## 4 Discussion
Since the shock reflections at a water-air interface are rarefaction waves [34], pronounced pressure oscillations should occur in jets and drops exposed to XFEL pulses. Two previously observed effects of these pressure oscillations are spallation in droplets [17] and the formation of shock trains in jets [24,30]. Recent numerical simulations of experiments on microscale ablation in water [16,45,46,47] allow us to compare qualitatively the waveform of shocks produced by XFEL pulses and by optical laser pulses. To simulate the shock dynamics and match it to the experimental conditions, proper initial conditions need to be defined. A closed spherical bubble with 8 \(\upmu\)m diameter and 6 GPa pressure was used for an optical ablation experiment [16,45], and an open cylinder with 0.5 \(\upmu\)m diameter and 100 GPa pressure was used for an XFEL experiment [47]. In the case of optical ablation with spherical symmetry, the calculated shock waveforms were relatively long and did not reach zero pressure. In contrast, the simulation of the XFEL spallation experiment in drops predicted short waveforms with a negative pressure phase. Short-lived shocks that decay to approximately zero pressure were also predicted in simulations of laser ablation in a ring pattern, in a quasi-2D geometry [46]; in this case the excited region was chosen to have a width of 1.6 \(\upmu\)m and an initial pressure of 2 GPa, and the simulation did not include the formation of a gas bubble in the excited region. Overall, these simulations suggest that the generation of nanosecond shock waveforms that decay to zero pressure requires that the region where the energy is absorbed is at most a few microns in size, and that the ablation does not lead to high-pressure gas trapped inside bubbles. _Cavitation and spallation._ Cavitation and spallation were observed in additional experimental runs that probed time delays longer than the ones we used here for shock wave analysis. Qualitatively, these phenomena were the same as the ones reported previously [17], but quantitative properties such as the arrival time of the spall wave were different, because they depend on the droplet diameter and on the pulse energy. The present experimental setup should enable measurements of the cavitation pressures with improved accuracy and over a wider range of experimental parameters, because the raw data was less noisy and more accurate than the data previously recorded in vacuum. Our present work also indicates the necessity to consider how the short duration of the shock waveform affects the spall dynamics [48]. For example, simulations of XFEL-induced shocks in drops showed an increase in the rise time of the reflected wave as it traveled [47]. An increase in the rise time of the negative pressure pulse will lower the strain rate at which the liquid is stretched, and can lower the peak tension of the negative pressure wave. _Applicability and accuracy of pump-probe optical microscopy for characterization shock waves at the microscale._ The small size of the liquid droplets and their high surface curvature limits the range of techniques that can be used to characterize shock wave properties. For example, single-shot interferometric techniques such as the velocity interferometer system for any reflector (VISAR) [49] cannot be applied to microdrops because interferometry requires a sufficiently flat surface over the area probed by the light beam, such that the reflected light has an approximately constant phase. Currently, the minimum beam spot size of commercial interferometers, \(\sim\)100 \(\upmu\)m, is larger than the drops we used. The curvature of the droplet's surface makes them well suited, however, for methods based on optical imaging. Even a transparent drop can have a high-contrast dark edge, if the numerical aperture is sufficiently small. Spherical surfaces have their maximum lateral extent at a well-defined position along the optical axis, and if this position is in focus, a sharp image of the surface can be obtained.