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All sourcesNASA NTRSDOE OSTI
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 NTRS1988

Tabulation of Mie scattering calculation results for microwave radiative transfer modeling

In microwave radiative transfer model simulations, the Mie calculations usually consume the majority of the computer time necessary for the calculations (70 to 86 percent for frequencies ranging from 6.6 to 183 GHz). For a large array of atmospheric profiles, the repeated calculations of the Mie codes make the radiative transfer computations not only expensive, but sometimes impossible. It is desirable, therefore, to develop a set of Mie tables to replace the Mie codes for the designated ranges of temperature and frequency in the microwave radiative transfer calculation. Results of using the Mie tables in the transfer calculations show that the total CPU time (IBM 3081) used for the modeling simulation is reduced by a factor of 7 to 16, depending on the frequency. The tables are tested by computing the upwelling radiance of 144 atmospheric profiles generated by a 3-D cloud model (Tao, 1986). Results are compared with those using Mie quantities computed from the Mie codes. The bias and root-mean-square deviation (RMSD) of the model results using the Mie tables, in general, are less than 1 K except for 37 and 90 GHz. Overall, neither the bias nor RMSD is worse than 1.7 K for any frequency and any viewing angle.

Yeh, Hwa-Young M.↗
NASA NTRS2018

Far-Field Lorenz-Mie Scattering in an Absorbing Host Medium: Theoretical Formalism and FORTRAN Program

In this paper we make practical use of the recently developed first-principles approach to electromagnetic scattering by particles immersed in an unbounded absorbing host medium. Specifically, we introduce an actual computational tool for the calculation of pertinent far-field optical observables in the context of the classical Lorenzâ€"Mie theory. The paper summarizes the relevant theoretical formalism, explains various aspects of the corresponding numerical algorithm, specifies the input and output parameters of a FORTRAN program available at https://www.giss.nasa.gov/staff/mmishchenko/Lorenz-Mie.html, and tabulates benchmark results useful for testing purposes. This public-domain FORTRAN program enables one to solve the following two important problems: (i) simulate theoretically the reading of a remote well-collimated radiometer measuring electromagnetic scattering by an individual spherical particle or a small random group of spherical particles; and (ii) compute the single-scattering parameters that enter the vector radiative transfer equation derived directly from the Maxwell equations.

Far-field electromagnetic scattering; Absorbing ho↗
NASA NTRS2007

Mie Scattering of Growing Molecular Contaminants

Molecular contamination of optical surfaces from outgassed material has been shown in many cases to proceed from acclimation centers and to produce many roughly hemispherical "islands" of contamination on the surface. The mathematics of the hemispherical scattering is simplified by introducing a Virtual source below the plane of the optic, in this case a mirror, allowing the use of Mie theory to produce a solution for the resulting sphere .in transmission. Experimentally, a fixed wavelength in the vacuum ultraviolet was used as the illumination source and scattered light from the polished and coated glass mirrors was detected at a fixed angle as the contamination islands grew in time.

Herren, Kenneth A.↗
NASA NTRS2018

Far-field Lorenz-Mie Scattering in an Absorbing Host Medium. II: Improved Stability of the Numerical Algorithm

A recently developed FORTRAN program computing far-field optical observables for spherical particles in an absorbing medium has exhibited numerical instability arising when the product of the particle vacuum size parameter and the imaginary part of the refractive index of the host becomes sufficiently large. We offer a simple analytical explanation of this instability and propose a compact numerical algorithm for the stable computation of Lorenz–Mie coefficients based on an upward recursion formula for spherical Hankel functions of a complex argument. Extensive tests confirm an excellent accuracy of this algorithm approaching machine precision. The improved public-domain FORTRAN program is available at https://www.giss.nasa.gov/staff/mmishchenko/Lorenz-Mie.html.

