Electromagnetic scattering by rough conducting circular cylinders.II. Axial corrugation

For pt.I see ibid., vol.36, no.5, p.651 (1988). The coherent and incoherent responses of conducting axially corrugated surfaces (which are on the average circular cylinders) are calculated. The calculation encompasses second-order perturbation. The general approach used is to apply the extinction theorem to write an integral equation for the surface current density, and then to use the perturbation theory to solve it. The results are recast by using Pade approximants to achieve a significant extension of the domain of validity of the original formulation     

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     

粗糙金属和介质目标的太赫兹散射特性分析

太赫兹频段金属和介质粗糙目标的散射特性是研究太赫兹雷达目标特性的重要基础。当目标表面的主曲率半径远远大于入射波长,且粗糙表面高度起伏与斜率起伏远小于入射波长时,根据稳定相位法和标量近似法,可获得粗糙金属和介质目标的相干散射截面和非相干散射截面。基于稳定相位法,任意目标的相干散射截面可退化为粗糙导体、光滑介质和粗糙介质目标的相干散射。该文分析了电大尺寸光滑金属铝和介质白漆球的散射截面,与Mie理论计算的介质球的散射特性吻合,散射截面误差小于0.1 dBm2。采用朗伯定理,验证了粗糙介质球的太赫兹非相干散射精确解,当目标表面剖分精度越高,非相干散射的计算精度越高。该文数值计算了粗糙介质球的太赫兹相干和非相干散射特性,分析了表面粗糙度和表面材料对散射特性的影响,为电大尺寸空间目标太赫兹散射特性分析提供了理论基础。      

Gaussian rough surfaces and Kirchhoff approximation

Electromagnetic scattering is often solved by applying the Kirchhoff approximation to the Stratton-Chu scattering integral. In the case of rough surfaces, it is usually assumed that this is possible if the incident electromagnetic wavelength is small compared to the mean radius of curvature of the surface. Accordingly, evaluation of the latter is an important issue. This paper generalizes the groundwork of Papa and Lemon (see ibid., vol.36, p.647-50, May 1988) by computing the mean radius of curvature for Gaussian rough surfaces with no restriction on its correlation function. This is an interesting extension relevant to a variety of natural surfaces. Relations between the surface parameters and the mean radius of curvature are determined and particular attention is paid to the relevant small slope regime     

A combined steepest descent-fast multipole algorithm for the fastanalysis of three-dimensional scattering by rough surfaces

A new technique, the steepest descent-fast multipole method (SDFMM), is developed to efficiently analyze scattering from perfectly conducting random rough surfaces. Unlike other prevailing methods, this algorithm has linear computational complexity and memory requirements, making it a suitable candidate for analyzing scattering from large rough surfaces as well as for carrying out Monte Carlo simulations. The method exploits the quasiplanar nature of rough surfaces to efficiently evaluate the dyadic Green's function for multiple source and observation points. This is achieved through a combination of a Sommerfeld steepest descent integral and a multilevel fast multipole-like algorithm based on inhomogeneous plane wave expansions. The fast evaluation of the dyadic Green's function dramatically speeds up the iterative solution of the integral equation for rough surface scattering. Several numerical examples are presented to demonstrate the efficacy and accuracy of the method in analyzing scattering from extremely large finite rough surfaces     

An approach to include stochastic rough surface scattering into deterministic ray-optical wave propagation modeling

A new method to include stochastic rough surface scattering into deterministic ray-optical wave propagation modeling is derived. It can be utilized in conjunction with the concept of ray launching. Similar to the Kirchoff formulations, the approach is based on a tangential plane approximation, i.e., it is applicable to surfaces with gentle undulations, whose horizontal dimensions are large compared to the incident wavelength. However, in contrast to the Kirchoff models, which are only valid for either slightly rough or very rough surfaces, the proposed stochastic scattering approach includes both the coherent and incoherent components at the same time. The purely deterministic ray-based modeling is expanded by a "stochastic" component, allowing, for the first time, to account for nondeterministic scattering in ray-optical wave propagation modeling.     

