Mayerhöfer Thomas G, Pahlow Susanne, Hübner Uwe, Popp Jürgen
Leibniz Institute of Photonic Technology (IPHT), Albert-Einstein-Str. 9, 07745 Jena, Germany.
Analyst. 2020 May 7;145(9):3385-3394. doi: 10.1039/d0an00062k. Epub 2020 Apr 2.
Substantial refractive index mismatches between substrate and layers lead to undulating baselines, which are known as interference fringes. These fringes can be attributed to multiple reflections inside the layers. For thin and plane parallel layers, these multiple reflections result in wave interference and electric field intensities which strongly depend on the location within the layer and wavenumber. In particular, the average electric field intensity is increased in spectral regions where the reflectance is reduced. Therefore, the most important precondition for the Beer-Lambert law to hold, absorption as the single reason for electric field intensity changes, is no longer valid and, since absorption is proportional to the electric field intensity, considerable deviations from the Beer-Lambert law result. Fringe removal is consequently synonymous with correcting deviations from the Beer-Lambert law in the spectra. Within this contribution, we introduce an appropriate formalism based on wave optics, which allows a particularly fast and simple correction of any interference based effects. We applied our approach for correcting transmittance spectra of Poly(methyl methacrylate) layers on silicon substrates. The interference effects were successfully removed and correct baselines, in good agreement with the calculated spectra, were obtained. Due to its sound theoretical foundation, our formalism can be used as benchmark to test the performance of other methods for interference fringe removal.
衬底与各层之间存在显著的折射率失配会导致基线起伏，这被称为干涉条纹。这些条纹可归因于层内的多次反射。对于薄且平行平面的层，这些多次反射会导致波干涉以及电场强度强烈依赖于层内位置和波数。特别地，在反射率降低的光谱区域，平均电场强度会增加。因此，比尔 - 朗伯定律成立的最重要前提，即吸收作为电场强度变化的唯一原因不再有效，并且由于吸收与电场强度成正比，会导致与比尔 - 朗伯定律有相当大的偏差。因此，去除条纹就等同于校正光谱中与比尔 - 朗伯定律的偏差。在本论文中，我们基于波动光学引入了一种合适的形式体系，它能够对任何基于干涉的效应进行特别快速且简单的校正。我们将我们的方法应用于校正硅衬底上聚甲基丙烯酸甲酯层的透射光谱。成功去除了干涉效应，并获得了与计算光谱高度吻合的正确基线。由于其坚实的理论基础，我们的形式体系可作为基准来测试其他去除干涉条纹方法的性能。
