A general method is developed to formulate extinction and absorption efficiency for nonspherical particles at arbitrary and random orientations by use of anomalous diffraction theory (ADT). An ADT for finite circular cylinders is evaluated as an example. Existing ADT’s for infinite cylinders at arbitrary orientations and for finite cylinders at the normal incidence are shown to be special cases of the new formulation. ADT solutions for finite cylinders are shown to approach the rigorous T-matrix results when the refractive indices approach unity. The importance of some physical processes that are neglected in the ADT approximation are evaluated by comparisons between ADT and rigorous calculations for different particle geometries. For spheres, van de Hulst’s ADT and Mie theory are used, whereas the ADT that we present and T-matrix calculations are used for cylinders of different diameter-to-length ratios. The results show that the differences in extinction between ADT and exact solutions generally decrease with nonsphericity. A similar decrease occurs for absorption at wavelengths of relatively strong absorption. The influence of complex refractive index is evaluated. Our results suggest that ADT may provide a useful approximation in parameterization and remote sensing of cirrus clouds in the Christiansen bands where the real part of the refractive index approaches unity and/or where relative absorption is strong.
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