Spectroscopic separation of Čerenkov radiation in high-resolution radiation fiber dosimeters

Abstract. We have investigated Čerenkov radiation generated in phosphor-based optical fiber dosimeters irradiated with clinical electron beams. We fabricated two high-spatial resolution fiber-optic probes, with 200 and 400  μm core diameters, composed of terbium-based phosphor tips. A generalizable spectroscopic method was used to separate Čerenkov radiation from the transmitted signal by the fiber based on the assumption that the recorded signal is a linear superposition of two basis spectra: characteristic luminescence of the phosphor medium and Čerenkov radiation. We performed Monte Carlo simulations of the Čerenkov radiation generated in the fiber and found a strong dependence of the recorded Čerenkov radiation on the numerical aperture of the fiber at shallow phantom depths; however, beyond the depth of maximum dose that dependency is minimal. The simulation results agree with the experimental results for Čerenkov radiation generated in fibers. The spectroscopic technique used in this work can be used for development of high-spatial resolution fiber micro dosimeters and for optical characterization of various scintillating materials, such as phosphor nanoparticles, in ionizing radiation fields of high energy.


Introduction
Fiber-optic probes in conjunction with scintillating materials are promising candidates for radiation therapy dosimetry, such as in high-dose rate brachytherapy, 1,2 intensity-modulated radiation therapy, 3 superficial therapy, 4 and stereotactic radiosurgery. 5 Real-time measurements, small physical size of the probe, highspatial resolution, and ability of performing in vivo intracavity measurements are the main advantages of such probes. The working principle of such a device relies on the generation of an optical signal proportional to the absorbed dose in the irradiated scintillating medium, which is collected and transmitted by the optical fiber to a detector, usually a photodiode or photomultiplier tube. The total optical signal recorded by the detector, however, has unwanted components in addition to the useful scintillation signal. These artifactual signals, collectively termed "stem effect," 6,7 are composed primarily of the Č erenkov radiation generated in the irradiated portion of the fiber together with a small contribution of the intrinsic fiber fluorescence in the case of plastic fibers. Only the scintillation emission from the scintillator is directly proportional to the amount of energy deposited in the scintillator, i.e., absorbed dose; therefore, the total signal must be corrected for the contribution of Č erenkov radiation in order to accurately measure the absorbed dose in the scintillator. Generation of Č erenkov radiation in the fiber, particularly at angles where it is dominant, imposes a limit on the physical dimensions and spatial resolution of plastic fiber scintillators in order to achieve a reliable signal-to-background ratio.
Č erenkov radiation [8][9][10][11] occurs when charged particles traverse a dielectric medium with velocities greater than the phase velocity of light in that medium. It is a polarized, coherent, and directional emission; its direction is along the surface of a cone that makes the half-angle θ ¼ cos −1 ðnβÞ −1 with the particle's track, where n is the refractive index of the medium and β ¼ v∕c is the ratio of the velocity of the particle to that of light. Since the particle must travel faster than light, i.e., v > c∕n, to induce Č erenkov radiation, its minimum energy is E min ¼ m 0 c 2 ½ð1 − n −2 Þ −1∕2 − 1, where m 0 is the rest mass of the particle. For example, the threshold electron energies to generate Č erenkov radiation in water (n ¼ 1.33) and pure silica (n ¼ 1.55) are E min ¼ 264 and 158 keV, respectively. The number of Č erenkov photons generated by a charged particle with z times the charge of an electron along path length l in the wavelength region between λ 1 and λ 2 (λ 1 < λ 2 ), is proportional to λ −2 , and is given by where α ≈ 137 −1 is the fine structure constant. 11 Č erenkov radiation has a continuous spectrum spanning from near ultraviolet to near infrared with light intensity decreasing proportional to λ −3 as the wavelength increases; the spectrum of Č erenkov radiation is restricted from both ends of the visible spectrum by the absorption spectrum of the material in which it is generated.
