Dosimetry of ultra-high dose rate electron beams using thermoluminescence and optically stimulated luminescence detectors

Objective. The aim of this work is to investigate the dose rate dependence of thermoluminescence and optically stimulated luminescence detectors (TLDs and OSLDs) in a wide uniform ultra-high dose rate electron beam and demonstrate the potential use of TLDs and OSLDs to correct the ion recombination in air-filled ionization chambers. This study avoids previously reported complications related to the field size and homogeneity. Approach. Two types of OSLDs (BeO and Al2O3:C) and three types of TLDs (LiF:Mg,Ti, LiF:Mg,Cu,P, CaF2:Tm) were irradiated simultaneously in a uniform 16 MeV electron beam generated by a clinically decommissioned C-Arm LINAC, modified to deliver doses per pulse between 8.3 × 10−4 Gy and 1.255 Gy, corresponding to instantaneous dose rates between 2 × 102Gy s−1 and 3 × 105 Gy s−1. A prototype ultra-thin parallel plate ionization chamber was employed as reference detector. Main results. Reproducible results were achieved both at conventional (standard deviation of the data <2%) and at the highest dose per pulse (standard deviation of the data <4%). No trend in the dose rate response of the TLDs and OSLDs was observed in the investigated dose per pulse range. The Al2O3:C OSLD was found to be the most precise detector, with a standard deviation of the data <2% at all investigated dose rates and dose levels. Significance. The dose rate independence of the investigated TLDs and OSLDs make them good candidates for dosimetry at ultra-high dose rates, at least up to 3 × 105 Gy s−1. A dose rate independent method to measure the dose per pulse is proposed, which can be applied to characterize ultra-high dose rate electron beams and correct for ion recombination in ionization chambers.


