Correction method for the energy spectrum of laser-accelerated protons measured by CR-39 track detectors with stepwise energy filters

•Laser-accelerated protons from hydrogen cluster targets were measured by a combination of CR-39 track detector and a stepwise energy filter.•The correction method for the energy spectrum from the number of etch pits was developed to avoid overestimation of the number of etch pits for each energy region.•The combination of the detector unit and the developed correction method allows us to evaluate the energy spectrum of laser-accelerated protons.