Timing Estimation and Limits in TOF-PET Detectors Producing Prompt Photons

The production of prompt photons providing high photon time densities is a promising avenue to reach ultrahigh coincidence time resolution (CTR) in time-of-flight positron emission tomography. Detectors producing prompt photons are receiving high interest experimentally, ignited by past exploratory theoretical studies that have anchored some guiding principles. Here, we aim to consolidate and extend the foundations for the analytical modeling of prompt generating detectors. We extend the current models to a larger range of prompt emission kinetics where more stringent requirements on the prompt photon yield rapidly emerge as a limiting factor. Lower bound and estimator evaluations are investigated with different underlying models, notably by merging or keeping separate the prompt and scintillation photon populations. We further show the potential benefits of knowing the proportion of prompt photons within a detection set to improve the CTR by mitigating the detrimental effect of population (prompt versus scintillation) mixing. Taking into account the fluctuations on the average number of detected prompt photons in the model reveals a limited influence when prompt photons are accompanied by fast scintillation (e.g., LSO:Ce:Ca) but a more significant effect when accompanied by slower scintillation (e.g., bismuth germanate). Establishing performance characteristics and limitations of prompt generating detectors is paramount to gauging and targeting the best possible timing capabilities they can offer.