Analytical Proof of Principle for a Novel Approach to Imaging with Polyenergetic Proton Beams

In this work, the feasibility of imaging with polyenergetic proton beams is investigated outside the conventional tomographic imaging framework. The proposed approach is based on the integral inverse stopping power and scattering power of a polyenergetic proton beam. A polyenergetic proton beam provides a system of non-linear equations expressing the integral scattering power as a function of the unknown relative stopping power of the object of interest that can be solved by means of non-linear optimization. The 1D object of interest is arbitrarily designed as pixels of water-equivalent materials. According to typical laser-driven proton beams, the exponentially decay shape of the beam spectra assigns decreasing fraction of protons for increasing energy. Based on the Bethe-Bloch formula and the Fermi-Eyges theory, the residual energy and the standard deviation of the Gaussian distribution describing the angle deviation are calculated at the exit of the object of interest for each proton energy, and assumed as measurement. The objective function of the non-linear optimization quantifies the difference between "measured" and estimated. Results are mainly affected by the number of pixels representing the object of interest. Successful results are obtained when the amount of information collected by different protons and proton energies copes with the number of pixels and the related inhomogeneities. In particular, an object of interest made by 4 pixels highlight limitations of the optimization for a beam spectrum made of 10
³
protons with a maximum energy of 30 MeV. Future investigations includes application of the proposed approach to Monte Carlo simulations and non-traditional optimizations.