Simulation Study of a Shield-Free Directional Gamma-Ray Detector Using Small-Angle Compton Scattering

Gamma-ray imaging is a technique for visualizing the spatial distribution of radioactive materials. Visualization is performed by superimposing a distribution of radioactive materials on visible light or CT images. Many fields utilize gamma-ray imaging technology, including space observation [1], medicine [2,3], and nuclear security [4]. In particular, research related to the Fukushima Daiichi Nuclear Power Station (FDNPS) accident has actively made use of gamma-ray imaging in recent years.

Gamma-ray imagers, which are devices for acquiring distributions of radioactive materials, are roughly classified as either pinhole or Compton cameras. Each method has different advantages and disadvantages, and they are used for different purposes. A pinhole camera obtains directivity by limiting the direction of incident gamma rays with a shield. Therefore, the pinhole camera can estimate the incidence direction of gamma rays for each event. This feature allows the quantitative measurement of radio activity. A survey of the operating floor of FDNPS Unit 2 [5] using a pinhole camera [6] was conducted by the Nuclear Regulation Authority (Tokyo, Japan) and TEPCO Holdings, Inc. (Tokyo, Japan). In the survey, a quantitative evaluation was performed. This survey demonstrated the effectiveness of pinhole cameras for quantitative measurement of radio activity in the FDNPS-decommissioning field. However, since the pinhole camera requires a gamma-ray shield in principle, the detector's weight must be as large as several tens of kilograms. While it is very suitable for fixed-point measurement, it is not suitable for remote measurement with a small robot or drone.

On the other hand, a Compton camera obtains directivity using Compton scattering kinematics. Therefore, the Compton camera does not require a gamma-ray shield and the entire detector weight can be reduced to less than 1 kg. Hence, the Compton camera can be mounted on a drone to quickly monitor a wide contamination area from the sky [7,8]. Moreover, research has been conducted inside the FDNPS building. Since people cannot enter this building for a long periods of time, a small Compton camera was mounted on a robot and remote measurement was carried out [9,10]. The study demonstrated that the Compton cameras are effective for remote measurement in a narrow and high-dose-rate field. However, the Compton camera requires multiple events to estimate the radiation source's direction. The Compton camera statistically estimates the direction of the gamma-ray source from the information of multiple events. This feature makes the quantitative measurement of radio activity difficult, as well as a lower signal/noise (S/N) ratio compared to a pinhole camera.

A gamma-ray imager that is compact, lightweight, and capable of quantitative measurement of radio activity is desirable for FDNPS decommissioning. Therefore, we propose the gamma-ray imager using small-angle scattering (GISAS), which combines the advantages of pinhole and Compton cameras. GISAS is composed of a set of shield-free directional gamma-ray detectors, which obtain directivity using the kinematics of Compton scattering. By measuring very small energies with high accuracy, ultrasmall-angle Compton scattering events can be detected. The uncertainty in the radiation source's direction can be minimized by focusing only on such ultrasmall-angle Compton scattering, which appears almost straight. This feature makes it possible to estimate the source direction for one event; as a result, it becomes possible to perform a quantitative measurement.

In this study, the principles behind shield-free directional gamma-ray detectors, an elemental technology of GISAS, were investigated using the Monte Carlo simulation tool kit Geant4 [11]. Simulations were performed to investigate the feasibility of this new idea. We first investigated whether angle selection can be performed by detecting small-angle scattering. We also investigated the relationship between detector geometry and directivity.

The upper part of Fig. 1(a) shows the structure of a pinhole camera. A position-sensitive detector is placed in the shield, which has a tiny pinhole. Gamma rays enter from the tiny pinhole and are absorbed by this detector. Therefore, the gamma-ray-incidence direction can be estimated for every single event. This feature not only improves the S/N ratio of reconstructed images compared to a Compton camera, as shown as lower part of Fig. 1(a), but also allows quantitative measurement. The pair consisting of the pinhole and detector pixel acts as a directional gamma-ray detector. A pinhole camera can be considered to be composed of a set of directional gamma-ray detectors. The field of view (FOV) of each detector is determined by the pinhole size, detector-pixel size, and the distance between the pinhole and the detector. If the detector is calibrated in advance, the radio activity of each FOV can be quantitatively measured based on the distance to the radiation source and the count of the detector.

