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NASA NTRS2020

Electromagnetic scattering by discrete random media illuminated by a Gaussian beam I: Derivation of the radiative transfer equation

In this paper we present the vector radiative transfer theory for a discrete random medium illuminated by a Gaussian beam. The analysis is based on a plane wave spectrum representation for a Gaussian beam and uses an approach developed previously for a discrete random medium illuminated by a plane electromagnetic wave. Specifically, we establish an integral representation for the coherent field, define an approximate coherent field that satisfies the differential equation fulfilled by the coherent field corresponding to a plane electromagnetic wave and matches the Gaussian beam at the interface of the particulate medium, and finally, derive the vector radiative transfer equation. For weakly focused Gaussian beams, the resulting equation is the traditional radiative transfer equation

Gaussian beam↗
NASA NTRS1976

Electromagnetic scattering from a spherical polydispersion of coated spheres

The volume averaged cross sections for extinction, scattering, absorption, and radiation pressure along with the elements of the phase matrix were computed for a spherical polydispersion of water coated carbon particles. The wavelength used was 4910 A. The thickness of the water coating was held constant over the polydispersion, while the ratio of core radius to total radius was varied, or the ratio was held constant over the polydispersion, while the thickness of the coating varied. The results show large differences in both the intensity and degree of polarization between dry and wet aerosols. Also interference phenomena can occur, which demonstrate that the assignment of an average refractive index to aerosols can be misleading and can lead to erroneous results.

Kattawar, G. W.↗
NASA NTRS1975

Lunar electromagnetic scattering. IV - Transfer functions in the long-wavelength limit

The theory for asymmetric lunar magnetic induction in the long-wavelength limit, applicable to induction in the solar wind and magnetosheath plasmas at frequencies no higher than about 0.01 Hz, is presented. The lunar response to arbitrary ambient field orientations can be synthesized from the responses to field fluctuations parallel and perpendicular to the cavity axis. Radial and tangential transfer functions for a particular lunar electrical conductivity model are shown as functions of frequency and angular distance from the cavity axis for parallel and perpendicular field directions. Transfer functions based on asymmetric theory are significantly different from those based on symmetric approximations. Conductivity profiles from inversions of a given data set are strongly dependent on the theory incorporated in the inversions, the nature of the driving field, and the assumed location of the observer. Thus lunar conductivity models from surface and orbital magnetometer data, obtained either on the dayside or the nightside of the moon, must be determined using asymmetric theory.

Schwartz, K.↗
NASA NTRS1979

Transform approach to electromagnetic scattering

In this paper, a comprehensive review of the Fourier transform technique as applied to the problem of high-frequency scattering is presented and the concepts of the spectral theory of diffraction (STD) are introduced. In contrast to the more commonly employed ray-optical method for high-frequency scattering, the STD approach interprets the scattered field as the spectrum, or the Fourier transform of the induced current on the scatterer. Such an interpretation offers several important advantages: uniform nature of representation, capacity to improve and extend the ray-optical formulas in a systematic manner, and convenient accuracy tests for the results. Methods for combining integral equation methods with the Galerkin procedure and asymptotic techniques in the transform domain are described, and representative examples illustrating the application of the spectral approach are included.

Mittra, R.↗
NASA NTRS1980

Electromagnetic scattering from two identical pseudospheres

In an attempt to gain some insight into the problem of how close particles have to be on the average before phase effects become important, the cross section and phase matrices for two identical particles as a function of the distance between their centers for both broadside and end-on illumination have been calculated. The point dipole approximation is employed to build two pseudospherical particles each consisting of 32 dipoles with an effective size parameter of 0.9283 and refractive index of 1.54-0.0i. In regard to cross sections, it is found that in certain cases several percent deviation from the converged value, which is twice the single particle cross section, could be found up to distances of separation of 25 single particle diameters. The maxima and minima in the cross section curves can be explained in terms of simple interference effects. Also the element P11 of the phase matrix showed a great deal of structure, and the position of maxima and minima could be explained by phase shift analysis.

