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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1996

T-Matrix Computations of Light Scattering by Nonspherical Particles: A Review

We review the current status of Waterman's T-matrix approach which is one of the most powerful and widely used tools for accurately computing light scattering by nonspherical particles, both single and composite, based on directly solving Maxwell's equations. Specifically, we discuss the analytical method for computing orientationally-averaged light-scattering characteristics for ensembles of nonspherical particles, the methods for overcoming the numerical instability in calculating the T matrix for single nonspherical particles with large size parameters and/or extreme geometries, and the superposition approach for computing light scattering by composite/aggregated particles. Our discussion is accompanies by multiple numerical examples demonstrating the capabilities of the T-matrix approach and showing effects of nonsphericity of simple convex particles (spheroids) on light scattering.

Mischenko, Michael I.↗
NASA NTRS2001

Constraints on PSC Particle Microphysics Derived From Lidar Observations

Based on extensive T-matrix computations of light scattering by polydispersions of randomly oriented, rotationally symmetric nonspherical particles, we analyze existing lidar observations of polar stratospheric clouds (PSCs) and derive several constraints on PSC particle microphysical properties. We show that sharp-edged nonspherical particles (finite circular cylinders) exhibit less variability of lidar backscattering characteristics with particle size and aspect ratio than particles with smooth surfaces (spheroids). For PSC particles significantly smaller than the wavelength, the backscatter color index Alpha and the depolarization color index Beta are essentially shape-independent. Observations for type Ia PSCs can be reproduced by spheroids with aspect ratios larger than 1.2, oblate cylinders with diameter-to-length ratios greater than 1.6, and prolate cylinders with length-to-diameter ratios greater than 1.4. The effective equal-volume-sphere radius for type la PSCs is about 0.8 microns or larger. Type Ib PSCs are likely to be composed of spheres or nearly spherical particles with effective radii smaller than 0.8 microns. Observations for type II PSCs are consistent with large ice crystals (effective radius greater than 1 micron modeled as cylinders or prolate spheroids.

Liu, Li↗
NASA NTRS2011

A Sensitivity Study on the Effects of Particle Chemistry, Asphericity and Size on the Mass Extinction Efficiency of Mineral Dust in the Earth's Atmosphere: From the Near to Thermal IR

To determine a plausible range of mass extinction efficiencies (MEE) of terrestrial atmospheric dust from the near to thermal IR, sensitivity analyses are performed over an extended range of dust microphysical and chemistry perturbations. The IR values are subsequently compared to those in the near-IR, to evaluate spectral relationships in their optical properties. Synthesized size distributions consistent with measurements, model particle size, while composition is defined by the refractive indices of minerals routinely observed in dust, including the widely used OPAC/Hess parameterization. Single-scattering properties of representative dust particle shapes are calculated using the T-matrix, Discrete Dipole Approximation and Lorenz-Mie light-scattering codes. For the parameterizations examined, MEE ranges from nearly zero to 1.2 square meters per gram, with the higher values associated with non-spheres composed of quartz and gypsum. At near-IR wavelengths, MEE for non-spheres generally exceeds those for spheres, while in the thermal IR, shape-induced changes in MEE strongly depend on volume median diameter (VMD) and wavelength, particularly for MEE evaluated at the mineral resonant frequencies. MEE spectral distributions appear to follow particle geometry and are evidence for shape dependency in the optical properties. It is also shown that non-spheres best reproduce the positions of prominent absorption peaks found in silicates. Generally, angular particles exhibit wider and more symmetric MEE spectral distribution patterns from 8-10 micrometers than those with smooth surfaces, likely due to their edge-effects. Lastly, MEE ratios allow for inferring dust optical properties across the visible-IR spectrum. We conclude the MEE of dust aerosol are significant for the parameter space investigated, and are a key component for remote sensing applications and the study of direct aerosol radiative effects.

Hansell, R. A., Jr.↗
NASA NTRS1993

Light scattering by size-shape distributions of randomly oriented axially symmetric particles of a size comparable to a wavelength

Rigorously light scattering by size-shape distributions of randomly oriented axially symmetric particles are calculated by the T-matrix method, as extended to randomly oriented scatterers. The computational scheme is described along with a newly developed convergence procedure that makes it possible to substantially reduce computer time and storage requirements. The elements of the Stokes scattering matrix for a power-law size distribution of randomly oriented moderately aspherical spheroids are shown to be much smoother than and differ substantially from those of equivalent monodisperse spheroids; averaging over orientations does not eliminate the necessity of averaging over particle sizes. The angular-scattering behavior of the ensembles of nonspherical particles is found to be significantly different from that of the equivalent polydisperse spheres.

Mishchenko, Michael I.↗
NASA NTRS2011

Linearized T-Matrix and Mie Scattering Computations

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.

