Elagha Hassan A
J Opt Soc Am A Opt Image Sci Vis. 2017 Mar 1;34(3):335-343. doi: 10.1364/JOSAA.34.000335.
In this work, we generalize the paraxial ray-tracing formulas to include nonparaxial rays. For a refracting (reflecting) spherical surface, a new single meridional formula is derived. This formula can be easily reduced to a paraxial formula. It can also be applied to any aspheric (or general) surface with a known equation. Also, a new exact ray-tracing procedure for a centered system of spherical surfaces is derived. In this procedure, we apply just two simple equations for each surface of the system, which, to the best of our knowledge, makes it the shortest analytical ray-tracing technique ever. This procedure can be applied in some other applications. For example, it can be reduced to a new single paraxial formula that can be easily used to trace a paraxial ray propagating through a system of spherical surfaces. Also, it is applied to derive an exact meridional formula for both thick and thin lenses that can also be reduced to a new paraxial formula different from the Gaussian one. These results led us to easily derive an exact formula for the longitudinal spherical aberration for both thick and thin lenses and also for a single refracting (reflecting) spherical surface. Numerical examples are provided and discussed.
在这项工作中，我们将傍轴光线追迹公式推广到包括非傍轴光线的情况。对于折射（反射）球面，推导了一个新的单一子午面公式。该公式可以很容易地简化为傍轴公式。它也可以应用于具有已知方程的任何非球面（或一般）表面。此外，还推导了一种用于球面中心系统的新的精确光线追迹方法。在这个方法中，对于系统的每个表面，我们只应用两个简单的方程，据我们所知，这使其成为有史以来最短的解析光线追迹技术。这个方法可以应用于其他一些应用中。例如，它可以简化为一个新的单一傍轴公式，该公式可以很容易地用于追迹通过球面系统传播的傍轴光线。此外，它还被用于推导厚透镜和薄透镜的精确子午面公式，该公式也可以简化为一个不同于高斯公式的新傍轴公式。这些结果使我们能够轻松地推导出厚透镜和薄透镜以及单个折射（反射）球面的纵向球差的精确公式。文中提供并讨论了数值示例。
