Applications of position-sensitive detectors (PSDs) include high-energy physics experiments [1], muon imaging [2], and radiation therapy [3]. Plastic scintillation fibers (PSFs) coupled to silicon photomultipliers (SiPMs) [4] are employed in many cases. Conventional position sensing techniques are based on either time-of-flight (TOF) or attenuation of scintillation light due to scattering and absorption during propagation [5]. Photodetectors are required at both ends of a PSF. The degree of freedom for placing such all-optical PSDs would increase if a signal could be read out from one end only. For example, the PSDs could be laid out around nuclear reactors and fuel and waste storage facilities with less restriction. Irradiation doses in brachytherapy could be monitored continuously over a region rather than at pre-determined points [6].

Self-absorption in a luminescent material causes a redshift in the spectrum of the photoluminescence (PL) photons. This phenomenon can be utilized for position sensing. Namely, a spectrometer detects a redshift in the spectrum of the PL photons at one end of a PSF. The longer the propagation distance, the larger the redshift. Hence, the incident point of radiation along the PSF can be determined by measuring the degree of this redshift. One and two-dimensional position sensing was demonstrated for visible light [7]. For high-sensitivity applications, a dichroic mirror and two SiPMs can replace the spectrometer [8].

Depending on specific applications, requirement for sensitivity varies greatly. One can always attenuate a high-intensity photon flux by inserting neutral density filters in its optical path. Conversely, detection of a low-intensity flux requires sensitive photodetectors. In this regard, a minimum ionizing particle presents a tough challenge.

In this paper, we first describe the position sensing technique utilizing self-absorption in a PSF. Then, position detection of a beta particle emitter is demonstrated with a PSF, a dichroic mirror, and two SiPMs.

A configuration for detecting the position of a beta particle emitter (⁹⁰Sr) by this technique is depicted in Fig. 1. A dichroic mirror and two SiPMs are placed near the tip of a PSF. When a single spot on the PSF is excited by a beta particle, PL photons are emitted. The emission is usually isotropic and some of the photons are trapped in the PSF by total internal reflection. They propagate a distance z and exit from the tip of the PSF at various angles. The maximum angle is determined by the numerical aperture. Large-area SiPMs are used to collect as many photons as possible.

 

Fig. 1. Configuration of position sensing technique utilizing self-absorption in PSF.

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After propagating a distance z along the PSF axis, the spectral flux of PL photons ${S_{PL}}$ decreases to ${e^{ - \mu z}}{S_{PL}}$, where $\mu$ is a wavelength-dependent attenuation coefficient. Denoting the reflectance of a dichroic mirror as ${R_{dm}}$ and the quantum efficiency of a photodetector as ${\eta _d}$, the number of photoelectrons generated by each photodetector is given by integrating these quantities with wavelength $\lambda$, as

How we relate the distance z to these measurables is somewhat arbitrary. For example, the simple index

In an experiment, we first measured the sensitivity of a photodetector consisting of a SiPM and its readout electronics (Hamamatsu K. K., S13360-6025CS, C12332-01, respectively). A pulsed photon flux from an ultraviolet laser irradiated the SiPM. The wavelength was 377 nm, and the pulse duration was 100 ns. The photon flux was attenuated to the level of a few photons per pulse at most. The output waveform from the readout electronics was recorded using an oscilloscope. The peak voltages of these waveforms were sampled. The resultant pulse height spectrum is shown in Fig. 2. The solid curves are fit by Gaussian functions. The pedestal represents the noise level.

A single photoelectron is detected well above the noise. The linear relation between the pulse height and the number of photoelectrons in the inset of Fig. 2 reveals that the sensitivity of this photodetector is 0.59 mV/photoelectron.

 

Fig. 2. Pulse height spectra of SiPM and its electronics. Inset: the linear fit shows that the sensitivity is 0.59 mV/photoelectron.

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Next, a PSF (Kuraray Co Ltd., SCSF-78), a dichroic mirror (Thorlabs Inc., DMLP505T), and the two SiPMs from Hamamatsu were configured as shown in Fig. 3. The diameter and the numerical aperture of this PSF are 1 mm and 0.55, respectively. The sensitive area of the SiPM is 6 mm × 6 mm. Based on the observed spectra of this PSF [7], we chose a dichroic mirror with a cutoff wavelength of 505 nm, such that only the signal ${N_1}$ represented the redshift in the PSF.

 

Fig. 3. Key components in experiment.

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A radioisotope source (⁹⁰Sr, 10 kBq, Japan Radioisotope Association, SR303) was placed a few millimeters away from the PSF. Scintillation photons with wavelengths shorter than 505 nm were directed to SiPM1 and those with longer wavelengths to SiPM2. The distance z was varied from 40 cm to 240 cm in steps of 50 cm.

An oscilloscope was used to record the waveforms from the two SiPMs. The trigger levels for the two channels were both fixed at 3.60 mV, which corresponded to 6.1 photoelectrons. When the signals from both SiPMs exceeded this level, the two waveforms were recorded. The count rates with and without the radioisotope were 67.7 events/min and 1.7 events/min, respectively. The peak voltages were extracted from the data for 2000 events. The pulse height spectra corresponding to the data obtained at three selected positions are shown in Fig. 4. The bin width in this analysis is 1 mV, which corresponds to about 1.7 photoelectrons.

