# Towards real-time beam monitoring and quality assurance of proton beams using radioluminescent silica fiber

Marjorie Grandvillain, Franck Mady, Petter Hofverberg, Gaëlle Angellier, Gilles Mélin, Mourad Benabdesselam, Joël Herault, Marie Vidal

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Marjorie Grandvillain, Franck Mady, Petter Hofverberg, Gaëlle Angellier, Gilles Mélin, et al. Towards real-time beam monitoring and quality assurance of proton beams using radioluminescent silica fiber. Physics in Medicine and Biology, 2025, 71 (1), pp.015010. 10.1088/1361-6560/ae29e3. hal-05446779

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# Towards real-time beam monitoring and quality assurance of proton beams using radioluminescent silica fiber

To cite this article: Marjorie Grandvillain et al 2026 Phys. Med. Biol. 71 015010

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PAPER

Towards real-time beam monitoring and quality assurance of
proton beams using radioluminescent silica fiber

Marjorie Grandvillain<fnref n="1" />,<fnref n="2" />,* ID, Franck Mady<fnref n="1" /> ID, Petter Hofverberg<fnref n="2" /> ID, Gaëlle Angellier<fnref n="2" />, Gilles Mélin<fnref n="3" />, Mourad Benabdesselam<fnref n="1" />, Joël Herault<fnref n="2" /> and Marie Vidal<fnref n="2" />

E-mail: grandvillain.marjorie@outlook.fr

Keywords: dosimetry, proton therapy, high dose rate, radioluminescence, optical fiber, real-time

Abstract

**Objective.** Due to the emergence of ultra-high dose rate proton therapy techniques, the need for advanced *in-vivo* dosimetry tools able to monitor such beams has become more critical. This study evaluates the potential of silica optical fibers as real-time scintillating detectors for quality assurance of scattered and scanned pulsed proton beams at high and standard dose rates. *Approach.* The radioluminescence (RL) of short pieces of thin Gd<fnref n="3" />⁺-, Ce<fnref n="3" />⁺-, and N-doped silica fibers was studied focusing on their response to dose rate and energy, and their ability to perform depth-dose measurements, and for pencil beam scanning proton beams, spot size evaluation and real-time beam monitoring. The fibers response was evaluated in a continuous scattered proton beam and a synchrocyclotron scanned pulsed proton beam. *Main results.* Up to 130 Gy·s⁻<fnref n="1" />, fibers response was linear as a function of dose rate. For both proton beams, range was measured with less than 1.1 mm deviation with the three fibers, despite scintillation quenching (SQ) from 63 to 226 MeV. With the same data, spot size was estimated with less than 0.3 mm difference from the reference, taking advantage of the real-time RL acquisitions for scanned beams. Also, characterization of synchrocyclotron specific dose delivery by repainting, was investigated. Fibers were able to measure the relative dose contribution of each painting, according to the system log-files (less than 2% difference). Moreover, the ability of the system to resume properly the irradiation after beam interruption was validated in real-time through fibers acquisitions and were correlated to the system log-files. *Significance.* RL-based silica fiber sensors appeared to be viable detectors for proton beam quality assurance (proton range, spot size) at standard and high dose rates despite showing SQ and showed potential for real-time dosimetry for scanned proton beams and log-files QA, in addition to high dose rate proton beams.

**1. Introduction**

Proton therapy allows for localized deposition of radiation to the tumor while sparing surrounding
healthy tissue, thanks to the proton's narrow spread and specific penetration range. Moreover, the use
of pulsed scanned beams through the pencil beam scanning (PBS) (Gillin et al 2010, Pidikiti et al 2018)
technique makes it possible to treat tumors with millimetric precision adapted to the treated volume.
With the evolution of protontherapy machines with high-dose-rate proton beams and the emergence of
flash therapy (Favaudon et al 2014, Favaudon 2019), the need for sophisticated in-vivo dosimetry tools
capable of monitoring and verifying PBS treatment quality at high dose rates has become increasingly
crucial.

In particular, synchro-cyclotron based installations deliver high dose rate per pulse pulsed and
scanned proton beams, such as MEVION S250TM (Mevion Medical System) (Vilches-Freixas et al 2020)

<footnote n="1">¹ Université Côte d'Azur, Fédération de recherche Claude Lalanne, Institut de Physique de Nice, CNRS UMR7010, 17 rue Julien Lauprétre, 06200 Nice, France</footnote>

<footnote n="2">² Centre Antoine Lacassagne, Fédération de recherche Claude Lalanne, 227 avenue de la Lanterne, 06200 Nice, France</footnote>

<footnote n="3">³ Exail Photonics, rue Paul Sabatier, 22300 Lannion, France</footnote>

<footnote>* Author to whom any correspondence should be addressed.</footnote>
or Proteus®ONE (IBA PT, Louvain-la-Neuve, Belgique) (Vidal et al 2024). In order to reduce dose delivery uncertainties due to pulsed beam extraction, the total dose irradiation is delivered by inherent repainting, controlled by an internal feedback loop. In case of interruptions during treatment delivery, the capacity of the system to compensate the dose delivery has to be verified and real-time dosimetry would be beneficial. The high dose rates and high doses per pulse favor recombination and space charge effects that noticeably impair the sensitivity of radio-electric dosimeters, which rely on the collection and transport of charge carriers created by ionization, such as ionization chambers (ICs). ICs commonly used for proton beam quality assurance, require high voltage and their response is driven by the transport of radio-induced charge carriers. Thus, the charge recombination, negligible at conventional dose rates, requires significant correction at high dose rate (Konradsson et al 2020, Romano et al 2022). Semiconductor dosimeters, diodes for example, could be used, but their sensitivity can also be hampered at high dose rate while being additionally affected by the pulsed structure of the beam (Jursinic 2013, Romano et al 2022). None of these detectors are transparent to radiation, which would affect the dose delivered to the patient if they were used in vivo (Romano et al 2022, Zou et al 2023). Consequently, they are not good candidates for high dose-rate per pulse pulsed scanned proton beams in-vivo dosimetry. Conversely, scintillation-based optical fiber dosimeters produce luminescence upon recombination of electron-hole pairs. The radioluminescence (RL) intensity (radiative recombination rate) is, in steady state conditions, necessarily proportional to the pair generation rate, i.e. proportional to the proton fluence rate and therefore to the absorbed dose rate at any given proton energy. The proportionality coefficient, defined as the ‘sensitivity’ of the detector to the dose rate (i.e. the RL response per unit dose rate) remains constant, even under very high fluence rate. They thus offer the combined advantages of RL, whose sensitivity is maintained at high dose rates, and reduced fiber size, which meets the need for beam miniaturization and transparency. Such dosimeters have shown promising results for high dose rate and real-time measurements with good spatial resolution (O’Keeffe et al 2015, Vanreusel et al 2022, Vidalot et al 2022a, Ciarrocchi et al 2024). Moreover, the physical processes at play in scintillators are also immune to electromagnetic perturbations and to fluctuations in humidity and pressure, contrary to ICs. Although the energy deposition and the Cerenkov emission in the scintillator itself can be affected by the magnetic field, this may lead to a change in luminescence intensity (Simiele et al 2018, Beddar et al 2021, Madden et al 2022).

