Dual-storage phosphor proton therapy dosimetry: simultaneous quantification of dose and linear energy transfer

Abstract

Purpose:

To investigate the feasibility of using the high Z_eff storage phosphor material BaFBrI:Eu²⁺ in conjunction with the low Z_eff storage phosphor material KCl:Eu²⁺ for simultaneous proton dose and linear energy transfer (LET) measurements by 1) measuring the fundamental optical and dosimetric properties of BaFBrI:Eu²⁺, 2) evaluating its compatibility in being readout simultaneously with KCl:Eu²⁺ dosimeters and 3) modeling and validating its LET dependence under elevated proton LET irradiation.

Methods:

A commercial BaFBrI:Eu²⁺ storage phosphor detector (Model ST-VI, Fujifilm) was characterized with energy dispersive x-ray analysis (EDS) to obtain its elemental composition. The dosimeters were irradiated using both a Mevion S250 proton therapy unit (at the center of a spread-out Bragg peak, SOBP) and a Varian Clinac iX linear accelerator with the latter being a low LET irradiation. The photostimulated luminescence (PSL) emission spectra, excitation spectra and luminescent lifetimes of the detector were measured post proton and photon irradiations. Dosimetric properties including dose linearity, dose rate dependence, radiation hardness, temporal and readout stabilities were studied using a laboratory optical reader after proton irradiations. In addition, its proton energy dependence was analytically modeled and experimentally validated by irradiating the detectors at various depths within the SOBP (Range: 15.0 g/cm², Modulation: 10.0 g/cm²).

Results:

The active detector composition for the high Z_eff storage phosphor detector was found to be BaFBr_0.85I_0.15:Eu²⁺. The BaFBr_0.85I_0.15:Eu²⁺ material’s excitation and emission spectra were in agreement under proton and photon irradiations, with peaks of 586 ± 1 nm and 400 ± 1 nm respectively with a full-width-at-half-maximum (FWHM) of 119 ± 3 nm and 30 ± 2 nm respectively. As dosimeter response under photon irradiation is generally believed to be free from LET effect, these results suggest LET independence of charge storage center types resulted from ionizing radiations. There is sufficient spectral overlaps with KCl:Eu²⁺ dosimeters allowing both dosimeters to be readout under equivalent readout conditions, i.e. 594 nm stimulation and 420 nm detection wavelengths. Its PSL characteristic lifetime was found to be less than 5 microseconds which would make it suitable for fast 2D readout post irradiation. Its 420 nm emission band intensity was found to be linear up to 10 Gy absolute proton dose under the same irradiation conditions, dose rate independent, stable in time and under multiple readouts, and with high radiation hardness under cumulative proton dose histories up to 200 Gy as tested in this study. BaFBr_0.85I_0.15:Eu²⁺ showed significant proton energy- dependent dose under-response in regions of high LET which could be modeled by stopping power ratio calculations with an accuracy of 3% in low LET regions and a distance-to-agreement (DTA) of 1 mm in high LET regions (>5 keV/μm).

Conclusion:

We have proven the feasibility of dual-storage phosphor proton dosimetry for simultaneous proton dose and LET measurements. BaFBr_0.85I_0.15:Eu²⁺ has shown equally excellent dosimetry performance as its low Z_eff complement KCl:Eu²⁺ with distinctive LET dependence merely as a result of its higher Z_eff. These promising results pave the way for future studies involving simultaneous proton dose and LET measurements using this novel approach.

1. Introduction

Proton therapy offers dosimetric advantages due to unique dose deposition characteristics where the bulk of proton dose is deposited at the Bragg peak near the end of its range.¹ Proton therapies enable improved sparing of organs-at-risk (OARs) and thus reduce treatment related complications.^2–8 Current practice for dose prescription and reporting in proton therapy assumes a radiobiological effectiveness (RBE) of 1.1.⁹ While this assumption simplifies dose calculation and reporting, published literature^10,11 has shown that RBE is a function of proton dose, linear energy transfer (LET) and cell radiosensitivities. The clinical consequences of these RBE uncertainties manifest most significantly as range uncertainties¹² on the order of 2–3 mm. Protons tend to increase in LET near the end of their range¹¹ which could correspond to an increase in both RBE and range relative to the assumption of constant RBE of 1.1. Recent work has investigated the viability of proton planning assuming variable RBE or LET optimization^13–15 to support strategic LET mapping to maximize the LET delivered to tumor^16,17 while avoiding high LET deliveries to OARs. Results have been promising with several authors demonstrating the possibility of minimizing LET in OARs without significantly altering the physical dose.^13,17,18

For the clinical implementation of these dose/LET optimization protocols, dosimeters must be developed to verify beam parameters such as proton dose and LET prior to beam delivery. Ideally, these new dosimeters should have the ability to measure both proton dose and LET values simultaneously for their effective and quick implementation in proton clinics. Proton LET is notoriously difficult to measure directly with only a very limited number of devices commercially available such as the tissue-equivalent proportionality counter (TEPC),¹⁹ silicon spectrometer²⁰ or CR-39 etch detectors.²¹ Other authors have presented creative strategies for simultaneous proton dose and LET measurements such as the use of organic scintillators,²² thermoluminescent dosimeters^23,24 (TLDs), Al₂O₃:C OSLD²⁵ detectors and Gafchromic EBT3 films.²⁶ In this work, we present a novel solution to this problem by proposing the use of a proton energy dependent high Z_eff storage phosphor (Z_eff = 49, BaFBr_0.85I_0.15:Eu²⁺) in conjunction with a near-proton energy independent low Z_eff storage phosphor (Z_eff = 18, KCl:Eu²⁺).

This approach was inspired by our most recent work²⁷ demonstrating the near water-equivalence of europium-doped potassium chloride (KCl:Eu²⁺) storage phosphor dosimeters in proton dosimetry. Storage phosphors function using the mechanism of photostimulated luminescence (PSL).²⁸ Irradiation of these materials produce electron-hole pairs that are stored in metastable charge storage centers. The spatial distribution of these charge carriers forms a latent image which can be read out by optically stimulating the charge carriers to recombine and release PSL photons proportional in number to the locally deposited dose. Charges remaining trapped after readout can be erased with a bright, broadband light and the material can then be re-used. Readout entails optical detection of PSL and can be done quickly, repeatedly and with temporal stability²⁹ in ambient laboratory conditions.³⁰

In addition to being nearly energy independent in proton fields, KCl:Eu²⁺ dosimeters also respond linearly to proton dose, exhibit dose-rate independence, and show both high radiation hardness and dynamic range. The near proton energy independence is thought to be consequence of the resistance of KCl:Eu²⁺ to permanent or temporary proton radiation damage and its low Z_eff.³¹ Thus, our strategy for simultaneous LET measurements hinges upon searching for a corresponding storage phosphor with higher Z_eff with greater proton energy dependence that can be compared with KCl:Eu²⁺. This proposed complementary material should also be comparable to KCl:Eu²⁺ in terms of its other properties and readout processes namely dose linearity, dose-rate independence, temporal signal stability, strong radiation hardness and reusability. Ultimately, we envision this dual storage-phosphor reusable dosimeter to be used clinically following initial calibrations to 1) characterize the intrinsic outputs of both the high and low Z_eff materials to a known absolute proton dose within a low proton LET radiation environment and 2) a second subsequent calibration to characterize magnitude of the relative under-response of the high Z_eff side as compared with the low Z_eff side as a function of proton LET.

