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In PET imaging, the information needed to form an image is obtained from the detection of pairs of gamma-ray photons emitted by electron-positron annihilations. An optimal timing resolution allows the system to include time-of-flight (TOF) information, which improves image quality. The two methods to approach timing estimation are analog processing and digital captured waveform analysis. In digital analysis, there is a trade-off between the amount of data acquired and the timing resolution of a detector. In order to develop an efficient data acquisition system, we want to minimize the number of digital samples by acquiring the samples that contains the most information for timing estimation. We developed a simulation package to perform Fisher information analysis on the waveform samples in order to quantify the timing information conveyed by segments of the waveform. The diagonal components of the inverse of the Fisher information matrix set the bound that establishes the Cramér-Rao inequality on the variance of an unbiased estimator. The Maximum-Likelihood (ML) estimator is unbiased and asymptotically achieves the Cramér-Rao lower bound; for this reason, the ML estimator is ideal for performing timing estimation and extracting information as described by Fisher information analysis. This document explains the simulation of the waveforms, ML estimation method, Fisher information analysis and the calculation of the Cramér-Rao lower bound, for different lengths of the pulse. The results show that the timing resolution approaches a limit using just a segment of the waveform and there are parts of the pulse that are redundant information. The yields of this work will be used to build an efficient data acquisition (DAQ) system that will acquire less amount of data, and therefore, the complexity and cost of the DAQ system will be reduced.
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