Introduction
The increasing use of ultra-high dose rate (UHDR) beams has created new challenges for dosimetry and metrology (Schüller et al 2020, Romano et al 2022), as the detectors most commonly used are affected by saturation effects when operating at high dose per pulses (Petersson et al 2017, Di Martino et al 2020).Biological and clinical experiments in those conditions (e.g., for the implementation of FLASH radiotherapy) require nonetheless a precise knowledge of the delivered dose, and this constitutes a major challenge for metrologists and dosimetrists.In particular, this has led not only to the development of new detector technologies (Marinelli et al 2023, Romano et al 2023), but also to the improvement of existing detectors, such as ionization chambers, the 'gold standard' of radiotherapy reference dosimetry (IAEA 2000).
Ionization chambers used at UHDR still require large correction factors for ion recombination, thus yielding larger uncertainties (Petersson et al 2017, McManus et al 2020).An example of the procedure used to evaluate such correction factors can be found in Petersson et al (2017), where they proposed an empirical methodology to evaluate the ion recombination correction factor of an air-filled chamber comparing the signal of the ionization chamber with dose measurements performed with alanine detectors.This approach could, in principle, be used in combination with any other type of dose-rate independent detector.Several solutions have been proposed in the literature to minimize the effect of the decreasing ion collection efficiency in ionization chambers when exposed to UHDR beams (Kranzer et al 2021, Di Martino et al 2022).For example, Gómez et al (2022) developed an ultra-thin parallel plate ionization chamber, suitable for UHDR dosimetry due to its lower ion recombination, based on the principle that a reduced electrode distance improves the ion collection efficiency (Kranzer et al 2021(Kranzer et al , 2022)).
Amongst the detectors used for medical dosimetry, thermoluminescence and optically stimulated luminescence detectors (TLDs and OSLDs) are of interest for passive dosimetry of UHDR beams.They show a wide dose linearity range, high precision and accuracy when specific protocols are used (Yukihara et al 2008, Motta et al 2023c), and their small size make them suitable for in vivo dosimetry.Furthermore, compared with alanine detectors, the readout of luminescence detectors is less time-consuming.
Several TLDs and OSLDs were demonstrated to be dose rate independent in photon (Jursinic 2007, Zorloni et al 2020), electron (Karsch et al 2012, Motta et al 2023a), and proton beams (Christensen et al 2021, Motta et al 2023b), indicating their suitability for UHDR dosimetry.For example, TLDs and OSLDs were used to support radiobiological experiments for FLASH radiotherapy (Jorge et al 2019, Christensen et al 2021), and TLDs were used for cross validation of UHDR beams (Jorge et al 2022).The experimental evidence that such luminescence detectors are dose rate independent is in contrast with theoretical studies that point to the possibility of dose rate effects (Chen and Leung 2001).Such models, however, are purely mathematical and not based on experimental data of a specific material.
Recently, Motta et al (2023a) showed that the extent of the TLD and OSLD dose rate independence in a UHDR electron beam was significantly affected by the dose delivery uncertainties, e.g., beam uniformity and reference dosimetry.In that experiment, irradiations were carried out with a beam showing a maximum 10% variation over 4 cm along one direction perpendicular to the beam.Such beam non-uniformity resulted in a variability of the TLD and OSLD measured dose as high as ∼20% over a matrix of 24 detectors at the highest dose rate.This effect had to be distinguished from possible dose rate effects, rendering a definitive conclusion on the presence or absence of dose-rate effects challenging.
In Motta et al (2023a), the authors also observed an unexpected decreasing response up to 6% for Al 2 O 3 :C OSLDs at increasing dose rate (>190 kGy s −1 ).As Al 2 O 3 :C used as an OSLD was shown to be the most precise material for dose assessments, additional experiments were needed to confirm or refute such result.
Therefore, this study aims to investigate further and better constraining the dose rate dependence of various luminescence detectors (LiF:Mg,Ti, LiF:Mg,Cu,P, CaF 2 :Tm, BeO, Al 2 O 3 :C) by minimizing the uncertainties associated with the beam delivery relative to the previous study.In this worka different accelerator was used to provide a more uniform field with flatness <5% for a 10 cm × 10 cm field (Dal Bello et al 2023).Indeed, when dealing with a uniform beam, the uncertainty of the TLD and OSLD dose measurement would be only affected by the intrinsic response variability, and not by the beam uniformity, allowing us to confirm or refute previous results from Motta et al (2023a).Additionally, we investigated the application of the TLDs and OSLDs to estimate the correction for ion recombination in an air-filled ionization chamber at UHDR, similarly to the work carried out by Petersson et al (2017).For the electron irradiations, the materials were packaged in a 3D-printed holder, containing four detectors of each detector material, as shown in figure 1.The 3D-printed holder, made of polylactic acid (PLA, polyester with a density of 1.24 g cm −3 ), was designed with a diameter of 43.5 mm and a thickness of 10 mm to fit the insertion in the phantom used in the experiment (figure 1).A 1-mm thick PLA layer was used as a cover.

