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NASA NTRS1995

An experimental study of light scattering by large, irregular particles

The intensity and polarization of light scattered by a variety of types of artificial partices large compared to the wavelength were measured as a function of phase angle. Shape, surface roughness, absorption coefficient, and internal scattering coefficient were varied systematically and their effects studied. Scattering by clear, smooth-surfaced spheres is in quantitative agreement with the predictions of the geometrical optics (ray theory) approximation to physical optics (Mie theory). The phase functions of almost all of the particles measured have both forward and backward scattering lobes. A two-parameter, double Henyey-Greenstein function generally provides reasonably good descriptions of the data, while keeping the number of free parameters to the minimum necessary. On a double Henyey- Greenstein parameter plot all of the particles fall into an L-shaped area of restricted size in which the location is characteristic of the particle type. Formalisms based on the equivalent slab model are also given for estimating the scattering efficiency of a large, irregular particle. For most dielectric particles the transmitted, forward scattered light is partially negatively polarized. It is this component that is respopnsible for the well-known maximum in the polarization curves of planetary regoliths at phase angles around 100 deg. For phase angles between about 30 deg and 70 deg the internally scattered light is found to be randomly polarized in the particles studied here, so that the only contribution to the second component of the Stokes vector is by Fresnel reflection from the particle surface. If this empirical result is general, measurement of the second Stokes vector of the light scattered from a regolith at these angles may provide a method of remotely measuring the mean refractive index.

Mcguire, Audrey F.↗
NASA NTRS2012

Rainbow Fourier Transform

We present a novel technique for remote sensing of cloud droplet size distributions. Polarized reflectances in the scattering angle range between 135deg and 165deg exhibit a sharply defined rainbow structure, the shape of which is determined mostly by single scattering properties of cloud particles, and therefore, can be modeled using the Mie theory. Fitting the observed rainbow with such a model (computed for a parameterized family of particle size distributions) has been used for cloud droplet size retrievals. We discovered that the relationship between the rainbow structures and the corresponding particle size distributions is deeper than it had been commonly understood. In fact, the Mie theory-derived polarized reflectance as a function of reduced scattering angle (in the rainbow angular range) and the (monodisperse) particle radius appears to be a proxy to a kernel of an integral transform (similar to the sine Fourier transform on the positive semi-axis). This approach, called the rainbow Fourier transform (RFT), allows us to accurately retrieve the shape of the droplet size distribution by the application of the corresponding inverse transform to the observed polarized rainbow. While the basis functions of the proxy-transform are not exactly orthogonal in the finite angular range, this procedure needs to be complemented by a simple regression technique, which removes the retrieval artifacts. This non-parametric approach does not require any a priori knowledge of the droplet size distribution functional shape and is computationally fast (no look-up tables, no fitting, computations are the same as for the forward modeling).

Alexandrov, Mikhail D.↗
NASA NTRS1990

Scattering properties of natural snow and frost - Comparison with icy satellite photometry

The Hapke (1986) equation is presently fit to ascertain the single-scattering albedo of the icy satellites of Uranus and Neptune and the one-term Henyey-Greenstein particle-phase function g for each of the Middleton and Mungall (1952) goniophotometric data samples. There emerge both very high single-scattering albedos and strongly forward-scattering particle phase functions; while these are in keeping with Mie theory-based theoretical considerations, they contrast with the observed backscattering behavior of icy satellites. It is suggested the icy satellite frost grains are aggregated into particles of complex texture, which produce the unusual backscattering behavior.

