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Entirely rigorous proofs of the symmetries induced by the phase matrix into the reflection and transmission operators used in the matrix operator theory are given. Results are obtained for multiple scattering in both homogeneous and inhomogeneous atmospheres. These results will be useful to researchers using the method since large savings in computer time and storage are obtainable.
S matrix elements for diatomic molecule rotational excitation by scattered atom computed by Amplitude Density Functions method
- Combined lidar and polarimeter retrievals of aerosol, cloud and ocean microphysical properties involve single scattering cloud calculations that are time consuming. - We create a look-up table to speed up calculations for water droplets in the atmosphere. The gained increase in computational efficiency is up to 10^(4). - In our new Lorenz-Mie look-up table we tabulate the light scattering by an ensemble of homogeneous isotropic spheres at wavelengths starting from 0.35 µm. - The look-up table covers liquid water cloud particles with radii in the range of 0.001—500 µm. - The covered complex refractive indices range from 1.25 to 1.36 for the real part and from 0 to 0.001 for the imaginary part. - Using look-up table, we can precisely compute inherent optical properties for the particle size distributions ranging up to 100 µm for the effective radius and up to 0.6 for the effective variance. - We test wavelengths from 0.35 to 2.3 µm and find that the P12 element of the normalized scattering matrix is precise to within 1% for 96.7% of cases; the absorption and backscatter coefficients, and lidar ratio are precise to within 1% for 99% of cases; the P11 , P33 and P34 elements of the normalized scattering matrix, the asymmetry parameter, the extinction and scattering coefficients are precise to within 1% for all cases. - We provide an example of using the look-up table with in situ measurements to determine agreement with remote sensing. - The look-up table along with examples of its use soon will be freely available at https://science.larc.nasa.gov/polarimetry
The Stokes scattering operator is noted to be the most useful characterization of incoherent scattering in radar imaging; the polarization that would yield an optimum amount of power received from the scatterer is obtained by assuming a knowledge of the Stokes scattering operator instead of the 2x2 scattering matrix with complex elements. It is thereby possible to find the optimum polarizations for the case in which the scatterers can only be fully characterized by their Stokes scattering operator, and the case in which the scatterer can be fully characterized by the complex 2x2 scattering matrix. It is shown that the optimum polarizations reported in the literature form the solution for a subset of a more general class of problems, so that six optimum polarizations can exist for incoherent scattering.
A general technique to characterize asymmetric coplanar waveguide (CPW) discontinuities with air bridges where both the fundamental coplanar and slotline modes may be excited together is presented. First, the CPW discontinuity without air bridges is analyzed using the space-domain integral equation (SDIE) approach. Second, the parameters (phase, amplitude, and wavelength) of the coplanar and slotline modes are extracted from an amplitude modulated-like standing wave existing in the CPW feeding lines. Then a 2n x 2n generalized scattering matrix of the n-port discontinuity without air bridges is derived which includes the occurring mode conversion. Finally, this generalized scattering matrix is reduced to an n x n matrix by enforcing suitable conditions at the ports which correspond to the excited slotline mode. For the purpose of illustration, the method is applied to a shielded asymmetric short-end CPW shunt stub, the scattering parameters of which are compared with those of a symmetric one. Experiments are performed on both discontinuities and the results are in good agreement with theoretical data. The advantages of using air bridges in CPW circuits as opposed to bond wires are also discussed.
A polarimetric radar measures the complete scattering matrix of a target. For the forest and other natural targets, the average return is, in general, partially polarized. Conditions on the second-order statistics of the scattering matrix under which the return is fully polarized are derived, and it is shown that these conditions are connected with the eigenvalues of the covariance matrix. The result of this analysis is a set of three quantities which indicate the ability of a scatterer to generate an unpolarized component. These quantities for forested areas are shown.
