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.

比较了通过精确Mie溶液和所谓的van de Hulst近似计算得出的透明尖晶石和YAG陶瓷的在线透射率，该透射率具有较小体积分数的球形球形孔隙。结果表明，通过van de Hulst近似计算得出的透射率与精确的Mie解具有令人惊讶的良好定性一致性。尤其是，可以正确预测透射率与波长和孔径的关系图的所有相关趋势和特征，因此可以将van de Hulst近似视为用于材料设计和工艺优化目的的理想工具。它避免了孔径大小超出其有效性的Rayleigh和Fraunhofer近似中可能出现的“非物理”结果，并且比Rayleigh-Gans-Debye近似要简单得多。