Statistics of the Charge Spectrum of Photo-Multipliers and Methods for Absolute Calibration

TL;DR

This paper derives an analytical model for the charge spectrum of photo-multiplier tubes under low light conditions, enabling precise calibration and improved data analysis in physics experiments.

Contribution

It provides a comprehensive analytic expression for the charge spectrum, including dark noise and pedestal, applicable to calibration and data fitting in photo-multiplier applications.

Findings

Analytic formula accurately models charge spectrum including noise components.

Strategies for using the model to achieve absolute calibration.

Flexible models using Gaussian or Poisson gain assumptions.

Abstract

We derive the full expression for the shape of the charge spectrum that results from the illumination of a photo-multiplier tube. The derivation is for low intensity illumination with constant gain, a common condition for most nuclear and particle physics applications. Under these conditions, it is shown that an analytic expression can be formulated that describes details of the spectrum including the pedestal and dark noise with excellent fidelity to allow statistical fits to data. The derivation and full formula using either Gaussian or Poisson models for gain, and its limiting forms under various simplifying assumptions are presented with strategies on their use. The analytic description can be used to formulate data acquisition strategies to perform precise absolute calibration of photo-multipliers, the digitizers, and the data acquisition system.