The scatterer measures $Ee′$⁠, and the absorber measures $Eγ′$⁠. m_e is the electron's mass and c is the speed of light.

As already mentioned, a single event is not sufficient to determine where the incident gamma rays originated on the Compton cone. As shown in the lower part of Fig. 1(b), the direction of the radiation source can be statistically estimated by drawing multiple Compton cones. It can be said that the more the cones overlap, the higher the probability that the radiation source exists. At least three Compton cones must be drawn to locate the radiation source. When Compton cones are drawn, they are also drawn where there is no actual radiation source. This makes quantitative measurement difficult and causes a decrease in the reconstructed image's S/N ratio.

The upper part of Fig. 1(c) shows the structure of a GISAS. The GISAS consists of a scatterer and an absorber. Since the GISAS estimates the scattering angle θ of gamma rays using the same principle as the Compton camera, it does not need a shield. Therefore, the size and weight of the imager can be reduced. As described above, unlike the Compton camera, the GISAS is designed to only detect events with extremely small scattering angles. Thus, each pixel of the absorber has its FOV like a pinhole camera, as shown in the lower part of Fig. 1(c).

As shown in Fig. 2, the GISAS can be considered to be a set of directional gamma-ray detectors as well as a pinhole camera. In the case of a pinhole camera, each pinhole–detector pair acts as a directional gamma-ray detector. In the case of the GISAS, scatterer—absorber-pixel pairs act as directional gamma-ray detectors.

For example, substituting the scattering angle θ = 5 deg and the energy of the incident gamma-ray $Eγ$ = 662 keV into Eq. (2), the scattered-electron energy $Ee′$ becomes 3.2 keV. Therefore, by setting the upper energy threshold $Emax$ = 3.2 keV in the scatterer, only events with a scattering angle θ of 5 deg or less can be selected. In practice, it is necessary to consider the detector's energy resolution and the Doppler-broadening effect. Therefore, the energy threshold should be determined by experiments or simulations, not calculation. Since a lower detection limit $Emin$ exists, scattering-angle selection is performed by setting an energy window from $Emin$ to $Emax$⁠.

It is necessary to detect $Ee′$ values of several keV to select only small-angle Compton scattering events. However, it is difficult to detect such small energies with high accuracy by the same technique as the conventional Compton camera such as scintillator or semiconductor at room temperature. The energy resolution of a scintillator and semiconductor at room temperature is insufficient to measure several keV energies.

In this study, a silicon-drift detector (SDD) is used for measuring such extremely small energy differences in simulation. SDD has a unique electrode structure [12] and a high energy resolution. In particular, in a low-energy region such as several keV and a high-count-rate environment, the SDD shows high performance compared with conventional semiconductor detectors [13]. Also, since it does not require a large cooling device, it is very small. In a recent report, a full width at half maximum (FWHM) below 130 eV was achieved at 5.9 keV by incorporating the input field effect transistor onto the detector and cooling them together with a Peltier device [14]. Also, since Si has a small atomic number, the photoelectric absorption cross section for gamma rays is small, and Compton scattering is the dominant interaction. From this viewpoint, SDD has advantageous properties as a scatterer.

Since the absorber's purpose is to stop and completely absorb scattered gamma rays, the stopping power for the gamma rays is more important than the energy resolution. Therefore, an inorganic scintillator is used for the absorber, as in the conventional Compton camera. In this study, simulations were performed using a Bi₄Ge₃O₁₂ (BGO) scintillator as an absorber.

