Characterization and on-field performance of the MuTe Silicon Photomultipliers
J. Sánchez-Villafrades, J. Peña-Rodríguez, H. Asorey, L. A. Núñez
PPrepared for submission to JINST
Characterization and on-field performance of the MuTeSilicon Photomultipliers
J. Sánchez-Villafrades, 𝑎, J. Peña-Rodríguez, 𝑏, H. Asorey 𝑑,𝑒, and L. A. Núñez 𝑏,𝑐, 𝑎 Escuela de Ingeniería Eléctrica, Electrónica y de Telecomunicaciones,Universidad Industrial de Santander, Bucaramanga-Colombia 𝑏 Escuela de Física, Universidad Industrial de Santander, Bucaramanga-Colombia 𝑐 Departamento Física Médica, Centro Atómico Bariloche, Comisión Nacional de Energía Atómica,Bariloche-Argentina 𝑑 Instituto de Tecnologías en Detección y Astropartículas, Buenos Aires-Argentina. 𝑒 Departamento de Física, Universidad de Los Andes, Mérida-Venezuela.
E-mail: [email protected]
Abstract: The Muon Telescope is a muography experiment for imaging volcanoes in Colombia. Itconsists of a scintillator tracking system and a water Cherenkov detector used for particle depositedenergy measurement. The MuTe operates autonomously in high altitude environments where thetemperature gradient reaches up to 10 ◦ C. In this work, we characterize the breakdown voltage,gain, and noise of the telescope silicon photomultipliers for temperature variations spanning 0 to40 ◦ C. We demonstrated that the discrimination threshold for the MuTe hodoscope must be above 5pe to avoid contamination due to the SiPM dark count, crosstalk, and afterpulsing. We also assessthe MuTe counting rate depending on day-night temperature variations.Keywords: Muography, Silicon Photomultipliers, Dark Count, Crosstalk, AfterpulsingArXiv ePrint: xxxx.xxxxx Corresponding author. a r X i v : . [ phy s i c s . i n s - d e t ] F e b ontents Muography is a non-invasive technique for imaging anthropic and geologic structures [1–12] bymeasuring the crossing muon flux using sensitive hodoscopes made of nuclear emulsions [2, 13],gaseous chambers [14–17] and scintillators [4, 8, 11, 18–20]. Scintillation hodoscopes provideflexibility on the implementation, low cost, and robustness against environmental variables suchas humidity, temperature, and atmospheric pressure [21]. When an ionizing particle interacts withthe scintillator crystal lattice, it knocks electrons out from the valence band to bound states calledexcitons. Then excitons emit photons in the near-ultraviolet spectrum because of de-excitation byrecombination. Some dopants are added to the basic scintillation material to obtain a light output ina longer wavelength taking into account the absorption length of the ultraviolet light is quite short.The resultant emission range of the scintillator mismatches the sensitivity of the most photosensors(Photomultipliers or SiPMs) being necessary to add a wavelength shifting fiber [22].SiPMs offer a solution for high granularity hodoscopes to be deployed in volcanic areas becauseof their small dimensions, robustness, and low power consumption [23]. SiPMs contain a densearray of small photon avalanche diodes operating in Geiger mode. When a photon interacts with a– 1 –iPM microcell, an avalanche process starts generating a photocurrent flowing through a quenchingresistor, which causes that the diode bias drops below the breakdown value preventing furtherGeiger-mode avalanches. The electrical pulses generated by the SiPM are directly related to thenumber of incident photons. The main drawback of SiPMs is that performance parameters likegain, photodetection efficiency, and breakdown voltage are susceptible to temperature variations.Thermo-electric cells can control the SiPM temperature, but this methodology carries an increase inthe power consumption [23], which reduces the powering efficiency of autonomous muon telescopes.The Muon Telescope (MuTe) is a hybrid detector composed of a hodoscope and a WaterCherenkov Detector (WCD) which will be installed in one of the most dangerous volcanoes inColombia, the Cerro Machin, located at 2750 m.a.s.l. on the Cordillera Central near to themunicipality of Cajamarca [24]. The MuTe hodoscope consists of two scintillation panels each of30 ×
