Low grazing incidence millimeter-wave scattering models andmeasurements for various road surfaces

Systematic characterization of the scattering behavior of traffic targets, clutter, and their associated interactions are required in order to design and assess the performance of millimeter-wave-based sensors for automated highway system (AHS) applications. In this paper, the polarimetric radar backscatter response of various road surfaces is investigated both theoretically and experimentally. In general, it is found that the overall scattering response of road surfaces is composed of volume and surface scattering components. Previously a hybrid volume scattering model was developed for predicting the backscatter response of smooth asphalt surfaces at millimeter-wave frequencies. There, only the volume scattering was accounted for, however, experimental results show that the surface scattering cannot be ignored when the surface roughness parameters become comparable to the radar wavelength. In this paper, the previous study is extended to include the radar backscatter response of concrete surfaces, snow-covered smooth surfaces, and rough asphalt or concrete surfaces. Radiative transfer (RT) theory is used to model the volume scattering and the integral equation model is used to describe the surface scattering. Asphalt and concrete mixtures are dense random media whose extinction and phase matrices are characterized experimentally. Ice and water over asphalt and concrete surfaces are modeled by homogeneous layers. Fresh snow is modeled by a sparse random medium whose extinction and phase matrices are obtained analytically. The University of Michigan 94-GHz polarimetric radar system was used to perform polarimetric backscatter measurements of the aforementioned road surfaces at near grazing incidence angles (70°-88°). Comparison of the measured and theoretically predicted backscattering coefficients and polarimetric phase difference statistics shows excellent agreement     

Fluctuation statistics of millimeter-wave scattering fromdistributed targets

The applicability of the Rayleigh fading model for characterizing radar scattering from terrain is examined at 35 GHz for both backscattering and bistatic scattering. The model is found to be in excellent agreement with experimental observations for single-frequency observations of uniform targets such as asphalt and snow-covered ground. The use of frequency averaging to reduce signal fading variations was examined experimentally by sweeping the radar signal from 34-36 GHz in 401 steps. The results show that the formulation based on the Rayleigh model relating the reduction in signal fluctuation to the bandwidth used provides a reasonable estimate for the improvement provided by frequency averaging     

Bistatic scattering from three-dimensional layered rough surfaces

An analytical method to calculate the bistatic-scattering coefficients of a three-dimensional layered dielectric structure with slightly rough interfaces is presented. The interfaces are allowed to be statistically distinct, but possibly dependent. The waves in each region are represented as a superposition of an infinite number of up- and down-going spectral components whose amplitudes are found by simultaneously matching the boundary conditions at both interfaces. A small-perturbation formulation is used up to the first order, and the scattered fields are derived. The calculation intrinsically takes into account multiple scattering processes between the boundaries. The formulation is then validated against known solutions to special cases. New results are generated for several cases of two- and three-layer media, which will be directly applicable for modeling of the signals from radar systems and subsequent estimation of a layered medium subsurface properties, such as moisture content and layer depths.     

Bistatic specular scattering from rough dielectric surfaces

An experimental investigation was conducted to determine the nature of bistatic scattering from rough dielectric surfaces at 10 GHz. This paper focusses specifically on the dependence of coherent and incoherent scattered fields on surface roughness for the specular direction. The measurements, which were conducted for a smooth surface with ks<0.2 (where k=2π/λ and s is the RMS surface height) and for three rough surfaces with ks=0.5, 1.39, and 1.94, included observations over the range of incidence angles from 20° to 65° for both horizontal and vertical polarizations. For the coherent component, the reflectivity was found to behave in accordance with the prediction of the physical optics model, although it was observed that the Brewster angle exhibited a small negative shift with increasing roughness. The first-order solution of physical optics also provided good agreement with observations for hh-polarized incoherent scattering coefficient, but it failed to predict the behavior of the vv-polarized scattering coefficient in the angular range around the Brewster angle. A second-order solution is proposed which appears to partially address the deficiency of the physical optics model     

Numerical simulation of scattering from three-dimensional randomlyrough surfaces

Randomly rough surface patches in three dimensions are generated on the computer. The FD-TD method is used to compute scattering from surface patches by converting the Maxwell's equations into difference equations using a central difference approximation for the space and time derivatives. The volume of grids above the rough surface is divided into the total field and the scattered field regions. In between these two regions, obliquely incident waves are generated. To reduce computation, the volume of grids is chosen to be small, and a transformation is used to convert the scattered field into far zone fields for bistatic scattering coefficient calculations. Possible errors near the edge of the surface due to the use of a relatively small volume are suppressed by introducing a windowing function. Very good agreements are obtained between the results obtained by this method and those calculated by an integral equation method (IEM) for scattering from randomly rough perfectly conducting and dielectric surfaces     

Modal analysis of scattering from two-layer frequency-selective surfaces

A mode-matching analysis of double-layer frequency-selective surfaces is described. The integral equations given can be applied to pairs of plane periodic arrays with different element geometries, if required, but with identical lattices. Predictions are compared with experimental transmission curves for a pair of closely spaced concentric ring arrays.     