Lorenz-Mie theory↗
NASA NTRS1973

Mie scattering of the interplanetary magnetic field by the whole moon

It is known from the Apollo magnetometer experiments that significant electromagnetic induction takes place in the lunar interior. This induction is excited by fluctuations of the interplanetary magnetic field and is detected by the induced fields on the surface of the moon. These results are reviewed briefly and the formal properties of the theory are discussed. It is shown that the mathematical treatment parallels that for classical electromagnetic scattering. Further the wavelength spectrum of the fluctuations of the interplanetary magnetic field include scales consistent with the radius of the moon. The consequence is that the moon is excited in several modes. Quadrupole and possibly octupole magnetic multipoles are found in the data. The electric type radiation corresponding to transverse magnetic excitation appears suppressed and far below the detection threshold of the magnetometers.

Sonett, C. P.↗
NASA NTRS1972

Mie scattering by three polydispersions.

Review of the results of aerosol scattering calculations using models representative of the atmospheric aerosol for three laser wavelengths and two kinds of materials. These calculations show that measurements of scattering and polarization parameters can help significantly in characterizing the earth's aerosol.

Harris, F. S., Jr.↗
NASA NTRS1974

Mie scattering of the interplanetary magnetic field by the whole moon

Based on the results of the Apollo magnetometer experiments, it is shown that the wavelength spectrum of the fluctuations of the interplanetary magnetic field includes scales consistent with the radius of the moon. Quadrupole and possibly octupole magnetic multipoles are found in the data and indicate that the moon is excited in several modes.

Sonett, C. P.↗
NASA NTRS1976

Effective mie-scattering and CO2 absorption in the dust-laden Martian atmosphere and its impact on radiative-convective temperature changes in the lower scale heights

A time dependent computer model of radiative-convective-conductive heat transfer in the Martian ground-atmosphere system was refined by incorporating an intermediate line strength CO2 band absorption which together with the strong-and weak-line approximation closely simulated the radiative transmission through a vertically inhomogeneous stratification. About 33,000 CO2 lines were processed to cover the spectral range of solar and planetary radiation. Absorption by silicate dust particulates, was taken into consideration to study its impact on the ground-atmosphere temperature field as a function of time. This model was subsequently attuned to IRIS, IR-radiometric and S-band occultation data. Satisfactory simulations of the measured IRIS spectra were accomplished for the dust-free condition. In the case of variable dust loads, the simulations were sufficiently fair so that some inferences into the effect of dust on temperature were justified.

Pallmann, A. J.↗
NASA NTRS2023

New Mie Scattering Diffuse Targets Development and Characterization

Earth science remote sensing observations require the detection and measurement of light originating from bright targets, such as clouds, and darker targets, such as an open ocean. This requirement drives the need to design, develop, and characterize improved calibration targets in support of current and future NASA instruments. New diffuse targets to be used as spectral albedo calibration standards were developed and characterized. The new targets based on fused silica or/and pressed and sintered Polytetrafluoroethylene (PTFE) were developed to be Earth scene specific. The various reflectance levels are achieved by modifying the material parameters, thickness, and surface finish. The new targets were characterized in laboratory and simulated space environments. We acquired high accuracy reflectance and transmittance data using a precision optical scatterometer and spectrophotometer located in the NASA Goddard Space Flight Center (GSFC) Diffuser Calibration Lab. The Total hemispherical reflectance (THR) and Bidirectional Reflectance Distribution Function (BRDF) were measured over the range of solar incident and scattered elevation and azimuthal angles typically realized on orbit by remote sensing instruments. We intend to space certify the new calibration targets after concluding on-orbit testing on the International Space Stations (ISS) scheduled for the second half of 2023.

Georgi Georgiev↗
NASA NTRS1997

Elucidation of Free Radical and Optogalvanic Spectroscopy Associated with Microgravity Combustion via Conventional and Novel Laser Platforms

