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NASA NTRS2003

Properties of the Hermean Regolith: New Optical Reflectance Spectra, Comparison with Lunar Anorthosites and Mineralogical Modelling - 5

We present new optical (0.4-0.65 micron) spectra of Mercury and lunar pure anorthosite locations, obtained quasi-simultaneously with the Nordic Optical Telescope (NOT) in 2002. A comparative study is performed with the model of Lucey et al. between iron-poor, mature, pure anorthosite (less than 90% plagioclase feldspar) Clementine spectra from the lunar farside and a combined 0.4-1.0 micron mercurian spectrum, obtained with the NOT, calculated for standard photometric geometry. Mercury is located at more extreme locations in the Lucey ratio-reflectance diagrams than any known lunar soil, specifically with respect to the extremely iron-poor mature anorthosites. Though quantitative prediction of FeO and TiO2 abundances cannot be made without a more generally applicable model, we find qualitatively that the abundances of both these oxides must be near zero for Mercury. We utilize the theory of Hapke, with realistic photometric parameters, to model laboratory spectra of matured mineral powders and lunar soils, and remotely sensed spectra of lunar anorthosites and Mercury. An important difference between fabricated and natural powders is the high value for the internal scattering parameter necessary to interpret the spectra for the former, and the requirement of rough and non-isotropically scattering surfaces in the modelling of the latter. The mature lunar anorthosite spectra were well modelled with binary mixtures of calcic feldspars and olivines, grain sizes of 25-30 micron and a concentration of submicroscopic metallic iron (SMFe) of 0.12-0.15% in grain coatings. The mercurian spectrum is not possible to interpret from terrestrial mineral powder spectra without introducing an average particle scattering function for the bulk soil that increases in backscattering efficiency with wavelength. The observed spectrum is somewhat better predicted with binary mixture models of feldspars and pyroxenes, that single-component regoliths consisting of either albite or diopside. Correct spectral reflectance values were predicted with a concentration of 0.1 wt% SMFe in coatings of 15-30 micron sized grains. Since reasonable cosmogonical formation scenarios for Mercury, or meteoritic infall, predict iron concentrations at least this high, we draw the conclusion that the average grain size of Mercury is about a factor of two smaller than for average returned lunar soil samples. The 0.6-2.5 micron spectrum of McCord and Clark is used to further limit the possible range of mineralogical composition of Mercury. It is found that an intimately mixed and matured 3 : 1 labradorite-to-enstatite regolith composition best matches both the optical and near-infrared spectra, yielding an abundance of approx. 1.2 wt% FeO and -approx. 0 wt% TiO2.

Warell, J.↗
NASA NTRS2010

Notes on SAW Tag Interrogation Techniques

We consider the problem of interrogating a single SAW RFID tag with a known ID and known range in the presence of multiple interfering tags under the following assumptions: (1) The RF propagation environment is well approximated as a simple delay channel with geometric power-decay constant alpha >/= 2. (2) The interfering tag IDs are unknown but well approximated as independent, identically distributed random samples from a probability distribution of tag ID waveforms with known second-order properties, and the tag of interest is drawn independently from the same distribution. (3) The ranges of the interfering tags are unknown but well approximated as independent, identically distributed realizations of a random variable rho with a known probability distribution f(sub rho) , and the tag ranges are independent of the tag ID waveforms. In particular, we model the tag waveforms as random impulse responses from a wide-sense-stationary, uncorrelated-scattering (WSSUS) fading channel with known bandwidth and scattering function. A brief discussion of the properties of such channels and the notation used to describe them in this document is given in the Appendix. Under these assumptions, we derive the expression for the output signal-to-noise ratio (SNR) for an arbitrary combination of transmitted interrogation signal and linear receiver filter. Based on this expression, we derive the optimal interrogator configuration (i.e., transmitted signal/receiver filter combination) in the two extreme noise/interference regimes, i.e., noise-limited and interference-limited, under the additional assumption that the coherence bandwidth of the tags is much smaller than the total tag bandwidth. Finally, we evaluate the performance of both optimal interrogators over a broad range of operating scenarios using both numerical simulation based on the assumed model and Monte Carlo simulation based on a small sample of measured tag waveforms. The performance evaluation results not only provide guidelines for proper interrogator design, but also provide some insight on the validity of the assumed signal model. It should be noted that the assumption that the impulse response of the tag of interest is known precisely implies that the temperature and range of the tag are also known precisely, which is generally not the case in practice. However, analyzing interrogator performance under this simplifying assumption is much more straightforward and still provides a great deal of insight into the nature of the problem.

