Polarimetric scattering from two-layered two-dimensional random rough surfaces with and without buried objects

A three-dimensional polarimetric analysis of the two-layered rough ground with and without buried objects is investigated here. A rigorous electromagnetic surface integral-equation-based model is used in this analysis. The statistical average of the polarimetric scattering matrix elements is computed based on the Monte Carlo simulations for both the vertically and horizontally polarized incident waves. The results show a significant impact on the scattered intensities due to the two-layer nature of the ground. However, these intensities show almost no difference between the ground signature with or without the object. On the other hand, the statistical average of the covariance matrix elements shows a distinct difference between these two signatures despite the small size of the buried object.     

Electromagnetic scattering by buried objects of low contrast

The Born approximation is used to derive the plane-wave scattering matrix for objects of low dielectric contrast. For general shapes a numerical integration over the volume of the scatterer is required, but analytical expressions are derived for a sphere, a circular cylinder and a rectangular box (parallelepiped). The plane-wave scattering-matrix theory is used to account for the air-Earth interface. Numerical results are presented for the scattered field and far field for plane-wave excitation. The scattered field are weak for low-contrast objects, but the near-field results have application to electromagnetic detection of buried objects     

Electromagnetic scattering from two adjacent objects

In the paper, the problem of electromagnetic scattering from two adjacent particles is considered and an iterative solution that accounts for multiple scattering up to second-order is proposed. The first-order solution can easily be obtained by calculating the scattered field of isolated particles when illuminated by a plane-wave. To get the second-order solution, the scattered field from one of the particles, with nonuniform phase, amplitude, and polarization, is considered as the illuminating wave for the other particle and vice versa. In the work, the second-order scattered field is derived analytically using a novel technique based on the reciprocity theorem. In specific, the analytical solution for bistatic specular scattering from a cylinder and sphere pair is discussed and the results are compared with numerical computations based on the method of moments     

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     

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.     

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 a buried cylinder in layered media with rough interfaces

A solution to scattering from a cylinder buried arbitrarily in layered media with rough interfaces based on extended boundary condition method (EBCM) and scattering matrix technique is developed. The reflection and transmission matrices of arbitrary rough interfaces as well as an isolated single cylinder are constructed using EBCM and recursive T-matrix algorithm, respectively. The cylinder/rough surface interactions are taken into account by applying the generalized scattering matrix technique. The scattering matrix technique is used to cascade reflection and transmission matrices from individual systems (i.e., rough surfaces or cylinders) in order to obtain the scattering pattern from the overall system. Bistatic scattering coefficients are then obtained by incoherently averaging the power computed from the resulting Floquet modes of the overall system. In numerical simulations, the bistatic scattering coefficients are first validated by comparing the simulation results with the existing solutions which are the limiting cases including scattering from two-interface rough surfaces without any buried object and from a buried cylinder beneath a single rough surface. Subsequently, the numerical simulations of scattering from a buried cylinder in layered rough surfaces are performed to investigate the relative importance and sensitivity of various physical parameters of layered rough surfaces to incoherent scattering coefficients. Results show layered rough interfaces can significantly alter the scattering behaviors of a buried cylinder.     

Electromagnetic scattering from a dielectric cylinder buried beneath a slightly rough surface

An analytical solution is presented for the electromagnetic scattering from a dielectric circular cylinder embedded in a dielectric half-space with a slightly rough interface. The solution utilizes the spectral (plane-wave) representation of the fields and accounts for all the multiple interactions between the rough interface and the. buried cylinder. First-order coefficients from the small perturbation method are used for computation of the scattered fields from the rough surface. The derivation includes both TM and TE polarizations and can be easily extended for other cylindrical buried objects (e.g., cylindrical shell, metallic cylinder). Several scattering scenarios are examined utilizing the new solution for a dielectric cylinder beneath a flat, sinusoidal, and arbitrary rough surface profile. Results indicate that the scattering pattern of a buried object below a slightly rough surface differs from the flat surface case only when the surface roughness spectrum contains a limited range of spatial frequencies. Furthermore, the illuminated area of the incident wave is seen to be a critical factor in the visibility of a buried object below a rough surface.     

Monte Carlo simulation of electromagnetic scattering fromtwo-dimensional random rough surfaces

The fast multipole method fast Fourier transform (FMM-FFT) method is developed to compute the scattering of an electromagnetic wave from a two-dimensional (2-D) rough surface. The resulting algorithm computes a matrix-vector multiply in O(N log N) operations. This algorithm is shown to be more efficient than another O(N log N) algorithm, the multilevel fast multipole algorithm (MLFMA), for surfaces of small height. For surfaces with larger roughness, the MLFMA is found to be more efficient. Using the MLFMA, Monte Carlo simulations are carried out to compute the statistical properties of the electromagnetic scattering from 2-D random rough surfaces using a workstation. For the rougher surface, backscattering enhancement is clearly observable as a pronounced peak in the backscattering direction of the computed bistatic scattering coefficient. For the smoother surface, the Monte Carlo results compare well with the results of the approximate Kirchhoff theory     

