The van de Hulst approximation for light scattering and its use for transmittance predictions in transparent ceramics

The in-line transmittances of transparent spinel and YAG ceramics with a low volume fraction of monosized spherical pores calculated via the exact Mie solution and the so-called van de Hulst approximation are compared. It is shown that the transmittances calculated via the van de Hulst approximation are in surprisingly good qualitative agreement with the exact Mie solutions. In particular, all relevant trends and features of transmittance-versus-wavelength-and-pore-size plots are correctly predicted, so that the van de Hulst approximation may be considered as a perfect tool for material design and process optimization purposes. It avoids the unphysical results that can occur in the Rayleigh and Fraunhofer approximations for pores sizes beyond their validity and is much simpler than the Rayleigh-Gans-Debye approximation. Tables listed in the Appendix to this paper allow the reader reconstruct the exact Mie solution results from the easily calculated van de Hulst approximation, if required.