Stochastic modelling of diffused and specular reflector efficiencies for scintillation detectors

Scintillation detectors find wide application in detection of ionizing radiation. To prevent lateral loss of scintillation photons out of the scintillator volume, it is a regular practice in radiation detectors to cover the scintillator surfaces with some kind of reflective material. Typical choices of reflective materials are diffused reflectors such as PTFE sheets/tapes and specular reflectors like Aluminium coatings. The study proposes structured probabilistic modelling of purely diffused and specular reflection mechanisms for an ideal scintillator in the shape of a regular cube, for which conditional probabilities associated with individual reflection events have been obtained through Monte Carlo simulations and compiled in the form of a look-up table (LUT). This work presents a novel approach of modelling specular and diffused reflection processes as stochastic Markov processes and compares between their respective collection efficiencies on the basis of their respective governing principles. The study also involves computation of probabilities for all reflection scenarios and aggregation of individual reflection event probabilities and volumetric photon loss probabilities as a function of the photon-ray path-length in scintillator bulk, for determination of total photon collection efficiencies. The study also proposes generalizations in the ideal model to make it suitable for modelling real-world scintillators with arbitrary shapes and surface conditions. It suggests a possible means of volumetric discretization of arbitrarily shaped scintillators into voxels in the shape of regular cubes, for which photon transport probabilities can be computed by referring to data available in the form of the LUTs.