One-dimensional Random Rough Surfaces Research Articles

Electromagnetic scattering characteristics of a hypersonic vehicle with a microrough surface in the millimeter wave band

The rough structure may affect the flow field and electromagnetic (EM) scattering characteristics of a hypersonic vehicle. In this study, the EM scattering characteristics of the hypersonic vehicle RAM C-II with a microrough surface were investigated in the millimeter wave band. We first simulated the flow field of a smooth RAM C-II vehicle and calculated the radar cross section (RCS) in the wideband using the physical optics method. The calculation results show that many factors contribute to the variation in the RCS; however, it is occasionally difficult to predict. We then used a one-dimensional Gaussian random rough surface to generate a RAM C-II with a microrough surface through a point-coordinate transformation and simulated its flow field. The electron density flow field of the rough surfaced aircraft fluctuates greatly on the wall. Finally, we calculated the RCS of RAM C-II with different values of roughness in the millimeter wave band. The change of surface structure can be reflected in millimeter waves, and the RCS is determined by both plasma and rough structure.

Dynamics study of integrable turbulence with fourth-order nonlinear Schrödinger equation.

In this paper, we focus on the fourth-order nonlinear Schrödinger equation, which can describe the optical system and the Heisenberg spin system. We consider a continuous wave perturbed by the one-dimensional random rough surface as the initial condition. First, we numerically resolve the eigenvalues under different control parameters utilizing the Fourier collocation method. Then, we simulate the evolution of this equation under the above initial conditions via the symmetrical split-step Fourier method. Moreover, we investigate the "steady" chaotic state by evolving a large number of initial conditions for the same control parameters. We find that the control parameters of the initial condition affect the number and intensity of rogue waves (RWs) in integrable turbulence. In particular, we locate the inflection point where the control parameter affects the velocities of solitons and the inconsistency within the parameter of the contribution to the generation of RWs. We further verify that the collision between breathers, solitons, and breathers and solitons can generate RWs. These results will enable us to understand the turbulent state and the formation mechanism of RWs.

Accuracy improvement of the radar backscatter simulation from sea surface covered by oil slick using fetch-dependent waveheight spectrum: Comparison with the 2007 Heibei Spirit Case in the Yellow Sea

In this paper, results are presented on the comparison of X-band radar backscattering coefficient (RBC) from an oilcovered sea surface that features the Elfouhaily and Durden-Vesecky waveheight spectra. The Durden-Vesecky spectrum applies to a fully-developed sea, while the Elfouhaily spectrum accounts for the fetch of arbitrary length. Using these two waveheight spectra, a one-dimensional random rough surface is simulated by the Monte Carlo method, and the method of moments (MoM) is applied to yield the RBC. Comparison of the results with TerraSAR-X synthetic aperture radar (SAR) data acquired over the coastal waters polluted by the Hebei Spirit oil tanker shows that the Elfouhaily spectrum yields better agreement than the Durden-Vesecky spectrum for the fully-developed sea, and that the fetch-dependent Elfouhaily spectrum improves the agreement with SAR data in comparison with the fetch-independent spectrum for the fully developed sea. A possible application to estimate the amount of spilled oil is also suggested.

Implementation of coordinate transformations in periodic finite-element method for modeling rough surface scattering problems

The coordinate transformation technique (with its current name of transformation electromagnetics) is applied to the finite-element method (FEM) with periodic boundary conditions for efficient Monte Carlo simulation of one-dimensional random rough surface scattering problems. In a unit cell of periodic structure, two coordinate transformations are used, one of which is a real transformation designed to model the rough surface with flat surface, and the other is a complex transformation used to design a perfectly matched layer for mesh truncation. The approach is easily implementable because only the nodal coordinates are replaced by the transformed coordinates in a standard FEM. Since a simple and single mesh with flat surface is used, Monte Carlo simulations are performed in an efficient manner. Numerical results are presented for various rms surface heights, correlation lengths, and angles of incidence. © 2016 Wiley Periodicals, Inc. Int J RF and Microwave CAE 26:322–329, 2016.

Modeling Bidirectional Reflectance Distribution Function of One-dimensional Random Rough Surfaces with the Finite Difference Time Domain Method

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.

Scattering of electromagnetic waves from random rough metallic surfaces with one-dimensional structure calculated by the surface impedance boundary condition method (SIBC)

A comparison between exact solutions and surface impedance boundary condition method, for the phenomenon of light scattering from one-dimensional random rough metallic surfaces in both cases of polarization (s- and p-) is presented. The reflective properties of random rough metallic surfaces at a large angle of incidence have been reported on due to their potential applications in some of the radiative heat transfer research areas. The influence of surface roughness, shadowing effects, the nature of polarization, and the nature of the material on the behavior of reflectivity and emissivity has been quantified.

Modeling Bidirectional Reflectance Distribution Function of One-dimensional Random Rough Surfaces with the Finite Difference Time Domain Method

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.

