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Brightness ratio near solar horizon from Ly alpha predawn and postdawn rocket observations consistent with radiation multiple scattering geocoronal model
Skylight polarization dispersion in relation to multiple scattering in molecular atmosphere
A theory of the multiple scattering of polarized light is discussed using the doubling method of van de Hulst. The concept of the Stokes parameters is derived and used to develop the form of the scattering phase matrix of a single particle. The diffuse reflection and transmission matrices of a single scattering plane parallel atmosphere are expressed as a function of the phase matrix, and the symmetry properties of these matrices are examined. Four matrices are required to describe scattering and transmission. The scattering matrix that results from the addition of two identical layers is derived. Using the doubling method, the scattering and transmission matrices of layers of arbitrary optical thickness can be derived. The doubling equations are then rewritten in terms of their Fourier components. Computation time is reduced since each Fourier component doubles independently. Computation time is also reduced through the use of symmetry properties.
The microwave characteristics of calm, rough, and foam-covered ocean surfaces were studied, and a technique was developed for deriving thermodynamic ocean surface temperatures from brightness temperatures measured by an earth-orbiting radiometer. This investigation encompassed frequencies in the range 1 to 10 GHz (wavelength range of 30 to 3 cm) and was based on the use of a one-dimensional geometrical optics roughness model, including shadowing and multiple scattering of radiant electromagnetic energy. Provision is made in the model for characterizing surface roughness through the rms slope versus wind velocity relations previously established. Suitable foam and atmospheric models were superimposed on the roughness model.
The matrix operator approach to radiative transfer is shown to be a very powerful technique in establishing symmetry relations for multiple scattering in inhomogeneous atmospheres. Symmetries are derived for the reflection and transmission operators using only the symmetry of the phase function. These results will mean large savings in computer time and storage for performing calculations for realistic planetary atmospheres using this method. The results have also been extended to establish a condition on the reflection matrix of a boundary in order to preserve reciprocity. Finally energy conservation is rigorously proven for conservative scattering in inhomogeneous atmospheres.
This paper presents an invariant imbedding theory of multiple scattering phenomena contributing to errors in telephotometer experiments. The theory indicates that there is a simple relationship between the magnitudes of the errors introduced by successive orders of scattering and it is shown that for all optical thicknesses each order can be represented by a coefficient which depends on the field of view of the telescope and the properties of the scattering medium. The verification of the theory and the derivation of the coefficients have been accomplished by a Monte Carlo program. Both monodisperse and polydisperse systems of Mie scatterers have been treated. The results demonstrate that for a given optical thickness the coefficients increase strongly with the mean particle size particularly for the smaller fields of view.
For the first time measurements in the multiple scattering regime of the diffuse reflectivity as a function of single scattering albedo have been made in a geometry that may be simulated by a plane parallel atmosphere of large optical depth. A comparison between the measurements and a theoretical computation of the diffuse reflectivity is presented. The measurements are within 1% agreement with the theoretical calculations for two different sizes of scattering particles which are larger than and smaller than the wavelength of the incident light, corresponding to the Mie and Rayleigh regimes, respectively.
A recently completed calibration facility for the NASA Mississippi Test Site is described. It combines the spectrum of water cooled long arc xenon radiation sources with the integration sphere concept covered by a special barium sulfate diffusely reflecting paint. The sphere is six feet in diameter and completely encompasses the four xenon sources (2.5 kW each) and the five pyranometers under calibration. The sources are contained within the base of the central pedestal and allow the radiation to be emitted into the lower hemisphere. Only through diffuse reflection and multiple scattering is the radiation finally incident upon the test zone, which is in the equatorial plane of the sphere on the top of the pedestal. The sphere is temperature controlled.
Proton recoil distributions were obtained by using organic liquid scintillators of different size. The measured distributions are converted to neutron spectra by differentiation analysis for comparison to the unfolded spectra of the largest scintillator. The approximations involved in the differentiation analysis are indicated to have small effects on the precision of neutron spectra measured with the smaller scintillators but introduce significant error for the largest scintillator. In the case of the smallest cylindrical scintillator, nominally 1.2 by 1.3 cm, the efficiency is shown to be insensitive to multiple scattering and to the angular distribution to the incident flux. These characteristics of the smaller scintillator make possible its use to measure scalar flux spectra within media high efficiency is not required.
