In PET imaging, one measures lines of response which are produced by the tracks

Question

In PET imaging, one measures lines of response which are produced by the tracks followed by the two gamma rays released from the positron-electron annihilation process. In 'time of flight' PET imaging, the 'time of flight' measurement enables one to determine where on the line of response the annihilation occurred. What timing resolution (in seconds) is required in the PET gamma ray detectors in order that the annihilation can be located to within 1 cm accuracy? Neglect scattering and assume that the two photons follow exactly opposite trajectories.

Explanation / Answer

To locate 1 cm accuracy, we must have a time resolution t, in which tume, a gamma ray photon covers the distance

d = 1 cm

As speed of light c = 3 x 1010 cm/s

For d = 1 cm,

Required time to cross 1 cm is

t = d/c = 1/(3 x 1010) s

t = 3.333.. nano seconds

t = 3.333... x 10-9 seconds

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