  We present a method for the reconstruction of ion kinetic energy
distributions from ion time-of-flight mass spectra through ion trajectory
simulations. In particular, this method is applicable to complicated
spectrometer geometries with largely anisotropic ion collection efficiencies. A
calibration procedure using a single ion mass peak allows the accurate
determination of parameters related to the spectrometer calibration,
experimental alignment and instrument response function, which improves the
agreement between simulations and experiment. The calibrated simulation is used
to generate a set of basis functions for the time-of-flight spectra, which are
then used to transform from time-of-flight to kinetic-energy spectra. We
demonstrate this reconstruction method on a recent pump-probe experiment by
Asmussen et al. (J. D. Asmussen et al., Phys. Chem. Chem. Phys., 23, 15138,
(2021)) on helium nanodroplets and retrieve time-resolved
kinetic-energy-release spectra for the ions from ion time-of-flight spectra.
