Modeling of Multiple Scattering Effects in Fraunhofer Diffraction Particle Size Analysis

  • E. D. Hirleman


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.


Optical Depth Multiple Scattering Laser Diffraction Discrete Ordinate Successive Order 




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


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


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


scattering redistribution function


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


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


optical depth (dimensionless)


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


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


the number of particles in a finite volume


the expected number of particles in a finite volume


the probability that exactly n particles are in a finite volume


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


det, i

refers to the ith detector


forward scattering


incident, for radiation incident on a particle




refers to x component in cartesian coordinate system


refers to y component in cartesian coordinate system


refers to z component in cartesian coordinate system



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



direction cosines of scattered rays

the length of the medium (m)


azimuthal scattering angle in local coordinate system


azimuthal scattering angle in inertial coordinate system


particle number density (particles/m3)


scattering angle in local coordinate system


scattering angle in inertial coordinate system


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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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