A borehole muon detector with SiPM-on-tile technology
October 05, 2025
1 Introduction↩︎
Muon tomography is a well-established technique for reconstructing the three-dimensional density of objects [1], [2]. Since detectors can only probe volumes above their position, several designs have been developed for deployment in boreholes [3]–[29]. Existing systems broadly fall into scintillator- and gas-based detectors, as summarized in Table 1.
Among these, plastic scintillator designs are the most mature. However, three-dimensional hit measurement requires either multiple layers, which increase the detector diameter and limit compatibility with smaller boreholes, or picosecond-level timing electronics when long bars or fibers are read out from both ends to infer the longitudinal coordinate of hits.
We address these limitations with a compact design based on scintillator tiles individually read out by SiPMs, which provide three-dimensional hit positions while reducing detector diameter and easing timing requirements. This concept follows the SiPM-on-tile technology developed for collider-physics calorimetry [30]–[33], where it has largely replaced fiber-based readout.
| Year & Ref. | Detector technology | Ø (mm) | Ch./Length | SiPM size |
|---|---|---|---|---|
| 2025 – This work | Tile scintillator + SiPM | 80 | 64/0.9 m | 1.3 mm |
| 2024 – Yin et al. [29] | Arc & bar scintillator + SiPM | 100 | 176/1.0 m | 6 mm |
| 2024 – Zhao et al. [28] | Cylindrical scintillator + WLS fiber + SiPM | 143 | 64/0.23 m | n.a |
| 2024 – Li et al. [27] | Annular & bar scintillator + WLS fiber + SiPM | 250 | 148/1.5 m | 6 mm |
| 2023 – Yao et al. [26] | CsI + SiPM | 100 | 34/1.0 m | 6 mm |
| 2022 – Yamazaki et al. [25] | Bar scintillator + WLS fiber + PMT | 90 | 32/1.0 m | n.a |
| 2022 – Gauvreau et al. [24] | TPC + MPGD | \(<\)90 | n.s | n.a |
| 2021 – Cimmino et al. [21]–[23] | Arc & bar scintillator + SiPM | 240 | 384/1.0 m | 3 mm |
| 2021 – Schouten et al. [20] | Drift tubes | \(<\)89 | n.s | n.a |
| 2020 – Holma et al. [19] | Bar scintillator + SiPM | \(<\)100 | n.s | n.s |
| 2018 – Schouten et al. [17], [18] | Helix scintillator + bar scintillator + WLS fiber + PMT | \(<\)89 | 128/1.0 m | n.a |
| 2018 – Suenaga et al. [16] | Scintillator bars + WLS fiber + PMT | 114 | 124/2.4 m | n.a |
| 2018 – Olah et al. [14], [15] | MWPC | 100 | 64/0.2 m | n.a |
| 2017 – Bonneville et al. [12], [13] | Bar scintillator + WLS fiber + SiPM | 150 | 90/0.7 m | 3 mm |
| 2017 – Yaish et al. [10], [11] | MPGD | n.s | n.s | n.a |
| 2015 – Klinger et al. [8], [9] | Bar scintillator + PMT | 230 | 14/1.0 m | n.a |
| 2006 – Basset et al. [7] | Bar and fiber scintillator + PMT | 140 | 384/2.2 m | n.a |
| 2004 – Schwitters et al. [4]–[6] | Helix scintillator + WLS fiber + PMT, and gas Cherenkov | 1500 | 448/4.2m | – |
| 1981 – Levy et al. [3] | MWPC | n.s. | n.s. | n.a |
2 Borehole detector design↩︎
The detector design is modular, with each unit (“SiPM board”) consisting of a printed circuit board equipped with eight SiPMs (1.3 mm, Hamamatsu S14160-1315PS), each air-coupled to a 4 mm thick EJ-212 scintillator tile (\(5 \times 5\) cm\(^{2}\)) featuring a central spherical dimple of radius \(3.8\,\mathrm{mm}\) and depth \(1.6\,\mathrm{mm}\), following Ref. [33]. The tiles are wrapped in enhanced specular reflector (ESR) foil to maximize light yield and covered with polyimide film for protection. The analog signals from each unit are routed to the readout electronics via a flat cable.
Eight SiPM boards form a four-sided detector with 64 channels in total, measuring 90 cm in length and 80 mm in diameter. The detector skeleton, to which the SiPM boards are mounted, is fabricated by 3D printing. To improve polar-angle reconstruction, two of the four sides are shifted longitudinally by a quarter of a cell; to improve azimuthal-angle resolution, the two detector halves are rotated by 45\(^\circ\) relative to each other.
For our prototype we used the CAEN A5202, which provides the power supply and trigger/readout for 64 SiPMs, as well as two temperature sensor inputs. The CAEN unit and auxiliary sensors (e.g., temperature and humidity monitors) are controlled by a Raspberry Pi. In the borehole configuration, power is supplied externally via umbilical cables. The detector is encased in a waterproof carbon-fiber housing.
Figure 1 shows the SiPM board, an assembled 32-channel half-detector unit, and a 3D rendering of the 64-channel detector (140 cm long, 80 mm in diameter).
Figure 1: Top: basic SiPM-on-tile module (left) and 32-channel half-detector unit (right). Bottom: 3D rendering of 64-channel unit (140 cm long, 80 mm in diameter) highlights the scintillators, DAQ module, Raspberry Pi, and end caps..
The 64-channel detector unit can in turn serve as a modular unit for longer detectors by stacking multiple modules, with each additional 64-channel unit rotated to further enhance azimuthal-angle reconstruction.
