Effective collecting area represents one of principal parameters of optical systems. The common requirement is to obtain as large effective collecting area as it is possible. The paper presents an analytical method of calculating effective collecting length and its maximization for lobster eye optics. The results are applicable for a Schmidt as well as for an Angel lobster eye geometry used in an astronomical telescope where the source is at infinity such that the incoming rays are parallel. The dependence of effective collecting area vs. geometrical parameters is presented in a form of a simple compact equation. We show that the optimal ratio between mirrors depth and distance (effective angle) does not depend on other geometrical parameters and it is determined only by reflectivity function, i.e. by mirrors (or their coating) material and photon energy. The results can be also used for approximate but fast estimation of performance and for finding the initial point for consequent optimization by ray-tracing simulations.

中文翻译：

---

龙虾眼光学有效采集面积及有效角度最佳值

有效收集面积是光学系统的主要参数之一。常见的要求是获得尽可能大的有效收集区域。本文提出了一种计算龙虾眼光学有效采集长度及其最大化的解析方法。结果既适用于施密特，也适用于天文望远镜中使用的天使龙虾眼几何结构，其中源在无穷远处，因此入射光线是平行的。有效收集面积与几何参数的相关性以简单紧凑方程的形式呈现。我们表明反射镜深度和距离（有效角）之间的最佳比率不依赖于其他几何参数，它仅由反射率函数决定，即 通过镜子（或其涂层）材料和光子能量。结果也可用于近似但快速的性能估计，以及通过光线追踪模拟寻找后续优化的初始点。