Barton, Richard J.↗
NASA NTRS2012

Sensitivity of Multiangle, Multispectral Polarimetric Remote Sensing Over Open Oceans to Water-Leaving Radiance: Analyses of RSP Data Acquired During the MILAGRO Campaign

For remote sensing of aerosol over the ocean, there is a contribution from light scattered underwater. The brightness and spectrum of this light depends on the biomass content of the ocean, such that variations in the color of the ocean can be observed even from space. Rayleigh scattering by pure sea water, and Rayleigh-Gans type scattering by plankton, causes this light to be polarized with a distinctive angular distribution. To study the contribution of this underwater light polarization to multiangle, multispectral observations of polarized reflectance over ocean, we previously developed a hydrosol model for use in underwater light scattering computations that produces realistic variations of the ocean color and the underwater light polarization signature of pure sea water. In this work we review this hydrosol model, include a correction for the spectrum of the particulate scattering coefficient and backscattering efficiency, and discuss its sensitivity to variations in colored dissolved organic matter (CDOM) and in the scattering function of marine particulates. We then apply this model to measurements of total and polarized reflectance that were acquired over open ocean during the MILAGRO field campaign by the airborne Research Scanning Polarimeter (RSP). Analyses show that our hydrosol model faithfully reproduces the water-leaving contributions to RSP reflectance, and that the sensitivity of these contributions to Chlorophyll a concentration [Chl] in the ocean varies with the azimuth, height, and wavelength of observations. We also show that the impact of variations in CDOM on the polarized reflectance observed by the RSP at low altitude is comparable to or much less than the standard error of this reflectance whereas their effects in total reflectance may be substantial (i.e. up to >30%). Finally, we extend our study of polarized reflectance variations with [Chl] and CDOM to include results for simulated spaceborne observations.

Chowdhary, Jacek↗
NASA NTRS2023

Simulated Inherent Optical Properties of Aquatic Particles Using the Equivalent Algal Populations (EAP) Model

Paired measurements of phytoplankton absorption and backscatter, the inherent optical properties central to the interpretation of ocean colour remote sensing data, are notoriously rare. We present a dataset of Chlorophyll a (Chl a) -specific phytoplankton absorption, scatter and backscatter for 17 different phytoplankton groups, derived from first principles using measured in vivo pigment absorption and a well-validated semi-analytical coated sphere model which simulates the full suite of biophysically consistent phytoplankton optical properties. The optical properties of each simulated phytoplankton cell are integrated over an entire size distribution and are provided at high spectral resolution. The model code is additionally included to enable user access to the complete set of wavelength-dependent, angularly resolved volume scattering functions. This optically coherent dataset of hyperspectral optical properties for a set of globally significant phytoplankton groups has potential for use in algorithm development towards the optimal exploitation of the new age of hyperspectral satellite radiometry.

Equivalent Algal Populations↗
NASA NTRS1975

A three-parameter analytic phase function for multiple scattering calculations

A very simple procedure has been developed to fit the first three moments of an actual phase function with a three-parameter analytic phase function. The exact Legendre polynomial decomposition of this function is known which makes it quite suitable for multiple scattering calculations. The use of this function can be expected to yield excellent flux values at all depths within a medium. Since it is capable of reproducing the glory, it can be used in synthetic spectra computations from planetary atmospheres. Accurate asymptotic radiance values can also be achieved as long as the single scattering albedo is not less than 0.9.

