The skew ray $\bar{\textrm{R}}_{\textrm{n}}$ on the image plane of an optical system possessing n boundary surfaces has the form of an n-layered deep composite function. It is hence difficult to evaluate the system performance using ray tracing alone. The present study therefore uses the Taylor series expansion to expand $\bar{\textrm{R}}_{\textrm{n}}$ with respect to the source ray variable vector. It is shown that the paraxial ray tracing equations, point spread function, caustic surfaces and modulation transfer function can all be explored using the first-order expansion. Furthermore, the primary and secondary ray aberrations of an axis-symmetrical system can be determined from the third- and fifth-order expansions, respectively. It is thus proposed that the Taylor series expansion of the skew ray serves as a useful basis for exploring a wide variety of problems in geometrical optics.

中文翻译：

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基于偏射线泰勒级数展开的几何光学路线图

具有n个边界面的光学系统像面上的歪斜射线$ \ bar {\ textrm {R}} _ {\ textrm {n}} $具有n层深复合函数的形式。因此，仅使用光线跟踪很难评估系统性能。因此，本研究使用泰勒级数展开来展开$ \ bar {\ textrm {R}} _ {\ textrm {n}} $关于源射线变量矢量。结果表明，可以使用一阶展开来探索近轴射线跟踪方程，点扩散函数，苛性表面和调制传递函数。此外，可以分别根据三阶和五阶展开来确定轴对称系统的一次和二次射线像差。因此提出，偏射线的泰勒级数展开是探索几何光学中各种问题的有用基础。