We identified a storage phosphor dosimetry material based on barium as a candidate as the complementary material to KCl:Eu²⁺. In this study, we initially characterized the optical and dose response of this barium-based storage phosphor dosimeter to proton fields. We then compared its response to that of KCl:Eu²⁺ and developed approaches for integrating these materials into the simultaneous measurement of dose and LET in proton dosimetry.

2. Methods and materials

2.A. Material characterization and preparation of dosimeters

A barium-based storage phosphor film (Model ST-VI, SN: 53841407, Fujifilm) was used for all optical and dosimetric measurements. The elemental composition of the storage phosphor material in these films was needed for dosimeter modeling but not fully available from the manufacturer. Thus, a small sample of the storage phosphor film was crushed for energy dispersive x-ray analysis (EDS) using scanning electron microscopy (Thermofisher Quattro Environmental SEM) to measure K and L shell characteristic lines (Oxford AzTec EDS). The elements of barium, fluorine, bromine, iodine and europium were detected in an elemental composition that corresponded to the compound BaFBr_0.85I_0.15:Eu²⁺ which had a Z_eff number of 49 as compared to the lower Z_eff number of 18 for KCl:Eu²⁺. Previous studies showed that the presence of iodine resulted in an increase in the intensity of the PSL signal and the red-shifting of the peak excitation wavelength.³²

Square samples of edge length 4 mm were then measured, cut out and affixed onto cylindrical holders of 6 mm in diameter for ease of handling. They were then calibrated using reference proton fields under equal proton doses prior to any dosimetric or optical measurements.

2.B. Proton and photon irradiations

Proton irradiations were performed on a Mevion S250 proton therapy unit. The unit was pre-calibrated using IAEA TRS-398 protocols³³ with 1 monitor unit (MU) corresponding to 1 cGy of absorbed dose-to-water at a beam setting of 15.0 g/cm² range and 10.0 g/cm² modulation. The dosimeters were placed at the isocenter of the treatment machine at a depth of 10.0 cm (i.e. middle of the spread-out Bragg peak, SOBP) in solid water (Plastic Water^®, CIRS). This setup was used for all proton irradiations in this study with the exception of relative SOBP depth-dose measurements in which the center of the SOBP was still at machine isocenter but the dosimeters were placed at various depths in solid water. This beam setting and setup geometry were used as it corresponded to absolute dose calibration conditions as measured with a parallel-plate ion chamber (PPC05) with ADCL calibration using IAEA TRS-398 protocols.³³ For clarification, all proton doses reported are given as absolute proton dose without application of an RBE factor.

Photon irradiations were performed using a Varian Clinac iX linear accelerator at photon energies of 6 MV which is a low LET (0.3 keV/μm LET³⁴) ionizing radiation for the purposes of spectroscopic and temporal stability comparisons. The dosimeters were irradiated by a beam calibrated by the TG-51³⁵ protocol, i.e. at a depth of 1.5 cm (depth at maximum dose) with a source-to-surface distance of 100 cm and a field size of 10 × 10 cm² under full backscatter conditions where 1 MU corresponded to 1 cGy of absorbed dose-to-water.

2.C. Spectroscopic Measurements

For PSL emission spectrum measurements, the dosimeter samples were irradiated and placed in the middle of a 15.2 cm Spectralon-coated (Labsphere, Inc.) plastic integrating sphere. Spectralon is a thermoplastic resin which has a reflectance of greater than 99% for visible light.³⁶ Light was produced from a 450 W xenon lamp, passed through a motorized grating system of a fluorescence spectrophotometer for wavelength selection and subsequently fed into the integrating sphere through a fiber optic cable. Optical stimulation was performed at a wavelength of 586 nm with light directly incident on the dosimeters for the signal maximization. The emitted signal was directed back into the spectrophotometer through a second motorized grating system for the separation of the spectral content and intensity measurement with a photomultiplier tube (PMT).

An annotated photograph of the fluorescence spectrophotometer setup is provided in Fig. 1a.

Figure 1.

(a): Experimental setup used to measure optical emission spectrum of dosimeters. Stimulation light from a 450 W xenon lamp was passed through a motorized grating for wavelength selection and directed into an integrating sphere containing the dosimeters. Emitted light was passed back into the main chamber for spectral analysis. (b): Experimental setup used to measure optical excitation spectrum of dosimeters. Light from a 500 W xenon lamp was passed through a monochromator for wavelength selection and focused into a housing containing the dosimeters. Intensity of 420 nm light was detected by the PMT. (c): Experimental setup used to measure optical signals of dosimeters post-irradiation. Light from a 2 mW, 594 nm He-Ne laser tube was directed into an integrating sphere containing the dosimeters. Intensity of the PSL light was measured subsequently by the PMT. (d): 4 ×4×0.4 mm³ dosimeter mounted on a plastic sample holder (shown in Fig. 1c).

For the PSL excitation spectrum measurements, a monochromator was used. Light from a 500 W xenon lamp was made to pass through a motorized grating of 1200 lines/mm for wavelength selection. The emitted light was then detected with a PMT with an attached narrowband filter of wavelength 420 ± 10 nm. The intensity of the 420 nm emission line was recorded with respect to the wavelength of the excitation light that was used to optically excite the dosimeters. An annotated photograph of the monochromator setup is provided in Fig. 1b. The monochromator also had a wavelength-dependent power output for which a correction was applied before excitation measurements. These corrections were pre-determined by measuring the spectral intensity of the stimulating light with a photodiode and normalizing the emitted light intensity with this recorded photodiode signal.

