Pulse-to-pulse field characterization at x-ray free-electron lasers using a speckle-correlation scattering matrix

In coherent diffraction experiments, knowledge of the incident field is important to extract pure sample-induced data from measured diffraction patterns. However, this becomes challenging in x-ray free-electron lasers (XFELs), as incident fields vary from pulse to pulse due to the stochastic nature of self-amplified stimulated emission. Despite various proposed field retrieval methods, single-shot characterization of each pulse remains elusive. To address this, we propose the speckle-correlation scattering matrix as a solution. Our method directly reconstructs the complex field without sample constraints or multiple acquisitions by introducing a designed diffuser before the detector. We demonstrate the robustness of our approach through successful field reconstructions in various experimental configurations. Based on the retrieved field results, pulse-to-pulse variations in pulse intensity, position, illumination angle, and shape were analyzed. We believe our method can readily serve as an on-field and real-time pulse diagnostic tool at XFELs and improve the overall quality of all experiments performed at XFELs. (c) 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement