Gao Lihong, Lemarchand Fabien, Lequime Michel
Institut Fresnel, UMR 6133 CNRS, Campus de St Jérôme, 13397 Marseille cedex 20, France.
Opt Express. 2012 Jul 2;20(14):15734-51. doi: 10.1364/OE.20.015734.
In the present paper we determine the optical constants and thicknesses of multilayer thin film stacks, in the visible and near infrared ranges. These parameters are derived from the transmittance and reflectance spectra measured by a spectrophotometer, for several angles of incidence. Several examples are studied, from a simple single layer structure up to a 22-layer dielectric filter. We show that the use of a large number of incidence angles is an effective means of reducing the number of mathematical solutions and converging on the correct physical solution when the number of layers increases. More specifically, we provide an in-depth discussion of the approach used to extract the index and thickness of each layer, which is achieved by analysing the various mathematical solutions given by a global optimization procedure, based on as little as 6 and as many as 32 variable parameters. The results show that multiple incidences, lead to the true solution for a filter with a large number of layers. In the present study, a Clustering Global Optimization algorithm is used, and is shown to be efficient even for a high number of variable parameters. Our analysis allows the accuracy of the reverse engineering process to be estimated at approximately 1 nm for the thickness, and 2 10(-3) for the index of each layer in a 22-layer filter.
在本文中，我们测定了多层薄膜堆栈在可见光和近红外范围内的光学常数和厚度。这些参数是通过分光光度计在几个入射角下测量的透射率和反射率光谱推导出来的。我们研究了几个例子，从简单的单层结构到22层介质滤波器。我们表明，当层数增加时，使用大量入射角是减少数学解的数量并收敛到正确物理解的有效方法。更具体地说，我们深入讨论了用于提取每层折射率和厚度的方法，这是通过分析全局优化程序给出的各种数学解来实现的，该程序基于少至6个多达32个可变参数。结果表明，多次入射角可得出具有大量层数的滤波器的真实解。在本研究中，使用了聚类全局优化算法，并且即使对于大量可变参数也显示出高效性。我们的分析表明，对于一个22层滤波器，逆向工程过程的厚度精度估计约为1nm，每层折射率精度估计约为2×10⁻³。