Preconditioned iterative solution of scattering from rough surfaces

Extensions to the functionally identical forward-backward (FB) and method of ordered multiple interactions iterative techniques have been introduced that improve the convergence characteristics with specific scattering geometries. These extensions are shown to be mathematically equivalent to applying preconditioners to the discretized integral equation that is iteratively solved. The same preconditioners can be used with any iterative solution technique. Numerical examples show that the generalized minimal residual (GMRES) and bi-conjugate gradient-stable (BICGSTAB) algorithms give similarly rapid convergence when applied to a preconditioned discretized integral equation     

Forward-backward method for scattering from dielectric rough surfaces

The iterative forward-backward (FB) method is a recently proposed efficient technique for numerical evaluation of scattering from perfectly conducting rough surfaces. Extension of the method to include scattering from imperfect conducting surfaces, with a high imaginary part of the complex dielectric constant, has also been proposed. The FB method is further generalized to analyze scattering from dielectric rough surfaces with arbitrary complex dielectric constant. Electric and magnetic equivalent surface currents are split into forward and backward components and equations governing these current components are obtained. As a solution, an iterative scheme is proposed and its convergence rate is analyzed. Finally, the effectiveness of the method is assessed by comparing the obtained scattering results with "exact" ones, computed by employing the usual method of moments (MoM).     

A nonrectangular patch model for scattering from surfaces

A model is derived for treatment of surfaces using nonrectangular patches. Tests show good agreement, where comparison is possible, with results published elsewhere. The results are shown to be reasonable even in cases where some of the quadrilaterals degenerate to triangles.     

Polarimetric scattering from natural surfaces at 225 GHz

Polarimetric radar measurement at 225 GHz which demonstrate that the normalized Mueller matrix may be approximated in terms of a single parameter are presented. The depolarization ratio, defined as the ratio of cross-polarized to co-polarized normalized radar cross section, is shown to accurately predict backscatter from vegetation (trees and grass), as well as scattering from terrain at low incidence angles (snowcover and sand). The depolarization ratio also predicts the standard deviation of the scattered field ellipse parameters     

A model for edge scattering from dichroic surfaces

This paper discusses experimental and theoretical results for edge scattering from dichroic (frequency selective) surfaces. Measurements presented for half planes show the nature of the scattering from the edge for both reflection and transmission frequencies. An impedance boundary condition approach is used to calculate the diffraction from dichroic edges. In the analysis the dichroic surface is replaced with an equivalent surface impedance and the total scattered field calculated. Measurements support the theory demonstrating the usefulness of the approach. The method is also useful for calculating diffraction from dielectric edges.     

Parallel analysis of electromagnetic scattering from random rough surfaces

An efficient approach for simulation of random rough surface scattering is developed based on using a single integral equation formulation and a multilevel sparse-matrix canonical-grid method. Merits of the scheme are demonstrated using two wind-driven ocean surfaces, one which is very rough and the other large in size.     

大粗糙度表面激光散射特性实验研究

本文利用激光散射自动测量系统,对经喷丸处理后的钢基粗糙表面及其喷漆表面的后向激光雷达散射截面(LRCS)进行了测量。测量波长分别为λ=633nm和λ=904nm.在λ=904nm,利用粗糙面电磁散射理论的基尔霍夫方法对上述样片进行了理论计算,其中将粗糙表面视为双尺度模型,根据驻留相位法和标量近似法理论计算双尺度模型随机粗糙表面的散射强度角分布,其理论值与实验测量结果有较好的吻合。     

Measurement and modeling of the millimeter-wave backscatterresponse of soil surfaces

