Calibration of Gamma Ray Impacts in Monolithic-Based Detectors Using Voronoi Diagrams

Molecular imaging systems, such as positron emission tomography (PET), use detectors providing energy and a 3-D interaction position of a gamma ray within a scintillation block. Monolithic crystals are becoming an alternative to crystal arrays in PET. However, calibration processes are required to correct for nonuniformities, mainly produced by the truncation of the scintillation light distribution at the edges. We propose a calibration method based on the Voronoi diagrams. We have used <inline-formula> <tex-math notation="LaTeX">$50 \times 50 \times 15$ </tex-math></inline-formula> mm³ LYSO blocks coupled to a <inline-formula> <tex-math notation="LaTeX">$12\times 12$ </tex-math></inline-formula> SiPMs array. We have first studied two different interpolation algorithms: 1) weighted average method (WAM) and 2) natural neighbor (NN). We have compared them with an existing calibration based on 1-D monomials. Here, the crystal was laterally black painted and a retroreflector (RR) layer added to the entrance face. The NN exhibited the best results in terms of <italic>XY</italic> impact position, depth of Interaction, and energy, allowing us to calibrate the whole scintillation volume. Later, the NN interpolation has been tested against different crystal surface treatments, allowing always to correct edge effects. Best energy resolutions were observed when using the reflective layers (12%–14%). However, better linearity was observed with the treatments using black paint. In particular, we obtained the best overall performance when lateral black paint is combined with the RR.