TDC Array Tradeoffs in Current and Upcoming Digital SiPM Detectors for Time-of-Flight PET

Radiation detection used in positron emission tomography (PET) exploits the timing information to remove background noise and refine position measurement through time-of-flight information. Fine time resolution in the order of 10 ps full-width at half-maximum (FWHM) would not only improve contrast in the image, but would also enable direct image reconstruction without iterative or back-projected algorithms. Currently, PET experimental setups based on silicon photomultipliers (SiPMs) reach 73 ps FWHM, where the scintillation process plays the larger role in spreading the timing resolution. This will change with the optimization of faster light emission mechanisms (prompt photons), where readout optoelectronics will once more have a noticeable contribution to the timing resolution limit. In addition to reducing electronic jitter as much as possible, other aspects of the design space must also explored, especially for digital SiPMs. Unlike traditional SiPMs, digital SiPMs can integrate circuits like time-to-digital converters (TDCs) directly with individual or groups of light sensing cells. Designers should consider the number of TDCs to integrate, the area they occupy, their power consumption, their resolution, and the impact of signal processing algorithms and find a compromise with the figure of merit and the coincidence timing resolution (CTR). This paper presents a parametric simulation flow for digital SiPM microsystems that evaluates CTR based on these aspects and on the best linear unbiased estimator (BLUE) in order to guide their design for present and future PET systems. For a small $1.1\times 1.1\times3.0$ mm³ LYSO crystal, the simulations indicate that for a low jitter digital SiPM microsystem with 18.2% photon detection efficiency, fewer than four timestamps with any multi-TDC configuration scheme nearly obtain the optimal CTR with BLUE (just below 100 ps FWHM), but with limited 5% improvement over only using the first observed photon. On the other hand, if a similar crystal but with 2.5% prompt photon fraction is considered, BLUE provides an improvement between 80% and 200% (depending on electronic jitter) over using only the first observed photon. In this case, a few tens of timestamps are required, yielding very different design guidelines than for standard LYSO scintillators.