Analytic linearization↗
NASA NTRS1993

Intensity and polarization of light scattered by size distributions of randomly oriented nonspherical particles

Calculations of light scattering by small particles are important in many diverse fields of science and engineering. In many cases of practical interest, scattering particles are nonspherical and are distributed over sizes and orientations. However, accurate light scattering computations for ensembles of nonspherical particles are difficult and time-consuming, and the literature in which such calculations are reported is rather scarce. In this paper, the T-matrix approach, as extended recently to randomly oriented particles, is used to calculate rigorously light scattering by size distributions of randomly oriented axially symmetric particles. To model the variation of particle sizes in real ensembles, we use a power law distribution typical of some terrestrial aerosols. Contour plots of intensity and degree of linear polarization for polydisperse prolate and oblate spheroids of different aspect ratios and effective equivalent-sphere size parameters from 0 to 10 are calculated and compared with calculations for equivalent spheres. The angular scattering behavior of nonspherical polydispersions is found to be greatly different from that of spheres, while the scattering properties of oblate and prolate spheroids of the same aspect ratio are similar. With increasing particle size, both intensity and polarization become more shape-dependent. In general, nonspherical particles are stronger side scatterers and weaker backscatterers than equivalent spheres. With increasing aspect ratio of nonspherical particles polarization tends to be predominantly positive. Possible effects of particle nonsphericity on optical remote sensing of atmospheric aerosols are discussed.

Mishchenko, M. I.↗
NASA NTRS2001

Retrieval of Polar Stratospheric Cloud Microphysical Properties From Lidar Measurements: Dependence on Particle Shape Assumptions

Knowledge of particle sizes and number densities of polar stratospheric clouds (PSCs) is highly important, because they are critical parameters for the modeling of the ozone chemistry of the stratosphere. In situ measurements of PSC particles are rare. the main instrument for the accumulation of PSC data are lidar systems. Therefore the derivation of some microphysical properties of PSCS from the optical parameters measured by lidars would be highly beneficial for ozone research. Inversion of lidar data obtained in the presence of PSCs formed from crystalline particles type 11 and the various nitric acid tri Ydrrate (NAT) types cannot be easily accomplished, because a suitable scattering theory for small faceted crystals has not been readily available tip to now. As a consequence, the T-matrix method is commonly used for the interpretation of these PSC lidar data. Here the assumption is made that the optical properties of an ensemble of spheroids resemble those of crystalline PSCs, and microphysical properties of the PSC are inferred from the optical signatures of the PSC at two or more wavelengths. The problem with the T-matrix approach is that the assumption of spheroidal instead of faceted particles can lead to dramatically wrong results: Usually cloud particle properties are deduced from analysis of lidar profiles of backscatter ratio and depolarization ratio. The particle contribution to the backscatter ratio is given by the product of the particle number density and the backscattering cross section. The latter is proportional to the value of the particle's scattering phase function at 180 degrees scattering angle. At 180 degrees however, the phase functions of rough, faceted crystals and of spheroids with same maximum dimension differ by a factor of 6. From this it follows that for a PSC consisting of faceted crystals, the particle number density is underestimated by roughly the same factor if spheroidal particles are unrealistically assumed. We are currently developing a retrieval technique for determining the microphysical parameters of crystalline PSCs that takes into account the faceted shape of the PSC particles. This approach utilizes finite-difference time-domain (FDTD) calculations of particle optical properties. The accuracy and the free choice of the shape of the scattering particle make the FDTD technique a promising tool for the inversion of PSC lidar data. A first comparison of FDTD and T-matrix calculations will be presented.

Reichardt, Susanne↗
NASA NTRS2001

Microwave Polarized Signatures Generated within Cloud Systems: SSM/I Observations Interpreted with Radiative Transfer Simulations

Special Sensor Microwave /Imager (SSM/I) observations in cloud systems are studied over the tropics. Over optically thick cloud systems, presence of polarized signatures at 37 and 85 GHz is evidenced and analyzed with the help of cloud top temperature and optical thickness extracted from visible and IR satellite observations. Scattering signatures at 85 GHz (TbV(85) less than or = 250 K) are associated with polarization differences greater than or = 6 K, approx. 50%, of the time over ocean and approx. 40% over land. In addition. over thick clouds the polarization difference at 37 GHz is rarely negligible. The polarization differences at 37 and 85 GHz do not stem from the surface but are generated in regions of relatively homogeneous clouds having high liquid water content. To interpret the observations, a radiative transfer model that includes the scattering by non-spherical particles is developed. based on the T-matrix approach and using the doubling and adding method. In addition to handling randomly and perfectly oriented particles, this model can also simulate the effect of partial orientation of the hydrometeors. Microwave brightness temperatures are simulated at SSM/I frequencies and are compared with the observations. Polarization differences of approx. 2 K can be simulated at 37 GHz over a rain layer, even using spherical drops. The polarization difference is larger for oriented non-spherical particles. The 85 GHz simulations are very sensitive to the ice phase of the cloud. Simulations with spherical particles or with randomly oriented non-spherical ice particles cannot replicate the observed polarization differences. However, with partially oriented non-spherical particles, the observed polarized signatures at 85 GHz are explained, and the sensitivity of the scattering characteristics to the particle size, asphericity, and orientation is analyzed. Implications on rain and ice retrievals are discussed.