30 strips 120 cm length, and 4 cm width. Each strip has a 1 . . . × . , 667 pixels, a fill factor of 74%, a gain from 10 to 10 and a photon-detectionefficiency of 40% at 450 nm [27–29].This paper shows the characterization of the SiPM breakdown voltage, gain, dark count,crosstalk, and afterpulsing depending on temperature and over-voltage. In section 2 we describethe experimental setup and the data acquisition system for the SiPM parameter measurements. Thebreakdown voltage, gain, and noise characterization results are described in section 3. Section 4presents the temperature conditions at the Cerro Machín volcano and their affectation on the MuTemechanical structure, and section 5 exhibits the dependence between the flux and the temperatureof the MuTe tracking system in on-field conditions. Conclusions and remarks are summarized insection 6. The first experimental setup measures the SiPM dark current depending on temperature and biasvoltage. A sketch of the setup is shown in figure 1. The SiPM is placed on an isolated aluminiumholder whose temperature is controlled by two Peltier cells (TEC1-12706 from Hebei I.T) andmeasured using an LM35 sensor. A proportional-integral-derivative (PID) control (implementedin a microcontroller Atmega328) generates two pulse-width-modulate signals whose duty cycledepends on the control error. The error is defined as the difference between the measured temperatureand the pre-established set-point. The control signals drive the direction (cooling or heating) andamplitude (fast or slow) of the current flowing through the Peltier cells using an H-bridge with anoptically coupled isolator circuit.A C11204 power module biases the SiPM S13360-1350CS covering a voltage range from 40 Vto 60 V. The dark current is measured by a 2 nA accuracy picoammeter. The SiPM bias voltage andtemperature are recorded individually by a 10-bit analog to digital converter (ADC) with a samplingrate of 1 Hz. All the setup components are placed inside a grounded dark box to avoid external lightcontamination and electromagnetic interference.– 2 – eltier cellsFB driverController PC Picometer
SiPMLM35
Dark boxUART
Figure 1 . Experimental setup for measuring the SiPM dark current in darkness conditions. The SiPM ispositioned in the aluminium holder inside the dark box. The holder temperature is controlled via Peltier cellsby means a PID controller implemented in a microcontroller Atmega328.
In the second experimental setup, we estimate the SiPM gain and noise at several temperaturesand over-voltages after stimulating with pulsed light. The light source must fulfill two features:a wavelength matching the SiPM spectral sensitivity and a pulse width of the order of a few ns[30, 31].The light pulser generates an ultra-short ( <
10 ns) 480 nm light pulse with a frequency of500 Hz. A 50 cm WLS fiber (Saint-Gobain BCF-92) transports the light towards the SiPM, atthe same time, a square signal triggers the DAQ system. The signals generated by the SiPM areamplified 94 times using a low noise current feedback operational amplifier (OPA691 from TexasInstruments) and digitized by a Red Pitaya ADC channel with a sampling frequency of 125 MHzand 14-bit resolution. A sketch of the setup is shown in figure 2.
The breakdown voltage (V 𝑏𝑟 ) is the point where the SiPM enters in Geiger mode. Such a point canbe established using several methods [32]. In this case, we use the tangent method which consistsof finding the interception between a tangent line fitted to the IV (dark current vs bias voltage)curve and the baseline. In figure 3 we show the SiPM IV curve at 25 ◦ C where the V 𝑏𝑟 was found ∼ . ◦ C and 40 ◦ C with5 ◦ C step as shown in figure 4 (left-panel). In the Geiger region, the IV slope increases with thetemperature reaching a dark current above 400 nA at 40 ◦ C. The breakdown voltage has a linearrelation with temperature decreasing with a ratio of 41 . ◦ C as is shown in figure 4 (right-panel).– 3 – eltier cellsFB driverController PC SiPMLM35
Dark boxLED pulser Red PitayaFiber TriggerAmpli fi er Figure 2 . Experimental setup for measuring the gain and noise of the SiPM S13360-1350CS understimulated conditions. The SiPM is stimulated by a 480 nm pulsed light of ∼
10 ns width at 500 Hz. TheSiPM signal is digitized by the Red Pitaya at 14-bit/125 MHz. V Bias [V] l o g ( I ) [ n A ] Breakdown voltagecurvefit
Figure 3 . Breakdown voltage value found using the tangent method for the IV curve of SiPM S13360-1350CSoperating at 25 ◦ C. The V 𝑏𝑟 (52 . In on-field applications, an adaptive bias voltage to compensate for temperature changes in the SiPMcould be taken into account to guarantee a stable gain and low noise levels [31].
