Renormalized Born approximation.
Renormalizing approximate wave functions so that amplitude is correct by means of matrix, with applications to Born approximation
BORN APPROXIMATION↗
SEARCH · Search NASA
Results for “SCATTERING MATRIX”
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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
CM-like Interplanetary Dust Particles in Lower Stratosphere During 1989 October and 1991 June/July
The stratospheric interplanetary dust particles L2005T12 and L2011O3 are linked to CM chondrite matrix. Particle L2005T12 is dominated by tabular grains of partially dehydrated greenalite-rich serpentine. Its amorphous matrix contains abundant smectite nanocrystals and annular Fe,Ni,S units. A uniquely stratified (partial) maghemite rim occurs only on S-rich parts of the matrix. Formation of this rim and Mg depletions in the matrix occurred during atmospheric entry heating of this particle. Particle L2011O3 has large iron sulfide and magnesiowustite grains in an amorphous low-Al, ferromagnesiosilica matrix. Hydrous crystallisation of this matrix produced ultrafine-grained smectites and disseminated iron sulfides. Atmospheric entry heating of both particles is indicated by the partial iron oxide rim, vesicular sulfides, and the scatter of matrix compositions due to loss of Mg. While many uncertainties remain, the high incidence of chondritic rough particles, which include an unknown amount of CM-like particles, in the lower stratosphere during 1984, 1989, and 1991 suggests annual variations in their abundances. The timing of lower stratospheric dust samplings is critical to collect these particles.
Rietmeijer, Frans J. M.↗
Polarized Radiative Transfer of a Cirrus Cloud Consisting of Randomly Oriented Hexagonal Ice Crystals: The 3 x 3 Approximation for Non-Spherical Particles
The reflection and transmission of polarized light for a cirrus cloud consisting of randomly oriented hexagonal columns were calculated by two very different vector radiative transfer models. The forward peak of the phase function for the ensemble-averaged ice crystals has a value of order 6 x 10(exp 3) so a truncation procedure was used to help produce numerically efficient yet accurate results. One of these models, the Vectorized Line-by-Line Equivalent model (VLBLE), is based on the doubling- adding principle, while the other is based on a vector discrete ordinates method (VDISORT). A comparison shows that the two models provide very close although not entirely identical results, which can be explained by differences in treatment of single scattering and the representation of the scattering phase matrix. The relative differences in the reflected I and Q Stokes parameters are within 0.5 for I and within 1.5 for Q for all viewing angles. In 1971 Hansen showed that for scattering by spherical particles the 3 x 3 approximation is sufficient to produce accurate results for the reflected radiance I and the degree of polarization (DOP), and he conjectured that these results would hold also for non-spherical particles. Simulations were conducted to test Hansen's conjecture for the cirrus cloud particles considered in this study. It was found that the 3 x 3 approximation also gives accurate results for the transmitted light, and for Q and U in addition to I and DOP. For these non-spherical ice particles the 3 x 3 approximation leads to an absolute error 2 x 10(exp -6) for the reflected and transmitted I, Q and U Stokes parameters. Hence, it appears to be an excellent approximation, which significantly reduces the computational complexity and burden required for multiple scattering calculations.
Polarization↗
Determining water cloud particle sizes from lidar depolarization measurements and time dependent multiple scattering coefficients
We present a technique of extracting water cloud particle size information from lidar measurements in conjunction with double scattering calculations. In this presentation, we describe the technique and give examples using data taken with the Air Force Phillips Laboratory's (Geophysics Directorate) low altitude Nd:YAG, elastic backscatter lidar. In a related presentation we describe the double scattering lidar model which we developed for this work. The technique uses simultaneous measurements of two orthogonal linear polarization components of lidar returns from water clouds or other media composed of spherical particles. Any depolarization of the incident lidar radiation backscattered by such a media can only be due to multiple scattering. The amount of depolarization is dependent on the extinction coefficient and the single scatter phase matrix, both of which are functions of position in the medium. The phase matrix is dependent on the index of refraction of the particles and the particle size distribution. Our technique is a modification of a procedure presented in Reference 1. There, particle sizes of water clouds are determined from double scattering calculations together with measurements of radiation scattered from volumes outside the lidar receiver's field of view (which can only be multiply scattered radiation). The methodology of our technique is similar but our 'probe' of the scattering phase function (and thus the particle size distribution) is different.
Garner, R. C.↗
Effect of Thin Cirrus Clouds on Dust Optical Depth Retrievals From MODIS Observations
The effect of thin cirrus clouds in retrieving the dust optical depth from MODIS observations is investigated by using a simplified aerosol retrieval algorithm based on the principles of the Deep Blue aerosol property retrieval method. Specifically, the errors of the retrieved dust optical depth due to thin cirrus contamination are quantified through the comparison of two retrievals by assuming dust-only atmospheres and the counterparts with overlapping mineral dust and thin cirrus clouds. To account for the effect of the polarization state of radiation field on radiance simulation, a vector radiative transfer model is used to generate the lookup tables. In the forward radiative transfer simulations involved in generating the lookup tables, the Rayleigh scattering by atmospheric gaseous molecules and the reflection of the surface assumed to be Lambertian are fully taken into account. Additionally, the spheroid model is utilized to account for the nonsphericity of dust particles In computing their optical properties. For simplicity, the single-scattering albedo, scattering phase matrix, and optical depth are specified a priori for thin cirrus clouds assumed to consist of droxtal ice crystals. The present results indicate that the errors in the retrieved dust optical depths due to the contamination of thin cirrus clouds depend on the scattering angle, underlying surface reflectance, and dust optical depth. Under heavy dusty conditions, the absolute errors are comparable to the predescribed optical depths of thin cirrus clouds.
