Deconvolving Instrumental and Intrinsic Broadening in Excited State X-ray Spectroscopies

TL;DR

This paper introduces a robust iterative deconvolution method using the Richardson-Lucy algorithm to separate intrinsic and instrumental broadening in excited-state X-ray spectroscopies, improving spectral resolution and analysis accuracy.

Contribution

It demonstrates the application of the Richardson-Lucy algorithm for deconvolving broadening effects in XAS and XRS data, providing a practical methodology for enhanced spectral analysis.

Findings

Nearly complete removal of broadening in Ag K-edge XAS

Significant reduction of instrumental broadening in diamond XRS

Methodology emphasizes stability testing against noise and uncertainties

Abstract

Intrinsic and experimental mechanisms frequently lead to broadening of spectral features in excited-state spectroscopies. For example, intrinsic broadening occurs in x-ray absorption spectroscopy (XAS) measurements of heavy elements where the core-hole lifetime is very short. On the other hand, nonresonant x-ray Raman scattering (XRS) and other energy loss measurements are more limited by instrumental resolution. Here, we demonstrate that the Richardson-Lucy (RL) iterative algorithm provides a robust method for deconvolving instrumental and intrinsic resolutions from typical XAS and XRS data. For the K-edge XAS of Ag, we find nearly complete removal of ~9.3 eV FWHM broadening from the combined effects of the short core-hole lifetime and instrumental resolution. We are also able to remove nearly all instrumental broadening in an XRS measurement of diamond, with the resulting improved spectrum comparing favorably with prior soft x-ray XAS measurements. We present a practical methodology for implementing the RL algorithm to these problems, emphasizing the importance of testing for stability of the deconvolution process against noise amplification, perturbations in the initial spectra, and uncertainties in the core-hole lifetime.