Light scattering by hexagonal columns in the discrete dipole   approximation
  Scattering by infinite hexagonal ice prisms is calculated using Maxwell's equations in the discrete dipole approximation for size parameters up to x=400. Birefringence is included in the calculations. Applicability of the geometric optics approximation is investigated. Excellent agreement between wave optics and geometric optics is observed for large size parameter in the outer part of the 22 degree halo feature. For smaller ice crystals halo broadening is predicted, and there is appreciable "spillover" of the halo into shadow scattering angles <22 degrees. Ways to retrieve ice crystal sizes are suggested based on the full width at half-maximum of the halo, the power at <22 deg, and the halo polarization. 
P. J. Flatau and B. T. Draine
physics.ao-ph