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Scattering matrix, M, of a particle, also referred to as Mueller matrix, is a 4x4 matrix operator (for example, Bohren and Huffman 1983), with all elements being functions of the scattering angle. The scattering matrix converts the Stokes vector, S0, of the incident electromagnetic radiation (ER) beam into the Stokes vector, Ss, of ER scattered by the particle:
| Ss(ξ) = [1 / (kr)2] M(ξ) Si | (1) |
where k [length-1] is the wavenumber of the ER wave in the dispersion medium and r [length] is the distance from the scattering center (particle or volume element of a dispersion) to the observation point, and ξ is the direction of observation of the scattered light, i.e. (θ, φ), or simply θ, i.e. the scattering angle in the axially-symmetrical case. The dimensions of the Stokes vector elements are that of irradiance, i.e. power length-2. Thus, Eq. 1 implies that the scattering matrix elements are non-dimensional.
The wave scattered by a particle is spherical, with a direction-dependent irradiance. This implies that scattering matrix can be also thought of as an operator that transforms the irradiance of the ER incident onto the particle into the intensity of the scattered ER. Consequently, as shown in Differential scattering cross section and the scattering matrix, the scattering matrix can be considered to have a dimension of (solid angle)-1. This does not conflict with the statement that the scattering matrix elements are nondimensional. Indeed, the SI unit system 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 [the solid angle] is treated as [a dimensionless quantity]" (the ellipses and modifications in [] are by the author).
Scattering matrix is frequently presented in a normalized form, m = M / M11, i.e. as a matrix of elements mij = Mij / M11. This removes the magnitude effect in ER scattering (light scattering) at a given scattering angle, θ, and accentuates the polarization effects.
| CITATION: Jonasz M. 2006. Scattering matrix (www.tpdsci.com/Tpc/ScaMtx.php). In: Top. Part. Disp. Sci. (www.tpdsci.com). |
HISTORY: Published: 18-Mar-2006 Modified: 29-Sep-2006 Reviewed: PENDING |
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