Theoretical analysis of the use of germanium detectors for time-of-flight emission tomography

A theoretical analysis of the timing capabilities of Ge semiconductor detectors in time-of-flight positron emission tomography is presented. The effect of detector size on efficiency and time resolution is discussed. The relevant noise sources are determined and the optimum filter is derived to optimize the slope-to-noise ratio, while minimizing the effect of collection time variations on time resolution. The performance of the ideal filter is compared with a single RC integrator. For a lower energy threshold of 200 keV, time resolution of better than 250 ps seems to be a realistic goal for a detector of 0.5 x 0.5 cm cross section and 3 cm length. This detector would yield an overall efficiency of 36% for 511 keV gamma-rays and 80% of the detected photons would fall in the Gaussian part of the timing spectrum.