# A Two-Dimensional Non-Destructive Beam Monitoring Detector for Ion Beams
## 3 Experimental Results  
### Linearity with Respect to Beam Current  
The \(\pi^{2}\) can be calibrated to track the integrated proton flux during irradiations. To this end, an experiment to probe the change of the output signal as a function of the proton flux was carried out. The beam line was set up as shown in Figure 4a: a high-sensitivity Faraday Cup was installed 10 cm downstream of the \(\pi^{2}\), providing an accurate measurement of the beam current, and the second quadrupole magnet on the BTL was switched off to obtain an almost-parallel beam. It is therefore assumed that the proton flux remains constant between the \(\pi^{2}\) and Faraday cup positions. A \((1\times 1)\) cm\({}^{2}\) square collimator, installed upstream of both instruments, was used to define the area over which the beam current was measured.  
Figure 5 shows the red, green and blue pixel values measured by the camera against the proton flux for three different exposure time settings. The pixel value is the average of the pixel values over the region of the image corresponding to the collimated beam, while the proton flux is calculated from the current measured by the Faraday Cup divided by the  
Figure 4: Beam line arrangements for the different experiments presented in Section 3: (**a**) Output signal versus proton flux and radiation tolerance studies; (**b**) Parallel beam profile comparison with radiochromic film measurement; (**c**) Focused beam profile comparison with UniBeM measurement; (**d**) Measurement of the beam scattering introduced by the \(\pi^{2}\) foil.  
collimator aperture area times the elementary charge. For each data point, 10 individual pictures and current measurements were taken and averaged. Changing the exposure time of the camera allows extension of the particle flux range that can be observed by avoiding the saturation of the image at high flux, and increasing the sensitivity at low flux. Given that the P47 compound emits blue light, the signal is mostly contained in the blue channel. Its sub-linear behaviour, apparent in the plot, may be due to three different causes:  
1. A saturation of the scintillator light yield at high incident proton flux.
2. A saturation of the camera sensor or front-end electronics at high photon count rates.
3. A non-linear encoding of the photon count into pixel value.  
To exclude hypotheses 1 and 2, in Figure 6, the pixel value (only the blue channel in this case) is plotted against the product of proton flux and exposure time: \(\phi\cdot T_{exp}\). Assuming a linear response of the scintillator and the camera sensor, this quantity should then be proportional to the sensor photon count and a unique function reflecting the encoding from photon count to pixel value should be obtained. The very good overlap of the three curves for different exposure times confirms indeed the hypothesis that the scintillator and sensor response are linear for a proton flux ranging from \(2\cdot 10^{10}\) cm\({}^{-2}\cdot\) s\({}^{-1}\) to \(5\cdot 10^{11}\) cm\({}^{-2}\cdot\) s\({}^{-1}\). A third order polynomial is found to well describe the transfer function and can be used to calibrate the beam profile image directly in terms of proton flux.  
It is worth noting that the minimum proton flux of \(2\cdot 10^{10}\) cm\({}^{-2}\cdot\) s\({}^{-1}\) used in this calibration was given by the minimum setting of the cyclotron's ion source current. At this intensity level the beam could easily be observed with an exposure time of 2.5 ms. However, the Raspberry Pi camera accepts an exposure time as long as 1 s, i.e., 400 times longer; so, with the current hardware, the \(\pi^{2}\) is expected to be sensitive to proton fluxes lower than the ones used in this characterisation.  
Figure 5: Average red, green and blue pixel values in the collimated region, as a function of the incident proton flux, for three different exposure time settings. As expected for the P47 scintillator, most of the signal is contained in the blue channel. A sublinear characteristic is observed for all three exposure times.