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NASA NTRS1974

Particle distribution functions in modulation theory

Development of a simple formulation of the cosmic ray modulation problem which involves the use of the omnidirectional part of the distribution function in phase space, and the magnitude of the momentum or the rigidity. It is shown that, by employing the proposed formulation, the Compton-Getting factor is greatly simplified, and the well-known force-field equation is reduced to a one-dimensional Vlasov equation. In addition, another Vlasov equation can be written for the very low energy galactic particles which are convected by the solar wind.

Forman, M. A.↗

NASA NTRS1981

Far-infrared /FIR/ optical black bidirectional reflectance distribution function /BRDF/

A nonspecular reflectometer and its operation at far-infrared wavelengths are described. Large differences in nonspecular reflectance were found to exist between different optically black coatings. Normal incidence bidirectional reflectance distribution function /BRDF) measurements at wavelengths between 12 and 316 microns of three black coatings show that their mean BRDFs increase with wavelength. The specularity of two of these coatings also showed a strong wavelength dependence, while the specularity of one coating seemed independent of wavelength. The BRDF of one coating depended on the angle of incidence at 12 and 38 microns, but not at 316 microns. Beyond 200 microns, it was found necessary to correct the measurements for the beam spread of the instrument.

Smith, S. M.↗

NASA NTRS2010

Solar Wind Halo Formation by the Scattering of the Strahl via Direct Cluster/PEACE Observations of the 3D Velocity Distribution Function

It has been suggested by a number of authors that the solar wind electron halo can be formed by the scattering of the strahl. On frequent occasions we have observed in electron angular skymaps (Phi/Theta-plots) of the electron 3D velocity distribution functions) a bursty-filament of particles connecting the strahl to the solar wind core-halo. These are seen over a very limited energy range. When the magnetic field is well off the nominal solar wind flow direction such filaments are inconsistent with any local forces and are probably the result of strong scattering. Furthermore, observations indicates that the strahl component is frequently and significantly anisotropic (Tper/Tpal approx.2). This provides a possible free energy source for the excitation of whistler waves as a possible scattering mechanism. The empirical observational evidence between the halo and the strahl suggests that the strahl population may be, at least in part, the source of the halo component.

Figueroa-Vinas, Adolfo↗

NASA NTRS2004

Use of Probability Distribution Functions for Discriminating Between Cloud and Aerosol in Lidar Backscatter Data

In this paper we describe the algorithm hat will be used during the upcoming Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) mission for discriminating between clouds and aerosols detected in two wavelength backscatter lidar profiles. We first analyze single-test and multiple-test classification approaches based on one-dimensional and multiple-dimensional probability density functions (PDFs) in the context of a two-class feature identification scheme. From these studies we derive an operational algorithm based on a set of 3-dimensional probability distribution functions characteristic of clouds and aerosols. A dataset acquired by the Cloud Physics Lidar (CPL) is used to test the algorithm. Comparisons are conducted between the CALIPSO algorithm results and the CPL data product. The results obtained show generally good agreement between the two methods. However, of a total of 228,264 layers analyzed, approximately 5.7% are classified as different types by the CALIPSO and CPL algorithm. This disparity is shown to be due largely to the misclassification of clouds as aerosols by the CPL algorithm. The use of 3-dimensional PDFs in the CALIPSO algorithm is found to significantly reduce this type of error. Dust presents a special case. Because the intrinsic scattering properties of dust layers can be very similar to those of clouds, additional algorithm testing was performed using an optically dense layer of Saharan dust measured during the Lidar In-space Technology Experiment (LITE). In general, the method is shown to distinguish reliably between dust layers and clouds. The relatively few erroneous classifications occurred most often in the LITE data, in those regions of the Saharan dust layer where the optical thickness was the highest.

Liu, Zhaoyan↗

NASA NTRS2010

Initial Studies of the Bidirectional Reflectance Distribution Function of Multi-Walled Carbon Nanotube Structures for Stray Light Control Applications

The presentation examines the application of low reflectance surfaces in optical instruments, multi-walled carbon nanotubes (MWCNTs), research objects, MWCNT samples, measurement of 8 deg. directional/hemispherical reflectance, measurement of bidirectional reflectance distribution function (BRDF), and what is current the "blackest ever black".