Silica optical fiber dosimeters can basically operate on two mechanisms, namely radiation-induced attenuation (RIA) or radiation-induced emission, a term that covers both scintillation (RL) and Cerenkov emission (Girard et al 2019, Veronese et al 2024). RIA grows with cumulated dose; it is better suited to the measurement of high dose levels in nuclear applications (a few tens of kGy in (Faustov et al 2016) or more than 1 MGy in (Rizzolo et al 2015) for instance). RL, which is sensitive to the proton fluence rate, is much more suited to real-time dosimetry at the dose levels involved in radiotherapy. In this field, research has primarily focused on plastic or inorganic scintillators coupled to the end of a PMMA transport fiber (guiding the light to photodetectors), which both usually have diameters between 0.5 and 1 mm. The RL response of these devices has shown good linearity against dose rate (Beddar et al 1992, Andersen et al 2009, Jørgensen et al 2021, Poirier et al 2022). In addition, these detectors are being evaluated with heavy particle beams, including protons and carbon ions (de Freitas Nascimento et al 2022, Kanouta et al 2023). Silica-based scintillating optical fibers provide a relevant alternative to organic scintillators. Their RL can be activated by doping with a variety of luminescent ions (Mizanur Rahman et al 2015, Zubair et al 2019, Benabdesselam et al 2021, Fricano et al 2024) to provide highly sensitive sensors offering key advantages such as a small external size (125 µm in diameter), an even smaller sensitive volume (the doped core of the fiber, from 10 to 60 µm in diameter). The optical fiber itself is thus the scintillating dosimeter; its RL can be activated by doping over a significant length to achieve spatially-resolved dosimetry along the fiber. We will also show that silica glasses are nearly tissue equivalent within the therapeutic energy range.

Despite these qualities, three critical aspects need to be considered when studying scintillators. First, the potential impact of dose history on the RL response (Laub et al 1999, Andersen et al 2007). Second, scintillators are known to have particle energy dependency: their ‘sensitivity’ to the dose rate, i.e. the RL production efficiency per unit dose rate absorbed to the fiber probe, decreases with the proton energy (i.e. at high linear energy transfer, LET) (Wang et al 2012, Robertson et al 2013, Valdes Santurio et al 2020, de Freitas Nascimento et al 2022). This effect is referred to as ‘scintillation quenching’ (SQ) (Birks 1951, Blanc et al 1964, Awe et al 2021), originates from high local ionization densities along charged-particle tracks, and can become apparent in measurements as a deviation from proportionality with absorbed dose. Finally, optical fibers can produce Cherenkov emission during irradiation, depending on the beam energy. This emission is sometimes directly studied (Christensen et al 2018) but most of the time, the Cherenkov signal is mixed with other contributions from secondary particles, creating a
spurious signal that is difficult to separate from the RL signal (Veronese et al 2013, Darafsheh et al 2016, Archer et al 2017).

This article aims to explore the capabilities and benefits of Gadolinium, Cerium or Nitrogen-doped silica fiber dosimeters in the context of quality assurance for proton radiotherapy, for scattered and scanned proton beams, with dose repainting or not, for high and standard dose rates. These dopants have been the subject of preliminary characterization (Hoehr et al 2019, Vidalot et al 2022a). Moreover, energy (and LET) and dose rate dependency will also be investigated for these dopants. As recommended for quality assurance for proton PBS beams (Arjomandy et al 2019) the proposed detectors need to provide precise range and spot size estimation. In addition, this article focuses on the evaluation of fiber's potential for real-time beam measurements in the context of quality assurance of proton beams.

## 2. Materials and methods

### 2.1. Radioluminescent silica fibers

Three types of scintillating dosimeters, which showed best potential for the targeted applications, were used in this study: gadolinium (Gd$^{3+}$), cerium (Ce$^{3+}$), and nitrogen (N)-doped silica fibers. These optical fibers were made using two very different techniques. Gd- and Ce-doped silica samples were obtained by the sol-gel technique at PhLAM laboratory of Lille University (France) (Bahout et al 2020), whereas the N-doped fiber supplied by the EXAIL company (Lannion, France) was made using the surface plasma chemical vapor deposition technique (Isaev et al 2023). The Gd$^{3+}$-doped silica was prepared in the form of a uniformly doped rod with an external diameter of 220 µm. Conversely, the Ce- and N-doped fibers were prepared according to a classical core-cladding structure. Dopants were introduced into the core, which constitutes the sensitive volume of the fiber. The core diameter was 50 and 60 µm for the Ce- and N-doped fibers, respectively. In both cases, the external diameter of the glass cladding was 125 µm. All scintillating probes consisted of 1 cm-long pieces of doped fibers. The latter were spliced to radiation-hard pure silica-core fibers capable of transmitting the radiation-induced luminescence to the detector. The signal was collected with a Hamamatsu H7421-40 photomultiplier tube associated with a C8855-01 counting unit from the same manufacturer. A non-doped silica fiber probe of the same diameter as the doped fiber probe was used to evaluate Cerenkov and other spurious emissions, as well as the (weak) intrinsic scintillation of the silica matrix. This non-doped fiber probe, connected to a second but identical detection channel, was exposed to protons at the same time and in the same irradiation field as the radioluminescent fiber piece.

The evolution of the RL signal during irradiation follows the physical process we described in detail (Grandvillain et al 2024), and pre-irradiation accelerates the transient rise towards equilibrium. Reaching the equilibrium (plateau) of the RL intensity is needed to ensure the proportionality of the RL response with the proton fluence rate and hence dose rate, which, before-plateau measurements, could result in a supra-linear growth. Pre-irradiation of the fiber appears to be especially important when used in a pulsed beam as the irradiation time is shorter. Consequently, the fiber probes were pre-irradiated at more than 5 kGy, to avoid repeatability problems, as also suggested by Fricano et al (2023).

### 2.2. Irradiation setups

Proton irradiations at low energy were performed using the isochronous cyclotron MEDICYC of Center Antoine Lacassagne (Nice, France), producing a 65 MeV proton beam considered as nearly continuous with a period of 40 ns between the bunches (Hérault et al 2005, 2007, Hofverberg et al 2021). Once the protons are extracted, they can be transported towards a dedicated treatment room, where the beam is scattered and delivered passively (Hérault et al 2007), or towards a research and development beam line (referred to as R&D) (Hofverberg et al 2022). In this beam line, the flux of extracted particles produces an adjustable current ranging from 10 pA to 10 µA and the energy can be degraded from 63 MeV up to 15 MeV with PMMA range degraders.