Combustion studies under both normal gravity and microgravity conditions depend a great deal on the availability and quality of the diagnostic systems used for such investigations. Microgravity phenomena are specially susceptible to even small perturbations and therefore non-intrusive diagnostic techniques are of paramount importance for successful understanding of reduced-gravity combustion phenomena. Several non-intrusive diagnostic techniques are available for probing and delineating normal as well as reduced gravity combustion processes, such as Rayleigh scattering, Raman scattering, Mie scattering, velocimetry, interferometric and Schlieren techniques, emission and laser-induced fluorescence (LIF) spectroscopy. Our approach is to use the LIF technique as a non-intrusive diagnostic tool for the study of combustion-associated free radicals and use the concomitant optogalvanic transitions to accomplish precise calibration of the laser wavelengths used for recording the excitation spectra of transient molecular species. In attempting to perform spectroscopic measurements on chemical intermediates, we have used conventional laser sources as well as new and novel platforms employing rare-earth doped solid-state lasers. Conventional (commercially available) sources of tunable UV laser radiation are extremely cumbersome and energy-consuming devices that are not very suitable for either in-space or in-flight (or microgravity drop tower) experiments. Traditional LIF sources of tunable UV laser radiation involve in addition to a pump laser (usually a Nd:YAG laser with an attached frequency-doubling stage), a tunable dye laser. In turn, the dye laser has to be provided with a dye circulation system and a subsequent stage for frequency-doubling of the dye laser radiation, together with a servo-tuning system (termed the 'Autotracker') to follow the wavelength changes and also an optical system (called the 'Frequency Separator') for separation of the emanating visible and UV beams. In contrast to this approach, we have devised an alternate arrangement for recording LIF excitation spectra of free radicals (following appropriate precursor fragmentation) that utilizes a tunable rare-earth doped solid state laser system with direct UV pumping. We have designed a compact and portable tunable UV laser system incorporating features necessary for both in-space and in-flight spectroscopy experiments. For the purpose of LIF excitation, we have developed an all-solid-state tunable UV laser that employs direct pumping of the solid-state UV-active medium employing UV harmonics from a Nd:YAG laser. An optical scheme with counterpropagating photolysis and excitation beams focused by suitable lenses into a reaction vacuum chamber was employed.

Misra, Prabhakar↗
NASA NTRS2007

Solutions Network Formulation Report. Reducing Light Pollution in U.S. Coastal Regions Using the High Sensitivity Cameras on the SAC-C and Aquarius/SAC-D Satellites

Light pollution has significant adverse biological effects on humans, animals, and plants and has resulted in the loss of our ability to view the stars and planets of the universe. Over half of the U.S. population resides in coastal regions where it is no longer possible to see the stars and planets in the night sky. Forty percent of the entire U.S. population is never exposed to conditions dark enough for their eyes to convert to night vision capabilities. In coastal regions, urban lights shine far out to sea where they are augmented by the output from fishing boat, cruise ship and oil platform floodlights. The proposed candidate solution suggests using HSCs (high sensitivity cameras) onboard the SAC-C and Aquarius/SAC-D satellites to quantitatively evaluate light pollution at high spatial resolution. New products modeled after pre-existing, radiance-calibrated, global nighttime lights products would be integrated into a modified Garstang model where elevation, mountain screening, Rayleigh scattering, Mie scattering by aerosols, and atmospheric extinction along light paths and curvature of the Earth would be taken into account. Because the spatial resolution of the HSCs on SAC-C and the future Aquarius/SAC-D missions is greater than that provided by the DMSP (Defense Meteorological Satellite Program) OLS (Operational Linescan System) or VIIRS (Visible/Infrared Imager/Radiometer Suite), it may be possible to obtain more precise light intensity data for analytical DSSs and the subsequent reduction in coastal light pollution.

Andrews, Jane C.↗
NASA NTRS1996

Absorption Filter Based Optical Diagnostics in High Speed Flows

Two major regimes where laser light scattered by molecules or particles in a flow contains significant information about the flow are Mie scattering and Rayleigh scattering. Mie scattering is used to obtain only velocity information, while Rayleigh scattering can be used to measure both the velocity and the thermodynamic properties of the flow. Now, recently introduced (1990, 1991) absorption filter based diagnostic techniques have started a new era in flow visualization, simultaneous velocity and thermodynamic measurements, and planar velocity measurements. Using a filtered planar velocimetry (FPV) technique, we have modified the optically thick iodine filter profile of Miles, et al., and used it in the pressure-broaden regime which accommodates measurements in a wide range of velocity applications. Measuring velocity and thermodynamic properties simultaneously, using absorption filtered based Rayleigh scattering, involves not only the measurement of the Doppler shift, but also the spectral profile of the Rayleigh scattering signal. Using multiple observation angles, simultaneous measurement of one component velocity and thermodynamic properties in a supersonic jet were measured. Presently, the technique is being extended for simultaneous measurements of all three components of velocity and thermodynamic properties.

