Backscattering Matrix Research Articles

TRANSPORT PROPERTIES AND SUPERCONDUCTIVITY IN PRESENCE OF BACKSCATTERING

We achieve an exact evaluation of the Kubo formula for electrical resistivity, within a model in which random impurity scattering is parametrized by random back-scattering matrix elements. If the alloy is a superconductor, our theory allows us to correlate T c with the normal-phase resistivity. The results are in nice agreement with experiment.

Determination of the characteristic polarization states of the radar target scattering matrix [S(AB)] for the coherent monostatic and reciprocal propagation space by using the complex polarization ratio ρ transformation formulation

We consider a problem originating in radar polarimetry for which the radar target is to be characterized by the properties of its coherent polarization state, given complete coherent backscattering matrix data sets at one frequency and for one target aspect angle. First, the Jones vector formalism for the coherent monostatic case and Sinclair’s backscattering matrix [S(AB)] for the general polarization basis (AB) are introduced. Using the unitary change of polarization state transformation, we present the concept of the characteristic polarization states of a scatterer, which was introduced by Kennaugh and Huynen. The generalized unitary transformation matrix formulation under the change-of-basis transformation, expressed in terms of the generalized polarization ratio ρ(AB), is developed for emphasizing the unique properties of the interrelation among the existing characteristic polarization states. For the monostatic reciprocal case (SAB = SBA) treated here, it is shown that there exist in total five pairs of characteristic polarization states: the orthogonal cross-polarization null and the copolarization maximum-state pairs, which are identical and share one main circle with the copolarization null and the orthogonal cross-polarization maximum-state pairs, the latter being at right angles to the cross-polarization null pairs; and a newly identified pair, the orthogonal cross-polarization saddle-point extrema that are normal to the plane (main circle) spanned by the other four pairs. With this complete and unique mathematical description of Huynen’s polarization fork concept, it is possible to study the problem of polarimetric radar target optimization more rigorously. Various examples are provided and interpreted by comparing the unique result with the results of previous incomplete analyses. In conclusion, the relevance of these canonical results to optical polarimetry are highlighted and interpreted.

Backscattering matrix of dielectric objects at 9.6 GHz

Results are presented from measurements of the backscatter matrix, including phase, at 9.6 GHz. The measured targets include dielectric spheroids with dimensions in the resonance region. Comparison with theoretical calculations based on the Fredholm integral equation approach shows good agreement, thus giving confidence in the results. Some new effects noted at resonance are described.

Electromagnetic Scattering from Dielectric Bodies of Revolution: Theoretical and Experimental Results

ABSTRACT The scattering of electromagnetic waves from axisymmetric bodies of lossy dielectric in the resonance region is considered. A theoretical formulation to the problem is used in terms of equivalent currents on the surface of the scatterer, leading to a set of surface integral equations which are solved numerically using the method of moments. The excitation is considered to be a circularly polarized plane wave at oblique incidence. Various sizes and shapes are considered which simulate ice, and for which experimental results of the backscattering matrix elements are available. The measurements and the computations are carried out at two different frequencies, 2.86 GHz and 9.6 GHz. Very good agreement between the numerical results and the experimental data is obtained for the backscattering direction. The numerical results of the forward scattering are also calculated and presented.

A practical method for determining backscattering factors and matrix correction in quantitative aes analysis of binary alloys

AbstractThe composition‐dependent backscattering factor in quantitative AES analysis is investigated by comparing experimental results from different approaches with several theoretical methods. Backscattering factor ratios are presented as a function of the composition of homogeneous CuPd alloys cleaned in situ by scribing. The values were calculated in a simple way by the proposed approximation method which takes into account the importance of the primary electron incident angle. This approach can be recommended for practical use in determining matrix correction. Application of the approximation method for matrix correction to different binary alloy systems gives a better agreement with the experimental matrix correction factor than Reuter's backscattering factor equation. Matrix correction factors for binary alloys were evaluated by a simple equation considering the weak linear composition dependence which was found experimentally. With matrix correction the accuracy of quantitative AES analysis can be improved by 5% or more as was shown for the CuPd alloys.

