2.1. Theoretical analysis on optical transmission

Plastic scintillator is widely used in radiation detection, and to improve the detection efficiency, large size detectors are usually used [12-14]. According to theoretical and experimental studies on fluorescence photons transmission in large plate-shaped plastic scintillators in the past decade [15-22], the optical transmission follows the rules as below:

(1) The photons caused by the interaction of beta-ray with plastic scintillator are distributed evenly around the interaction point within the plastic scintillator;

(2) The attenuation of photons in a plastic scintillator has an exponential relationship with the propagation distance, that is, the number of photons that can be collected depends on the distance between light collection device and the incident point.

(3) For a relatively thin plastic scintillator, most of the fluorescent photons generated will be shot from the scintillator edge even in the absence of reflector. By adding the top and bottom surface reflector or improving the reflectivity of surface reflectors, the ratio of photons leaving from the edge will increase.

(4) For a plastic scintillator of a certain size, an appropriate collection way can be designed to ensure that the number of photons collected by photosensitive components will not be affected by their distances from the incident location of the ray.

Therefore, for a determined detector structure and a uniformly emitting source, there is a correlation between the number of photons collected by light collection devices at different positions and device-source distances. So, we shall be able to determine the center of gravity of the light source (also the geometric center of beta-ray incident positions here) according to the signal intensities produced by light collection devices located at different distances.

2.2. Structure design of the detector

By fully referring to previous studies on the rules of fluorescence photons transmission in plastic scintillator, the collection capabilities of WLS fibers [23-27] and the method to connect fibers with scintillator [28-32], a position sensitive detector for beta contamination using the “light center of gravity” method is designed, as shown schematically in Fig. 1.

Fig. 1Full-screen View

A schematic diagram of the detector structure.

The detector consists of a large-area plastic scintillator, WLS fibers, and organic glass. The WLS fiber has an inner core of Φ1 mm and cladding materials of 0.15 mm in thickness. The plastic scintillators were size at 40 cm × 30 cm, but the design was changed to 37 cm × 30 cm, considering that a greater distance between the two parallel WLS fibers would weaken efficiencies of light collection and coincidence measurement (see the simulation results in Section 3.1). They are 1.5 mm thick, determined according to the fiber diameter and influence of the scintillator thickness on the beta/gamma sensitivity [33]. Organic glass of 5 mm thickness is used for structural support and light transmission. Aluminum foil of about 2 mg/cm³ mass thickness is used on the lower surface to shield and reflect light. In addition, to increase the optical collection efficiency as much as possible, a piece of reflection glass used as a reflector is installed on upper surface of the organic glass and around the composite structure. All optical interfaces are polished and applied with silicone oil.

In theory, because of different distances between the beta-ray incident points and the two parallel WLS fibers in the same fiber layer, the numbers of fluorescence photons collected by the two parallel WLS fibers are different (i.e. the corresponding amplitudes of output pulses generated after the PMT photoelectric conversion are different). Therefore, the incident position can be determined by analyzing the differences of output pulse amplitudes.

2.3. Simulation and optimization analysis

The detector structure was simulated with Geant4 toolkit to verify feasibility of the detection method and analyze position resolution of the detector. The bottom view from lower surface of the simulation model is shown in Fig. 2(a). The sectional drawing perpendicular to the X axis is shown in Fig. 2(b), in which Fibers Y1 and Y2 are fully embedded in the scintillator, while X1 and X2 are embedded half in the scintillator and half in the organic glass.

Fig. 2Full-screen View

Bottom view from lower surface of the simulation model (a) and structure model (side view) of the detector (b) in the simulation.

To analyze the relationship between the number of photons emitted from the end faces of WLS fibers and the location of beta source, a series of initial (x, y) positions of fluorescence photon emission were specified as indicated in Fig. 2(a), and the photons were collected and counted when they reached the end faces of WLS fiber.

It was assumed that the photons were homogeneously and isotropically distributed and the center depth of photon emission is 0.75 mm. The refraction indexes of organic glass and silicone oil were respectively 1.49 and 1.53, and the refractivity of mirror glass around the plastic scintillator was 0.99. The refraction indexes of the inner core and the cladding materials of WLS fiber were respectively 1.68 and 1.49. The optical attenuation time of the fiber was about 2.7 s, and the light absorption length was over 3.5 m. The ranges of absorption and emission wavelengths of the fiber were respectively 350–475 nm and 460–600 nm, and the central absorption wavelength and central emission wavelength were respectively 435 nm and 490nm.

The optical physical processes added in this work included G4Cerenkov, G4Scintillation, G4OpAbsorption, G4RayleighScattering, G4OpBoundaryProcess and G4OpWLS. In order to improve the simulation accuracy, the number of incident photons sampled randomly at each incident location was 10,000, higher than the actual quantity produced during the interaction process of beta-ray and the plastic scintillator.

2.4. Experiment system

Based on the simulation results, an experiment system for position sensitive measurement of beta contamination was built to test and verify feasibility of the method and validity of the data acquisition and processing system. The overall scheme of the experiment system is shown in Fig. 3.

Fig. 3Full-screen View

Overall scheme of the experiment system.

The experiment system was composed of four parts:

(1) position sensitive detector, which was implemented as the structure described above;

(2) photoelectric conversion device, which was a CR110 photomultiplier tube (PMT) from Beijing Hamamatsu Company;

(3) electronics system, which consisted of low-voltage power supply 4001C, pre-amplifier 142A, linear amplifier 572, 8-channel discriminator CF8000, 4-input logic unit CO4020 (all of the types above were produced by ORTEC from USA) and programmable high-voltage power supply N1471produced by CAEN from Italy; and

(4) data acquisition system, which consisted of a computer and a data acquisition card PCI-9812 produced by D-Link Company. Output signal from the logic unit was used as the trigger signal to the data acquisition card.

