Annihilation Photon Acolinearity with Ultra-fast ToF-PET

It was recently demonstrated that using ultra-fast Time-of-Flight (ToF) in positron emission tomography can mitigate the blur induced by the detector size. In another study, it was also observed that resolution beyond the expected Gaussian blur of annihilation photon acolinearity (APA) could be achieved, even though APA was not modeled in the system matrix. This incongruity is further investigated in this work. With perfect ToF resolution, the resulting response function is shown to be the product between the expected Gaussian APA and the 1/r function. A 2D scanner with 1-mm wide detectors and 2-mm ToF resolution is used to further explore the issue. Simulation of point sources shows that the reconstructed profiles were indeed not Gaussian. A Hot Spots phantom was also simulated to evaluate qualitatively the scanner resolving power and, again, resolution beyond the expected 0.0044R, R being the scanner radius, was achieved. These results highlight that the spatial response function induced by neglecting APA in the reconstruction scheme is sharper than expected, approaching an 1/r shape, when ultra-fast ToF is available.