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It follows from Eq. 1 in Scattering matrix, that for a unpolarized incident electromagnetic radiation (ER) beam we have (see Scattering matrix: Problems, Problem 1):
| S1(ξ) = M11(ξ) / ( r2 k2 ) S1i | (1) |
where S1 is the element [1] of the Stokes vector of the ER scattered at direction ξ, M11 is an element [1, 1] of the scattering matrix, r is the distance from the particle at which the scattered light is measured, k is the wavenumber of ER illuminating a particle, and S1i is the element [1] of the Stokes vector of the incident ER.
The elements of the Stokes vector are irradiances, hence we can rephrase Eq. 1 as follows:
| dΦbp, 1(ξ) / dA(ξ) = M11(ξ) / ( r2 k2 ) S1i | (2) |
where dΦbp, 1 is essentially the power of ER scattered by the particle at direction ξ. However, dA = r2dω, where dω is a solid angle at which the scattered light is observed. Hence:
| dΦbp, 1(ξ) / dω(ξ) = [M11(ξ) / k2] S1i | (3) |
By using Eq. 2 in Differential scattering cross section, it thus follows that
| dCb(ξ) / dω(ξ) | = (1 / S1i ) [dΦbp(ξ) / dω] | |
| = M11 / k2 | (4) |
since S1i is the irradiance of the ER beam illuminating the particle.
From Eq. 4 it follows that the dimension of the scattering matrix, M, can be written as sr -1. See also Scattering matrix for comments on the formats of that matrix dimension.
| CITATION: Jonasz M. 2006. Differential scattering cross section and the scattering matrix (www.tpdsci.com/Tpc/ScaFnDifCsScaMtxDv.php). In: Top. Part. Disp. Sci. (www.tpdsci.com). |
HISTORY: Published: 27-Sep-2006 Modified: 18-Jan-2007 Peer-reviewed: PENDING |
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