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NASA NTRS1977

Single scattering solution for radiative transfer through Rayleigh and aerosol atmosphere

A solution is presented to the radiative transfer of the solar irradiation through a turbid atmosphere, based on the single-scattering approximation, i.e., an assumption that a photon that underwent scattering either leaves the top of the atmosphere or strikes the surface. The solution depends on a special idealization of the scattering phase function of the aerosols. The equations developed are subsequently applied to analyze quantitatively the enhancement of the surface irradiation and the enhancement of the scattered radiant emittance as seen from above the atmosphere, caused by the surface reflectance and atmospheric back scattering. An order of magnitude error analysis is presented.

Otterman, J.↗

NASA NTRS1977

Scattering from a moving spherical particle by two crossed coherent plane waves

The Mie scattering properties of a homogeneous, isotropic spherical particle, moving at a constant velocity and illuminated by two intersecting coherent plane waves having the same polarization direction, have been analyzed based upon an exact solution to Maxwell's equations. The solutions are in a form suitable for the calculation of the time varying scattered signal integrated across a detector aperture of variable size that is centered on either the forward or backward scattering direction. This problem is of importance in defining the scattered signal in a cross beam laser Doppler velocimeter (LDV). Results obtained from calculating the integrated scattered signal indicate a strong dependence upon the following physical parameters: particle size, index of refraction, cross beam angle, and collection solid angle.

Chu, W. P.↗

NASA NTRS1977

The Crab Nebula pulsar - Variability of dispersion and scattering

Previous investigations of the effects of interstellar dispersion and scattering on the waveform of the Crab Nebula pulsar (NP 0532) have indicated a two-screen scattering model with one variable screen and have revealed anomalously large phase residuals at 73.8 MHz. The relevant observational data are reanalyzed in order to bring the two-screen model into better agreement with theoretical models of the interstellar medium and to account for the low-frequency (73.8-MHz) phase anomaly. The wavenumber spectrum of electron-density fluctuations is examined along with its role in scattering models involving an extended medium, a thick screen, or a thin screen. A tenable unit impulse response is constructed for a thin screen, its Fourier transform is analyzed, and an attempt is made to obtain the dispersion measure and scattering constants for two screens. A comparison of the resulting pulse-broadening and delay effects with other theoretical predictions shows that all observed pulse-broadening and delay effects in NP 0532 are consistent with scattering by a single thick slab of plasma occupying no more than one quarter of the line of sight.

Isaacman, R.↗

NASA NTRS1977

Turbulent scattering in an exponential atmosphere - A wave-optical solution

The thin-screen model for scattering of radiation by a turbulent atmosphere is generalized to the case where the mean phase change decreases exponentially as a function of distance across the screen. This is of interest because it models the effect of turbulent scattering in an isothermal average atmosphere. We present both the change in average intensity and average bending angle in terms of the r-m-s scattering angle introduced by the turbulence. We find, for example, that the effect of turbulent scattering on the mean scattering angle (and hence Doppler residuals) is approximately the same as that obtained from more heuristic calculations. The effect depends on wavelength only to the extent that the refractivity is a function of wavelength.

Hubbard, W. B.↗

NASA NTRS1978

Determination of particle size using measurement of scatter

A literature search was conducted to determine the state of the art particle size measurement by the light scatter technique. This technique may involve diffraction pattern analysis, location of minima and maxima in angular dependence of scattered light, magnitude of intensity verses angle, forward lobe scattered intensity ratio using two small angles, forward scatter in a small cone, and total scatter. Some of the more modern recordings and detection systems are video, holographic, and systems using optical processing.

Scott, R. L., Jr.↗

NASA NTRS1977

Elastic scattering of deuterons by carbon

Deuteron-carbon elastic scattering is studied within the framework of the Glauber approximation. The full Glauber multiple scattering series is evaluated with simplified nuclear wave functions. An approximation in which deuteron-nucleus scattering is expressed in terms of nucleon-nucleus scattering amplitudes is shown to be accurate for small momentum transfers. The effects of the Coulomb field and the deuteron D state are investigated. The impressive fit to the 650 MeV d-(C-12) elastic scattering data, obtained in a recent calculation, is shown to be due to additional approximations made in that analysis.

