## 2 Sideband Method for X-ray Pulse Characterization
Secondly, by changing the relative arrival time between the two pulses successively, a cross-correlation curve is acquired as shown in Figure 4[82]. Again, the width of the correlation is determined by the dominant parameters of the X-ray and the NIR pulse durations as well as by the relative arrival time jitter. In this scheme, photoelectrons generated via two-photon ionization in a single shot were measured at FLASH [9; 83] using a magnetic bottle electron spectrometer (MBES) [84]. This efficient type of spectrometer allows the collection of all electrons emitted over the complete solid angle for small kinetic energies <100 eV [85], and still over approximately 0.8 sr corresponding to a 30\({}^{\circ}\) half-angle emission cone at higher electron kinetic energies around 0.8 keV [51]. Hence, the MBES setup can be applied to low-density targets and enables, in the case of the intense FEL beam, an analysis of the photoionization process on a shot-to-shot basis [75; 84]. The best energy resolution, 1-2% of the electron kinetic energy, is achieved by decelerating the electrons with the aid of electrostatic retardation fields at the entrance of the flight tube. Figure 4: Sideband amplitudes. The amplitude of the first-order sideband measured in Xe is plotted as function of the set delay between the NIR laser and the free-electron laser in Hamburg (FLASH) free-electron laser (FEL) pulse. The uncorrected X-ray pump/NIR probe delay scan (x, fit as solid black line) is entirely dominated by the relative arrival time jitter and shows a width of 410 fs rms. A measurement technique based on electro-optical sampling [82] is able to provide an independent measurement of this jitter and can thus be used to correct the arrival time. This leads to an about 4 times narrower correlation width of 100 fs rms (o, fit as solid red line), which is already close to the simulated jitter-free case (dashed blue line). Normalized signal amplitudes are used throughout these plots (reproduced with permission from [82], Copyright AIP Publishing, 2009). First experiments were mainly able to reveal the effect and show the NIR pulse duration, which was at least an order of magnitude larger than the other two parameters [78]. By reducing the NIR pulse duration from several picoseconds to about 120 fs it was possible to determine the relative arrival time jitter [84]. Eventually, by minimizing the timing jitter and NIR pulse duration even further, the final goal was reached to directly determine the X-ray pulse duration of a SASE XFEL [51]. For seeded FELs like FERMI, the relative arrival time jitter is strongly reduced in contrast to unseeded (SASE) FELs. Thus in this case the jitter is significantly less than the X-ray and NIR pulse durations, allowing for an even more precise measurement of the X-ray pulse duration [86]. Generally, the sideband method has been extensively used at FERMI to characterize the pulse length, and its results are in agreement with a complementary method and with theory [59]. A few distinctive aspects of its use at FERMI are related to the fact that this is a seeded source, resulting in predictable timing and coherence of the pulses. The measurements are intrinsically jitter-free, and concentrated on characterizing the pulse properties as a function of machine parameters. In particular, pulse coherence was exploited to implement a compression scheme [87], and the pulse duration was measured with the sideband method. **Sideband formation of Auger electrons**  
The typical bandwidth of a SASE FEL pulse is in the range of 0.1 to 1% of the nominal photon energy. For the photon energies at FLASH this results in a width less than the spacing of the sidebands (see Figure 3), such that they can be analyzed individually. On the other hand for shorter wavelengths in the X-ray regime as available at LCLS, the linewidth of the XFEL radiation can exceed the separation of the sidebands significantly (e.g., a linewidth of 7 eV at a photon energy of 1 keV was measured in Ref. [51]).