TPDSci Phase function

Phase function

Phase function is the scattering function normalized by the scattering coefficient, b. For axially-symmetrical scattering functions, i.e. scattering functions that depend only on the scattering angle, the phase function, usually denoted by p [steradian^-1], is defined as follows:

p(θ) = β(θ) / b

(1)

The phase function can be regarded as a distribution of probability of a photon being scattered at an angle θ. Indeed, for an axially-symmetrical phase function we have:

2π ∫₀^π p(θ) sinθ dθ	= [ 2π ∫₀^π β(θ) sinθ dθ ] / b
	= b / b
	= 1	(2)

i.e. a normalization condition required of a probability distribution. The factor of 2π in the above equation arises from an integration over the azimuth angle over its full range: from 0 to 2π.

Note that another definition of the phase function is popular in the radiative transfer literature (for example, Kokhanovsky 2004, Liou and Hansen 1971):

p(θ) = 4π β(θ) / b

(3)

leading to a normalization condition different from that expressed by Eq. 2 (for example, Kokhanovsky 2004, Haltrin 1998):

½ ∫₀^π p(θ) sinθ dθ = 1

(4)

CITATION:
Jonasz M. 2006. Phase function (www.tpdsci.com/Tpc/ScaPhsFn.php). In: Top. Part. Disp. Sci. (www.tpdsci.com).

HISTORY:
Published: 17-Jan-2006
Modified: 20-Jul-2006
Peer-reviewed: 11-Oct-2006

Topics in Particle and Dispersion Science