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     

A stable integral equation for electromagnetic scattering fromhomogeneous dielectric bodies

It is shown that a previously derived integral equation for electromagnetic scattering from a homogeneous dielectric body (see ibid., vol.AP-32, p.166-172, Feb. 1984) does not have a unique solution at resonant frequencies of the cavity formed by making the surface S of the body perfectly conducting and filling the region internal to S with the external medium. This integral equation was formulated so that an equivalent electric current radiates in the presence of the homogeneous external medium to produce the scattered field external to the body. A combination of equivalent electric and magnetic currents is used to formulate an integral equation whose solution is always unique     

On the canonical grid method for two-dimensional scatteringproblems

The banded matrix iterative approach with a canonical grid expansion (BMIA/CAG) has been shown by Tsang et al. (see ibid., vol.43, p.851-9, 1995) to be an efficient method for the calculation of scattering for near planar two-dimensional (2-D) geometries such as one-dimensional rough surfaces. However, in the article of Tsang et. al, only the first three terms in the canonical grid series for TE polarization above a perfectly conducting surface were discussed and methods for implementing only a portion of these terms were presented. In this paper, a general form for all terms in the canonical grid series is provided for both TE and TM polarizations above an impedance surface and an efficient algorithm for calculating their contributions is described. The relationship between the canonical grid and operator expansion methods is also discussed. A sample surface scattering problem is shown to illustrate the utility of higher order terms in the canonical grid method     

Monte-Carlo simulations of large-scale problems of random roughsurface scattering and applications to grazing incidence with theBMIA/canonical grid method

Scattering of a TE incident wave from a perfectly conducting one-dimensional random rough surface is studied with the banded matrix iterative approach/canonical grid (BMIA/CAG) method. The BMIA/CAG is an improvement over the previous BMIA. The key idea of BMIA/CAG is that outside the near-field interaction, the rest of the interactions can be translated to a canonical grid by Taylor series expansion. The use of a flat surface as a canonical grid for a rough surface facilitates the use of the fast Fourier transform for nonnear field interaction. The method can be used for Monte-Carlo simulations of random rough surface problems with a large surface length including all the coherent wave interactions within the entire surface. We illustrate results up to a surface length of 2500 wavelengths with 25000 surface unknowns. The method is also applied to study scattering from random rough surfaces at near-grazing incidence. The numerical examples illustrate the importance of using a large surface length for some backscattering problems     

On the far-field approximation for scattering from randomly rough surfaces

Various authors have justified the far-fields approximation for rough surface scattering using one of the classical approximations for the scattered fields, usually considering either the coherent scattered field or the incoherent scattered intensity. An exact expression for the field scattered from a perfectly conducting rough surface is considered. The expression for the incoherent scattered intensity is formally derived, and a condition under which the far-field approximation is valid is found, independent of specific approximations for the surface or scattered fields or for the surface height statistics. The condition so derived is, under many circumstances, substantially less restrictive than that derived before in the general case. Furthermore, the previous results may be easily recovered by further specialization of our result.     

Guidance of waves by a moving unidirectionally conducting screen

The scattering problem for a moving, unidirectionally conducting screen excited by a conical wave is analyzed using the exact relativistic integral representation previously derived by the author (see ibid., vol.37, no.1, p.64-70, Jan. 1989). The screen is in uniform motion in its own plane and in a direction perpendicular to that of conduction. The screen is found to respond with a conical scattered field and a certain type of surface waves which are of a different nature from that which a stationary screen allows. An equivalent image source is found, and low-velocity effects are show explicitly     

Comments on “The EM field of an improved lightning returnstroke representation”

V. Amoruso and F. Lattarudo (see ibid., vol.35, p.317-28, Aug. 1993) claim to produce valid field expressions, on the surface of a finitely conducting Earth, for a lightning return stroke using a TL (transmission line) representation for the current. The present author comments on their surface field calculation. His main concern is how they approximate the exact vector potential in the form they quote from his book (Wait 1962). Since their subsequent development is based on these approximated near- and far-field forms, it is important that the matter be clarified     

Scattering, transmission, and absorption by a rough resistive sheet - E polarization

Motivated by the use of thin conducting textiles in absorbers, the interaction of electromagnetic waves with a rough resistive sheet is examined. Expressions for the fields above and below the sheet are derived in terms of an equivalent current using Gaussian beam illumination. These field expressions are then used with equations derived from the conservation of energy to find the distribution of scattered, transmitted, and absorbed power using an exact numerical solution and the Kirchhoff approximation. As a consequence of the lack of refraction, the Kirchhoff single scattering solution produces strong coherent transmitted intensities at the forward angles with an attendant minimum in the incoherent intensity. A second minimum in the incoherent intensity is observed in the antispecular direction. Fields arising from multiple scattering interactions are observed independent of the Kirchhoff single scatter contributions at these angles for surfaces of large root-mean-square slope. An increase in the absorption in the sheet is also observed as surface roughness is increased. The increase in absorption is believed due to multiple scattering interactions on the surface.     

