Fast frequency sweep analysis of dielectric rough surface by Maehly approximation

ABSTRACTA generalized hybrid scheme combining finite element method (FEM) and the method of moments (MOM) is first presented to investigate scattering from a 3-D dielectric object above a 2-D dielectric rough surface. The hybrid FEM/MOM scheme is divided into the FEM region for the object based on Helmholtz’s equation and the MOM region for the rough surface based on coupled integral function, which can greatly reduce the computed region. With the rough surface getting larger, the unknowns of the rough surface get more. So MLFMA is employed to reduce computation complexity of MOM region itself and coupling interaction matrices between MOM region and FEM region. Consequently, the iterative process can be greatly accelerated. This generalized hybrid FEM/MOM is very suitable for investigating scattering from composite model of a complex material object and electrically large dielectric rough surface. Some examples verify this generalized hybrid FEM/MOM in high efficiency, low storage requirement, high precision and generality.

To study wave scattering from random lossy dielectric rough surfaces with large permittivities using the method of moments, a dense grid is needed for accurate results. A dense grid requires more CPU and memory. The physics‐based two‐grid (PBTG) method can reduce both CPU and memory requirements. In this paper, the PBTG is used in conjunction with the multilevel fast multipole method (FMM) to solve wave scattering from one‐dimensional random lossy dielectric rough surfaces. The proposed algorithm has the computational complexities of O(Ndg) for near‐field interactions and O(Ncg) for nonnear‐field interactions, where Ndg and Ncg are the number of sampling points on the dense and coarse grids, respectively. Using the proposed algorithm, wave scattering from Gaussian and non‐Gaussian rough surfaces is investigated and illustrated. Special emphasis is put on checking the accuracy of the algorithm and energy conservation.

Presents analytical expressions, based on the first- and second-order Kirchhoff approximations with shadowing corrections; and millimeter-wave experimental data for the angular correlation functions of electromagnetic waves scattered from two-dimensional, very rough, high-slope, metallic and dielectric surfaces. The angular correlation functions represent the correlation of the waves at different scattering angles for different incident angles at a given frequency. The angular correlations clearly show the "memory effects" and are used in the inverse problems of remote sensing of rough surface characteristics.

An efficient multiregion model is extended with the single integral equation (SIE) method to calculate the EM scattering from a dielectric rough surface. In the multiregion model, the rough surface is divided into multiple regions depending on their positions along the rough surface as well as the energy distribution of the incident wave. Two intermediate regions are chosen as the domain region on which the method of moment (MoM) is adopted. The mutual couplings between different regions are considered approximately based on the magnetic and field integral equations, from which closed-form approximations for electric current on other regions are derived.

In order to study light scattering from randomly rough surface, the linear filtering method is used to generate Gaussian randomly rough surface, and the method of moments is used to calculate the scattering light intensity distribution from perfect conduct and dielectric surfaces. The calculation results show that scattering characteristics between conductor and dielectric surfaces exist several significant differences: (1) the scattering peak value of perfectly conduct is larger than scattering peak value of dielectric on the same roughness; (2) the difference between s- and ppolarized scattering results are rather small in perfectly conduct randomly rough surfaces, while there is a obvious difference between s- and p-polarized scattering results in the condition of dielectric randomly rough surfaces; (3) though in both conditions of perfectly conduct and dielectric randomly rough surfaces, there is a shift from specular to backscattering direction when incident is p-polarized light, however, in dielectric randomly rough surface situation, the shift is much more obvious than in conduct situation.

The method of moments (MOM) in conjugation with the best uniform rational approximation is applied to predict the broad-band radar cross-section of arbitrarily shaped three-dimensional (3D) bodies. The surface integral equations are solved using MOM to obtain the equivalent surface currents at the frequency points corresponding to the Chebyshev nodes, and then the surface current within the given frequency band is represented by the Chebyshev series. To improve the accuracy, the Chebyshev series is matched via the Maehly approximation to a rational function, which can be as good as the best uniform rational approximation. Using the rational function, the surface current is obtained at any frequency point within the frequency band. Numerical results for 3D arbitrarily shaped perfectly electric conducting objects and homogenous dielectric bodies are considered. Compared with the asymptotic waveform evaluation technique and the model-based parameter estimation, the proposed technique is accurate in much broader frequency band with lower memory required.

An efficient iterative analytical-numerical method is proposed for three-dimensional (3D) electromagnetic scattering from an inhomogeneous object buried beneath a two-dimensional (2D) randomly dielectric rough surface. In the hybrid method, the electric and magnetic currents on the dielectric rough surface are obtained by current-based Kirchhoff approximation (KA), while the scattering from the inhomogeneous object is rigorously studied by finite element method (FEM) combined with the boundary integral method (BIM). The multiple interactions between the buried object and rough surface are taken into account by updating the electric and magnetic current densities on them. Several numerical simulations are considered to demonstrate the algorithm’s ability to deal with the scattering from the inhomogeneous target buried beneath a dielectric rough surface, and the effectiveness of our proposed method is also illustrated.