Materials and methods
After irradiation, the packages were kept in light-tight bags and handled under subdued red light conditions to avoid a light-induced loss of the OSL signal.The TLDs and OSLDs were read out one week after irradiation using two available lexsyg smart TL/OSL automated readers (Freiberg Instruments GmbH, Freiberg, Germany).
LiF:Mg,Ti and CaF 2 :Tm TLDs were heated at a constant heating rate of 5 °C s −1 up to a maximum temperature of 400 °C.LiF:Mg,Cu,P TLDs were heated up to 240 °C with a heating rate of 1 °C s −1 .The TLD  Al 2 O 3 :C OSLDs were read using the continuous-wave technique (CW-OSL), stimulating the detectors for 300 s using constant-irradiance green LEDs (60 mW cm −2 , 525 nm).The linear modulation technique (LM-OSL) was used for BeO, using linearly increasing irradiance blue LEDs (max.80 mW cm −2 , 458 nm) for 240 s.The LM-OSL technique was employed to reduce the maximum luminescence intensity to be measured and, thereby, extend the measurable dose range for the available hardware (detection filters and photomultiplier tube).The OSL signal was calculated as the integral of the OSL curve, after background subtraction.A constant background was used for CW-OSL and a linearly increasing background was used for LM-OSL.
The readout protocol used the readers' 90 Sr/ 90 Y beta sources to individually correct the detector response for differences in sensitivity (Yukihara et al 2008, Motta et al 2023c).The electron beam-irradiated TLD or OSLD was first stimulated to record the signal S, then irradiated with the built-in source for a duration t R , after which the S R signal was measured.The resulting S/S R signal was hence calculated and, upon calibration, used to estimate the doses.
The reference time t R was chosen depending on the material and the dose level to be measured (∼0.8 Gy or ∼10 Gy), as described in Motta et al (2023c).For Al 2 O 3 :C and BeO OSLDs, t R was chosen such that the reference dose D R is larger than the dose to be measured D, to minimize sensitization effects (Yukihara et al 2005(Yukihara et al , 2008(Yukihara et al , 2016)).For LiF:Mg,Cu we chose D R > D to minimize the effect of the high temperature residual on the S R TL curve after high-dose irradiation (Motta et al 2023c).Finally, D R < D was used for LiF:Mg,Ti and CaF 2 :Tm as no sensitization effects were reported in these materials (Motta et al 2023c).The used t R and corresponding reference dose D R values are reported in table 1, together with the used optical filters.As two levels of doses were delivered, two filter combinations were used for all detectors except Al 2 O 3 :C OSLDs, to prevent the photomultiplier tube saturation.
Accordingly, two calibration curves were obtained for each material: one for the low dose range ∼0.3 Gy-2.1 Gy, and one for the high dose range ∼6 Gy-13 Gy.The use of a low dose calibration curve and a high dose calibration curve was needed as the resulting large differences in photon counts between low dose and high dose required adjustment of the readout unit (e.g., filters, readout parameters).The detector type-specific S/S R calibration curves were determined using the built-in beta sources by irradiating bleached/annealed detectors at various irradiation times and following the procedure illustrated in Motta et al (2023c), with the reference time t R listed in table 1. Examples of S/S R calibration curves for the investigated materials can be found in Motta et al (2023aMotta et al ( , 2023c)).The calibration coefficients, to convert from source irradiation time to absorbed dose to water, were calculated based on the detector signal S/S R and the delivered absorbed dose to water at conventional dose rate in the electron field.The instantaneous dose rate, namely the dose rate within a single pulse, was varied by changing the dose per pulse (DPP), keeping the pulse duration constant.Seven beam configurations were employed, providing the DPPs listed in table 2. The dose control was carried out by monitoring the number of delivered monitor units (MU) at DPP = 8.3 × 10 −4 Gy (conventional dose rate), or the number of delivered pulses in the UHDR configurations (Dal Bello et al 2023).The delivered doses were ∼0.8 Gy or ∼10 Gy.The conventional dose output was calibrated providing an output of 1 Gy = 1 MU at D max , according to the Recommendation No. 10 of the Swiss Society of Radiobiology and Medical Physics ( Haerle 2019).The seven beam configurations used in the study were achieved by varying the following LINAC parameters: grid tension of the electron gun, radiofrequency driver power output, and time delay between gun and radiofrequency driver pulses (Dal Bello et al 2023).
The DPPs provided in table 2 refer to measurements at the isocenter (source-surface distance = 100 cm), with a 10 cm × 10 cm electron field collimated by the primary LINAC jaws and the electron applicator.The measurements were carried out with an Advanced Markus chamber (T34045, PTW-Freiburg GmbH, Freiburg, Germany) and Gafchromic EBT3 films (Ashland ISP Advanced Materials, Kearny, NJ, USA) at 3 cm depth in a water-equivalent slab phantom (RW3, PTW-Freiburg GmbH, Freiburg, Germany).More details about the DPP determination can be found in Dal Bello et al (2023).The upper limit of the uncertainty for the DPP determination is estimated to be 5% (k = 1), with a traceability chain to the primary standard laboratory METAS at which a reference detector was calibrated at conventional dose rates.The ionization chamber operated with a +300 V polarizing voltage and was connected to a UNIDOS electrometer (T10022, PTW-Freiburg GmbH, Freiburg, Germany).To correct for ion recombination effects in the ionization chamber, the correction factor k s was calculated using the logistic model where U is the chamber polarizing voltage and the fitting parameters were extracted from Petersson et al (2017) (table 2, γ = 3.1, δ = 0.180).The TLDs and OSLDs irradiations were carried out with a 10 cm × 10 cm field and the 3D-printed package at 3 cm depth in the RW3 phantom.Additionally, in the second irradiation session, an ultra-thin parallel plate ionization chamber prototype (UTIC, PTW-Freiburg GmbH, Freiburg, Germany) was placed off-axis on the beam applicator and used as reference detector due to its negligible ion recombination (Gómez et al 2022).A +300 V polarizing voltage was applied to the UTIC.

