## 4 Discussion on the Spatial Resolution  
The spatial resolution of the LaGEMPix was evaluated, using different methods and experimental configurations. The results are summarized in Table 3. The measurements with the lead block (ESF) yielded a spatial resolution of 9.70 \(\pm\) 0.09 mm for 40 kV X-rays. On the other hand, the LSF method showed that the detector can resolve two 5 mm holes separated by 3 mm. This suggests that the ESF method reported here underestimates the spatial resolution of the LaGEMPix, whose intrinsic spatial resolution is better than 9.70 \(\pm\) 0.09 mm. It also means that the results obtained from the different methods cannot be directly compared. Additionally, the MTF measurements only allow to conclude that slits at 2 mm distance cannot be distinguished. These results show that the spatial resolution of the current LaGEMPix does not fulfil the criterion of sub-millimeter resolution for hadron therapy and that the exact value depends on the method applied to evaluate the spatial resolution. In order to disentangle the effects on the spatial resolution from different sources, such as the experimental setup, electron diffusion in the gas, and isotropic emission of photons in the detector, measurements were performed with the GEMPix and GAFCHROMIC(r) XR-SP2 films. Table 3 summarizes the values of spatial resolution obtained for the various detectors and experimental configurations. As expected, the GAFCHROMIC(r) films show the best spatial resolution. The edge response worsens from 0.86 mm with the film to 5.20 mm with the GEMPix, while slight differences are observed with the LSF method. Figure 17: One-dimensional projection of the 1.3 mm holes with 2.5 mm pitch. The LSF of the selected area gives a distribution with an average hole diameter of 1.47 mm. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & & **Spatial Resolution (mm)** \\ \hline
**Detector** & **Edge Response** & **5 mm Cu Hole** & **Minimum Resolvable** \\  & & & **Hole Spacing** \\ \hline LaGEMPix & 9.70 \(\pm\) 0.09 & 6.73 \(\pm\) 0.08 & 3 mm (edge to edge) \\ GEMPix & 5.20 \(\pm\) 0.10 & 5.23 \(\pm\) 0.05 & 1 mm \({}^{1}\) (edge to edge) \\ GAFCHROMIC® & 0.86 \(\pm\) 0.07 & 5.09 \(\pm\) 0.03 & 1 mm \({}^{1}\) (edge to edge) \\ FLUKA simulation of & 4.53 \(\pm\) 0.01 & 4.87 \(\pm\) 0.03 & 1 mm \({}^{1}\) (edge to edge) \\ LaGEMPix & & & \\ \hline \hline \end{tabular}  
* minimum distance between holes in the Cu plate.  
\end{table} 
Table 3: Summary of the spatial resolution obtained for different experimental configurations and by different detectors. Results from the FLUKA Monte Carlo simulation are also included for comparison. In both cases, holes separated by a distance of 1 mm can still be resolved. The GEMPix yielded an MTF below 10% at 1.4 LP/mm. The ESF of the LaGEMPix and the FWHM of a 5 mm hole are higher than with the GEMPix. A further decrease in the spatial resolution is observed with the LaGEMPix, associated to the isotropic emission of scintillation photons. The results show that with the current design of the LaGEMPix, holes at a distance of 1 mm can no longer be resolved; the MTF method also shows that slits spaced by 2 mm cannot be resolved. Finally, the results of a FLUKA Monte Carlo simulation of the LaGEMPix were compared with the experimental results. Unsurprisingly, the resolution obtained from the simulation is much better than the experimental one. This can be explained by the fact that the simulation does not take into account some phenomena associated with the detector working principle, such as the isotropic emission of the scintillation photons. On the other hand, the simulation predictions agree with the GEMPix results.