Irradiations at higher energies were performed using a scanned pulsed high dose-rate per pulse proton beam, from the Proteus® One (IBA PT, Louvain-la-Neuve, Belgium). This installation consists of an S2C2® synchrocyclotron (AIMA, Nice /IBA PT), which accelerates protons to an energy of 226 MeV, and a compact isocentric gantry allowing patient irradiation in a dedicated treatment room. The energy can be degraded down to 100 MeV. The beam is extracted by pulses whose duration is $\tau = 7–8$ µs (Lehrack et al 2017), and these pulses are repeated at a frequency of $f = 1000$ Hz, corresponding to a period of $T = 1$ ms. Each micro-pulse itself consists of proton bursts of 8 ns occurring every 17 ns (Van De Walle et al 2017). The beam delivers the dose using the PBS technique (Sepulchre et al 2000). The beam energy is adjusted depending on the irradiated layer of the tumor, then the beam is scanned using deflection magnets in X and Y direction. On a given energy layer, at each beam position, the pencil beam
<table><caption>**Table 1.** Mean LETs simulated, using GATE, in a 220 µm silica thickness and in the 60 µm core of a 125 µm optical fiber. The uncertainties include the error on the central energy value and its dispersion, as well as the energy-related error for the LET.</caption><thead><tr><th>Energy (MeV)</th><th>Mean LET for 220 µm thickness (keV µm<sup>-1</sup>)</th><th>Mean LET for 60 µm thickness (keV µm<sup>-1</sup>)</th></tr></thead><tbody><tr><td>61.3 ± 0,28</td><td>1.939 ± 0,007</td><td>1.973 ± 0,007</td></tr><tr><td>30.1 ± 0,55</td><td>3.485 ± 0.053</td><td>3.470 ± 0.053</td></tr><tr><td>15.4 ± 0,95</td><td>6.094 ± 0.312</td><td>5.994 ± 0.306</td></tr></tbody></table>

intensity can be adjusted according to the parameters defined during planning (through the number of Monitor Units). Depending on the dose to be delivered, several pulses can contribute to each spot. The charge per pulse varies from $1.5 \times 10^{-14}$ C/pulse to $7.4 \times 10^{-12}$ C/pulse for the highest energy and from $2.0 \times 10^{-15}$ C/pulse to $1.0 \times 10^{-12}$ C/pulse for the lowest (Vidal et al 2024). For better accuracy, the dose per spot, defined by the total charge of each spot position, is delivered by the pulsed beam in three successive ‘paintings’ of decreasing contribution over each layer according to IBA’s ‘blind golfer algorithm’. This algorithm is a feedback loop based on the previous painting and adjusts the charge to each spot position accordingly (Zhao et al 2022).

## 2.3. Characterization of the RL response as a function of the dose rate and energy

The linearity of the RL signal with respect to dose rate is measured to evaluate the detector’s operating dose rate range. The equilibrium level of the RL intensity was measured as a function of the dose rate on the R&D beam line for the three types of doped-silica fibers. The fibers have been placed in air, at the center of a 2 cm diameter collimated homogeneous proton beam. To study separately the effect of flux and energy on RL response on the dose rate dependence, the dose rates were varied by changing the fluence rate from $7.3 \times 10^7$ cm$^{-2}$ s$^{-1}$ to $1.1 \times 10^9$ cm$^{-2}$ s$^{-1}$ at a fixed energy. The flux was monitored by a transmission IC, which was calibrated using a faraday cup for each energy and each decade in flux. The nominal proton energy was specified at the isocenter, where the fiber is positioned. Three energies from 15 MeV to 61 MeV have been investigated. The mean stopping power in silica probe was determined using SRIM 2013 (Ziegler and Biersack 1985), for the 220 µm probes and for the 60 µm probes and shown in table 1. Thus, the absorbed dose rate varies from (1.02 ± 0.05) $10^{-1}$ Gy s$^{-1}$ to (2.06 ± 0.21) $10^3$ Gy s$^{-1}$. Exposure time was set to 60 s, with an integration time of 100 ms for signal acquisition, in order to optimize the signal-to-noise ratio and to reach an apparent RL intensity equilibrium level in all measurements.

A second sequence of measurements was carried out on the nitrogen-doped fiber only, at a very high average dose rate to silica: up to $130$ Gy s$^{-1}$ achieved with a maximum fluence rate of $9.4 \times 10^{10}$ cm$^{-2}$ s$^{-1}$ and an energy of 61.3 MeV. This comes close to the conditions of ultra-high dose rate radiotherapy. Exposure time has then been reduced to 5 s to reduce neutronic activation. A 20 dB optical attenuator has been added between the transport fiber and the photocounting unit to prevent saturation of the photodetector while maintaining a sufficient signal-to-noise ratio.

## 2.4. Bragg curves measurements

Depth distributions of the RL response were acquired under a scattered and continuous 63 MeV clinical proton beam, and under scanned and pulsed 100 MeV and 226 MeV proton beams. These distributions were compared to reference depth-dose profiles (Bragg curves) acquired in the same conditions, with the usual detectors adapted to the beams. The conditions are detailed below.

For all experiments, one doped fiber and one undoped fiber were centered in water phantom with a specifically made PMMA holder. The undoped fiber was used to evaluate the Cerenkov signal and the RL emission of the silica matrix simultaneously to the signal provided by the scintillating silica probe. The holder was then attached to a support which can be translated with a translation motor, moving in three dimensions and which enables measurement of percentage depth dose curve (PDD). In silica, protons can be directly responsible for Cerenkov emission only if their energy is above ~350 MeV. But delta electrons set in motion by protons can produce Cerenkov. The requirement is that the maximum energy transferred by protons to those electrons exceeds the Cerenkov threshold for electrons in silica, that is about 190 keV. Thus, it was necessary to evaluate the presence of Cerenkov during the measurements.

In the case of MEDICYC, the three doped (Gd$^{3+}$), (Ce$^{3+}$) and (N) fibers were tested on the 63 MeV clinical beam line of MEDICYC. Pristine Bragg peak measurements were performed by moving the fiber step by step with a displacement step adapted to the dose gradient. To map the Bragg peak with high spatial resolution, measurements were conducted in 0.05 mm increments on either side of it. MEDICYC delivered a clinically used dose rate of $50$ Gy min$^{-1}$ in a brass-collimated homogenous field measuring 2 cm of diameter. A constant dose, corresponding to 0.8 Gy in water at the isocenter, is delivered to
each position in approximately 10 s. The fiber signal is recorded with an integration time of 100 ms on the acquisition system. The results were compared with the clinical reference PDD measured by a diode BAS21 in water.

In the case of the Proteus®One beam line, only the nitrogen fiber, selected because of its high sensitivity, was evaluated at 100 MeV and 226 MeV. The pristine Bragg peak measurements were performed step by step with a displacement step of 1 mm in the Bragg peak maximum region. Irradiation plans of a mono-energetic 10.4 × 10.4 cm² field scanned by 2881 spots, spaced 2 mm apart in x and y directions, with 1 MU/spot, at energies of 100 MeV and 226 MeV, were used to irradiate the fibers and a plane parallel chamber PPC05 (IBA Dosimetry, Schwarzenbrück, Germany) in water. The latter was used as the reference detector in this case.

The RL level was evaluated by integrating the signal intensity over the entire exposure time. Background noise was subtracted. Both doped and undoped RL fibers signals were analyzed.

To characterize the SQ and for the sake of comparison with published results see (Torrisi 2000), the Birks-Craun equation (Birks 1964, Craun and Smith 1970) was used. N-doped RL intensity was plotted as a function of the mean LET in silica, determined by GATE simulations (Grevillot et al 2012, Schnürle et al 2018) at various depths in water, the resulting curve is not shown here.

## 2.5. Real-time measurements and spot size estimation

The time-resolved response of RL probes allowed for real-time measurements of scanned pulsed beams. This part of the study therefore aimed at characterizing the irradiation sequences offered by PBS irradiations with dose repainting.

