Large Scatterers Research Articles

A generalized method for two dimensional scattering problems under TE incidence with the use of spectral techniques

A new method for characterizing electrically large scatterers and solving the scattering of multiple objects in two dimensions for TE polarization of the incident field is presented. Large objects are divided into smaller ones. The method of moments and spectral techniques are used to compute a transference matrix for each single subscatterer, which relates the incident and scattered fields. Then, with the use of an iterative method for solving the interaction between all of them, the response for the whole system is obtained. This procedure is more efficient than the method of moments when applied to the scatterer considered as a single element. © 1996 John Wiley & Sons, Inc.

Light scattering by ellipsoids in a physical optics approximation

A physical optics approximation based on Presnel's laws is developed to calculate the intensity of light scattered by a three-axis ellipsoid of any orientation and any refractive index. Some results concerning totally reflecting spheres and dielectric spheroids are presented. An approach suitable for large scatterers is particularly good for small scattering angles. The angular intensities, i(1) and i(2), are then plotted versus θ for large axially oriented ellipsoids of various thicknesses. Theoretical small-angle light-scattering patterns are also presented and discussed. The data from one of them correspond to red cells in a shear flow.

Combining an extrapolation technique with the method of moments for solving large scattering problems involving bodies of revolution

The purpose of this work is to combine an extrapolation technique with the method of moments (MoM) to solve scattering problems involving large bodies. It has been shown in a previous work that the current induced on the smooth parts of large scatterers may be represented as a series of complex exponential functions with a few terms. Based on this concept, a hybrid set of basis functions is constructed using entire domain functions of complex exponential type on the smooth portion of the scatterer, complemented by subdomain basis functions near edges and discontinuities. An extrapolation procedure is developed in which the scattering problem is first solved for a portion of the scatterer using the conventional MoM. Next, a set of entire-domain basis functions, whose behaviour could be extrapolated with an increase in the size of the scatterer, is extracted from this original solution. The procedure outlined has the very desirable feature that the total number of basis functions remains unchanged even as the scatterer size is increased, allowing for large scatterers to be handled with a relatively small number of unknowns. The extrapolation technique is applied to scattering problems from bodies of revolution (BORs), and numerical results for an open cylinder and a barrel-shaped BOR are presented.

Efficient representation of induced currents on large scatterers using the generalized pencil of function method

It is shown that the currents induced over large and smooth scatterers can often be represented by a series of complex exponentials with only a few terms. The generalized pencil of function method is employed to extract these exponentials from the numerical solution of the scattering problem derived by using the method of moments. Illustrative examples include a partially-coated two-dimensional scatterer modeling a helicopter blade and the three-dimensional problem of scattering by a thin plate. The ultimate objective of this effort is to solve a class of large-body scattering problems, for arbitrary angles of incidence including the grazing angle, by utilizing the numerically-derived, complex exponential type of basis functions extrapolated to higher frequencies. It is well known that the physical optics approximation for the induced current becomes inaccurate when the angle of incidence is close to grazing, and the asymptotic methods, e.g., the GTD can become unwieldy for scatterers with edge treatments and those with complex geometrical shapes. The approach based upon the use of numerically derived entire domain basis functions on a portion of the body is proposed as a means to circumventing this difficulty.

Boundary conditions for finite element analysis combined with geometrical theory of diffraction

In this paper a method is presented to enforce boundary conditions for a Finite Element (FE) analysis when free space or large external scatterers are present. The equivalence theorem is used to divide the original problem into an internal and an external part via introduction of equivalent sources. FE analysis solves the internal problem with standard metallic or magnetic boundary conditions while an asymptotic method, here the uniform version of the Geometrical Theory of Diffraction (GTD), deals with the external scatterers. A time harmonic variation of the fields is assumed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A technique for solving 2D method‐of‐moments problems involving large scatterers

AbstractThe article demonstrates that a Method‐of‐Moments solution for large, smooth, two‐dimensional scatterers, requiring matrices that are several hundreds to several thousands in size, can be constructed efficiently by using a combination of transformations based upon FFT and partial QR decomposition of off‐diagonal blocks. The primary contribution of the article is to demonstrate that these techniques, applied in tandem, can typically reduce the active RAM requirements by a factor of 60‐100 for moderately large problems, and by as much as 225 (estimated) for matrix sizes around 100,000. It is also estimated that an effective flop rate of about 8‐35 N2 In N to 0.01N3 can be achieved via this transformation. The reduction factors for RAM requirements and the accuracy of the solution are demonstrated for the problem of a 2D elliptic cylinder with a large aspect ratio, requiring matrix sizes up to 10,000.

