Annihilation photon acollinearity is a fundamental but little investigated problem in positron emission tomography (PET). In this paper, the cause of the angular deviation from 180.00 degrees is described as well as how to evaluate it under conditions of a spatially distributed radiation source and a limited acquisition time for the human body. A relationship between the shape of the photopeak spectrum and the angular distribution is formulated using conservation laws of momentum and energy over the pair annihilation. Then the formula is used to evaluate the acollinearity for a pool phantom and the human body with FDG injected. The angular distribution for the pool phantom agrees well with that for pure water which had been directly measured by Colombino et al in 1965 (Nuovo Cimento 38 707-23), and also with that for the human body determined in this study. Pure water can be considered as a good approximation of the human body regarding the angular deviation. The blurring coefficient to be multiplied by the ring diameter in calculations of the PET spatial resolution is experimentally determined for the first time as 0.00243 +/- 0.00014; this is 10% larger than the value widely used by investigators.
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