Results and discussion
3.1.TLD and OSLD response at conventional DPP The TLD and OSLD response at conventional DPP was investigated for two dose levels, one package at 0.8 Gy and two packages at 10 Gy.The ratio of the TLDs and OSLDs measured dose and the delivered dose is plotted in figure 2. It is important to note that at conventional DPP we could not evaluate the detectors accuracy, as these irradiations aimed at determining the detector calibration coefficients and, therefore, this ratio is expected to be unity.
The results in figure 2 show that, except for Al 2 O 3 :C OSLDs, the standard deviation of the mean for the four dosimeters in the same package increases with the dose.The TLD and OSLD standard deviation of the mean is lower than 1% at 0.8 Gy, in agreement with previous results (Motta et al 2023c), whereas it increases to up to 3% for CaF 2 :Tm at 10 Gy.Such effect is attributed to sensitization effects, which may not have been completely cancelled out by the S R normalization and calibration curves.Specifically, at high dose, the deep trap filling results in a reduced sensitization caused by the reduced competition for stimulated electrons by deep traps and other recombination centers.The S R normalization cancels sensitivity changes in the material if all detectors have the same behavior with dose history, which may not be the case here.Except for Al 2 O 3 :C OSLDs, the other TLDs and OSLDs have been extensively re-used before and, therefore, one cannot guarantee that their sensitization behavior remains identical, even if they belonged to the same batch.The irradiation and heating history of the BeO OSLDs and the TLDs might affect their sensitivity, whereas the Al 2 O 3 :C OSLDs are from the same batch and were not used before.
The reproducibility of the measurement at 10 Gy, indicated by the standard deviation of the two packages, is better than 2%, with a minimum of 0.1% for BeO OSLDs.

TLD and OSLD response at the highest DPP
At the highest DPP = 1.255Gy, the TLD and OSLD packages were irradiated with 1 and 8 pulses, to investigate the detectors and the beam delivery reproducibility at two dose levels.The session-to-session reproducibility was also studied with a single delivered pulse.
The TLD and OSLD measured doses, divided by the number of pulses, are plotted in figure 3 for each material.Figure 3 shows that results with a reproducibility better than 4% (standard deviation of the data) are achieved with the TLDs and OSLDs irradiated in various conditions, i.e. total dose and irradiation day.Within the uncertainties (k = 1), no variation in the detector response with the session and with the number of pulses is observed, with a maximum deviation from the average value of −4% measured by LiF:Mg,Cu, P TLDs.
In agreement with the results at conventional DPP (figure 2), figure 3 shows that the package precision, namely the standard deviation of the mean of the four detectors, depends on the dose, being better than 1.5% at low dose (1 pulse) and better than 3% at high dose (8 pulses).The Al 2 O 3 :C OSLDs were the most precise detectors, with a standard deviation of the mean <1% at the two dose levels, as already shown in other studies (Yukihara et al 2008, Motta et al 2023c).
Due to the achieved precision of each package, the measurement reproducibility, quantified by the standard deviation of the packages irradiated in the same conditions (i.e.irradiation session and number of pulses), is <1.5% at 1 pulse, whereas it increases to <3.5% at 8 pulses.Comparable reproducibility results were achieved by Al 2 O 3 :C OSLDs for the two dose levels.