Solution of electrically large planar scattering problems using parallel computed method of moments technique

Parallel computations of an integral equation technique in conjunction with a Method of Moments (MoM) is introduced, in examining electromagnetic illumination of electrically large scatterers. To this end, the electromagnetic scattering of an incident wave illuminating an electrically large conducting rectangular plate of infinitesimal thickness is analyzed. An integral equation is derived in terms of the conductivity currents induced on the plate surface, which is solved by employing entire domain Galerkin technique, with Chebyshev type basis functions. The resulting algorithm parallelization enables extension of the proposed methodology above the resonance region. Numerical results are computed for several scatterer sizes and excitation source types, with significant near-linear speedups.

Multiwavelength three-dimensional scattering with dual-surface integral equations

We apply dual-surface integral equations, which have the same form as, and yet eliminate, the spurious solutions from conventional electric- and magnetic-field integral equations, to determine the scattering from multi-wavelength, three-dimensional perfect conductors. We determine accuracy by increasing the patch density and by comparisons with a high-frequency solution, a finite-difference time-domain solution, and measurements. Surface currents and scattered far fields computed with the dual-surface magnetic-field equation are displayed for perfectly conducting cubes 3 and 15 wavelengths on a side. Condition numbers and the number of iterations for convergence of the conjugate gradient method are shown to be linearly related to the electrical size of the scatterer. The logarithmic relationship between the number of iterations and the inverse of the residual error is also confirmed. For large scatterers the number of computer operations increases as the fifth power of electrical size; however, on massively parallel computers the run time increases only as the third power of the electrical size.

Multiple light scattering in a two-dimensional medium with large scatterers

A study is presented of the two-dimensional case of light propagation in a turbid medium involving sharply anisotropic one-center scattering in accordance with the Heney–Greenstein law, with strong absorption (when the photon absorption length is shorter than the transport length). An exact analytic solution that takes into account fluctuations of the photon paths is obtained within the framework of the small-angle approximation for the transfer equation in the case of a light beam normally incident upon the plane surface of the medium. The parameters of the radiation distribution (angular spectrum and attenuation coefficient) for the deep-propagating mode are analyzed in detail.

Intensity correlation in a disordered medium with large scatterers

We consider the long-range intensity correlation in a speckle pattern. We find an analytical solution for the intensity correlation function for the case of a plane wave propagation through a random slab with large scatters (their size a is much larger than the wavelength λ). Both single and multiple wave scattering are assumed to have a sharply anisotropic (small-angle) character. The qualitative differences between the intensity correlations in a disordered medium with purely elastic scattering and those in an absorbing medium are analyzed in detail.

Intensity fluctuations of light propagated in system of large scatterers. II. Multiple scattering

An equation is derived for the propagation of the autocorrelation function of radiant intensity in an optically thick layer of discrete scatterers with a prolate indicatrix. An effective method for its numerical solution is constructed. The autocorrelation function is computed for the light intensity in a medium containing large absorbing and scattering particles. Comparisons are made with known theoretical and experimental results.

Asymptotic expansion of morphological resonance frequencies in Mie scattering

A high-order asymptotic expansion for the size parameters x(n)((l)) of electromagnetic resonances of large spherical dielectric scatterers is reported. The expansion is calculated up to order n(-8/3), where n is the mode number and is valid for small orders l. Its accuracy is studied as a function of n, l, and the refractive index. For the l = 1 mode, the relative accuracy is better than 10(-4) for n > 50.

Intensity fluctuations of light propagating in system of large scatterers. I. Single scattering

An autocorrelation function for wave-field fluctuations detected by a square-law receiver behind a layer of large scatterers is found by means of nonclassical photometry in a single-scattering approximation.

Backscattering enhancement from a random distribution of large discrete spherical scatterers with a size distribution

We study backscattering enhancement from a sparse random distribution of large scatterers with a size distribution. Second-order multiple-scattering theory based on the Bethe–Salpeter equation is used to compute the scattered field. The second-order cyclical term is used to account for the enhancement. The effects of polarization are included by using the Mie theory to account for scattering by individual particles, and the result is then averaged over the size distribution. Comparisons are made with experimental data for the case of a slab medium of sparsely distributed dielectric spheres with average ka of 298 and moderate optical thickness. Agreement between theory and experiment is good for both the copolarized and the cross-polarized returns. The Mueller matrix is also derived, and the degree of polarization is computed for the same case. Results show that including the cyclical term reduces the degree of polarization of the computed backscattered return.

