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

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

http://dx.doi.org/10.1364/AO.39.005827

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### Abstract

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

**History**

Original Manuscript: February 28, 2000

Revised Manuscript: July 3, 2000

Published: November 1, 2000

**Citation**

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

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-39-31-5827

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