The gain of a SiPM microcell is defined as the ratio of the output charge to the charge on an electron 𝑒 [33]. The output charge can be calculated as, 𝑄 = 𝑄 𝐴𝐷𝐶 𝑉 𝐴𝐷𝐶 Δ 𝑇 𝑅𝐺 𝑎 (3.1)where 𝑄 𝐴𝐷𝐶 is the digitized area under pulse, 𝑉 𝐴𝐷𝐶 is the equivalent voltage for one ADC unit, Δ 𝑇 is the digitization time step, 𝑅 is the input resistor and 𝐺 𝑎 the gain of the electronics front-end.In figure 5 the charge spectrum of the SiPM operating at 56 V and 25 ◦ C is shown.– 4 – V Bias [V] D a r k C u rr e n t [ n A ] T=0 ∘ CT=5 ∘ CT=10 ∘ CT=15 ∘ CT=20 ∘ CT=25 ∘ CT=30 ∘ CT=35 ∘ CT=40 ∘ C B r e a k d o w n V o l t a g e [ V ] Temperature [ C] ∘ Figure 4 . Temperature dependence of the breakdown voltage for the SiPM S13360-1350CS from Hama-matsu. (Left): IV curves ranging from 0 ◦ C to 40 ◦ C. (Right): 𝑉 𝑏𝑟 variance ratio depending on the temperature. Charge [C]
1e 12050100150200 C o un t s Figure 5 . Charge spectrum of the SiPM S13360-1350CS operating at 56 V/25 ◦ C. The first peak is thepedestal and the following represent the photoelectron equivalents. The inter-peak charge Δ 𝑄 determines theSiPM gain. The separation between two adjacent peaks Δ 𝑄 in the charge histogram corresponds to thecharge from a single Geiger discharge. This can be used to accurately calculate the gain 𝐺 asfollows, 𝐺 = Δ 𝑄𝑒 (3.2)The SiPM gain depends on the bias voltage ( 𝑉 𝑏𝑖𝑎𝑠 = 𝑉 𝑏𝑟 + Δ V), the higher the bias voltage thehigher the gain. To estimate the gain dependence on the over-voltage ( Δ 𝑉 ) in the SiPM S13360-1350CS we measured three charge spectra for Δ V = 1 . . . ◦ C. Figure 6 showsthe charge spectra (left-panel) and the estimated gain (right-panel) for these cases.The separation between charge peaks grows as the over-voltage increases –indicating a gainincrement. The gain change ratio was estimated ∼ . × /V, i.e., for Δ V = 1 . 𝑉 𝑏𝑖𝑎𝑠 =
53 V)the gain is roughly 0 . × and Δ V = 3 . 𝑉 𝑏𝑖𝑎𝑠 =
56 V) the gain is 1 . × .– 5 – h a r g e [ p C ] O v e r V o l t a g e [ V ] C o un t s Over Voltage [V] G a i n Figure 6 . (Left): Charge spectrum for Δ 𝑉 = . . . The output pulse amplitude from SiPMs is proportional to the number of incident photons basedon the fact they are made of an array of APDs connected in parallel. The photoelectron spectrumdetermines the equivalent value (voltage or current) of a photon interacting with the active area ofthe SiPM. This value establishes the threshold for measuring dark count rate (DCR), crosstalk andafterpulsing noise.
Time [ns] A m p li t u d e [ m V ] Peak [mV] C o un t s Figure 7 . (Left): Waveform of the Hamamatsu S13360-1350CS under stimulation. Photo-electron spectrumresulting from integrating the area under pulse over a time window of 300 ns.
In figure 7 the persistence histogram (left-panel) of the pulse shape and the peak histogram(right-panel) for 10 pulses at 56 V/25 ◦ C are shown.The histograms reveal that pulses of 1 pe and 2 pe have more probability of occurrence thanothers. These pulses are mainly generated by the SiPM noise. The resulting equivalent voltage for1 pe is ∼ . . .4 Noise SiPMs are affected by correlated noise (crosstalk and afterpulsing) and non-correlated noise (DCR)[34]. These noise sources impose the lower measurement limit in SiPM based experiments. Weperformed a noise analysis of the MuTe SiPMs taking into account its temperature and over-voltagedependency. We also established the minimum pe threshold above which the noise is negligible.