Data acquisitions were performed using an N-doped fiber placed together with an undoped fiber (for Cerenkov emission) within RW3 solid water plates (IBA-Dosimetry, Schwarzenbrück, Germany). Fibers were centered in the middle of the fields parallel to the beam propagation, in a specific holder made by cutting grooves in a sheet of PMMA. Integration times were set at 100 ms and 10 ms, depending on the requirements. For the analysis, background noise was subtracted, and the RL signal was integrated over the entire irradiation period until all three paintings were completed.

First, spot spacing varied from 2 mm to 8 mm for 100 MeV single layer plan of 10 × 10 cm² field size with 1 MU/spot, and integration time was changed from 1 ms to 1 s, to evaluate their impact on the RL signal.

Secondly, spot size was estimated for single layer plans of 10 × 10 cm² field size, with spot spacing 2 mm, 1 MU/spot at various energies of 100 MeV, 150 MeV and 226 MeV, following the formalism below, more detailed in the appendix. Assuming a Gaussian spot profile, the particle fluence rate at a point (x, y) for a spot centered at (x₀, y₀) in the field (see figure 1) can be written as:

$$ \Phi(x, y) = \Phi_0 \times \exp\left(\frac{(x - x_0)^2 + ((y - y_0)^2)}{2 \sigma^2}\right) \quad (1) $$

where Φ₀ is the maximum fluence rate at the center of the spot and σ the characteristic standard deviation of the spot. Modeling of the particle flux on the fiber was then possible and used for spot size analysis. The estimated values were compared to Lynx 2D scintillator (IBA Dosimetry, Schwarzenbrück, Germany) measurements for the 3 energies. The analysis was also performed for the data extracted from the Bragg peak measurements at 226 MeV in water in order to estimate the spot size as a function of depth in water. Then, clinical beam interruptions were investigated. During clinical irradiation on patients, the Proteus® One treatment delivery could be occasionally interrupted. The system then automatically adjusts the beam position and the dose to be delivered when treatment resumes. Therefore, we evaluated the possibility of monitoring the accurate regulation of the delivered dose using the fibers. Two types of plans with interruptions were evaluated. The first plan, named plan A, was a 100 MeV mono-energetic 10.4 × 10.4 cm² field, with intensity of 1 MU/spot and a spot spacing of 2 mm. The second plan, named Plan B, was a 226 MeV mono-energetic 10 × 10 cm² field, with intensity of 3 MU/spot and a spot spacing of 5.8 mm, corresponding to a clinical spot spacing, and comprising 278 spots. This plan was delivered in 'clinical' mode through the oncology information system, allowing the recording and access of machine system files (log files). Each plan was first delivered in its entirety without interruption to establish a reference measurement. Subsequently, both plans were delivered with induced interruptions, at various time points, sometimes in the middle of one of the three paintings and sometimes between two paintings, thus generating different 'partials'. This approach allowed us to observe how the dose was redistributed across each painting when irradiation resumed, depending on the stage at which the interruption occurred.
<figure><img src="image_4.png" /><figcaption>**Figure 1.** Scheme of the scanning pattern with the doped optical fiber (dimensions d and L) centered in the middle of a square field (side length a). The number of spots per line depends on p, the spot spacing: 53 × 53, 27 × 27, 18 × 18, and 14 × 14 for square fields of 2 mm, 4 mm, 6 mm, and 8 mm respectively.</figcaption></figure>

All analyses based on the ‘real-time’ character of the RL measurement, including spot size extraction and the monitoring of interrupted irradiations sequences, only use the temporal structure of the RL signal (time is plotted in abscissa). This structure depends solely on the scanning parameters (spot spacing, size and speed); it is completely independent of the RL intensity (plotted in ordinate), i.e. completely independent of the detector’s sensitivity and thus of the SQ phenomenon. There is therefore no reason why the existence of SQ should limit the validity, the usefulness, or the relevance of these analyses and of the related new control opportunities.

## 3. Results

### 3.1. RL signal and response to dose rate and energy variation

Figure 2 shows the RL intensity measured for the three doped fibers studied here as a function of time. Fluctuations in the dose rate are estimated to less than 0.2% during irradiation, according to Hofverberg et al (2022). During irradiation, an equilibrium intensity level is reached after a transient increase of the RL. The detailed study of the intrinsic kinetics of inorganic scintillation in silica allowed us to demonstrate that this equilibrium intensity is proportional to the electron-hole pair generation rate (Grandvillain et al 2024). Since the latter is obviously proportional to the proton flux on the silica fiber, we have used this equilibrium level to characterize the RL response. The Gd-doped fiber exhibits a build-up during the first second. Hence the mean value of the RL signal was considered between 20 s and 70 s. The signal deviation is higher for the Gd-doped fiber due to the low intensity. At the end of irradiation, the RL intensity exhibits a rapid initial decay, with approximately 80%–90% of the signal decaying within 0.3 s. However, achieving a 99% decay requires several minutes and is therefore not represented in the figure. Fluctuations between identical RL measurements were less than 0.5%, giving excellent repeatability.

Figure 3 shows the dependence of RL intensity on the dose rate (here varied by changing the proton fluence rate). For all probes, the RL signal was scaled by the value corresponding to the highest dose rate at 61 MeV. Normalization is introduced to improve the clarity of presentation and has no bearing on the interpretation of the results. Linear regressions are also displayed for each energy with their slope coefficients. For all investigated fiber probes, the RL intensity increases linearly with the dose rate for each
<figure><img src="image_5.png" /><figcaption>**Figure 2.** Typical radioluminescence signal obtained during 60 s irradiation with a continuous 15.4 MeV proton beam, for the three scintillating detectors: N-doped (upper curve), Ce-doped (middle curve), and Gd-doped (lower curve) fiber probes and signal deviation to mean value.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**Figure 3.** Radioluminescence response to the dose rate varied by fluence rate for three energies for Ce-doped (a) Gd-doped (b) and N-doped (c) fiber. The RL signals are normalized to the highest fluence rate at 61 MeV. Linear fits are plotted, and the slope coefficients are indicated together with the R² values.</figcaption></figure>

energy ($R^2 > 0.98$) although the slopes obviously depend on the proton energy. The linear slope coefficient increases with increasing energy. Hence these curves also indicate that the RL exhibits a decreased sensitivity at lower proton energies.

Figure 4 shows in particular the RL response of the N-doped fiber as a function of the dose rate at a proton energy of 61 MeV, for a larger range of dose rates. A linear fit of the measurement points
<figure><img src="image_7.png" /><figcaption>**Figure 4.** Evolution of the equilibrium RL intensity at very high dose rates in silica for the N-doped fiber, using a 61.3 MeV proton beam, logscales. Measurements are represented by symbols. A linear fit of the measurement points between 0.1 Gy s⁻¹ and 130 Gy s⁻¹ is shown. Residuals correspond to the relative deviation between the measurements and the linear fit.</figcaption></figure>

between 0.1 and 130 Gy s⁻¹ again demonstrates, with R² = 0.9984, the excellent linearity of the RL response over this range, which already encompasses the domain of medical irradiations under UHDR conditions.

## 3.2. Bragg peak measurements

The depth dose distributions obtained in the 63 MeV clinical continuous beam are shown in figure 5(a). The Bragg curve obtained for the different fibers were compared to the one measured with the diode BAS21, considered as a reference, the measured values are reported in 2. The difference between the range R₈₀ measured by the fibers and the diode was less than 0.2 ± 0.2 mm, for the three considered fibers (table 2). However, regarding the shape of the Bragg peak, an underestimation of the relative dose in the maximum dose region could be observed. Indeed, the peak-to-plateau ratios were calculated and were equal to 4.1 for the diode, 3.1 for the Gd-doped fiber probes, and 2.9 for the Ce- and N-doped fibers.

