## 3 Results  
To cover a wide range of pulse energies, multiple runs were recorded with XFEL pulses attenuated in different amounts by a combination of thin Si wafers and Al foils. Measurements with 29.9-30.5 \(\upmu\)m diameter drops were made for pulse energies ranging from 7.1 \(\upmu\)l to 243 \(\upmu\)l at the droplets. Injection of the 61 \(\upmu\)m diameter drops was affected by drifts in the undisturbed drop diameters, and these drifts were often larger than the measured signal. Only one experimental run with 61 \(\upmu\)m diameter drops had sufficiently stable drops, and allowed measurements for pulse energies ranging from 47 \(\upmu\)l to 79 \(\upmu\)l.  
Raw data sets extracted from one experimental run are shown in Figure 2a. As the pulse energy increased, (i) the surface displacement became larger, which implies a higher shock pressure, and (ii) shocks arrived at the surface earlier, because the shock velocity increases with the shock amplitude. Figure 2a also shows the slowly-drifting undisturbed drop diameter D\({}_{0}(t)\), calculated by linear fitting of the diameter data just before the arrival of the shock. The drift was less than one thousandth of the drop diameter over the time delays used for measurements (8-10 ns) and the subtraction of D\({}_{0}(t)\) from the data was sufficient to correct for the drifts. The fitting of data is illustrated in Figure 2b. After subtracting D\({}_{0}(t)\), the data was fitted in a limited range of time delays, as explained in Appendix A. The fit parameters for all recorded data sets are given in Table 1 in Appendix C, along with the initial shock pressure. Figure 2: Experimental measurements and the fit of surface motion data. (**a**) Typical drop diameter measurements from a single experimental run. For clarity, only four of the 10 extracted data sets are shown. Since these data sets were recorded simultaneously, they exhibit the same drift in the undisturbed droplet diameter, D\({}_{0}(t)\). (**b**) The change in drop diameter during the shock reflection, \(D_{D}(t)\)–D\({}_{0}(t)\), for two of the data sets shown in the left panel, and their analytical fits made using Equation (1). To reduce the influence of shock wave reflections, the data is fitted only up to the delay corresponding to the propagation of pressure waves at the speed of sound. that as the pulse energy increased, the initial shock pressure (\(P_{S}\)(t\({}_{\rm decay}\))) increased, the arrival time of the shock (t\({}_{\rm shock}\)) decreased, and the decay time of the surface velocity (t\({}_{\rm decay}\)) increased. The dependence of the initial shock pressure (the jump pressure) on the pulse energy and on the linear energy density deposited by X-rays is shown in Figure 3 for all data sets. The linear energy deposited is given by the product of the X-ray pulse energy and the X-ray energy-absorption coefficient (493 m\({}^{-1}\) at 10 keV for water). At the lowest pulse energies, the relative quality of the fit decreased because the displacement of the interface was approaching the typical jitter and drift of the initial droplet diameter. The reproducibility of the peak pressure measurements, estimated as the largest difference between independent measurements made at the same pulse energies in different runs, was approximately 25 MPa. For 29.9-30.5 \(\upmu\)m diameter drops, the initial shock pressure can be fit with a power-law dependence on the pulse energy \(E_{xray}\), \(P_{S}\)(t\({}_{\rm shock}\))-\(E_{xray}\)[65; 0]. The data for 61 \(\upmu\)m diameter drops does not have sufficient dynamic range in the pulse energies for a power law fit. The temporal evolution of the incoming shock pressure, at the equatorial surface of the drop, was calculated through integration of Equation (4) and is shown in Figure 4 for a subset of measurements.