 

Fig. 4. Pulse height spectra for 2000 events detected by (a) SiPM1 and (b) SiPM2. The trigger levels of the two channels were set at 3.60 mV. Only the data recorded for distances z = 0 cm, 140 cm, and 240 cm are shown here.

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Each pulse height spectrum in Fig. 4 has a wide distribution, owing to fluctuations in every statistical event involved: division of the decay energy between an electron and an antineutrino; energy transfer to the scintillating materials from a fast electron; generation of scintillation photons; trapping in the fiber; reflection or transmission at the dichroic mirror; and the signal generation process in the SiPM. These fluctuations are reduced by averaging the waveforms from many detection events. Waveforms averaged for 2000 events are shown in Fig. 5. For the case of SiPM1 in Fig. 5(a), the peak height decreases with the distance z, as expected. By contrast, the averaged waveform from SiPM2 remains the same. This is because photons with wavelengths longer than 505 nm are immune to self-absorption.

 

Fig. 5. Output waveforms of two SiPMs averaged for 2000 events: (a) SiPM1, (b) SiPM2. Each inset shows a magnified peak region.

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Using the sensitivity of SiPM (0.59 mV/photoelectron), each peak pulse height in Fig. 5 is converted to the number of photoelectrons, to detect a single beta particle. The result is plotted in Fig. 6. The empty circles and squares represent the numbers of photoelectrons detected by SiPM1 and SiPM2, respectively. When the distance z increases, the number of scintillation photons with shorter wavelengths decreases. The number of scintillation photons with longer wavelengths does not depend on the distance.

 

Fig. 6. Average numbers of photoelectrons detected by the two SiPMs for each detection event of a single beta particle emitted by the radioisotope, and index E calculated from them.

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The solid triangles in Fig. 6 are the index E defined by Eq. (2). The dotted curve is a fit by a quadratic function. Nevertheless, once this curve is obtained by a calibration process, the distance is calculated from the two measurables. In our experiment, such a calibration curve was acquired to detect the position of a ⁹⁰Sr source up to a distance of 240 cm. One can play with the definition of this index to have different calibration curves. If such an index is a monotonic function of the distance, the source position can be determined from the signals from the two SiPMs.

As shown in Fig. 6, the total yield of photoelectrons from the two SiPMs ranges from about 15 to 17 in this experiment. Depending on the propagation distance in the PSF, the photoelectrons are unevenly divided by the two SiPMs. Honda et al. [9] coupled a SiPM directly to a similar PSF with multi-cladding configuration (Kuraray, SCSF-78M) to detect single beta particles from a ⁹⁰Sr source. Their yield of about 17 photoelectrons is comparable to our value. Borshchev et al. [10] coupled a SiPM directly to the same PSF with a single cladding structure (Kuraray, SCSF-78). They measured the change in the number of photoelectrons when the distance between the SiPM and the incident point of beta particles was varied. Their values are 24 photoelectrons at 40 cm and 13 photoelectrons at 240 cm. Our values are 17 photoelectrons at 40 cm and 15 photoelectrons at 240 cm (Fig. 6). The discrepancy might be attributed to the difference in the source condition. Borshchev et al. [10] set an energy window for the beta particles from a ⁹⁰Sr source to 1.1 ± 0.1 MeV using a magnetic field and collimators. Our source had a 0.1-mm-thick Al window and no such energy-selecting means.

In our proof-of-concept experiment with an off-the-shelf PSF, the range of position sensing was 240 cm. In principle, one should be able to design the range and spatial resolution for each specific application. For example, one can increase the concentration of luminescent materials in a plastic fiber to enhance self-absorption. This would result in a steeper calibration curve, which in turn would shorten the range and enhance the spatial resolution of position detection.

Position sensing of minimum ionizing particles (beta particles in this experiment) has been demonstrated using this technique. It is challenging in terms of signal-to-noise ratio because a single particle is detected by this technique. Other ionizing particles deposit more energy per unit distance in the PSF and they would generate more scintillation photons. Hence, the same calibration procedure can be applied for them, just as in the case of the pulsed light from a laser diode emitting at 377 nm [8]. Gamma rays, however, are likely to pass through plastic scintillators without interactions. To detect them efficiently, some types of converter are required. This is an interesting field to explore in the future.

Finally, on the academic side, the addition of a dichroic mirror does not change the total number of photoelectrons. Even for an extremely low photon flux, an interference filter performs just as in the case of a high photon flux, where the wave nature of light explains the interference phenomenon. This is reminiscent of Young’s double slit experiment with single photons.

In summary, position sensing of a beta particle emitter was demonstrated by utilizing self-absorption in a PSF. A dichroic mirror was placed at the tip of the PSF to direct scintillation photons with shorter wavelengths to one SiPM and those with longer wavelengths to another SiPM. The mirror’s cutoff wavelength was selected such that only the signal from the first SiPM varied with the distance between the tip of the PSF and the incident point of a beta particle. A simple index was defined to relate the distance to the signals from the two SiPMs. This relation serves as a calibration curve with which one can determine the distance based on the two signals. The total number of photoelectrons generated by a single beta particle was about 15 to 17 in this experiment. This is comparable to values published in the literature that were measured using a SiPM attached to the same PSF.