The Effect of Anisotropic Scattering on Radiant Transport

1965 ◽  
Vol 87 (3) ◽  
pp. 381-387 ◽  
Author(s):  
L. B. Evans ◽  
C. M. Chu ◽  
S. W. Churchill
Keyword(s):  
Angular Distribution ◽  
Integrodifferential Equation ◽  
Legendre Polynomials ◽  
Rayleigh Scattering ◽  
Single Scattering ◽  
Anisotropic Scattering ◽  
Reflection And Transmission ◽  
Scattering Material ◽  
Phase Functions ◽  
Infinite Media

Numerical values are presented for the reflection and transmission of radiation falling obliquely on finite slabs of absorbing and anisotropically scattering material. The angular distribution for single scattering was represented by a finite series of Legendre polynomials. The method of Chandrasekhar was used to reduce the representation of radiant transport from an integrodifferential equation to a set of integral equations. This set of equations was solved reiteratively on a digital computer. Previous solutions have been limited to isotropic and Rayleigh scattering or infinite media. The results for different phase functions for single scattering can be interpreted reasonably well in terms of only the forward-scattered fraction.

Atmospheric Scattering

2017 ◽  
Author(s):  
Kelly Chance ◽  
Randall V. Martin
Keyword(s):  
Function Approximation ◽  
Legendre Polynomials ◽  
Rayleigh Scattering ◽  
Scattered Light ◽  
Incident Light ◽  
Mie Scattering ◽  
Spherical Particles ◽  
Atmospheric Scattering ◽  
Phase Functions ◽  
Scatterer Size

This chapter describes elastic scattering events, where the wavelength of the scattered light is unchanged from that of the incident light and conservative scattering, scattering without absorption, sometimes closely approximated in clouds. The scattering regime, scattering versus wavelengths and scatterer size are introduced. Polarization in scattering is described by the Stokes vector and the polarization ellipse. Molecular (Rayleigh) scattering is presented and its atmospherically-important inelastic component, Raman scattering (the Ring effect) quantified. Mie scattering for spherical particles is described as is the commonly-used Henyey-Greenstein Mie phase function approximation. Non-spherical scatterers are introduced. The Ångstrom exponent and the expansion of phase functions in Legendre polynomials are described.

scholarly journals The Multiple Scattering of Electrons and Positrons

1954 ◽  
Vol 7 (2) ◽  
pp. 217 ◽  
Author(s):  
CBO Mohr ◽  
LJ Tassie
Keyword(s):  
Angular Distribution ◽  
Multiple Scattering ◽  
Born Approximation ◽  
Single Scattering ◽  
Mean Square ◽  
Wkb Method ◽  
Electrons And Positrons

The angular distribution of the single scattering of 33, 121, and 1065 keV electrons at small angles in gold is calculated and compared with the distributions given by the Born approximation and by the WKB method as used by Moli�re. The single scattering distribution for 1065 keV electrons is integrated numerically to give mean square angles of multiple scattering, and these are compared with the values given by the various multiple scattering theories.

Spectral and angular distribution of Rayleigh scattering from plasmon-coupled nanohole chains

2009 ◽  
Vol 94 (2) ◽  
pp. 021112 ◽  
Author(s):  
Yury Alaverdyan ◽  
Eva-Maria Hempe ◽  
A. Nick Vamivakas ◽  
Haibo E ◽  
Stefan A. Maier ◽  
...  
Keyword(s):  
Angular Distribution ◽  
Rayleigh Scattering

A note on the enhancement of J values in optically thick scattering atmospheres

1991 ◽  
Vol 69 (8-9) ◽  
pp. 1166-1174 ◽  
Author(s):  
Jacek W. Kaminski ◽  
John C. McConnell
Keyword(s):  
Multiple Scattering ◽  
Rayleigh Scattering ◽  
Large Fraction ◽  
Coherent Scattering ◽  
Single Scattering ◽  
Average Density ◽  
Infinite Medium ◽  
Scattering Medium ◽  
Surface Reflection ◽  
Thick Medium

In a planetary atmosphere the J value is determined by the angular-averaged radiance, or the average density of photons in an element of volume. The average density may be enhanced by multiple scattering of photons in a conservative, or near-conservative scattering atmosphere. We show that in a conservative semi-infinite medium this enhancement will be a factor of 5, for optical depths greater than about 20 for coherent scattering. We investigate the modification of the J values owing to multiple scattering in an optically thick medium of various optical depths, various single-scattering albedos of the scattering medium, and a range of surface albedos. We have applied the results to the calculation of J values in clouds in the terrestrial atmosphere and in the Rayleigh-scattering atmosphere of Uranus. We note that J values in a realistic atmosphere may be enhanced by as much as a factor of 5 throughout a large fraction of the atmosphere over those calculated without multiple scattering and surface reflection.

scholarly journals The anomalous scattering of protons in light elements

1936 ◽  
Vol 157 (891) ◽  
pp. 302-310 ◽  
Keyword(s):  
Single Scattering ◽  
Anomalous Scattering ◽  
Light Elements ◽  
Inverse Square Law ◽  
Atomic Nuclei ◽  
Coulomb Law ◽  
Scattering Material ◽  
Thick Layers

By a study of the scattering of protons by atomic nuclei we can gain information about the interactions of these particles. For sufficiently low velocities of the impinging protons, corresponding to 30 electron kilovolts, it has been shown by Gerthsen that they are scattered by celluloid according to the Rutherford law, and by hydrogen according to the Mott law of scattering of similar particles. At a distance of approach represented by this energy, the inverse square law of force still holds between the particles. Schneider has investigated the scattering of protons of energies up to 300 e.-kv. in aluminium, carbon, and boron. He found a pronounced maximum in the scattering by boron, compared with that by aluminium, at 200 e.-kv. It is not possible to say whether this anomaly is due to a breakdown in the Coulomb law of force between the boron nucleus and a proton, as he used thick layers of scattering material, a fact which renders the interpretation of his results difficult. The present work was undertaken with a view to checking these results, using sufficiently thin targets to ensure single scattering. Schneider’s observations have not been confirmed, although other anomalies have presented themselves.

