Zero-thickness model and slab model are two important models in the description of optical behaviors in two-dimensional atomic crystals. The predicted difference in optical behaviors between the two models is very small, which is difficult to distinguish by established measurement methods. Here, we present an optical spatial differentiation method to examine the difference in edge images of different graphene layers. The theoretical results show that the edge imaging is significantly different between the two different models. When the beam reflection is at the Brewster angle, different graphene layers are used to adjust the spatial differentiation. It is shown that the slab model is more sensitive to the number of graphene layers. The zero-thickness model is more suitable for one-dimensional optical differential operation. Moreover, the spatial differentiation plays the role of a band-pass filter. The high-frequency edge information components will pass through the filter, thus realizing layer-sensitive edge-enhanced imaging. In addition, we do not focus on the verification of the exact model, but only provide an alternative method to characterize the number of graphene layers based on two models, and also provide possibilities for achieving imaging edge detection by graphene differential operators. This study may provide a possible method for the optical characterization of two-dimensional atomic crystals.

中文翻译：

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光学空间微分实现二维原子晶体的层传感

零厚度模型和平板模型是描述二维原子晶体光学行为的两个重要模型。两个模型之间光学行为的预测差异非常小，很难通过现有的测量方法来区分。在这里，我们提出了一种光学空间微分方法来检查不同石墨烯层边缘图像的差异。理论结果表明，两种不同模型的边缘成像存在显着差异。当光束反射处于布儒斯特角时，使用不同的石墨烯层来调整空间差异。结果表明，平板模型对石墨烯层数更敏感。零厚度模型更适合一维光学微分运算。此外，空间微分起到带通滤波器的作用。高频边缘信息分量将通过滤波器，从而实现层敏感的边缘增强成像。此外，我们并不专注于精确模型的验证，而只是提供一种基于两种模型来表征石墨烯层​​数的替代方法，也为石墨烯微分算子实现成像边缘检测提供了可能。这项研究可能为二维原子晶体的光学表征提供一种可能的方法。