The determination of the true profile of XPS line by regularization method: I. Mathematical algorithm and numerical simulations

Abstract The resolution of XPS spectra is limited mainly by instrumental parameters like the spectral line width of exciting X-ray source and the finite energy resolution of the electron analyzer. A new algorithm of an inverse ill-posed problem has been proposed in which low resolution experimental XPS data can be enhanced by removing the instrumental functions. The regularization method with a special fast iteration algorithm is applied for determining the true profile line of a complex chemical compound if we know excitation and instrumental functions. This paper is structured as follows: (I) a mathematical algorithm is described and numerical simulation results are presented. (II) These algorithms have been applied to the poorly resolved C 1s spectrum of a poly-methyl methacrylate (PMMA) film studied by the conventional technique with monochromatic and polychromatic radiation. The resulting enhancement allows previously unresolved structure to be observed without any assumptions concerning number, position, shape of peaks and their ratio.