Error Analysis Of An Underdetermined, Spectral Unfold Problem As Applied To An X-ray Absorption Spectrometer

Random error propagation and unfold accuracy have been studied for the spectral unfold method used in the x-ray absorption spectrometer reported by Carlson [1]. This system of 13 measurements and 30 spectral bins (0.01 - 8 MeV) is underdetermined; a trial spectrum prevents unphysical solutions. Accuracy of the unfold was tested with simulated data from known spectra; the unfolds agreed with the known spectra to better than 10%, between 0.05 MeV and near the endpoints. Error propagation was studied by perturbing the input data randomly and unfolding the resulting data sets. In each unfold energy bin the standard deviation was taken as the propagated error. Above 0.05 MeV the unfold roughly doubled the input errors. The trial spectrum affects the unfold accuracy more strongly than the propagated errors.