Phillip Phu

A Banded Matrix Iterative Approach to Monte Carlo Simulations Of Large-Scale Random Rough Surface Scattering: TE Case

A banded matrix iterative approach is applied to study scattering of a TE incident wave from a perfectly conducting one-dimensional random rough surface. It is much faster than the full matrix inversion approach or the conjugate gradient method. When compared to the Kirchhoff iterative approach, it is of comparable CPU time, and works for cases when the Kirchhoff iteration is erroneous. The method is illustrated for a variety of parameters with particular application to large scale rough surface problems. The largest surface length used is 400 wavelengths with 3200 unknowns, and all the coherent wave interactions are included within the entire surface length. The accuracy of the banded iterative approach is demonstrated by showing that the results overlie those of the exact matrix inversion and the conjugate gradient method. The numerical method is also easy to implement. With this approach, we are able to compute the new response characteristics of composite rough surfaces with much larger scales. The ca...

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 ...

Monte Carlo simulations of large-scale composite random rough-surface scattering based on the banded-matrix iterative approach

Scattering of a TE incident wave from a perfectly conducting one-dimensional composite random rough surface is studied. A composite random surface contains roughness of more than one scale. With the recently developed efficient numerical technique known as the banded-matrix iterative approach, we are able to study large-scale composite roughness with two correlation lengths that are many times different from each other. It is shown that small-scale roughness, with its large rms slope, rather than large-scale roughness, with its small rms slope, can dominate bistatic scattering. It is also shown that backscattering enhancement can also exist in a composite rough surface.

Controlled millimeter‐wave experiments and numerical simulations on the enhanced backscattering from one‐dimensional very rough surfaces

We present experimental results on the scattering of electromagnetic waves at millimeter-wave frequencies from one-dimensional very rough conducting surfaces with controlled surface roughness statistics. Very rough surfaces are defined as surfaces with rms height and correlation length of the order of a wavelength such that the rms slope is at least unity. It is expected that scattering experiments using these surfaces can provide useful insights since their statistics lie outside the range of validity of the present theories, namely, the Kirchhoff and perturbation theories. Strong backscattering enhancement at different incident angles, both in the transverse electric and transverse magnetic polarizations, are observed experimentally. Numerical calculations based on the exact integral equation method for cylindrical beam wave illumination compare favorably with the experimental results. The agreement between measurements and numerical calculations is good over a wide range of incident angles and for all scattering angles. The close agreement between the experimental results and numerical simulations indicates that this controlled experimental setup can be used to study scattering phenomena from one-dimensional very rough surfaces with different roughness statistics as well as from two-dimensional rough surfaces.

Copolarized and cross‐polarized enhanced backscattering from two‐dimensional very rough surfaces at millimeter wave frequencies

Wideband millimeter wave experiments from 75–100 GHz on the scattering from two-dimensional very rough conducting surfaces are presented. The two-dimensional very rough surfaces are manufactured using a computer-numerical-controlled milling machine so that the surface statistics are precisely controlled. The surfaces have both Gaussian roughness statistics and Gaussian surface correlation functions. Bistatic scattering experiments on surfaces with either isotropic or anisotropic correlation functions are performed. Copolarized and cross-polarized bistatic scattering cross sections are measured for both transverse electric and transverse magnetic incidence at 20°. For isotropic surfaces, backscattering enhancement exists for both copolarized and cross-polarized returns and is found to be a function of the surface rms slope. In addition, a strong frequency dependence is observed across the 25-GHz bandwidth in the cross-polarized returns. To investigate the effect of surface correlation anisotropy, scattering experiments on anisotropic rough surfaces are also performed. It is found that the bistatic scattering cross section for an anisotropic surface is a function of the effective correlation length projected along the plane of scattering. Results on the bistatic scattering experiments presented here serve as a motivation to further pursue more elaborate and complete scattering experiments in order to advance research on scattering from very rough surfaces.

Transmission, reflection, and depolarization of an optical wave for a single leaf

Optical scattering by a single leaf is investigated, taking into account the structures inside a leaf and the leaf surface roughness. An optical scattering model, which includes both volume scattering and rough surface scattering, is developed using vector radiative transfer theory and Kirchhoff rough surface scattering theory. A leaf is modeled as a slab of water with an irregular surface containing randomly distributed spherical particles. The degree of polarization and the normalized scattering cross section per unit area for the transmitted and reflected copolarized and cross-polarized intensities are obtained for corn, potato, and laurel leaves. The theoretical results are compared with measured data to determine the parameters for the scatterers inside the leaf, the surface roughness, and the optical thickness. The agreement between the calculation and experiment for a wide variety of cases shows that this is a reasonable leaf model in the optical frequency regime.

Pulse broadening and two-frequency mutual coherence function of the scattered wave from rough surfaces

Abstract Analytical expressions for the two-frequency mutual coherence function and angular correlation function of the scattered wave from rough surfaces based on the Kirchhoff approximation are presented. The coherence bandwidth depends on the illumination area as well as on the incident and scattered angles and the surface characteristics. Scattered pulse shapes are calculated as the Fourier transform of the two-frequency mutual coherence function. Calculations based on analytical solutions are compared with millimetre wave experimental data and Monte Carlo simulations showing good agreement.

Monte Carlo simulations and backscattering enhancement of random metallic rough surfaces at optical frequencies

The finite element method of Monte Carlo simulations of random rough surface scattering is extended to plane and tapered wave scattering from random metallic surfaces at optical frequencies. The backscattering enhancement associated with these rough surfaces is studied for both TE and TM incident waves. Numerical results of the finite element method are presented and compared with those of the tapered wave integral equation method. In all the cases considered, both the TE and TM incident waves show backscattering enhancement. The lossy surfaces scatter more power for TE incident waves than those of TM due to the TM surface waves. No TE surface wave is supported by rough surfaces simulated in this paper.

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...

Millimetre-wave scattering from one-dimensional surfaces of different surface correlation functions

High spectral components contained in surfaces with non-Gaussian correlation functions are believed to increase the magnitude of backscattering enhancement. In this paper, we present experimental and numerical studies of bistatic scattering from one-dimensional surfaces with Gaussian and power-law roughness spectral densities. Rough surfaces with an rms height of σ = 3 mm and correlation lengths of l = 3, 6 and 9 mm were fabricated and measured with a millimetre-wave scatterometer. The corresponding rms slopes were m = 1.41, 0.707 and 0.47, respectively. Both experimental and numerical simulation data show that surfaces obeying the power-law roughness spectral density have stronger backscattering enhancement than those with a Gaussian roughness spectral density for the same surface rms slope. Good agreement between experiments and numerical simulations was obtained. In addition, the numerical studies were conducted to obtain the scattering characteristics of surfaces with Gaussian and power-law roughness ...