In addition, as both these spectroscopic scans had a finite temporal duration, the stimulation light was always maintained at a sufficiently low intensity to avoid inducing significant optical bleaching during the course of the measurements. Peak wavelengths on these scans were verified by reversing the direction of wavelength selection and ascertaining the coincidence of the spectroscopic peaks in both scan directions.

2.D. Photoluminescence and photostimulated luminescence lifetime measurements

Photoluminescence (PL) and PSL lifetime measurements were both performed using the aforementioned fluorescence spectrophotometer setup (Fig. 1a). For these measurements, the 450 W xenon lamp was operated in a pulsed mode and the temporal PSL intensity profiles were recorded after the dosimeter was briefly photostimulated by the light pulse to evaluate its corresponding lifetimes. The machine was pre-calibrated to the published PL decay profile of Eu³⁺ ions as included in the manufacturer’s manual prior to actual measurements with our dosimeters. Our lamp source required an 8 μs time delay prior to data collection to allow for the decay of the lamp source.

For PL lifetime measurements, the dosimeters were stimulated in the UV band at 300 nm and the emission was detected at 400 nm. For PSL lifetime measurements, the dosimeters were pre-irradiated with both protons and photons and then stimulated at 586 nm with the detection band set at 400 nm. For each readout, the signal was averaged over 6 μs intervals at 1 μs increments with signal averaging repeated 50 times for each measurement.

2.E. Dosimetry readouts

For all other dosimetric measurements that were non-spectroscopic, light from a 594 nm helium-neon (He-Ne) laser was used to stimulate the dosimeters optically. The dosimeters were mounted within a 5.1 cm Spectralon coated plastic integrating sphere to maximize the optical signal measured. The stimulation light was directed through an optical chopper at a frequency of 150 ± 1 Hz before entering the integrating sphere. The modulated stimulation light was then collected by a PMT with an attached narrowband optical filter of wavelength 420 ± 10 nm. The current from the PMT was then collected by a lock-in amplifier that had been configured to look for signals with a frequency matching that of the optical chopper, i.e. 150 Hz. An annotated photograph of the detection setup is provided in Fig. 1c.

A single readout for the purposes of dose measurement is defined as follows. Signal stabilization was allowed to occur for 2.5 s after the laser shutter was activated and the data were stored digitally (National Instruments LabVIEW) at a frequency of 10 Hz over a duration of 1 s (10 readings at 0.1 s time intervals). The dosimeter was then allowed to relax for 10 s after the deactivation of the laser shutter before any subsequent readings were obtained. Due to the slight depletion of the measured optical signal during a readout of approximately 0.4% as experienced in the past for KCl:Eu²⁺ dosimeters,²⁷ this depletion was characterized by repeatedly exciting the dosimeters and performing a simple linear fit of the form 1-λn where λ corresponds to the percentage of the initial PSL intensity that was depleted in the course of each readout and n corresponds to the number of readouts performed.

The temporal stability of the dosimeters was also measured over the course of 24 h post-irradiation by repeating readout at 30 mins intervals, with depletion corrections performed to account for signal depletions arising from multiple readouts. All other dosimeter readings were obtained 17 h post-irradiation, corresponding to the temporal delay previously employed for the measurement of stable post-irradiation KCl:Eu²⁺ PSL signals. All of the described readout parameters, i.e. stimulation and detection wavelengths and post-irradiation readout time, were selected as they corresponded to the parameters used for KCl:Eu²⁺ dosimeters.²⁷

2.F. Analytical determination of LET

Previously, we had used an analytical approach to successfully model the response of KCl:Eu²⁺ under proton irradiation.²⁷ We used the same analytical approach for the modeling of BaFBr_0.85I_0.15:Eu²⁺. The depth dose distribution of the calibration clinical proton SOBP field was obtained first using a model PPC05 parallel-plate ionization chamber. Then, an analytical fit was performed for this clinical SOBP. Pristine proton peaks were constructed using Bortfeld’s analytical formulas,³⁷ which take into account the effects of inelastic fluence reductions,^38,39 machine-dependent range straggling and low energy proton contamination. Then, 20 such pristine beams were fitted and summed with beam weights initially specified using methods as described by Jette and Chen.⁴⁰ A slight dip in the middle of the analytical SOBP was corrected by tweaking the initial weights.

The LET values of the calibration clinical proton SOBP field were then calculated with the aid of Wilkens’ analytical solutions for LET of proton beams in water.⁴¹ The LET values of a pristine proton beam could be obtained either by dose- (LED_d) or track-averaging (LET_t), both of which have clinical significance depending on the model used for the calculation of the RBE. These analytical LET values are plotted in Figs. 3a and 3b. These analytical solutions required both the range and the width of each pristine peak and these were incorporated from the aforementioned fitting. Wilkens et al., reported a maximum deviation of 0.5 keV/μm as compared to Monte Carlo simulations at the end of the proton range⁴¹ which resulted in a percentage deviation of approximately 3.6% corresponding to an LET value of approximately 14 keV/μm.⁴¹ This maximum uncertainty value at the end of the proton range had been also independently verified by other investigators performing Monte Carlo simulations on both an SOBP geometry⁴² and a pristine Bragg peak.⁴³ The analytical LET values were reported to match Monte Carlo values more closely in the other regions away from the distal edge of the proton beam.^41,43 Thus, we conservatively estimated an inherent LET uncertainty of approximately 4% in all of our analytical calculations.

Figure 3.

(a): Calculated dose-averaged proton energies across the clinical SOBP with PSTAR data interpolation for $\left(\frac{\stackrel{-}{L}}{\rho }\right)$ of protons in water. (b): Calculated track-averaged proton energies across the clinical SOBP with PSTAR data interpolation for $\left(\frac{\stackrel{-}{L}}{\rho }\right)$ of protons in water.

2.G. Analytical proton stopping power ratio and experimental LET determination

The mass stopping powers of BaFBr_0.85I_0.15:Eu²⁺ were then analytically calculated as a function of proton energy from the Bethe-Bloch theory⁴⁴ with the various necessary corrections^9,45,46 as shown in Fig. 2a. From the proton mass stopping powers of BaFBr_0.85I_0.15:Eu²⁺, the stopping power ratios with respect to water were then plotted as a function of proton energy in Fig. 2b with the corresponding mass stopping powers of water extracted from the PSTAR database.⁴⁷ Due to the higher Z_eff of BaFBr_0.85I_0.15:Eu²⁺, there was a significantly higher dependence of its mass stopping power ratios on the proton energy as compared with KCl:Eu²⁺. Based on Fig. 2b, we hypothesize that the ratio of signal response between BaFBr_0.85I_0.15:Eu²⁺ and KCl:Eu²⁺ could be measured to infer LET. Given the monotonic relationship between mass stopping power ratio and proton energies (Fig. 2b), a unique 1:1 mapping between this signal ratio and LET could be achieved.

