The mathematical theory of photomultiplier tube calibration
Abstract
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 SR(x), are also presented. As an example, we plot SR(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.
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BibTeX
@misc{kalousis2026mathematical,
title = {{The mathematical theory of photomultiplier tube calibration}},
author = {L. N. Kalousis and E. A. Dris and A. Vynias},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.24250},
eprint = {2607.24250},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.24250},
}
RIS
TY - UNPB
TI - The mathematical theory of photomultiplier tube calibration
AU - L. N. Kalousis
AU - E. A. Dris
AU - A. Vynias
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2607.24250
UR - https://arxiv.org/abs/2607.24250
AB - 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.
ER -