Butler, J. J.↗

NASA NTRS2021

Deconvolution of SNPP VIIRS Solar Diffuser Bidirectional Reflectance Distribution Function On-orbit Change Factor

The Earth-observing Visible Infrared Imaging Radiometer Suite (VIIRS) on the Suomi National Polar-orbiting Partnership satellite regularly calibrates its reflective solar bands (RSBs), primarily through observing an onboard sunlit solar diffuser (SD). The on-orbit change of the value of the SD bidirectional reflectance distribution function (BRDF) is quantified by a numerical factor, called the H-factor, and is determined by the onboard SD stability monitor (SDSM). Because the spectral response function of an SDSM detector spreads in wavelength, the directly measured H-factor is the true H-factor convolved with the spectral response function. To find the true H-factor, we use the traditional direct method and an innovative iterative approach to separately deconvolve the measured H-factor. Our iterative approach relies on two properties of the SDSM detector spectral response function: the central peak width is narrow enough so that the H-factor does not change much over the peak width, and the dominance of the spectral response function’s integral with respect to the wavelength over the width. The iterative approach is more accurate, of a smaller noise impact, much more flexible in terms of interpolation and extrapolation of function values, and faster. We have used deconvolved H-factors to calibrate the NASA SNPP VIIRS RSB Collections 1 and 2 Level-1B products.

SNPP VIIRS↗

NASA NTRS1994

Electron distribution function behavior during localized transverse ion acceleration events in the topside auroral zone

The Topaz3 auroral sounding rocket made the following observations concerning the transfer of precipitating auroral electron energy to transverse ion acceleration in the topside auroral zone. During the course of the flight, the precipitating electron beam was modified to varying degrees by interaction with VLF hiss, at times changing the beam into a field-aligned plateau. The electron distribution functions throughout the flight are classified according to the extent of this modification, and correspondences with ion acceleration events are sought. The hiss power during most of this rocket flight apparently exceeded the threshold for collapse into solitary structures. At the times of plateaued electron distributions, the collapse of these structures was limited by Landau damping through the ambient ions, resulting in a velocity-dependent acceleration of both protons and oxygen. This initial acceleration is sufficient to supply the number flux of upflowing ions observed at satellite altitudes. The bursty ion acceleration was anticorrelated, on 1-s or smaller timescales, with dispersive bursts of precipitating field-aligned electrons, although on longer timescales the bursty ions and the bursty electrons are correlated.

Lynch, K. A.↗

NASA NTRS1995

Wigner distribution function and entropy of the damped harmonic oscillator within the theory of the open quantum systems

The harmonic oscillator with dissipation is studied within the framework of the Lindblad theory for open quantum systems. By using the Wang-Uhlenbeck method, the Fokker-Planck equation, obtained from the master equation for the density operator, is solved for the Wigner distribution function, subject to either the Gaussian type or the delta-function type of initial conditions. The obtained Wigner functions are two-dimensional Gaussians with different widths. Then a closed expression for the density operator is extracted. The entropy of the system is subsequently calculated and its temporal behavior shows that this quantity relaxes to its equilibrium value.

Isar, Aurelian↗

NASA NTRS1980

Distribution function representation of energy spectra of H, He, C, O and Fe in corotating particle streams

From an analysis of nine corotating events observed near 1 AU during the 1974-1976 solar minimum, the spectral parameters for H, He, C, O and Fe and relative abundances of these elements and of Ne, Mg, Si, and S-Ca were determined. The distribution functions of H, He, O and Fe are well represented by an exponential in particle speed over the energy range of the measurements from 0.3 to 5 MeV/nucleon. The composition resembles that of the solar corona, particularly in the O/C ratio which is 0.95 + or - 0.19, and the He/H and He/Ne ratios are similar to the respective ratios in the solar wind. The results are consistent with interplanetary statistical acceleration of these particles out of the high-energy tail of the high-speed solar wind.

Gloeckler, G.↗

NASA NTRS1986

Determination of grain size distribution function using two-dimensional Fourier transforms of tone pulse encoded images

Microstructural images may be tone pulse encoded and subsequently Fourier transformed to determine the two-dimensional density of frequency components. A theory is developed relating the density of frequency components to the density of length components. The density of length components corresponds directly to the actual grain size distribution function from which the mean grain shape, size, and orientation can be obtained.