scholarly journals Application of a diode array spectroradiometer to measuring the spectral scattering properties of cloud types in a laboratory

2007 ◽  
Vol 7 (22) ◽  
pp. 5803-5813 ◽  
Author(s):  
A. R. D. Smedley ◽  
A. R. Webb ◽  
C. P. R. Saunders
Keyword(s):  
Single Scattering ◽  
Small Scale ◽  
Diode Array ◽  
Full Spectrum ◽  
Solar Radiation Incident ◽  
Scattering Phase ◽  
Set Up ◽  
Phase Functions ◽  
Mixed Phase Clouds ◽  
Ultraviolet Solar Radiation

Abstract. In the last few years diode array spectroradiometers have become useful complements to traditional scanning instruments when measuring visible and ultraviolet solar radiation incident on the ground. This study describes the application of such an instrument to the problem of measuring the radiation scattered by different cloud-types in a laboratory environment. Details of how the instrument is incorporated into the experimental set-up are given together with the development of the system as a whole. The capability to measure a full spectrum for each scattering angle is an undoubted advantage, although the limited sensitivity impacts on the usefulness for optically thin clouds. Nevertheless example results are presented: (1) scattering phase functions at a range of wavelengths recorded simultaneously for water clouds, showing spectral deviation at the rainbow angle and verification of Mie theory; (2) likewise for mixed phase clouds, with evidence of both halo and rainbow features in a single scattering function; and, (3) detail of the forward scattering region in a glaciated cloud showing a barely perceptible halo feature, with implications for the small-scale structure of the ice crystals produced.

Angular Distribution of Intensity of Rayleigh Scattering from Comblike Branched Molecules

1968 ◽  
Vol 41 (2) ◽  
pp. 437-451
Author(s):  
Edward F. Casassa ◽  
Guy C. Berry
Keyword(s):  
Angular Distribution ◽  
Rayleigh Scattering ◽  
Large Fraction ◽  
Limited Range ◽  
Radius Of Gyration ◽  
Molecular Weights ◽  
Vinyl Polymers ◽  
Linear Chains ◽  
Angular Distribution Function ◽  
Number Of Branches

Abstract The angular distribution function P(θ) for intensity of light scattered by a dilute solution of comblike branched molecules has been determined for three situations of some interest for evaluation of experimental data: (1) the molecules are identical with branches of equal length attached equidistantly along linear backbone chains; (2) the molecules are homogeneous in mass, with the same number of branches on each molecule, but the branches are distributed at random along the chain; (3) branches and main chains are still uniform, but the molecules are heterogeneous in mass with the number of branches per molecule distributed according to the binomial distribution and the branches in any molecule spaced randomly along the backbone. Examination of numerical results shows that the scattering functions for models (1) and (2) arc not very different. The function for case (3) is somewhat different from the others when the mean number of branches per molecule is small but they contain a large fraction of the mass of the molecule. Over a limited range of the pertinent variables (corresponding roughly to observations on typical vinyl polymers of molecular weights up to 106) all three functions agree quite well with P(θ) for homogeneous linear chains with the same mean square radius of gyration.

The nature of seismic noise

1966 ◽  
Vol 290 (1422) ◽  
pp. 290-296 ◽  
Keyword(s):  
Rayleigh Scattering ◽  
Single Scattering ◽  
Phase Shifts ◽  
Body Waves ◽  
Fourth Power ◽  
Frequency Effect ◽  
Power Dependence ◽  
End Effects ◽  
Comparative Efficiency ◽  
Large Phase

When seismic signals from impulsive sources are reflected or refracted by discrete inhomogeneities in the seismic medium, ‘arrivals’ are recorded. If, however, the number of inhomogeneities becomes large and the distance between them becomes small, then interference among the arrivals takes place and source-caused ‘noise ’ is recorded. If the spacing between observatories is large compared with the spacing between and dimensions of the scatterers, the source-caused noise is incoherent. If the number of scatterers is large enough for the problem to be treated statistically, the noise has a random character. The properties of the noise can be computed by averaging statistically over all the signals due to the scattering from the ensemble of scatterers. Single scattering only is treated here. There are ‘local’ or ‘end’ effects corresponding to scattering near the source or the receiver which cannot be taken into account in the calculations. The main problem which has been treated is that of the scattering of body waves of P and S types in an unbounded inhomogeneous medium. The magnitudes of the scattered waves of all types— PP, PS, SP, SS —have been computed. In addition the phase shifts (time delays or advances) in incident P and S can be computed. It is found that body waves of either P or S type convert into scattered S waves with considerably greater ease than into scattered P waves. The comparative efficiency of these processes is about two orders of magnitude. Thus P waves show small phase shifts; S waves show large phase shifts. The waves between P and S are most likely of the character of S . The approximations in the calculations involve the assumptions of wavelength long compared with the dimensions of the scatterer and the dimensions of the scattering region long compared with wavelength. Under these conditions the approximations are those for Rayleigh scattering. Hence, in all the results, the scattering varies as the fourth power of the frequency and the mean square scattered energy is proportional to the linear dimension of the scattering region. At higher frequencies, the scattering changes from a fourth power dependence upon frequency to a second power dependence. This is a result which is obtained only for scattering by elastic media; it is not found in media without shear modulus. Experimental evidence for this high frequency effect has been found.

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