# Analysis Strategies for MHz XPCS at the European XFEL
## 3 Results
### Corrections on the Dynamical Quantities  
Despite of the correction of single patterns, we have not yet reached an optimal result, as the value of the correlation at large lag times, visible also from the \(g_{2}(t)-1\) in Figure 4d (green triangles), is still well above 0. This additional baseline originates from the static variance of the recorded intensity in the investigated \(q\)-ROI. It can have several origins, such as the natural change of the intensity as a function of \(q\), small misalignments of the modules or other artifacts which have yet to be clearly identified. However, this non-zero baseline is not the only concern; in low-intensity regions, the data are much more exposed to the appearance of \"hot pixels\" or other similar defects, which usually affect the TTC with strongly correlated streaks or blocks. Figure 5a reports an example of such artefacts, with a typical block of 32 memory cells that shows a very high, and unphysical, correlation. For clarification, this does not mean that all those memory cells are affected, but only the memory cell of a sub-group of the pixels (in most cases, only a single pixel) in the investigated \(q\)-ROI. On conventional detectors, it would be possible to identify and mask such pixels, but, in the present case, such effects can also be observed on different memory cells on different runs, suggesting a variability which is not yet completely under control. Luckily, there are methods to tackle this problem thanks to the cross-correlation matrices introduced in the previous section. In fact, correlating neighbouring trains, a precise estimation of such a baseline can be obtained because illumination and detector conditions are very similar, but the speckle patterns are completely uncorrelated. For a given train \(tr_{n}\) then, two cross-correlation matrices are calculated as  
\[X_{-1}=\langle\delta I(tr_{n-1},t_{1})\delta I(tr_{n},t_{2})\rangle/(I(tr_{n-1},t_{1})I(tr_{n},t_{2})) \tag{5}\]  
between \(tr_{n-1}\) and \(tr_{n}\), and  
\[X_{+1}=\langle\delta I(tr_{n},t_{1})\delta I(tr_{n+1},t_{2})\rangle/(I(tr_{n}, t_{1})I(tr_{n+1},t_{2})) \tag{6}\]  
between \(tr_{n+1}\) and \(tr_{n}\). The cross-correlations are then made symmetric with \(XT_{-1}=(X_{-1}+X_{-1}^{T})/2\) and finally the correction matrix is defined by  
\[XC=(XT_{-1}+XT_{+1})/2. \tag{7}\]  
Finally, simply subtracting \(XC\) from the TTC corrects the baseline and some of the more common artefacts [27], as can be seen in the corrected TTC shown in Figure 5b. To obtain a more quantitative insight on the effects of this correction in Figure 5c, the \(g_{2}(t)\) functions calculated from uncorrected and corrected TTC are displayed. There it is possible to notice how strongly the presence of the \"wrong\" memory cells influence the signal showing a large relaxation where the expected dynamics would be already almost  
Figure 5: Effects of the correction scheme on low-intensity \(q\)-regions, \(q=0.233\) nm\({}^{-1}\) in this example. (**a**) TTC from a photonized dataset without applying further corrections. A typical artefact of the AGIPD represented by a group of 32 neighbouring memory cells that display a non-physical high correlation is highlighted (red square in the upper right corner); (**b**) the same TTC after the cross-correlation correction; (**c**) autocorrelation functions obtained from the TTC (**a,b**) compared with the expected behaviour (black line).  
completely decorrelated. It must be pointed out that this correction scheme is based on two conditions: the speckle patterns in two different trains are uncorrelated and the azimuthal average of \(I(q,\tau)\) is the same in all trains. In other words, each train probes a reproducible condition and is a statistically independent measurement of the dynamics.