Extinction Matrices Research Articles

Polarized extinction properties of plates with large aspect ratios

The extinction matrices for both infinite-radius plates and finite-size particles are derived by assuming the far-field scattered waves to be either plane waves or spherical waves, and the connection between the two formalisms is discussed. In both cases, the elements of the extinction matrix are compared numerically for various incident angles and size parameters. Agreement is found between the results for the infinite-radius plates and plates with large aspect ratios and small incident angles. The differences between the two treatments provide insight into the understanding of the extinction properties of non-spherical particles illuminated by polarized incident light.

Electromagnetic scattering by a fixed finite object embedded in an absorbing medium

This paper presents a general and systematic analysis of the problem of electromagnetic scattering by an arbitrary finite fixed object embedded in an absorbing, homogeneous, isotropic, and unbounded medium. The volume integral equation is used to derive generalized formulas of the far-field approximation. The latter serve to introduce direct optical observables such as the phase and extinction matrices. The differences between the generalized equations and their counterparts describing electromagnetic scattering by an object embedded in a non-absorbing medium are discussed.

Radar and scattering parameters through falling hydrometeors with axisymmetric shapes

Falling raindrops and other hydrometeors have, in general, nonspherical shapes and mean canting angles that are due to aerodynamic and gravitational forces. We use the T matrix and the quantum theory of angular momentum to compute extinction matrices, scattering and absorption cross sections, backscattering matrices, and, from these quantities, radar parameters. A monodisperse population of rain with axially symmetric distribution over orientations where the axis of symmetry is the local direction of air flow about the raindrops is considered. Oblate spheroids with axial ratios that depend on size and appropriate series of Chebyshev polynomials were assumed for definition of the shapes of raindrops. Computations were performed at common microwave frequencies for several temperatures, incidence angles, and degrees of particle wobble about a preferred orientation. Results reveal the importance of the role of orientation distribution and particle size and the shape of radar parameters in these computations for a region of moderate-sized raindrops.

Modeling and measurements of scattering from road surfaces at millimeter-wave frequencies

Millimeter-wave radar-based sensors are being considered for a number of automotive applications including obstacle detection and collision warning, true-speed, and road-surface recognition. The interaction of electromagnetic waves with asphalt road surfaces, possibly covered with ice or water, at millimeter-wave frequencies is studied. First, an experimental procedure for determining the effective dielectric constant of bituminous mixtures used in road-surface constructions is developed. In this procedure, the effective dielectric constant is derived using a simple inverse-scattering algorithm to the measured radar cross sections of cylindrical specimen of a standard asphalt mixture. Then the vector radiative transfer equation is used to formulate the scattering from a multilayer medium representing an ice- or water-covered asphalt surface. The University of Michigan polarimetric 94-GHz radar system was deployed for characterizing the polarimetric backscatter responses of asphalt surfaces under many physical conditions near grazing incidence angles (70/spl deg/-88/spl deg/). The measured backscatter coefficients and parameters of copolarized phase difference statistics of a dry asphalt surface with smooth interface at one incidence angle were used to derive the phase and extinction matrices of the asphalt medium. The experimentally determined phase and extinction matrices are substituted in the radiative transfer formulation to predict the scattering from asphalt surfaces under all conditions. Excellent agreement between theoretical predictions and measured quantities is obtained.

A microwave polarimetric scattering model for forest canopies based on vector radiative transfer theory

A microwave polarimetric scattering model for a forest canopy is developed based on the iterative solution of the vector radiative transfer equations up to the second order. The forest canopy constituents (branches, leaves, stems, and trunks) are embedded in a multi-layered medium over a rough interface. The branches, stems, and trunks are modeled as finite randomly oriented cylinders. Deciduous leaves are modeled as randomly oriented discs and coniferous leaves are modeled as randomly oriented needles. The vector radiative transfer equations contain non-diagonal extinction matrices that account for the difference in propagation constants and the attenuation rates between the vertical and horizontal polarizations. For a plane wave exciting the canopy, the average Mueller matrix is formulated, and then used to determine the linearly polarized backscattering coefficients including both the copolarized and cross-polarized power returns. Comparisons of the model with measurements from Les Landes Forest of France showed good agreements over a wide frequency band and gave a quantitative understanding of the relation between the backscattering coefficients and the age of the trees in the forest and forest biomass.

Modified Radiative Transfer Theory for a Two-Layer Anisotropic Random Medium

The modified radiative transfer (MRT) equations which describe propagation and scattering of the electromagnetic field intensity in a layered anisotropic random medium are derived from the Bethe-Salpeter equation with the ladder approximation and the Dyson equation with the nonlinear approximation. The extinction matrices and scattering phase matrices for both mean and incoherent field intensities are obtained. Backscattering enhancement is observed due to the spatial coherent effect between upward and downward propagating waves. It also occurs for the half-space case, because of coupling between ordinary and extraordinary waves. The depolarization effect is predicted in the first-order renormalization approximation to the MRT equation.