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Volume scattering function (VSF), usually denoted by β [(solid angle)-1 length-1], describes the angular (i.e. directional) dependency of the intensity of unpolarized electromagnetic radiation (ER) scattered by the dispersion. In general, the scattering function depends on the direction in space, as defined by two angles, the scattering angle, θ and an azimuth angle, φ, that specifies rotation of the scattering plane about the direction of the incident ER:
| β(θ, φ) = dI(θ, φ) / (E dV) | (1) |
where I [power (solid angle)-1] is the intensity of ER, scattered at a direction (θ, φ), E [power length-2] is the irradiance of the dispersion at the volume V [length3] of the dispersion.
The dimension of (solid angle)-1 in the dimension of the scattering function is sometimes omitted and the dimension of the scattering function is stated as length-1. The two notations are in fact equivalent in the SI unit system, which specifies "that in the equations .. one generally expresses .. solid angle as the ratio between an area and the square of a length, and consequently that [this quantity is treated as a dimensionless quantity]" (the ellipsis and modifications in [] by the author). However, by adopting a dimension format of (solid angle)-1 length-1 one facilitates the understanding of the role of the scattering function in transforming the irradiance of the incident beam into the intensity of the scattered ER.
It is important to note that the scattering function is a function of two directions: (1) that of the incident ER, (θ ', φ'), implied in Eq. 1, and (2) that of observation of the scattered ER, (θ, φ). In addition, the scattering function may depend on position in the scattering medium (x, y, z). Thus, in general, the scattering function should be specified as β(x, y, z; θ ', φ'; θ, φ), or (in vector notation) as β(r, ξ', ξ), where r is the position vector, and unit vectors ξ' and ξ define respectively the direction of the incident ER and that of observation of the scattered ER (see also Radiative transfer equation).
For a spatially homogeneous dispersion with an axially symmetrical scattering function, i.e. one that depends only on the scattering angle, the scattering function, β, is defined as follows:
| β(θ) = dI(θ) / (E dV) | (2) |
Thus, the scattering function is simply the intensity of the scattered ER per unit irradiance of the incident ER, per unit volume of the dispersion. If not specified otherwise, the scattering function refers to single scattering of ER by the dispersion. An integral of the scattering function over the full solid angle (4π) equals the scattering coefficient.
In the case of polarized ER scattering (light scattering), one can define a matrix form of the scattering function, β, i.e. the scattering matrix for a dispersion. The scattering function, an element β11 of the matrix form of the scattering function, is - to within a factor independent of the scattering angle - the element [1,1] of the scattering matrix.
Related topics: Phase function, Average cosine of the scattering angle, Volume scattering function of natural waters, Relationship between the scattering matrix and function, Scattering matrix for a dispersion.
| CITATION: Jonasz M. 2006. Volume scattering function (www.tpdsci.com/Tpc/ScaFn.php). In: Top. Part. Disp. Sci. (www.tpdsci.com). |
HISTORY: Published: 18-Mar-2006 Modified: 29-Sep-2006 Peer-reviewed: PENDING |
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