Verbiscer, Anne J.↗
NASA NTRS1994

Simulations of the effects of water vapor, cloud liquid water, and ice on AMSU moisture channel brightness temperatures

Radiative transfer simulations are performed to determine how water vapor and nonprecipitating cloud liquid water and ice particles within typical midlatitude atmospheres affect brightness temperatures T(sub B)'s of moisture sounding channels used in the Advanced Microwave Sounding Unit (AMSU) and AMSU-like instruments. The purpose is to promote a general understanding of passive top-of-atmosphere T(sub B)'s for window frequencies at 23.8, 89.0, and 157.0 GHz, and water vapor frequencies at 176.31, 180.31, and 182.31 GHz by documenting specific examples. This is accomplished through detailed analyses of T(sub B)'s for idealized atmospheres, mostly representing temperate conditions over land. Cloud effects are considered in terms of five basic properties: droplet size distribution, phase, liquid or ice water content, altitude, and thickness. Effects on T(sub B) of changing surface emissivity also are addressed. The brightness temperature contribution functions are presented as an aid to physically interpreting AMSU T(sub B)'s. Both liquid and ice clouds impact the T(sub B)'s in a variety of ways. The T(sub B)'s at 23.8 and 89 GHz are more strongly affected by altostratus liquid clouds than by cirrus clouds for equivalent water paths. In contrast, channels near 157 and 183 GHz are more strongly affected by ice clouds. Higher clouds have a greater impact on 157- and 183-GHz T(sub B)'s than do lower clouds. Clouds depress T(sub B)'s of the higher-frequency channels by suppressing, but not necessarily obscuring, radiance contributions from below. Thus, T(sub B)'s are less closely associated with cloud-top temperatures than are IR radiometric temperatures. Water vapor alone accounts for up to 89% of the total attenuation by a midtropospheric liquid cloud for channels near 183 GHz. The Rayleigh approximation is found to be adequate for typical droplet size distributions; however, Mie scattering effects from liquid droplets become important for droplet size distribution functions with modal radii greater than 20 micrometers near 157 and 183 GHz, and greater than 30-40 micrometers at 89 GHz. This is due mainly to the relatively small concentrations of droplets much larger than the mode radius. Orographic clouds and tropical cumuli have been observed to contain droplet size distributions with mode radii in the 30-40 micrometers range. Thus, as new instruments bridge the gap between microwave and infrared to frequencies even higher than 183 GHz, radiative transfer modelers are cautioned to explicitly address scattering characteristics of such clouds.

Muller, Bradley M.↗
NASA NTRS1976

Pulse height response of an optical particle counter to monodisperse aerosols

The pulse height response of a right angle scattering optical particle counter has been investigated using monodisperse aerosols of polystyrene latex spheres, di-octyl phthalate and methylene blue. The results confirm previous measurements for the variation of mean pulse height as a function of particle diameter and show good agreement with the relative response predicted by Mie scattering theory. Measured cumulative pulse height distributions were found to fit reasonably well to a log normal distribution with a minimum geometric standard deviation of about 1.4 for particle diameters greater than about 2 micrometers. The geometric standard deviation was found to increase significantly with decreasing particle diameter.

Wilmoth, R. G.↗
NASA NTRS1974

Multichannel forward scattering meter for oceanography

An instrument was designed and built that measures the light scattered at several angles in the forward direction simultaneously. The instrument relies on an optical multiplexing technique for frequency encoding of the different channels suitable for detection by a single photodetector. A Mie theory computer program was used to calculate the theoretical volume scattering function for a suspension of polystyrene latex spheres. The agreement between the theoretical and experimental volume scattering functions is taken as a verification of the calibration technique used.

Mccluney, W. R.↗
NASA NTRS1977

Planetary isophotes as a clue to aerosol characteristics

A study was made to see how much information could be extracted from the Mariner 9 Mars isophotes taken at phase angle roughly 60 deg. Minnaert functions and both isotropic and Rayleigh scattering could easily be ruled out, and it was essential to use forward-peaked phase functions computed from Mie theory. Isophotes similar to those observed are plotted assuming a semi-infinite dust cloud with a considerable variation in particle properties and size distribution, so long as the ratio of the multiply to singly scattered light is held within certain limits. These conditions are met by micron-sized, moderately absorbing mineral grains whose mean size should not be much larger than a micron. It was also found that a dust cloud of finite optical thickness bounded from below by a Lambert ground would fit the isophote data.

