## 3 Experimental Results
### Improved Proton Beam Profile  
Another benefit of the DPM is the significant improvement in the proton beam profile. Figure 6 compares the raw RCF data from direct and DPM shots. The spatial dose distribution at low proton energy (\(\lesssim\)11 MeV) proves to be much wider with a DPM (middle and bottom rows) than without it (top row). In the latter case, the distribution exhibits two components, one along the laser axis (red arrow) and one along the target normal (black arrow), as previously observed in Ref. [54]. With the DPM, however, the beam profile is preferentially concentrated around the target normal.  
At higher proton energy, the beam profile becomes filamentary in the absence of a DPM, while it retains a rather collimated and round shape with a DPM. This trend, which differs from previous measurements [41], still holds in foils as thin as 20 nm (bottom row), likely a consequence of the shorter pulse duration used in our experiment, which minimizes the target pre-expansion. This may have important implications for proton radiography [4], where a smooth profile translates into better image quality, and for medical applications that necessitate homogeneous irradiation profiles [5; 7].  
The nonuniform profile of the proton beam produced without a DPM is attributed to the extended low-density plasma created by the laser prepulse. This preplasma causes the main pulse to filament, which affects the hot-electron distribution and ultimately the angular profile of the accelerated protons. In contrast, when a DPM is used, the laser interacts directly with the sharp surface of the solid target, likely resulting in a more homogeneous hot-electron profile.  
Figure 7 quantifies the improved beam collimation achieved with the DPM. It shows the half-width of the beam angular distribution for the same shots discussed previously, as a function of energy normalized to the respective maximum cutoff energy. We observe a significantly wider divergence for direct shots, with angles exceeding 20\({}^{\circ}\) at low energies and remaining above 10\({}^{\circ}\) at high energies. The error bars of the data are compatible with the expected energy-dependent divergence of TNSA protons [21], plotted as a black curve. However, the DPM shots on 20 nm and 150 nm thick foils give much smaller divergence angles, consistent with Ref. [38]. These angles decrease from \(\sim\)12\({}^{\circ}\) at low relative energy (\(E/E_{\rm max}\sim\) 0.2) down to \(\sim\)5\({}^{\circ}\) near the cutoff energy.  
Figure 6: Spatial dose distribution on the RCF stack. (**Top row**) No-DPM shot on a 800 nm thick Al target. (**Middle row**) DPM shot on a 150 nm (100 nm + 50 nm Al) thick target. (**Bottom row**) DPM shot on a 20 nm thick Si target. The first two shots yield similar maximum proton energies, but different spatial beam profiles. The same colormap is used in all images. The arrows locate the laser propagation direction (red) and the target normal (black) direction. The marks on the films are used for traceability: the number on the top left is the shot sequence number, the one on the bottom right is the number of the film in the stack. The last film, void of visible proton beams, is shown to demonstrate that the proton beam cutoff corresponds to the second to last film in the stack.  
Figure 7: Measured half-width of the proton angular distribution as a function of proton energy (normalized to the cutoff energy). Filled blue squares: direct shots on 800 nm thick Al foils (symbols represent the average values and error bars the maximum and minimum values over the considered normalized energy (\(E/E_{\rm max}\))  
series of shots). Filled red circles: DPM shots on 150 nm (100 nm Si + 50 nm Al) thick foils. Empty red circles: DPM shots on 20 nm thick Si foils. The black dashed curve represents the energy-dependent angular distribution observed in many experiments to be characteristic of TNSA protons [21].