Figure 2.

(a): Calculated mass stopping power of protons in BaFBr_0.85I_0.15:Eu²⁺ for proton energies from 10⁻³ to 10⁴ MeV. KCl:Eu²⁺ plotted alongside for reference. (b): Calculated mass stopping power ratio of BaFBr_0.85I_0.15:Eu²⁺ to water normalized at 150 MeV proton energy. KCl:Eu²⁺ and air plotted alongside for reference. Significant proton energy dependence for BaFBr_0.85I_0.15:Eu²⁺ is evident.

However, there were two plausible ways in which the LET values could be determined (dose- and track-averaging). Briefly, dose-averaging will lead to slightly elevated LET values than track-averaging as dose-averaging will be biased in favor of the lower energy, higher LET protons as these protons will deposit a greater amount of dose in media.⁴¹ Their applicability in describing physical effects such as the experimental under-responses is a choice that seems to be detector-dependent. For instance, Christensen et al., had shown that track-averaged LET values were more accurate in predicting the magnitude of proton quenching of plastic scintillators⁴⁸ whereas other authors have shown that dose-averaging was a more accurate measure for other dosimeters such as OSLDs²⁵ and radiochromic films.^26,49 As such, it is important for us to determine the more accurate averaging scheme (dose- or track-averaging) that is more relevant to BaFBr_0.85I_0.15:Eu²⁺ dosimeters. From the experimental under-response values of BaFBr_0.85I_0.15:Eu²⁺, we attempted to restore the original SOBP curve by normalizing it with their expected under-response (Fig. 2b) as determined by dose- and track-averaging to determine the more accurate averaging scheme relevant to our dosimeter.

We followed a 3-step procedure:

1. At each depth of measurement, we first determined the LET_d and LET_t values.

2. Then, we performed a mapping from LET to proton energies from the interpolation of the published PSTAR data⁴⁷ for protons in water with the assumption⁵⁰ that the mass stopping power of protons in water is approximately equal to the LET values.

3. Finally, we determined the expected under-response as a function of proton energy from Fig. 2b from the proton energies obtained both from LET_d and LET_t.

The results of Step 2) are plotted in Figs. 3a and 3b. As shown later in Section 3.D, we will determine which averaging scheme, LET_d or LET_t, would be a more accurate LET determination by comparing the restored SOBP measured using a non-water equivalent dosimeter versus that using an ionization chamber. Any discrepancy would also be clearly indicative of the presence of any possible deviations from known physics (stopping power ratio dependence).

2.H. Reproducibility of measurements

The BaFBr_0.85I_0.15:Eu²⁺ dosimeter samples were found to be have a high degree of consistency in their measured optical signals. For added reproducibility, we strictly adhered to a post-irradiation readout time of 17 h to account for the possibility of a time-dependent signal component. The dosimeters were handled in the dark to minimize the fading effects of ambient light. After each readout, they were optically bleached using a 500 W quartz halogen lamp (Bayco Products Inc.) for at least 15 mins to reduce any residual signals to background levels. Laser intensity fluctuations were negligible and the day-to-day variations in the output of the proton unit were measured to be 1%. To account for these day-to-day variations and random sources of error, all dosimetric readings other than the radiation hardness experiments were repeated and averaged over a period of at least three days where three dosimeters were used for the measurement of a proton field condition each day. The dosimeters were also found to be highly resistant to radiation damage (i.e. having a high radiation hardness) which contributed to the reproducibility of the results.

The overall sources of uncertainty yielded a cumulative measurement uncertainty in the dosimeter that had an average standard uncertainty of 1.0%. 24 dosimeter samples with uncertainties below 1.5% were chosen and calibrated for the actual measurements. Within the group sample, their individual raw signals had a signal variation of 1.4% across the set with a maximum signal of 102.4% and a minimum signal of 97.8%.

3. Results

3.A. Spectroscopic results

The excitation spectrum was obtained for both proton and photon irradiation and is plotted in Fig. 4a. The excitation peaks were found to be at 586 ± 1 nm for both proton and photon irradiations respectively in agreement with previous studies.²⁸ The full-width-at-half-maximum (FWHM) values were measured to be 116 ± 3 nm for protons and 122 ± 3 nm for photons. The emission spectrum was obtained for both proton and photon irradiation by exciting the samples at the peak excitation spectrum of 586 nm as shown in Fig. 4b. The Poissonian noise present within the experimental data were smoothened through the application of a Savitzky-Golay⁵¹ digital filter and overlaid as a reference to guide the reader’s eyes. The emission peaks were found to be at 400 ± 1 nm for both proton and photon irradiations respectively with an FWHM of 30 ± 2 nm, corresponding with expected values as published previously²⁸ and overlapping sufficiently with previously studied spectral data for KCl:Eu²⁺ (i.e. excitation peak of 560 ± 1 nm and emission peak of 421 ± 1 nm).²⁷

Figure 4.

(a): Excitation spectra of BaFBr_0.85I_0.15:Eu²⁺ as detected at 420 nm. Peaks were located at 586 ± 1 nm for both radiation modalities with an FWHM of 116 ± 3 nm and 122 ± 3 nm for proton and photon irradiation respectively. (b): Emission spectra of BaFBr_0.85I_0.15:Eu²⁺ as stimulated at 586 nm. Data were smoothened with the application of the Savitzky-Golay digital filter and overlaid as a reference to guide the reader’s eyes. Peaks were located at 400 ± 1 nm with an FWHM of 30 ± 2 nm for both proton and photon radiation modalities.

The excitation spectra were found to be of the same shapes from 10 Gy to 60 Gy of absorbed proton doses as shown in Fig. 5a. Dose response was infralinear for doses above 10 Gy. The emission spectra were also found to be of similar shapes as plotted in Fig. 5b and was not affected by increasing proton doses. As with the previous data, the Poissonian noise present was smoothened through the application of a Savitzky-Golay digital filter. The difference in the magnitudes of the dynamic ranges between Figs. 5a and 5b was found to be primarily due to the different detection bands between the two plots, with excitation spectra measured using a 420 nm narrowband filter and emission spectra measured across the entire spectrum.

Figure 5.

