Lin Psang Dain
Opt Express. 2020 Mar 30;28(7):10124-10133. doi: 10.1364/OE.387463.
The skew ray R¯ 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 R¯ 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.
具有n个边界表面的光学系统像平面上的斜光线R¯具有n层深度复合函数的形式。因此，仅使用光线追迹来评估系统性能是困难的。因此，本研究使用泰勒级数展开式，相对于源光线变量向量展开R¯。结果表明，近轴光线追迹方程、点扩散函数、焦散面和调制传递函数都可以通过一阶展开来研究。此外，轴对称系统的初级和次级光线像差可以分别从三阶和五阶展开式中确定。因此，建议斜光线的泰勒级数展开式作为探索几何光学中各种问题的有用基础。
