An analytical model for photomultiplier tube calibration

The purpose of the present article is to offer an analytical model that can be used for the calibration of photomultiplier tubes (PMTs). The derivation of the mathematical formulae is discussed extensively and we apply this machinery to a real problem; the gain determination of the R7081 Hamamatsu PMT. We hope that our work can provide a third, powerful alternative to the task of gain deconvolution. We also believe that the techniques explained in this article can be applied to other problems in PMT calibration and monitoring.