The undoped control fiber, irradiated at the same time, did not provide a signal level higher than that of the background noise, leading to the conclusion that no Cerenkov signal was detected at that energy.

The PDD obtained with the N-doped fiber in PBS irradiation at 100 MeV and 226 MeV are represented in figure 5(b). For comparison, we also present the curves measured point by point with a standard PPC05 IC which served as the reference dosimeter. The R₈₀ ranges measured at 100 MeV and 226 MeV are (77.3 ± 0.8) mm and (319.0 ± 0.8) mm, respectively. We obtain good agreement for the range and the position of the maximum, deviations from reference values being (0.3 ± 0.8) mm at 100 MeV and (1.1 ± 0.8) mm at 226 MeV. Regarding the shape of the Bragg peak, again an underestimation of the signal in the maximum region was observed. At 100 MeV, the peak-to-plateau ratio is 2.9 for the N-doped fiber compared to 4.3 for the PPC05 chamber, whereas at 226 MeV the ratio is 3.2 vs 4.0.
<figure><img src="image_8.png" /><figcaption>**Figure 5.** (a) Depth-dose profiles of a 63 MeV proton continuous beam deposited in a water phantom. (b) Depth-dose profiles built from RL measurements made with the N-doped fiber probe, the undoped fiber, and from the reference IC, for 100 and 226 MeV proton pulsed beam deposited in a water phantom. Curves are normalized to the entrance region of reference detector, except that associated with the undoped control fiber which is normalized with respect to the maximum of the curve built with the N-doped fiber.</figcaption></figure>

The signal produced in the control non-doped fiber was also measured to quantify the impact of the Cerenkov emission. It appeared that the latter had no impact on the 100 MeV Bragg curve, representing less than 1% of the signal given by the N-doped fiber. At 226 MeV, the signal measured with the undoped fiber is shown in figure 5(b), the curve is normalized with respect to the maximum of the doped curve to preserve the scale ratio. The luminescence level emitted from the control fiber is up to 20% of the maximum RL signal from the doped fiber and decreases with depth until a slight increase in the Bragg peak. In any case, the Cerenkov emission correction did not impact the range estimation.

The peak-to-plateau ratio appeared to be systematically lower than expected according to the reference curve. Differences in peak-to-plateau ratio should originate essentially from SQ (Birks 1964, Craun and Smith 1970, Torrisi 2000). The RL intensity from the N-doped fiber was plotted as a function of the mean LET in silica. The resulting curve, not shown here, was then fitted using Birks' equation. The Birk's constant $k_b$ and the secondary constant C were found as follows $k_b = (8.9 \pm 0.51) \times 10^{-3}$ cm MeV$^{-1}$, $C = (0.8 \pm 0.2) \times 10^{-5}$ cm$^2$ MeV$^{-2}$. Considering the silica density equals 2.22, the Birk's constant is, finally, $k_b = 1.97$ g MeV$^{-1}$ cm$^2$.

### 3.3. Real time response in a PBS irradiation and spot size estimation

Figure 6 shows the RL signal obtained under PBS irradiation for several integration times. This signal was characterized by an internal structure and an external envelope. The outer envelope could be described as three pseudo-Gaussian shapes of decreasing amplitude. Proteus® One delivered the total dose in three 'paintings' for each depth, described by the three peaks of figure 6. For the 100 MeV measurement, the relative doses for the 3 paintings were 64.0 %, 30.5% and 5.5% respectively. The internal structure consisted of a series of sharp peaks, passing relative intensity maxima, related to the pencil beam moving. Each sub-peak of the internal structure corresponded to the scanning of a line of spots (pencil beam positions), with the maximum RL response being proportional to the average flux falling on the fiber. This flux increased as the pencil beam approaches the fiber, reaching a maximum when the pencil beam is aligned with the fiber axis, and decreased as it moved away.

Figure 6(a) also shows the effect of the integration time of the photodetector on the real time signal. The gate times of 1 s and 200 ms are too large compared to the pseudo-period between sub-peaks, so the apparent structure is deteriorated. The temporally resolved measurements enabled an estimate of the scanning time along an axis, and by knowing the number of spots, the duration of a single spot could be computed. Under irradiation conditions with a 2 mm spot spacing, the duration of each spot (including both irradiation and movement) was measured at 12 ms. Thus, in practice, a 10 ms integration time provides the best signal-to-noise/sampling ratio. The temporal structure of the RL signal was strongly influenced by the choice of spot spacing. Indeed, the denser the plane coverage is, the more resolved this structure becomes, allowing for a more detailed analysis of the signal and finer characterization of the scanning. As an example, signal/dose ratio was calculated for the four plans with the same energy 100 MeV, the same field size $10 \times 10$ cm$^2$, with different spot spacings, and comparison was made using
<figure><img src="image_9.png" /><figcaption>**Figure 6.** Radioluminescence intensity over time during PBS irradiation, (a) response for different integration times, (b) focus on the first peak of the outer envelope with an integration at 10 ms with represented fit used for spot size analysis.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>**Figure 7.** Measured spot size as a function of depth for a 226 MeV beam, an integration time of 10 ms. Standard deviations are shown for each painting. The surface reference size was indicated.</figcaption></figure>

the 2 mm spot spacing plan used as a reference. The differences were (−1.8 ± 0.5) %, (−1.0 ± 0.5) % and (5.3 ± 0.5) % for the 4 mm, 6 mm and 8 mm spot spacing plans respectively.

The spot sizes have been estimated by extracting for each painting the maximum of each sub-peak and analyzing the envelope as shown in figure 6(b) for the first and most intense passage. The spot sizes obtained were (6.15 ± 0.08) mm, (4.50 ± 0.04) mm, and (3.30 ± 0.03) mm at 100, 150, and 226 MeV respectively. It is important to note that regardless of the considered painting, the estimated spot sizes were the same within 10%, which is in the tolerance of constancy suggested by Arjomandy et al (2019). These values have been compared to the spot sizes obtained with the Lynx 2D scintillator (IBA Dosimetry, Schwarzenbrück, Germany) at the same energies, which were (5.82 ± 0.3) mm, (4.26 ± 0.3) mm, and (3.19 ± 0.3) mm at 100, 150, and 226 MeV respectively. The maximum difference is thus 0.33 mm which falls within the measurement uncertainty range of the Lynx detector.

The spot size was estimated by the fiber in function of depth while acquiring the PDD and did not require additional irradiation. Figure 7 shows the measured spot size as a function of depth at 226 MeV, with 10 ms integration time. Only the reference measurement at the surface is represented for comparison. It is an unusual way to look at the spot size evolution depending on the residual energy of the protons in water.
<figure><img src="image_11.png" /><figcaption>**Figure 8.** RL signal obtained with a partially delivered beam, irradiation breaks during the first painting and restarts to deliver the remaining dose.</figcaption></figure>

### 3.4. Real-time quality assurance for PBS partial irradiations

Figure 8 shows an example of the RL signal measured during an irradiation of a 100 MeV single layer plan, which was interrupted during the first painting (referred to as partial 1 of plan A in table 3). The beam interruption occurred during the first painting. It can be observed that when irradiation resumed, the RL intensity started from an almost null level and not at the same level as before the interruption. This indicates that the beam did not resume at the position where it stopped, which is near the center of the field, but restarted over the beginning of the layer. The beam delivered a low dose to spots already irradiated, and then a higher dose from the position where the beam was interrupted to the end of the painting, which was consistent with the log-files information.

