Application of the Van Cittert Algorithm for Deconvolving Loss Features in X-ray Photoelectron Spectroscopy Spectra

Abstract

The convolution of two physical entities, denoted as f and g, delineates the manner in which one entity undergoes modification in response to the other. This transformative process is mathematically represented by the expression f ⨂ g, symbolizing the convolution of the two entities in a resultant function h. Frequently, it becomes imperative to comprehend the magnitude of the induced modifications. From the derived function h, a crucial step involves the separation of the two original signals, a process commonly referred to as deconvolution. Various techniques have been proposed to facilitate the calculation of the deconvolution, with one notable approach originating in 1931 by van Cittert. The algorithm, based on an iterative method, has been scrutinized over time, notably by Bracewell and, more recently, by Jansson. This work represents the current state-of-the-art, focusing specifically on the analysis of Auger spectra obtained through XPS. Emphasis is placed on delineating the procedural aspects of the analysis, and the algorithm utilized in the open-source software RxpsG is comprehensively described.