Geometric Optics Approximation with Considering Interference for Reflection from Random Rough Surface

The geometrical optics ray-tracing approach is an effective and simple method of studying the radiative properties of rough surfaces. The conventional geometrical optics ray-tracing method does not consider the interference effect, and therefore limits its application. In this paper, the conventional geometrical optics ray-tracing method is updated by considering the effect of the interference. Two geometrical optics ray-tracing methods and a finite different time domain method are used to study the radiative properties of a one-dimensional random rough surface. By comparing the results of the different methods, the effect of interference is quantified and discussed under various conditions. The interference effect cannot be neglected for the case of strong roughness and oblique incidence. Compared with the conventional geometrical optics ray-tracing method, the improved geometrical optics ray-tracing method has a higher precision and wider application. The interaction between the surface roughness and multiple scattering is also discussed.

Decoherence effect of target roughness in synthetic aperture ladar

Optical heterodyne detection is one of the key techniques for developing synthetic aperture ladar. The decoherence effect caused by the roughness of the target surface is particularly important for the practical use of the synthetic aperture ladar. The effect of the target surface roughness on the echo signal detection is discussed in the paper. One-dimensional and two-dimensional Gaussian random rough surface model are created by the use of the Monte Carlo method. The detection process of the target echo signal is simulated to study the effect of the target surface roughness on the intermediate frequency signal. And two optical heterodyne detection experiments are conducted in which the targets each include a rough surface and a smooth surface to verify the serious decoherence effect of the target roughness on the synthetic aperture laser radar echo signal. Meanwhile, the wavefronts of both the local oscillator and the signal beam are monitored at the position of the detector with a digital wavefront analyzer. The measured phase distribution accords well with the simulation result. It is shown that the phase of the echo signal from a rough surface has a serious distortion. The results obtained could be useful for designing the parameters of the laser source and the receiver, as well as for estimating the detection range of the ladar system.

Analysis of one-dimensional rough surface scattering based on bidirectional reflectance distribution function model

Through in-depth analysis of the scattering properties of a one-dimensional random rough surface, a method to calculate the spatial bidirectional reflectance distribution function (BRDF) characteristics of a randomly rough surface is proposed. The scattering characteristics of an electrically large rough surface can be substituted by combination of subsection electromagnetic fields. The radar cross-section (RCS), which is transformed from the BRDF, is compared with numerical results from the Method of Moment (MoM). The agreement of the results verifies that this method could calculate the electromagnetic scattering field efficiently and straightforwardly. Moreover, the resulting combined fields from the BRDF of subsections in the rough surface show a good match with the entire scattering field of a whole surface, which indicates that a large electrically rough surface could be feasibly and effectively substituted with the combination of scattering elements using the BRDF method and the statistical method.

Intensity Correlation Function of Light Scattering from a Weakly One-Dimensional Random Rough Surface

Based on the Kirchhoff approximation and Gaussian moment theorem, we present a general expression of the intensity correlation scattered from a weakly one-dimensional rough surface, which is applicable to the cases by either two different wavelengths or two different angles of incidence. By using a Gaussian surface model, we give the numerical results for the intensity correlation function with two different wavelengths specially. The results show that with the increasing surface roughness and the decreasing surface correlation length, the correlation function decreases in specular direction and increases in other directions, which indicates that the study of the correlation of the intensities is helpful when investigating the statistical parameters of rough objects. Also the results show that the increase of rms roughness can result in the narrower correlation bandwidth.

有耗介质高斯随机粗糙面对光波散射的矩量法和基尔霍夫近似的统一

The optical wave scattering from one-dimensional (1D) lossy dielectric Gaussian random rough surface is studied. The tapered incident wave is introduced into the classical Kirchhoff approximation (KA), and the shadowing effect is also taken into account to make the KA results have a high accuracy. The definition of the bistatic scattering coefficient of the modified KA and the method of moment (MOM) are unified. The characteristics of the optical wave scattering from the lossy dielectric Gaussian random rough surface of different parameters are analyzed by implementing MOM.

The curvilinear coordinate method associated with the short-coupling-range approximation for the study of scattering from one-dimensional random rough surfaces

This paper deals with the scattering of an incident plane wave from a mono-dimensional rough surface. The analysis of the scattering phenomenon is performed using the curvilinear coordinate method (C method) associated with the short-coupling-range approximation (SCRA) and the Huygens principle. The C method is based on the solving of Maxwell’s equations under their covariant form written in a nonorthogonal coordinate system which fits the scattering surface profile. This leads to eigenvalue problems. The scattered surface fields are expressed as linear combinations of eigensolutions and the combination coefficients are determined using the boundary conditions. Electromagnetic fields are obtained using the surface fields and the Huygens principle. The short-coupling-range approximation (SCRA) applied with the C method allows a significant saving in computation time. We confirm the efficiency and the validity of this new approach with respect to the C method.