When high-energy charged particles pass through a thin detector, the ionization energy loss in that detector is subject to fluctuations or straggling which must be considered in interpreting the data. Under many conditions, which depend upon the charge and energy of the incident particle and the detector geometry, the ionization energy lost by the particle is significantly different from the energy deposited in the detector. This problem divides naturally into a calculation of the energy loss that results in excitation and low-energy secondary electrons which do not travel far from their production points, and a calculation of energy loss that results in high-energy secondary electrons which can escape from the detector. The first calculation is performed using a modification of the Vavilov energy loss distribution. A cutoff energy is introduced above which all electrons are ignored and energy transferred to low energy particles is assumed to be equivalent to the energy deposited by them. For the second calculation, the trajectory of the primary particle is considered as a source of secondary high-energy electrons. The electrons from this source are transported using Monte Carlo techniques and multiple scattering theory, and the energy deposited by them in the detector is calculated. The results of the two calculations are then combined to predict the energy deposition distribution. The results of these calculations are used to predict the charge resolution of parallel-plate pulse ionization chambers that are being designed to measure the charge spectrum of heavy nuclei in the galactic cosmic-ray flux.
Vibrations of an elastic string when the separation between the ends varies randomly are studied. The emphasis is on the evolution of the coherent, or ordered, oscillations of the string. Using a perturbation technique borrowed from quantum field theory and the modified Kryloff-Bogoliuboff method, the 'multiple scattering' effect of the random separation between the ends on the linear and nonlinear coherent oscillations are investigated. It is found that due to the random interactions the coherent fundamental oscillation as well as the harmonies are damped. Their frequencies are also modified.
The matrix operator approach to radiative transfer is shown to be a very powerful technique in establishing symmetry relations for multiple scattering in inhomogeneous atmospheres. Symmetries are derived for the reflection and transmission operators using only the symmetry of the phase function. These results will mean large savings in computer time and storage for performing calculations for realistic planetary atmospheres using this method. The results have also been extended to establish a condition on the reflection matrix of a boundary in order to preserve reciprocity. Finally energy conservation is rigorously proven for conservative scattering in inhomogeneous atmospheres.
Circular polarization at 0.84 micron has been discovered for four stars with characteristics similar to VY CMa and NML Cyg. This polarization is attributed to multiple scattering in an asymmetric circumstellar dust cloud. Some common properties of the class of stars expected to show circumstellar circular polarization are discussed.
Knowledge of the probability distribution of photon path lengths for diffuse reflection in the continuum from a planetary atmosphere greatly simplifies computation of the shape and strength of absorption lines formed under conditions of multiple scattering. Graphs of this probability distribution are presented for diffuse reflection from a semiinfinite conservative atmosphere for both isotropic and forward-directed scattering, and for several angles of incidence and reflection. Graphs showing distributions for the case of absorption in the continuum are also discussed. The distributions are obtained from an analytic expression for the path-length distribution for nth-order scattering and a tabulation of nth-order intensities. It is found that te shape of the probability distribution depends markedly on the degree of forward scattering due to the phase function. The results are compared with those obtained by a Monte Carlo computation of the sort which might be used if tabulated nth-order intensities were not available.
Ground-based photometric measurements of spectral sky radiation have been made using a simple filter instrument. Sky radiation intensities measured in the solar vertical at 3200 and 3600 A are compared to infer total ozone. A model of a multiple scattering Rayleigh atmosphere serves as a primary reduction parameter. Spectral measurements of all-sky radiance distribution are used to study the effects of haze and clouds on the inference of total ozone. The brightness distribution of clear and overcast sky in ultraviolet is also described.
The relation between the apparent angular extent of a reflection nebula and the apparent magnitude of its illuminating star was reconsidered under a less restrictive set of assumptions. A computational technique was developed which permits the use of fits to the observed m-log a values to determine the albedo of particles composing reflection nebulae, providing only that a phase function and average optical thickness are assumed. Multiple scattering, anisotropic phase functions, and illumination by the general star field are considered, and the albedo of reflection nebular particles appears to be the same as that for interstellar particles in general. The possibility of continuous fluorescence contributions to the surface brightness is also considered.
A method is described for rapidly computing the amount of solar energy absorbed at the earth's surface and in the atmosphere as a function of altitude. The method is a parametric treatment, but the form of the solution and the coefficients involved are based on accurate multiple-scattering computations. In this treatment the absorption varies with the amount and type of clouds, the humidity, the zenith angle of the sun, and the albedo of the earth's surface. Within the stratosphere the absorption also depends on the vertical distribution of ozone. This parameterization for solar radiation is being used in current versions of the global atmospheric circulation model developed at the Goddard Institute for Space Studies.
The application of pattern recognition to ocean color data analysis is considered. Due to weight, cost, and data transmission rate limitations, any mapping type remote sensor of ocean color must necessarily collect light from the sea in a finite number of channels. The optical properties of the sea are discussed together with the remote sensing of ocean color, an optical model of natural water, the microscopic optical model, the macroscopic optical model, multiple scattering theory, measurements of subsurface oceanographic parameters, measurements of bulk absorption and scattering properties, measurements of the up- and down-welling light field, and the techniques for ocean color data analysis.