# Analysis Strategies for MHz XPCS at the European XFEL
## 2 Materials and Methods  
As a model system with well-known dynamic properties, we use silica nanoparticles dispersed in water. The samples were produced such that their intrinsic dynamics match the MHz time scale of the European XFEL. The colloidal silica nanoparticles were synthesized with a modified Stober method [23]. We used a particle concentration of 2.5 wt% which corresponds to about 1.2 vol%, chosen to ensure a system in which particle-particle interactions are negligible and capable at the same time to provide speckle patterns with sufficient intensity. Monodisperse diluted colloids are extremely useful for calibration purposes because their intermediate scattering function is described by a simple exponential relaxation  
\[f(q,t)=\exp(-\Gamma(q)t)\,, \tag{3}\]  
where \(\Gamma(q)=D_{0}q^{2}\) and \(D_{0}\) is the Stokes-Einstein diffusion constant. The colloidal dispersions were filled into thin-walled quartz capillaries with an outer diameter of 1.5 mm that were sealed afterwards and placed in a specifically designed sample-holder. The experiment was performed in air at the MID instrument. A detailed description of the instrument can be found in [20]. The intensity of the X-ray pulses was measured on a single-pulse basis with a gas monitor placed upstream the beamline. The beam-size at the sample position was about 10 um in diameter, obtained by focusing the beam by compound refractive lenses (CRL). Figure 1: Summary of the individual steps of the XPCS analysis pipeline. A short description is given in the figure. More details can be found in the text. We only sketch the analysis of one train for demonstration purposes. Usually, a run contains more than 1000 trains. \(t_{m}\) is the measurement time that can extend over several minutes. The X-ray flux was controlled with stacks of chemically vapour deposited (CVD) diamond windows. For the data reported here, the total thicknesses ranged from 4.7 mm to 2.7 mm. The X-ray intensity measured by the gas monitor was 1.13 mJ on average. Taking the beamline and air transmission into account, we found that the total attenuation was about \(2.44\times 10^{-4}\) for the data shown here, yielding a fluence on the sample of 3.5 mJ/mm\({}^{2}\) per pulse. The AGIPD installed at MID is composed of four quadrants each consisting of four modules. A module is an array of \(2\times 8\) ASICs (application-specific integrated circuits) where each ASIC is a square of \(64\times 64\) pixels [24] (see Figure 2). The positions of the modules within the same quadrant are fixed, but the relative positions of the four quadrants depend on the configuration. The European XFEL developed a set of software tools that enable an easy geometry definition with the aid of a known reference sample [25]. Once the positions of the direct beam and the modules are defined, it is possible to associate with each pixel the respective magnitude of the exchanged wave vector, \(q\). This geometry calibration is fundamental for analyzing the static scattering signal and for defining regions of interest (ROIs) for the XPCS analysis. The intensity is measured by the pixels of AGIPD and is expressed analogous to digital units (ADUs). These are affected by a certain offset, depending on the gain stage in which each individual pixel is operating. Subtracting this offset and calculating the histogram of the data, a red line in Figure 3a, it is possible to identify the ADU value associated with the detection of one or more photons marked as local maxima in the histogram. With this information, it is then possible to perform \"photonization\" and convert the ADUs to the number of detected photons (see Figure 2). A precise calibration of the AGIPD geometry is achieved with the aid of a previous measurement of the sample at a well-characterized synchrotron beamline. Once the relative positions of the AGIPD modules had been identified, we performed the azimuthal average of the scattered intensity to obtain the \(I(q)\) of our sample.