Inelastic x-ray scattering (IXS) now a widely used technique for studying the dynamics of electrons in condensed matter. We previously posed a solution to the phase problem for IXS [P. Abbamonte, et. al., Phys. Rev. Lett. {\bf 92}, 237401 (2004)], that allows explicit reconstruction of the density propagator of a system. The propagator represents, physically, the response of the system to an idealized, point perturbation, so provides direct, real-time images of electron motion with attosecond time resolution and A˚-scale spatial resolution. Here we show that the images generated by our procedure, as it was originally posed, are spatial averages over all source locations. Within an idealized, atomic-like model, we show that in most cases a simple relationship to the complete, un-averaged response can still be determined. We illustrate this concept for recent IXS measurements of single crystal graphite.
@article{arxiv.0904.0795,
title = {Implicit spatial averaging in inversion of inelastic x-ray scattering data},
author = {P. Abbamonte and J. P. Reed and Y. I. Joe and Yu Gan and D. Casa},
journal= {arXiv preprint arXiv:0904.0795},
year = {2013}
}