Nonlinear least-squares modeling of 3D interaction position in a monolithic scintillator block.

This paper presents a study of possible models to describe the relation between the scintillation light point-of-origin and the measured photo detector pixel signals in monolithic scintillation crystals. From these models the X, Y and depth of interaction (DOI) coordinates can be estimated simultaneously by nonlinear least-square fitting. The method depends only on the information embedded in the signals of individual events, and therefore does not need any prior position training or calibration. Three possible distributions of the light sources were evaluated: an exact solid-angle-based distribution, an approximate solid-angle distribution and an extended approximate solid-angle-based distribution which includes internal reflection at side and bottom surfaces. The performance of the general model using these three distributions was studied using Monte Carlo simulated data of a 20 x 20 x 10 mm lutetium oxyorthosilicate (Lu₂SiO₅ or LSO) block read out by 2 Hamamatsu S8550 avalanche photo diode arrays. The approximate solid-angle-based model had the best compromise between resolution and simplicity. This model was also evaluated using experimental data by positioning a narrow 1.2 mm full width at half maximum (FWHM) beam of 511 keV photons at known positions on the 20 x 20 x 10 mm LSO block. An average intrinsic resolution in the X-direction of 1.4 mm FWHM was obtained for positions covering the complete block. The intrinsic DOI resolution was estimated at 2.6 mm FWHM.