(a): Excitation spectrum of BaFBr_0.85I_0.15:Eu² as detected at 420 nm for absorbed proton doses from 10 Gy to 60 Gy. Data were obtained 17 h post-irradiation. Slight signal saturation detected at proton doses above 10 Gy, worsening above 30 Gy. No changes to the spectral shape with increasing proton doses. (b): Emission spectrum of BaFBr_0.85I_0.15:Eu² as stimulated at 586 nm for absorbed proton doses from 10 Gy to 60 Gy. Data were obtained 17 h post-irradiation. Poissonian noise was smoothened with the application of the Savitzky-Golay digital filter and overlaid as a reference to guide the reader’s eyes. No changes to the spectral shape with increasing proton doses.

3.B. PL and PSL lifetime measurements

The results of the PL and PSL lifetime measurements are plotted in Figs. 6a and 6b respectively. Within experimental fitting uncertainty, the characteristic PL lifetimes BaFBr_0.85I_0.15:Eu²⁺ dosimeter samples were found to be 2.2 ± 0.1 μs regardless of proton dose history. The PSL lifetimes were found to be 4.0 ± 0.1 μs regardless of radiation modality.

Figure 6.

(a): PL signal vs. time after pulsed UV stimulations at a wavelength of 300 nm with a detection wavelength of 400 nm. Fitted formula: $y(t)=e^{-0.45t}$ for fresh samples and $y(t)=e^{-0.46t}$ for dosimeter with 200 Gy proton dose history. Within fitting errors, the characteristic PL lifetimes for fresh samples and samples with proton dose histories were found to be similar at 2.2 ± 0.1 μs. (b): PSL signal vs. time after pulsed stimulations at a wavelength of 586 nm with a detection wavelength of 400 nm. PL time profile of a fresh sample was plotted for reference. Characteristic PSL lifetime was found by curve fitting to be 4.0 ± 0.1 μs for both radiation modalities.

3.C. Dosimetric results

The dosimeter samples exhibited dose response linearity from 0 to 10 Gy of absorbed dose-to-water under proton irradiation and as shown in Fig. 7 with the proton dose normalization chosen at 1 Gy. They were also confirmed to be independent of proton dose rates in the range of clinically relevant dose rates of 83 cGy/min to 500 cGy/min as shown in Fig. 8 where the normalization was performed at 250 cGy/min.⁵²

Figure 7:

PSL signal intensity vs absorbed proton dose, normalized at 1 Gy. The y = x line was plotted for reference. Measurements were performed 17 h post-irradiation. Error bars corresponded to 95.5% confidence intervals (2σ).

Figure 8:

PSL signal intensity vs dose rate, normalized at 250 MU/min, where 1 MU/min = 1 cGy/min. The y = 1 line was plotted for reference. Measurements were performed 17 h post-irradiation. Error bars corresponded to 95.5% confidence interval (2σ). Lower and upper bounds were at ±3% intervals.

Temporal stability measurements are plotted in Fig. 9 for both photon and proton irradiations. An apparent short-lived initial signal fading of the optical signal was likely caused by fast electron-hole recombination. Subsequent signal indicates slow fading over the course of 24 h. An exponential fitting of the form: Ae^-t/τ was fitted to the slow fading data, i.e. 1 h post-irradiation and the characteristic time constant τ was found to be 409.8 ± 0.1 h and 420.2 ± 0.1 h for proton irradiation and photon irradiation respectively. This was found to resemble the fading curve at room temperatures⁵³ of a closely related material BaFBr:Eu²⁺, which showed a quick initial signal fading followed by a slow signal fading over several days.

Figure 9:

PSL signal intensity vs. post irradiation time, normalized at 17 h post-irradiation. The y=1 line was plotted for reference. Error bars shown corresponded to 95.5% confidence interval (2σ). Lower and upper bounds were at ±3% interval. Proton fitted function: $y\left(t\right)=1.02e^{-0.00244t}$. Photon fitting: $y\left(t\right)=1.03e^{-0.00238t}$.

The readout stability was assessed by quantifying the signal depletion per readout as presented in Fig. 10. Signal depletion was measured to be 0.38% per readout through linear fitting. This value was used to correct for readout depletion in the event that multiple readouts were performed such as in the temporal signal stability measurements.

Figure 10:

PSL signal intensity vs. number of readout, normalized at first readout number. Data were obtained 17 h post-irradiation with aforementioned clinical proton beam. Linear fit was plotted for reference. Fitted formula: $y\left(n\right)=1.0016-0.00377n,r^2=0.979.$ This corresponds to approximately a 0.38% signal depletion per readout. Error bars shown corresponded to 95.5% confidence interval (2σ).

Radiation hardness measurements were performed by measuring the relative responses of the dosimeter samples under increasing proton dose histories. Measurements were performed in increments of 10 Gy doses up to 200 Gy and the results were normalized with respect to the signal response of the freshly prepared dosimeters serving as a baseline for comparison as shown in Fig. 11. Up to a cumulative proton dose history of 120 Gy, the signal response followed that of a random distribution about the baseline followed by an apparent slight decrease at proton dose histories of 130 Gy and above that was not statistically significant.

Figure 11:

PSL signal intensity vs proton dose history, normalized at 0 Gy dose history with 10 Gy dose history intervals. The y = 1 line was plotted for reference. Measurements were performed 17 h post-irradiation. Error bars corresponded to 95.5% confidence interval (2σ). Lower and upper bounds were at ±3% intervals. Slight decrease after 130 Gy dose history not statistically significant.

The proton SOBP depth dose measurements were performed at depths of 1.0, 3.0, 5.0, 10.0, 13.0, 14.0, 14.5, 15.0, 15.5 and 16.0 cm in solid water. The data for the proton depth dose measurements as performed with BaFBr_0.85I_0.15:Eu²⁺ are plotted in Fig. 12. Also overlaid are similar measurements as performed with a PPC05 parallel-plate ionization chamber representing the actual proton doses and those that were measured with KCl:Eu²⁺ dosimeters which did not exhibit any significant proton under-responses. As expected with high Z_eff dosimeters⁵⁴ exhibiting strong proton stopping power ratio dependence, BaFBr_0.85I_0.15:Eu²⁺ under-responded significantly even in the shallower depths leading to the middle of the proton SOBP.

Figure 12:

PSL signal intensity vs. depth in solid water for proton clinical beam with a range of 15 g/cm² and an SOBP of 10 g/cm². Parallel-plate ion chamber data and KCl:Eu²⁺ measurements were plotted for reference. Measurements were obtained 17 h post-irradiation. Data were normalized at the entrance dose (d = 1.0 cm) for the calculation of the LET effect. Error bars shown corresponded to 99.7% confidence intervals (3σ).