Using the light scattering matrix elements measured by a polar nephelometer, a procedure for estimating the characteristics of atmospheric particulates was developed. A theoretical library data set of scattering matrices derived from Mie theory was tabulated for a range of values of the size parameter and refractive index typical of atmospheric particles. Integration over the size parameter yielded the scattering matrix elements for a variety of hypothesized particulate size distributions. A least squares curve fitting technique was used to find a best fit from the library data for the experimental measurements. This was used as a first guess for a nonlinear iterative inversion of the size distributions. A real index of 1.50 and an imaginary index of -0.005 are representative of the smoothed inversion results for the near ground level atmospheric aerosol in Tucson.
Using light scattering matrix elements measured by a polar nephelometer, a procedure for estimating the characteristics of atmospheric particulates was developed. A theoretical library data set of scattering matrices derived from Mie theory was tabulated for a range of values of the size parameter and refractive index typical of atmospheric particles. Integration over the size parameter yielded the scattering matrix elements for a variety of hypothesized particulate size distributions. A least squares curve fitting technique was used to find a best fit for the experimental measurements. This was used as a first guess for a nonlinear iterative inversion of the size distribution. A real index of 1.50 and an imaginary index of -0.005 are representative of the smoothed inversion results for the near ground level atmospheric aerosol in Tucson.
We present a new linearization of T-Matrix and Mie computations for light scattering by non-spherical and spherical particles, respectively. In addition to the usual extinction and scattering cross-sections and the scattering matrix outputs, the linearized models will generate analytical derivatives of these optical properties with respect to the real and imaginary parts of the particle refractive index, and (for non-spherical scatterers) with respect to the ''shape'' parameter (the spheroid aspect ratio, cylinder diameter/height ratio, Chebyshev particle deformation factor). These derivatives are based on the essential linearity of Maxwell's theory. Analytical derivatives are also available for polydisperse particle size distribution parameters such as the mode radius. The T-matrix formulation is based on the NASA Goddard Institute for Space Studies FORTRAN 77 code developed in the 1990s. The linearized scattering codes presented here are in FORTRAN 90 and will be made publicly available.
The scattering matrix and Stokes matrix formats for multipolarization synthetic aperture radar (SAR) images are introduced. The effects of converting to the Stokes matrix format, without first doubling the sampling rate to allow for the conversion from a complex to an intensity format is quantified and discussed. It is shown that for most applications the Stokes matrix format is acceptable, since errors introduced by undersampling tend to average out when large numbers of pixels are averaged. For those applications requiring analysis of single image pixels, the scattering matrix format is recommended.
We use the recently extended superposition T-matrix method to calculate scattering and absorption properties of micrometer-sized water droplets contaminated by black carbon. Our numerically exact results reveal that, depending on the mode of soot-water mixing, the soot specific absorption can vary by a factor exceeding 6.5. The specific absorption is maximized when the soot material is quasi-uniformly distributed throughout the droplet interior in the form of numerous small monomers. The range of mixing scenarios captured by our computations implies a wide range of remote sensing and radiation budget implications of the presence of black carbon in liquid-water clouds. We show that the popular Maxwell-Garnett effective-medium approximation can be used to calculate the optical cross sections, single-scattering albedo, and asymmetry parameter for the quasi-uniform mixing scenario, but is likely to fail in application to other mixing scenarios and in computations of the elements of the scattering matrix.
Radar polarimetry theory is reviewed, and comparison between theory and experimental results obtained with an imaging radar polarimeter employing two orthogonally polarized antennas is made. Knowledge of the scattering matrix permits calculation of the scattering cross section of a scatterer for any transmit and receive polarization combination, and a new way of displaying the resulting scattering cross section as a function of polarization is introduced. Examples of polarization signatures are presented for several theoretical models of surface scattering, and these signatures are compared with experimentally measured polarization signatures. The coefficient of variation, derived from the polarization signature, may provide information regarding the amount of variation in scattering properties for a given area.
