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Solid-state radiation detectors based on the visible photoluminescence of radiation-induced F2 and F3+ color centers in lithium fluoride crystals have been used for advanced diagnostics of 18 and 27 MeV proton beams, produced by the TOP-IMPLART linear accelerator, which is under development for protontherapy applications at ENEA C.R. Frascati, Italy. Visible fluorescence microscopy was successfully used to read the latent proton beam images stored in the lithium fluoride crystals, thanks to high emission efficiency of the F2 and F3+ color centers obtained by simultaneous optical excitation in the blue spectral range. High intrinsic spatial resolution and wide dynamic range of these novel LiF detectors allow obtaining two-dimensional images of both the beam transverse intensity distribution and of the Bragg curve. By using a simple defect formation model that takes into account the energy released in the material and the saturation of defect concentration, not only the two-dimensional dose map was obtained from the beam transverse intensity distribution image, but also the full Bragg curve was reconstructed, allowing the thorough characterization of proton beams produced by the accelerator.