  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.
