## Timing Resolution and Coincidence Detection

The timing resolution of a PET detector describes the uncertainty in the timing characteristics of the scintillation detector on an event-by-event basis due to statistical fluctuations. With a fast signal (or short decay time), the timing resolution is small as well. The timing resolution of a PET detector is important because it involves the detection of two photons originating from a single coincident event. Since the timing resolution represents the variability in the signal arrival times for different events, it needs to be properly accounted for when detecting coincident events. Figure 2.23 gives a schematic representation of two detectors set up to measure coincident photons being emitted from a point equidistant from the two detectors.

The amplitude of the signal from the two detectors (V: and V2 in Fig. 2.23) may be different owing to incomplete deposition of energies or varying gains of the photo-detectors in the two detectors. The coincidence circuitry, however, generates a narrow trigger pulse when the detector signals cross a certain fixed fraction of their individual amplitudes. At time t:, signal A triggers pulse 1 which also produces a coincidence time window of a predetermined width, 2t. Signal B, depending upon the timing resolution of the detector, will trigger at a later time, t2. Depending upon the difference t2 - t:, the start of pulse 2 may or may not overlap with the coincidence window. For detectors with poor timing resolution, a large value for 2t needs to be used in order to detect most of the valid coincidence events.

In a PET scanner, the two coincident photons will be emitted from anywhere within the scanner field-of-

view (FOV), and so the distance travelled by each of them before interaction in the detectors will be different. For a typical whole-body scanner, this distance can be as large as the scanner diameter (about 100 cm). Using the value of speed of light (c = 3 x 108 m/s), one can calculate an additional maximum timing difference of about 3-4 ns between the two signals (the photons travel 1 m in 3.3 ns). As a result, the coincidence timing window (2t) of a PET detector needs to be increased even more than the requirements of the timing resolution. For an extremely fast scintillator such as BaF2, the timing resolution is very small. However, the coincidence timing window cannot be reduced to less than 3-4 ns (in a whole-body scanner geometry) due to the difference in arrival times of two photons emitted at the edge of the scanner field of view, as this would restrict the transverse field of view.