Research on the Composite Electromagnetic Scattering of Rough Surface and Buried Target Based on G-PILE

In recent years, considerable interest has been focused on the study of scattering from very rough surfaces. Very rough surfaces are defined as those with an rms height variation of the order of a wavelength and an rms slope of the order of unity. These surfaces occur in several practical problems including underwater acoustics, microwave scattering by terrain, ultrasound scattering by tissues, and optical scattering by rough metallic surfaces. In addition, recent experimental and numerical studies show backscattering enhancement phenomena from very rough surfaces.16 In spite of their theoretical interest and practical importance, theories of scattering by very rough surfaces are scarce7 and outside the range of validity of conventional theories such as the perturbation method and the Kirchhoff approximation.811 Recently, we proposed a theory based on the modified Kirchhoff approximation (KA) with angular and propagation shadowing for one—dimensional Dirichlet rough surfaces.12 This paper extends our previous theory to include scattering by very rough metallic and dielectric surfaces. The range of validity of the theory is examined by comparing it with the Monte Carlo simulation. Some material in this paper is also in our recent papers.2022 Numerical studies on very rough surfaces show that the second—order KA, when the surface integral is limited within the distance of double bounces without being intercepted by the surface, agrees well with the exact Monte Carlo simulation.13 This is consistent with the observation made by Liszka and McCoy that any signal which intersects the rough surface, one or more times, will be canceled by some higher iteration.14 This cancellation is accomplished by the shadowing function. This also indicates that the first— and second— order KA with proper shadowing gives a good approximate solution to very rough surface scattering. Conventional shadowing functions are used for first—order KA scattering. For second—order KA, in addition to the conventional shadowing, the shadowing representing the probability that the wave scattered from a point on the surface arrives at the other point on the surface without being intercepted by the surface is included. This shadowing is given by the angular and the propagation distance probabilities. These two shadowing functions, angular and propagation, modify the second—order KA and give the proper energy conservation and enhanced backscattering. The shadowing functions for the second—order KA used in this paper are similar to that used by Jin.15 The effect of shadowing for double scattering by random surfaces is also studied by Pavel'yev.16 Our analytical method employs the positive and negative traveling waves for the second— order KA and this results in a clear physical interpretation of the processes for the ladder and the cross or cyclic terms. The cyclic terms represent two waves propagating over the surface in opposite directions, giving rise to the backscattering enhancement. We also use Fourier transform in the vertical direction to facilitate computation of the second moments. Figure 1 shows the approximate range where our theory is applicable in terms of an rms height o and a correlation distance 1. The ranges where the Kirchhoff approximation, field perturbation, and phase perturbation methods are valid are noted by KA, FP and PP, respectively. The range where backscattering enhancement takes place is noted by E, and this is the range where none of the conventional techniques is applicable. Those points marked with fl are where our theory agrees well with exact numerical simulations, and the energy is conserved within 5 % error. Our theory covers most of the range E where the enhancement takes place, and the theory also reduces to conventional KA in the range where KA is applicable.

An efficient multiregion model is extended by the single integral equation (SIE) method for the first time to calculate electromagnetic (EM) scattering from a dielectric rough surface with or without a perfectly electric conducting target above it. In the multiregion model, the rough surface is divided into multiple regions depending on their positions along the rough surface and the energy distribution of the incident wave. Two intermediate regions are chosen as the dominant regions in which the method of moment is adopted. If a target is located above the surface, the target is also included in the dominant region. Hence, the new model can markedly reduce the number of unknowns compared with full SIE analysis. Mutual couplings between different regions are approximately considered based on magnetic and electric field integral equations from which closed-form approximations for currents in other regions are derived.

