AI 中文总结
本文提出一种利用轴锥透镜的几何光学类比模型，用于教学和计算，可生成类引力透镜的图像形态，探究表面几何与对称性对光线偏转及图像的影响。
AI 中文摘要
引力透镜常通过质量使光线弯曲来介绍，但若不借助完整的广义相对论机制，其几何本质难以直观呈现。本文提出一种几何光学类比方法，通过对轴锥型透镜进行光线追迹生成类透镜的选定图像形态。与基于空间变化折射率的类比不同，本模型使用具有恒定折射率的光学元件，光线的重新分布由折射面的几何结构产生。在推导一般双表面轴锥的光线追迹方程后，将模型应用于锥形和指数轮廓。轴对称构型产生环状图像，非对准入射产生部分弧，轴向对称性破缺产生类似爱因斯坦十字的四图像图案。该模型并非要替代相对论透镜方程作为物理工具，而是作为计算和教学工具，用于探究表面几何与对称性如何控制光线偏转、重新分布及图像多重性。
英文摘要
Gravitational lensing is often introduced through the bending of light by mass, but its geometrical nature can be difficult to visualize without invoking the full machinery of general relativity. We present a geometrical-optics analogy in which selected lensing-like image morphologies are generated by ray tracing through axicon-type lenses. In contrast with analogies based on a spatially varying refractive index, the present model uses optical elements with a constant refractive index; the redistribution of rays is produced by the geometry of the refracting surfaces. After deriving the ray-tracing equations for a general two-surface axicon, we apply the model to conical and exponential profiles. Axially symmetric configurations generate ring-like images, misaligned incidence produces partial arcs, and broken axial symmetry leads to four-image patterns reminiscent of an Einstein cross. The model is not intended as a physical substitute for a relativistic lens equation, but as a computational and pedagogical tool for exploring how surface geometry and symmetry control ray deflection, redistribution, and image multiplicity.
Comments11 pages, 5 figures, 1 table
