Fig. 1. Sample of Gafchromic HD-V2 radiochromic films irradiated by protons at the Spanish Center for Pulsed Laser (CLPU).

Fig. 2. 2D top view of detector; the proton beam solid angle is parametrized by the internal half-angle $\unicode[STIX]{x1D703}$, the detector dimension $D$ is represented by the length of the scintillator plate $L$ and the relative half-angle between the plates $\unicode[STIX]{x1D719}$, and $n$ is the number of layers. $L_{0}$ is the distance between the proton source and the detector, $d$ is the longitudinal dimension of the scintillator plate, and $T_{1},\ldots ,T_{n}$ represent the projections of the proton beam solid angle for each plate.

Fig. 3. Case $L_{0}=0$. Plot of the number of layers $n_{0}$ versus the half-angle between the plates $\unicode[STIX]{x1D719}$ (according to Equation (5)) for different divergence half-angles $\unicode[STIX]{x1D703}$. When the curves $n_{0}$ ($\unicode[STIX]{x1D719}$) are above a given fixed $n_{0}$ value, the design of the detector is such that proton energies corresponding to the $n_{0}$ value are detectable. As an example, for a proton beam with a 40$^{\circ }$ divergence ($\unicode[STIX]{x1D703}=20^{\circ }$), six layers can work with a maximum angle $\unicode[STIX]{x1D719}\sim 13^{\circ }$, while for eight layers $\unicode[STIX]{x1D719}\sim 10^{\circ }$. It is important to note that the proton energy corresponding to the $n$th layer depends on the thickness and composition of the layer.

Fig. 4. The number of scintillator layers $n$ is represented as a function of the scintillator foil size ($L$) for different values of $L_{0}$ and for fixed values of $\unicode[STIX]{x1D719}=12^{\circ }$ and $\unicode[STIX]{x1D703}=20^{\circ }$. Different values of $L_{0}$ are plotted, representing the distance between the detector and the interaction point position. As an example (dashed line in the graph), a detector with $n=5$ layers needs to be built with a size $L$ greater than: ${\sim}1.5~\text{cm}$ ($L_{0}=0.5~\text{cm}$); ${\sim}3.5~\text{cm}$ ($L_{0}=1~\text{cm}$), ${\sim}6.5~\text{cm}$ ($L_{0}=2~\text{cm}$); ${\sim}12~\text{cm}$ ($L_{0}=4~\text{cm}$).

Fig. 5. Lateral view of the detector with a longitudinal dimension of the base between the first and the last plate of approximately 90 mm ($L_{10}=90~\text{mm}$ with $L_{0}=0$). The plates are separated from each other with a relative angle $\unicode[STIX]{x1D719}=12.5^{\circ }$ and have a dimension of $L=20~\text{mm}$.

Fig. 6. Top view of the interaction chamber with the detector placed inside and the camera set outside the chamber to record the signal.

Fig. 7. The top picture represents configuration 1, in which an odd number of scintillator plates are imaged by the camera. The bottom picture represents configuration 2 with the imaging of the pair scintillator plates.

Fig. 8. Top view of a Monte Carlo simulation (using the FLUKA code) of the proton energy deposited in the scintillator layers of the detector. The proton beam arrives with an incidence angle of $12.5^{\circ }$ on each plate. To facilitate the simulation procedure, the scintillator foils are placed parallel to each other; this configuration is totally equivalent to the original one and does not affect the general results. The colour scale represents the amount of energy lost by a 10 MeV proton beam in each scintillator. The $x$ axis and $y$ axis represent the respective spatial distribution of the deposited energy (plate thicknesses are not shown to scale for easier visualization).

Fig. 9. (a) Experimental signal obtained by the CCD camera during irradiation with a 10 MeV proton beam, with the colour scale giving pixel values artificially overlaid on a 3D representation of the detector. (b) Example of Monte Carlo simulation (obtained with FLUKA) representing the transversally integrated deposited energy per particle for each scintillator plate irradiated by a 10 MeV proton beam. (c) Response of the scintillator (light output) to 10 MeV proton beam irradiation. We can observe a peak of energy in layer 2 (in panels (b) and (c)) due the thickness difference between layers 2 and 3 ($180~\unicode[STIX]{x03BC}\text{m}$ against $140~\unicode[STIX]{x03BC}\text{m}$). Then, far from the Bragg peak, a proton will deposit more energy in layer 2 than in layer 3. Each plate ($n$) has a different thickness (due to uncontrollable variation during the fabrication process): $n_{1}=120~\unicode[STIX]{x03BC}\text{m}$; $n_{2}=180~\unicode[STIX]{x03BC}\text{m}$; $n_{3}=140~\unicode[STIX]{x03BC}\text{m}$; $n_{4}=160~\unicode[STIX]{x03BC}\text{m}$; $n_{5}=190~\unicode[STIX]{x03BC}\text{m}$; $n_{6}=130~\unicode[STIX]{x03BC}\text{m}$; $n_{7}=150~\unicode[STIX]{x03BC}\text{m}$ (lines in panels (b) and (c) are visual guides and not fits).