Wave propagation and scattering in random media and rough surfaces

The author presents a comprehensive review highlighting historical as well as new developments in the area of random media. Both discrete and continuous media are considered as well as rough surfaces. The author discusses wave propagation in turbulence and in a random continuum where the refractive index is a random function of space and time. Examples are optical propagation in the atmosphere, microwaves in the troposphere, ionosphere, planetary atmosphere, and solar wind, and acoustic scattering in ocean turbulence. The author describes multiple scattering by random distributions of discrete scatterers. Examples are optical and microwave scattering by rain, fog, smog, snow, ice particles, and vegetation, optical and ultrasound scattering by tissues and blood, optical and acoustic scattering in the ocean, and scattering in composite materials. Scattering by rough surfaces and interfaces is discussed. Examples are acoustic scattering by ocean surfaces, microwave and optical scattering by vegetation, terrain, and snow cover, and ultrasound scattering by rough interfaces in biological media     

Monte Carlo simulations for clutter statistics in minefields: AP-mine-like-target buried near a dielectric object beneath 2-D random rough ground 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.     

Experimental studies of bistatic scattering from two-dimensionalconducting random rough surfaces

Despite the recent development of analytical and numerical techniques for problems of scattering from two-dimensional rough surfaces, very few experimental studies were available for verification. The authors present the results of millimeter-wave experiments on scattering from two-dimensional conducting random rough surfaces with Gaussian surface roughness statistics. Machine-fabricated rough surfaces with controlled roughness statistics were examined. Special attention was paid to surfaces with large rms slopes (ranging from 0.35 to 1.00) for which enhanced backscattering is expected to take place. Experimentally, such enhancement was indeed observed in both the copolarized and cross-polarized returns. In addition, it was noticed that at moderate angles of incidence, the scattering profile as a function of observation angle is fairly independent of the incident polarization and operating frequency. This independence justifies the use of the geometric optics approximation embodied in the Kirchhoff formulation for surfaces with large surface radius of curvature. When compared with the experimental data, this analytical technique demonstrates good agreement with the experimental data     

Electromagnetic scattering from perfectly conducting rough surfaces in the resonance region

A rigorous integral formalism for the problem of scattering of electromagnetic radiation from a cylindrical, perfectly conducting rough surface of arbitrary shape is introduced. The computer code obtained from this theory enables us to show that the range over which the incident field affects the surface current density is of the order of the radiation wavelength. This phenomenon is explained using a new approximate theory, able to express the scattered field in the form of an integral whose integrand is known in closed form. Using the rigorous computer code, we show that the new approximate theory is better than the Kirchhoff approximation in the resonance region. Finally, it is shown that the phenomenon of short interaction range of the incident field permits the rigorous computation of the field scattered from a rough surface of arbitrary width.     

分层粗糙面下方介质目标散射的快速算法

为快速获取分层粗糙面与下方介质目标的复合电磁散射特性,提出了一种基于前后向迭代算法(FBM)和双共轭梯度法(Bi-CG)的快速互耦迭代算法。推导了一维分层粗糙面与下方介质目标(二维散射问题)的耦合边界积分方程组,用FBM求解分层粗糙面的表面积分方程,而用Bi-CG求解目标的表面积分方程,目标和粗糙面的相互耦合作用通过更新两方程的激励项来迭代求解。应用该算法计算了下方存在介质目标时双层介质粗糙面的双站散射系数,与传统矩量法得到的结果相吻合,验证了该算法的正确性;分析了不同极化波入射时该算法的收敛性,讨论了目标尺寸和位置变化对双站散射系数的影响。     

Wavelet-based simulations of electromagnetic scattering fromlarge-scale two-dimensional perfectly conducting random rough surfaces

Simulations of electromagnetic waves scattering from two-dimensional perfectly conducting random rough surfaces are performed using the method of moment (MoM) and the electric field integral equation (EFIE). Using wavelets as basis and testing functions, the resulting moment matrix is generally sparse after applying a threshold truncation. This property makes wavelets particularly useful in simulating large-scale problems, in which reducing memory storage requirement and CPU time are crucial. In this paper, scattering from Gaussian conducting rough surfaces of a few hundred square wavelengths are studied numerically using Haar wavelets. A matrix sparsity less than 10% is achieved for a range of root mean square (RMS) height at eight sampling points per linear wavelength. Parallelization of the code is also performed. Simulation results of the bistatic scattering coefficients are presented for different surface RMS heights up to 1 wavelength. Comparisons with sparse-matrix/canonical-grid approach (SM/CG) and triangular discretized (RWG basis) results are made as well. Depolarization effects are examined for both TE and TM incident waves. The relative merits of the SM/CG method and the present method are discussed     

Full-wave electromagnetic scattering at extremely large 2-D objects

Recent advances in the parallel multilevel fast multipole algorithm have paved the way for large-scale full-wave electromagnetic simulations. The introduction of the hierarchical partitioning technique and the use of an asynchronous parallel implementation have resulted in a scalable algorithm that runs efficiently, even on low-cost clusters. Presented is the accurate solution of the two-dimensional (2-D) transversemagnetic scattering at both a perfect electric conducting cylinder with a diameter of onemillion wavelengths and a dielectric cylinder with a diameter of half a million wavelengths.     

