In this work, the polarized beams tightly focused through a cylindrical refractive-indices discontinuous dielectric interface was numerically investigated. The corresponding focal pattern calculation formula was deduced base on vectoral diffraction integration theory for the first time. The patterns through the cylindrical dielectric interface with different radii were revealed by numerical calculating and discussed in detail. In addition, the aberration factor of the integration formula was found out, and the phase compensation maps were successfully carried out for focal patterns correcting. The findings will be helpful to improve the spatial resolution of advanced optical microscope in probing samples encapsulated by micro pipes.

在这项工作中，对通过圆柱形折射率不连续介电界面紧密聚焦的偏振光束进行了数值研究。首次基于矢量衍射积分理论推导出相应的焦斑计算公式。通过数值计算揭示并详细讨论了穿过具有不同半径的圆柱形介电界面的图案。此外，还找出了积分公式的像差因子，成功地进行了相位补偿图，用于焦点图案校正。这些发现将有助于提高先进光学显微镜在探测微管封装样品时的空间分辨率。