3.D. Physics-inspired under-response predictions from stopping power ratios

As discussed earlier, the ratio of the optical signals of BaFBr_0.85I_0.15:Eu²⁺ and KCl:Eu²⁺ may be used to measure LET values within the proton SOBP and we performed a restoration using the 3-step procedure as outlined previously to compare and determine the relevant LET averaging scheme. From the results of our prior analytical work, we extracted both the values of LET_d and LET_t (Figs. 3a and 3b) along with their corresponding effective proton energies in Table 1. These proton energies were then used to determine the expected under-response (Fig. 2b) for normalization.

Table 1:

Extracted values for relevant LET_d, LET_t and their corresponding effective proton energies from analytical modeling of proton SOBP.

Depth (cm)	Dose-averaging		Track-averaging
	LETd (keV/μm)	Energy (MeV)	LETt (keV/μm)	Energy (MeV)
1.0	0.64	120.1	0.63	122.8
3.0	0.72	102.4	0.69	108.2
5.0	1.04	62.9	0.81	86.8
10.0	1.86	30.4	1.17	54.1
13.0	2.81	18.3	1.74	33.2
14.0	3.67	13.2	2.26	24.0
14.5	4.66	9.8	2.80	18.3
15.0	6.61	6.3	3.79	12.6
15.5	9.02	4.2	5.09	8.7
16.0	11.1	3.2	6.35	6.6

The results of the procedure are plotted in Fig. 13. Results showed that the overall under-response was described more accurately by the effective proton energies as obtained from LET_d values than LET_t values. The results are consistent with both our²⁷ previous experiences with KCl:Eu²⁺ and also those of other researchers studying similar LET effects in similar inorganic materials.²⁵ For the restored SOBP curve as normalized by dose-averaging procedures, it agreed to within a maximum dose deviation of 3.3% (at 14.5 cm depth) and a maximum DTA deviation of 1 mm (at 15.0 cm depth) as shown in Fig. 13.

Figure 13:

Restoration of under-response in SOBP measurements of BaFBr_0.85I_0.15:Eu²⁺ from stopping power ratio calculations. Effective proton energies derived from both the analytical LET_d and LET_t values were used and the corresponding restored SOBP data points are labelled in the legend accordingly. Actual SOBP curve was restored within 3.3% maximum deviation (depth 14.5 cm) and within a maximum DTA uncertainty of 1 mm (15.0 cm).

For completeness, we also re-expressed our results differently and constructed a simple calibration curve between under-response and LET_d as shown in Fig. 14. Characteristics of this fit included 1) intersection of the y-axis at low LETs, 2) the presence of a point of inflection at intermediate LET values, 3) the presence of an asymptotic upper at high LET values and 4) monotonically increasing under-response with increasing proton LET values. Given these criteria, we constructed the calibration from a fit of the form y(x) = A-(1+exp([x-B]/C))⁻¹ with three fitting parameters (A, B and C) where y corresponds to the percentage under-response and x is LET_d. The fit included the aforementioned desirable mathematical properties, approaches an asymptote (A) at high LETs and is dimensionally consistent.

Figure 14:

Calibration curve for under-response as function of LET_d values. Formula: y(x) = 100% × [A-(1+exp([x-B]/C))⁻¹]. A = 0.933 ± 0.4, B = 7.87 ± 0.05 keV/μm, C = 2.88 ± 0.03 keV/μm. Vertical error bars were obtained from the combination of experimental uncertainties of the signals measured from BaFBr_0.85I_0.15:Eu²⁺ and KCl:Eu²⁺. Typical deviations from Monte Carlo results were reported⁴¹ and subsequently verified^42,43 to be at a maximum of 0.5 keV/μm at the end of the proton range and as such, a conservative estimate of 4% analytical calculation uncertainty is assumed to be inherent in analytical LET values calculated.

The results of the fit are plotted in Fig. 14. The optimal values were obtained by minimizing the sum of chi squares between the experimental data and the model. The uncertainties of the fitting parameters A, B and C were obtained from the standard deviations of 10 least squares minimization routines of the experimental data, each of which performed with random initial seed values. The least squares minimization was performed using the Metropolis-Hastings algorithm⁵⁵ for a quick convergence to a unique global minimum solution in the parameter space while bypassing any problematic local minima.

4. Discussion

Previously, we found KCl:Eu²⁺ to be an ideal, near water-equivalent dosimeter exhibiting little proton energy dependence or LET effects.²⁷ These properties are also prevalent in other low Z_eff dosimeters such as Al₂O₃:C OSLDs.²⁵ Repurposing KCl:Eu²⁺ for simultaneous LET and dose measurement required us to identify a suitable storage phosphor material with a high Z_eff. Our proposed strategy was to create a device incorporating both materials in order to artificially impart proton energy dependence without compromising accurate dose measurements. This added material must share the desirable properties of KCl:Eu²⁺ such as dose linearity, dose-rate independence, strong radiation hardness, temporal stability, readout stability, and the ability to be casted into a 2D film. Additionally, there must also be sufficient overlap in their optical spectra for the possibility of simultaneous measurements.

4.A. Spectroscopic measurements

BaFBr_0.85I_0.15:Eu²⁺ showed no new optical peaks or shifts in the excitation and emission spectra under proton irradiation and therefore there were no new underlying solid-state physics processes under proton irradiation that might have affected the PSL mechanism of BaFBr_0.85I_0.15:Eu²⁺ such as new optical energy storage centers or changes in the energy levels in the bandgap. Changes in the response of BaFBr_0.85I_0.15:Eu²⁺ in different proton LET environments can therefore be better established to be caused by proton energy dependences of the stopping power ratios. The excitation spectra were broad enough for it to be excited by a wide range of economical diode lasers and were found to be sufficiently separated from the emission spectra to allow for the stimulation light to be filtered from the emission spectra. Most importantly, there was a sufficient overlap between both the optical spectra of BaFBr_0.85I_0.15:Eu²⁺ with that of KCl:Eu²⁺ for them to share an optical readout apparatus.

