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NASA NTRS2016

Optics of Water Microdroplets with Soot Inclusions: Exact Versus Approximate Results

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.

cloud droplets↗

NASA NTRS1986

Models of polarized infrared emission from bipolar nebulae

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).

Burns, M. S.↗

NASA NTRS1992

Measurement and calibration of differential Mueller matrix of distributed targets

A rigorous method for calibrating polarimetric backscatter measurements of distributed targets is presented. By characterizing the radar distortions over the entire mainlobe of the antenna, the differential Mueller matrix is derived from the measured scattering matrices with a high degree of accuracy. It is shown that the radar distortions can be determined by measuring the polarimetric response of a metallic sphere over the main lobe of the antenna. Comparison of results obtained with the new algorithm with the results derived from the old calibration method show that the discrepancy between the two methods is less than 1 dB for the backscattering coefficients. The discrepancy is more drastic for the phase-difference statistics, indicating that removal of the radar distortions from the cross products of the scattering matrix elements cannot be accomplished with the traditional calibration methods.

Sarabandi, Kamal↗

NASA NTRS2012

Theory of a Traveling Wave Feed for a Planar Slot Array Antenna

Planar arrays of waveguide-fed slots have been employed in many radar and remote sensing applications. Such arrays are designed in the standing wave configuration because of high efficiency. Traveling wave arrays can produce greater bandwidth at the expense of efficiency due to power loss in the load or loads. Traveling wave planar slot arrays may be designed with a long feed waveguide consisting of centered-inclined coupling slots. The feed waveguide is terminated in a matched load, and the element spacing in the feed waveguide is chosen to produce a beam squinted from the broadside. The traveling wave planar slot array consists of a long feed waveguide containing resonant-centered inclined coupling slots in the broad wall, coupling power into an array of stacked radiating waveguides orthogonal to it. The radiating waveguides consist of longitudinal offset radiating slots in a standing wave configuration. For the traveling wave feed of a planar slot array, one has to design the tilt angle and length of each coupling slot such that the amplitude and phase of excitation of each radiating waveguide are close to the desired values. The coupling slot spacing is chosen for an appropriate beam squint. Scattering matrix parameters of resonant coupling slots are used in the design process to produce appropriate excitations of radiating waveguides with constraints placed only on amplitudes. Since the radiating slots in each radiating waveguide are designed to produce a certain total admittance, the scattering (S) matrix of each coupling slot is reduced to a 2x2 matrix. Elements of each 2x2 S-matrix and the amount of coupling into the corresponding radiating waveguide are expressed in terms of the element S11. S matrices are converted into transmission (T) matrices, and the T matrices are multiplied to cascade the coupling slots and waveguide sections, starting from the load end and proceeding towards the source. While the use of non-resonant coupling slots may provide an additional degree of freedom in the design, resonant coupling slots simplify the design process. The amplitude of the wave going to the load is set at unity. The S11 parameter, r of the coupling slot closest to the load, is assigned an arbitrary value. A larger value of r will reduce the power dissipated in the load while increasing the reflection coefficient at the input port. It is now possible to obtain the excitation of the radiating waveguide closest to the load and the coefficients of the wave incident and reflected at the input port of this coupling slot. The next coupling slot parameter, r , is chosen to realize the excitation of that radiating waveguide. One continues this process moving towards the source, until all the coupling slot parameters r and hence the S11 parameter of the 4-port coupler, r, are known for each coupling slot. The goal is to produce the desired array aperture distribution in the feed direction. From an interpolation of the computed moment method data for the slot parameters, all the coupling slot tilt angles and lengths are obtained. From the excitations of the radiating waveguides computed from the coupling values, radiating slot parameters may be obtained so as to attain the desired total normalized slot admittances. This process yields the radiating slot parameters, offsets, and lengths. The design is repeated by choosing different values of r for the last coupling slot until the percentage of power dissipated in the load and the input reflection coefficient values are satisfactory. Numerical results computed for the radiation pattern, the tilt angles and lengths of coupling slots, and excitation phases of the radiating waveguides, are presented for an array with uniform amplitude excitation. The design process has been validated using computer simulations. This design procedure is valid for non-uniform amplitude excitations as well.

