A simple empirical forward model for combined nuclear and multiple Coulomb scattering in proton radiography of thick objects

A deterministic forward model that includes the essential physics of all of the elements of the radiographic chain is required to extract volume density distributions and material interface surface positions from proton transmission radiographs by iterative non-linear fitting of parametric forward models. An essential part of the forward model is an analytic description of the angular distribution that an incident pencil beamlet acquires in passing through a thick slab of material. The angular-distribution model described here includes nuclear attenuation, multiple Coulomb scattering, coherent nuclear elastic scattering, and quasielastic nuclear scattering. The model is in good agreement with experimental step-wedge proton transmission data from experiments at the AGS proton accelerator at Brookhaven National Laboratory.