4.B. Dose linearity

Under ideal readout conditions for KCl:Eu²⁺ dosimeters, i.e. application of a 420 nm narrowband filter, BaFBr_0.85I_0.15:Eu²⁺ was found to be linear up to 10 Gy which corresponds to the range of relevant doses for the purposes of clinical proton dosimetry. Without dose linearity, application to LET determination would be highly complicated as the magnitude of the under-response would have to be corrected for dose linearity effects. When the whole spectrum of the emission light was taken into account, the dynamic range fared better but it had slight saturation effects for proton doses above 40 Gy. Previous studies performed with 75 kVp imaging x-rays showed dose saturation at levels below 1 Gy;^56,57 however, this was not our observation with clinical proton beams. In particular, we did not observe the visible blue colorations⁵⁶ as reported by Thoms during our linearity measurements and it was very likely that the concentration of latent electron traps was well below any saturation levels. A possible explanation for this deviation from prior results using imaging x-rays might be the tendency for BaFBr_0.85I_0.15:Eu²⁺ to over-respond disproportionately via the photoelectric effect given its high Z_eff and the relatively low energies of the x-ray photons. Finally, we also noted that recent heavy ion irradiation studies performed showed wider dynamic ranges up to doses as high as 10³ Gy⁵⁸ while 60 kV x-rays showed dose saturations below 1 Gy doses.

A more theoretical investigation into the local saturation effects of BaFBr_0.85I_0.15:Eu²⁺ would be desirable; however, this is difficult to perform due to the current gaps in the understanding of the properties of BaFBr_0.85I_0.15:Eu²⁺ especially from a fundamental solid-state physics perspective. Even within the older and relatively more studied parent material BaFBr:Eu²⁺, there remain a lack of consensus on the physical mechanisms underlying the PSL process. While it is well understood that F-center anionic defects of F(F⁻) and F(Br⁻) are created following irradiation,⁵⁹ the exact roles of these F-centers to the overall PSL process are not fully understood. Von Seggern claimed that the F(Br⁻) centers⁶⁰ were only responsible for the PSL process while Spaeth et al. claimed that F(F⁻) centers also contributed to the process.⁶¹ In addition, competing models describe the production mechanism of the F-centers within BaFBr:Eu²⁺. Von Seggern proposed a model involving the radiation-induced creation of an anionic defect⁶⁰ while other researchers^61,62 proposed models involving the assumption of the pre-existence of such anionic defects. Lastly, previous studies performed on BaFBr_0.85I_0.15:Eu²⁺ determined the average energy per F-center creation to be 190 eV for ⁶⁰Co and 160 eV for 6 MV photon irradiation.⁶³ Thus, it would be entirely likely that this value for proton irradiations would be different as compared with photon irradiation especially as it was found to be a function of photon energies. Such a value has not been reported as of yet for proton irradiation and would have to be known before the performance of any solid-state physics theoretical investigations.

Other storage phosphor materials such as potassium chloride alkali halides were more well understood in terms of the nature of their F-centers and their production mechanisms,⁶⁴ F-center saturation concentration levels and their energy of formation.⁶⁵ This might be due to the relatively simpler lattice structure of alkali halides and had allowed for a more theoretical investigation to be performed into such storage phosphors, as was previously performed for KCl:Eu²⁺.

4.C. Dose rate independence

Previous experimental studies of the interaction of protons within alkali halide storage phosphors showed that the protons would deposit their energies locally within infratracks on timescales in the order of 10⁻¹³ s,⁶⁶ corresponding to microscopic dose rates that were well beyond the maximum dose rates that were capable of clinical proton units. While the microscopic effects of proton interaction on BaFBr_0.85I_0.15:Eu²⁺ have not been studied, their interaction timescales would likely be on the same order as that of alkali halides, justified by their related PSL charge-storage mechanisms. This would likely mean that there would be dose rate independence in the range of clinically relevant dose rates. The range of dose rates that were studied (83 to 500 cGy/min) corresponded to the range of stable dose rates where the proton unit was able to deliver the beam uninterrupted. Dose rates that were too low or too high would result in frequent beam interruptions due to safety interlock issues due to the inability of the proton unit to maintain a stable dose rate consistently.

4.D. Radiation hardness

BaFBr_0.85I_0.15:Eu²⁺ was found to be highly resistant to proton damage and its sensitivity did not drop significantly under accumulated proton dose histories despite the relatively highly damaging effects of proton beams. This result was consistent with previous high dose irradiation experiments performed on BaFBr:Eu²⁺ which demonstrated stable PSL values up to cumulated doses of 10⁴ Gy for megavoltage photons.⁶⁷ The physical mechanism behind the signal degradation within BaFBr:Eu²⁺ and closely related materials under accumulated doses was thought to be caused by the creation of non-photostimulable defect centers known as “flaw centers”⁶⁷ that would compete with the photostimulable defect centers. It is likely that the formation of such flaw centers was naturally found to be a slow process in these BaFBr_0.85I_0.15:Eu²⁺ crystal lattice structures. For comparison, materials such as CsBr:Eu²⁺ or CsI:Eu²⁺ presented crystal structures that resulted in the enhanced mobility of the divalent Eu²⁺ ions.⁶⁸ This mobility caused the rapid aggregation of these Eu²⁺ ions into stable, non-photostimulable agglomerates under irradiation resulting in PSL sensitivity decreases to less than 20% of its initial value after cumulative doses of only 25 Gy.⁶⁹

In addition to these properties, BaFBr_0.85I_0.15:Eu²⁺ is an inorganic storage phosphor compound and therefore, would be more impervious to proton radiation damage than dosimeters that are based on organic compounds. For example, plastic scintillators that are based on the water-equivalent organic polymer polyvinyltoluene are known to exhibit molecular damage in addition to a strong quenching effect. This molecular damage is unique to organic compounds and involves the ejection of hydrogen and C_xH_y groups along with other scission and cross-link damages⁷⁰ which reduced PSL sensitivities under increasing dose histories.

4.E. Proton signal under-response

The under-response of BaFBr_0.85I_0.15:Eu²⁺ was found to occur in regions of high LET within the proton SOBP. Such under-response in these regions is thought to have two main causes³¹ including: 1) proton energy dependence of the proton stopping power ratio which is prevalent in non-water equivalent materials of high Z_eff or 2) LET dependence that is not solely explained by the energy dependence of the stopping power ratios alone. The former effect could be modelled and thus corrected while the latter effect, sometimes colloquially known as “quenching” is thought to be dosimeter-specific with exact physical mechanisms not well understood. As seen from Fig. 13, the actual SOBP curve could be reproduced from the under-responded SOBP measurements as performed by the BaFBr_0.85I_0.15:Eu²⁺ dosimeters to a maximum percentage deviation of 3.3% at a depth of 14.5 cm and a maximum DTA shift of 1 mm at a depth of 15.0 cm. The under-response phenomena of BaFBr_0.85I_0.15:Eu²⁺ could therefore be sufficiently attributed primarily to the well-understood energy dependence of high Z_eff materials and best described by the dose-averaging scheme for the determination of effective proton energies. While we managed to explain the experimental under-response sufficiently using stopping power ratio differences within measurement uncertainties, there might be inherent additional “quenching” effects hidden underneath these experimental uncertainties in our study. This would have to be investigated further in more complex proton LET environments in future work.