Microphysical Interpretation of Multi-Parameter Radar Measurements in Rain. Part I: Interpretation of Polarization Measurements and Estimation of Raindrop Shapes

The backscattered electric field received by a radar is related to the transmitted field by a backscatter matrix. In the case of single raindrops the elements in this matrix are determined by raindrop size and shape. At long radar wavelength certain combinations of elements, however, only depend on raindrop shape. These combinations form the basis of current linear and circular polarization measurables. An ensemble of raindrops will usually exhibit a variety of shapes because of the variation in raindrop size and because of oscillations induced by drop oscillations. This shape variation can be described by an axis ratio distribution. Since at long wavelengths in rain the radar polarization measurables are largely determined by shape, they are sensitive to this axis ratio distribution. In this study, the sensitivity of some linear and circular polarization measurables to the mean and variance of the raindrop axis ratio distribution is investigated. These measurables are then used to formulate estimators of radar-power-weighted mean axis ratio and variance. These estimators appear to be applicable to a wide variety of drop size distributions.

Measurements of the backscatter matrix of dielectric bodies

Results are presented from the measurement of the backscatter matrix of dielectric bodies, \epsilon \approx 3.2 , having moderate eccentricity. Included are prolate and oblate spheroids of axial ratio 0.2 and rods and disks of axial ratios 0.1, 0.2, and 0.4. Measurements were made at 2.86 GHz with the maximum dimension of the samples varying from 0.242\lambda to 1.212\lambda where \lambda is the wavelength.

The Backscatter Matrix of Ice Samples: Its Relation to the Identification of Hail by Radar

Measurements of the backscatter matrix, including phase, have been made at 2.86 GHz on blocks of ice intended to approximate oblate and prolate spheroids with axial ratios of 0.6 and 0.8. For 2.5<ka<4.5 respective cancellation ratios in the order of 0 and 5 dB were obtained compared with Rayleigh values of 19 and 25 dB. The relevance of these and other polarization characteristics for the identification of hail is considered with examples from Ku-band radar observations.

Measurements of the backscatter matrix of dielectric spheroids

Measurements at 2.86 GHz of the backscatter matrix of 57 spheroidal samples at all aspect angles in the low-resonance region are presented. Sample size ranges up to ka = 3.4 , and axial ratios of 0.5, 0.6, and 0.8 have been used. Dielectric constants include 2.6, 3.3, and 6.5. The presentation is in terms of circular polarization, but the results are readily convertible to linear (or any other) polarization.

Low-energy electron diffraction intensities from the clean nickel (001) surface

Experimental absolute intensity curves, I h,k , of the 00, 11 and 20 diffraction beams from a nickel (001) surface have been obtained at normal incidence for incident electron energies 0–175 eV. Results for the 00 beam are given for energies to 600 eV at 3° angle of incidence. A comparison with the corresponding copper results shows that the nickel intensities in general are higher, which at energies above 200 eV can be accounted for by the different Debye-Waller factors. At the lowest energies it seems necessary to assume that the atomic scattering strength is larger for nickel than for copper. The structure in the intensity curves from the two materials shows expected but not trivial close correspondence. Lattice spacings normal to the surface, determined from integer order peaks in I 00, were found to be 3.51 ± 0.02 Å and 3.62 ± 0.02 Å for nickel and copper respectively. These figures agree well with the accepted bulk values but they reflect the spacings in the surface region, as the electron penetration is small due to strong absorption. A small change in the spacing between the two outermost layers may not, however, be revealed, as the contribution from the surface layer to I 00 is greatly reduced by the excess vibrational amplitude of the surface atoms along the surface normal. Special attention is given to the nickel intensities in the energy region 0–175 eV where strong multiple scattering gives rise to a rich structure with intense noninteger order peaks and asymmetrical peaks. In spite of the strong interaction the scattering events associated with the peaks can be inferred from the free electron band structure with remarkable success. Thus are the noninteger order peaks 1 1 2 , 2 1 2 , 2 7 10 , 3 1 6 , 3 1 3 and 3 1 2 in I 00 identified. The deviations in energy the free electron values of the integer order peaks in I 00, I 11 and I 20 are found to be considerably larger than Pendry's calculated inner potential for nickel but show a similar energy dependence. The damping rate, due to inelastic electron-electron collisions, was inferred from the peak widths and used to estimate “effective” back-scattering matrix elements in a two-beam approximation. For the integer order peaks 2 and 3 the elements are 1 eV and 2 eV respectively, somewhat larger than expected from Pendry's calculation for the nickel (111) surface.