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NASA NTRS1977

Multiple scattering in reflection nebulae. I - A Monte Carlo approach. II - Uniform plane-parallel nebulae with foreground stars. III - Nebulae with embedded illuminating stars

A method for calculating the surface brightness distribution on a plane-parallel reflection nebula of uniform density illuminated by a star located either in front of, behind, or arbitrarily inside the scattering medium is proposed. The Monte Carlo technique is used to find solutions to the radiative transfer problem. The scattering properties of the nebular particles are parameterized by the albedo for single scattering and a three-parameter analytic phase function. Calculations are then presented for the surface brightness distribution across the face of such nebulae with (1) a foreground star and (2) immersed stars. The calculations include the full effects of multiple scattering, are independent of a particular assumed grain material or size distribution, and are applicable to any wavelength region for which observations can be obtained.

Witt, A. N.↗

NASA NTRS1977

The theory and measurement of noncoherent microwave scattering parameters

The radar equation for incoherent scenes is derived and scattering coefficients are introduced in a systematic way to account for the complete interaction between the incident wave and the random scene. Intensity (power) and correlation techniques similar to that for coherent targets are proposed to measure all the scattering parameters. The sensitivity of the intensity technique to various practical realizations of the antenna polarization requirements is evaluated by means of computer simulated measurements, conducted with a scattering characteristic similar to that of the sea. It was shown that for scenes satisfying reciprocity one must admit three new cross-correlation scattering coefficients in addition to the commonly measured autocorrelation coefficients.

Claassen, J. P.↗

NASA NTRS1977

On the early scattering processes of the outer planets

The gradual scattering of small bodies by the Jovian planets in the late stage of their accretion is simulated by Monte Carlo calculation. The effects of collisional interaction of the scattered planetesimals with the inner planets and asteroidal belt are estimated. The total mass influx injected into the terrestrial zones from the outer planetary zone could be appreciable; however, if the damping effects due to the mutual inelastic or catastrophic collisions among the small bodies were significant, the total mass influx would be greatly reduced. The origin of the cometary Oort cloud in relation to these scattering processes is also discussed. The calculation indicates that, in addition to Jupiter, Uranus and Neptune were likely to be the major contributors to the population of long-period comets if they originated from such scattering processes.

Ip, W. H.↗

NASA NTRS1978

Comparison of satellite self-contamination experiments and scattering return flux calculations

Gaseous emissions from a spacecraft modify the orbital environment and degrade the observations of distant radiation sources. These emissions also provide contamination fluxes induced by self-scattering and scattering with ambient particles. Experiments were carried out on the orbiting Atmosphere Explorer D satellite (AE-D) to verify the calculated return fluxes of a neon source. Known rates of neon were emitted in the direction of the velocity vector on command from the MRMU (molecular return measurement unit). At 250 km the neutral mass spectrometer indicated a total neon return flux of 0.0246 times the emitted flux. The calculated fraction was 0.0123, including 0.00914 for the ambient scatter and 0.00354 for the altitude-independent self-scatter. The pressure gages indicated pressures less than 7 microtorr at altitudes from 161 to 210 km. The maximum pressure for the 161-km orbit was calculated as 0.74 microtorr.

Scialdone, J. J.↗

NASA NTRS1978

Model consideration of the bombardment event of the asteroidal belt by the planetesimals scattered from the Jupiter zone

The temporal evolutions of the planetesimals scattered from the Jupiter zone for different masses of the proto-Jupiter (2 = 0.1 and b = 1.0 of the present mass) are investigated. Due to the combined effects of the orbital evolution of the planetesimals and the elimination of these projectiles either via impact capture or injection into escape velocity by the outer planets, the whole scattering process lasts about 100 million yr for case (a) and about 10 million yr for case (b). The longer time scale may be a good estimate for the accretion time interval of Jupiter while the shorter one gives the upper time limit of the late heavy-bombardment epoch of the terrestrial planets due to planetesimals scattered from the Jupiter zone. Consideration of the collisional interaction of these projectiles with the asteroids indicates that the corresponding bombardment effect could be rather appreciable. From this point of view, the structure of the asteroidal belt could be affected significantly not only by Jupiter's gravitational perturbation effect but also by its early scattering process.

Ip, W.-H.↗

NASA NTRS1978

Effect of molecular anisotropy on beam scattering measurements

Within the energy sudden approximation, the total integral and total differential scattering cross sections are given by the angle average of scattering cross sections computed at fixed rotor orientations. Using this formalism the effect of molecular anisotropy on scattering of He by HCl and by CO is examined. Comparisons with accurate close coupling calculations indicate that this approximation is quite reliable, even at very low collision energies, for both of these systems. Comparisons are also made with predictions based on the spherical average of the interaction. For HCl the anisotropy is rather weak and its main effect is a slight quenching of the oscillations in the differential cross sections relative to predictions of the spherical averaged potential. For CO the anisotropy is much stronger, so that the oscillatory pattern is strongly quenched and somewhat shifted. It appears that the sudden approximation provides a simple yet accurate method for describing the effect of molecular anisotropy on scattering measurements.

