## 5 Results
### Event Selection and Cluster Parameters  
The first step of the analysis of data from the Timepix3 Radiation Monitor irradiations is the pixel clustering procedure described in Section 3.3, aimed at identifying the results of single-particle hits. Secondly, several parameters are computed for each cluster, in particular, the cluster ToT volume, given by the sum of the individual pixel ToT values, used for calibration purposes. The cluster's shapes are analyzed to define morphological parameters that could allow to distinguish the signal from the background, taking advantage of the information about the experimental test setup (namely, perpendicular irradiation for calibration purposes), as well as the beam particles species (hadrons, leaving round blobs inside the detector, as compared to wiggly lines in the case of electrons). Before the calibration can be carried out, it is beneficial to define a cluster filtering method to ensure that the clusters from single-particle hits are fully reconstructed and isolated protons, hence removing partially reconstructed clusters and/or pileup events from the analysis. The filtering approach used in this paper is based on the definition of geometric cluster properties [55], which is relevant in this study as follows :  
* Cluster size/area \(A\): The number of pixels within the cluster;
* Cluster centre of geometry \((c_{x},c_{y})\): The centre of the cluster, computed as the average point amongst the rows and columns, divided by the cluster area. (Additionally, one could compute the centre of gravity by weighing each pixel by its ToT);
* Cluster radius \(R\): The maximum distance between each pixel and the cluster centre of geometry;
* Cluster density \(\rho\): Defined as the cluster area divided by the area of a circle (\(A=\pi R^{2}\)); therefore, circular clusters will have a density close to unity. Figure 7 shows the distributions of cluster size, radius, and density parameters, as obtained from the clustered data of \(3\,\mathrm{MeV}\) protons at CNA. From these quantities, one can define appropriate selections to identify just the nominal clusters, i.e., those corresponding to fully reconstructed single beam particle hits. For instance, by applying a selection on the cluster density (set to \(\rho>0.6\) for all beam energies), one can filter out partially reconstructed clusters or non-hadronic particle species (background), as well as occasional pileup events leading to partially or fully overlapping clusters. By applying an additional  
cut on the cluster radius (for 3 MeV protons, \(3<R<4\)), one can further remove the lower energy fragments from the clustering. To assess the performance of the clustering algorithm and the subsequent data filtering procedure, it is helpful to analyse the 2D graphs of the clusters' total ToT volume against the number of pixels (cluster area) before and after the filtering, as shown in Figure 8 for 3 MeV protons. For all beam energies, already before the filtering, a central peak is clearly visible, which can be attributed to clusters from single particle hits. Nevertheless, additional clusters are reconstructed, either with a lower cluster size and ToT volume or with higher values of both quantities. Those clusters with a lower size and/or ToT with respect to the main peak are generally the result of partially reconstructed hits in the clustering algorithm or (less likely) interactions of secondary particles, while the fraction of mis-reconstructed clusters tends to increase for higher beam energies, the filtering procedure has proved to be very efficient in removing them, hence providing a clean data set of well-reconstructed clusters for the calibration analysis. On the other end, dedicated analysis on the clusters with higher ToT volume and size than the main peak has shown that they originate from two (or more) closeby particle hits, resulting in two touching clusters that are reconstructed as a single one by the algorithm, denoted here as clustering pile-up.