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 Topics in Particle and Dispersion Science

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Problems: Scattering matrix  

  1. Consider Eq. 1 in Scattering matrix. Prove that for a unpolarized incident electromagnetic radiation (ER) beam and an arbitrary scattering matrix, M, we can write:

     Ss1(ξ) = M11(ξ) / ( r2 k2 ) Si1  (1)

    where Ss1 is an 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, and k is the wavenumber of ER illuminating a particle, and Si1 is the element [1] of the Stokes vector of the incident ER. [Hint topic]
     

  2. Prove that an element M12 of the scatttering matrix can be obtained from the following equation resulting from using the following combinations of an analyzer and a polarizer (HO and VO; see Scattering matrix measurement for the explanation of this notation) with an arrangement shown in Fig. 1 in Scattering matrix measurement for a unpolarized [hint topic] incident electromagnetic radiation (ER) beam with unity irradiance and for an arbitrary scattering matrix, M:

     M12 = (Ss1HO - Ss1VO) / 2  (2)

    where Ss1 is an element [1] of the Stokes vector of the scattered ER. Neglect a factor of 1 / ( r2 k2 ).
CITATION:
Jonasz M. 2006. Problems: Scattering matrix (www.tpdsci.com/Tpc/ScaMtx_P.php). In: Top. Part. Disp. Sci. (www.tpdsci.com). 		HISTORY:
Published: 29-Sep-2006
Modified: 15-Oct-2006
Peer-reviewed: PENDING
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