, where Ndg and Ncg are the number of sampling points on the dense and coarse grids, respectively. Using the proposed algorithm, wave scattering from Gaussian and non‐Gaussian rough surfaces is investigated and illustrated. Special emphasis is put on checking the accuracy of the algorithm and energy conservation.