In this study, 662 keV gamma rays emitted by ¹³⁷Cs are targeted for detection, assuming the application in FDNPS. To achieve a spatial resolution of about 50 cm at a distance of 3 m, we aim to develop a directional gamma-ray detector with a directivity of about 10 deg.

When setting an energy threshold $Emax$ for the scatterer, it should be noted that the $Ee′$ calculated in Eq. (2) does not match the detected energy precisely. Equation (2) describes Compton scattering of gamma rays with free electrons that are not bound to atoms. However, inside an actual SDD detector, incident gamma rays cause Compton scattering with orbital electrons bound to Si atoms. Therefore, the energy of scattered electrons generated in Compton scattering is distributed around the $Ee′$ calculated by Eq. (2). This is called the Doppler-broadening effect [15,16]. Also, the energy resolution of the detector causes fluctuation in the detected energy.

In addition to statistical fluctuation due to the Doppler-broadening effect and the energy resolution, it is also necessary to consider the effect of electrons escaping from the scatterer after imparting some energy to it. General SDD has a thickness of about 300 μm–1000 μm, which is too thin to stop scattered electrons generated by large-angle scattering with $Eγ$ = 662 keV. For example, if a gamma ray with $Eγ$ = 662 keV is scattered by 70 deg, $Ee′$ will be about 300 keV. Since electrons with $Ee′$ = 300 keV can move in Si by several hundred μm before being absorbed, scattered electrons can escape to the outside of the scatterer depending on the scattering position. If the energy given to the scatterer before escaping is within the range of the energy window set in the scatterer (from $Emin$ to $Emax$⁠), it cannot be distinguished from the small-angle-scattering event.

A simulation was conducted to investigate the effects of Doppler broadening, energy resolution, and escape electrons. Figure 3 is a simulation result of the relationship between the Compton scattering angle θ and the detected energy in the scatterer when 10⁸ gamma rays of energy $Eγ$ = 662 keV are incident on Si with a thickness of 1,000 μm. The energy resolution R = FWHM/$Edet$ was calculated based on the FWHM of 124 eV at 5.9 keV [17]. $Edet$ represents the detected energy at Si detector. Because FWHM is proportional to $Edet$⁠, R is proportional to $1/Edet$⁠. The calculated R is applied to the whole energy region. The solid line is calculated from Eq. (2), and the red dots are the simulation results. The effects of energy resolution and Doppler broadening can be seen around the solid line. Also, it can be seen that the effect of escape electrons spreads to the low-energy side of the solid line.

Figure 4(a) shows the result whereby only events in which the energy detected by the scatterer ranges from 0.1 keV to 3.2 keV are extracted from the data obtained in Fig. 3; that is, Fig. 4(a) shows the angular distribution of the events detected in an energy window of $Emin$ = 0.1 keV to $Emax$ = 3.2 keV. $Emin$ was determined based on the lower detection limit of common SDD. A sharp peak stands around 5 deg, indicating that small-angle-scattering events can be selectively extracted. On the other hand, escape electrons' influence is strongly visible in the region 20 deg to 170 deg.

90% of all detected events have a scattering angle less than $θcut$⁠. $θcut$ in Fig. 4(a) was 124 deg. The strong influence of escape electrons was found to increase $θcut$⁠.

Therefore, we tried to eliminate the influence of escape electrons using the scattered-gamma-ray energy $Eγ′$ by providing an energy window centered at 662 keV on the absorber. Figure 4(b) shows the data from Fig. 3 under the condition that the energy detected by the scatterer is from $Emin$ = 0.1 keV to $Emax$ = 3.2 keV and the scattered gamma ray's energy is $Eγ′$ = 662 keV±32 keV. The energy window of the absorber was determined by considering the energy resolution of the BGO scintillator (9.7% at 662 keV [18]). Compared to Fig. 4(a), it can be seen that the effect of escape electrons is eliminated cleanly. The $θcut$ was about 5 deg under these conditions.