Goldflam, R.↗

NASA NTRS1978

Single and multiple scattering contributions to circumsolar radiation

The contributions to the angular distribution of the almucantar radiance in the forward direction due to multiple scattering are compared to those due to single scattering. The contributions have been calculated by a computer code employing the Gauss-Seidel iterative approach to the solution of the radiative transfer equation for a plane parallel atmosphere composed of air molecules, aerosol particles, and ozone. The code is similar to that of Dave (1972) except in the construction of the source matrix. In the near-forward direction the multiple scattering contributions are significant for optical depths of the order of 0.4. The shape of the angular distribution of almucantar radiance to 10 degrees is less sensitive to multiple scattering.

Box, M. A.↗

NASA NTRS1978

Electron scattering by highly polar molecules. II - LiF

The crossed electron-beam - molecular-beam scattering technique has been used to measure relative values of differential 'elastic' scattering cross sections at electron impact energies of 5.4 and 20 eV for the angular range from 20 to 130 deg. The absolute values of these cross sections have been obtained by normalization to the classical perturbation theory of Dickinson (1977) at a scattering angle of 40 deg. These differential cross sections have then been used to calculate the integral and momentum-transfer cross sections. An energy-loss spectrum at 100 eV electron impact energy and 15 deg scattering angle has also been obtained. Two weak features at the energy losses of 6.74 and 8.82 eV appear. Their energy positions are compared with the recent calculations of Kahn et al. (1974).

Vuskovic, L.↗

NASA NTRS1978

Scattering by non-spherical particles of size comparable to a wavelength - A new semi-empirical theory

Mie theory, which is generally used to describe the scattering behavior of particles at a certain wavelength, is only rigorously correct for spherical particles. Particles found as atmospheric constituents, with the exception of cloud droplets, are, however, decidedly nonspherical. An investigation is, therefore, conducted regarding the significant ways in which the scattering behavior of irregularly shaped particles differs from that of spheres. A systematic method is formulated for treating the real scalar scattering behavior. A description is presented of a new semiempirical theory based on simple physical principles and data obtained in laboratory measurements, which successfully reproduces the single scattering phase function for a wide range of particle shapes, sizes, and refractive indices.

Pollack, J. B.↗

NASA NTRS1979

Redistribution of scattered radiation by collisions in the nonimpact region of the spectral line profile

The scattering of radiation in the presence of collisions can be described quantum-mechanically in terms of essentially two processes. The first may be thought of as an absorption to the excited state followed subsequently (after propagating in the excited state) by emission. This gives rise to radiation redistributed about the transition frequency. The effects of m-degeneracy are particularly interesting for this first process. As an example a case is considered in which the incident frequency is in the quasi-static line wing, while the scattered frequency is close to the line center. It is found that under these circumstances the dominant contribution from this process in the scattered spectrum is obtained for an absorption of the incident frequency taking place during a strong (close) collision and reemission of the scattered frequency when the atom is essentially unperturbed

Cooper, J.↗

NASA NTRS1979

Two-potential approach for electron-molecular collisions at intermediate and high energies - Application to e-N2 scatterings

A general theoretical approach is proposed for the calculation of elastic, vibrational, and rotational transitions for electron-molecule scattering at intermediate and high-electron-impact energies. In this formulation, contributions to the scattering process come from the incoherent sum of two dominant potentials: a short-range shielded nuclear Coulomb potential from individual atomic centers, and a permanent/induced long-range potential. Application to e-N2 scattering from 50-500 eV incident electron energies has yielded good agreement with absolutely calibrated experiments. Comparisons with other theoretical approaches are made. The physical picture as well as the general features of electron-molecule scattering process are discussed within the framework of the two-potential approach.

Choi, B. H.↗

NASA NTRS1979

Numerical results for the thermal scattering functions

A recent formulation in radiative transfer defined the thermal scattering functions that characterize radiative transfer from a general plane-parallel finite medium driven solely by an internal distribution of thermal sources. Exiting diffuse intensities are expressed as space convolutions of the thermal scattering functions with any thermal source distribution. A parametric study is presented to obtain the basic structure of these scattering functions. The independent variables of these azimuthally independent functions are the direction cosine and source location, while the parameters are the single-scattering albedo, total optical depth, and the asymmetry factor in the Henyey-Greenstein phase function. The basic functional trends are discussed by using various parametric plots, and selected results are given to allow numerical checks. The computational method is invariant imbedding.