Feng, Qian↗
Scattering By Relatively Small Oblate Spheroidal Drops of Water in the Rainbow Region: T-Matrix Results and Geometric Interpretation
Late in 1999 Michael Mishchenko carried out T-matrix calculations of light scattered by oblate spheroidal drops of water at Marston's request. The purpose of the investigation was to determine if the caustic features, known by that time to be visible in the far-field scattering near the primary rainbow region for horizontally illuminated relatively large drops, would also be present in T-matrix calculations of the scattering by small drops. The axis of rotational symmetry of the drop was taken to be vertical, and the illumination was taken to be horizontal. Scattering into the relevant angular region was evaluated for drop aspect ratios D/H = 1, 1.23, 1.311, and 1.37 where D denotes the equatorial diameter and H the vertical diameter. The results are limited to polarized monochromatic illumination with ka = 140 where a = D/2 and k = 2π/λ with λ being the wavelength of the illumination. As expected from geometrical analysis, a horizontal “V” shaped caustic is visible for D/H = 1.311. The T-matrix results, gray-tone intensity displays provided by Mishchenko, remain instructive.
Scattering by spheroids↗
An analysis of simultaneous beam formation by means of passive scattering matrices and uniform planar antenna arrays
Simultaneous beam formation by passive scattering matrices and uniform planar arrays
SCATTERING MATRIX↗
Theory for the polarization of cosmic OH super minus 18-cm radiation.
Anomalous circular polarization of hydroxyl radical 18-cm radiation from cosmic sources
COSMIC RADIATION↗
Analysis of Absorption Profiles of Autoionizing Lines
Scattering theory parameterization of absorption cross sections, and profiles of autoionizing spectral lines
ABSORPTION CROSS SECTION↗
Scattering theory of absorption-line profiles and refractivity.
Attenuation cross section and refractive index using collision theory, calculating resonance profiles of autoionizing lines based on scattering theory
SCATTERING MATRIX↗
Exchange character of the Anderson Hamiltonian.
Anderson model Hamiltonian exchange character application to conduction electron Green function determination
CONDUCTION ELECTRON↗
Robotic Vision Would Combine Optics And Microwaves
Conceptual robot-vision system processes data from both microwave and visible-wavelength sensors. Concept, called "fusion of sensors," yields better information on shapes of some objects than obtained from one type of sensor alone. Proposed system fuses data from television images with polarized low-resolution radar-scattering cross sections. Using iterative procedure, generates successive approximations to shape of target by minimizing differences between observed radar returns and radar returns observed if object characterized by computed scattering transfer matrix.
Krishen, Kuma↗
NASA/JPL AIRSAR: System Overview and Introduction to Data Interpretation
The JPL airborne synthetic aperture radar is a quadpol system operating at three frequencies, which measures the complete stokes matrix of scattering targets and hence their polarization signature.
quadpol system polarization signature data interpr↗
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.↗
T-Matrix Method and its Applications to Electromagnetic Scattering by Particles: A Current Perspective
This note serves as a short introduction to the reprint of our article "T-matrix computations of light scattering by nonspherical particles: a review" (JQSRT 1996; 55:535:75). We first discuss the motivation for writing that article and explain its historical context. This is followed by a short overview of more recent developments.
Mishchenko, Michael I.↗
Applicability of the Effective-Medium Approximation to Heterogeneous Aerosol Particles.
The effective-medium approximation (EMA) is based on the assumption that a heterogeneous particle can have a homogeneous counterpart possessing similar scattering and absorption properties. We analyze the numerical accuracy of the EMA by comparing superposition T-matrix computations for spherical aerosol particles filled with numerous randomly distributed small inclusions and Lorenz-Mie computations based on the Maxwell-Garnett mixing rule. We verify numerically that the EMA can indeed be realized for inclusion size parameters smaller than a threshold value. The threshold size parameter depends on the refractive-index contrast between the host and inclusion materials and quite often does not exceed several tenths, especially in calculations of the scattering matrix and the absorption cross section. As the inclusion size parameter approaches the threshold value, the scattering-matrix errors of the EMA start to grow with increasing the host size parameter and or the number of inclusions. We confirm, in particular, the existence of the effective-medium regime in the important case of dust aerosols with hematite or air-bubble inclusions, but then the large refractive-index contrast necessitates inclusion size parameters of the order of a few tenths. Irrespective of the highly restricted conditions of applicability of the EMA, our results provide further evidence that the effective-medium regime must be a direct corollary of the macroscopic Maxwell equations under specific assumptions.
aerosols↗
Light Scattering by Wavelength-Sized Particles "Dusted" with Subwavelength-Sized Grains
The numerically exact superposition T-matrix method is used to compute the scattering cross sections and the Stokes scattering matrix for polydisperse spherical particles covered with a large number of much smaller grains. We show that the optical effect of the presence of microscopic dust on the surfaces of wavelength-sized, weakly absorbing particles is much less significant than that of a major overall asphericity of the particle shape.
Mishchenko, Michael I.↗
Adhesion of Mineral and Soot Aerosols can Strongly Affect their Scattering and Absorption Properties
We use the numerically exact superposition T-matrix method to compute the optical cross sections and the Stokes scattering matrix for polydisperse mineral aerosols (modeled as homogeneous spheres) covered with a large number of much smaller soot particles. These results are compared with the Lorenz-Mie results for a uniform external mixture of mineral and soot aerosols. We show that the effect of soot particles adhering to large mineral particles can be to change the extinction and scattering cross sections and the asymmetry parameter quite substantially. The effect on the phase function and degree of linear polarization can be equally significant.
Mishchenko, Michael I.↗