Three-dimensional position reconstruction of a cascade gamma ray-emitting source based on geometric back-projection through the angle of incidence

A novel technique has been developed to determine the three-dimensional position of a source emitting multiple cascade γ-rays with sub-millimeter accuracy using dual-layered GSO (Ce) scintillation detectors. This method reconstructs the source position by processing filtered energy and detector hit positions through a back-projection algorithm along the paths of incident γ-rays. The detector array and an 111In-ion point source at five locations within the central detection volume were simulated using the GATE Monte Carlo framework. For a source at the detector center (0, 0, 0), the reconstructed coordinates are − 0.001 mm, − 0.001 mm, and − 0.001 mm along X, Y, and Z. This indicates that the reconstructed source centroid was centrally located and well within the spatial resolution limits of the detector system. For other simulated source positions, the reconstructed coordinates matched approximately 99.8% of the actual simulated positions, although some positions varied between 70.9% and 125% of the true values. Except for source at the center, other source positions were reported with uncertainty ranging from 0.006 × 10–3 mm to ± 5.480 × 10–3 mm. While reconstruction at the transaxial and axial edges is less precise due to limited valid coincidence events, the results demonstrate the method’s robustness. The achieved reconstruction precision indicates potential applications in nuclear medicine, nuclear security, radioactive waste assay, and proton beam therapy.