The difference field RCS from a target above a rough surface is derived. The electric field integral equations (EFIE) of the difference induced currents Jsd on the surface and J0 on target are developed. Because of the strongest scattering in the specular direction, a small interface taken along the converse specular direction is attributed to computation of the surface scattering upon the target. A fast mutual-coupling iterative method is developed to solve the two EFIEs. The interface length for effective computation is discussed. Using the Monte Carlo method, scattering from a target, such as a cylinder and a square column, above the P-M rough surface is numerically simulated. Scattering from a cylinder above the rough surface in the specular direction is enhanced significantly. The Bi-RCS of a square column above the rough surface shows two peaks in forward and backward directions. As a model of rough sea surface, when the surface wind speed increases, the scattering peaks become lower, and more defused scattering shows the angular scattering pattern. Introduction Scattering from the targets above a rough surface has attracted more interests in recent years. In the combined target-surface problem, the difference field cross section was introduced by Johnson [1] to remove the dependence on incident taper wave width. Scattering for the combined target-surface problem and surfaceonly problem are respectively calculated, and their difference shows scattering attributed by the target and interaction between the target and rough surface. In this paper, we derive the EFIEs of the difference induced current on rough surface and current on the target. A mutual-coupling iterative approach is developed to solve the EFIEs. The interface length for the iterative calculation is discussed. As examples, scattering from a cylinder and a square column above a rough surface are simulated. It can be seen that scattering from the cylinder above a rough surface is significantly enhanced in the specular direction due to interactions of the target and the underlying surface. Variation of the difference induced currents on the interface also demonstrates such interactions. Scattering from a square column has two peaks in the backward and forward directions due to its specific geometry. As a model of a target located above the wind-driven sea surface, numerical simulations show the angular pattern of bistatic scattering versus oceanic status. When the surface wind speed increases, scattering peaks become weaker and more angular defused scattering are dominated. Theory and Method In a model of the target above rough surface, both the total and differential cross section are previously related to the surface length illuminated by incident wave. In order to remote the dependence on illuminated surface length, the difference of the scattering field, Es1, attributed by both the target and surface and the scattering field by a rough surface only, Es0, is calculated as Esd, which is used to compute the difference field cross section σd [1], which demonstrates how much the scattering attributed by the target and interaction between the target and underlying rough surface. It does not depend upon the illuminated rough surface length. As shown in Fig.1, a two-dimensional (2D) target (perfect electric conductor, PEC) is located above a 2D PEC rough surface. As the incident tapered wave is incident on the target and rough surface, the induced current on the target is defined as J0, and the induced current on the surface is Js1. The EFIEs are written as [2] 0 = ET (r)− jkη ∫ c Jo(r ′) ·G(r, r′)dr′ − jkη ∫ S Js1(r ′) ·G(r, r′)dr′(r ∈ c) (1) 202 Progress In Electromagnetics Research Symposium 2005, Hangzhou, China, August 22-26

Using a generalization of the integral theory of metallic and dielectric gratings developed in our laboratory 15 years ago, we propose a rigorous integral theory of scattering by metallic or dielectric nonperiodic rough surfaces leading to a single integral equation. The numerical implementation has been carried out despite strong difficulties for TM polarization and metallic surfaces because of propagation of surface plasmon waves outside the illuminated region of the rough surface. Numerical results show the influence of the statistical parameters of the asperities on the absorption phenomena for metallic surfaces. Then the influence of asperities on the total transmission around Brewster incidence is studied. Finally numerical results of enhanced backscattering from perfectly conducting, metallic, and dielectric random rough surfaces are given.

In this paper, an efficient hybrid approach to study the ElectroMagnetic (EM) scattering from a three-dimensional (3-D) Perfectly Electric Conducting (PEC) object buried under a two-dimensional (2-D) dielectric rough surface is developed. The electric and magnetic current densities on the rough surface are obtained through the current-based asymptotic Kirchhoff Approximation (KA) formulation whereas the electric current density on the buried object is rigorously determined by solving the Electric Field Integral Equation (EFIE) using the Galerkin's Method of Moments (MoM) with Rao-Wilton-Glisson (RWG) basis functions. The matrix equation arising from the MoM discretization of the hybrid KA-EFIE formulation is then efficiently solved by the iterative PILE (Propagation-Inside-Layer-Expansion) method combined with the algebraic Adaptive Cross Approximation (ACA). The current densities on the dielectric rough surface are thereafter used to handle the bistatic Normalized Radar Cross Section (NRCS) patterns.

The electromagnetic scattering from the composite model of a three-dimensional (3-D) dielectric object located above a two-dimensional (2-D) dielectric rough surface is analyzed in this work. The 3DMLUV has been successfully applied in the scattering of PEC targets, however, when the object or rough surface become dielectric, the coupling between dielectric object and dielectric rough surface will lead to slow constriction. The FIA is applied to further speed up the constricted speed of the matrix required in 3DMLUV. The efficiency, stability and accuracy of the proposed method are demonstrated in a variety of scattering problems.

An efficient hybrid KA-EFIE formulation is deployed to analyze the electromagnetic (EM) scattering from a 3-D perfectly electric conducting (PEC) object buried beneath a 2-D dielectric rough surface. In this approach, the electric and magnetic current densities on the rough surface are analytically obtained through the current-based Kirchhoff approximation (KA), whereas the electric current density on the buried object is rigorously determined by solving the electric field integral equation (EFIE) using the Galerkin’s method of moments (MoM) with Rao–Wilton–Glisson (RWG) basis functions. The KA-EFIE matrix system is then efficiently solved by the iterative propagation-inside-layer-expansion (PILE) method combined with the algebraic adaptive cross approximation (ACA). The current densities on the dielectric rough surface are thereafter used to handle the bistatic normalized radar cross-section (NRCS) patterns. The proposed hybrid approach allows a significant reduction in computation time and memory requirements compared to the rigorous Poggio–Miller–Chang–Harrington–Wu (PMCHW)-EFIE formulation which requires solving a large MoM matrix equation. Moreover, the hybridization of the ACA algorithm with the PILE method improves further the computational cost thanks to the rank-deficient propriety of the coupling matrices. To validate the hybrid approach, we compare its results with those of the rigorous PMCHW-EFIE approach.

