## 3 Results and Discussion
The optimized spectrally resolved FVU is shown in Figure 2 and reproduces the structure of the spectrum as it scales inversely with the reflected intensity: The scaling of the FVU with intensity is shown in Figure 3a and is compared to a simulation of the FVU which may be expected from of a Poisson-distributed noise process, scaling with the square root of the intensity like a photon shot noise (orange), and an additional normally-distributed noise process with constant variance like readout noise (green). Since the fast readout of the CCD preventeda calibration of the sensitivity from single-photon incidences, the number of photons per detector count was estimated based on the assumption that the noise level at high intensities is dominated by photon shot noise, as was found in a similar setup before [15]. This assumption is supported by the scaling behavior shown in Figure 3a and is in rough agreement with the manufacturer specifications of the CCD. Figure 3b further illustrates the uncertainty with which the ratio between the reflectivity probed by both beams may be determined with increasing acquisition time. This uncertainty is the precision with which pump-probe changes in one spectrum could be detected. To this purpose, the undulators are tuned to the Ni \(L_{3}\)-edge. Without scanning the undulators, the ratio between the intensities in both spectra was evaluated. Two exemplary regions in the spectra were analyzed: First, a 245 meV region around the \(L_{3}\)-edge peak at 857 eV (corresponding to two rows on the detector). Second, an equally sized window from the same dataset was evaluated 1 eV above the peak, where the detected intensity was lower by about a factor of nine on average, due to both the lower reflectivity and the FEL being tuned to the \(L_{3}\)-edge. The plot shows the relative uncertainty with which the ratio may be determined for increasingly larger subsets of CCD images, randomly drawn (without replacing) from an 80-min measurement. Two different measures for the uncertainty are shown: First, the uncertainty regarding the parallel acquisition, which considers that the correlation between the two intensities reduces the uncertainty for the estimator of the mean. This error propagation was discussed previously [15] and is reiterated in Appendix B. Second, the error is calculated under the assumption that the fluctuations of both intensities are uncorrelated, which would be the case if the spectra had been recorded consecutively instead of in-parallel. Figure 3: Evaluations of the setup sensitivity: (**a**) The fraction of variance unexplained, (FVU, see Equation 3) between the two FEL-spectra shown in Figure 2b plotted against intensity, given as an estimated number of detected photons within a given spectral interval. We show experimental data points (blue) along with a simulation that accounts for photon shot noise only (orange), as well as additionally including a Gaussian readout noise contribution (green). (**b**) Uncertainty to spectral changes, such as pump–probe effects, considering two methods of acquisition. The plot shows the uncertainty of the average ratio between intensities at the Ni \(L_{3}\)-edge (orange) and 1 eV beyond the edge (green, each within a 245 meV window), measured with the FEL photon energy at the \(L_{3}\)-edge. The uncertainty for parallel acquisition (crosses) considers the correlation between the two intensities and thus, yields an order of magnitude lower uncertainties for this measurement mode. The consecutive acquisition uncertainty (circles) is calculated from the same data, assuming no correlation between the intensity fluctuations.