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With the use of the anomalous diffraction approximation, analytical expressions for the absorption and scattering coefficients and for the single scattering albedo of a polydispersion of horizontally oriented hexagonal columns and hexagonal plates are derived. By comparison of the anomalous diffraction results with those obtained using the dipole superposition method, it is estimated that the accuracy of the derived expressions are within 5% in the two narrow bands from 2.77 to 3.02 and from 10.6 to 11.1 μm and within 15% from 0.8 to 3.05 from 5.4 to 6.1 and from 8.3 to 11.9 μm. The equivalent spheres of equal volume or of equal surface area do not provide a suitable approximation for the scattering properties of the polydispersion of horizontally oriented hexagonal columns or plates. The errors due to the use of equivalent spheres in calculation of the absorption and scattering coefficients and in single scattering albedo are typically of the order of several hundred percent. Equal volume or equal surface area cylinders approximate well the scattering proprieties of hexagonal columns; however, they are not suitable as equivalent particles for the case of hexagonal plates.
Chýlek et al. (Sat,) studied this question.