Č erenkov radiation has been the subject of considerable research in recent years for potential applications in life sciences and engineering. A number of articles have appeared introducing its potential applications in molecular imaging, [12][13][14][15][16][17][18][19] monitoring of tissue optical properties, 20 ionizing radiation beam monitoring, quality assurance and dosimetry, 21-33 and particle detection. [34][35][36][37][38] When optical fibers pass through ionizing radiation fields of high energy, as in fiber-optic dosimetry, Č erenkov radiation generated inside the fibers' core is guided through the fiber if the emitted ray hits the core-cladding boundary with an angle greater than the critical angle satisfying the total internal reflection condition required for guided rays. Transmission of Č erenkov radiation is, therefore, dependent on the angle between the particle's track and the fiber's axis. Therefore, the recorded raw signal is not directly related to the dose absorbed by the scintillator. Č erenkov radiation signal is strongest when the angle between the fiber's axis and particle's track is close to the Č erenkov cone half-angle. It should be mentioned that depending on the dosimetry protocol, Č erenkov light generated in the optical fiber may be the useful signal. In scintillation fiber-optic dosimetry, however, Č erenkov light is an unwanted background signal and separating it from the total optical signal is crucial; using raw signals without removing it would lead to errors higher than 20%.
Four general methods have been applied to separate the Č erenkov light from the total optical signal: (1) Subtraction method, 6,39 where a parallel fiber identical to the one that is connected to the scintillating piece is used to generate similar background light that can be subtracted from the total signal. For fields with high-dose gradient, however, such a technique is not reliable. (2) Optical filtering, 40 where a long-wavelengthemitting scintillator in conjunction with a long-pass filter is used to selectively measure the signal in longer wavelengths of the spectrum where contribution of Č erenkov radiation is minimal due to its λ −3 profile. Nevertheless, this method is not very effective since the filtered signal is still contaminated with the Č erenkov radiation due to the fact that the Č erenkov radiation has a continuous spectrum. (3) Temporal separation 41 that relies on different time scales associated with Č erenkov radiation and the scintillation process. This method requires fast responding electronics and works only with pulsed radiation fields. (4) Chromatic removal, [42][43][44] which is the current state-of-theart method and requires two different optical filters to measure the signal at two different spectral regions; the dose is then calculated by using coefficients obtained from calibration.
It should be noted that it has been suggested 45 that the use of hollow waveguides with an air core instead of conventional solid core fibers would reduce the deteriorating effect of Č erenkov radiation because the production of Č erenkov light is minimal in air since its refractive index is close to 1; such hollow waveguides, however, have optimal design parameters for transmission of infrared wavelengths, 46,47 whereas the scintillators of interest here emit primarily visible light.
In this work, we address two aspects of the problem of Č erenkov contamination in optical fibers used for scintillation dosimetry: first, we demonstrate the rigorous spectroscopic separation of the contributions from scintillator emission and Č erenkov radiation using a low-cost single-channel spectrometer and a straightforward linear superposition fitting algorithm. This allows detection of the scintillation signal using a single optical fiber and robust rejection of Č erenkov contamination. Second, using Monte Carlo simulation, we investigate in detail the dependence of the Č erenkov contamination on the details of the optical fiber used for detection, specifically on the numerical aperture. These results explain the variations in the degree of Č erenkov contamination with depth in electron beams, and inform the design of future generations of high-resolution optical fiber dosimetry systems.

