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.

The multiple scattering of waves by weak random irregularities in the medium

1960 ◽  
Vol 252 (1015) ◽  
pp. 431-462 ◽  
Keyword(s):  
Energy Transfer ◽  
Multiple Scattering ◽  
Rayleigh Scattering ◽  
Approximate Solutions ◽  
Single Scattering ◽  
Difficult Problem ◽  
Angular Distributions ◽  
Average Intensity ◽  
Angular Deviation ◽  
Scattering Medium

Papers by Lighthill (1953) and Fejer (1953) have treated multiple scattering by supposing a wave to be scattered any number of times in accordance with the cross-section for single scattering. This paper extends this idea, and uses the equation of energy transfer for radiation in a uniform scattering atmosphere to describe the variation of average intensity in a randomly inhomogeneous medium. In part I, the results of the single-scattering theory are reviewed, and an estimate is made of the conditions under which they should be correct. The justification for the treatment of multiple scattering by an equation of energy transfer is then discussed, and conditions under which it may be expected to be valid are obtained. In part II, the general solution of the equation of transfer for a spatially homogeneous radiation field, varying with time, is given first, and compared with Lighthill’s result for the angular distribution of radiation in terms of the length of path travelled. The much more difficult problem of a steady-state field with spatial variation has been treated by Chandrasekhar (1950), who gives many exact solutions for special types of scattering (such as isotropic and Rayleigh scattering). But his methods are not well suited to some other types, especially small-angle forward scattering. Most of part II is devoted to finding approximate solutions for this case, first generalizing Fejer’s solution for a slab of scattering medium which produces a small total angular deviation of the radiation, and then deriving an approximate partial differential equation of transfer to treat problems where the total angular deviation is not small. Methods of solving this equation by eigenfunction expansions are explained, and some numerical results are given, especially angular distributions of emergent and reflected radiation for a semi-infinite scattering region.

Background Fitting in the Low-Loss Region of Electron Energy Loss Spectra

1990 ◽  
Vol 48 (2) ◽  
pp. 56-57
Author(s):  
C P Scott ◽  
A J Craven ◽  
C J Gilmore ◽  
A W Bowen
Keyword(s):  
Energy Loss ◽  
Multiple Scattering ◽  
Simple Form ◽  
Single Scattering ◽  
Low Loss ◽  
Characteristic Energy ◽  
Normal Method ◽  
Fitting In ◽  
Electron Energy Loss ◽  
Electron Energy Loss Spectra

The normal method of background subtraction in quantitative EELS analysis involves fitting an expression of the form I=AE-r to an energy window preceding the edge of interest; E is energy loss, A and r are fitting parameters. The calculated fit is then extrapolated under the edge, allowing the required signal to be extracted. In the case where the characteristic energy loss is small (E < 100eV), the background does not approximate to this simple form. One cause of this is multiple scattering. Even if the effects of multiple scattering are removed by deconvolution, it is not clear that the background from the recovered single scattering distribution follows this simple form, and, in any case, deconvolution can introduce artefacts.The above difficulties are particularly severe in the case of Al-Li alloys, where the Li K edge at ~52eV overlaps the Al L2,3 edge at ~72eV, and sharp plasmon peaks occur at intervals of ~15eV in the low loss region. An alternative background fitting technique, based on the work of Zanchi et al, has been tested on spectra taken from pure Al films, with a view to extending the analysis to Al-Li alloys.

scholarly journals Cramér-Rao Bound Study of Multiple Scattering Effects in Target Separation Estimation

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Edwin A. Marengo ◽  
Paul Berestesky
Keyword(s):  
Multiple Scattering ◽  
Born Approximation ◽  
Single Scattering ◽  
Scattering Data ◽  
Approximation Model ◽  
Scattering Parameters ◽  
Helmholtz Operator ◽  
Scattering Effects ◽  
Cramer Rao Bound ◽  
Multiple Scattering Effects

