Practical time mark estimators for multichannel digital silicon photomultipliers

Abstract

Multiple time-to-digital converters coupled with silicon photomultipliers allow to timestamp several light photons generated by a scintillation event. Multichannel digital silicon photomultipliers opened the possibility to estimate a gamma-photon time mark by using several photoelectrons timestamps. We studied the already-existing statistics models of pho-toeletron time-stamping generation, while extending the current models by adding the skipping effect. Which accounts for the inability of the system to timestamp a continuous set of photoelectrons. In addition, we proposed two multiple photoelectron timemark estimators based on the best linear unbiased and the maximum likelihood estimation methods. We calculated the Cramér Rao lower bound for several system parameter and compared it to the proposed estimators' performance. We concluded that under certain system configurations the proposed estimators are efficient. Moreover, we investigated the effect of dark count rate on the timing performance. Also, we introduced a filtering method that is based on measuring the time distance between adjacent timestamps. We performed a full Monte Carlo simulation to evaluate the proposed filter efficiency. Finally, we performed a full Monte Carlo simulation to compare the timemark estimators' performance. We concluded that the best linear unbiased estimator is as efficient as the maximum likelihood estimator. In addition, it was verified that multichannel digital silicon photomultipliers have a stronger tolerance to dark counts in comparison with current digital silicon photomultiplier architectures.