The main source of noise in SiPMs is the DCR. It appears as a consequence of avalanches processesfired by electrons thermally generated in the silicon crystal. Signals generated by thermal electronsand single-photons are identical. The DCR is measured under dark conditions by counting eventsabove a 0 . Threshold [p.e] D C R [ H z ] Figure 8 . Dark count rate as a function of the detection threshold. The curve shape presents three breaksat 1 pe, 2 pe and 3 pe because of the discretization effect on the pulse amplitude.
The DCR is calculated as follows,
𝐷𝐶 𝑅 = 𝑁 𝐵 𝑝𝑒 𝑇 𝐵 𝑁 𝑝 (3.3)where 𝑁 𝐵 𝑝𝑒 is the number of events above 0.5 pe in the time window 𝑇 𝐵 (before stimulation) and 𝑁 𝑝 is the total number of recorded events.We measured the DCR for different thresholds spanning from 0 . . ◦ C asshown in figure 8. The resulting curve has a stepped shape because of the amplitude discretizationof the SiPM pulses. At 0 . ∼ × Hz corresponding with the expected valueprovided by the SiPM S13360-1350CS datasheet which range between 0 . × Hz and 2 . × Hz. The DCR drastically decreases while the measurement threshold increases. We found a DCRof 9 × Hz at 1 . × Hz at 2 . . <
10 Hz).To characterize the DCR as a function of the over-voltage, we carried out DCR measurementsfor three cases (1 . . . ◦ C. Figure 9 (left-panel) shows that the DCR increaseswith a slope ∼ .
16 kHz/V. – 7 – .5 2.0 2.5 3.0 3.5 4.0
Over Voltage [V] D C R [ k H z ] Temperature [ C] D C R [ k H z ] Figure 9 . (Left): Dark count rate as a function of the over-voltage spanning from (1 . . ◦ C.(Right): Dark count rate as a function of temperature spanning from 0 ◦ C to 40 ◦ C at 56 V. The variation ratiois 0 .
85 kHz/ ◦ C. The DCR correlation with the SiPM temperature was also evaluated. We estimated a ratio0 .
85 kHz/ ◦ C after analyzing DRC measurements from 0 ◦ C to 40 ◦ C at 56 V as shown figure 9(right-panel).
Afterpulsing is generated by trapped electrons in silicon impurities during an avalanche process.These electrons are released few nanoseconds later creating new avalanches –consecutive pulses[35]. The amplitude of afterpulses increases with the retention time of the trapped electron.The afterpulsing probability 𝑃 𝐴𝑃 is calculated as follows 𝑃 𝐴𝑃 = 𝑁 𝐴 𝑝𝑒 − 𝑁 𝐵 𝑝𝑒 𝑁 𝑝 ×
100 (3.4)where 𝑁 𝐴 𝑝𝑒 is the number of events above 0 . 𝑇 𝐴 (after stimulation).Crosstalk occurs when charge carriers (inside the avalanche) emit photons that interact withneighboring cells. Such interactions trigger secondary avalanches in these cells with amplitudes of2 pe or 3 pe.The crosstalk probability [36] is defined as 𝑃 𝐶𝑇 = 𝑁 𝐵 𝑝𝑒 𝑁 𝐵 𝑝𝑒 ×
100 (3.5)where 𝑁 𝐵 𝑝𝑒 is the number of events with amplitude above 1 . ◦ C while the crosstalk 5%.The correlated noise dependency on temperature was analyzed by performing afterpulsing andcrosstalk measurements from 0 ◦ C to 40 ◦ C at 56 V. The results are displayed on Figure 10 (Left).At 0 ◦ C the afterpulsing probability is below 2% and the crosstalk below 4%. The afterpulsing– 8 – .0 1.5 2.0 2.5 3.0 3.5 4.0
Over Voltage [V] C o rr e l a t e d n o i s e [ % ] CrosstalkAfterpulse −
10 0 10 20 30 40
Temperature [ C] C o rr e l a t e d n o i s e [ % ] CrosstalkAfterpulse
Figure 10 . MuTe-SiPM crosstalk (black line) and afterpulsing (blue line) depending on its over-voltage (left)and temperature (right). increases faster than crosstalk with the temperature, rising up almost 5% at 40 ◦ C while crosstalkreaches 6%.To reduce the noise caused by dark count, crosstalk, and afterpulsing, we concluded that theminimum discrimination threshold for the scintillator hodoscope of MuTe must be above 5 pe. Thebreakdown voltage shifting due to temperature variations will cause a modulation of the detectionrate. This can be solved using closed-loop control of the SiPMs bias voltage or corrected in theoffline data analysis.