TLD and OSLD dose rate response
The TLD and OSLD dose rate response was investigated by means of the ratio between the detector measured dose and the UTIC measured charge at the different DPPs.The results are plotted in figure 4, where each point was normalized to the average of the six or seven packages.In this study, we considered only the TLDs and OSLDs uncertainties to focus on the precision achievable with these detectors.
No trend in the response of the studied TLDs and OSLDs was found in the investigated DPP range, indicating a dose rate independence, which confirms our previous results (Motta et al 2023a).This corresponds to a maximum 3% band for LiF:Mg,Ti and a minimum 1.5% for both CaF 2 :Tm and Al 2 O 3 :C.
A maximum deviation from the average value of −6% was measured by BeO OSLDs at a DPP of 0.934 Gy, with a large uncertainty of 4.4%.However, the repeated measurement with BeO OSLD at this DPP did not show such discrepancy.Upon further investigation of the BeO OSL curves, its was found that one OSLD exhibited an anomalous OSL curve, with a large offset of the peak intensity position.Such feature is attributed to the fact that the OSLD erroneously may come from a higher sensitivity batch.If the anomalous BeO OSLD were to be excluded, the standard deviation of the mean would reduce to 3.6% and the deviation to the average value to −2%.
Contrarily to our previous study (Motta et al 2023a), no trend in the Al 2 O 3 :C OSLD response was measured with increasing dose rate.This is also demonstrated in figure 5, where the data were fitted with a constant and a linear model, whose Akaike information criterion (AIC, Akaike (1974)) values are provided in the figure legend.Given the smaller AIC of the constant model, we can conclude that the constant model better reproduce the experimental data.As already observed in figure 2 and figure 3, Al 2 O 3 :C OSLDs are the most precise detectors with a standard deviation of the data better than 2% at all dose rates.The dose rate independence and the high precision of Al 2 O 3 :C OSLDs make them the most suitable detector for passive dosimetry of UHDR beams.

Estimation of k s
The Advanced Markus chamber was used for an independent determination of the delivered dose.Nevertheless, it requires the application of an ion recombination correction factor, k s .Usually, this factor is derived from empirical models, such as presented in Petersson et al (2017) (see equation (1)).Given the demonstrated dose-rate independence of luminescence detectors in electron beams, here we propose to combine the TLD and OSLD measured dose per pulse with the Advanced Markus chamber data to experimentally estimate k s .
To determine the chamber correction factor, we used data collected in an independent measurement session, where three beam configurations (i.e.DPPs) were used.A different number of pulses was also delivered compared to the TLDs and OSLDs irradiations.To improve the methodology used here, one would need to irradiate the ionization chamber and the TLDs and OSLDs with the same beam parameters (e.g., number of delivered pulses).For each beam configuration, k s values were calculated as the ratio between the TLD and OSLD measured DPP and the chamber dose per pulse, uncorrected for ion recombination.facility (see section 2.2).The relative difference between the TLDs and OSLDs based k s and the logistic model is also included in figure 6.
Except for two outliers (BeO OSLD at 170 mGy and LiF:Mg,Cu,P TLD at 356 mGy), the k s calculated from the different detectors DPPs are in agreement within the experimental uncertainties.
Compared to the logistic model, a maximum deviation of +3% is measured at 170 mGy and −5% at 740 mGy.Such difference can be due to the dependence of the model parameters on the chamber specification and on the beam parameters.For example, the pulse width was 1.8 μs in the parametrization performed by Petersson et al (2017), whereas 4.2 μs in the current study.Therefore, a longer pulse duration might result in a lower ion recombination and hence a smaller k s .If the logistic model with the parameters from Petersson et al (2017) has to be used to determine the correction factor of the USZ Advanced Markus chamber, a 5% uncertainty (k = 1) on k s needs to be included.Alternatively, the values of k s based on TLDs and OSLDs measurement can be fitted with a logistic model, whose fitting parameters can be determined specifically for the used chamber and the used beam.Due to the highest precision, the k s estimated from the Al 2 O 3 :C OSLDs DPP are plotted in figure 7, together with the fitted logistic model (dotted line) and the logistic model with Petersson's parameters (solid line).Figure 7 shows the different trend of the two logistic models, specifically at the highest DPP.The k s fitted curve based on Al 2 O 3 :C OSLDs can be used to correct the response of the USZ Advanced Markus chamber.A similar approach can be applied to other facilities, or other beam configurations.

