利用μ子环校准切伦科夫望远镜阵列：基于矢量几何的双镜望远镜解析解
Using Muon Rings for the Calibration of the Cherenkov Telescope Array: An Analytical Solution for the Dual-Mirror Telescope Using Vector Geometry
AI总结：
研究利用矢量几何形式推导双镜望远镜中μ子产生切伦科夫光的解析解，通过与已知解及极限情况对比验证，分析了相关效应，结果可直接用于切伦科夫望远镜阵列天文台基于μ子的校准。
AI中文摘要：
成像大气切伦科夫望远镜（IACTs）中μ子产生的环图像分析，为校准仪器光通量和监测其光学点扩展函数提供了强大而精确的方法。目前已得到单镜望远镜的解析解，但双镜望远镜因问题复杂，尚未有完整解析描述。本文利用矢量几何形式，借助计算机代数系统SageMath进行符号运算和泰勒展开，推导了双镜望远镜的解析解。通过与简单配置下的已知解析解及预期物理行为的极限情况对比验证。结果表明，双镜望远镜中倾斜μ子产生的切伦科夫光遮蔽效应显著，与先前方法相比偏差达40%。还得到了主镜曲率对μ子发射切伦科夫光子最大发射高度的一阶修正及彗差对单镜抛物面望远镜中μ子环的影响。研究结果直接适用于切伦科夫望远镜阵列天文台（CTAO）基于μ子的校准。
英文摘要：
The analysis of ring images produced by muons in Imaging Atmospheric Cherenkov Telescopes (IACTs) provides a powerful and precise method for calibrating the optical throughput of the instrument and monitoring its optical point-spread function. To date, analytical solutions have been derived for single-mirror telescopes with reflectors assumed flat. However, a complete analytical description of the Cherenkov light produced by muons and detected by a dual-mirror telescope - accounting for both the secondary mirror and the camera - has remained elusive, owing to the complexity of the problem. In this work, we derive such a solution using a vector-geometry formalism supported by symbolic manipulation and Taylor expansions performed with the computer algebra system SageMath. We validate the formalism against known analytical solutions in simpler configurations and, for more complex terms, against limiting cases exhibiting the expected physical behavior. The behavior of the full solution is illustrated visually by varying the relevant parameters. The largest effects were found in the shadowing of Cherenkov light produced by inclined muons in dual-mirror telescopes, particularly for the Schwarzschild-Couder Telescope (SCT) design with baffles surrounding the secondary mirror. Deviations of up to 40% are observed relative to previously employed methods. As a by-product, we derive the first-order correction to the maximum emission height of Cherenkov photons emitted by a muon, arising from the curvature of the primary mirror - an effect neglected in previous studies - as well as the impact of coma aberration on the muon rings in single-mirror parabolic telescopes. Our results are directly applicable to muon-based calibration of the Cherenkov Telescope Array Observatory (CTAO).
