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Acolinearity of the annihilation photons observed in Positron EmissionTomography (PET) is described as following a Gaussian distribution. However, itis never explicitly said if it refers to the amplitude of the acolinearityangle or its 2D distribution relative to the case without acolinearity (hereindefined as the acolinearity deviation). Since the former is obtained byintegrating the latter, a wrong interpretation would lead to very differentresults. The paper of Shibuya et al. (2007), differs from the previous studiessince it is based on the precise measurement of the energy of the annihilationphotons. They also show that acolinearity follows a Gaussian distribution inthe context of PET. However, their notation, which relies on being on the planewhere the two annihilation photons travel, could mean that their observationrefers to the amplitude of the acolinearity angle. If that understanding iscorrect, it would mean that acolinearity deviation follows a 2D Gaussiandistribution divided by the norm of its argument. Thus, we revisited the proofpresented in Shibuya et al. (2007) by using an explicit description of theacolinearity in the 3D unit sphere.

A rewriting of the relation between the acolinearity of annihilation photons and their energy in the context of positron emission tomography