The Cerro-Machín volcano has typical weather conditions of the Andean mountains in Colom-bia. According to the Colombian Hydrology, Meteorology and Environmental Studies Institute(IDEAM), at the Cerro-Macín the average temperature is 16 ◦ C, the relative humidity 85%, andthe maximum wind speed 30 m/s. During the rainy season, the temperature drops to 0 ◦ C, andduring the dry season, it rises to 25 ◦ C. The rainy season comes from April to May and Octoberto November, and the dry season is usually from December to January and July to August. Theday-night temperature gradient at the Cerro-Machín volcano is around 10 ◦ C along the dry and rainyseasons.
We computed a thermal analysis of the MuTe mechanical structure using the Solidworks CADSoftware. The heat sources were: the environmental temperature (16 ◦ C), solar radiation (4.5 kWhm − day − ), cooling by wind (30 m/s), and heating by electronics power consumption (12.5 W). Wealso input thermal features of the metallic chassis supporting the WCD and the hodoscope [37].Figure 11 displays the temperature distribution on the MuTe structure resulting from the thermalsimulation. The direct incidence of the solar radiation (solid arrow) causes a maximum temperatureof 60 ◦ C in the middle of the scintillation panels, but this drops to 26 ◦ C due to the convection created– 9 – ir fl ow sun Figure 11 . Heat distribution of the MuTe structure under environmental conditions at the Cerro-Machinvolcano. The solid-arrow represents the incident solar radiation while the dashed-arrow indicates the winddirection. The maximum temperature at the center of the scintillation panels reaches 60 ◦ C. by the frontal wind (dashed arrow). The water volume inside the WCD dissipates the heat of thestainless steel cube. The maximum temperature on the WCD is ∼ ◦ C. In this section, we analyze how temperature affects the SiPM parameters under real observationconditions. This procedure uses the characterization ratios presented above and temperature mea-surements.We use temperature data recorded at the Cerro Machin volcano during the 2017 rainy seasonbetween November 22-23. The day-night temperature cycle stars/ends at the 00:00 hour with ∼ ◦ C. The temperature drops to a minimum value of ∼ . ◦ C at morning (06:30) and rises to amaximum of ∼ . ◦ C at day (13:00) as shown figure 12.The estimated SiPM breakdown voltage and DCR along the day-night cycle is presented infigure 13. The maximum temperature gradient is ∼ . ◦ C which represents a breakdown voltage(41 . ◦ C) deviation of ±
126 mV from the nominal value (53 . . × /V) causing a deviation ∼ . × .As the temperature on the SiPM increases, the number of thermally generated electrons on thesilicon material also increases. The DCR absolute variation is ∼ . . . Δ 𝑇 ∼ . ◦ C whichrepresents roughly 6% of the voltage separation between two consecutive photoelectrons ( ∼ . 𝑇 𝑅 ) and frontal– 10 – igure 12 . Day-night temperature cycle at the Cerro-Machín volcano during the rainy season (November22-23). The gray shadow indicates the night period starting at 18:00 and ending at 06:00. The minimumtemperature ( ∼ . ◦ C) is recorded at 06:30 and the maximum ( ∼ . ◦ C) at 13:00.
Figure 13 . MuTe SiPM breakdown voltage and DCR variation as a function of typical temperature valuesat the Cerro-Machín volcano.
Figure 14 . Photoelectron and pulse amplitude variation of the MuTe-SiPM for typical temperature valuesat the Cerro-Machín volcano. – 11 – 𝑇 𝐹 ) panels, as well as the in-coincidence detection rate. The MuTe was set pointing towards thehorizon, with an angular aperture of 52 ◦ , and an inter-panel separation of 2.5 m.
20 21 22 23 24 25 dat e [ day] R a t e [ / s ] Frontal-T F Rear-T R T e m pe r a t u r e [ ◦ C ] T R T F Figure 15 . Hodoscope rate modulation depending on the environmental temperature of the MuTe recordedfrom 2019/12/20 to 2019/12/25. The green line displays the rear panel rate under temperature 𝑇 𝑅 and theblue line the frontal panel rate under temperature 𝑇 𝐹 . The panel temperature oscillates from 20 ◦ C to 30 ◦ C representing a gradient of 10 ◦ C. A 10 ◦ Cgradient represents a variation in the pulse amplitude around 14.8%. But this variation increasesthe breakdown voltage ∼
417 mV, reducing the overvoltage and the SiPM gain causing a reductionof the detected rate. The measured average flux is ∼ ◦ C [38].