It has been known for several years that not only a rough metallic surface but also a rough dielectric surface can produce an enhanced backscattering peak. Due to the difficulty in fabricating one- or two-dimensional dielectric rough surfaces with a high index of refraction or a free-standing film, no experiments have been able to reveal such a peak in scattering from a dielectric rough surface. In this paper we present experimental results of the enhanced backscattering from a free-standing dielectric film and compare these with theoretical analysis. The vacuum/dielectric interface is one-dimensional, randomly rough, while the second dielectric/vacuum interface is approximately planer. The numerical simulations for a one- dimensional, randomly rough free-standing dielectric film reveal some important information about the main mechanism for the enhanced backscattering peak, primarily the presence of the flat dielectric/vacuum interface. We believe that the coherent addition from a given light path that interacts with the rough dielectric surface at two different points due to its reflection from the back surface and its time-reversed partner leads to an enhancement of the intensity of scattering into the retroreflection direction with respect to the intensity of scattering into other directions.

The analysis of the target’s broadband electromagnetic scattering characteristics plays an important role in radar stealth and recognition areas. The traditional method of moments (MoM) needs to calculate the currents at each frequency point when analyzing the target. With the increase of the target electrical size and complexity, the radar cross section (RCS) of the target changes drastically with frequency, it is necessary to calculate the accurate frequency response with a small frequency interval, which is very time-consuming in calculation and not feasible. This paper proposes to combine the subdomain method of moments (SMoM) with the Chebyshev approximation technique (CAT) to efficiently analyze the electromagnetic scattering of arbitrary shaped objects over a broad frequency band. In the SMoM technique, the whole object can be divided into several regions, each of which can be independently solved by the method of moments (MoM). The CAT technique is employed to expand the unknown current coefficients into a Chebyshev series for achieving fast frequency sweeping. Instead of direct point-by-point simulations, it is only necessary to calculate the currents by SMoM at several Chebyshev-Gauss frequency sample points. Furthermore, the Chebyshev series are matched via the Maehly approximation to a rational function to improve the accuracy. Numerical examples show that the hybrid technique can greatly reduce the computation time without loss of accuracy.

Compared with scattering from a rough surface only, composite scattering from a target above a rough surface has become so practical that it is a subject of great interest. At present, this problem has been solved by some numerical methods which will produce an enormous calculation amount. In order to overcome this shortcoming, the reciprocity theorem (RT) and the method of equivalent edge currents (MEC) are used in this paper. Due to the advantage of RT, the difficulty in computing the secondary scattered fields is reduced. Simultaneously, MEC, a high-frequency method with edge diffraction considered, is used to calculate the scattered field from the cone-cylinder target with a high accuracy and efficiency. The backscattered field and the polarization currents of the rough sea surface are evaluated by the Kirchhoff approximation (KA) method and physical optics (PO) method, respectively. The effects of the backscattering radar cross section (RCS) and the Doppler spectrum on the size of the target and the windspeed of the sea surface for different incident angles are analysed in detail.

Based on the polarimetric scattering model of second-order small-slope approximation (SSA-II) with tapered wave incidence for reducing the edge effect caused by limited surface size, monostatic and bistatic polarimetric scattering signatures of two-dimensional dielectric rough sea surface with a ship-induced Kelvin wake is investigated in detail by comparison with those of sea surface without ship wake. The emphasis of this paper is on an investigation of depolarized scattering and enhanced backscattering of sea surface with a ship wake that changes the sea surface geometric structure especially for low wind conditions. Numerical simulations show that in the plane of incidence rough sea surface scattering is dominated by copolarized scattering rather than cross-polarized scattering and that under low wind conditions a larger ship speed gives rise to stronger enhanced backscattering and enhanced depolarized scattering. For both monostatic and bistatic configuration, simulation results indicate that electromagnetic scattering signatures in the presence of a ship wake dramatically differ from those without ship wake, which may serve as a basis for the detection of ships in marine environment.

An approach is introduced for the non-parametric reconstruction of the statistical properties of penetrable, isotropic randomly rough surfaces from in-plane, co-polarized light scattering data. Starting from expressions within the Kirchhoff approximation for the light scattered diffusely by a two-dimensional randomly rough surface, an analytic expression for the normalized surface height correlation function is obtained as an integral over the in-plane and co-polarized scattering data with the introduction of only a couple of additional approximations. The inversion approach consists of two main steps. In the first step the surface roughness is estimated. Next, this value is used to obtain the functional form of the surface height correlation function without initially assuming any particular form for this function (non-parametric inversion). The input data used in validating this inversion approach consist of in-plane and co-polarized scattering data obtained for different forms of the correlation function by either computer simulations or by experiments for two-dimensional randomly rough dielectric or metallic surfaces. Good agreement was obtained between the correlation function and surface roughness obtained during the reconstruction and the corresponding quantities assumed when generating the input scattering data; this was the case for both dielectric and metallic surfaces, for both p- and s-polarized light, and for different polar angles of incidence. The proposed inversion approach provides an accurate, efficient, robust and contact-less method based on in-plane and co-polarized scattering data for the non-parametric characterization of the statistical properties of isotropic two-dimensional randomly rough dielectric and metallic surface.

Based on the Propagation-Inside-Layer Expansion (PILE) and Forward-Backward method (FBM), the composite scattering from the target below a dielectric rough soil surface using the extended PILE (EPILE) combined with the Forward-Backward method (FBM) is studied. The accuracy and e-ciency of the EPILE + FBM for this speciflc type of composite scattering is researched by comparing with the method of moments (MOM), the in∞uences of the target size, target depth, target horizontal distance, the rms height, the correlation length, the incident angle and the soil moisture content, etc., to the bistatic scattering coe-cient (BSC) are also investigated.

A numerical procedure for random generation of rough surfaces

Catastrophe theory interpretation of multiple peaks produced by light scattering from very rough dielectric surfaces