## 3 Linear Streaking Measurements at Free-Electron Lasers
### Experimental implementation
In order to not overestimate the actual value of the vector potential for the conversion into the time domain, the minimum possible value of the vector potential compatible with each specific shot is used for the analysis, that is the value that corresponds to the observed shift of the central photoelectron energy for each of these single-spike pulses. This is a very conservative approach and will again result in the determination of an upper limit for the respective pulse duration. Figure 12: Average XFEL pulse duration. A histogram of the possible pulse duration values in agreement with the measurement (blue) for the described parameter range at LCLS. The red solid line shows a Gaussian fit to the distribution, indicating an upper limit for the average X-ray pulse duration of \(\sim\)4.5 fs (reproduced with permission from [69], Copyright Nature Publishing Group, 2014). For the shot marked as the bigger light blue dot in panel b in Figure 13, the energy shift amounts to \(\Delta\varepsilon\) = 17.4 eV. Following deconvolution of the initial unstreaked X-ray photon energy bandwidth, which was determined by separate measurements, from the measured signal and using \(\Delta\varepsilon\) as a calibration factor the spectral bandwidth of this single peak was found to correspond to an X-ray pulse with a duration of maximum 800 attoseconds FWHM. In general, the derived upper limits for the duration of X-ray single-spike pulses are mainly in a range of 750 as to 1500 as (FWHM) (marked by the green oval in Figure 13b), which is in good agreement with the predictions based on equations for the SASE process under the conditions of the LCLS machine parameters [48]. However, in case the X-ray shot is actually overlapping with a maximum of the vector potential, this method breaks down the pulse duration, and the pulse duration is not well defined. Figure 13: Measurement of an attosecond X-ray pulse. Panel (**a**) on the right-hand side shows a measured spectrum of a single XFEL intensity spike (solid dark blue line) and the corresponding Gaussian fit (dashed red line). The shift of the peak from the unstreaked central energy at 920 eV (green dotted line) defines the energy-to-time ramp (top left), with the help of which the width of the deconvoluted spectrum (yellow dashed-dotted line) can be converted into a pulse duration upper limit of 800 as, depicted as the light blue line on the bottom left. Panel (**b**) at the bottom right shows the derived upper limits for the pulse duration of all single-spike shots as a function of the spectral energy shift of the peak. The very short pulse described in panel (**a**) is marked as the bigger light blue dot. The outliers towards longer pulse durations are all associated with small energy shifts (\(\leq\)5 eV), and therefore potentially stemming from an underestimation of the actual streaking vector potential by our method. Nevertheless, most of the measured single-spike X-ray pulse durations are in the range of 1.5 femtoseconds and below, highlighted by the green oval (reproduced with permission from [69], Copyright Nature Publishing Group, 2014). down; therefore, novel streaking concepts have to be developed for the unambiguous and complete characterization of X-ray FELs, as presented in Section 3.1.2 for femtosecond pulse structures, and in the outlook (Section 4) for the determination of the full time-energy information of SASE X-ray pulses with attosecond resolution.