Practical time mark estimators for multichannel digital silicon photomultipliers

Abstract

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 gammaphoton time mark by using several photoelectrons timestamps.We studied the already-existing statistics models of photoeletron 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 the 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 the multichannel digital silicon photomultipliers have a stronger tolerance to dark counts in comparison current digital silicon photomultiplier architectures. I. CRAMÉR RAO LOWER BOUNDThe Cramér Rao Lower Bound (CRLB) determines a maximum estimation performance for problems that satisfy certain regularity conditions. The CRLB for the particular case of gamma-photon timemmark estimation was analyzed byIn single-photoelectron (q th ) timestamp estimation there is only one possible unbiased estimator, which is given bŷwhere t q represents the time-of-registration of the q th photoelectron and A is expressed asThe root mean square error (root-MSE) of the singlephotoelectron estimation method is equal to the square root of the variance of the PDF (probability density function) of the time-of-registration of the q th photoelectron [2].The maximum timing performance in the singlephotoelectron estimation case is determined by Eq. (3). We calculated the performance as a function of the photoelectron order for two different system parameter configurations (see Figs. 1 and 2) called datasets I and II. Dataset I is characterized by 100 ps FWHM jitter and 300 photoelectrons; dataset II by 700 ps FWHM jitter and 3800 photoelectrons. The scintillation decay constants were the same for both cases (LSO with properties [1]). We also calculated the CRLB (intrinsic limit) for each data set [2], [1]. II. MAXIMUM LIKELIHOOD ESTIMATIONThe likelihood function that corresponds to the t 1:Q timestamps of the first Q photoelectrons, when estimating the location parameter (T 0 ) is defined bywhere R repres...