The millimeter-wave (MMW) backscatter response of bare-soil was examined by conducting experimental measurements at 35 and 94 GHz using a truck-mounted polarimetric scatterometer and by developing appropriate models to relate the backscattering coefficient to the soil's surface and volume properties. The experimental measurements were conducted for three soil surfaces with different roughnesses under both dry and wet conditions. The experimental measurements indicate that in general the backscattering coefficient is comprised of a surface scattering component σ^s and a volume scattering component σ ^v. For wet soil conditions, the backscatter is dominated by surface scattering, while for dry conditions both surface and volume scattering are significant, particularly at 94 GHz. Because theoretical surface scattering models were found incapable of predicting the measured backscatter, a semiempirical surface scattering model was developed that relates the surface scattering component of the total backscatter to the roughness parameter ks, where k=2π/λ and s is the rms height, and the dielectric constant of the soil surface. Volume scattering was modeled using radiative transfer theory with the packed soil particles acting as the host material and the air voids as the scattering particles. The combined contribution of surface and volume scattering was found to provide good agreement between the model calculations and the experimental observations     

粗糙平面的激光散射特性研究

为了检测目标的边缘信息,采用激光扫描目标表面、通过回波信号变化来得到目标的边缘信息的方法,利用随机面元模型,分析了刚性随机粗糙平面的激光散射特点,建立了实用化的随机粗糙平面激光散射理论模型,并给出了正入射时几种情况下的激光散射图像,分析了平面目标的激光散射能量计算方法,仿真了光束在平面目标表面做正弦摆动时,光斑在不同位置的反射能量,利用激光信号的强度变化,采用峰(谷)检出法或者过零检出法就可以得到物体的边缘信息。结果表明,通过回波信号的变化,可以得到目标的边缘轮廓。     

Electromagnetic scattering from slightly rough surfaces withinhomogeneous dielectric profiles

Remote sensing of soil moisture using microwave sensors require accurate and realistic scattering models for rough soil surfaces. In the past, much effort has been devoted to the development of scattering models for either perfectly conducting or homogeneous rough surfaces. In practice, however, the permittivity of most soil surfaces is nonuniform, particularly in depth, for which analytical solution does not exist. The variations in the permittivity of a soil medium can easily be related to its soil moisture profile and soil type using the existing empirical models. In this paper, analytical expressions for the bistatic scattering coefficients of soil surfaces with slightly rough interface and stratified permittivity profile are derived. The scattering formulation is based on a new approach where the perturbation expansion of the volumetric polarization current instead of the tangential fields is used to obtain the scattered field. Basically, the top rough layer is replaced with an equivalent polarization current and, using the volumetric integral equation in conjunction with the dyadic Green's function of the remaining stratified half-space medium, the scattering problem is formulated. Closed-form analytical expressions for the induced polarization currents to any desired order are derived, which are then used to evaluate the bistatic scattered fields up to and including the third order. The analytical solutions for the scattered fields are used to derive the complete second-order expressions for the backscattering coefficients as well as the statistics of phase difference between the scattering matrix elements. The theoretical results are shown to agree well with the backscatter measurements of rough surfaces with known dielectric profiles and roughness statistics     

An approach to high-frequency scattering from smooth convex surfaces

A method based on the Galerkin procedure in the transform domain that not only allows accurate solutions for both the farfield and the induced surface current be derived but also provides a convenient accuracy check for the solutions thus obtained is introduced. The total solution is constructed using only the geometrical optics method and a newly introduced synthetic aperture technique well suited for deriving efficient transform solutions forn-dimensional, smooth curved objects using (n - 1)-dimensional transforms. The need for the conventional creeping-wave contribution is obviated in this method.     

Numerical simulation of scattering from rough surfaces: awavelet-based approach

In this paper, a preliminary study is carried out to demonstrate the application of wavelets for improving the computation time and reducing computational memory required for evaluating the statistics of the scattered field from rough surfaces using the method of moments (MoM) in conjunction with a Monte Carlo simulation. In specific, Haar and the first order B-spline wavelet basis functions are applied to the MoM formulation of one-dimensional rough surfaces in order to compare the computation time and sparsity for wavelets in the same family but of higher order. Since the scattering coefficient (the second moment of the backscatter field per unit area) is a gentle function of the surface parameters and the radar attributes, it is demonstrated that a relatively high thresholding level can be applied to the impedance matrix, which leads to a sparser impedance matrix and faster computation time. It is also shown that applying a high threshold level the coefficients of the high-order wavelets would increase out of proportion, however, the effect of these current components averages out when computing the scattering coefficients. The resulting sparse impedance matrices are solved efficiently using fast search routines such as the conjugate gradient method. A systematic study is carried out to investigate the effect of different threshold levels on the accuracy versus computing speed criterion. The computed scattering coefficients are compared to previous results computed using a conventional pulse basis function as well as the existing theoretical solutions for rough surfaces. It is shown that wavelet basis functions provide substantial reductions in both memory requirements and computation time