Deconvolution problems in x-ray absorption fine structure spectroscopy

A Bayesian method applied to the deconvolution of x-ray absorption spectra is presented. It is shown that due to the ill-posedness of the deconvolution problem, an infinitely large number of different Bayesian solutions (absorption coefficients) exist. However, each solution is shown to give the same Fourier transform (FT) of extended x-ray absorption fine-structure (EXAFS), in a wide range of real space. Since it is the FT which is used for analysis in most EXAFS applications, instrumental and lifetime broadening can reliably be removed from raw EXAFS spectra. Several approaches for the determination of the optimal Bayesian regularization parameter are proposed. Bayesian deconvolution is compared with deconvolution which uses the FT together with the optimal Wiener filtering. In addition, it is shown that using a corresponding XPS spectrum as a deconvolution kernel, one-electron absorptance can, in principle, be extracted from the total absorptance, which gives the opportunity to use a more simple XAFS theory for analysis of experimental spectra.