Modeling of Multiple Scattering Effects in Fraunhofer Diffraction Particle Size Analysis

  • E. D. Hirleman

Abstract

A model for the direct problem of calculating the forward scattering signature of a multiple scattering medium is presented. The new formulation is optimized for integration into schemes for reconstructing the particle size distribution from laser diffraction (forward scattering) signatures obtained from optically thick media. The analysis is valid for media where the particle sizes and interparticle spacings are large (relative to the wavelength and the particle size, respectively) such that Fraunhofer diffraction theory adequately describes the properties of the forward scattered light from individual scattering events. The simulated performance of laser diffraction particle sizing instruments was then studied using predictions of the scattered light signatures which would be measured by laser diffraction instrument under multiple scattering conditions. The results were compared with experimental data and theoretical calculations based on other models.

Keywords

Optical Depth Multiple Scattering Laser Diffraction Discrete Ordinate Successive Order 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Abbreviations

Nomenclature

a

albedo, ratio of the scattering cross-section to the total extinction cross-section of a particle, i.e. the fraction of the incident energy intercepted by a particle which is scattered rather than absorbed

af

forward scattering albedo, ratio of forward scattering cross-section to total extinction cross-section for a particle, af =0.5 in the geometric optics case, independent of particle composition

fn

probability that a photon will be scattered (in the forward direction) exactly n times while passing through a medium

h

scattering redistribution function

Cabs

optical absorption cross-section of a particle (m2/particle)

Cext

optical extinction cross-section of a particle (m2/particle)

b

optical depth (dimensionless)

Csct

optical scattering cross-section of a particle (m2/particle)

L

scattering phase function which is the discrete angular distribution function for scattered light normalized to 1.0

n

the number of particles in a finite volume

<n>

the expected number of particles in a finite volume

Pn

the probability that exactly n particles are in a finite volume

T

transmittance of a medium, the probability that a photon will traverse a medium without being scattered or absorbed

Subscripts

det, i

refers to the ith detector

fwd

forward scattering

inc

incident, for radiation incident on a particle

sct

scattered

x

refers to x component in cartesian coordinate system

y

refers to y component in cartesian coordinate system

z

refers to z component in cartesian coordinate system

Superscripts

/

the prime superscript indicates quantity is in local light scattering coordinate system rather than inertial system

Greek

γ

direction cosines of scattered rays

the length of the medium (m)

φ

azimuthal scattering angle in local coordinate system

Φ

azimuthal scattering angle in inertial coordinate system

ρ

particle number density (particles/m3)

θ

scattering angle in local coordinate system

Θ

scattering angle in inertial coordinate system

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References

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Copyright information

© Springer Science+Business Media New York 1988

Authors and Affiliations

  • E. D. Hirleman
    • 1
  1. 1.Laser Diagnostics Laboratory Mechanical and Aerospace Engineering DepartmentArizona State UniversityTempeUSA

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