Kattawar, G. W.↗
NASA NTRS1975

Planetary isophotes as a clue to aerosol characteristics

A study was conducted to see how much information could be extracted from the Mariner 9 Mars isophotes taken at a phase angle of approximately 60 deg. It was found that the Minnaert functions and both isotropic and Rayleigh scattering could easily be ruled out, and that it was essential to use forward-peaked phase functions, which were computed from Mie theory. Isophotes similar to those observed assuming a semi-infinite dust cloud with a considerable variation in particle properties and size distribution could be obtained, so long as the ratio of the multiply- to singly-scattered light was held within certain limits. These conditions are met by micron-sized, moderatly absorbing mineral grains whose mean size should not be much larger than a micron. It was also found that a dust cloud of finite optical thickness bounded from below by a Lambert ground would fit the isophote data.

Kattawar, G. W.↗
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

Laser anemometer signals - Visibility characteristics and application to particle sizing

Investigations have been conducted concerning the characteristics of the visibility function as determined by the parameters of the laser anemometer system and the electromagnetic scattering properties of the particles. Experiments have been performed to evaluate the backscatter visibility of signals from a symmetric, s polarization laser anemometer as a function of the particle diameter and a parameter ratio. The results have been compared with the predictions of an analysis based on Mie's scattering theory. The analysis has also been used to evaluate the effects of the collecting aperture's size and location.

Adrian, R. J.↗
NASA NTRS1972

Formation of spectral lines in planetary atmospheres. III - The use of analytic scattering diagrams in computations of synthetic spectra for cloudy atmospheres.

Results of some comparisons that have been made of line profiles and equivalent widths computed from atmospheric models where the scattering has been represented by the Mie theory and a simple analytic expression, the Heyney-Greenstein function. These results show that the spectroscopic features for these models are indistinguishable and demonstrate the value of using this simple analytic function in terms of the great saving in computer time when computing synthetic spectra for any cloudy planetary atmosphere.

Hunt, G. E.↗
NASA NTRS1973

Preliminary data on the optical properties of solid ammonia and scattering parameters for ammonia cloud particles.

The infrared absorption spectrum of solid ammonia is obtained from 2 to 125 microns as a composite of the published measurements. From this, the absorption coefficient and the complex refractive index are calculated as a function of frequency by integration of the Kramers-Kroenig dispersion relations. These data are used in a Mie theory analysis to obtain the basic parameters for scattering of long wavelength radiation by solid ammonia particles; this is believed to be an important process in radiative transfer within the atmospheres of the giant planets.

Taylor, F. W.↗
NASA NTRS1995

Nonsphericity of dust-like tropospheric aerosols: Implications for aerosol remote sensing and climate modeling

T-matrix computations of light scattering by polydispersions of randomly oriented nonspherical aerosols and Mie computations for equivalent spheres are compared. Findings show that even moderate nonsphericity results in suubstantial errors in the retrieved aerosol optical thickness if satellite reflectance measurements are analyzed using Mie theory. On the other hand, the use of Mie theory for nonspherical aerosols produces negligible errors in the computation of albedo and flux related quantities, provided that the aerosol size distribution and optical thickness are known beforehand. The first result can be explained by large nonspherical-spherical differences in scattering phase function, while the second result follows from small nonspherical-spherical differences in single-scattering albedo and asymmetry parameter. No cancellation of errors occurs if one consistently uses Mie theory in the retrieval algorithm and then in computing the albedo for the retrieved aerosol optical thickness.

