1.

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, high-spatial 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 Čerenkov 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 Čerenkov radiation in order to accurately measure the absorbed dose in the scintillator. Generation of Čerenkov 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.

Čerenkov radiation^8–11 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 $\theta ={\cos }^{-1}{(n\beta )}^{-1}$ with the particle’s track, where $n$ is the refractive index of the medium and $\beta =v/c$ 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 Čerenkov radiation, its minimum energy is $E_{\min }=m_0{c}^2[{(1-n^{-2})}^{-1/2}-1]$, where $m_0$ is the rest mass of the particle. For example, the threshold electron energies to generate Čerenkov radiation in water ($n=1.33$) and pure silica ($n=1.55$) are $E_{\min }=264$ and 158 keV, respectively. The number of Čerenkov photons generated by a charged particle with $z$ times the charge of an electron along path length $l$ in the wavelength region between ${\lambda }_1$ and ${\lambda }_2$ (${\lambda }_1<{\lambda }_2$), is proportional to ${\lambda }^{-2}$, and is given by $N=2\pi \alpha zl({\lambda }_1^{-1}-{\lambda }_2^{-1})[1-{(n\beta )}^{-2}]$, where $\alpha \approx {137}^{-1}$ is the fine structure constant.¹¹Čerenkov radiation has a continuous spectrum spanning from near ultraviolet to near infrared with light intensity decreasing proportional to ${\lambda }^{-3}$ as the wavelength increases; the spectrum of Čerenkov radiation is restricted from both ends of the visible spectrum by the absorption spectrum of the material in which it is generated.

Čerenkov 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,^12–19 monitoring of tissue optical properties,²⁰ ionizing radiation beam monitoring, quality assurance and dosimetry,^21–33 and particle detection.^34–38 When optical fibers pass through ionizing radiation fields of high energy, as in fiber-optic dosimetry, Čerenkov 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 Čerenkov 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. Čerenkov radiation signal is strongest when the angle between the fiber’s axis and particle’s track is close to the Čerenkov cone half-angle. It should be mentioned that depending on the dosimetry protocol, Čerenkov light generated in the optical fiber may be the useful signal. In scintillation fiber-optic dosimetry, however, Čerenkov 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 Čerenkov 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-wavelength-emitting scintillator in conjunction with a long-pass filter is used to selectively measure the signal in longer wavelengths of the spectrum where contribution of Čerenkov radiation is minimal due to its ${\lambda }^{-3}$ profile. Nevertheless, this method is not very effective since the filtered signal is still contaminated with the Čerenkov radiation due to the fact that the Čerenkov radiation has a continuous spectrum. (3) Temporal separation⁴¹ that relies on different time scales associated with Čerenkov radiation and the scintillation process. This method requires fast responding electronics and works only with pulsed radiation fields. (4) Chromatic removal,^42–44 which is the current state-of-the-art 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 suggested⁴⁵ that the use of hollow waveguides with an air core instead of conventional solid core fibers would reduce the deteriorating effect of Čerenkov radiation because the production of Čerenkov 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 Čerenkov contamination in optical fibers used for scintillation dosimetry: first, we demonstrate the rigorous spectroscopic separation of the contributions from scintillator emission and Čerenkov 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 Čerenkov contamination. Second, using Monte Carlo simulation, we investigate in detail the dependence of the Čerenkov 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 Čerenkov contamination with depth in electron beams, and inform the design of future generations of high-resolution optical fiber dosimetry systems.

2.

Materials and Methods

In order to experimentally study the induced Čerenkov radiation in fiber dosimeters, we fabricated high-resolution fiber-optic microprobes and performed luminescence spectroscopy. Our dosimetry system consisted of four components: (1) a phosphor-based 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 $\sim 1$ to 3 mm layer of ${\mathrm{TbF}}_3$ (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 $\mathrm{NA}=0.39$ (pure silica core with refractive index 1.51 and fluoropolymer cladding with index 1.46 at $\lambda =500\mathrm{nm}$) and core diameter of $400\mu \mathrm{m}$ 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 $200\text{-}\mu \mathrm{m}$ core diameter (FT200UMT, Thorlabs) with $\mathrm{NA}=0.39$. The effective radiation-sensitive portion of our probes is $\sim 0.1$ to $0.5{\mathrm{mm}}^3$.

Fig. 1

Schematic illustration of: (a) fiber-optic probe design and (b) the experimental setup. (c) Experimental setup with a clinical linac: the fiber probe was positioned in a virtual water phantom labeled as the sample-phantom and additional phantom layers (labeled as top phantoms) were placed sequentially over the sample-phantom.

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 Čerenkov 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 $30\times 30\times 1{\mathrm{cm}}^3$ 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-to-surface-distance (SSD), measured to the top surface of the top most phantom, was adjusted to 100 cm. In all experiments, a 5-cm 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 $10\times 10{\mathrm{cm}}^2$ 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 Čerenkov radiation in pure silica ($E_{\min }\approx 0.158\mathrm{MeV}$). The dose rate in all experiments was set to $6\mathrm{Gy}/\min$ at the depth of the maximum dose.

