论文标题
超越ABCD：通过使用均匀坐标的几何光学矩阵方法更好
Beyond the ABCDs: A better matrix method for geometric optics by using homogeneous coordinates
论文作者
论文摘要
几何光学元件通常被描述为通过光学系统追踪非划分光线的路径。在近端极限中，可以使用射线传输矩阵（俗称ABCD矩阵）计算射线痕迹，该矩阵是作用在射线高度和斜率上的2x2矩阵。射线传输矩阵的已知限制是它们仅适用于以光轴为中心且正常的光学元件。在本文中，我们提供了一种改进的3x3矩阵方法，用于计算光学系统的近端射线痕迹，该方法适用于这些系统实际上如何在光学表上排列：透镜和镜像在任何方向或位置（例如，在实验室坐标中），以及沿桌子上的光路路径Zig-Zagging。使用投影二元性，我们还展示了如何使用从系统的射线传输矩阵计算的点传输矩阵直接通过光学系统进行映像。我们通过几个示例证明了这些方法的有用性，并讨论了扩展该技术应用的未来方向。
Geometric optics is often described as tracing the paths of non-diffracting rays through an optical system. In the paraxial limit, ray traces can be calculated using ray transfer matrices (colloquially, ABCD matrices), which are 2x2 matrices acting on the height and slope of the rays. A known limitation of ray transfer matrices is that they only work for optical elements that are centered and normal to the optical axis. In this article, we provide an improved 3x3 matrix method for calculating paraxial ray traces of optical systems that is applicable to how these systems are actually arranged on the optical table: lenses and mirrors in any orientation or position (e.g.~in laboratory coordinates), with the optical path zig-zagging along the table. Using projective duality, we also show how to directly image points through an optical system using a point transfer matrix calculated from the system's ray transfer matrix. We demonstrate the usefulness of these methods with several examples and discuss future directions to expand applications of this technique.
