Good timing resolution of a PET detector, besides helping reduce the number of random coincidences, can also be use to estimate the annihilation point between the two detectors by looking at the difference in arrival times of the two photons. For this, an extremely fast scintillator, such as BaF2, is needed.
In Fig. 2.24, point P marks an annihilation point which is located a distance d: from the point which is exactly halfway (distance d) between the two detectors. A photon moving along PA will travel a distance d - d:, while the coincident photon travels a total distance d + d: along PB before entering detector B. Thus, one photon will travel an extra distance (d + d:) - (d - d:) = 2d: relative to the other. The coincident detectors can be used to measure the difference in arrival times (8t) of the two photons. Using the speed of light, c, for the speed of the photons, d: can be calculated from 2d: = c8t. In order to obtain a good estimation of d:, however, an accurate measurement of 8t is needed, which in turn requires a fast scintillator with a timing resolution of less than 0.8 ns. Thus, the timing resolution of a PET detector introduces a blurring in the estimation of d:. It can be shown from the above calculation that for BaF2 with 8t = 0.8 ns, a blurring of about ±6 mm is introduced in the d: estimation. Slow scintillators will increase this blurring significantly. Presently, only BaF2 is feasible for use as a scintillator in time-of-flight measuring PET scanners, and such scanner designs have been successfully implemented. The advantage of estimating the location of the annihilation point is the improved signal-to-noise ratio obtained in the acquired image, arising due to a reduction in noise propagation during the image reconstruction process. However, since BaF2 also has a very low stopping power, time-of-flight scanners have a reduced sensitivity leading to lower signal-to-noise ratios. Hence, the overall design of such scanners requires a careful trade-off between the scanner sensitivity and the time-of-flight measurement so that the overall SNR for the scanner remains high.
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