## 4 Results and Discussion
### Influence of Beam Current  
To validate Equations (3) and (4), coincidence measurements have been performed at five different incoming beam currents \(I\) on a silicon K-edge in a silicon reference sample. The beam current is measured using the current meter which is connected to the fluorescent screen of the microscope. In Figure 2a, the different time coincidence histograms are shown  
Figure 1: **(a)** Conventional electron energy loss (EEL) spectrum where the K-edge of aluminum is shown from an Al-Mg-Si-Cu alloy. The background is subtracted using power-law fit (blue area). The background is used to determine \(N_{ELEL}^{\prime}\). **(b)** The conventional energy dispersive X-ray (EDX) spectrum where the main peak is a characteristic peak of aluminum. The background value is determined by fitting the spectrum to the sum of three Gaussian’s and a linear slope from which one Gaussian peak is the peak of interest. **(c)** Histogram of the number of correlated events as a function of time difference between the X-rays and electrons. The number of identified coincidence events \(N_{C}\) is indicated on the figure. where the RUP is the constant background, and the peak reveals the actual coincidence events. The acquisition time is kept constant, and the incoming electron current is varied. Please note that the center of the coincidence window is around 2500 ns which is not due to the lifetime of the atom itself since this is multiple orders of magnitude faster. The offset is due to the analog filter that we used for the synchronization. Fortunately, this only gives a constant offset which is of no importance for the coincidence method. Using the method explained in Section 4.1 we extract the \(N_{RUP}\) and \(N_{C}\). In Figure 2b,c \(N_{RUP}\) and \(N_{C}\) are plotted as a function of beam current and labeled as non-corrected. By inspecting Figure 2c some deviation from the fitted linear curve is seen. The origin of this discrepancy is that the electron detection efficiency (\(e_{e}\)) depends on the beam current which is shown in Figure 2d. This can be explained by the fact that every individual pixel has a certain dead time during which it cannot detect a new event. Hence when the count rate increases, more events are lost since they arrive inside this dead time interval. The method for collection efficiency determination was used to extract \(e_{e}\) at the different incoming beam currents. The values obtained for the efficiency are used to correct the observed \(N_{C}\) and \(N_{RUP}\) and in Figure 2b,c the corrected values are shown which better approximate the expected linear and quadratic dependencies. Even when current reading from the current meter has a limited precision, the data shows a clear linear and quadratic trend. From the information on \(N_{C}\) and \(N_{RUP}\), the SNR can be calculated using Equation (5) as shown in Figure 2e which theoretically should increase with increasing current (Equation (7)). The non-corrected curve shows a decrease in SNR which is due to the loss of \(e_{e}\) at higher currents indicating that Equation (7) only holds when the efficiency stays constant as a function of incoming current which for the electron detector used here is not the case. The validity of Equation (7) can still be investigated by incorporating the measured electron efficiency into the SNR which is shown in Figure 2e (green) where an increase with current is observed. The validation of Equation (8) is performed by varying the acquisition time  
Figure 2: (**a**) Coincidence histograms as a function of time delay between EELS and EDX event streams for a varying beam current at constant acquisition time (y scale logarithmic). (**b**) The uncorrelated background signal as a function of incoming beam current (brown). The background scales quadratically with incoming current. In green, the corrected expected background signal which would be recorded for an ideal electron detector with constant efficiency as a function of current.