The recorded luminescence signal ($S_{\mathrm{tot}}$) by the spectrograph was considered as the linear superposition of two basis components: luminescence from the phosphors ($L_{\mathrm{ph}}$) and the Čerenkov radiation (${\mathrm{Č}}_f$) 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 previously⁴⁸ for fitting fluorescent spectra in studying the photobleaching kinetics of photosensitizers in photodynamic therapy. The basis spectrum for the Čerenkov radiation is calculated from the theoretical ${\lambda }^{-3}$ dependency expected for Čerenkov radiation, where $\lambda$ is the wavelength of light. We experimentally verified the ${\lambda }^{-3}$ 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 Čerenkov 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),

Monte Carlo simulation was conducted by using the GEANT4-based toolkit GAMOS for Monte Carlo modeling to stochastically simulate radiation transport, dose deposition, and Čerenkov radiation emission. A phase space file (from the IAEA database) of a $10\times 10{\mathrm{cm}}^2$ 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, $30\times 30\times 30{\mathrm{cm}}^3$) at $\mathrm{SSD}=100\mathrm{cm}$. Optical fibers were modeled and placed at depths from 1 to 49 mm with an increment of 2 mm. For any Čerenkov photon generated in the fiber, initial positions, directions, and energies were recorded. Any Čerenkov 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.

3.

Results and Discussion

The normalized basis spectra for the Čerenkov radiation with ${\lambda }^{-3}$ wavelength dependency and the luminescence of the ${\mathrm{TbF}}_3$ phosphors with peaks at $\lambda =489$, 542, 587, and 620 nm are presented in Figs. 2(a) and 2(b), respectively.

Fig. 2

Basis spectra corresponding to (a) Čerenkov radiation and (b) luminescence of ${\mathrm{TbF}}_3$ phosphors (peaks are at $\lambda =489$, 542, 587, and 620 nm) used for singular value decomposition method. Both spectra were normalized to have maximum value of 100 within the spectral range of $\lambda =460$ to 630 nm.

We performed measurements at various exposure times in the range from 0.5 to 20 s and dose rates from 1 to $200\mathrm{cGy}/\min$ and found that $\sim 2\mathrm{cGy}$ 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 ${\mathrm{TbF}}_3$ with four characteristic peaks at $\lambda =489$, 542, 587, and 620 nm due to the f-f transition of a terbium ion, on a continuous Čerenkov radiation background, with ${\lambda }^{-3}$ 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 ${\mathrm{TbF}}_3$ and Čerenkov 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 Čerenkov 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 Čerenkov radiation.

Fig. 3

(a) Recorded spectrum from the Tb-based probe showing cathodoluminescence of ${\mathrm{TbF}}_3$ with peaks at $\lambda =489$, 542, 587, and 620 nm superimposed on a continuous Čerenkov 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 Čerenkov radiation generated in the fiber. There is an excellent agreement between the measured spectrum and linear superposition of the decomposed spectra.

Figure 4(a) shows the simulation results of the absorbed dose, total Čerenkov radiation generated in the fiber, and the amount of Čerenkov 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 Čerenkov radiation and the Čerenkov radiation coupled to the fiber. The discrepancy arises mainly from the fact that not all of the generated Čerenkov 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 Čerenkov 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 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).

Fig. 4

(a) Monte Carlo simulation results of absorbed dose, total Čerenkov radiation generated in the fiber, and coupled Čerenkov radiation to the fiber ($\mathrm{NA}=0.39$) as a function of phantom depth for a monoenergetic 6-MeV electron beam with $10\times 10{\mathrm{cm}}^2$ field size. (b) Comparison with the experimental results and Monte Carlo simulation.

Fig. 5

Schematic illustration of Čerenkov radiation generated in the fiber when it is (a) guided through and (b) leaked from the fiber. $\theta$ is the Čerenkov semicone angle and $\varphi$ is the critical angle.

The effect of the numerical aperture of the fiber on the Čerenkov 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 Čerenkov radiation to its maximum at $d_{\max }$ are shown in Fig. 6. We found that the intensity of the collected Čerenkov 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 Čerenkov 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.

Fig. 6

Monte Carlo simulation results of the transmitted Čerenkov radiation by the fiber, irradiated with 6-MeV electron beam, as a function depth for different values of fiber numerical aperture in the range $\mathrm{NA}=0.1$ to 1.

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 $200\text{-}\mu \mathrm{m}$ core fiber probe was used in this study. The field size at 100-cm SSD was $10\times 10{\mathrm{cm}}^2$ 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 standard⁵³ 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.

Fig. 7

Spatial beam profile at the phantom depth of maximum dose ($d_{\max }=1.5\mathrm{cm}$) for 6-MeV electron beam measured by the fiber probe compared to electron diode measurements.

4.

Conclusions

We have investigated Čerenkov 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 Čerenkov 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 Čerenkov 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 Čerenkov 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.^54–56