A hybrid integral equation is developed to solve the problem of electromagnetic (EM) scattering from a three-dimensional (3D) perfect electric conducting (PEC) object above a two-dimensional (2D) PEC or dielectric Gaussian rough surface. Firstly, the Kirchhoff–Helmholtz (KH) equation is adopted to describe the wave reflection on the rough surface; only one integral operation on the rough surface is needed, and the scattering from the object can be described by solving the electric field integral equation (EFIE) on the surface of the object. Moreover, according to scattering theory, the KH equation and the EFIE are coupled together (KH-EFIE) to describe wave propagation between the object and the rough surface. Then method of moments (MoM) is adopted to solve the KH-EFIE, and the current is obtained to calculate the scattering field. Finally, compared with other methods, the accuracy of the proposed approach is validated, and its efficiency is proved to be much higher than numerical solutions. Furthermore, by calculating the statistic composite radar cross-section (RCS) of the object/surface and the difference radar cross-section (DRCS) of the object, the influence of the rough surface root mean square (rms) height, the correlation length, the medium permittivity, the shape of the object, and the altitude of the object on the scattering characteristic is investigated.

This article proposes a new fast solution algorithm (IGFBM-SAA), which combines the Improved Generalized Forward and Backward Method (IGFBM) with Spectral Acceleration Approach (SAA), which can effectively solve the electromagnetic scattering problem of layered rough surface. In this article, the electric field integral equations (EFIE) for layered rough surfaces is established, and the traditional forward and backward method (FBM) is introduced. Then, based on the traditional FBM algorithm, an Improved Generalized Forward and Backward Method is proposed and, by using the SAA technique in its iterative process, the computation of matrix-vector multiplication is accelerated, thus enabling rapid solution. In the algorithm validation, the same rough surface was calculated using the MoM, FBM, and IGFBM-SAA. The study found that when root mean square (RMS) heights are h1=h2=0.1λ, the convergence accuracy can reach τ=10−7 after 14 iterations. However, as the roughness increases to h1=h2=0.3λ and h1=h2=0.5λ, the convergence accuracy falling to τ=10−5 and τ=10−5, respectively. This indicates that it is necessary to adjust the integration parameters to improve the convergence accuracy. In addition, it was found that when the size of the rough surface is 25.6λ, the computational times for calculations are 91 s (IGFBM-SAA), 197 s (FBM), and 410 s (MoM), respectively. When the size of the rough surface increases to 51.2λ, the computational time differences become more significant, with 236 s, 756 s, and 2547 s being the respective values. This indicates that the proposed algorithm in this article has significant computational speed advantages when dealing with larger rough surfaces. Based on this algorithm, this article studied the electromagnetic scattering characteristics of layered rough surfaces with different parameters (RMS height, dielectric constant, and correlation length), and relevant research results can provide valuable references for areas such as radar target recognition and radar stealth technology, thereby enhancing the accuracy and reliability of radar detection as well as radar stealthperformance.

A new hybrid analytical‐numerical iterative algorithm, which combines the Kirchhoff approximation (KA) and the Method of Moment (MoM), is developed for computing the electromagnetic scattering from a three‐dimensional (3‐D) perfect electric conducting (PEC) target above a 2‐D infinite randomly rough dielectric surface. The equations of difference scattering due to the target presence above the rough surface are derived. The induced difference fields on the rough surface due to the interactions between the target and the rough surface are calculated by using the KA method. The excitation term on the right‐hand‐side (RHS) of target's surface integral equation (SIE), which contains the difference scattering of the rough surface, is then updated for calculating new target currents with the Conjugate Gradient (CG) procedure. Then the target currents are used to compute the difference field induced on the rough surface with the KA method. Multiple iterations take account of the multiorder interactions between the target and the underlying rough surface. Numerical quadrature upon the rough surface is performed only once to compute the coupling scattering field from the rough surface to the target, and it takes N steps (N is the discretized mesh number of rough surface). By using this hybrid KA‐MoM algorithm, the requirements of memory and CPU time can be reduced significantly. Moreover, the validity conditions and the convergence performance of this hybrid algorithm are also discussed. With Monte‐Carlo generations of randomly rough surfaces, bistatic scattering from different‐shaped targets above a Gaussian rough surface is numerically simulated. Finally, dependence of bistatic scattering pattern on the surface dielectric property and the target geometry is discussed.