Next, a simulation was performed to investigate the relationship between $θcut$ and the width of the energy window set in the scatterer. Using data from Fig. 3, $θcut$ was calculated when $Emax$ was changed. The energy window of the absorber is fixed at 662 keV±32 keV. Table 1 shows the result. $θcut$ is considered to become larger because the angle range to be selected widens under increase of $Emax$⁠. Table 1 clearly shows this trend. Since $θcut$ has a strong influence on the directivity of the directional gamma-ray detector, this directivity can be adjusted by changing $Emax$⁠.

The relationship between the Si thickness and $θcut$ was also investigated by simulation. $θcut$ was calculated by changing the thickness of Si while the energy windows of the scatterer (⁠$Emin$ = 0.1 keV, $Emax$ = 3.2 keV) and the absorber (662 keV±32 keV) were fixed. The escape electrons increase as Si becomes thinner. If the effect of escape electrons is not completely eliminated, $θcut$ will be affected. Table 2 shows little effect upon $θcut$⁠. This indicates that the influence of escape electrons can be effectively eliminated using the energy information of the scattered gamma rays, $Eγ′$⁠.

Figure 5 shows a schematic diagram of the detector geometry, FOV, and directivity. As mentioned above, the directional detector's FOV is determined by the geometry (scatterer size S_l, absorber size A_l, and distance between the scatterer and the absorber L) and $θcut$⁠. Furthermore, since the distribution of detection efficiency exists inside the FOV, the area with effective detection efficiency is smaller than this FOV. We define this effective area as the directivity of the detector.

The FOV can be calculated from $θcut$ and the detector's geometry. However, the detection-efficiency distribution in the FOV is difficult to calculate. Then, a simulation was performed to confirm the efficiency distribution in the FOV under the following conditions: S_l = 5.6 mm, A_l = 9.0 mm, L = 100 mm, and $θcut$ = 4.4 deg (⁠$Emin$ = 0.1 keV and $Emax$ = 2.5 keV). The thickness of Si was 1,000 μm, and the thickness of the BGO scintillator was 30 mm. The coordinate system was set, as shown in Fig. 5, and 1.8 × 10¹¹ gamma rays of 662 keV were uniformly irradiated on the entire surface of the scatterer in the +z direction from the -z side of the scatterer. The gamma-ray-incidence angle was randomly generated in the range of ±30 deg.

Recorded event count represents the number of coincidence events that have dropped energy in the scatterer's energy window (from $Emin$ to $Emax$⁠) and absorber's energy window (662 keV±32 keV) at each detector. The calculated FOV is about ±9.0 deg. The detection-efficiency distribution is highest near the center of the FOV, and it decreases toward the edges. The detection-efficiency distribution approaches 0 at the FOV boundary.

Figure 6(b) shows how to determine the directivity. The detection-efficiency distribution is considered to be symmetrical around the incidence angle of 0 deg. Therefore, as shown in Fig. 6(b), the detection-efficiency distributions on both sides centered on 0 deg were averaged, and the angle at which the cumulative percentage became 90% was calculated. That is, 90% of detected events are included in the range of directivity. The directivity of the directional detector with S_l = 5.6 mm, A_l = 9 mm, L = 100 mm, and $θcut$ = 4.4 deg was ±5.2 deg.

For detectors with the same $θG$ and $θcut$⁠, similar directivity can be obtained. For example, as shown in Fig. 7, detectors with different geometries such as (S_l, $Al1$⁠, L₁) and (S_l, $Al2$⁠, L₂) have similar directivity because they have the same $θG$⁠.