Materials and Methods
In order to experimentally study the induced Č erenkov radiation in fiber dosimeters, we fabricated high-resolution fiber-optic microprobes and performed luminescence spectroscopy. Our dosimetry system consisted of four components: (1) a phosphorbased probe to convert the absorbed dose to an optical signal, (2) an optical fiber to transmit the generated light from the probe to the spectrometer, (3) a spectrometer to acquire the spectrum of light collected by the fiber, and (4) a computer for signal processing to calculate the luminescence of phosphors. Figure 1(a) is a schematic illustration of the probe design. An ∼1 to 3 mm layer of TbF 3 (Sigma-Aldrich) in the form of a white powder was packed in a plastic capillary (Cole-Parmer). The distal end of the capillary was optically sealed. A 15-m long silica optical fiber (FT400UMT, Thorlabs) with numerical aperture NA ¼ 0.39 (pure silica core with refractive index 1.51 and fluoropolymer cladding with index 1.46 at λ ¼ 500 nm) and core diameter of 400 μm was inserted 3 mm into the capillary from the other end to capture and transport the emitted light from the phosphors to the spectrometer. The size match between internal diameter of the plastic capillary and the external diameter of the fiber provided tight packing of the phosphors and the fiber. In another probe design, we used an optical fiber with a 200-μm core diameter (FT200UMT, Thorlabs) with NA ¼ 0.39. The effective radiation-sensitive portion of our probes is ∼0.1 to 0.5 mm 3 .
Optical spectroscopy was performed using a thermoelectrically cooled CCD array spectrometer (BTC112E, BWTEK Inc.) with a 0.4-nm spectral resolution. In order to minimize direct interaction of the ionizing radiation with its CCD, the spectrometer was placed outside the treatment room. Dark current spectra were obtained by collecting spectra with the spectrometer's input aperture covered, and were subtracted from each spectrum acquired. The spectra were corrected for wavelength-dependent instrument response and wavelength-dependent transmission of fibers using an instrument-specific calibration function. This function was determined for each fiber by taking the ratio of the measured spectrum of a lamp with an NIST-traceable calibration (LS1-cal, Ocean Optics) to its known spectrum.
In order to study Č erenkov radiation generated in the fiber and evaluate the performance of the fiber probes, we performed optical characterization experiments in a tissue equivalent environment by using virtual water phantoms (standard imaging). 15 cm of the distal end of the fiber was positioned in a drilled channel parallel to the sides and passing along the center of a 30 × 30 × 1 cm 3 virtual water phantom, labeled "sample-phantom" in Fig. 1(b). The fiber was completely embedded in the sample-phantom, allowing us to place additional phantom layers on top of the sample-phantom. Additional phantom layers were sequentially added after each measurement to provide measurements at different phantom depths. In all cases, the source-tosurface-distance (SSD), measured to the top surface of the top most phantom, was adjusted to 100 cm. In all experiments, a 5cm base layer of virtual water phantom was placed under the sample-phantom. A black rubberized fabric (BK5, Thorlabs) was used to cover the sample-and base-phantoms during the experiments to assure no background light, such as the alignment laser or device indicator light, is collected by the fiber.
The fiber probe was irradiated by a 6-MeV electron beam in a square 10 × 10 cm 2 field generated by using a clinical medical linear accelerator (Clinac 2100 IX, Varian Medical Systems), see Fig. 1(c). The selected beam energy is much greater than the energy threshold required for emission of Č erenkov radiation in pure silica (E min ≈ 0.158 MeV). The dose rate in all experiments was set to 6 Gy∕min at the depth of the maximum dose.
The recorded luminescence signal (S tot ) by the spectrograph was considered as the linear superposition of two basis components: luminescence from the phosphors (L ph ) and the Č erenkov radiation (Č f ) generated in the fiber. Therefore, the recorded spectrum in each case, corrected for instrument response, was analyzed as a linear combination of basis luminescence spectra using a singular value decomposition (SVD) fitting algorithm implemented in MATLAB®, similar to that used previously 48 for fitting fluorescent spectra in studying the photobleaching kinetics of photosensitizers in photodynamic therapy. The basis spectrum for the Č erenkov radiation is calculated from the theoretical λ −3 dependency expected for Č erenkov radiation, where λ is the wavelength of light. We experimentally verified the λ −3 dependency by curve fitting to spectra, obtained from irradiated standalone fibers in various conditions. The basis spectrum for the characteristic luminescence of phosphors was obtained according to the following manner. First, we recorded the spectrum of the irradiated fiber probe with its phosphor tip connected. Then we removed the phosphor tip and recorded the spectrum of the irradiated bare fiber. By subtracting the latter from the former, we obtained the basis spectrum for the luminescence of the phosphors. We verified that basis spectrum by irradiating the phosphors with incident beams of energies below the threshold for generating Č erenkov radiation. The SVD fitting algorithm has additional Fourier terms to take into account the potential presence of any other contributions in the fiber. The two basis spectra and the Fourier series (F 0 ) are fit to the instrument-corrected data using Eq. (1), E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 1 ; 3 2 6 ; 7 0 1 where the numbers in subscript are the weights used in the SVD fitting algorithm. This choice of the weighting factors provided reliable fits to the experimental data. It should be noted that their exact values are not critical as the SVD fits were remarkably insensitive to the choice of weighting factors. The coefficients a 100 and b 100 in each beam condition were considered as the measure of the absorbed dose and Č erenkov radiation, respectively. [49][50][51] Monte Carlo simulation was conducted by using the GEANT4-based toolkit GAMOS for Monte Carlo modeling to stochastically simulate radiation transport, dose deposition, and Č erenkov radiation emission. A phase space file (from the IAEA database) of a 10 × 10 cm 2 6-MeV electron beam for the LINAC (Varian Clinic 2100CD) was adopted as the irradiating source. The phase space file was used to irradiate the cubic phantom (water equivalent, 30 × 30 × 30 cm 3 ) at SSD ¼ 100 cm. Optical fibers were modeled and placed at depths from 1 to 49 mm with an increment of 2 mm. For any Č erenkov photon generated in the fiber, initial positions, directions, and energies were recorded. Any Č erenkov photon with initial directions that fell into the collection angle of the fiber was assumed to be detectable. Additionally, radiation doses deposited in each fiber were scored. In total, 10 9 primary particles were initialized from the phase space file.

Results and Discussion
The normalized basis spectra for the Č erenkov radiation with λ −3 wavelength dependency and the luminescence of the TbF 3 phosphors with peaks at λ ¼ 489, 542, 587, and 620 nm are presented in Figs. 2(a) and 2(b), respectively.
We performed measurements at various exposure times in the range from 0.5 to 20 s and dose rates from 1 to 200 cGy∕ min and found that ∼2 cGy is the minimum dose that can be measured with less than 4% uncertainty. We selected 20 s exposure times for the rest of the measurements. A typical recorded spectrum at a 1.5-cm phantom depth and the SVD results from the irradiated fiber probe are presented in Fig. 3. The measured spectrum is a superposition of the cathodoluminescence signal from TbF 3 with four characteristic peaks at λ ¼ 489, 542, 587, and 620 nm due to the f-f transition of a terbium ion, on a continuous Č erenkov radiation background, with λ −3 wavelength dependence. By using the SVD algorithm, we decomposed the recorded signal into its constituent components. Figure 3(b) shows the decomposed spectra, i.e., emission of TbF 3 and Č erenkov radiation, corresponding to the spectrum presented in Fig. 3(a). The presence of four characteristic features in the terbium spectrum makes the spectral separation of Č erenkov radiation generated in the fiber more robust to noise. We observed an excellent agreement between the recorded spectrum and the fit obtained from the linear combination of the decomposed spectra, as illustrated in Fig. 3(b), demonstrating the feasibility of the spectral separation of Č erenkov radiation. Figure 4(a) shows the simulation results of the absorbed dose, total Č erenkov