Samimy, Mo↗
NASA NTRS1992

Time and polarization dependent double scattering calculations of lidar returns from water clouds

We describe and present results of a double scattering lidar model which we use to calculate lidar returns from water clouds. The model is used in conjunction with the Phillips Laboratory's (Geophysics Directorate) low altitude Nd:YAG lidar system to determine microphysical properties of water clouds. The model determines the Stokes parameters of the backscattered lidar radiation, from media composed of spherical particles, as a function of time. The Stokes parameters of the radiation of the lidar return are determined, at each time, by considering all radiation which has traveled the same path length from transmitter to receiver while making two successive single scatters. Each single scatter is considered a Mie scatter. We have also developed a Mie scattering program for use with the double scattering model. Each single scatter takes into account the polarization of the incident and scattered radiation. Inputs to the double scattering mode include the receiver area and field of view, the receiver integration time, the extinction coefficient as a function of distance into the cloud, the particle size distribution (assumed independent of position), and the complex index of refraction of the spherical particles.

Garner, R. C.↗
NASA NTRS1975

Microwave emission from dry and wet snow

A microscopic model was developed to study the microwave emission from snow. In this model, the individual snow particles are considered to be the scattering centers. Mie scattering theory for spherical particles is then used to compute the volume scattering and extinction coefficients of the closely packed scattering spheres, which are assumed not to interact coherently. The results of the computations show significant volume scattering effects in the microwave region which result in low observed emissivities from cold, dry snow. In the case of wet snow, the microwave emissivities are increased considerably, in agreement with earlier experimental observations in which the brightness temperatures have increased significantly at the onset of melting.

Chang, T. C.↗
NASA NTRS1999

Global and Seasonal Aerosol Optical Depths Derived From Ultraviolet Observations by Satellites (TOMS)

It has been shown that absorbing aerosols (dust, smoke, volcanic ash) can be detected in the ultraviolet wavelengths (331 nm to 380 nm) from satellite observations (TOMS, Total Ozone Mapping Spectrometer) over both land and water. The theoretical basis for these observations and their conversions to optical depths is discussed in terms of an aerosol index AI or N-value residue (assigned positive for absorbing aerosols). The theoretical considerations show that negative values of the AI frequently represent the presence of non-absorbing aerosols (NA) in the troposphere (mostly pollution in the form of sulfates, hydrocarbons, etc., and some natural sulfate aerosols) with particle sizes near 0.1 to 0.2 microns or less. The detection of small-particle non-absorbing aerosols from the measured backscattered radiances is based on the observed wavelength dependence from Mie scattering after the background Rayleigh scattering is subtracted. The Mie scattering from larger particles, 1 micron or more (e.g., cloud water droplets) has too small a wavelength dependence to be detected by this method. In regions that are mostly cloud free, aerosols of all sizes can be seen in the single channel 380 nm or 360 nm radiance data. The most prominent Al feature observed is the strong asymmetry in aerosol amount between the Northern and Southern Hemispheres, with the large majority of NA occurring above 20degN latitude. The maximum values of non-absorbing aerosols are observed over the eastern U.S. and most of western Europe corresponding to the areas of highest industrial pollution. Annual cycles in the amount of NA are observed over Europe and North America with maxima occurring in the summer corresponding to times of minimum wind transport. Similarly, the maxima in the winter over the Atlantic Ocean occurs because of wind borne transport from the land. Most regions of the world have the maximum amount of non-absorbing aerosol in the December to January period except for the eastern North America and Europe. Comparisons of the estimated TOMS aerosol optical depths show good agreement in magnitude and seasonal dependence with sun-photometer optical depths obtained at Goddard Space Flight Center (39degN 76.88degW) in the U.S. and in Lille (50.63degN 3.07degE) in France. The study of these aerosols is important for detecting the sources of industrial pollution and its redistribution by winds on a global basis, as well as its effect on reducing the UV irradiance at the Earth's surface.

Herman, J. R.↗