Kattawar, G. W.↗
NASA NTRS1981

UTD analysis of electromagnetic scattering by flat structures

The different scattering mechanisms that contribute to the radar cross of finite flat plates were identified and analyzed. The geometrical theory of diffraction, the equivalent current and the corner diffraction are used for this study. A study of the cross polarized field for a monopole mounted on a plate is presented, using novel edge wave mechanism in the analysis. The results are compared with moment method solutions as well as measured data.

Sikta, F. A.↗
NASA NTRS1983

Analysis of regolith electromagnetic scattering as constrained by high resolution Earth-based measurements of the lunar microwave emission

When high resolution measurements of the phase variation of the lunar disk center brightness temperature revealed that in situ regolith electrical losses were larger than those measured on returned samples by a factor of 1.5 to 2.0 at centimeter wavelengths, the need for a refinement of the regolith model to include realistic treatment of scattering effects was identified. Two distinct scattering regimes are considered: vertial variations in dielectric constant and volume scattering due to subsurface rock fragments. Models of lunar regolith energy transport processes are now at the state for which a maximum scientific return could be realized from a lunar orbiter microwave mapping experiment. A detailed analysis, including the effects of scattering produced a set of nominal brightness temperature spectra for lunar equatorial regions, which can be used for mapping as a calibration reference for mapping variations in mineralogy and heat flow.

Keihm, S. J.↗
NASA NTRS1984

Numerical methods for analyzing electromagnetic scattering

The wave propagation inside a cylindrical waveguide, coated with lossy dielectric material due to the incidence of a plane wave at the open end of the guide, was studied. The general properties of the normal mode propagation were investigated.

Lo, Y. T.↗
NASA NTRS1984

Numerical methods for analyzing electromagnetic scattering

The wave attenuation in a cylindrical waveguide coated with lossy dielectric material was studied. The scope was extended to the high frequency case for calculating attenuation coefficients and propagation constants of a dielectric coated circular waveguide. The magnetic material coating was studied. At low frequency a one way 3dB attenuation was achieved within a longitudinal distance of one diameter. A software program was generated to plot the field patterns of the lowest 30 modes in the cylindrical waveguides.

Lee, S. W.↗
NASA NTRS1985

Numerical methods for analyzing electromagnetic scattering

Attenuation properties of the normal modes in an overmoded waveguide coated with a lossy material were analyzed. It is found that the low-order modes, can be significantly attenuated even with a thin layer of coating if the coating material is not too lossy. A thinner layer of coating is required for large attenuation of the low-order modes if the coating material is magnetic rather than dielectric. The Radar Cross Section (RCS) from an uncoated circular guide terminated by a perfect electric conductor was calculated and compared with available experimental data. It is confirmed that the interior irradiation contributes to the RCS. The equivalent-current method based on the geometrical theory of diffraction (GTD) was chosen for the calculation of the contribution from the rim diffraction. The RCS reduction from a coated circular guide terminated by a PEC are planned schemes for the experiments are included. The waveguide coated with a lossy magnetic material is suggested as a substitute for the corrugated waveguide.

Lee, S. W.↗
NASA NTRS1986

On the electromagnetic scattering from infinite rectangular grids with finite conductivity

A variety of methods can be used in constructing solutions to the problem of mesh scattering. However, each of these methods has certain drawbacks. The present paper is concerned with a new technique which is valid for all spacings. The new method involved, called the fast Fourier transform-conjugate gradient method (FFT-CGM), represents an iterative technique which employs the conjugate gradient method to improve upon each iterate, utilizing the fast Fourier transform. The FFT-CGM method provides a new accurate model which can be extended and applied to the more difficult problems of woven mesh surfaces. The formulation of the FFT-conjugate gradient method for aperture fields and current densities for a planar periodic structure is considered along with singular operators, the formulation of the FFT-CG method for thin wires with finite conductivity, and reflection coefficients.

