Effect of particle asphericity on single-scattering parameters: comparison between Platonic solids and spheres.

The single-scattering properties of the Platonic shapes, namely, the tetrahedron, hexahedron, octahedron, dodecahedron, and icosahedron, are investigated by use of the finite-difference time-domain method. These Platonic shapes have different extents of asphericity in terms of the ratios of their volumes (or surface areas) to those of their circumscribed spheres. We present the errors associated with four types of spherical equivalence that are defined on the basis of (a) the particle's geometric dimension (b) equal surface area (A), (c) equal volume (V), and (d) equal-volume-to-surface-area ratio (V/A). Numerical results show that the derivations of the scattering properties of a nonspherical particle from its spherical counterpart depend on the definition of spherical equivalence. For instance, when the Platonic and spherical particles have the same geometric dimension, the phase function for a dodecahedron is more similar than that for an icosahedron to the spherical result even though an icosahedron has more faces than a dodecahedron. However, when the nonspherical and spherical particles have the same volume, the phase function of the icosahedral particle essentially converges to the phase function of the sphere, whereas the result for the dodecahedron is quite different from its spherical counterpart. Furthermore, the present scattering calculation shows that the approximation of a Platonic solid with a sphere based on V/A leads to larger errors than the spherical equivalence based on either volume or projected area.

Use of circular cylinders as surrogates for hexagonal pristine ice crystals in scattering calculations at infrared wavelengths.

We investigate the errors associated with the use of circular cylinders as surrogates for hexagonal columns in computing the optical properties of pristine ice crystals at infrared (8-12-microm) wavelengths. The equivalent circular cylinders are specified in terms of volume (V), projected area (A), and volume-to-area ratio that are equal to those of the hexagonal columns. We use the T-matrix method to compute the optical properties of the equivalent circular cylinders. We apply the finite-difference time-domain method to compute the optical properties of hexagonal ice columns smaller than 40 microm. For hexagonal columns larger than 40 microm we employ an improved geometric optics method and a stretched scattering potential technique developed in previous studies to calculate the phase function and the extinction (or absorption) efficiency, respectively. The differences between the results for circular cylinders and hexagonal columns are of the order of a few percent. Thus it is quite reasonable to use a circular cylinder geometry as a surrogate for pristine hexagonal ice columns for scattering calculations at infrared (8-12-microm) wavelengths. Although the pristine ice crystals can be approximated as circular cylinders in scattering calculations at infrared wavelengths, it is shown that optical properties of individual aggregates cannot be well approximated by those of individual finite columns or cylinders.

Inherent and apparent scattering properties of coated or uncoated spheres embedded in an absorbing host medium.

The conventional Lorenz-Mie formalism is extended to the case for a coated sphere embedded in an absorbing medium. The apparent and inherent scattering cross sections of a particle, derived from the far field and near field, respectively, are different if the host medium is absorptive. The effect of absorption within the host medium on the phase-matrix elements associated with polarization depends on the dielectric properties of the scattering particle. For the specific cases of a soot particle coated with a water layer and an ice sphere containing an air bubble, the phase-matrix elements -P12/P11 and P33/P11 are unique if the shell is thin. The radiative transfer equation for a multidisperse particle system embedded within an absorbing medium is discussed. Conventional multiple-scattering computational algorithms can be applied if scaled apparent single-scattering properties are applied.