On the formation and unfolding of pulse height distributions

Spacecraft measurements of X-ray or particle pulse height distributions have become increasingly accurate during the last fifteen years, and they will continue to do so. The present paper deals with the question how one can reconstruct original photon or particle spectra from measured pulse height distributions. The statistical aspects of the formation of pulse height distributions are investigated. A method is presented that allows for a reliable reconstruction of the original spectrum. Its essentials are the formulation and subsequent solution of a matrix equation connecting pulse height distribution with photon/particle spectrum; an error analysis of the reconstructed spectrum is given. The present method has two advantages over the usualχ ²-minimum method: It is able to recover more spectral detail and it requires less computing time. Finally, a numerical example is given.