New approach to calibration of low gain PMTs and SiPMs using transit time histograms

Calibration of low light level photon detector with an internal charge multiplication like vacuum photomultiplier tube (PMT) and silicon photomultiplier (SiPM) assumes precise determination of the photomultiplier gain, excess noise factor (ENF), and photon detection efficiency (PDE). The direct measurements of these key parameters require clear distinction of the output signals at the level of a single photoelectron response from the noise. There are many situations when it is impossible to rely on single photoelectron pulse height histogram or photon counting measurements (e.g. in case of low gain, high noise, limited instrumentation), and this direct approach could not be applied. On the other hand, the large signal level measurements of the pulse height distribution provide reliable results, but the parameters of our interest are coupled in the non-separable combinations in the known mean, standard deviation or resolution of the measured histogram. A new approach on how to determine the photomultiplier gain, ENF, and PDE separately using large signal measurements is proposed. It is based on a unique feature of Erlang and Gamma probability distributions providing additional information on mean time between photoelectron arrivals from specific transit time measurements. The method is considered to be rather simple and robust, and especially relevant and useful for the low gain PMT and SiPM with low crosstalk and afterpulsing.