In this paper, we present the characterization of a novel 4mmx4mm position-sensitive silicon photomultiplier, called linearly-graded SiPM (LG-SiPM). The 2D position encoding is obtained through a charge sharing approach, implemented by means of a current divider directly integrated on die. The microcells of the detectors have a size of 45umx45um and are fabricated with the FBK RGB (Red Green Blue) technology, modified with the addition of a second metal interconnection layer and a second quenching resistor in every cell, required by the encoding architecture. We verified that the LG-SiPM scheme does not alter the signal temporal shape, when illuminating the detector in different positions. We performed a XY scan with light spots of 1 mm diameter and spaced by 0.25 mm, showing that the reconstructed positions are easily separated. No visible pincushion distortion was present. We measured the energy resolution and the encoding capability in PET-like and in SPECT-like conditions using pixelated LYSO and CsI(Tl) crystal arrays (with 0.8 and 1 mm pitch, respectively), irradiating them with 511 keV and 122 keV photons, respectively. In both cases, we were able to clearly distinguish the scintillator pixels.
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