Prigent, Catherine↗
NASA NTRS2010

Comprehensive T-Matrix Reference Database: A 2007-2009 Update

The T-matrix method is among the most versatile, efficient, and widely used theoretical techniques for the numerically exact computation of electromagnetic scattering by homogeneous and composite particles, clusters of particles, discrete random media, and particles in the vicinity of an interface separating two half-spaces with different refractive indices. This paper presents an update to the comprehensive database of T-matrix publications compiled by us previously and includes the publications that appeared since 2007. It also lists several earlier publications not included in the original database.

Mishchenko, Michael I.↗
NASA NTRS1989

A covariant multiple scattering series for elastic projectile-target scattering

A covariant formulation of the multiple scattering series for the optical potential is presented. The case of a scalar nucleon interacting with a spin zero isospin zero A-body target through meson exchange, is considered. It is shown that a covariant equation for the projectile-target t-matrix can be obtained which sums the ladder and crossed ladder diagrams efficiently. From this equation, a multiple scattering series for the optical potential is derived, and it is shown that in the impulse approximation, the two-body t-matrix associated with the first order optical potential is the one in which one particle is kept on mass-shell. The meaning of various terms in the multiple scattering series is given. The construction of the first-order optical potential for elastic scattering calculations is described.

Gross, Franz↗
NASA NTRS1997

Particle Scattering in the Resonance Regime: Full-Wave Solution for Axisymmetric Particles with Large Aspect Ratios

Reliable descriptions of the optical properties of clouds and aerosols are essential for studies of radiative transfer in planetary atmospheres. The scattering algorithms provide accurate estimates of these properties for spherical particles with a wide range of sizes and refractive indices, but these methods are not valid for non-spherical particles (e.g., ice crystals, mineral dust, and smoke). Even though a host of methods exist for deriving the optical properties of nonspherical particles that are very small or very large compared with the wavelength, only a few methods are valid in the resonance regime, where the particle dimensions are comparable with the wavelength. Most such methods are not ideal for particles with sharp edges or large axial ratios. We explore the utility of an integral equation approach for deriving the single-scattering optical properties of axisymmetric particles with large axial ratios. The accuracy of this technique is shown for spheres of increasing size parameters and an ensemble of randomly oriented prolate spheroids of size parameter equal to 10.079368. In this last case our results are compared with published results obtained with the T-matrix approach. Next we derive cross sections, single-scattering albedos, and phase functions for cylinders, disks, and spheroids of ice with dimensions extending from the Rayleigh to the geometric optics regime. Compared with those for a standard surface integral equation method, the storage requirement and the computer time needed by this method are reduced, thus making it attractive for generating databases to be used in multiple-scattering calculations. Our results show that water ice disks and cylinders are more strongly absorbing than equivalent volume spheres at most infrared wavelengths. The geometry of these particles also affects the angular dependence of the scattering. Disks and columns with maximum linear dimensions larger than the wavelength scatter much more radiation in the forward and backward directions and much less radiation at intermediate phase angles than equivalent volume spheres.

Zuffada, Cinzia↗
NASA NTRS2001

Shape and Structure

The convenient availability and simplicity of the Lorenz-Mie theory has resulted in a widespread practice of treating nonspherical particles (especially those in random orientation) as if they were spheres to which Lorenz-Mie results are applicable. However, the assumption of sphericity is rarely made after first having studied the effects of nonsphericity and having concluded that they are negligible. On the contrary, overwhelming evidence suggests that scattering properties of nonspherical particles, including those in random orientation, can significantly differ from those of volume- or surface-equivalent spheres. Hence, the last few decades have demonstrated major research efforts aimed at a significantly better understanding of the effects of particle shape and morphology on electromagnetic scattering. The goal of this presentation is to provide a concise summary of these efforts. The recent availability of theoretical techniques for computing single and multiple scattering of light by realistic polydispersions of spherical and nonspherical particles and the strong dependence of the Stokes scattering matrix on particle size, shape, and refractive index make polarization and depolarization measurements a powerful particle characterization tool. This presentation will focus on recent applications of photopolarimetric and lidar depolarization measurements to remote sensing characterization of tropospheric aerosols, polar stratospheric clouds (PSCs) and contrails. The talk will include (1) a short theoretical overview of the effects of particle microphysics on particle single-scattering characteristics; (2) the use of multi-angle multi-spectral photopolarimetry to retrieve the optical thickness, size distribution, refractive index, and number concentration of tropospheric aerosols over the ocean surface; and (3) the application of the T-matrix method to constraining the PSC and contrail particle microphysics using multi-spectral measurements of lidar backscatter and depolarization

