Calibration of the Hamamatsu R7081 photomultiplier tube

Abstract

The purpose of the present article is to demonstrate the calibration of the Hamamatsu R7081 photomultiplier using a numerical method based on the Discrete Fourier Transform (DFT). Conventional techniques, usually 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. The same scheme can be applied to other photomultiplier tubes that share the same properties with R7081