Generazio, E. R.↗

NASA NTRS1988

Determination of grain-size distribution function using two-dimensional Fourier transforms of tone-pulse-encoded images

Microstructural images may be tone pulse encoded and subsequently Fourier transformed to determine the two-dimensional density of frequency components. A theory is developed relating the density of frequency components to the density of length components. The density of length components corresponds directly to the actual grain-size distribution function from which the mean grain shape, size, and orientation can be obtained.

Generazio, E. R.↗

NASA NTRS1977

Distribution functions for energetic oxygen atoms in the earth's lower atmosphere

Direct photolysis of O3 and quenching of O(1D) by N2 provide abundant sources of fast oxygen atoms for earth's lower atmosphere. The concentration of atoms with energy above 0.7 eV may exceed the concentration of O(1D) for all altitudes below 18 km, and these atoms may play an important role in lower-atmospheric chemistry. Distribution functions for O(3P) are given for the energy interval 0.1-1.3 eV and a range of altitudes from 0 to 62 km.

Logan, J. A.↗

NASA NTRS2016

A Proton-Cyclotron Wave Storm Generated by Unstable Proton Distribution Functions in the Solar Wind

We use audification of 0.092 seconds cadence magnetometer data from the Wind spacecraft to identify waves with amplitudes greater than 0.1 nanoteslas near the ion gyrofrequency (approximately 0.1 hertz) with duration longer than 1 hour during 2008. We present one of the most common types of event for a case study and find it to be a proton-cyclotron wave storm, coinciding with highly radial magnetic field and a suprathermal proton beam close in density to the core distribution itself. Using linear Vlasov analysis, we conclude that the long-duration, large-amplitude waves are generated by the instability of the proton distribution function. The origin of the beam is unknown, but the radial field period is found in the trailing edge of a fast solar wind stream and resembles other events thought to be caused by magnetic field footpoint motion or interchange reconnection between coronal holes and closed field lines in the corona.

instabilities - plasmas↗

NASA NTRS1982

Bidirectional reflectance distribution function of the Infrared Astronomical Satellite solar-shield material

The Infrared Astronomical Satellite (IRAS) telescope has an outer shield on it which is used to reduce the amount of thermal radiation that enters the telescope. The shield forms the first part of the baffle structure which reduces the photon incidence on the focal plane. It was, therefore, necessary to model this structure for scattering, and a required input for such modeling is the scattering characteristic of this surface. Attention is given to the measurement of the bidirectional reflectance distribution function (BRDF), the reflected radiance divided by the incident irradiance at 10.6 micrometers, 118 micrometers, and at several angles of incidence. Visual observation of the gold sample shows that there are striations which line up in a single direction. The data were, therefore, taken with the sample oriented in each of two directions.

Hubbs, J. E.↗

NASA NTRS1994

Modeling the bidirectional reflectance distribution function of mixed finite plant canopies and soil

An analytical model of the bidirectional reflectance for optically semi-infinite plant canopies has been extended to describe the reflectance of finite depth canopies contributions from the underlying soil. The model depends on 10 independent parameters describing vegetation and soil optical and structural properties. The model is inverted with a nonlinear minimization routine using directional reflectance data for lawn (leaf area index (LAI) is equal to 9.9), soybeans (LAI, 2.9) and simulated reflectance data (LAI, 1.0) from a numerical bidirectional reflectance distribution function (BRDF) model (Myneni et al., 1988). While the ten-parameter model results in relatively low rms differences for the BRDF, most of the retrieved parameters exhibit poor stability. The most stable parameter was the single-scattering albedo of the vegetation. Canopy albedo could be derived with an accuracy of less than 5% relative error in the visible and less than 1% in the near-infrared. Sensitivity were performed to determine which of the 10 parameters were most important and to assess the effects of Gaussian noise on the parameter retrievals. Out of the 10 parameters, three were identified which described most of the BRDF variability. At low LAI values the most influential parameters were the single-scattering albedos (both soil and vegetation) and LAI, while at higher LAI values (greater than 2.5) these shifted to the two scattering phase function parameters for vegetation and the single-scattering albedo of the vegetation. The three-parameter model, formed by fixing the seven least significant parameters, gave higher rms values but was less sensitive to noise in the BRDF than the full ten-parameter model. A full hemispherical reflectance data set for lawn was then interpolated to yield BRDF values corresponding to advanced very high resolution radiometer (AVHRR) scan geometries collected over a period of nine days. The resulting parameters and BRDFs are similar to those for the full sampling geometry, suggesting that the limited geometry of AVHRR measurements might be used to reliably retrieve BRDF and canopy albedo with this model.

