The statistical distribution of the number of counted scintillation photons in digital silicon photomultipliers: model and validation.

In the design and application of scintillation detectors based on silicon photomultipliers (SiPMs), e.g. in positron emission tomography imaging, it is important to understand and quantify the non-proportionality of the SiPM response due to saturation, crosstalk and dark counts. A new type of SiPM, the so-called digital silicon photomultiplier (dSiPM), has recently been introduced. Here, we develop a model of the probability distribution of the number of fired microcells, i.e. the number of counted scintillation photons, in response to a given amount of energy deposited in a scintillator optically coupled to a dSiPM. Based on physical and functional principles, the model elucidates the statistical behavior of dSiPMs. The model takes into account the photon detection efficiency of the detector; the light yield, excess variance and time profile of the scintillator; and the crosstalk probability, dark count rate, integration time and the number of microcells of the dSiPM. Furthermore, relations for the expectation value and the variance of the number of fired cells are deduced. These relations are applied in the experimental validation of the model using a dSiPM coupled to a LSO:Ce,Ca scintillator. Finally, we propose an accurate method for the correction of energy spectra measured with dSiPM-based scintillation detectors.