  High-intensity ultrashort X-ray free-electron laser (XFEL) pulses are
revolutionizing the study of fundamental nonlinear x-ray matter interactions
and coupled electronic and nuclear dynamics. To fully exploit the potential of
this powerful tool for advanced x-ray spectroscopies, a noninvasive spectral
characterization of incident stochastic XFEL pulses with high resolution is a
key requirement. Here we present a methodology that combines high-acceptance
angle-resolved photoelectron time-of-flight spectroscopy and ghost imaging to
enhance the quality of spectral characterization of x-ray free-electron laser
pulses. Implementation of this non-invasive high-resolution x-ray diagnostic
can greatly benefit the ultrafast x-ray spectroscopy community by functioning
as a transparent beamsplitter for applications such as transient absorption
spectroscopy in averaging mode as well as covariance-based x-ray nonlinear
spectroscopies in single-shot mode where the shot-to-shot fluctuations inherent
to a self-amplified spontaneous emission (SASE) XFEL pulse are a powerful
asset.
