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Average cosine, g, of the scattering angle, θ, characterizes the asymmetry of the scattering function of the dispersion. For axially-symmetrical scattering functions, the average cosine can be expressed as follows:
| g | = <cosθ> | |
| = 2π ∫-11 p[cos(θ)] cosθ dcosθ | ||
| = 2π ∫0π p(θ) cosθ sinθ dθ | ||
| = 2π ∫0π β(θ) cosθ sinθ dθ / b | ||
| = ∫0π β(θ) cosθ sinθ dθ / ∫0π β(θ) sinθ dθ | (1) |
where b [length-1] is the scattering coefficient, p [steradian-1] is the phase function, and β [steradian-1length-1] is the volume scattering function. The factor of 2π arises from integration of an axially-symmetrical phase function (scattering function) over the azimuth angle in its full range, from 0 to 2π. The second line of Eq. 1 is the definition of the average cosine of the scattering angle - note that 2π ∫1-1 p[cos(θ)] dcosθ = 1.
For a dispersion with the scattering function being symmetrical about the scattering angle of 90° (i.e. when particles of the dispersion are much smaller than the wavelength of light in the medium surrounding the particles), g = 0. If a dispersion consists of particles much greater than the wavelength of light, the scattering function is strongly asymmetrical, with a strong maximum at the scattering angle of 0. In this case, the average cosine is close to unity. For this reason, the average cosine, g, of the scattering angle is frequently referred to as the asymmetry factor or asymmetry parameter of the scattering function.
| CITATION: Jonasz M. 2006. Average cosine of the scattering angle (www.tpdsci.com/Tpc/ScaAvgCos.php). In: Top. Part. Disp. Sci. (www.tpdsci.com). |
HISTORY: Published: 17-Jan-2006 Modified: 13-Jun-2007 Reviewed: PENDING |
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