Scattering from non-Gaussian randomly rough surfaces-cylindricalcase

A numerical method is developed to simulate electromagnetic wave scattering from computer-generated two-dimensional randomly rough surfaces. The rough surface generated for scattering simulation is specified only up to the second moment statistics, i.e. the height distribution and the autocorrelation function. The coherent and noncoherent scattering from four different types of random surfaces is examined. The four different types of surfaces are: Gaussian distributed heights and Gaussian correlation, Gaussian distributed height and non-Gaussian correlation, modified exponential distributed height and non-Gaussian correlation, modified exponential distributed height and Gaussian correlation, modified exponential distributed height and non-Gaussian correlation surfaces. It is shown by simulation that the dominating factor in coherent scattering is the surface height density and the autocorrelation can cause a higher order effect     

On the control of edge diffraction in numerical rough surface scattering using resistive tapering

The use of resistive loading to remove edge effects in electromagnetic scattering from rough surfaces with finite conductivity has been considered. An electric field integral equation formulation using impedance boundary conditions was implemented to model the conductivity of sea water at X band. The resistive loading was added over surface sections within three wavelengths of the modeled edges. A resistive taper synthesized to control the sidelobe level in scattering from flat, perfectly conducting plates proved better able to reduce edge diffraction than a power-law taper of a type that is often used. The calculated scattering from test profiles that model breaking water waves using the resistive loading show good agreement with those found using a reference scattering approach provided that the local grazing angle on the loaded surface section is greater than 20/spl deg/.     

Coherent scattering of a spherical wave from an irregular surface

The scattering of a spherical wave from a rough surface using the Kirchhoff approximation is considered. An expression representing the measured coherent scattering coefficient is derived. It is shown that the sphericity of the wavefront and the antenna pattern can become an important factor in the interpretation of ground-based measurements. The condition under which the coherent scattering-coefficient expression reduces to that corresponding to a plane wave incidence is given. The condition under which the result reduces to the standard image solution is also derived. In general, the consideration of antenna pattern and sphericity is unimportant unless the surface-height standard deviation is small, i.e., unless the coherent scattering component is significant. An application of the derived coherent backscattering coefficient together with the existing incoherent scattering coefficient to interpret measurements from concrete and asphalt surfaces is shown.     

Electromagnetic scattering from grassland. II. Measurement andmodeling results

For pt.I see ibid., vol.38, no.1, p.339-48 (2000). The validity of a coherent, grassland scattering model is determined by comparing the model predictions with direct measurements of a representative grass canopy. A wheat field was selected as the test target, and polarimetric, multifrequency backscattering data were collected over an entire growing season, along with a complete set of ground-truth data. The L-band measured data demonstrated a strong dependence on azimuthal look direction in relation to the row direction of the wheat. The C-band measurements likewise showed an interesting backscattering response, wherein σ_νν⁰ actually increased with incidence angle for many cases. The coherent scattering model provides backscattering data that match and predict these measured data and most of the other measured data well. The model shows that at L-band, the incoherent scattering power alone is insufficient for predicting the measured results, as the coherent terms can dominate the total scattered energy. Additionally, the model, which accounts for this nonuniform illumination of the wheat elements, demonstrates the peculiar data observed for C-band. Likewise, it is demonstrated that the fidelity used to model grass constituents (e.g., curvature) is required to match the scattering measurements accurately     

Electromagnetic scattering and radiation by surfaces of arbitraryshape in layered media. II. Implementation and results for contiguoushalf-spaces

For pt.I see ibid., vol.38, no.3, p.335-44 (1990). In pt.I, three mixed-potential electric field integral equations (MPIEs) for conducting surfaces of arbitrary shape residing in plane-stratified dielectric media with an arbitrary number of layers were formulated. One of the MPIEs (formulation C) was found to be particularly well suited for the application of the method of moments (MM). In pt.II, formulation C is specialized to the important case of a scatterer or antenna of arbitrary shape residing in contiguous half-spaces. This MPIE is solved by the MM employing a triangle-patch model of the surface of the object. Sample numerical results for several cases of interest are presented     

Comments on “Scattering from conducting rough surfaces: ageneral perturbative solution” [and reply]

The author comments that Vazouras et al. (see ibid. vol.41, no.9, p.1232-1241, 1993) presented an analysis leading to the general term of the perturbation series for scattering of horizontally polarized plane incident waves from a perfectly conducting rough surface. Other than Rice's 1951 seminal paper, they mention none of the other early work on this topic. Beyond this lack of references to other than the most recent work, however, Vazouras et al. state, "thus it seems that the scope of perturbation methods is considerably restricted by the fact that the general term of the perturbation series was, until recently, unknown." I (see RadioSci., vol.12, no. 5, p.719-729, 1977) was the first to derive the general term of a perturbation series for electromagnetic scattering from a rough surface. Vazouras et al. reply that the criterion for the selection of previous work cited in our paper was one of topic relevance rather than of chronological order. In view of the large amount of literature pertinent to the region of interest, we chose to mention mainly works dealing with the foundation of the particular class of perturbation solutions developed within the framework of the extended boundary condition, thus being important to the course of our treatment, plus some works the results of which we were explicitly commenting