In our previous work,²⁷ we have shown that the initial densities of F-centers in KCl:Eu²⁺ were likely to be below saturation levels and that proton infratrack-infratrack crossings were negligible at clinical proton doses of 2 Gy. These were compelling factors explaining the lack of quenching in KCl:Eu²⁺ dosimeters. Such an analysis had not been done for BaFBr_0.85I_0.15:Eu²⁺ dosimeters but it is also likely that they will lead to similar findings given the related PSL mechanisms of the two inorganic dosimeters. However, we have since noted a successful application of a more fundamental and quantitative alternative to the cylindrical infratrack theory by Christensen et al. to organic plastic scintillators⁴⁸ and for our future work, we will be investigating the theoretically predicted quenching magnitudes of BaFBr_0.85I_0.15:Eu²⁺ dosimeters using this more fundamental approach.

For data points collected at a depth of 15.0 cm and beyond, maximum distance-to-agreement was 1 mm and likely due to combined uncertainties stemming from factors such as beam range stability,⁷² experimental setup uncertainties and uncertainties in the effective point of measurements of the dosimeters. It would be highly improbable for these deviations to be related to “quenching” due to the lack of apparent effects in the proximal parts of the restored SOBP, the high radiation hardness of BaFBr_0.85I_0.15:Eu²⁺ against proton radiation damage and the experimental challenges of dose measurements and effective depth determination in regions of high proton dose and LET gradients (Fig. 3).

4.F. Uncertainties in LET and RBE determination

There were 2 main sources of experimental errors contributing to LET and ultimately RBE determination uncertainties: 1) inherent uncertainties of the measured optical signals of KCl:Eu²⁺ and BaFBr_0.85I_0.15:Eu²⁺ dosimeters and 2) maximum DTA uncertainties of ±1 mm (measured at a depth of 15.0 cm, Fig. 13).

For the estimation of the former source of experimental error, we began with the assumption of a realistic and conservative 3σ dosimetric measurement uncertainty of ±3.0% (our current dataset) for both KCl:Eu²⁺ and BaFBr_0.85I_0.15:Eu²⁺ dosimeters. The subsequent percentage uncertainties for the relative under-response ratios would therefore be ±4.2% as obtained from the square root summation of the squares of their individual percentage uncertainties. Then, from the calibration formula used, the formula for LET_d could be obtained by inverting the original calibration formula to result in the formula: x = B + C ln ((A-y/100)⁻¹ - 1), where x is the LET_d and y is the under-response percentages, to be used for the direct translation to LET uncertainties. For example, for a measured under-response of 17.2% at depth of 14.5 cm, the calibration formula would yield an LET value of 4.5 keV/μm with a lower and upper uncertainty limits of 4.4 keV/μm and 4.7 keV/μm respectively. This would ultimately correspond to an uncertainty range of 5.1% for the LET_d determination from the optical measurement uncertainties of each of the individual dosimeter materials.

Then, we factored in the latter source of error with an estimation of a DTA uncertainty of ±1 mm corresponding to the maximal DTA shifts within the experimental dataset (Fig. 13). For the aforementioned example at the depth of 14.5 cm, we estimated the LET uncertainty ranges as a result of DTA uncertainties by looking up the corresponding analytical LET_d values (Fig. 3) at depths of 14.4 cm and 14.6 cm which were 4.4 keV/μm and 4.9 keV/μm respectively. This would correspond to an LET uncertainty range of 12.3% leading to an overall realistic LET determination uncertainty range of 13.3% from the square root summation of the squares of the 2 error sources. This would correspond to percentage standard deviations of ±6.7% for the overall LET determination.

A typical RBE calculation was performed to evaluate the impact of a combined percentage standard deviation of ±6.7% using the parameters of a phenomenological RBE model published by McNamara et al.⁷³ For a proton dose of 2 Gy and an (α/β)_x value of 2.1 Gy corresponding to brainstem,¹⁴ the LET_d of 4.5 keV/μm corresponds to an RBE value of 1.78. Assuming a percentage uncertainty of ±6.7% for the LET_d, upper and lower bounds of the RBE are 1.76 and 1.80 respectively, i.e. a total percentage uncertainty width of 1.9%. Further improvements to the precision of LET_d measurements would be attractive but might lead to marginal improvements in the precision in the RBE calculations and thus would incur diminishing returns. Actual RBE uncertainties would likely be dominated by uncertainties related to the choice of the biophysical RBE models and the accuracy of biological data collected.⁷⁴ For example, similar calculations repeated with a percentage standard deviation of ±2.6% corresponding to the complete elimination of DTA related uncertainties would lead to a total percentage uncertainty width of 0.9% for the RBE determination.

4.G. Simultaneous dose and dose-averaged LET measurements

We have both validated the proton energy dependence physics model and proven the feasibility of using BaFBr_0.85I_0.15:Eu²⁺ and KCl:Eu²⁺ simultaneously within the same readout conditions. A likely protocol for the simultaneous proton dose and LET_d measurements can be realized as follows. We will perform the irradiation twice, one with the KCl:Eu²⁺ dosimeter and the other with BaFBr_0.85I_0.15:Eu²⁺ dosimeter positioned at the same location in a dosimetry phantom. Then, they will be readout separately using a commercial storage phosphor reader. Prior to use, the device would be calibrated to both absolute absorbed proton dose-to-water in the entrance region of a proton SOBP within a region of low LET_d and LET_d values in a wide spectrum of LET_d environments.

The optical signal from the KCl:Eu²⁺ detector would contain the absolute proton dose information while the relative under-response from the BaFBr_0.85I_0.15:Eu²⁺ detector would store the relevant LET_d information. The magnitude of the under-response could be easily converted to LET_d values for the purposes of RBE calculations either through the use of proton stopping power ratio calculations or alternatively, an initial calibration curve as described in the aforementioned section.

5. Conclusion

Reusable BaFBr_0.85I_0.15:Eu²⁺ storage phosphor demonstrates excellent proton dosimetry performance with a large dynamic range in both physical dose and LET. Its LET dependence is merely a result of its stopping power ratio with respect to water under proton irradiation which is a function of proton energy and thus LET. This feasibility study suggests that the high Z_eff storage phosphor could be used in conjunction with a low Z_eff KCl:Eu²⁺ for simultaneous proton dose and LET measurements.

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.