发表机构
National Technical University（国立技术大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文介绍光电倍增管校准数学理论，阐述其工作原理及相关数学方案，介绍常用数值方法，通过实例展示函数特征，介绍校准技术并分析数据，展示软电荷成分影响，最后对大规模探测器原位校准作评论，为相关人员提供参考。
AI 中文摘要
在本技术说明中，我们描述了光电倍增管（PMT）校准数学理论的主要特征。以简单且便于理解的方式解释了各种论点和概念。从理论角度讨论了PMT的基本工作原理，阐述了其功能的基本步骤（光电转换、聚焦、倍增等）以及模拟微弱泊松光源照射下PMT电荷输出所需的数学方案。介绍了计算电荷放大函数\(S_R(x)\)的最常用数值方法，并以伽马函数模型为例绘制\(S_R(x)\)并展示其主要特征。还介绍了增益校准的基本技术，并使用玩具蒙特卡罗数据探究其精度。此外，分析了滨松R1408 PMT的数据。最后，展示了软电荷成分的存在如何影响增益测定结果。我们以关于大规模探测器原位校准的一些一般性评论结束本报告。希望本文档能为想更多了解PMT校准理论的学生和年轻研究人员提供参考。
英文摘要
In this technical note we describe the main features of the mathematical theory of photomultiplier tube (PMT) calibration. Attention was paid to explain the various arguments and concepts in a simple and pedagogical manner that everybody understands. The basic operational principles of a PMT are discussed from a theoretical standpoint. The essential steps of its function (photoconversion, focusing, multiplication, etc.) are laid down together with the mathematical schemes necessary to model the charge output of a PMT when illuminated by a faint poissonian light source. In case of important omissions we direct the reader to some of the standard references. The most common numerical methods, used to calculate the charge amplification function $S_R(x)$, are also presented. As an example, we plot $S_R(x)$ utilizing a gamma function model for the single photoelectron (SPE) response and showcase its main characteristics. The basic techniques for gain calibration are also introduced, and we probed their precision using toy Monte Carlo data. Additionally, data from a Hamamatsu R1408 PMT were analyzed. Finally, we show how the presence of soft charge component can affect the results of gain determination. We conclude this report with some general comments regarding \emph{in situ} calibration of large-scale detectors. We hope that this document can serve as a reference for students and young researchers that want to learn more about the theory of PMT calibration.
CommentsTechnical Note