Rengarajan, Sembiam↗

NASA NTRS2013

T-Matrix Modeling of Linear Depolarization by Morphologically Complex Soot and Soot-Containing Aerosols

We use state-of-the-art public-domain Fortran codes based on the T-matrix method to calculate orientation and ensemble averaged scattering matrix elements for a variety of morphologically complex black carbon (BC) and BC-containing aerosol particles, with a special emphasis on the linear depolarization ratio (LDR). We explain theoretically the quasi-Rayleigh LDR peak at side-scattering angles typical of low-density soot fractals and conclude that the measurement of this feature enables one to evaluate the compactness state of BC clusters and trace the evolution of low-density fluffy fractals into densely packed aggregates. We show that small backscattering LDRs measured with groundbased, airborne, and spaceborne lidars for fresh smoke generally agree with the values predicted theoretically for fluffy BC fractals and densely packed near-spheroidal BC aggregates. To reproduce higher lidar LDRs observed for aged smoke, one needs alternative particle models such as shape mixtures of BC spheroids or cylinders.

atmospheric radiation↗

NASA NTRS1974

Lectures on the scattering of light

The exact (Mie) theory for the scattering of a plane wave by a dielectric sphere is presented. Since this infinite series solution is computationally impractical for large spheres, another formulation is given in terms of an integral equation valid for a bounded, but otherwise general array of scatterers. This equation is applied to the scattering by a single sphere, and several methods are suggested for approximating the scattering cross section in closed form. A tensor scattering matrix is introduced, in terms of which some general scattering theorems are derived. The application of the formalism to multiple scattering is briefly considered.

Saxon, D. S.↗

NASA NTRS1991

Data volume reduction for single-look polarimetric imaging radar data

An 8-b quantization scheme to reduce the data volume for single-look complex scattering matrix data measured by polarimetric imaging radar systems is described. The scattering matrices are not symmetrized before compression, thereby retaining information about background noise and system effects. The data volume is reduced by a factor of 3.2. It is shown, with measured data, that the signal to quantization noise ratio for the compression scheme is more than 35 dB for the cross-polarized channels, and more than 45 dB for the copolarized channels.

Van Zyl, Jakob J.↗

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 NTRS1994

Errors induced by the neglect of polarization in radiance calculations for Rayleigh-scattering atmospheres

Although neglecting polarization and replacing the rigorous vector radiative transfer equation by its approximate scalar counterpart has no physical background, it is a widely used simplification when the incident light is unpolarized and only the intensity of the reflected light is to be computed. We employ accurate vector and scalar multiple-scattering calculations to perform a systematic study of the errors induced by the neglect of polarization in radiance calculations for a homogeneous, plane-parallel Rayleigh-scattering atmosphere (with and without depolarization) above a Lambertian surface. Specifically, we calculate percent errors in the reflected intensity for various directions of light incidence and reflection, optical thicknesses of the atmosphere, single-scattering albedos, depolarization factors, and surface albedos. The numerical data displayed can be used to decide whether or not the scalar approximation may be employed depending on the parameters of the problem. We show that the errors decrease with increasing depolarization factor and/or increasing surface albedo. For conservative or nearly conservative scattering and small surface albedos, the errors are maximum at optical thicknesses of about 1. The calculated errors may be too large for some practical applications, and, therefore, rigorous vector calculations should be employed whenever possible. However, if approximate scalar calculations are used, we recommend to avoid geometries involving phase angles equal or close to 0 deg and 90 deg, where the errors are especially significant. We propose a theoretical explanation of the large vector/scalar differences in the case of Rayleigh scattering. According to this explanation, the differences are caused by the particular structure of the Rayleigh scattering matrix and come from lower-order (except first-order) light scattering paths involving right scattering angles and right-angle rotations of the scattering plane.

