The direct deconvolution of X-ray spectra

The method of deconvolution of proportional counter X-ray spectra as outlined by Blissett and Cruise is reviewed with particular emphasis on low-energy spectra. This method involves the expansion of the incident spectrum in terms of a set of orthonormal singular functions which propagate independently through the detector matrix. When applied to low-energy detectors which typically exhibit absorption features in their efficiency curves, the initial Blissett and Cruise prescription is shown to be unstable. Alternative methods for handling the efficiency are described and evaluated. In the deconvolution of steep spectra, additional distortions are shown to arise as a result of sidelobe oscillations in the effective response functions. A selective weighting procedure is thus introduced to suppress spurious features of this type. Finally, the role of filtering in the deconvolution procedure is discussed and several suitable forms for the filter are suggested.