It is important to consider the total dose, as well as the relative dose of the three paintings. Tables 3 and 4 sum up for each irradiation the relative dose for each painting and the deviation from the reference total RL signal of the reference plan without interruption. For plan A, for both partials 1 and 2, interruptions occurred during the first painting and deviations were less than 0.5%, that is within the uncertainty range. It shows that despite the SQ, relative dose measurements with the N-doped fiber are reliable. The comparison of relative distributions indicates that the ‘overdose’ delivered during the first paintings due to its interruption and resumption is compensated by a reduction in the dose delivered during the subsequent two paintings, particularly the second painting. Thus, although the beam resumes scanning well before the interruption position, the system effectively regulates the dose delivered in each painting to compensate for the effect of the interruption and deliver the intended dose.

For plan B, partial 1 was interrupted once during the first painting. More than 90% of the total dose was then delivered in the first painting and the integrated intensity differed by less than 0.22% from reference. Partial 2 was interrupted once during the second painting and the interruptions did not result in additional visible particle passes since the third painting is not detectable. For both partial 1 and 2, regardless of the interruption position, the system compensated and ensured that the planned dose was delivered within less than 2%. The only exception was partial 3 with 4 interruptions, where the total signal deviation was approximately 2% higher than the reference, a value beyond the uncertainty margin.

The uncertainties were estimated based on the reproducibility of the analysis. Since the number of sub-peaks constituting each painting was reduced for this plan and the intensity was lower, the uncertainty increased. Furthermore, the multiplication of interruptions produced more fluorescence photons, which led to signal decay tails.

When looking at each painting measurement separately, for plan B, delivered in ‘clinical’ mode, we had access to log-files and could retrieve the dose delivered by each painting by summing the charge collected by the monitor chamber over all spots delivered, for both the reference and partial irradiations.

Information recorded in log-files confirmed the results of RL measurements: the beam did not necessarily resume at the position where it had stopped, but rather at the beginning of the irradiated layer, depending on the interruption position. We also analyzed the doses delivered at each painting, along
<table><caption>**Table 2.** Proton range in water for 63 MeV.</caption><thead><tr><th rowspan="2">Energy</th><th colspan="4">Range R<sub>80</sub> (mm)</th></tr><tr><th>N-doped fiber</th><th>Ce-doped fiber</th><th>Gd-doped fiber</th><th>Diode</th></tr></thead><tbody><tr><td>63 MeV</td><td>32.1</td><td>32.0</td><td>31.9</td><td>32.0</td></tr></tbody></table>

<table><caption>**Table 3.** Comparison between plan A delivered with interruption and the reference plan without interruption. Comparisons are presented for both the relative signal of each painting and the total signal.</caption><thead><tr><th>Irradiation</th><th>Relative signal<br/>painting 1</th><th>Relative signal<br/>painting 2</th><th>Relative signal<br/>painting 3</th><th>Total RL signal<br/>(deviation ± uncertainty)</th></tr></thead><tbody><tr><td>Reference</td><td>64.0 ± 0.5%</td><td>30.5 ± 0.5%</td><td>5.5 ± 0.5%</td><td>Ref</td></tr><tr><td>Partial 1</td><td>81.6 ± 0.5%</td><td>14.9 ± 0.5%</td><td>3.5 ± 0.5%</td><td>-0.48%</td></tr><tr><td>Partial 2</td><td>75.4 ± 0.5%</td><td>19.3 ± 0.5%</td><td>5.2 ± 0.5%</td><td>-0.13%</td></tr></tbody></table>

<table><caption>**Table 4.** Relative RL signal for each burst integrated during plan B irradiations, interrupted 0–4 times, along with the relative deviation of the total signal compared to the reference (without interruption). The values are sorted according to the corresponding interrupted painting. ‘N.D.’ (not detectable) indicates that no noticeable signal was detected after the interruption.</caption><thead><tr><th>Irradiation</th><th>Number of interruptions</th><th>Relative signal<br/>painting 1</th><th>Relative signal<br/>painting 2</th><th>Relative signal<br/>painting 3</th><th>Total RL Signal<br/>(deviation ± uncertainty)</th></tr></thead><tbody><tr><td>Reference</td><td>0</td><td>65.2%</td><td>30.1%</td><td>4.7%</td><td>Ref</td></tr><tr><td>Partial 1</td><td>1</td><td>52.4% + 39.2%</td><td>7.6%</td><td>0.8%</td><td>(0.22 ± 1.5)%</td></tr><tr><td>Partial 2</td><td>1</td><td>64.7%</td><td>30.5% + 4.77%</td><td>N.D.</td><td>(0.69 ± 1.5)%</td></tr><tr><td>Partial 3</td><td>4</td><td>0.9% + 61.4%<br/>+ 29.7%</td><td>7.3% + 0.7%</td><td>N.D.</td><td>(1.94 ± 1.5)%</td></tr></tbody></table>

with the deviations calculated relative to the measurements taken with the fiber. For reference, discrepancy was less than 0.5% between the values recorded by the system log files and those measured by RL. This confirmed that the fiber accurately measured the relative dose for each painting in an uninterrupted irradiation. For plans B, we observed a correlation between the RL fiber measurements and the log files, but the discrepancies are more significant, when considering painting by painting, particularly in the case with four interruptions (partial 3), as shown in table 4.

# 4. Discussion

## 4.1. RL signal and dose rate dependence

RL curves of figure 2 have the typical shape of RL signals, initial two-phase growth, equilibrium plateau, immediate decay after beam off, (Veronese et al 2017, Vidalot et al 2022b) showing that our fibers perform as expected and that the RL intensity at equilibrium can be used for measurements. This longer-term decay, which corresponds to phosphorescence, is due to the radiative recombination of those radiation-induced carriers that were previously trapped in shallow bandgap states but that are progressively released after irradiation. It is worth noting that such ‘shallow traps’ correspond to traps whose dwell times are of the order of the irradiation time (as a result, the fall time increases with the exposure duration and is not equal to the rise time). RL intensity was shown to be proportional to the proton beam dose rate up to 130 Gy s⁻¹ when the incident energy was fixed and the flux varied. We also expect linearity at higher dose rates for proton beams, as found by Vidalot et al (2022a) and predicted by theory (Grandvillain et al 2024), but the R&D beam line equipment would have to be adapted for verification at higher dose rates than the ones presented in this work. Nonetheless, the pre-irradiated fibers, particularly the nitrogen-doped fiber, met the key criteria for a detector: repeatability and linear sensitivity to fluence rate in conditions of ultra high dose rate proton therapy and high dose rate per pulse pulsed scanned protontherapy.

