Ptychographic wavefront characterization for single-particle imaging at x-ray lasers

A well-characterized wavefront is important for many x-ray free-electron laser (XFEL) experiments, especially for single-particle imaging (SPI), where individual biomolecules randomly sample a nanometer region of highly focused femtosecond pulses. We demonstrate high-resolution multiple-plane wavefront imaging of an ensemble of XFEL pulses, focused by Kirkpatrick-Baez mirrors, based on mixed-state ptychography, an approach letting us infer and reduce experimental sources of instability. From the recovered wavefront profiles, we show that while local photon fluence correction is crucial and possible for SPI, a small diversity of phase tilts likely has no impact. Our detailed characterization will aid interpretation of data from past and future SPI experiments and provides a basis for further improvements to experimental design and reconstruction algorithms.