Kattawar, G. W.↗
NASA NTRS1979

Global operators for delta functions - Extension to scattering states and the inclusion of spin

The paper presents an extension of the identities of Hiller, Sucher, and Feinberg for the evaluation of bound-state matrix elements of delta function operators, to scattering states. Attention is given to the technical difficulties encountered in the application of the scattering-state identities and how they can be overcome, including infrared singularities which arise if Coulomb forces are present and the velocity of the incident particle is small. In addition, both the scattering and bound-state identities are generalized to include spin-dependent contact interactions and spin-dependent Hamiltonians. Finally, it is stressed that the identities can be used to improve the accuracy of calculations of interest for diverse physical phenomena, ranging from positron annihilation to hyperfine structure.

Sucher, J.↗
NASA NTRS1993

Inference of cirrus cloud properties using satellite-observed visible and infrared radiances. II - Verification of theoretical cirrus radiative properties

The study presents a methodology developed to apply a parameterization of radiative transfer calculations to satellite analyses of cirrus clouds. Cloud heights and optical depths are derived from visible and IR window measurements taken during FIRE when cirrus clouds were present. Geostationary satellite retrievals are compared to lidar-derived cloud heights and retrievals from a polar-orbiting satellite taken at different angles to determine which theoretical models of scattering phase function and single-scattering albedo best represent actual cirrus clouds. Models using small scattering phase function and single-scattering albedo best represent actual cirrus clouds. It is concluded that interpretation of cirrus reflectance with water-droplet models leads to biased results. The cloud-height and optical depth biases can be minimized with the aid of the C20 or cirrostratus models.

Minnis, Patrick↗
NASA NTRS1975

Derivation of phase functions from multiply scattered sunlight transmitted through a hazy atmosphere

The intensity of sunlight multiply scattered in model atmospheres is derived from the equation of radiative transfer by an analytical small-angle approximation. The approximate analytical solutions are compared to rigorous numerical solutions of the same problem. Results obtained from an aerosol-laden model atmosphere are presented. Agreement between the rigorous and the approximate solutions is found to be within a few per cent. The analytical solution to the problem which considers an aerosol-laden atmosphere is then inverted to yield a phase function which describes a single scattering event at small angles. The effect of noisy data on the derived phase function is discussed.

Weinman, J. A.↗
NASA NTRS1980

Collisional redistribution of radiation. II - The effects of degeneracy on the equations of motion for the density matrix. III - The equation of motion for the correlation function and the scattered spectrum

The effect of correlations between an absorber atom and perturbers in the binary-collision approximation are applied to degenerate atomic systems. A generalized absorption profile which specifies the final state of the atom after an absorption event is related to the total intensities of Rayleigh scattering and fluorescence from the atom. It is suggested that additional dynamical information to that obtainable from ordinary absorption experiments is required in order to describe redistributed atomic radiation. The scattering of monochromatic radiation by a degenerate atom is computed in a binary-collision approximation; an equation of motion is derived for the correlation function which is valid outside the quantum-regression regime. Solutions are given for the weak-field conditions in terms of generalized absorption and emission profiles that depend on the indices of the atomic multipoles.

Burnett, K.↗
NASA NTRS1980

Collisional redistribution of radiation. III - The equation of motion for the correlation function and the scattered spectrum

Computations were made of the scattering of monochromatic radiation by a degenerate atom in the binary-collision approximation for field strengths whose products of the Rabi frequency for atomic transition and the duration of a strong collision are much less than 1. An expression of motion for the correlation function is derived which does not exclude the region where thermal correlations may be neglected; the equation is valid outside the quantum-regression regime, and has a straightforward solution for practical cases. Solutions for the weak-field linear response regime are presented in terms of generalized absorption and emission profiles which depend on the indices of the atomic multipoles.

Burnett, K.↗
NASA NTRS1980

Photometry of Saturn at large phase angles

In the present paper, the single-scattering phase function of Saturn's aerosols is determined from the vertical structure of Saturn's atmosphere, derived in a previous analysis, and Pioneer's imaging photometry of bright and dark zones on Saturn in red and blue light. The single-scattering phase function is well represented by a combination of two Henyey-Greenstein functions. Moderately forward scattering functions fit well both in red and blue light, although a definite difference between the two colors is found.

Tomasko, M. G.↗
NASA NTRS1980

Investigation of numerical properties of Hovenier's exit function equation for multiple scattering of light

A technique of deriving Hovenier's exit function equation (1978) for multiple scattering, starting with a set of invariant imbedding equations, is presented. The feasibility of the exit function equation as a means to obtain reflection and transmission functions is investigated for isotropic, Rayleigh, and Henyey-Greenstein phase functions with emphasis on the numerical stability, accuracy and timing. It is possible to compute the reflection function rather accurately with an efficiency comparable to that of the standard doubling technique for the same phase functions with moderate anisotropy. The resulting transmission is slightly less accurate than the reflection function, but it may be acceptable for practical purposes.

Kawabata, K.↗
NASA NTRS1975

Lunar electromagnetic scattering. IV - Transfer functions in the long-wavelength limit

The theory for asymmetric lunar magnetic induction in the long-wavelength limit, applicable to induction in the solar wind and magnetosheath plasmas at frequencies no higher than about 0.01 Hz, is presented. The lunar response to arbitrary ambient field orientations can be synthesized from the responses to field fluctuations parallel and perpendicular to the cavity axis. Radial and tangential transfer functions for a particular lunar electrical conductivity model are shown as functions of frequency and angular distance from the cavity axis for parallel and perpendicular field directions. Transfer functions based on asymmetric theory are significantly different from those based on symmetric approximations. Conductivity profiles from inversions of a given data set are strongly dependent on the theory incorporated in the inversions, the nature of the driving field, and the assumed location of the observer. Thus lunar conductivity models from surface and orbital magnetometer data, obtained either on the dayside or the nightside of the moon, must be determined using asymmetric theory.

Schwartz, K.↗
NASA NTRS1990

The Galactic far ultraviolet background

Investigations of the FUV background are discussed in the light of the methods employed and significant results of data interpretation. Attention is given to the data that confirm the generally accepted theory that the FUV flux originates in the Galaxy. The relationship between the flux measurements and the types of scattering by dust are investigated with attention given to the discrepancies inherent in reported scattering properties. Recent evidence shows wide ranges of albedo values and scattering-phase functions, and UV scattering grains are noted in all directions of the Galaxy that have low albedos and scatter isotropically. Recent detections of spectral emission features support the Galactic fountain model for the scattering material, and molecular hydrogen emission suggests that the emitting material tends to clump in hydrogen clouds.

Bowyer, Stuart↗
NASA NTRS2001

Columnar Aerosol Single-Scattering Albedo and Phase Function Retrieved from Sky Radiance Over the Ocean: Measurements of African Dust

The single-scattering albedo and phase function of African mineral dust are retrieved from ground-based measurements of sky radiance collected in the Florida Keys. The retrieval algorithm employs the radiative transfer equation to solve by iteration for these two properties which best reproduce the observed sky radiance using an assumed aerosol vertical structure and measured aerosol optical depth. Thus, no assumptions regarding particle size, shape, or composition are required. The single-scattering albedo, presented at fourteen wavelengths between 380 and 870 nm, displays a spectral shape expected of iron-bearing minerals but is much higher than current dust models allow. This indicates the absorption of light by mineral dust is significantly overestimated in climate studies. Uncertainty in the retrieved albedo is less than 0.02 due to the small uncertainty in the solar-reflectance-based calibration (12.2%) method employed. The phase function retrieved at 860 nm is very robust under simulations of expected experimental errors, indicating retrieved phase functions at this wavelength may be confidently used to describe aerosol scattering characteristics. The phase function retrieved at 443 nm is very sensitive to expected experimental errors and should not be used to describe aerosol scattering. Radiative forcing by aerosol is the greatest source of uncertainty in current climate models. These results will help reduce uncertainty in the absorption of light by mineral dust. Assessment of the radiative impact of aerosol species is a key component to NASA's Earth System Enterprise.

Cattrall, Christopher↗