Mishchenko, Michael↗
NASA NTRS2001

Retrievals of Aerosol and Cloud Particle Microphysics Using Polarization and Depolarization Techniques

The recent availability of theoretical techniques for computing single and multiple scattering of light by realistic polydispersions of spherical and nonspherical particles and the strong dependence of the Stokes scattering matrix on particle size, shape, and refractive index make polarization and depolarization measurements a powerful particle characterization tool. In this presentation I will describe recent applications of photopolarimetric and lidar depolarization measurements to remote sensing characterization of tropospheric aerosols, polar stratospheric clouds (PSCs), and contrails. The talk will include (1) a short theoretical overview of the effects of particle microphysics on particle single-scattering characteristics; (2) the use of multi-angle multi-spectral photopolarimetry to retrieve the optical thickness, size distribution, refractive index, and number concentration of tropospheric aerosols over the ocean surface; and (3) the application of the T-matrix method to constraining the PSC and contrail particle microphysics using multi-spectral measurements of lidar backscatter and depolarization.

Mishchenko, Michael↗
NASA NTRS2011

Coherent Backscattering by Polydisperse Discrete Random Media: Exact T-Matrix Results

The numerically exact superposition T-matrix method is used to compute, for the first time to our knowledge, electromagnetic scattering by finite spherical volumes composed of polydisperse mixtures of spherical particles with different size parameters or different refractive indices. The backscattering patterns calculated in the far-field zone of the polydisperse multiparticle volumes reveal unequivocally the classical manifestations of the effect of weak localization of electromagnetic waves in discrete random media, thereby corroborating the universal interference nature of coherent backscattering. The polarization opposition effect is shown to be the least robust manifestation of weak localization fading away with increasing particle size parameter.

Mishchenko, Michael I.↗
NASA NTRS2011

Direct Simulation of Multiple Scattering by Discrete Random Media Illuminated by Gaussian Beams

The conventional orientation-averaging procedure developed in the framework of the superposition T-matrix approach is generalized to include the case of illumination by a Gaussian beam (GB). The resulting computer code is parallelized and used to perform extensive numerically exact calculations of electromagnetic scattering by volumes of discrete random medium consisting of monodisperse spherical particles. The size parameters of the scattering volumes are 40, 50, and 60, while their packing density is fixed at 5%. We demonstrate that all scattering patterns observed in the far-field zone of a random multisphere target and their evolution with decreasing width of the incident GB can be interpreted in terms of idealized theoretical concepts such as forward-scattering interference, coherent backscattering (CB), and diffuse multiple scattering. It is shown that the increasing violation of electromagnetic reciprocity with decreasing GB width suppresses and eventually eradicates all observable manifestations of CB. This result supplements the previous demonstration of the effects of broken reciprocity in the case of magneto-optically active particles subjected to an external magnetic field.

Mackowski, Daniel W.↗
NASA NTRS1986

Absorption and scattering of light by nonspherical particles

Using the example of the polarization of scattered light, it is shown that the scattering matrices for identical, randomly ordered particles and for spherical particles are unequal. The spherical assumptions of Mie theory are therefore inconsistent with the random shapes and sizes of atmospheric particulates. The implications for corrections made to extinction measurements of forward scattering light are discussed. Several analytical methods are examined as potential bases for developing more accurate models, including Rayleigh theory, Fraunhoffer Diffraction theory, anomalous diffraction theory, Rayleigh-Gans theory, the separation of variables technique, the Purcell-Pennypacker method, the T-matrix method, and finite difference calculations.

Bohren, C. F.↗
NASA NTRS2000

Scattering Properties of Needle-Like and plate-like Ice Spheroids with Moderate Size Parameters

We use the current advanced version of the T-matrix method to compute the optical cross sections, the asymmetry parameter of the phase function, and the scattering matrix elements of ice spheroids with aspect ratios up to 20 and surface-equivalent-sphere size parameters up to 12. We demonstrate that plate-like and needle-like particles with moderate size parameters possess unique scattering properties: their asymmetry parameters and phase functions are similar to those of surface-equivalent spheres, whereas all other elements of the scattering matrix are typical of particles much smaller than the wavelength (Rayleigh scatterers). This result may have important implications for optical particle sizing and remote sensing of the terrestrial and planetary atmospheres.

Zakharova, Nadia T.↗