Cogley, A. C.↗

NASA NTRS1979

Scattering of emitted radiation from inhomogeneous and nonisothermal layers

A parametric study is performed for the exiting monochromatic intensities scattered from finite plane-parallel inhomogeneous layers that are driven solely by a distribution of thermal sources. Intensities are obtained by invariantly imbedding the standard and thermal scattering functions. The single-scattering albedo and the Henyey-Greenstein phase-function parameter are varied independently, and both linear and exponential profiles are considered. Linear temperature profiles are used, including temperature inversions. The resulting intensities, as a function of the direction cosine of propagation, are discussed from a remote-sensing point of view. For an isothermal and homogeneous medium, the gross characteristics of the exiting intensity, represented by its overall slope, mean value (magnitude), and an interior maximum value, can be related to the total optical depth, single-scattering albedo, and phase function, respectively. For a homogeneous medium, linearly decreasing (in the line of sight) temperature profiles tend to obscure the phase-function information and decrease the apparent optical depth. On the other hand, linearly increasing temperature profiles tend to retain phase-function information and increase the apparent optical depth. Temperature inversion profiles give intensities very similar to those for purely linear profiles.

Bergstrom, R. W.↗

NASA NTRS1979

Accuracy of RGD approximation for computing light scattering properties of diffusing and motile bacteria

The study tests the accuracy of the Rayleigh-Gans-Debye (RGD) approximation against a rigorous scattering theory calculation for a simplified model of E. coli (about 1 micron in size) - a solid spheroid. A general procedure is formulated whereby the scattered field amplitude correlation function, for both polarized and depolarized contributions, can be computed for a collection of particles. An explicit formula is presented for the scattered intensity, both polarized and depolarized, for a collection of randomly diffusing or moving particles. Two specific cases for the intermediate scattering functions are considered: diffusing particles and freely moving particles with a Maxwellian speed distribution. The formalism is applied to microorganisms suspended in a liquid medium. Sensitivity studies revealed that for values of the relative index of refraction greater than 1.03, RGD could be in serious error in computing the intensity as well as correlation functions.

Kottarchyk, M.↗

NASA NTRS1979

Polarization and scattering characteristics in the atmospheres of earth, Venus, and Jupiter

Our understanding of atmospheric scattering phenomena has increased through the combined developments of new electro-optical instrumentation, theoretical solutions for complex model atmospheres, and large computers enabling computation of such solutions. Earth satellites permit external, planetwide observations of our atmosphere, while spacecraft permit detailed measurements of the scattering by other planetary atmospheres. Some recent results are: elucidation of the effects of ozone absorption and high-altitude aerosol scattering on twilight colors and polarization; identification of a cloudbow on Venus and consequent deduction of the cloud particle shape, size distribution, and refractive index; and, the interpretation of Rayleigh scattering on Jupiter in terms of cloud-top topography.

Coffeen, D. L.↗

NASA NTRS1980

Method and means for helium/hydrogen ratio measurement by alpha scattering

An apparatus for determining helium to hydrogen ratios in a gaseous sample is presented. The sample is bombarded with alpha particles created by a self contained radioactive source and scattering products falling within a predetermined forward scattering angular range impact a detector assembly. Two detectors are mounted in tandem, the first completely blocking the second with respect to incident scattering products. Alpha particle/hydrogen or alpha particle/helium collisions are identified by whether scattering product impacts occur simultaneously in both detectors or only in the first detector. Relative magnitudes of the two pulses can be used to further discriminate against other effects such as noise and cosmic ray events.

Whitehead, A. B.↗

NASA NTRS1979

Transform approach to electromagnetic scattering

In this paper, a comprehensive review of the Fourier transform technique as applied to the problem of high-frequency scattering is presented and the concepts of the spectral theory of diffraction (STD) are introduced. In contrast to the more commonly employed ray-optical method for high-frequency scattering, the STD approach interprets the scattered field as the spectrum, or the Fourier transform of the induced current on the scatterer. Such an interpretation offers several important advantages: uniform nature of representation, capacity to improve and extend the ray-optical formulas in a systematic manner, and convenient accuracy tests for the results. Methods for combining integral equation methods with the Galerkin procedure and asymptotic techniques in the transform domain are described, and representative examples illustrating the application of the spectral approach are included.

Mittra, R.↗

NASA NTRS1980

Effect of molecular anisotropy on the intensity and degree of polarization of light scattered from model atmospheres

Computations of the properties of sunlight scattered from models of the earth-atmosphere system are presented to show the effect of molecular anisotropy on the intensity, flux, and degree of polarization of the scattered light. The values of these parameters change significantly when the anisotropy factor is neglected in the molecular optical thickness and scattering phase matrix. However, if the Rayleigh scattering optical thickness is kept constant and the molecular anisotropy factor is included only in the Rayleigh phase matrix, the flux does not change, the intensity changes by a small amount, but the changes in the degree of polarization are still significant.

Bahethi, O. P.↗