Varma, G. K.↗

NASA NTRS1979

Radiative transfer theory for scattering by layered media

Remote sensing of brightness temperatures of a scattering medium composed of spherical scatterers beneath a homogeneous surface layer is studied by using Mie scattering functions. We illustrate the effects of a surface layer by plotting the brightness temperatures as functions of frequency and viewing angle for different layer thicknesses, dielectric constants, and fractional scattering volumes. It is found that the brightness temperature increases when the loss tangent of the surface layer is increased and when the fractional volume occupied by the scatterers is decreased. In the absence of a surface layer the brightness temperature is usually decreasing as a function of frequency. The presence of a homogeneous layer may cause the brightness temperature to increase with frequency. At all viewing angles the vertical polarization is brighter than the horizontal polarization.

Tsang, L.↗

NASA NTRS1979

Multiple scattering and charged-particle - hydrogen-atom collisions

Glauber-approximation scattering amplitudes for charged-particle - hydrogen-atom elastic and inelastic collisions are derived directly in terms of the known particle-electron and particle-proton Coulomb scattering amplitudes and the known hydrogen-atom form factors. It is shown that the particle-hydrogen amplitude contains no single-scattering term. The double-scattering term is obtained as a two-dimensional integral in momentum space. It is demonstrated how the result can be used as the starting point for an alternative and relatively simple derivation, in closed form, of the Glauber particle-hydrogen scattering amplitude for transitions from the ground state to an arbitrary (nlm) state.

Franco, V.↗

NASA NTRS1980

A multiphoton treatment of near resonant light scattering in intense fields

The scattering by a two-state atom of monochromatic light of arbitrary intensity and detuning, is treated by solving Schroedinger's equation directly for the state of the scattered field. The calculation is performed in a basis of dressed atom states, which include to all orders the coupling of the incident field to the atom. Amplitudes describing sequences of scattering events are found by a nonperturbative method. A scattered intensity spectrum, directly related to the rate of change of energy in any given scattered field mode, is constructed in terms of bilinear products of the amplitudes representing all possible sequences of photon emission, and in the steady state limit the spectrum is found to be identical to the widely quoted results of Mollow. A discussion is devoted to understanding in physical terms the various quantities appearing in the expression for the intensity spectrum.

Ballagh, R. J.↗

NASA NTRS1980

Refraction and scattering of sound by a shear layer

The angle and amplitude changes for acoustic waves refracted by a circular open jet shear layer were determined. The generalized refraction theory was assessed experimentally for on axis and off axis acoustic source locations as source frequency varied from 1 kHz to 10 kHz and free stream Mach number varied from 0.1 to 0.4. Angle and amplitude changes across the shear layer show good agreement with theory. Experiments confirm that the refraction theory is independent of shear layer thickness, acoustic source frequency, and source type. A generalized theory is, thus, available for correcting far field noise data acquired in open jet test facilities. The effect of discrete tone scattering by the open jet turbulent shear layer was also studied. Scattering effects were investigated over the same Mach number range as frequency varied from 5 kHz to 15 kHz. Attenuation of discrete tone amplitude and tone broadening were measured as a function of acoustic source position and radiation angle. Scattering was found to be stronger at angles close to the open jet axis than at 90 deg, and becomes stronger as the acoustic source position shifts downstream. A scattering analysis provided an estimate of the onset of discrete tone scattering.

Schlinker, R. H.↗

NASA NTRS1981

Scatter of X-rays on polished surfaces

In investigating the dispersion properties of telescope mirrors used in X-ray astronomy, the slight scattering characteristics of X-ray radiation by statistically rough surfaces were examined. The mathematics and geometry of scattering theory are described. The measurement test assembly is described and results of measurements on samples of plane mirrors are given. Measurement results are evaluated. The direct beam, the convolution of the direct beam and the scattering halo, curve fitting by the method of least squares, various autocorrelation functions, results of the fitting procedure for small scattering, and deviations in the kernel of the scattering distribution are presented. A procedure for quality testing of mirror systems through diagnosis of rough surfaces is described.

Hasinger, G.↗

NASA NTRS1981

Visible light scatter measurements of the Advanced X-ray Astronomical Facility /AXAF/ mirror samples

NASA is studying the properties of mirror surfaces for X-ray telescopes, the data of which will be used to develop the telescope system for the Advanced X-ray Astronomical Facility. Visible light scatter measurements, using a computer controlled scanner, are made of various mirror samples to determine surface roughness. Total diffuse scatter is calculated using numerical integration techniques and used to estimate the rms surface roughness. The data measurements are then compared with X-ray scatter measurements of the same samples. A summary of the data generated is presented, along with graphs showing changes in scatter on samples before and after cleaning. Results show that very smooth surfaces can be polished on the common substrate materials (from 2 to 10 Angstroms), and nickel appears to give the lowest visible light scatter.

