A comparison of spectral reduction techniques in X-Ray astronomy

We report the results of a numerical investigation of three methods of cosmic X-ray spectral reduction, with an emphasis on the apodization technique of Dolan (1972). The study is carried out in the energy range 10–100 keV on pulse height distributions which were synthesized from simple X-ray source spectra with predetermined parameters. The spectral response function used was that of a balloon-borne, large area, xenon-filled proportional counter; however, we believe that our results are generally relevant to other non-dispersive systems such as scintillators and low energy (1–10 keV) proportional counters. We agree that the ill-conditioned energy resolution matrix cannot be inverted using standard procedures without propagating unacceptable errors. The apodization solution was investigated as a function of counter resolution, fluorescence escape probability, extent of energy window, number of pulse height channels, dataS/N ratio, and the so-called apodization instrument factor. We conclude that in most circumstances apodization should be the preferred reduction technique, but that the present widely and improperly used minimum –x ² method may be useful as the final step in obtaining refined spectral parameters estimates.