## 3 Results and Discussion
### Analysis of the Laser Driven Proton Tracks in CR-39 Detectors by Visible Light Microscopy  
The surfaces of the both front side of the CR-39 post-etched detectors exposed to laser driven proton beams were also investigated by optical microscopy, as the shape and size of the identified tracks were measured, counted and analyzed. Counting of the track diameters was performed using the Python [25; 26] wrapper for the OpenCV library [27], and numerical processing was performed using the NumPy [28] packages. The first step of this process lies in adjusting the picture contrast for better track edge detection. An algorithm for counting and contour detection was implemented. It uses a simple chain approximation approach which allows performing measurement of the track diameters on the x, y axes. The major and minor axes of the counted tracks were determined. Slight deviations in the values of the major axes relatively to values of the minor axes indicate circular shapes of the tracks. For major differences between the minor and the major axis a correlation with the incident angle of the proton on the detector surface plane can be obtained. A standard deviation of about 1.56 degrees was obtained between the minor and major axes as an indication of a reduced elipticity of the tracks, for all the analyzed CR-39 detectors. This means that the protons incidence angle on the detector varies mainly between 0\({}^{\circ}\) (normally incident on the detector surface) and 30\({}^{\circ}\) (relative to the normally incident on the detector surface). Simultaneous measurements of the track diameters were also performed with ImageJ software. As a result of counting and geometrical shape analysis of protons, the histograms of the minor axes of the track diameters obtained from the acquired optical images of the post-etched CR-39 detectors were plotted (see Figure 9). The x axis of each graph begins at 0.88 \(\upmu\)m, as it represents the minimum number (within \(\pm\)15% error) of tracks in CR-39 detectors that can be attributed to protons (as seen in Figure 4b). Figure 8: Evolution of proton track diameters on first (red points) and second (blue points) post-etched CR-39 detector, as it results from the AFM images for: (**a**) 5 \(\upmu\)m thick Ag target; (**b**) 5 \(\upmu\)m thick Al target; (**c**) 10 \(\upmu\)m thick Ag target; (**d**) 10 \(\upmu\)m thick Al target. The black line represents the fitting curve. The dependence between the proton track diameter (within the 0.88-8 \(\upmu\)m range) identified on the front side of each CR-39 detectors and the incident proton energy was established using the calibration  
Figure 9: Histograms of the track diameters measured from optical images of post-etched CR-39 detectors irradiated by proton beams produced by high-power laser pulse interaction with: (**a**) 5 \(\upmu\)m thick Ag target; (**b**) 5 \(\upmu\)m thick Al target; (**c**) 10 \(\upmu\)m thick Ag target; (**d**) 10 \(\upmu\)m thick Al target. curve from Figure 4b and Table 2. Thus, the evolution of the tracks counted on the front side of the second CR-39 detector as a function of proton energy was calculated. In Figure 10, the spectral distribution of protons stopped in each CR-39 detector after the interaction of the high-power laser pulse with the Al target of 5 \(\upmu\)m thickness is presented. It can be observed that the experimental data presented in Figure 10 are similar with the theoretical predicted one shown in Figure 6b in the 1-9 MeV energy range. The graphical representation of the counted number of protons stopped in the first and second CR-39 slab (see Figure 10a,b) present discontinuity points at \(\sim\)3.3, 5.5 and 6.7 MeV respectively at 4.3, 5.5 and 6.6 MeV. As the revealing of the proton track depends on the etching conditions of the CR-39 detectors, we suppose that these discontinuity points can be linked with the etching process of the detector material as they are slightly different from those identified in Figure 6b.