As shown in Fig. 6(b), a directivity of $10.4deg$ (±$5.2deg$⁠) was obtained under the conditions of $θG$ = $4.2deg$ (S_l = 5.6 mm, A_l = 9 mm, L = 100 mm) and $θcut$ = $4.4deg$⁠. In order to obtain similar directivity using an absorber with A_l = 6 mm, L = 80 mm should be set according to Eq. (5). While L is adjusted so as to keep $θG$ constant, simulation is performed under different A_l conditions: A_l = 3 mm, 6 mm, 9 mm, and 12 mm, with S_l and absorber thickness fixed at 5.6 mm and 30 mm, respectively. For comparison, the directivity when L is changed while S_l = 5.6 mm and A_l = 9 mm are fixed is also shown. The result is shown in Fig. 8. When L was changed with A_l fixed, it was seen that the shorter L was, the larger the directivity became. On the other hand, when $θG$ was the same, similar directivity was obtained even if L was changed. Even if $θG$ is the same, the directivity becomes slightly larger as A_l becomes larger. This is because the flight distance of gamma rays inside the scintillator becomes longer as A_l becomes larger. When gamma rays are incident vertically on the absorber, the flight distance of the gamma rays within the scintillator is 30 mm, which does not change depending on the size of A_l. However, when the incidence angle of gamma rays becomes large, the flight distance in the scintillator becomes longer as A_l becomes larger. Therefore, it is considered that the scintillator with larger A_l has slightly expanded directivity.

It was confirmed that by using SDD for the scatterer and setting an appropriate energy window for the scatterer and absorber, it is possible to detect only small-angle scattering events and obtain directivity. On the other hand, it was also found that the detection efficiency is extremely low. If the detection efficiency is extremely low, problems such as a decrease in the S/N ratio and a longer measurement time may occur. Especially in a high background environment, such as inside the FDNPS building, accidental coincidence due to background occurs frequently. If the accidental coincidence rate is too large for the true count rate, the S/N ratio will deteriorate and correct measurement results will not be obtained. To verify that the directional detector could be used in a high background environment, the accidental coincidence rate was estimated by simulation and compared with the true count rate expected from the detection efficiency obtained in the previous chapter.

The accidental coincidence rate due to background $CBG$ can be expressed as $CBG=$$CS×τ×$$CA$ using the scatterer and absorber count rate $CS$ and $CA$⁠, and the time window τ. $CS$ and $CA$ were calculated by simulation as the count per second that satisfied an energy window of 0.1–2.5 keV and 630–694 keV, respectively. τ was set to 100 ns. The flux rate of monochromatic gamma rays was calculated by using the conversion factor of the flux and the ambient dose equivalent described in ICRP Publication 74 [19]. Actually, the gamma-ray energy in the building of FDNPS is not monochromatic, and there are many scattering components of a gamma-ray by ¹³⁷Cs. However, it is difficult to simulate the actual energy distribution. For that reason, we conducted simulations using monochromatic gamma rays with different energies of 662 keV, 600 keV, and 500 keV to examine the effects of different energies on $CBG$⁠. The ambient dose equivalent used in the simulation was 100 μSv/h, and the geometry of the directional detector was $θG=4.2deg$ (S_l = 5.6 mm, A_l = 9 mm, L = 100 mm) and $θcut$ = 4.4 deg. The results are shown in Table 3.

Table 3 shows that the $CBG$ decreases as the energy of the gamma ray moves away from 662 keV. At an energy of 500 keV, the $CBG$ is 0. In practice, it should be noted that if low-energy gamma rays are simultaneously incident on the absorber and the total energy fills the absorber's energy window, it may be counted as a $CBG$⁠. However, in an environment of about 100 μSv/h, there is no significant impact. Therefore, compared with the Compton camera, the influence of the scattered component is very small. In the simulation with monochromatic gamma rays of 662 keV, since the detection efficiency of the directional detector was very low, it was found that $CBG$ was also very small. In this case, when a hot spot of several tens MBq is 3 m ahead, a sufficient S/N ratio can be obtained. The simulation results show that the longer measurement time due to the lower detection efficiency is more problematic than the decrease in the S/N ratio due to $CBG$⁠. It is necessary to improve the detection efficiency by at least two orders of magnitude in view of practical application.

