## 2 Materials and Methods  
The experiments were performed using the PW class laser system from the CETAL-PW laboratory [15; 16; 17; 18]. The 40 fs laser pulse with a diameter of about 200 mm is focused on the target at 45\({}^{\circ}\) incidence angle with respect to the target normal, using an off-axis parabolic mirror with a focal length of 400 mm. The laser parameters at focus are: laser energy 8 J, laser spot surface area 207(9 \(\times\) 23) um\({}^{2}\), and laser intensity of about 5 \(\times\) 10\({}^{19}\) W/cm\({}^{2}\). The contrast ratio (prepulse domain pulse ratio) value is around 10\({}^{-8}\). The full width at half maximum (FWHM) of the spot contains \(\sim\) 30% of the laser energy.  
The experimental set-up used in these experiments to analyze the laser spot profile and the proton beams produced by high-power laser-target interaction is original, as shown in Figure 1a. It consists of a target and detector holder ensemble, and an optical analysis ensemble. The target and detector holder system contains translation and rotation mechanical stages for precise alignment of the target in the laser focus. The optical analysis system employed to investigate the laser beam focal spot, shown in Figure 1a, is placed in front of the target holder system. The target and detector holder system consists of two parallel metallic plates (with a diameter of 200 mm), as illustrated in Figure 1a. The first plate holds the targets, where the distance between the centers of two adjacent targets is around 20 mm. The second plate holds the CR-39 plastic detectors (13 \(\times\) 37 \(\times\) 1 mm\({}^{3}\), purchased from Track Analysis System Ltd (Bristol, UK)), located at 3 cm distance behind the first plate. The detectors are centered relative to the targets position. Both plates are rotated simultaneously by means of an electronically driven mechanical stage, thus avoiding any misalignment between targets and detectors. The target and detector holder ensemble is tightly fixed on mechanical translation stages, to achieve a precise x-y-z alignment in the focus of the laser beam. The optical analysis system located in front of the target and detector holder ensemble consists of an optical microscope coupled with a Basler Charge-Coupled Device (CCD) optical camera, with a resolution of 0.976 um/pixel. The CCD camera was placed in a sealed metallic cylinder at atmospheric pressure, allowing us to perform direct and continuous observation of the laser beam spot profile on target, under high vacuum conditions. As illustrated in Figure 1b,c, the system is used both for laser beam focal point profile analysis (see Figure 1b) and to visualize the laser spot reflected light on the target surface (see Figure 1c). Thus, the influence of the target surface morphology on the laser spot profile can be investigated. The target and detector holder ensemble, together with the laser spot analysis ensemble make up a compact system which exhibits significant advantages: lack of misalignments between targets and detectors; direct and front side visualization of the laser spot with high accuracy (1.25 um/full step of rotation stage), prior to each laser-target interaction.  
Our paper reports for the first time on a system that couples in a compact manner the target positioning system with the detection holder ensemble, and the optical analysis system. Previous work [19] only reports on a wheel system for the automated positioning of targets in the focal point of a high-power laser beam.  
Using the magnetron sputtering technique, target foils of Al and Ag with 5 and 10 \(\upmu\)m thickness were prepared. The morphological surface features of a 5 \(\upmu\)m thick Ag target investigated by scanning electron microscopy are shown in Figure 1d.  
In order to diagnose the proton beams produced as a result of the laser beam interaction with solid targets, a stack of 2 CR-39 detectors of 1 mm thickness covered with a 10 \(\upmu\)m Al foil was used. The Al foil shields the detector surface against interaction with protons and ions of low energies.