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We studied numerically (Vilaplana et al 2006) the sensitivity of selected elements (Mij) of the size-averaged scattering matrix of a dispersion of nonspherical, randomly-oriented, light absorbing particles to changes in the particle shape, porosity and refractive index. That study was performed at two visible light wavelengths (0.60 μm and 0.45 μm). We used a numerical model based on the discrete-dipole approximation (for example, Draine and Flatau 1994, Purcell and Pennypacker 1973) as implemented in the DDSCAT 6.x program (Draine and Flatau 2003). This model uses the equivalency of scattering properties of a dispersion of randomly-oriented particles and an ensemble average of the orientation-averaged scattering properties of the individual particles. In our study, the scattering properties at each particle size and shape, and at each scattering angle were all averages for 2000 different orientations of a particle. We modelled irregular particles as assemblies of side-connected cubes. Each particle was subdivided mostly into 25,000 but sometimes into as much as ~64,000 dipoles. The particle porosity was modelled by randomly removing 50% of the "dipoles" (Lumme and Rahola 1994). A power-law PSD of the dispersion was assumed for size averaging: n(D) = D -1.8, where D is the equivalent spherical diameter, limited mostly to a range of 0.2 to 2 µm that was sometimes extended to ~3.6 µm for the solid and to ~7 µm for the porous particles.
We considered two cases: (1) the effect of the particle shape and porosity at constant refractive index of 1.63 - 0.09i, and (2) the effect of the refractive index and porosity at constant regular particle shape. Our results lead to several conclusions. First, size-averaged normalized scattering matrices of dispersions of solid particles with regular shapes (rectangular prisms and cylinders) clearly depend on the aspect ratio of the particle. However, the matrices for particles of different regular shapes having the same aspect ratio tend to be remarkably similar. The largest differences are observed for particles having the extreme aspect ratios, especially for the m12 and m34 elements of the normalized scattering matrix. Gradual evolution in the m34 element with the aspect ratio suggests it to be a promising candidate for an aspect ratio indicator. In contrast, the solid irregular particles with aspect ratios in a similar range yield much smaller differences in the size-averaged scattering matrix elements. With the increasing particle size, the scattering matrix tends to that of a large sphere. Interestingly, the scattering matrix elements (except perhaps m34) of the most elongated prisms are similar to those representative of the irregular particles, a conclusion reached also by Veihelmann et al (2004) for spheroids.
Second, we found the scattering matrices of dispersions of irregular solid and porous particles differ significantly. For a single porous particle with size increasing from 0.2 - 2.8 µm the maximum of -m12 (the linear polarization ratio, PQ ) for the incident unpolarized light tends to decrease and shift from ~90° to ~70°, while m22 dips at the mid scattering angles. The size-averaged matrices are smoother but mimic the same pattern (Fig. 1, see also the phase functions in Fig. 2). Also, the backward scattering is gradually enhanced for the porous particles as their size increases, in contrast to the solid particles.
Third, by examining the size-averaged normalized scattering matrix of a dispersion of solid irregular particles of a single type, we found that the m12 element of that matrix is probably the most sensitive to changes in the particle refractive index. The maximum of -m12 tends to increase with the imaginary part of the refractive index, and to decrease with the increasing real part of the refractive index.
| CITATION: Vilaplana R. I. 2006. Scattering matrix of nonspherical particles: Sensitivity to particle characteristics (www.tpdsci.com/Tpc/ScaMtxNsp.php). In: Top. Part. Disp. Sci. (www.tpdsci.com). |
HISTORY: Published: 18-Jul-2006 Modified: 12-Feb-2007 Peer-reviewed: 08-Jul-2006 |
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