Schluessel, G.↗

NASA NTRS2019

Experimentally-Derived Bidirectional Reflectance Distribution Function Data in Support of the Orbital Debris Program Office

The NASA Orbital Debris Program Office (ODPO) has used various optical assets to acquire photometric data of Earth-orbiting objects to define the orbital debris environment. To better characterize and model optical data acquired from ground-based telescopes, the Optical Measurements Center (OMC) at NASA Johnson Space Center emulates illumination conditions seen in space by using equipment and techniques that parallel telescopic observations and source-target-sensor orientations. One of the OMC goals is to improve the size calculation used for optical data by developing an optical-based Size Estimation Model. The current size estimation requires applying a Lambertian phase function, a set albedo value, and range to the observed magnitude. The first step to improving the sampled brightness of laboratory targets is to remove aspect-angle dependencies. Then, the volume of possible object viewing angles is sampled at 21 combinations of azimuth and zenith angles for each solar phase angle. Finally, the acquired images are input into an image processing program that generates approximations for the object’s Bidirectional Reflectance Distribution Function (BRDF) and phase function. The BRDF is a radiometric concept that identifies an object’s material composition by matching a BRDF approximated with photometric data collected by ground-based telescopes with a BRDF generated experimentally from a known object in the laboratory. This paper discusses the validation of experimental BRDF and phase function approximations produced in the OMC and how the findings will be incorporated into ODPO models. A Lambertian sphere is imaged and the subsequent experimental functions are scrutinized to confirm that they correspond to an object that has an isotropic luminance. With the image processing algorithm validated, test objects with varying optical properties are then imaged to confirm that the produced photometric functions are both unique and repeatable. Once the validation is complete, the OMC will be used to evaluate a subset of fragments from a hypervelocity impact test of a mock-up satellite and assess the appropriate phase function and size estimates using BRDF measurements for a large volume of targets composed of various shapes, sizes, and materials.

Orbital Debris Program Office (ODPO)↗

NASA NTRS1980

Distribution functions of type III electrons observed in interplanetary space

Simultaneous energetic electron and solar radio observations from the ISEE-3 spacecraft of several solar type III radio bursts are analyzed and discussed. Two types of electron events are found: (1) normal flare associated electron events in the 20 to greater than 100 keV range, and (2) low energy, 2 to 10 keV, electron events which appear to be associated with individual type III bursts from low frequency type III storms. The arrival direction and frequency of the radio emission are identified and the temporal behavior of the in situ radio intensity and the electron intensity are compared. Calculations of the electron velocity distribution function parallel to the magnetic field are made, implying that for electron events above 20 keV, scattering in the pitch angle is significant in modifying this function.

Lin, R. P.↗

NASA NTRS2015

Role of Multiple Atmospheric Reflections in Formation of Electron Distribution Function in the Diffuse Aurora Region

The precipitation of high-energy magnetospheric electrons (E greater than 500-600 electronvolts) in the diffuse aurora contributes significant energy flux into Earth's ionosphere. In the diffuse aurora, precipitating electrons initially injected from the plasmasheet via wave-particle interaction processes degrade in the atmosphere toward lower energies and produce secondary electrons via impact ionization of the neutral atmosphere. These initially precipitating electrons of magnetospheric origin can be additionally reflected back into the magnetosphere by the two magnetically conjugated atmospheres, leading to a series of multiple reflections that can greatly influence the initially precipitating flux at the upper ionospheric boundary (700-800 kilometers) and the resultant population of secondary electrons and electrons cascading toward lower energies. We present the solution of the Boltzmann.Landau kinetic equation that uniformly describes the entire electron distribution function in the diffuse aurora, including the affiliated production of secondary electrons (E is less than or equal to 600 electronvolts) and their energy interplay in the magnetosphere and two conjugated ionospheres. This solution takes into account the role of multiple atmospheric reflections of the precipitated electrons that were initially moved into the loss cone via wave.particle interaction processes in Earth's plasmasheet.

Khazanov, George V.↗