Christodoulou, C. G.↗
NASA NTRS1986

Analysis and measurement of electromagnetic scattering by pyramidal and wedge absorbers

By modifying the reflection coefficients in the Uniform Geometrical Theory of Diffraction a solution that approximates the scattering from a dielectric wedge is found. This solution agrees closely with the exact solution of Rawlins which is only valid for a few minor cases. This modification is then applied to the corner diffraction coefficient and combined with an equivalent current and geometrical optics solutions to model scattering from pyramid and wedge absorbers. Measured results from 12 inch pyramid absorbers from 2 to 18 GHz are compared to calculations assuming the returns add incoherently and assuming the returns add coherently. The measured results tend to be between the two curves. Measured results from the 8 inch wedge absorber are also compared to calculations with the return being dominated by the wedge diffraction. The procedures for measuring and specifying absorber performance are discussed and calibration equations are derived to calculate a reflection coefficient or a reflectivity using a reference sphere. Shaping changes to the present absorber designs are introduced to improve performance based on both high and low frequency analysis. Some prototypes were built and tested.

Dewitt, B. T.↗
NASA NTRS1988

Electromagnetic scattering from a layer of finite length, randomly oriented, dielectric, circular cylinders over a rough interface with application to vegetation

A scattering model for defoliated vegetation is developed by treating a layer of defoliated vegetation as a collection of randomly oriented dielectric cylinders of finite length over an irregular ground surface. Both polarized and depolarized backscattering are computed and their behavior versus the volume fraction, the incidence angle, the frequency, the angular distribution and the cylinder size are illustrated. It is found that both the angular distribution and the cylinder size have significant effects on the backscattered signal. The present theory is compared with measurements from defoliated vegetations.

Karam, M. A.↗
NASA NTRS1988

The leaf-shape effect on electromagnetic scattering from vegetated media

Using the generalized Rayleigh Gans approximation along with the radiative transfer method, a bistatic backscattering model for a layer of randomly oriented, elliptic-shaped leaves is formulated. Following a similar procedure the bistatic scattering model for a layer of needle-shaped leaves is also developed to simulate coniferous vegetation. The differences between the scattering characteristics of the deciduous and coniferous leaves are illustrated numerically for different orientation and incidence angles. It is found that both like and cross polarizations are needed to differentiate the difference in scattering due to the shapes of the scatterers. The calculated backscattering coefficients are compared with measured values from artificial canopies with circular-shaped leaves.

Karam, M. A.↗
NASA NTRS1990

Electromagnetic scattering from two-dimensional thick material junctions

The problem of the plane wave diffraction is examined by an arbitrary symmetric two dimensional junction, where Generalized Impedance Boundary Conditions (GIBCs) and Generalized Sheet Transition Conditions (GSTCs) are employed to simulate the slabs. GIBCs and GSTCs are constructed for multilayer planar slabs of arbitrary thickness and the resulting GIBC/GSTC reflection coefficients are compared with exact counterparts to evaluate the GIBCs/GSTCs. The plane wave diffraction by a multilayer material slab recessed in a perfectly conducting ground plane is formulated and solved via the Generalized Scattering Matrix Formulation (GDMF) in conjunction with the dual integral equation approach. Various scattering patterns are computed and validated with exact results where possible. The diffraction by a material discontinuity in a thick dielectric/ferrite slab is considered by modelling the constituent slabs with GSTCs. A non-unique solution in terms of unknown constants is obtained, and these constants are evaluated for the recessed slab geometry by comparison with the solution obtained therein. Several other simplified cases are also presented and discussed. An eigenfunction expansion method is introduced to determine the unknown solution constants in the general case. This procedure is applied to the non-unique solution in terms of unknown constants; and scattering patterns are presented for various slab junctions and compared with alternative results where possible.

Ricoy, M. A.↗
NASA NTRS1990

The use of the FFT for the efficient solution of the problem of electromagnetic scattering by a body of revolution

The enhancement of the computational efficiency of the body of revolution (BOR) scattering problem is discused with a view to making it practical for solving large-body problems. The problem of EM scattering by a perfectly conducting BOR is considered, although the methods can be extended to multilayered dielectric bodies as well. Typically, the generation of the elements of the moment method matrix consumes a major portion of the computational time. It is shown how this time can be significantly reduced by manipulating the expression for the matrix elements to permit efficient FFT computation. A technique for extracting the singularity of the Green function that appears within the integrands of the matrix diagonal is also presented, further enhancing the usefulness of the FFT. The computation time can thus be improved by at least an order of magnitude for large bodies in comparison to that for previous algorithms.

Gedney, Stephen D.↗