The information about the distance of separation between two-point targets that is contained in scattering data is explored in the context of the scalar Helmholtz operator via the Fisher information and associated Cramér-Rao bound (CRB) relevant to unbiased target separation estimation. The CRB results are obtained for the exact multiple scattering model and, for reference, also for the single scattering or Born approximation model applicable to weak scatterers. The effects of the sensing configuration and the scattering parameters in target separation estimation are analyzed. Conditions under which the targets' separation cannot be estimated are discussed for both models. Conditions for multiple scattering to be useful or detrimental to target separation estimation are discussed and illustrated.

scholarly journals Investigation of the liquid density using Gamma scattering technique

2017 ◽  
Vol 1 (T1) ◽  
pp. 106-113
Author(s):  
Kien Thach Trung Vo ◽  
Tam Duc Hoang ◽  
Nguyen Hoang Vo ◽  
Chuong Dinh Huynh ◽  
Thanh Thien Tran ◽  
...  
Keyword(s):  
Multiple Scattering ◽  
Density Measurement ◽  
Single Scattering ◽  
Photon Beam ◽  
Scattered Photon ◽  
Liquid Density ◽  
Scattering Angle ◽  
Testing Sample ◽  
Scattering Technique

In this work, a gamma scattering technique using 137Cs (5mCi) source with the NaI(Tl) detector is arranged to record the scattered photon beam at scattering angle of 1200 for investigating the liquid density. We used standard liquid such as water, H2SO4, HCl, glycerol, HNO3, ethanol and A92 petrol to fit the single scattering peak, multiple scattering, and total counts versus standard liquid densities. The interpolating of the single scattering peak, multiple scattering, and total counts of the testing sample at scattering angle of 1200 is 0.702 g.cm-3, 0.783 g.cm-3, and 0.747 g.cm-3, respectively. The discrepancy of the experiment and true testing density is about 8 %, 3 %, and 2 %, respectively. The result shows that multiple scattering or total counts can be used to propose the density measurement.

scholarly journals Benchmarking the invariant embedding method against analytical solutions in model transport problems

2006 ◽  
Vol 21 (2) ◽  
pp. 3-13
Author(s):  
Malin Wahlberg ◽  
Imre Pázsit
Keyword(s):  
Half Space ◽  
Cross Sections ◽  
Length Distribution ◽  
Infinite Medium ◽  
Scattering Medium ◽  
Embedding Method ◽  
Invariant Embedding ◽  
Invariant Embedding Method ◽  
Transport Problems ◽  
Energy Dependent

The purpose of this paper is to demonstrate the use of the invariant embedding method in a few model transport problems for which it is also possible to obtain an analytical solution. The use of the method is demonstrated in three different areas. The first is the calculation of the energy spectrum of sputtered particles from a scattering medium without absorption, where the multiplication (particle cascade) is generated by recoil production. Both constant and energy dependent cross-sections with a power law dependence were treated. The second application concerns the calculation of the path length distribution of reflected particles from a medium without multiplication. This is a relatively novel application, since the embedding equations do not resolve the depth variable. The third application concerns the demonstration that solutions in an infinite medium and in a half-space are interrelated through embedding-like integral equations, by the solution of which the flux reflected from a half-space can be reconstructed from solutions in an infinite medium or vice versa. In all cases, the invariant embedding method proved to be robust, fast, and monotonically converging to the exact solutions.

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.

Polarization

2011 ◽  
Author(s):  
Sönke Johnsen
Keyword(s):  
Polarized Light ◽  
Coherent Scattering ◽  
Single Scattering ◽  
The Other ◽  
Butterfly Wings

This chapter examines polarization. As with radiometry, polarization can be a confusing topic. Unfortunately, unlike radiometry, its complexity is not primarily due to confusing units. The physics of polarized light is genuinely tricky. This is another subfield of optics that is made easier by thinking of light as a wave. Polarized light in nature is a scattering phenomenon. However, not all scattering is equally effective at polarizing light. Two kinds work best. The first is single scattering by particles much smaller than a wavelength of light. The other way in which scattering can create polarized light is via coherent scattering—in particular, reflection from smooth substances such as glass, water, and many leaves or structurally colored objects like iridescent butterfly wings.

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