Hébert Mathieu, Machizaud Jacques
Université de Lyon, Université Jean-Monnet de Saint-Etienne, CNRS, UMR 5516, Laboratoire Hubert Curien, Saint-Etienne F-42000, France. mathieu.hebert@univ‑st‑etienne.fr
J Opt Soc Am A Opt Image Sci Vis. 2012 Nov 1;29(11):2498-508. doi: 10.1364/JOSAA.29.002498.
This paper combines and extends two optical models based on a two-collimated-flux approach that we previously proposed for the reflectance and transmittance of nonscattering elements, i.e., stacked nonscattering plastic films on the one hand, and films printed in halftone on the other hand. Those two models are revisited and combined by introducing different reflectances and transmittances on the two sides of a printed film, a common situation in practice. We then address the special case of stacks of identical films for which we obtain closed-form expressions for the reflectance and transmittance of the stacks as functions of the number of films. Experimental testing has been carried out on several different films printed with an inkjet printer. The accuracy of the model is good up to 16 films in most cases, despite a slight decrease in the case of yellow ink, which is more scattering than the other inks. By transposing the model to thin diffusing layers and considering diffuse fluxes instead of collimated ones, the closed-form expressions yield the well-known Kubelka-Munk reflectance and transmittance formulas. When these stacks of films are backed by a colored specular reflector, the reflectance is in certain conditions independent of the number of films.
本文结合并扩展了基于双准直通量方法的两个光学模型，该方法是我们之前针对非散射元件的反射率和透射率提出的，一方面是堆叠的非散射塑料薄膜，另一方面是半色调印刷的薄膜。通过引入印刷薄膜两侧不同的反射率和透射率（这在实际中很常见），对这两个模型进行了重新审视和合并。然后，我们处理了相同薄膜堆叠的特殊情况，针对这种情况，我们得到了堆叠的反射率和透射率作为薄膜数量函数的闭式表达式。已使用喷墨打印机在几种不同的薄膜上进行了实验测试。在大多数情况下，该模型对于多达16层薄膜的准确性良好，尽管黄色墨水的情况略有下降，黄色墨水比其他墨水散射更强。通过将模型转换为薄漫射层并考虑漫射通量而非准直通量，闭式表达式得出了著名的库贝尔卡 - 蒙克反射率和透射率公式。当这些薄膜堆叠由彩色镜面反射器支撑时，在某些条件下反射率与薄膜数量无关。
