## 3 Experimental Results
### Covariance Analysis  
Once the synchronized acquisition of data from all the detectors is established, covariance analysis can be applied to different variables to reveal more information about the underlying physical processes during and after the photoionization. As a proof-of-principle demonstration, we use covariance mapping to achieve post-acquisition mass selection of different ionic species. The aim is to extract the momentum distributions for individual ionic species from the average momentum distribution Figure 6b by calculating the covariance image with respect to the corresponding peak in the ion TOF spectrum shown in Figure 6a. For mass selection, temporal windows around the two features in the time-of-flight spectrum in Figure 6a were chosen. For this, the partial covariance [49], pcov(**X**, **Y**), between every pixel in the ion velocity map image (**X**) with the total signal in the studied channel in the time-of-flight spectrum (**Y**) was calculated.  
The resulting covariance maps are displayed in Figure 7a for the N\({}_{2}^{+}\) channel and in Figure 7b for the N\({}^{+}\) channel. As expected, the N\({}_{2}^{+}\) map (a) is dominated by the zero kinetic energy parent ions from ionization to the X\({}^{2}\Sigma_{g}^{+}\), A\({}^{2}\Pi_{u}\) and B\({}^{2}\Sigma_{u}^{+}\) states. The N\({}^{+}\) map (b) shows correlation both at low kinetic energies, previously attributed to the predissociation of the N\({}_{2}^{+}\) C\({}^{2}\Sigma_{u}^{+}\) state and, at higher kinetic energies, previously attributed to dissociation from the F\({}^{2}\Sigma_{g}^{+}\) state, highly excited Rydberg-like states of N\({}_{2}^{+}\) and the H band. Further, in order to compare it to the accumulated ion VMI data, the same inversion procedure was applied to the covariance maps. The results are shown side by side with the reproduced inverted data from Figure 6b in the left halves of Figure 7c for N\({}_{2}^{+}\) and Figure 7d for N\({}^{+}\), with the right halves being the inverted covariance maps. These results clearly show that mass selection via covariance is a viable method to extract correlated information about the products of photoionization using the proposed instrument.  
A natural next step is to consider ion-electron covariance using this scheme. Consequently, the photoelectron covariance maps were calculated in an analogous way to the ion covariance maps shown in Figure 7a,b. Due to insufficient statistics, it was not possible to adequately invert the resulting covariance maps, and instead, the results of an angular integration of these are shown in Figure 8. Since, as shown in Figure 6f, the photoelectron spectrum primarily contains electrons from the X\({}^{2}\Sigma_{g}^{+}\), A\({}^{2}\Pi_{u}\) and B\({}^{2}\Sigma_{u}^{+}\) states that are all coupled to the N\({}_{2}^{+}\) channel, these completely dominate the covariance at photoelectron momenta between 1 and 2.6 yNs. While the individual peaks cannot be clearly resolved, partly due to a downsampling of the data for reasons of statistics, the contribution is stronger for the N\({}_{2}^{+}\) channel in this regime, as expected. However, at close to zero momentum, the contribution associated with the production of N\({}^{+}\) from dissociation is dominating, which is consistent with our previous attribution of these low kinetic energy electrons to excitation of inner valence states of N\({}_{2}^{+}\). Although qualitative, these first ion-electron covariance results indicate the feasibility of using covariance analysis to extract channel-specific photoelectron data from experiments with high single-shot count rates using the double VMIS presented here.