A deconvolution method for estimating proton range from measured intensity distribution of prompt gamma rays

This study developed a technique for proton range verification based on measuring the intensity distribution of prompt gamma rays (PGs) along the beam path in a target and applying a deconvolution method for retrieving the corresponding distribution of PG emissions. The end-of-range R_ret=d_γp + R_res can be estimated according to the peak position d_γp of the retrieved PG emission and the residual range R_res determined from the cross section of the relevant nuclear reaction. A 30-MeV, 1.5-nA proton beam irradiated polyethylene (PE) and polymethyl methacrylate (PMMA) targets, and spatial intensity distributions were obtained by measuring 4.4- and 6.13-MeV PGs from a depth of 0 mm to 10 mm; to this end, a collimator–detector arrangement comprising a 2-inch NaI(Tl) detector and a 2-mm-wide slit collimator was used. Simulations were conducted to identify the profile of PG emissions in a target and to determine the detector response; subsequently, the performance of the developed deconvolution algorithm was validated, and the limits of this approach were investigated. The data from the 30-MeV proton beam experiment were used, and the ranges R_ret were estimated to be 7.85 mm for the PE target and 7.07 mm for the PMMA target; these were considerably close to the range at 80% dose fall-off level R₈₀ achieved using Monte Carlo simulations. Our results demonstrated that a NaI(Tl)-based system with a millimeter-wide collimator can effectively resolve the spatial variation of PG emissions along a proton beam's path. The proposed deconvolution method exhibited strong potential for verifying proton ranges with a sub-millimeter-level accuracy in a relatively simple and reliable manner.