  X-ray and gamma fluxes from the high intensity laser-plasma interaction are
extremely short, well beyond temporal resolution of any detectors. If laser
pulses come repetitively, the single photon counting technique allows to
accumulate the photon spectra, however, its relation to the spectrum of the
initial fast electron population in plasma is not straightforward. We present
efficient and fast approach based on the Geant4 package that significantly
reduces computer time needed to re-construct the high energy tail of electron
spectrum from experimental data accounting for the pileup effect. Here, we
first tabulate gamma spectrum from monoenergetic electron bunches of different
energy for a given experimental setup, and then compose the simulated spectrum.
To account for the pileups, we derive analytical formula to reverse the data.
We also consider errors coming from the approximation of the initial electron
spectrum by the sum of monoenergetic impacts, the finite range of the electron
spectrum, etc. and give estimates on how to choose modelling parameters to
minimize the approximation errors. Finally, we present an example of the
experimental data treatment for the case of laser-solid interaction using 50 fs
laser pulse with intensity above 1018 W/cm2.
