Vázquez-Estrada Omar, García-Valenzuela Augusto
J Opt Soc Am A Opt Image Sci Vis. 2014 Apr 1;31(4):745-54. doi: 10.1364/JOSAA.31.000745.
Recently a multiple-scattering model for the reflectivity of a disordered monolayer of scattering particles on a flat surface was put forth [J. Opt. Soc. Am.29, 1161 (2012)]. The approximate theoretical model provides relatively simple formulas for the reflectivity, but it was developed for a monodisperse monolayer. Here we extend the model to the case of a polydisperse monolayer and derive the appropriate formulas to calculate the optical transmissivity of the monolayer supported by a flat interface. A second objective of this paper is to test the approximate theoretical model against experimental data with highly scattering particles. We prepared monolayers of three different surface coverage fractions of polydisperse alumina and titanium dioxide particles deposited randomly on a glass slide. We measured their optical reflectivity and transmissivity versus the angle of incidence using a laser with a wavelength of 670 nm. Using the nominal values for the particles' most probable radius and refractive index, we fitted the theoretical model to the experimental curves and found that it reproduces very well the experimental curves. Interestingly, a dip in the reflectivity curves at large angles of incidence is present for the alumina monolayers but not in the titanium dioxide monolayers. The dip corresponds to a maximum in the scattering efficiency by the alumina monolayers. The theoretical model reproduces very well this behavior.
最近，有人提出了一种关于无序单层散射颗粒在平面上反射率的多重散射模型[《美国光学学会杂志》29, 1161 (2012)]。该近似理论模型为反射率提供了相对简单的公式，但它是针对单分散单层开发的。在此，我们将该模型扩展到多分散单层的情况，并推导了用于计算由平面界面支撑的单层光学透射率的适当公式。本文的第二个目标是用高散射颗粒的实验数据来检验该近似理论模型。我们制备了三种不同表面覆盖率的多分散氧化铝和二氧化钛颗粒的单层，它们随机沉积在载玻片上。我们使用波长为670 nm的激光测量了它们的光学反射率和透射率随入射角的变化。利用颗粒最可几半径和折射率的标称值，我们将理论模型拟合到实验曲线上，发现它能很好地重现实验曲线。有趣的是，氧化铝单层在大入射角时反射率曲线存在一个凹陷，而二氧化钛单层则没有。该凹陷对应于氧化铝单层散射效率的最大值。理论模型很好地重现了这种行为。
