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Applied Optics

Applied Optics


  • Vol. 39, Iss. 31 — Nov. 1, 2000
  • pp: 5827–5833

Reciprocity theorem for the calculation of average scattering properties of agglomerated particles

Guocai Shu and Tryfon T. Charalampopoulos  »View Author Affiliations

Applied Optics, Vol. 39, Issue 31, pp. 5827-5833 (2000)

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The reciprocity theorem in light scattering is a general theorem that is verified theoretically and experimentally. However, violation of the reciprocity theorem has been encountered in previous investigations for simulation of light scattering from agglomerates. We demonstrate that the violations of the reciprocity theorem are due to inappropriate orientation averaging or the incorrect formulation of light-scattering quantities. In situ optical diagnostics of aggregated aerosols requires the calculation of the orientation averages of scattering quantities. Thus it is imperative to establish a criterion that can be used to determine a sufficient number of orientations for the reliable calculation of averages for the scattering quantities. It is demonstrated that the reciprocity theorem may serve as such a criterion for typical sizes of agglomerates such as flame soot with fractal dimensions D f = 1.8, primary particle size parameter x ≤ 0.3, and number of primary particles less than 260. It is shown that the use of 21 × 21 × 21 orientations will satisfy the reciprocity theorem to within 0.5%.

© 2000 Optical Society of America

OCIS Codes
(280.1100) Remote sensing and sensors : Aerosol detection
(280.1120) Remote sensing and sensors : Air pollution monitoring
(280.1740) Remote sensing and sensors : Combustion diagnostics
(290.3030) Scattering : Index measurements
(290.5850) Scattering : Scattering, particles

Original Manuscript: February 28, 2000
Revised Manuscript: July 3, 2000
Published: November 1, 2000

Guocai Shu and Tryfon T. Charalampopoulos, "Reciprocity theorem for the calculation of average scattering properties of agglomerated particles," Appl. Opt. 39, 5827-5833 (2000)

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