Effect of crystal-photodetector interface extraction efficiency on Cerenkov photons' detection time

Using Cerenkov photons to improve detector timing resolution in time-of-flight positron emission tomography scanners is promising since they constitute most of the signal rising edge. The main challenge in using Cerenkov light is its low yield per photoelectric interaction, which requires optimizing their complex optical transport in the detector. Monte Carlo simulations unlock information unavailable through benchtop measurements and help better understand the Cerenkov photon behavior. Although the first Cerenkov photons are emitted forward, part of the early triggering signal is lost due to poor light extraction at the crystal-photodetector interface. In addition, the electron path in the crystal, that determines the Cerenkov photon direction, is tortuous due to multiple scattering, causing the Cerenkov photons emitted after a few scatters to no longer be forward-directed. In this context, the transit time spread in the crystal, highly dependent on the detector geometry, plays a crucial role in the photon detection time. In this work, we performed optical simulations in bismuth germanium oxide using 511 keV gamma with GATE to investigate the optical photons extraction when modifying the index of refraction at the crystal-photodetector interface and the crystal aspect ratio. The mean detection time of the first, second, and third detected optical and Cerenkov photon separately was studied as a function of the total number of Cerenkov detected per event. For each configuration, we calculated the expected mean detection time using the probability of detection. Thinner crystals led to lower expected detection times due to the reduced transit time in the crystal. Reducing the refractive index discontinuity at the crystal-photodetector interface decreased all configurations expected mean detection time values. We showed that it not only improves the optical photons (scintillation and Cerenkov) detection efficiency at the photodetector face but directly ameliorates the probability of detecting the fastest one, reducing the effect of thicker materials and of losing the first detected photon information, both crucial to reduce the detector timing resolution. Thanks to their prompt emission and directionality at emission, Cerenkov photons represent the first detected optical photon in most configurations but increasing their detection efficiency is crucial to detect the fastest one.