Depth of γ-ray interaction within continuous crystals from the width of its scintillation light-distribution

We have studied a new and inexpensive method of measuring the depth of interaction (DOI) in γ-ray detectors with large-sized scintillation crystals. This method takes advantage of the strong correlation between the width of the undisturbed light-distribution in continuous crystals and the γ-ray´s DOI. In order to quantify the dependence of the distribution´s width with respect to the DOI, we first studied an analytical model of the light-distribution and tested it by means of Monte Carlo (MC) simulations of the light transport inside the crystal. Further we present an inexpensive modification of the commonly used charge division circuit that allows analog and instantaneous computation of the light-distribution´s second moment without affecting the determination of the centroid. This redesigned resistor network is based on the position-sensitive proportional counter (DPC) readout and allows, together with position sensitive photo-detectors, the additional measurement of the light-distribution´s standard-deviation σ. We tested the proposed circuit using the design-tool OrCAD and found the signal sufficiently large for digitalization. Finally, we conducted MC simulations of a realistic Positron Emission Tomography (PET) detector module setup that mimic a continuous Lu₂SiO₅:Ce³⁺ (LSO) crystal of dimensions 40×40×10 mm³ together with the new large area position-sensitive photo multiplier tube (PSPMT) H8500 from Hamamatsu. The influence of Compton scattering on the DOI determination was also estimated by MC simulations. Altogether, we obtained ≤ 5 mm DOI resolution. PACS: 87.57.Ce, 87.58.Fg, 87.62.+n, 07.85.-m.