The present volume on radar polarimetry for geoscience applications discusses wave properties and polarization, scattering matrix representation for simple targets, scattering models for point and distributed targets, polarimetric scatterometer systems and measurements, polarimetric radar system design, and polarimetric SAR applications. Attention is given to plane waves in a lossless homogeneous medium-wave polarization, polarization synthesis and response, and coordinate system transformations. Topics addressed include high- and low-frequency scattering, rough-surface scattering models, radiative transfer theory and deficiencies thereof, solutions for the radiative transfer equation, and a radiative transfer model for a forest canopy. Also discussed are network analyzer-based polarimetric scatterometers, calibration of polarimetric scatterometers, synthesized polarization response of distributed targets, and measurement of the propagation parameters of a forest canopy.
The modified unrestricted effective-medium refractive index is defined as one that yields accurate values of a representative set of far-field scattering characteristics (including the scattering matrix) for an object made of randomly heterogeneous materials. We validate the concept of the modified unrestricted effective-medium refractive index by comparing numerically exact superposition T-matrix results for a spherical host randomly filled with a large number of identical small inclusions and Lorenz-Mie results for a homogeneous spherical counterpart. A remarkable quantitative agreement between the superposition T-matrix and Lorenz-Mie scattering matrices over the entire range of scattering angles demonstrates unequivocally that the modified unrestricted effective-medium refractive index is a sound (albeit still phenomenological) concept provided that the size parameter of the inclusions is sufficiently small and their number is sufficiently large. Furthermore, it appears that in cases when the concept of the modified unrestricted effective-medium refractive index works, its actual value is close to that predicted by the Maxwell-Garnett mixing rule.
Tungsten neutron cross section, resonance parameters, and scattering matrixes for certain nuclear reaction concepts
We use the recently generalized version of the multi-sphere superposition T-matrix method (STMM) to compute the scattering and absorption properties of microscopic water droplets contaminated by black carbon. The soot material is assumed to be randomly distributed throughout the droplet interior in the form of numerous small spherical inclusions. Our numerically-exact STMM results are compared with approximate ones obtained using the Maxwell-Garnett effective-medium approximation (MGA) and the Monte Carlo ray-tracing approximation (MCRTA). We show that the popular MGA can be used to calculate the droplet optical cross sections, single-scattering albedo, and asymmetry parameter provided that the soot inclusions are quasi-uniformly distributed throughout the droplet interior, but can fail in computations of the elements of the scattering matrix depending on the volume fraction of soot inclusions. The integral radiative characteristics computed with the MCRTA can deviate more significantly from their exact STMM counterparts, while accurate MCRTA computations of the phase function require droplet size parameters substantially exceeding 60.
Many stars with circumstellar dust shells show a high degree of linear polarization (Sato et al. 1985). We are developing a model which assumes that the polarization arises from scattering by circumstellar dust. Our model assumes a geometry in which the star is surrounded by an optically thin spherical dust shell and embedded within an optically thick disk. This geometry is consistent with that proposed for objects with bipolar molecular outflow. This is important because many bipolar flow objects have also been observed to be highly polarized. The high degree of linear polarization is produced because the disk differentially attenuates the light from the star. The light incident from the point source is attenuated by a factor of exp(-tau/cos theta) where theta is the angle between a ray from the point source to the scatterer and a ray normal to the disk; tau is the optical depth at the wavelength of interest. Hence, the light scattered from the regions directly above and below the disk give the largest contribution to the total flux. The scattering angle for light from these regions is near 90 deg., so the light is strongly polarized and, in the Rayleigh scattering regime, is polarized parallel to the disk. The Stokes parameters for the scattered light from each particle in the shell are calculated by using the scattering matrix elements generated by a Mie scattering program. After the Stokes parameters for each particle are computed they are summed to give the Stokes parameters for the entire shell. Two graphs are presented which show the intensity and polarization spectrum generated by our model using the optical constants for astronomical silicates as defined by Draine and Lee (1984).