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 noninvasive 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.




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