Development of the self-calibration technique for γ -ray energy tracking arrays

Determining the three-dimensional γ -ray interaction position in γ -ray tracking arrays is achieved by comparing in real time the measured electronic signals against a pre-generated library of calculated signals (signal basis) that maps the detector response throughout the crystal volume. Obtaining a high-fidelity signal basis remains a significant technological challenge that often limits the ultimate performance of the arrays. To address this, a self-calibration method was proposed to generate the signal basis experimentally, in an iterative way and in situ; its potential has been demonstrated in a proof-of-concept study using a simplistic geometry. In this article, we extend and refine this innovative technique for γ -ray tracking arrays using realistic simulations of the actual crystal geometries and including pulse-shape analysis that mimics the reconstruction that takes place experimentally. Key factors determining the performance of the method, such as the conditions for position convergence, statistical requirements, the impact of convoluting electronic noise to the signals, and the time alignment are investigated systematically within this framework. The results show that the method is robust and holds promise for generating high-fidelity signal basis experimentally. The analysis framework established in this work sets the stage for applying the self-calibration technique to real experimental data.