Abstract: Continuous crystals can potentially obtain better intrinsic detector spatial resolution compared to pixelated crystals, additionally providing depth of interaction (DoI) information from the light distribution. To achieve high performance sophisticated interaction position estimation algorithms are required. There are a number of algorithms in the literature applied to different crystal dimensions and different photodetectors. However, the different crystal properties and photodetector array geometries have an impact on the algorithm performance. In this work we analysed, through Monte Carlo simulations, different combinations of realistic crystals and photodetector parameters to better understand their influence on the interaction position estimation accuracy, with special emphasis on the DoI. We used an interaction position estimation based on an analytical model for the present work. Different photodetector granulation schemes were investigated. The impact of the number of crystal faces readout by photodetectors was studied by simulating scenarios with one and two photodetectors. In addition, crystals with different levels of reflection and aspect ratios (AR) were analysed. Results showed that the impact of photodetector granularity is mainly shown near the edges and specially in the corners of the crystal. The resulting intrinsic spatial resolution near the centre with a 12 x 12 x 10 mm(3) LYSO crystal was 0.7-0.9 mm, while the average spatial resolution calculated on the entire crystal was 0.77 +/- 0.18 mm for all the simulated geometries with one and two photodetectors. Having front and back photodetectors reduced the DoI bias (Euclidean distance between estimated DoI and real DoI) and improved the transversal resolution near the corners. In scenarios with one photodetector, small AR resulted in DoI inaccuracies for absorbed events at the entrance of the crystal. These inaccuracies were slightly reduced either by increasing the AR or reducing the amount of reflected light, and highly mitigated using two photodetectors. Using one photodetector, we obtained a piecewise DoI error model with a DoI resolution of 0.4-0.9 mm for a 1.2 AR crystal, and we observed that including a second photodetector or reducing the amount of reflections reduced the DoI bias but did not significantly improve the DoI resolution. Translating the piecewise DoI error model obtained in this study to image reconstruction we obtained a spatial resolution variability of 0.39 mm using 85% of the FoV, compared to 2.59 mm and 1.87 mm without DoI correction or with a dual layer system, respectively.

Abstract: Effective geometries arising from a hypothetical discrete structure of spacetime can play an important role in the understanding of the gravitational physics beyond General Relativity (GR). To discuss this question, we make use of lessons from crystalline systems within solid state physics, where the presence of defects in the discrete microstructure of the crystal determine the kind of effective geometry needed to properly describe the system in the macroscopic continuum limit. In this work, we study metric-affine theories with nonmetricity and torsion, which are the gravitational analog of crystalline structures with point defects and dislocations. We consider a crystal-motivated gravitational action and show the presence of topologically nontrivial structures (wormholes) supported by an electromagnetic field. Their existence has important implications for the quantum foam picture and the effective gravitational geometries. We discuss how the dialogue between solid state physics systems and modified gravitational theories can provide useful insights on both sides.