Electromagnetic scattering from perfectly conducting rough surfaces(a new full wave method)

A method that does not make use of the telegraphist's equations and takes into account the two-dimensional roughness of the surface from the start is developed. It is shown that the scattering coefficients obtained agree with those given in earlier work by E. Bahar (1973, 1987). The method is based on reducing the three-dimensional scattering problem to a two-dimensional problem by expanding each rectangular component of Maxwell's equations in terms of local basis functions along the perpendicular direction to the mean surface. The transformed two-dimensional field equations are solved using Fourier transforms. The full wave solutions are also compared with the first-order perturbation solutions, the Kirchhoff-type solutions, and integral equation results     

Electromagnetic scattering interaction between a dielectriccylinder and a slightly rough surface

An electromagnetic scattering solution for the interaction between a dielectric cylinder and a slightly rough surface is presented in this paper. Taking the advantage of a newly developed technique that utilizes the reciprocity theorem, the difficulty in formulating the secondary scattered fields from the composite target reduces to the evaluation of integrals involving the scattered fields from the cylinder and polarization currents of the rough surface induced by a plane wave. Basically, only the current distribution of isolated scatterers are needed to evaluate the interaction in the far-field region. The scattered field from the cylinder is evaluated in the near-field region using a stationary phase approximation along the cylinder axis. Also, the expressions for the polarization current induced within the top rough layer of the rough surface derived from the iterative solution of an integral equation are employed in this paper. A sensitivity analysis is performed for determining the dependency of the scattering interaction on the target parameters such as surface root mean square (RMS) height, dielectric constant, cylinder diameter, and length. It is shown that for nearly vertical cylinders, which is of interest for modeling of vegetation, the cross-polarized backscatter is mainly dominated by the scattering interaction between the cylinder and the rough surface. The accuracy of the theoretical formulation is verified by conducting polarimetric backscatter measurements from a lossy dielectric cylinder above a slightly rough surface. Excellent agreement between the theoretical prediction and experimental results is obtained     

Scattering from multiple objects buried beneath two-dimensional random rough surface using the steepest descent fast multipole method

Generalized formulations are presented to analyze the electric field scattered from multiple penetrable shallow objects buried beneath two-dimensional random rough surfaces. These objects could have different materials, shapes, or orientations. In addition, their separation distance may range from a fraction of a wavelength to several wavelengths. The fast algorithm, steepest descent fast multipole method (SDFMM), is used to compute the unknown electric and magnetic surface currents on the rough ground surface and on the buried objects. Parametric investigations are presented to study the effect of the objects proximity, orientations, materials, shapes, the incident waves polarization, and the ground roughness on the scattered fields. A significant interference is observed between the objects when they are separated by less than one free space wavelength. Even when the clutter due to the rough ground is removed, the return from the second object, can be dominating causing a possible false alarm in detecting the target. The results show that the distortion in target signature significantly increases with the increase of both the proximity to a clutter item and the ground roughness.     

Three-dimensional subsurface analysis of electromagnetic scatteringfrom penetrable/PEC objects buried under rough surfaces: use of thesteepest descent fast multipole method

The electromagnetic scattering from a three-dimensional (3D) shallow object buried under a two-dimensional (2D) random rough dielectric surface is analyzed. The buried object can be a perfect electric conductor (PEC) or can be a penetrable dielectric with size and burial depth comparable to the free-space wavelength. The random rough ground surface is characterized with Gaussian statistics for surface height and for surface autocorrelation function. The Poggio, Miller, Chang, Harrington, and Wu (PMCHW) integral equations are implemented and extended. The integral equation-based steepest descent fast multipole method (SDFMM), that was originally developed at UIUC, has been used and the computer code based on this algorithm has been successfully modified to handle the current application. The significant potential of the SDFMM code is that it calculates the unknown moment method surface electric and magnetic currents on the scatterer in a dramatically fast, efficient, and accurate manner. Interactions between the rough surface interface and the buried object are fully taken into account with this new formulation. Ten incident Gaussian beams with the same elevation angle and different azimuth angles are generated for excitation as one possible way of having multiple views of a given target. The scattered electric fields due to these ten incident beams are calculated in the near zone and their complex vector average over the multiple views is computed. The target signature is obtained by subtracting the electric fields scattered from the rough ground only from those scattered from the ground with the hurled anti-personnel mine