Deconvolving instrumental and intrinsic broadening in core-shell x-ray spectroscopies

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.

Intermediate-range order in water ices: Nonresonant inelastic x-ray scattering measurements and real-space full multiple scattering calculations

“…1, we show our new XRS measurements ͑top curve, labeled "XRS"͒ and the same data after improving the effective energy resolution to 0.9 eV by use of the Richardson-Lucy iterative deconvolution algorithm 43 ͑middle curve, "XRS+ RL"͒. Despite using momentum transfers outside the nominal dipole-scattering limit ͑i.e., qa Ӷ 1͒ the observed spectra have good agreement with the previous dipole-limited XAS results ͑Fig.…”

Many-pole model of inelastic losses in x-ray absorption spectra

“…This behavior is absent in the many-pole self-energy which is naturally broadened by the width of the loss function. [38] In addition to our XANES calculations, we have performed a comparison of experiment and theory of the Cu K edge EXAFS using the analysis software ATHENA. [39] To reduce Debye Waller effects, which are highly correlated with the effects of the self-energy and many-body amplitude reduction factor, we used data taken at a low temperature of 10 K. The approach yields both the quasiparticle self-energy to account for extrinsic losses and the many-body amplitude factor S 2 0 to account for intrinsic losses and interference terms.…”

Fourier-ratio deconvolution and its Bayesian equivalent

“…Further sharpening could be achieved in a second RLdeconvolution step, using a Gaussian or Lorentzian kernel and with periodic smoothing to limit noise if necessary. With data that have sufficient signal/noise ratio, it is possible to go even further and remove the effect of lifetime and final-state broadening (Filipponi, 2000), although this possibility is ultimately limited by noise amplification (Fister et al, 2007).…”

“…They have been used successfully in astronomy and more recently in EELS (Overwijk and Reefman, 2000;Kimoto et al, 2003;Gloter et al, 2003;Ishizuka et al, 2003;Lazar et al, 2006;Egerton et al, 2006). However, these procedures are iterative and as the number of iterations increases, so do the noise and the visibility of spectral artifacts (Egerton et al, 2006;Lazar et al, 2006;Fister et al, 2007).…”