radiation generated in the fiber, and the amount of Č erenkov radiation coupled to the fiber, as a function of depth in the phantom for a 6-MeV monoenergetic electron beam. All values were normalized to 100% at a 1.5-cm depth. The dose exhibits the well-known characteristics of a 6-MeV electron beam in water, with a depth of maximum dose (d max ) around 1.5 cm resulting from the interplay of electron scattering and collisional energy loss. 52 Monte Carlo simulation results reveal a considerable discrepancy between the total generated Č erenkov radiation and the Č erenkov radiation coupled to the fiber. The discrepancy arises mainly from the fact that not all of the generated Č erenkov photons lie within the acceptance cone of the fiber, as schematically illustrated in Fig. 5. However, at depths beyond the depth of the maximum dose, the normalized total and coupled Č erenkov radiation curves converge and follow the same trend as the absorbed dose. When the effect of the NA of the fiber is taken into account in the simulation, there Fig. 3 (a) Recorded spectrum from the Tb-based probe showing cathodoluminescence of TbF 3 with peaks at λ ¼ 489, 542, 587, and 620 nm superimposed on a continuous Č erenkov radiation background. The probe was irradiated at 1.5-cm phantom depth by a 6 MeV electron beam. (b) The resultant decomposed spectra of luminescence of terbium and Č erenkov radiation generated in the fiber. There is an excellent agreement between the measured spectrum and linear superposition of the decomposed spectra.  is a good agreement between the calculated fit based on the SVD and the experimental data (coefficients b 100 ), as illustrated in Fig. 4(b). The effect of the numerical aperture of the fiber on the Č erenkov radiation collected by the fiber was studied through Monte Carlo simulation. The NA of the fiber was changed from 0.1 to 1. The resulting ratios of the collected Č erenkov radiation to its maximum at d max are shown in Fig. 6. We found that the intensity of the collected Č erenkov radiation in shallow phantom depths, i.e., in the build-up region, strongly depends on the NA of the fiber. This is due to the fact that the intensity of Č erenkov radiation strongly depends on the angle between the fiber axis and the electron trajectory, and the electrons at shallow depths are oriented primarily in the beam direction, perpendicular to the fiber axis. However, beyond the depth d max , the dependency on the NA is minimal due to the angular spread of the electron beam, see Fig. 6.
The dose dependency of the luminescence of the Tb-based probes was studied by electron beam spatial profile measurement at the 1.5-cm phantom depth. The 200-μm core fiber probe was used in this study. The field size at 100-cm SSD was 10 × 10 cm 2 and the table was laterally moved to perform measurements at each point to collect data from 12 points from the center of the beam to a 7-cm lateral distance. The a 100 coefficients obtained from the SVD fits, normalized to that corresponding to the maximum dose at the center of the beam, were used to measure the beam profile. For comparison, the profile measured by a diode-based radiation detector designed for measurements in electron beams is shown in the same figure. This profile was acquired as part of the commissioning procedure for the linear accelerator, in accordance with standard 53 commissioning procedures. In Fig. 7, the measured spatial beam profile is presented in comparison to the measurements performed by the electron diode that shows an excellent agreement (less than 1% deviation) between the two measurements.

Conclusions
We have investigated Č erenkov radiation generated in irradiated optical fibers and found that at depths shallower than the depth of maximum dose (build-up region), the intensity of the Č erenkov radiation coupled through the fiber is highly dependent on the numerical aperture of the fiber. However, beyond the depth of maximum dose, this effect disappears due to the angular spread of the electron beam. We used a generalizable method for separation of Č erenkov radiation generated in irradiated optical fibers based on optical spectroscopy measurements. This method works in fiber-optic applications, where optical fibers pass through high-energy ionizing radiation fields. We showed that the fiber-optic dosimetry of ionizing radiation fields based on phosphor-tipped fibers is feasible with submillimeter resolution provided that spectral separation of Č erenkov radiation is rigorously performed. The experimental method and apparatus developed in this work provide a robust platform for designing fiber-optic micro dosimeters and optical characterization of nanophosphors irradiated by medical beams to investigate them as potential imaging or therapeutic agents, e.g., when they are conjugated with photosensitizers used in photodynamic therapy. [54][55][56]