Mishchenko, M. I.↗

NASA NTRS1974

Radiation and scattering by thin-wire structures in the complex frequency domain

Piecewise-sinusoidal expansion functions and Galerkin's method are employed to formulate a solution for an arbitrary thin-wire configuration in a homogeneous conducting medium. The analysis is performed in the real or complex frequency domain. In antenna problems, the solution determines the current distribution, impedance, radiation efficiency, gain and far-field patterns. In scattering problems, the solution determines the absorption cross section, scattering cross section and the polarization scattering matrix. The electromagnetic theory is presented for thin wires and the forward-scattering theorem is developed for an arbitrary target in a homogeneous conducting medium.

Richmond, J. H.↗

NASA NTRS1976

Light scattering by tenuous particles - A generalization of the Rayleigh-Gans-Rocard approach

We consider scattering by arbitrarily shaped particles that satisfy two conditions: (1) that the polarizability of the particle relative to the ambient medium be small compared to 1 and (2) that the phase shift introduced by the particle be less than 2. We solve the integro-differential equation proposed by Shifrin by using the method of successive iterations and then applying a Fourier transform. For the second iteration, results are presented that accurately describe scattering by a broad class of particles. The phase function and other elements of the scattering matrix are shown to be in excellent agreement with Mie theory for spherical scatterers.

Acquista, C.↗

NASA NTRS1977

Problems in characterizing atmospheric aerosols by lidar alone

In this paper we review the scattering properties of real atmospheric aerosols as they relate to laser radar measurements. We address two major subjects: theoretical approximations for modeling lidar experiments and laboratory measurements for characterizing real aerosols. In the first category we review: (1) the Mueller algebra and Stokes vectors, (2) approximations for the single scattering properties of various aerosols, (3) the information content of the Mueller or scattering matrix and related limitations of lidar measurements, and (4) the effects of multiple scattering on lidar returns. In the second category we review: (1) polar nephelometers, (2) calibration procedures for nephelometers, and (3) characterization of the scattering medium. Finally, we summarize the outstanding problems in measuring the atmospheric aerosols by lidar alone.

Holland, A. C.↗

NASA NTRS1980

Polar nephelometer for atmospheric particulate studies

A polar nephelometer for use in studying atmospheric aerosols was developed. The nephelometer detects molecular scatter from air and measures scattering from very clean air using pure molecular scattering for calibration. A compact system using a folded light path with an air cooled argon laser for the light source was designed. A small, sensitive detector unit permits easy angular rotation for changing the scattering angle. A narrow detector field of view of + or - 1/4 degree of scattering along with a single wavelength of incident light is used to minimize uncertainties in the scattering theory. The system is automated for data acquisition of the scattering matrix elements over an angular range from 2 degrees to 178 degrees of scattering. Both laser output and detector sensitivity are monitored to normalize the measured light scattering.

Hansen, M. Z.↗

NASA NTRS1992

Algorithms For Compression Of Polarimetric-Radar Image Data

Two sets of algorithms provide moderate improvements in compression and decompression of scattering-matrix data from polarimetric imaging radar system. Algorithms operate on original single-look scattering matrices, do not symmetrize scattering matrices and, preserve asymmetrical data on background-noise and equipment effects.

Van Zyl, Jakob J.↗

NASA NTRS2011

A Multiple Sphere T-Matrix Fortran Code for Use on Parallel Computer Clusters

A general-purpose Fortran-90 code for calculation of the electromagnetic scattering and absorption properties of multiple sphere clusters is described. The code can calculate the efficiency factors and scattering matrix elements of the cluster for either fixed or random orientation with respect to the incident beam and for plane wave or localized- approximation Gaussian incident fields. In addition, the code can calculate maps of the electric field both interior and exterior to the spheres.The code is written with message passing interface instructions to enable the use on distributed memory compute clusters, and for such platforms the code can make feasible the calculation of absorption, scattering, and general EM characteristics of systems containing several thousand spheres.

