A study on a nonlinear least-squares fitting method for 3D positioning of gamma rays based on monolithic crystal and SiPM array

Purpose: In order to improve imaging quality of position sensitive gamma detectors, many research groups especially those interested in positron emission tomography (PET) imaging have done many efforts to develop detecting method with depth of interaction (DOI) capability. A detector with a monolithic lutetium yttrium silicate (LYSO) crystal and an silicon photomultiplier (SiPM) array is constructed by our group for DOI detecting research. Methods: 3D interaction coordinates of gamma rays are estimated by a nonlinear least-squares fitting method based on an analytical model in which photon number collected by an SiPM pixel is related to solid angle seen from gamma interaction point and boundary reflection. We have assessed the gamma positioning performance of our detector by projecting a line-like ¹³⁷Cs gamma beam on top and side surface of the crystal. Virtual source and solid angle factors in the analytical model have also been tested for the best performance both in simulations and experiments. Results: Good gamma positioning images are demonstrated with both X–Y and DOI positioning resolutions close to 2 mm full width at half maximum (FWHM). Conclusion: Comparing to former DOI methods, the performance of our DOI detector can be called competitive in positioning resolution, construction cost and difficulty of assembling.