Use of Debye's series to determine the optimal edge-effect terms for computing the extinction efficiencies of spheroids.

The extinction efficiencies of atmospheric particles are essential to determining radiation attenuation and thus are fundamentally related to atmospheric radiative transfer. The extinction efficiencies can also be used to retrieve particle sizes or refractive indices through particle characterization techniques. This study first uses the Debye series to improve the accuracy of high-frequency extinction formulae for spheroids in the context of Complex angular momentum theory by determining an optimal number of edge-effect terms. We show that the optimal edge-effect terms can be accurately obtained by comparing the results from the approximate formula with their counterparts computed from the invariant imbedding Debye series and T-matrix methods. An invariant imbedding T-matrix method is employed for particles with strong absorption, in which case the extinction efficiency is equivalent to two plus the edge-effect efficiency. For weakly absorptive or non-absorptive particles, the T-matrix results contain the interference between the diffraction and higher-order transmitted rays. Therefore, the Debye series was used to compute the edge-effect efficiency by separating the interference from the transmission on the extinction efficiency. We found that the optimal number strongly depends on the refractive index and is relatively insensitive to the particle geometry and size parameter. By building a table of optimal numbers of edge-effect terms, we developed an efficient and accurate extinction simulator that has been fully tested for randomly oriented spheroids with various aspect ratios and a wide range of refractive indices.