  Proton radiography has proved increasingly successful as a diagnostic for
electric and magnetic fields in high energy density physics experiments. Most
experiments use target-normal-sheath-acceleration sources with a wide energy
range in the proton beam, as the velocity spread can help differentiate between
electric and magnetic fields and provide time histories in a single shot.
However, in magnetised plasma experiments with strong background fields, the
broadband proton spectrum leads to velocity-spread-dependent displacement of
the beam and significant blurring of the radiograph. We describe the origins of
this blurring and show how it can be removed from the experimental measurement,
and we outline the conditions under which such deconvolutions are successful.
As an example, we apply this method to a magnetised plasma experiment that used
a background magnetic field of 3 T. The strong displacement and energy spread
of the proton beam reduced the spatial resolution from tens of microns to a few
millimetres. The deconvolution procedure is applied showing the accurate
recovery of radiographs with resolutions better than 100 microns, enabling the
recovery of more accurate estimates of the path integrated magnetic field. This
work extends accurate proton radiography to a class of experiments with
significant background magnetic fields, particularly those experiments with an
applied external magnetic field.