Conclusions
All five investigated TLDs and OSLDs were found suitable to support dosimetry of UHDR electron beams, as none of the materials showed dose rate effects in the investigated dose rate range, between 2 × 10 2 Gy s −1 and 3 × 10 5 Gy s −1 .This achievement confirms the results obtained in a different facility, which underlines the relevance of this work.Indeed, for UHDR beams, the beam properties variability in a facility or even from one facility to another might strongly influence the achievable results.This makes achieving reproducible results challenging.
Among the investigated materials, Al 2 O 3 :C OSLD was demonstrated to be the most precise detector in the studied dose rate and dose ranges, with a standard deviation of the data better than 2%.Al 2 O 3 :C OSLDs were subsequently used to map the ion recombination of the USZ Advanced Markus chamber in the specific UHDR electron beam.
Therefore, we demonstrated two applications of luminescence detectors for UHDR dosimetry of pulsed electron beams: (i) to determine the reproducibility of the beam delivery, and (ii) to resolve the ion recombination correction in ionization chambers at ultra-high dose rates.
dosimetric signal was obtained by fitting the TL curves with first-order peaks (Randall et al 1945, Horowitz and Yossian 1995) and calculating the area under specific peaks, as indicated in table 1 (Motta et al 2023c).

Figure 1 .
Figure 1.(a) 3D-printed holder containing the investigated TLDs and OSLDs.(b) The holder was inserted in the water-equivalent slab phantom for the irradiations with electron beams; additional slabs were placed on top of the package for measurements at 3 cm depth.(c) The electron beam applicator determines the beam size.

Figure 2 .
Figure 2. Comparison between the TLDs and OSLDs measured dose and the delivered dose at conventional dose per pulse (DPP = 8.3 × 10 −4 Gy), for two dose levels.Each point denotes the average of four detectors per material in a package, whereas the error bars indicate the standard deviation of the mean.The colored solid line represents the average of the three packages.The reported sigmas are the standard deviations of the packages irradiated under the same conditions.
The obtained k s values are plotted in figure 6 as a function of the chamber dose per pulse, uncorrected for ion recombination.The figure also includes the k s curve based on the logistic model with the parameters proposed by Petersson et al (2017) (equation (1)), which was used to determine the reference delivered dose in the USZ

Figure 3 .
Figure 3.The measured TLDs and OSLDs dose per pulse for two irradiation sessions at the highest dose rate (DPP = 1.255Gy).The number of pulses in the second session was varied, as indicated by the numbers on the data points.Each marker represents the average of four detectors per material in a package, while the error bars indicate the standard deviation of the mean.The colored band denotes the one standard deviation band around the mean, indicated by the colored line and used for the data normalization.

Figure 4 .
Figure 4. TLDs and OSLDs measured doses normalized by the charged collected in the ultra-thin ionization chamber.Each point denotes the average of four detectors per material in one package and the error bars indicate the standard deviation of the mean.The colored band denotes the one standard deviation band around the mean, indicated by the colored line and used for the data normalization.

Figure 5 .
Figure 5. Al 2 O 3 :C OSLD measured doses normalized by the charge collected in the ultra-thin ionization chamber, as in figure 4(d).The data points were fitted with a constant and a linear fitting model, where each fit quality is evaluated by the Akaike information criterion (AIC, Akaike 1974) given in the legend.

Figure 6 .
Figure 6.Ion recombination correction factor k s of the used Advanced Markus chamber based on dose per pulse measurements with TLDs and OSLDs.The black line denotes the logistic model (equation (1)) with parameters from Petersson et al (2017).

Figure 7 .
Figure 7. Ion recombination correction factor k s of the used Advanced Markus chamber based on dose per pulse measurements with Al 2 O 3 :C OSLDs.The black solid line denotes the logistic model with parameters from Petersson et al (2017), whereas the black dotted line indicates the logistic model fitted to the experimental data.In the model, the dose per pulse (DPP) is given in mGy and a +300 V polarizing voltage U was considered.

Table 1 .
Properties, preparation, readout technique, and readout parameters of the detectors used in this study.t R is the reference irradiation time with the reader source used in the protocol, as described in the text, and D R is the corresponding reference dose.When two filters or two t R values are provided, the first rowrefers to the readout after ∼0.8 Gy irradiation and the second rowto the ∼10 Gy irradiation.

Table 2 .
Beam parameters for the TLDs and OSLDs irradiations.The number of pulses was changed to deliver the same dose levels (∼0.8 Gy or ∼10 Gy).
a At DPP = 8.3 × 10 −4 Gy s −1 the number of monitor units was changed to deliver the desired dose level.