Since the probability that both 511 keV photons will escape from the body without scattering is very high in general, the line along which the positron annihilation occurred (i.e. the line of response, LoR) can be defined if both photons can be detected with two detectors at opposite ends of the line, as illustrated in Fig. 2.2. As the distance that a positron traveled before annihilation is generally very small, this is a good approximation to the line along which the emitted photons must be located. The scheme for detection of photon emissions is called
Pulse overlap => coincidence
Coincidence window = 2t o = Positron annihilation
-► = Accepted by coincidence detection
Figure 2.2: Annihilation coincidence detection. The two gamma-ray detectors are placed at the opposite ends of the object to detect the photons that originate from the positron annihilation site. The event is registered if the annihilation occurs within the region of coincidence detection of the detector pairs. If the gamma rays originate outside the region of coincidence detection of the two detectors but only one of the photons is detected, the event is not registered as the detection of a single photon violates the condition of coincidence.
coincidence detection , which is unique to PET imaging. It should be noted, however, that the condition of coincidence (or simultaneity) is not achievable in practice, and a coincidence resolving time (or a coincidence timing window) of less than 15 ns is often used to account for differences in arrival times of the two gamma rays, time taken to produce scintillation light in the detector, and time delays in the electronic devices in the PET system.
Once the signal leaves the detector module, it is processed by several electronic circuits. The choice of components depends upon the application and, therefore, there are many ways to implement the coincidence detection circuitry. A simplified schematic representation of detecting coincidence events with two detectors is also shown in Fig. 2.2. The output signal from each detector is fed into a pulse generator. Note that the signal amplitude from the two detectors (VA and VB) may not be the same due to incomplete deposition of photon energies or variation in efficiency among the detectors. In addition, there exists a time difference between the detectors to react upon the photons arrival, and a finite reaction time for the electronic devices to response, resulting in difference in the time t1 and fa at which the amplitude of the signal crosses a certain fixed voltage level (VT ), which triggered the pulse generator to produce a narrow pulse. The narrow pulse is then fed into the gate-pulse generator where a pulse of width 2t (coincidence timing window) is generated for individual detectors. A coincidence detection circuit is then used to check for a logical AND between the incoming pulses. For the example shown in Fig. 2.2, there is a pulse overlap between two signals produced by the gate-pulse generators. Therefore, the event is a true coincidence which is regarded as valid and is registered. It is easy to see that if fa — t1 > 2r, the event is not in coincidence, and thus it is not recorded by the coincidence detection circuit.
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