The original Apetz-van-Bruggen model for predicting the transmittance of dense polycrystalline ceramics with randomly oriented birefringent crystallites is shown to be incorrect. In a correct Apetz-van-Bruggen equivalent composite model (ECM) the volume fraction must be 1/3 instead of 1/2 and the factor 2/3 in front of the maximum birefringence must be abandoned. This ECM is in good agreement with the simplified version of Pecharromán’s dense polycrystalline model (DPM) and can be improved by replacing the Jobst approximation (i.e. the large-size limit of the Rayleigh-Gans approximation) by the van-de-Hulst approximation. Similarly, a new DPM is proposed that combines the van-de-Hulst approximation with Pecharromán’s texture function. However, all these models fail for small grains. Therefore two new models (infimum-supremum-based ECM and DPM) are proposed, which combine the full Rayleigh-Gans approximation (for small grains) with the van-de-Hulst approximation (for large grains) and provide (for all grain sizes) predictions almost identical to Mie theory.

原来的Apetz-van-Bruggen模型用于预测具有随机取向的双折射微晶的致密多晶陶瓷的透射率是不正确的。在正确的Apetz-van-Bruggen等效复合模型（ECM）中，体积分数必须为1/3而不是1/2，并且必须放弃最大双折射前面的系数2/3。该ECM与Pecharromán的致密多晶模型（DPM）的简化版本非常吻合，可以通过用van-de-Hulst近似代替Jobst近似（即Rayleigh-Gans近似的大极限）来进行改进。同样，提出了一种新的DPM，它将van-de-Hulst逼近与Pecharromán的纹理函数结合在一起。但是，所有这些模型对于小颗粒都失败了。