Griner, D. B.↗

NASA NTRS1981

An approximation to multiple scattering in the earth's atmosphere Almucantar radiance formulation

An empirical expression is derived to account for the molecular multiple scattering contribution to the almucantar radiance field. Formulas for the correction factors which incorporate the effects of multiple scattering and nonzero ground albedo are also given. The use and accuracy of the multiple-scattering approximation in direct problems of radiative transfer associated with almucantar radiance are discussed and illustrated by examples. It is shown that in almost all instances, inclusion of the molecular multiple-scattering contribution reduces the errors obtained with the single-scattering approximation by a factor of at least 2.

Box, M. A.↗

NASA NTRS1981

Near-ultraviolet scattering properties of Jupiter

Voyager 2 photometric observations of Jupiter at four phase angles between 20 and 80 deg and at various illumination angles are used to determine the altitude distribution and scattering properties of the material responsible for Jupiter's low geometric albedo at 2400 A. Center-to-limb measurements at midlatitudes indicate that most of the absorbing material lies deeper than 100 mbar, while the latitudinal distribution of stratospheric absorbers suggests that energy deposition from the magnetosphere is important in the formation of the absorbers. Scattering properties of model atmospheres containing three distinct aerosol size distributions are examined, and an upper limit to the column abundance of particles larger than the 0.05 micron radius in the north tropical zone and equatorial belt are derived. Rayleigh scattering fits the variation of intensity with phase angles between 20 and 80 deg better than any of the considered particle phase functions, although the Rayleigh scattering from the top 100 mbar obscures effects due to scattering from deeper absorbing particles.

West, R. A.↗

NASA NTRS1982

Radar scattering from a diffuse vegetation layer over a smooth surface

A simple model is presented for the oblique backscatter and bistatic scatter from a smooth surface overlain by a diffuse layer. Only single scattering in the diffuse layer is taken into account. The model analysis shows that the combination of volume scattering and oblique reflection at the surface may increase appreciably the waves scattering. The scattering strongly depends on the properties of the smooth surface. These results support some of the observations made with the Seasat spaceborne imaging radar over flooded regions with heavy vegetation cover.

Engheta, N.↗

NASA NTRS1983

Coherent scattering of a spherical wave from an irregular surface

The scattering of a spherical wave from a rough surface using the Kirchhoff approximation is considered. An expression representing the measured coherent scattering coefficient is derived. It is shown that the sphericity of the wavefront and the antenna pattern can become an important factor in the interpretation of ground-based measurements. The condition under which the coherent scattering-coefficient expression reduces to that corresponding to a plane wave incidence is given. The condition under which the result reduces to the standard image solution is also derived. In general, the consideration of antenna pattern and sphericity is unimportant unless the surface-height standard deviation is small, i.e., unless the coherent scattering component is significant. An application of the derived coherent backscattering coefficient together with the existing incoherent scattering coefficient to interpret measurements from concrete and asphalt surfaces is shown.

Fung, A. K.↗

NASA NTRS1983

Atmospheric scattering effects on ground-based measurements of thermospheric winds

Convergent or divergent thermospheric wind patterns detected by ground-based Fabry-Perot interferometric measurements of the Doppler shifts of atomic lines are demonstrated to occur in the presence of strong intensity gradients and a scattering atmosphere. Consideration is given to the color shifts observed when sighting to the north or the south, and a numerical model is developed to describe the wind patterns which produce the recorded shifts. An account is taken of the direct and scattered components of the brightness, with the atmosphere treated as a single scattering layer with a reflecting surface underneath. A scattering coefficient is calculated, together with the line shape of the wavelength shifts. The scattered light is demonstrated, both through simulations and measurements taken near Calgary, Alberta, to produce convergence or divergence of the color shifts, depending on the line-of-sight of the viewing.

Abreu, V. J.↗

NASA NTRS1983

Scattering from a V-shaped groove in the resonance domain

Radiation scattered from a V-shaped groove in the resonance domain is measured and compared with predictions from a rigorous theory. The calculated scattering is found to accurately predict the number of peaks and the general shape of the observed scattering. Small variations in groove shape are found to alter peak heights noticeably and peak positions slightly. The finite beam size causes unavoidable discrepancies between calculated and measured scattering. The theory of Maystre provides a very good tool for determining the scattering capabilities of different shapes without having to measure them.

White, G. S.↗