Mackowski, D. W.↗

NASA NTRS1982

Coaxial prime focus feeds for paraboloidal reflectors

A TE11 - TM11 dual mode coaxial feed for use in prime focus paraboloidal antenna systems is investigated. The scattering matrix parameters of the internal bifurcation junction was determined by the residue calculus technique. The scattering parameters and radiation fields of the aperture were found from the Weinstein solution. The optimum modeing ratio for minimum cross-polarization was determined along with the corresponding optimum feed dimensions. A peak cross-polarization level of -58 dB is predicted. The frequency characteristics were also investigated and a bandwidth of 5% is predicted over which the cross-polarization remains below -30 dB, the input VSWR is below 1.15, and the phase error is less than 10 deg. Theoretical radiation patterns and efficiency curves for a paraboloidal reflector illuminated by this feed were computed. The predicted sidelobe level is below -30 dB and aperture efficiencies greater than 70% are possible. Experimental results are also presented that substantiates the theoretical results. In addition, experimental results for a 'short-cup' coaxial feed are given. The report includes extensive design data for the dual-mode feed along with performance curves showing cross-polarization as a function of feed parameters. The feed is useful for low-cost ground based receiving antennas for use in direct television satellite broadcasting service.

Collin, R. E.↗

NASA NTRS2011

Compact Polarimetry in a Low Frequency Spaceborne Context

Compact polarimetry has been shown to be an interesting alternative mode to full polarimetry when global coverage and revisit time are key issues. It consists on transmitting a single polarization, while receiving on two. Several critical points have been identified, one being the Faraday rotation (FR) correction and the other the calibration. When a low frequency electromagnetic wave travels through the ionosphere, it undergoes a rotation of the polarization plane about the radar line of sight for a linearly polarized wave, and a simple phase shift for a circularly polarized wave. In a low frequency radar, the only possible choice of the transmit polarization is the circular one, in order to guaranty that the scattering element on the ground is illuminated with a constant polarization independently of the ionosphere state. This will allow meaningful time series analysis, interferometry as long as the Faraday rotation effect is corrected for the return path. In full-polarimetric (FP) mode, two techniques allow to estimate the FR: Freeman method using linearly polarized data, and Bickel and Bates theory based on the transformation of the measured scattering matrix to a circular basis. In CP mode, an alternate procedure is presented which relies on the bare surface scattering properties. These bare surfaces are selected by the conformity coefficient, invariant with FR. This coefficient is compared to other published classifications to show its potential in distinguishing three different scattering types: surface, doublebounce and volume. The performances of the bare surfaces selection and FR estimation are evaluated on PALSAR and airborne data. Once the bare surfaces are selected and Faraday angle estimated over them, the correction can be applied over the whole scene. The algorithm is compared with both FP techniques. In the last part of the paper, the calibration of a CP system from the point of view of classical matrix transformation methods in polarimetry is proposed.

radar polarization diversity↗

NASA NTRS1988

Remote sensing of earth terrain

A systematic approach for the identification of terrain media such as vegetation canopy, forest, and snow covered fields is developed using the optimum polarimetric classifier. The covariance matrices for the various terrain covers are computed from the theoretical models of random medium by evaluating the full polarimetric scattering matrix elements. The optimal classification scheme makes use of a quadratic distance measure and is applied to classify a vegetation canopy consisting of both trees and grass. Experimentally measured data are used to validate the classification scheme. Theoretical probability of classification error using the full polarimetric matrix are compared with classification based on single features including the phase difference between the VV and HH polarization returns. It is shown that the full polarimetric results are optimal and provide better classification performance than single feature measurements. A systematic approach is presented for obtaining the optimal polarimetric matched filter which produces maximum contrast between two scattering classes, each represented by its respective covariance matrix.

Kong, J. A.↗