## 4 Discussion
Our results show that a temporal resolution of at least 0.1-1 ns is needed to resolve the shock waveform in microdrops. This temporal resolution would require a very high-speed framing camera to record the surface velocity in a single shot. Framing cameras were used successfully to resolve the dynamics of underwater explosions in a millimeter-sized system [50], but for micron-sized drops such cameras must be able to operate at GHz frame rates, which is close to the state of the art for commercial systems. Nevertheless, since liquid micron-sized droplets can be generated reproducibly at high rates, pump-probe techniques can be used instead. To our knowledge, outside the XFEL droplet ablation experiments, the pump-probe measurement of surface velocities in microscale liquid systems was applied in a study of cavitation in an optofluidic chip [51], but in that case the surface position was measured only once, 40 ns after the shock arrival, therefore the shock waveforms could not be determined. The accuracy of our shock characterization method is primarily limited by the reproducibility of the drop diameters. At short time scales, this uncertainty arises from the jitter in drop diameter measurements, which typically was below 50 nm peak to peak. For a determination of surface velocity within a 1 ns interval, this corresponds to a 50 m/s uncertainty in the droplet expansion velocity (or 12.5 m/s for the particle velocity), which in turn corresponds to an uncertainty of approximately 20 MPa in the shock pressure. Nevertheless, this type of uncertainty can be reduced by averaging multiple measurements. At longer time scales, the magnitude and sign of the slow drifts in the unperturbed droplet diameter can become important. In this case the overall accuracy can be estimated as half the spread of V\({}_{0}\) data in Table 11, for measurements made at the same energy but in different runs; the uncertainty of surface velocity is approximately 25 m/s, one order of magnitude worse than commercial VISAR instruments. The cylindrical shock waves produced by hard X-ray laser pulses in liquid water can be detrimental or beneficial in different types of XFEL studies, and the ability to predict their properties, including their waveforms, is useful in both cases. The brief duration of XFEL-generated shocks could prove useful for subjecting samples to large pressures that last only \(\sim\)1 ns, which would allow, for example, to initiate a dynamic transformation in a material but not allow it to complete. Here we provided comprehensive amplitude and waveform data for shocks propagating in water and passing through a surface 15 \(\upmu\)m away from the beam's center, but the method can be applied to other liquids and propagation distances. Also, our experimental data could be used as a benchmark for future analytical or numerical models that might predict the properties of the XFEL-induced shocks for any propagation distance and any energy of the XFEL pulses. [PERSON] conceived the experiment; [PERSON] and [PERSON] coordinated the experimental team; [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON] and [PERSON] set up the experiment; [PERSON] and [PERSON] prepared the femtosecond optical pulses for imaging liquid droplets; [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON] and [PERSON] conducted the experiment; [PERSON], [PERSON], and [PERSON] analyzed the data; [PERSON] interpreted the data and wrote the paper. All authors have read and agree to the published version of the manuscript. **Funding:** The experiments were supported by the U.S. Department of Energy, Office of Science, Chemical Sciences, Geosciences, and Biosciences Division, by the X-ray Free Electron Laser Priority Strategy Program of the MEXT, by the Research Program of 'Dynamic Alliance for Open Innovation Bridging Human, Environment and Materials\" in \"Network Joint Research Center for Materials and Devices,' and by the IMRAM project.