Effect of the illumination length on the statistical distribution of the field scattered from one-dimensional random rough surfaces: analytical formulae derived from the small perturbation method

We consider a dielectric plane surface with a local cylindrical perturbation illuminated by a monochromatic plane wave. The perturbation is represented by a random function assuming values with a Gaussian probability density with zero mean value. Outside the perturbation zone, the scattered field can be represented by a superposition of a continuous spectrum of outgoing plane waves. The stationary phase method leads to the asymptotic field, the angular dependence of which is given by the scattering amplitudes of the propagating plane waves. The small perturbation method applied to the Rayleigh integral and the boundary conditions gives a first-order approximation of the scattering amplitudes. We show that the real part and the imaginary part of the scattering amplitudes are Gaussian stochastic variables with zero mean values and unequal variances. The values of variances depend on the length of the perturbation zone. In most cases, the probability density function for the amplitude is a Hoyt distribution and the phase is not uniformly distributed between –π and π. The standard Rayleigh and uniform distributions are obtained for special values of the length and in the case of an infinite illumination length.

Energy conservation of the scattering from one-dimensional random rough surfaces in the high-frequency limit

Energy conservation of the scattering from one-dimensional strongly rough dielectric surfaces is investigated using the Kirchhoff approximation with single reflection and by taking the shadowing phenomenon into account, both in reflection and transmission. In addition, because no shadowing function in transmission exists in the literature, this function is presented here in detail. The model is reduced to the high-frequency limit (or geometric optics). The energy conservation criterion is investigated versus the incidence angle, the permittivity of the lower medium, and the surface rms slope.

Complete determination of the conical Mueller matrix for one-dimensional rough metallic surfaces

We present results of the complete determination of the Mueller matrix for the light scattered by a one-dimensional random rough metallic surface under a conical or out-the-plane of incidence geometry. We present and apply a reduced method for its complete determination. This reduced method considers only 16 intensity-polarized measurements instead of the 36 intensity-polarized measurements recently reported. Effects related with the enhanced backscattering were observed.

Scattering of a plane wave by one-dimensional dielectric random rough surfaces—study with the curvilinear coordinate method

We present a method giving the bi-static scattering coefficient of a one-dimensional dielectric random rough surface illuminated by a plane wave. The theory is based on Maxwell's equations written in a nonorthogonal coordinate system. For each medium, this method leads to an eigenvalue system. The scattered field is expanded as a linear combination of eigensolutions satisfying the outgoing wave condition. The boundary conditions allow the diffraction amplitudes to be determined. The Monte Carlo technique is applied and the bi-static scattering coefficient is estimated by averaging the scattering amplitudes over several realizations. The results of a Gaussian random process with a Gaussian roughness spectrum are compared to published experimental and numerical data. Comparisons are conclusive.

Sparse matrix/canonical grid method applied to 3-D dense medium simulations

The sparse matrix/canonical grid (SMCG) method, which has been shown to be an efficient method for calculating the scattering from one-dimensional and two-dimensional random rough surfaces, is extended to three-dimensional (3-D) dense media scattering. In particular, we study the scattering properties of media containing randomly positioned and oriented dielectric spheroids. Mutual interactions between scatterers are formulated using a method of moments solution of the volume integral equation. Iterative solvers for the resulting system matrix normally require O(N/sup 2/) operations for each matrix-vector multiply. The SMCG method reduces this complexity to O(NlogN) by defining a neighborhood distance, r/sub d/, by which particle interactions are decomposed into strong and weak. Strong interaction terms are calculated directly requiring O(N) operations for each iteration. Weak interaction terms are approximated by a multivariate Taylor series expansion of the 3-D background dyadic Green's function between any given pair of particles. Greater accuracy may be achieved by increasing r/sub d/, using a higher order Taylor expansion, and/or increasing mesh density at the cost of more interaction terms, more fast Fourier transforms (FFTs), and longer FFTs, respectively. Scattering results, computation times, and accuracy for large-scale problems with r/sub d/ up to 2 gridpoints, 14/spl times/14/spl times/14 canonical grid size, fifth-order Taylor expansion, and 15 000 discrete scatterers are presented and compared against full solutions.

Field Prediction Describing Scattering by a One-Dimensional Smooth Random Rough Surface

The field due to a plane wave with a Gaussian profile incident on a perfectly conducting one-dimensional smooth random rough surface with finite size is studied. The distribution of the total field when the height of the surface changes in a random way is presented, together with a comparison with the distribution of the field obtained when a plane wave is incident on a finite flat surface of the same size, having a height varying in a random manner. The results show that the two cases are equivalent.

A statistical model of wave scattering from random rough surfaces

A statistical model based on the geometric optics approximation for predicting wave scattering from random rough surfaces is developed. This model uses statistical concepts, rather than bundle tracing employed in the geometric optics approximation. This model includes first-, second- and higher-order scatterings. Shadowing effects are included, and the model can be expressed in a closed form. For one-dimensional random rough surfaces, the statistical model is quantified by comparisons with the exact electromagnetic theory calculations, and the results are in good agreement for surfaces with a surface slope less than unity. For two-dimensional random rough surfaces, the approximate results are compared with the existing experimental findings and electromagnetic theory calculations. The statistical method is a computationally inexpensive wave scattering approach for surfaces with a surface slope less than 0.5, and the method can approximate the magnitude and the trend for surfaces with a surface slope greater than 0.5.