High-resolution microscopy technique is of significant importance for studying nanomaterials. It is necessary to understand the near-field interaction between the probe and substrate materials in order to get the fine structure of the nanomaterial in the subwavelength scale. The numerical methods such as FDTD, FEM, and MoM are inefficient for the SNOM problems because of the illness of the impedance matrix. The analytic method can only be used for some simple objects such as sphere. Here, a quasianalytical method is developed, in which the analytic formula is refined to adapt to various shapes of the probe approaching the curve of SNOM. By this way, it is helpful in comparing the performance of different probes and giving us a direction to design a new type probe in SNOM. As an application, the developed method is used to study the contrast in the SNOM for the interface between the two different surfaces that have different materials and topography.

中文翻译：

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改进的点偶极子模型用于亚波长分辨率散射近场光学显微镜（SNOM）

高分辨率显微镜技术对于研究纳米材料具有重要意义。有必要了解探针和基底材料之间的近场相互作用，以便在亚波长范围内获得纳米材料的精细结构。由于阻抗矩阵的问题，诸如FDTD，FEM和MoM之类的数值方法对于SNOM问题效率低下。解析方法只能用于一些简单的对象，例如球体。在这里，开发了一种准解析方法，其中解析公式经过改进以适应接近SNOM曲线的探针的各种形状。通过这种方式，有助于比较不同探针的性能，并为我们提供一种在SNOM中设计新型探针的指导。作为应用，