Ghost-imaging enhanced SASE x-ray free-electron laser spectral characterization

X-ray free-electron lasers (XFELs) provide ultrahigh intensity x-ray pulses with brightness 10 orders of magnitude larger than the synchrotron radiation light source. It opens the door of nonlinear light-matter interaction investigation in the x-ray regime. However, most XFELs around the world work in the self-amplified spontaneous radiation (SASE) mode, which starts from initial random bunching within the electron beam and generates spectrally stochastic x-ray pulses. Spectral characterization of the SASE pulses is important for x-ray spectroscopy. For hard x rays crystal Bragg diffraction and for soft x rays grating diffraction have been used to split the x rays and measure a reference spectrum.  Alternatively, the photoelectron spectrum from a dilute gas can act as a transparent beam splitter and the x-ray spectrum can be derived.  In this talk, we will discuss enhanced x-ray spectral characterization from photoelectron spectra using a ghost-imaging method [1]. The SASE pulses at European XFEL are measured by 16 electron time-of-flight (eToF) and a grating spectrometer simultaneously.  A response matrix is learned by comparing the eToF and spectrometer measurements of thousands of SASE pulses. The response matrix extracted can be used to predict yet-to-be-measured SASE pulses with excellent energy resolution.