The proportionality between the steady-state RL response and the dose rate can be explained from basic arguments. Under irradiation, electron-hole pairs are both generated by the ionizing radiation and annihilated by recombination. Under the influence of these two antagonistic processes, elementary physics dictates that the pair density must tend towards a constant after a certain time (RL rise time), meaning that the recombination rate becomes virtually equal to the generation rate. The steady-state radiative recombination rate, which defines the equilibrium RL intensity, must then represent a constant fraction of the pair generation rate. However, this generation rate is necessarily proportional to the particle
fluence rate, and therefore to the dose rate absorbed to the material at a given particle energy (i.e. at a given water depth). In other words, the steady-state RL intensity must be proportional to the dose rate at any given energy. It is this basic and very robust property that we verify experimentally through the measurements reported in figures 3 and 4. The proportionality coefficient between the dose rate and the RL response, defined as the RL 'sensitivity' to the dose rate (i.e. the RL intensity per unit dose rate) is not degraded at very high fluence rate, contrary to what happens for ion chambers or diodes. It is however energy-dependent (only). As one can see in figure 3, it decreases with the proton energy, due to SQ (the study of this energy-dependence provides a proper intrinsic characterization of SQ).

## 4.2. Energy dependence of the RL signal and Bragg peak measurements

Since the response level of the RL equilibrium is linearly proportional to the fluence rate, this means that the difference in response for the same dose rate was due to energy dependence, related to the common effect of SQ (Luntz 1971, Archambault *et al* 2008, Wang *et al* 2012). Experimentally, this is demonstrated by peak-to-plateau ratios of Bragg peak measurements performed by the fibers, lower than the ones obtained with ICs. Figure 3. Birks constant value $k_b$ calculated in this study is consistent with the values found by Torrisi *et al* (2000) which is $k_b = 1.6 \times 10^{-2} \text{ cm MeV}^{-1}$ for a plastic scintillator and with the values reported by Hoehr *et al* (2019) which range between $1.6 \times 10^{-2} \text{ cm MeV}^{-1}$ and $3.5 \times 10^{-2} \text{ cm MeV}^{-1}$ for silica fiber.

SQ has already been reported for silica-based scintillators, but only through its impact in the shape of the Bragg peak in depth dose distribution measurements (Girard *et al* 2017, Savard *et al* 2018, Hoehr *et al* 2019). The results presented in figure 3 originally provides an intrinsic characterization of SQ since it allows isolating the energy dependence at constant fluence and dose rates (along Bragg curves, not only the proton energy varies with depth in water, but also the fluence and dose rates). The SQ appears to be intrinsic and does not seem to depend on the dopant. It is comparable to what affects other scintillator detectors used in clinical routine (Almurayshid *et al* 2017, Russo *et al* 2017), but some detectors are calibrated and corrected for LET effects (Robertson *et al* 2013). Further explanations of the SQ mechanisms will be published separately, based on the theoretical model we developed (Grandvillain *et al* 2024).

This energy effect is certainly an obstacle to the use of scintillators for absolute dosimetry in particle therapy, but the proportionality of the RL intensity to the fluence rate remains a crucial property when measurements are performed at the same energy.

Despite the fact that the RL from our silica fibers is significantly quenched at low proton energy, leading to an error in the assessment of the maximum dose, this does not alter the determination of the proton range. Indeed, the depth-dose curves built from the measurements made with radioluminescent fibers provide an integrated observable that is correlated to the proton range with, with submillimetric accuracy, of the proton range, despite the fact they are 'distorted' by SQ (which remains uncorrected here). We find a relative difference of less than 0.6% from reference values at three very distinct but representative energies (63, 100 and 226 MeV) measured on two different machines with different beam delivery systems. This finding may seem unexpected, since it is precisely at the Bragg peak that the SQ effect is most significant and the fiber response most affected. One should however keep in mind that the falling edge of the Bragg peak mainly reflects the abrupt drop in the proton fluence around their mean range. In this falling edge, where $R_{80}$ range values are estimated, the decrease in RL signal is governed primarily by the sharp drop in the proton fluence rate entering the dosimetric probe, much more than by the energy dependence of the detector's sensitivity. Therefore, the good agreement between RL-based estimates (uncorrected for SQ) and reference $R_{80}$ values should be considered evidence that the fiber scintillator is correctly probing the distal fluence drop-off, despite the sensitivity loss due to SQ, in monoenergetic condition. This supports the potential use of the fibers for routine energy constancy checks.

## 4.3. Cerenkov emission

The signal from undoped fiber came from multiple sources of luminescence, composed not only of Cerenkov light but also of fluorescence (RL) and phosphorescence from the silica matrix it-self (Veronese *et al* 2013). In our conditions, Cerenkov light was essentially due to the delta electrons set in motion by protons. As mentioned in section 2, electrons must have an energy greater than 190 keV to generate Cherenkov radiation. This could be the case only if the proton energy is greater than 84 MeV. The very low luminescence from the undoped fiber under 63 MeV protons was consistent with the absence of Cerenkov radiation. It should be mentioned that some studies showed Cerenkov radiation from indirect interactions, such as non-elastic nuclear interactions (Helo *et al* 2014). The setup used in the present study may not be sensitive enough to discriminate this weak emission from the noise. At
higher proton energies (100–226 MeV), Cerenkov emission occurred in our fibers but it weakened as protons lose energy while penetrating deeper into water. The fact that the luminescence measured from the undoped silica probe well decreased suggested that the Cerenkov emission by delta electrons dominated the weak scintillation produced by the undoped silica fiber close to the water surface. Once proton energy dropped below 84 MeV, from a depth of ~28 cm for protons penetrating water at 226 MeV (see figure 5(b)), Cerenkov emission became negligible. Beyond this depth, the remaining spurious emission mainly came from the RL of the undoped silica matrix, thus explaining the small Bragg peak formed in figure 5(b), (green curve corresponding to the undoped silica fiber). When measured by silica scintillators, the Bragg peak was thus virtually not affected by Cerenkov emission and was made up almost entirely of RL. This reminds us that Cerenkov detectors are not suitable for measuring PDD, as already highlighted by simulations of Cerenkov radiation in plastic fiber conducted by Christensen et al (2018) and Darafresh et al (2017).

## 4.4. Real time response to a PBS

The silica-doped fibers enable a real-time acquisition of the RL intensity with high temporal resolution of the pulsed scanned irradiation of the proton beam. It is possible to visualize the three paintings of the irradiation and estimate the relative dose of each in real time, which is not readily achievable with classical detectors. However, the temporal structure of the RL signal cannot resolve individual 8 µs pulses, as achieved by Shen et al (2024). This is due to the rise time of RL, of the order of 1 ms, which is too long to offer sufficient sensitivity to a single pulse.

For the same irradiation plan delivered continuously, this distribution appears to be repeatable (with less than 0.5% deviation), allowing for consistency checks with the fiber detectors. The internal structure of the signal can be directly correlated with the scanning of the spots. Our interpretation of the time response of the pulsed PBS of the Proteus®One, is near to that made by Veronese et al (2010) and Christensen et al (2018) on different devices. The spot size can be easily estimated from RL measurements, by analyzing the painting's envelope. Unlike in Christensen et al (2020), where the width at half-height is directly considered the spot size, the standard deviation is extracted here from a non-Gaussian shape of the beam. This correction takes the geometry of our detector into account. The efficiency is not contingent upon the specific painting under consideration, which consolidates the measurement. The fiber sensor seems well adapted to measurement of spot size for beam quality assurance of PBS offering to measure simultaneously the spot size and the PDD.