Mishchenko, M. I.↗
NASA NTRS1993

A test of the applicability of independent scattering to high albedo planetary regoliths

We show that 'independent scattering' is a useful approximation for high albedo particles whose size and packing density are similar to typical particles in the lunar regolith. Laboratory measurements of the intensity and linear polarization of light scattered from a laboratory sample of glass spheres of know size and composition are compared to radiative transfer calculations of the same observable quantities. Mie scattering is integrated over the size distribution of the particles to determine the mean phase and polarization functions, or phase matrix, of the particle. Assuming that the particles scatter independently, the 'doubling method' is used to rigorously calculate multiple scattering in an optically thick layer of these anisotropically scattering particles. All of the major features 'predicted' in the calculated intensity (double peaks at small phase angles) and polarization (negative branch at small phase angles, large positive peak near 20 degrees phase, and small polarization elsewhere) are observed in the laboratory measurements, with good quantitative agreement indicated at phase angles less than 90 degrees. Even though the particles are supported by physical contact with each other in the sample, as are the particles in planetary regoliths, the independent scattering calculation yields a good approximation to both the intensity and polarization. The physical parameters input to the calculation are only the size distribution of the particles and their complex index of refraction (composition). Significant advantages of this approach are that the phase matrix is calculated from basic physical principles and both the intensity and polarization are determined simultaneously. This model may have broad applications to the interpretation of photometry, spectroscopy, and polarimetry of the icy regoliths of high albedo satellites. The intent of this effort is to perform a controlled experiment that tests the utility of the independent scattering assumption

Goguen, J. D.↗
NASA NTRS1987

Subcentimeter-size particle distribution functions in planetary rings from Voyager radio and photopolarimeter occultation data

Analysis of measurements of the scattered and direct components of Voyager 1 radio occultation signals at 3.5 and 13 cm wavelengths yield estimates of the distribution functions of supracentimeter-size particles and thickness of relatively broad regions in Saturn's rings. If mearurements of signal amplitude at a shorter wavelength are combined with the previously analyzed data, the shape of the distribution functions characterizing the smaller particles can be constrained. If size distributions of arbitrary form were considered, many solutions are found that are consistent with the three available observations of signal amplitude. The best-fit power law was calculated to the three observations at three wavelengths for several of the embedded Saturn ringlets. Mie scattering theory predicts that the measured phase of the radio occultation signal is highly sensitive to particles ranging from 0.1 to 1.0 wavelengths in size, thus additional constraints on the subcentimeter-size distribution functions for both the Saturn and Uranus rings can in principle be derived from radio phase measurements.

Zebker, Howard A.↗
NASA NTRS1983

LANDSAT-D investigations in snow hydrology

The atmospheric radiative transfer calculation program (ATARD) and its supporting programs (setting up atmospheric profile, making Mie tables and an exponential-sum-fitting table) were completed. More sophisticated treatment of aerosol scattering (including angular phase function or asymmetric factor) and multichannel analysis of results from ATRAD are being developed. Some progress was made on a Monte Carlo program for examining two dimensional effects, specifically a surface boundary condition that varies across a scene. The MONTE program combines ATRAD and the Monte Carlo method together to produce an atmospheric point spread function. Currently the procedure passes monochromatic tests and the results are reasonable.

Dozier, J.↗
NASA NTRS1989

Cirrus optical depth retrieval from satellite-measured bidirectional reflectance

In the framework of investigating the relationship between the visible optical depth and microphysics of cirrus clouds, the doubling scheme for radiative transfer in cirrus cloudy atmospheres, as developed by Takano and Liou (1988), has been used to compute the bidirectional reflectances at the top of the atmosphere. Reflectance data taken at about the same time from GOES and AVHRR over Waussau, as well as particle distributions observed during the FIRE IFO carried out in Wisconsin (1986) were the basis of the experiment. For the cirrus microphysical model, hexagonal ice crystals and area-equivalent ice spheres are considered. The single scattering phase functions for randomly oriented hexagonal columns and area-equivalent ice spheres are computed from geometric optics and Mie theory, respectively.

Takano, Y.↗