The feasibility and operational principles of a shield-free directional gamma-ray detector, an elemental technology for GISAS, were investigated using the Monte Carlo simulation tool kit Geant4. The directional detector in this study is based on Compton scattering kinematics and estimates the gamma-ray scattering angle by measuring the energy of Compton scattered electrons. However, as shown in Fig. 3, when a thin detector is used as a scatterer, the effect of electrons escaping from the detector after imparting it with some of their energy cannot be ignored. This effect makes angle selection using energy information difficult. Therefore, we first investigate whether angle selection can be performed by detecting small-angle scattering by Si.

As shown in Fig. 4, it was found that the influence of escaped electrons cannot be eliminated by setting the energy window only to the scatterer, but it can be eliminated by extending the energy window to the absorber as well. The cut angle $θcut$ can be adjusted by changing the energy window of the scatterer, as shown in Table 1. This means that directivity can be adjusted by an energy window. Table 2 shows that the thickness of Si does not significantly affect $θcut$⁠.

Next, the matter of designing a directional detector to obtain a directivity of 10 deg was examined. The directivity of a directional detector affects not only $θcut$ but also the detector-geometry parameters S_l, A_l, and L. Figure 6 shows the simulation results under the following conditions: $θcut=4.4deg$ (⁠$Emin$ = 0.1 keV, $Emax$ = 2.5 keV), S_l = 5.6 mm, A_l = 9 mm, L = 100 mm. Hence, a directivity of 10.4 deg was obtained.

Using this result, it was possible to find the condition that should be satisfied by a detector with a directivity of about 10 deg. The $θG$ defined in Eq. (5) is uniquely determined by the detector geometry. When $θcut$ is fixed, if $θG$ is the same for detectors of different geometries, similar directivity should be obtained. In order to confirm this, the directivity was measured under changes of the geometry so as to keep $θG$ constant. The results are shown in Fig. 8. It was confirmed that directional detectors with the same $θcut$ and $θG$ have similar directivity. Therefore, it is possible to freely change the geometry and design the detector under $θG$ that yields the desired directivity.

Finally, the effect of accidental coincidence events caused by background was examined. As shown in Table 3, $CBG$ is very small in the environment of 100 μSv/h, and there is no problem in viewpoint of the S/N ratio. On the other hand, low detection efficiency has become an issue. In order to put it into practical use, it is necessary to improve the detection efficiency by two digits. Improvement of detection efficiency is a future task.

A_l =

diameter of absorber, mm

BGO =

Bi₄Ge₃O₁₂

c =

speed of light, m/s

C_A =

absorber's count rate, cps

C_BG =

accidental coincidence rate due to background, cps

C_S =

scatterer's count rate, cps

cps =

count per second, 1/s

$Ee′$ =

energy of scattered electron, keV

$Edet$ =

detected energy at Si detector, keV

$Emin$ =

lower-level energy threshold of scatterer, keV

$Emax$ =

upper-level energy threshold of scatterer, keV

$Eγ$ =

energy of incident gamma ray, keV

$Eγ′$ =

energy of scattered gamma ray, keV

FDNPS =

Fukushima Daiichi Nuclear Power Station

FOV =

field of view

FWHM =

full width at half maximum

GISAS =

gamma-ray imager using small-angle scattering

L =

distance between scatterer and absorber, mm

m_e =

mass of electron, kg

MBq =

mega becquerel, 1/s

R =

energy resolution

S_l =

diameter of scatterer, mm

SDD =

silicon drift detector

S/N ratio =

signal/noise ratio

TEPCO Holdings, Inc =

Tokyo Electric Power Company Holdings, Incorporated

x, y, z =

coordinates, mm

$εint$ =

intrinsic efficiency

θ =

Compton scattering angle

$θcut$ =

cut angle by scatterer

$θG$ =

angle defined by detector geometry