## 4.5. Quality assurance of partial irradiations of PBS proton beams

Concerning the spot spacing impact on the RL measurements, the difference on the signal/dose ratio seems acceptable for the plans at 4 mm and 6 mm spacing, indicating like in Veronese et al (2010) that the system may allow for the measurement of the total dose at a single point independently of the irradiation sequence. However, spot spacing appears to affect central dose estimation when spots are located too far from the fiber. This could be exacerbated by an error in fiber placement.

Regarding partial irradiations, the results obtained with the fibers made it possible to verify beam resumption and accurate dose delivery. Our detector allows for the real time monitoring of the system dose delivery compensation in a simple case of a mono-energetic plan with constant spot spacing and dose/spot with a single interruption, but also for more complex cases involving multiple interruptions at different paintings. Our detector also appears to be suitable in the case of a simple poly-energetic plan. The measurement accuracy could certainly be improved with an automated analysis process. This verification is crucial for PBS beams, as it ensures that the correct dose is delivered to the intended location, regardless of the number of interruptions during the scanning process, as controlled by the 'end effect' test described in the TG-224 (Arjomandy et al 2019).

The difference obtained between the fiber measurement and the information contained in the log-files is likely due to the fact that the fiber is centered in the irradiation field and does not detect well the spots at the field edges. Therefore, when irradiation resumes at the beginning of a painting after an interruption, the centered fiber detects it too poorly, whereas it is correctly recorded by the system log-files. The use of multiple fiber probes in a 2D network could be a solution.

ICs and customary scintillators do not allow for real-time visualization of painting and interruption. Thus, fiber could offer an innovative solution for in vivo dosimetry to ensure accurate treatment delivery regardless of the number of beam interruptions. Such detectors may also give dosimetry information like IC (Mossahebi 2020, Spruijt et al 2024) All of this could make the silica-doped fibers detectors suitable to log-files QA (energy, spot size, relative dose, real-time measurements).
## 5. Conclusion

In this study, we demonstrated that scintillating silica fiber could be used at high dose rates, and could be considered as detectors for quality assurance in proton therapy, particularly for PBS (simultaneous range and spot size measurements), and for real-time beam monitoring in the context of beam interruptions. To summarize, this work shows that:

* Radioluminescent silica fibers have a linear response in function of dose rate at fixed energy up to at least 140 Gy s⁻¹, with a constant sensitivity.

* These detectors provide precise range measurement (with more than 1.1 mm accuracy) for continuous and high dose rate per pulse pulsed scanned proton beams from 63 MeV to 226 MeV, despite SQ, which will be investigated in a separate further work.

* We proposed an innovative characterization of important beam parameters (relative dose distribution, irradiation time, spot size) along with PDD measurements, i.e. without requiring additional protocols or complex post-processing. Note that the real-time measurement allows for extracting the spot size with an almost point-like detector (diameter of the sensitive volume much smaller than the spot). Discrepancies between reference 2D scintillator values and fibers measured values of spot size are below 0.3 mm.

* Fibers are able to detect beam interruptions and variations in irradiation plans (below 2% deviations for relative dose measurements), paving the way for real-time beam monitoring and for more robust and independent quality assurance processes.

It has been shown that silica fibers are tissue-equivalent for the clinical energy range, do not need an applied voltage, have a good sensitivity maintained at high dose rates, and are miniaturized, offering an economical and efficient alternative to traditional volumetric detectors. Although they are almost point detectors, we showed that they could provide information that can be correlated with data from system log-files, and if used in a 2D network distributed on the field, they could be potential detectors for log-files QA, enhancing the reliability of proton therapy treatments.

## Data availability statement

The data cannot be made publicly available upon publication because they are not available in a format that is sufficiently accessible or reusable by other researchers. The data that support the findings of this study are available upon reasonable request from the authors.

## Acknowledgment

This work has been conducted in the framework of the FIDELIO project funded by the French Research National Agency (ANR) under Grant #ANR-20-CE19-0024. In the context of FIDELIO, Gd- and Ce-doped fiber were produced by the Laboratory Physics of Lasers Atoms and Molecules from University of Lille, at the FIberTech platform.

## Appendix

### A.1. Extraction of the spot size

The proton flux 'falling' on the silica fiber probe is obtained by integrated equation (1) over the entire surface of the fiber. In the case of a probe situated at the center of the irradiation field with side a, of length L and diameter d (diameter of the sensitive volume), the mean flux is expressed as a function of the coordinates (x₀, y₀) of the spot in the field:

$$ \bar{\Phi}(x_0, y_0) = \frac{\Phi_0}{Ld} \times \left( \int_{-\frac{a}{2}}^{\frac{a}{2}} \int_{-\frac{d}{2}}^{\frac{d}{2}} \exp \left[ \frac{-(x-x_0)^2 + (y-y_0)^2}{2\sigma^2} \right] dx dy \right). \quad (2) $$

Equation (2) leads to the following expression for the mean proton flux on the fiber:

$$ \bar{\Phi}(x_0, y_0) = \frac{\Phi_0 \sigma^2 \pi}{2Ld} \times \left[ \erf\left(\frac{a+d-2x_0}{2\sqrt{2}\sigma}\right) - \erf\left(\frac{a-d-2x_0}{2\sqrt{2}\sigma}\right) \right] \times \left[ \erf\left(\frac{a+L-2y_0}{2\sqrt{2}\sigma}\right) - \erf\left(\frac{a-L-2y_0}{2\sqrt{2}\sigma}\right) \right]. \quad (3) $$
This average flux goes through a relative maximum when $x_0 = a/2$, that is when the spot passes at the center of a line (it is then in line with the fiber probe center). This flux maximum depends on the vertical position $y_0$ of the line according to:

$$ \overline{\Phi}_{\text{subpeak}}(y_0) = \frac{\Phi_0 \sigma^2 \pi}{2Ld} \times \text{erf}\left(\frac{d}{2\sqrt{2\sigma}}\right) \times \left[\text{erf}\left(\frac{a+L-2y_0}{2\sqrt{2\sigma}}\right) - \text{erf}\left(\frac{a-L-2y_0}{2\sqrt{2\sigma}}\right)\right]. \quad (4) $$

The relative maxima of the RL intensity (height of the sub-peaks in the internal structure of the time-resolved signal) are a priori proportional to this flux. They increase as the line ordinate $y_0$ approaches the center of the field and decrease when it moves away from it.

To link temporal data to spatial coordinates, it is necessary to measure the period of time $T$ separating two successive sub-peaks in data. During this period, the spot has crossed the half field twice (distance $2 \times a/2$) and one vertical spot spacing $p$. Thus, the scan speed is: $v = \frac{a+p}{T}$. The time $t_{max}$ at which the experimental envelope reaches its absolute maximum corresponds to the line at $y_0 = a/2$. Therefore, the vertical line position $y_0$ in equation (4) can be converted into the proper time scale, whatever the origin of the time axis in data, by writing:

$$ y_0(t) = \frac{a}{2} - \frac{p}{T}(t - t_{\text{max}}). \quad (5) $$

Plotting the RL external envelope passing through the subpeak maxima and fitting this curve to equation (4) ($y_0$ being given by equation (5)) allows us to obtain spot standard deviation $\sigma$.

## ORCID iDs

Marjorie Grandvillain ID 0000-0002-5240-2947

Franck Mady ID 0000-0002-7265-9870

Petter Hofverberg ID 0000-0002-3316-5931

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