3 Simulation framework↩︎
The simulation was carried out using the DD4HEP framework [34], as interface to Geant4[35] (v11.02.p2). We use the the FTFP_BERT physics list with otherwise standard parameters. The input to the Geant4 simulation consists of muons with trajectories generated according to the sea-level flux spectrum produced by CRY [36].
Simulated energy deposits were digitized according to the ADC capacity of the CAEN A5202, which is 13 bit. The production and transport of optical photons are not included in the Geant4 simulation in order to reduce computational cost. Instead, we adopt a data-driven approach in which laboratory measurements are used to determine a smearing factor that is applied to the simulated energy depositions in an ad hoc manner.
4 Laboratory tests↩︎
The system was characterized with cosmic-ray measurements to evaluate the performance of a single SiPM-on-tile unit. The SiPM was biased at 43 V, corresponding to +5 V above its nominal breakdown voltage. An external trigger was provided to the CAEN A5202 by two scintillator tiles read out with 6 mm SENSL SiPMs, powered by their evaluation boards. The trigger tiles were positioned about 2.5 cm above and below the tile under test. A DRS4 digitizer generated the coincidence between the two trigger tiles and delivered the external trigger pulse (TTL) to the CAEN A5202. The readout of the tile under test was calibrated from arbitrary ADC units to the number of photoelectrons (PE) using the SiPM finger spectrum measured with a dedicated LED setup.
Figure 2 shows the measured light yield. The observed distribution has a most probable value of about 8 PE. The distribution also exhibits individual photoelectron peaks that could be exploited for in situ calibration. From this data, the efficiency was evaluated for various thresholds and is shown in the right panel of Fig. 2. The efficiency exceeds 96% at a threshold of 3 PE. This threshold is sufficient to suppress the dark-count coincidence rate of two tiles to negligible levels. The intrinsic time resolution for this configuration is expected to be at the level of a few hundred picoseconds for a MIP deposition [37], thus in our design will be dominated by the resolution of the readout electronics which is about 0.5 ns.
Figure 2: Light yield (left) and efficiency (right) measurement of single tile using cosmic-ray measurement with external trigger..
Figure 3 shows the measured data (binned to average out the single-photon peaks) together with the simulation. The simulation reproduces the experimental setup, including the external trigger condition and geometry, and is smeared to approximately match the width of the Landau-like peak observed in data. Both data and simulation are calibrated such that the most probable value of the Landau-like distribution is unity, thereby defining the MIP scale. This MIP calibration can also be performed in situ on a channel-by-channel basis.
5 Simulated polar-angle performance↩︎
The zenith angle \(\theta_{\mathrm{reco}}\) and the azimuthal angle \(\phi_{\mathrm{reco}}\) are reconstructed from the 3D hit positions according to
\[\phi_{\mathrm{reco}} = \arctan \left( \frac{V_y}{V_x} \right), \qquad \theta_{\mathrm{reco}} = \arctan \left( \frac{\left| V_z \right|}{\sqrt{(V_x)^{2}+(V_y)^{2}+(V_z)^{2}}} \right),\]
where \(V_x\), \(V_y\), and \(V_z\) denote the components of the reconstructed muon vector, obtained from a fit to the 3D hit positions.
The zenith angle can also be inferred from the measured hit energies, since tracks closer to the zenith deposit, on average, more total energy than tracks at more oblique angles. The correlation between \(\theta_{\mathrm{reco}}\) and the reconstructed energy is obtained from simulation, with a fit providing the most probable \(\theta_{\mathrm{truth}}\) for a given reconstructed total energy \(E_{\mathrm{reco}}\). While this standalone method performs worse than the 3D hit approach, it provides an independent estimate.
A third approach uses a Graph Neural Network (GNN) that takes as input both the 3D hit positions and the measured energies to infer the muon track angle. Details of the GNN model can be found in Ref. [38].
Figure 4 shows the zenith-angle performances of the 3D hit, energy-based, and GNN methods as a function of \(\theta_{\mathrm{truth}}\), integrated over full azimuth. The 3D position method yields a Gaussian-like response up to \(\theta_{\mathrm{truth}} \approx 45^\circ\), after which bimodal distributions appear, attributed to discretization effects due to the cell size. The energy-based method performs more poorly overall but yields a smoother response without discretization effects. The GNN achieves performance comparable to the 3D hit method, but with reduced bias, which is interpreted as the result of incorporating the additional energy information. Hit time information can also be incorporated in future studies.
Figure 5 summarizes the zenith-angle performance in terms of bias and resolution obtained from Gaussian fits to the distributions shown in Fig. 4. These Gaussian metrics are presented for illustration, although they do not always capture the underlying distributions, which can exhibit multimodality due to discretization effects and ambiguities in zenith reconstruction. Solutions to these issues will be investigated in future designs, which may also incorporate timing information.
Figure 5: Zenith angle bias (left panel) and resolution (right panel) obtained using the 3D hit method, the energy-based method, and the graph-neural network method..
6 Conclusions↩︎
We have presented the first borehole muon detector based on a scintillator tile design. The modular detector fits within standard HQ boreholes, measures about 140 cm in length and 80 mm in diameter, and contains 64 channels. It achieves a zenith resolution of 1.5–4.0\(^\circ\), depending on the zenith angle. Although the azimuthal granularity is coarser, it can be improved by combining measurements from multiple detectors rotated axially with respect to each other. By enabling three-dimensional hit reconstruction with a single scintillator layer, the SiPM-on-tile concept reduces detector diameter, eliminates the need for picosecond timing electronics, and lowers production costs through the use of smaller 1.3 mm SiPMs. Overall, this detector provides a compact, rugged, and cost-effective solution for muon tomography.
We acknowledge the support from a UC Riverside Academic Senate Research Grant and ANID PIA/APOYO AFB230003. We thank Ryan Milton for his help with the GNN.