2.5. Experiment methods

In the experimental measurement, in order to eliminate the strongly random interfering noises such as those from PMT and only the signals from the WLS fibers kept, a coincidence measurement method was adopted, as shown in Fig. 3.

In order to ensure the accuracy, a thin sheet with the incident points marked on was laid on the beta-ray incident surface of the plastic scintillator. The spacing of the incident points shown in Fig. 2(a) was about 3 cm. The beta source used was about 5 mm in diameter, and its geometric center was about 1 cm away from the surface of the plastic scintillator. When the beta source was located at an incident point, the output signal amplitudes from each WLS fiber was measured separately. The acquisition time for each incident point was 10 minutes, and the sampling frequency for each pulse was 8 times per second.

3.1. Simulation results

The number of output photons from each WLS fiber was calculated at different incident positions, and the output photon were numbers averaged for all incident points at the same distance to the corresponding WLS fiber, by row or column. The data were fitted to obtain the relationship between the average number of output photons emitted from each WLS fiber and the distance from the incident point to the corresponding WLS fiber, as shown in Fig. 4.

Fig. 4Full-screen View

The number of the output photons from each fiber as a function of the incident position.

A comparison was performed to obtain the ratio of output photon numbers from the two parallel WLS fibers in one (X or Y) fiber layer when the beta source was located at the different incident positions. Similar trends could be found in the results for X or Y fiber layer. The results for Y fiber layer are shown in Table 1.

To verify the accuracy of data processing by this method, polynomial fitting was used to obtain the relationship between the average ratio of output photon numbers from the two parallel WLS fibers in X or Y fiber layer and the incident position-fiber distance. Fig. 5 shows the results for X and Y fiber layers.

Fig. 5Full-screen View

The average ratio of output photon numbers from the two parallel WLS fibers plotted as a function of incident position.

3.2. Experiment results

As shown in Fig. 6, evidences from two aspects proved effectiveness of the experiment data. Firstly, the pulse signals had the source correlation properties after using the coincidence method. Secondly, the amplitude spectrum of output pulses from the fibers were shaped almost the same as the beta-ray energy spectrum emitted from the ⁹⁰Sr source and the simulated spectrum for ⁹⁰Sr beta-ray energy deposit in the scintillator,.

Fig.6Full-screen View

Comparison of the energy spectra.

As the signal processing system was independently used for each fiber, inconsistency of photoelectric conversion could be introduced. Theoretically, when the beta-source was located at incident positions with the same distance to the two parallel WLS fibers in X or Y fiber layer, the average amplitudes of output signals from the two fibers should be equal. Therefore, a correction factor could be obtained to equalize the average output amplitudes from the two parallel fibers, so as to correct the inconsistency of the photoelectric conversion.

For each WLS fiber, the average amplitude of output pulses from the fiber was taken with the beta source being at different incident positions in the same distances to the fiber. By fitting the data, the relationship between the average amplitude of output pulses from the each WLS fiber and the incident point-fiber distance could be obtained, as shown in Fig. 7.

Fig. 7Full-screen View

Average amplitude of output pulse plotted as a function of incident position.

Then, by comparing the ratios of average pulse amplitudes output from the two parallel WLS fibers in X or Y fiber layer with the beta source being at the different incident positions, the data showed similar trends to the simulation results. The results for Y fiber layer are shown in Table 2.

The relationships between the average ratio of output pulse amplitudes from the two parallel WLS fibers in X or Y fiber layer and the incident position-fiber distance are shown in Fig. 8.

Fig. 8Full-screen View

Average ratio of the output pulse amplitudes plotted as a function of incident position.

4.1. Analysis of simulation results

When the beta source is located at different incident points in the same distance to the corresponding WLS fiber, the numbers of output photons emitted from the fiber are almost the same, and the photon numbers decreases with increasing vertical distance to the fiber.

When the beta source is located at different rows or columns of the grid, the average number of output photons from each WLS fiber is an exponential function of the source-fiber distance,

where, y is the average photon number output from the fiber, x is vertical distance from the source position to the fiber, and y₀ and R₀ are constants. R₀, in unit of centimeter, is negative reciprocal of the effective attenuation coefficient of photon transmission in the scintillator, also known as the fluorescence decay length of scintillator [34] (under certain conditions it is also known as the technical light attenuation length).

The results are consistent to the light transmission rules in the scintillator, with correlation coefficients of over 0.99. It indirectly proves the feasibility of embedding WLS fiber into the scintillator to improve the light collection.

When the beta source is located at different rows or columns of the grid, the average ratio of output photon numbers from the two parallel WLS fibers in X or Y fiber layer is a third-order polynomial function of the source-fiber distance,

where, y is the average ratio of output photon numbers from the two parallel WLS fibers in the same fiber layer; x is vertical distance from one of the two WLS fibers to the incident positions of beta-ray; and B₀, B₁, B₂ and B₃ are constants.

4.2. Analysis of experiment results

As a whole, the experiment results agree well with the simulation results in the curve shape, while the constant values obtained by fitting are different.

For a single WLS fiber, the R₀ values obtained from the experiment are about 0.2 cm⁻¹, significantly higher than the simulation results (about 0.06 cm⁻¹). This indicates a large gap between the actual light coupling effect and the model used in the simulation, though the scintillators are roughly of the same size and shape. So the layout of reflector and the light coupling process remain to be further improved.

For each WLS fiber layer, when the beta source is at different incident points over the scintillator surface, there is also a polynomial relationship between the average ratio of output pulse amplitudes from the two parallel WLS fibers and the beta-ray incident point-fiber distance.

To sum up, the incident position of the beta-ray can be determined by measuring the average amplitude ratio of the output pulses with the position sensitive detector calibrated.