In real life most ground surfaces are not flat but rough. The observation of surface roughness depends on the wavelength and angle of the incident wave. In order to be able to detect shallow subsurface objects, on one hand we need to use higher frequencies to achieve better range resolution. One the other hand we have to deal with rough surfaces relative to shorter wavelengths. In this paper a wideband ground-penetrating radar (GPR) phase measurement and processing technique for characterizing three-dimensional (3-D) rough dielectric surfaces is presented. The method is based on the measurement of phase data by a standoff GPR with wide-beam antennas at short range over 3-D rough ground surfaces. The principle of this method was verified experimentally in the measurement of a composite surface. The height of the composite surface varies from 0 to 8 cm. The antennas are open-ended waveguide antennas whose frequency range is 2.3 GHz to 4.3 GHz. They are broadband, have low gain and wide beamwidth. The experimental tests demonstrate that the 3-D rough surfaces can be characterized locally by using a monochromatic and multifrequency broadband phase processing and imaging method. The results show good agreement between the imagery of the surface height distribution obtained by this method and the actual geometry of the 3-D rough surfaces.

An iterative strategy combining Kirchhoff approximation^(KA) with the hybrid finite element-boundary integral (FE-BI) method is presented in this paper to study the interactions between the inhomogeneous object and the underlying rough surface. KA is applied to study scattering from underlying rough surfaces, whereas FE-BI deals with scattering from the above target. Both two methods use updated excitation sources. Huygens equivalence principle and an iterative strategy are employed to consider the multi-scattering effects. This hybrid FE-BI-KA scheme is an improved and generalized version of previous hybrid Kirchhoff approximation-method of moments (KA-MoM). This newly presented hybrid method has the following advantages: (1) the feasibility of modeling multi-scale scattering problems (large scale underlying surface and small scale target); (2) low memory requirement as in hybrid KA-MoM; (3) the ability to deal with scattering from inhomogeneous (including coated or layered) scatterers above rough surfaces. The numerical results are given to evaluate the accuracy of the multi-hybrid technique; the computing time and memory requirements consumed in specific numerical simulation of FE-BI-KA are compared with those of MoM. The convergence performance is analyzed by studying the iteration number variation caused by related parameters. Then bistatic scattering from inhomogeneous object of different configurations above dielectric Gaussian rough surface is calculated and the influences of dielectric compositions and surface roughness on the scattering pattern are discussed.

A novel multilevel algorithm to analyze scattering from dielectric random rough surfaces is presented. This technique, termed the steepest-descent fast-multipole method, exploits the quasi-planar nature of dielectric rough surfaces to expedite the iterative solution of the pertinent integral equation. A combination of the fast-multipole method and Sommerfeld steepest-descent-path integral representations is used to efficiently compute electric and magnetic fields that are due to source distributions residing on the rough surface. The CPU time and memory requirements of the technique scale linearly with problem size, thereby permitting the rapid analysis of scattering by large dielectric surfaces and permitting Monte Carlo simulations with realistic computing resources. Numerical results are presented to demonstrate the efficacy of the steepest-decent fast-multipole method.

Electromagnetic scattering from one-dimensional two-layered rough surfaces is investigated by using finite-difference time-domain algorithm (FDTD). The uniaxial perfectly matched layer (UPML) medium is adopted for truncation of FDTD lattices, in which the finite-difference equations can be used for the total computation domain by properly choosing the uniaxial parameters. The rough surfaces are characterized with Gaussian statistics for the height and the autocorrelation function. The angular distribution of bistatic scattering coefficient from single-layered perfect electric conducting and dielectric rough surface is calculated and it is in good agreement with the numerical result with the conventional method of moments. The influence of the relative permittivity, the incident angle, and the correlative length of two-layered rough surfaces on the bistatic scattering coefficient with different polarizations are presented and discussed in detail.

The difference field RCS (d-RCS) has been defined to analyze the scattering from the target above a rough surface, which takes account of the scattering from the target and multiple interactions of the target and underlying rough surface. The d-RCS removes the effect of the finite illuminated surface length, under the tapered wave incidence. In this paper, our newly fast iterative approach is briefly reported. The electric field integral equations (EFIE) of the difference induced current oil the rough surface and the induced current oil the target are derived. An iterative approach is developed to solving the two EFIEs and scattering from both the target and underlying surface. How to choose the illuminated length of the rough surface for numerical iterations is discussed. Using the Monte Carlo method to realize the ocean-like rough surface, bistatic scatterings from the target, e.g. a cylinder or a square column, above a P-M (Pierson-Morkowitz spectrum) rough oceanic surface are numerically simulated for TE tapered wave incidence.