## 3 Experimental Results  
To evaluate the performance of the instrument, measurements have been done at the high-intensity XUV beamline at the Lund Attosecond Science Center [42], where high-flux XUV pulses generated through the HHG process were focused by reflective optics into the interaction region of the double VMIS. The target gas was introduced using a pulsed molecular beam from an Even-Lavie solenoid valve, able to produce high density pulses with durations as short as 10 \(\upmu\)s [47,48]. In Figure 5, the spectrum of the XUV pulses generated in argon and recorded by an XUV spectrometer is displayed. It contains photons from harmonic order 13 (20.0 eV) up to harmonic order 29 (44.7 eV). Lower photon energy contributions and the remaining driving laser light are absorbed by a 200 nm-thick aluminum filter. The XUV light is redirected to the XUV spectrometer by a rotatable gold mirror prior to the focusing into the interaction region of the double VMIS, and thus, the spectrum cannot be recorded during measurements with the double VMIS. The displayed XUV spectrum has been corrected for the spectral responses of the employed grating and MCP detector. In the further analysis, the corrected spectrum is used. Figure 4: Simulation results for ion detection when the electron side is optimized for electron VMI (Operation Modes 2(a) and 2(b)). (**a**) shows the resulting mass resolution as a function of extractor voltage, \(V_{\rm E}^{\rm i}\), for ions with an initial velocity of \(v_{0}=1000\) m/s in the direction of the molecular beam; (**b**) shows the resulting VMI energy resolution for three different extractor voltages using the 27-particle model (blue, green and orange lines) and the Monte Carlo model for the optimum setting (solid black line). The dashed black line shows the resolution in Operation Mode 1(b) obtained by the Monte Carlo method, reproduced from Figure 2; (**c**,**d**) show the simulated detector image and the 3D momentum distribution after inversion, for the optimum voltages; (**e**) shows the kinetic energy spectrum calculated from the 3D momentum distribution. Figure 5: XUV spectrum recorded by the XUV spectrometer. The spectrum contains photons from harmonic order 13 (20.0 eV) up to harmonic order 29 (44.7 eV), indicated above the peaks. To be able to apply covariance analysis, synchronized single-shot data need to be acquired. At the high-intensity XUV beamline, the repetition rate is 10 Hz, and acquisition of single-shot data is relatively straightforward. However, the intensity of the XUV light generated by laser-driven HHG typically varies on a shot-to-shot basis, introducing false correlations between channels that are physically not correlated. To circumvent this problem, a partial covariance method was used [49], through which the covariance maps were corrected for the fluctuating source intensity, recorded on a single-shot basis by an in-vacuum XUV photodiode placed after the focus of the XUV pulses. In this section, we describe the acquisition of data and the subsequent proof-of-principle application of ion-ion and ion-electron covariance mapping. Figure 6: Experimental results in the high resolution electron mode 2(b) using high-order harmonics generated in argon to ionize N\({}_{2}\). (**a**,**d**,**g**) show ion TOF data (**a**), with the calibrated mass spectrum in (**d**) and the correlation between the total ion TOF signal and the XUV intensity measured by the XUV photodiode visualized by a color-coded scatter plot in (**g**); (**b**,**e**,**h**) show ion VMI data, with the average detector image (left part) and inverted image (right part) in (**b**). The inverted images represent the reconstructed initial 3D momentum distributions obtained by inversion of the 2D projections recorded on the detector [23]. The photoion kinetic energy spectrum is displayed in (**e**) with its attributed contributions shaded in different colors, calculated from the inverted image (**b**).