Calibration of photomultiplier tubes

TL;DR

This paper introduces a numerical DFT-based method for calibrating photomultiplier tubes with a Gaussian single photoelectron response, providing rigorous results without approximations and applicable across various light intensities.

Contribution

It presents a novel DFT-based calibration technique for photomultipliers that improves accuracy and efficiency over traditional methods, applicable to different light intensities.

Findings

DFT approach yields rigorous charge response calculations.

Method applied successfully to Hamamatsu R7081 photomultiplier.

Toy Monte Carlo analysis demonstrates high precision of the DFT method.

Abstract

The purpose of the present article is to demonstrate the calibration of photomultipliers with a gaussian single photoelectron response using a numerical method based on the Discrete Fourier Transform (DFT). Conventional techniques, commonly employed in the literature, use approximate models or brute force numerical calculations of the convolution integrals that lead to the charge response function of the photomultiplier, $S_R(x)$. In this publication, we explain how a truncated gaussian model for the single photoelectron amplification can lead to rigorous results if one leans on the DFT approach. The distinct feature of this procedure is that $S_R(x)$ is calculated to all orders in the Poisson mean $\mu$ that characterizes the light intensity and no approximations are needed. This scheme was applied to the calibration of the Hamamatsu R7081 photomultiplier tube and a comparison of the DFT approach with the more standard numerical integration method is also presented. Last, toy Monte Carlo data were analyzed for different values of $\mu$ to understand the precision of the DFT method.