Extinction of visible and infrared beams by falling snow

Classical optics holds that the extinction cross of particles should be equal to twice their geometric cross section, in the limit where the particles are much larger than the wavelength. It follows that the extinction coefficient of such large scatterers should be independent of wavelength. Snowflakes are much larger than the wavelengths of visible and infrared radiation, yet many investigators have found that the visible and infrared extinction coefficient of falling snow measured with transmissometers is wavelength dependent. This dependency is known to be a result of the scattering contribution to the transmissometer signal. Furthermore, many measurements in the visible and infrared show that extinction values measured simultaneously with two transmissometers are linearly related up to at least 12 km(-1). The slope depends on the wavelengths and optical characteristics of the transmissometers. We show that for small values of extinction, the observations can be explained by taking into account single-scattering contributions to transmissometer signals. For high values of extinction, a multiplescattering model gives good agreement with measurements.

Coherent-backscatter effect: A vector formulation accounting for polarization and absorption effects and small or large scatterers.

Previous theoretical work on the coherent-backscatter effect in the context of speckle time autocorrelation has gone beyond the diffusion approximation and the assumption of isotropic (point) scatterers. This paper extends the theory to include the effects of polarization and absorption, and to give the angular line shape. The results are expressions for angular variations valid for small and large scatterers and linear and circular polarizations, in lossless or lossy media. Calculations show that multiple anisotropic scattering results in the preservation of incident polarization. Application to a problem in radar astronomy is considered. It is shown that the unusual radar measurements (high reflectivity and polarization ratios) of Jupiter's icy Galilean satellites can be explained by coherent backscatter from anisotropic (forward) scatterers.

Radar Cross-Sectional Spectra of Rotating Multiple Skew-Plated Metal Fan Blades by Physical Optics/Physical Theory of Diffraction, Equivalent Currents Approximation

The monostatic radar cross-sectional spectra of rotating multiple skew-plated metal fan blades are investigated. The theoretical treatment of such a slowly rotating and electrically large scatterer is based on the quasi-stationary method together with physical optics/physical theory of diffraction (PO/PTD) equivalent current techniques. Only the θθ polarization case is considered here, but the φφ polarization case can be treated in the same way. This solution is applicable to any observation angle, and is represented by such a general form as one which enables us to treat a similar scatterer with multiple blades and with different skew angles. Three rotating skew-plated blades are taken as an example, and the agreements between the theoretical and experimental results are satisfactory.

Efficient analysis of planar scattering problems with multiple excitations using equivalent incident currents

Large planar scatterers can be analyzed either by a direct moment method scheme, leading to block Toeplitz matrices for certain geometries, or via iterative techniques. In any case the physical optics component of the solution is readily known, hence the burden of its computation should be eliminated. An inherent separation between the physical optics and the remaining “fringe current” components is achieved by the use of the equivalent current representation of the incident fields. This representation has been beneficial in the recently introduced “add‐on” scheme, as well as other methods based on modular computations. In this work it is used to provide an extra degree of efficiency to the analysis of electromagnetic scattering problems from planar structures with many incident fields. The approach extends the capability of a recently introduced method whereby a class of incident electric fields is represented by a set of basis functions. Here the equivalent incident current is expanded into a set of basis functions restricted to a limited aperture region only, facilitating the computation of the fringe current only. The response to any incident field is synthesized subsequently from the responses to these excitations. This results in a stable scheme which can efficiently treat large problems with many excitations.

Current-based hybrid analysis for surface-wave effects on large scatterers

Current-based hybrid analyses combine the method of moments (MM) with Ansatz currents derived from high-frequency methods such as physical optics, physical theory of diffraction (PTD), geometric theory of diffraction (GTD), and the Fock theory. The author introduces an analysis that incorporates a surface-wave basis set into the hybrid formulation. This approach substantially improves the modeling of nonspecular effects caused by surface waves. The discussion emphasizes the accurate representation of surface wave currents and the reduction of computational efforts in comparison with the conventional MM techniques. Scattering calculations for bodies of revolution (BORs) and two dimensional surfaces demonstrate the effectiveness of the analysis presented for large scatterers. >

Application of the fast recursive algorithm to a large inhomogeneous scatterer for TM polarization

AbstractA fast recursive algorithm has been developed to solve for the scattering solution of a large 2‐D inhomogeneous body for TM waves. The inhomogeneous body is first divided into N subscatterers. The algorithm uses an aggregate T̄ matrix and translation formulas to solve for the solution of n + 1 subscatterers from the solution for n subscatterers. The computational complexity of the algorithm is of O(NMP2), where NM is the number of unknowns and P is the number of harmonies required in the translation formulas. The memory requirement is proportional to the number of unknowns. The algorithm has been used to solve for the scattering solution of a 10‐λ‐diameter two‐dimensional scatterer with about 12,000 unknowns, taking about 30 s on a CRAY‐2 supercomputer.