We evaluated the SiPM S13360-1350CS from Hamamatsu to characterize the breakdown voltage,gain, and noise depending on the over-voltage and temperature. Temperature testes ranged from0 ◦ C to 40 ◦ C covering the temperature spectrum of the observation site at Cerro Machín Volcano,Colombia. The SiPM breakdown voltage variation ratio was about 41.7mV/ ◦ C indicating a pulseamplitude shift of 14.8%, which is not representative for jumping between photoelectron levels.We also estimated a gain increase ratio of about 3.07 × /V for over-voltage changes on the SiPM.In the noise characterization, we found that the dark count rate decreases by several magnitudeorders (< 100 Hz) at a threshold above 3 pe On the other hand, the DCR increases with a ratio of11.16 kHz/V as a function of the SiPM over-voltage. This proposes a trade-off challenge becausetemperature increase generates a breakdown voltage increase but also a rising of the DCR. In theSiPM S13360-1350CS, the afterpulsing and crosstalk probabilities showed a non-linear growth withthe temperature reaching up to 3% and 5% at an over-voltage of 3.7 V respectively. We recommenda discrimination threshold above 5 pe to reduce drastically the correlated and non-correlated noisefrom MuTe SiPMs. – 12 –n the on-field test, the hodoscope rate was modulated by the environmental temperaturereaching a maximum deviation of 11.2% with respect to the average. The modulation was inverselycorrelated to the temperature (-0.057 Hz/ ◦ C) because of the breakdown voltage increase and theSiPM gain reduction.
Acknowledgments
The authors acknowledge the financial support of Departamento Administrativo de Ciencia, Tec-nología e Innovación of Colombia (ColCiencias) under contract FP44842-082-2015 and to thePrograma de Cooperación Nivel II (PCB-II) MINCYT-CONICET-COLCIENCIAS 2015, underproject CO/15/02.
References [1] G. Blanpied et al. Material discrimination using scattering and stopping of cosmic ray muons andelectrons: Differentiating heavier from lighter metals as well as low-atomic weight materials.
NuclearInstruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors andAssociated Equipment , 784:352–358, jun 2015.[2] K. Morishima et al. Discovery of a big void in khufu pyramid by observation of cosmic-ray muons.
Nature , 552(7685):386, 2017.[3] H. Gómez et al. Studies on muon tomography for archaeological internal structures scanning.
Journalof Physics: Conference Series , 718:052016, May 2016.[4] H. Fujii et al. Performance of a remotely located muon radiography system to identify the innerstructure of a nuclear plant.
Progress of Theoretical and Experimental Physics , 2013(7), jul 2013.[5] G. Saracino et al. Imaging of underground cavities with cosmic-ray muons from observations at mt.echia (naples).
Scientific Reports , 7(1), apr 2017.[6] L. F. Thompson et al. The application of muon tomography to the imaging of railway tunnels. arXive-prints , page arXiv:1906.05814, Jun 2019.[7] K. Nagamine et al. Probing the inner structure of blast furnaces by cosmic-ray muon radiography.
Proceedings of the Japan Academy, Series B , 81(7):257–260, 2005.[8] H. K. Tanaka et al. Cosmic-ray muon imaging of magma in a conduit: Degassing process ofsatsuma-iwojima volcano, japan.
Geophysical Research Letters , 36(1), jan 2009.[9] N. Lesparre, D. Gibert, J. Marteau, Y. Déclais, D. Carbone, and E. Galichet. Geophysical muonimaging: feasibility and limits.
Geophysical Journal International , 183(3):1348–1361, oct 2010.[10] N. Lesparre, D. Gibert, and J. Marteau. Bayesian dual inversion of experimental telescope acceptanceand integrated flux for geophysical muon tomography.
Geophysical Journal International ,188(2):490–497, nov 2011.[11] N. Lesparre et al. Design and operation of a field telescope for cosmic ray geophysical tomography.
Geoscientific Instrumentation, Methods and Data Systems , 1(1):33–42, apr 2012.[12] H. K. M. Tanaka and L. Oláh. Overview of muographers.
Philosophical Transactions of the RoyalSociety A: Mathematical, Physical and Engineering Sciences , 377(2137):20180143, January 2019. – 13 –
13] K. Nagamine. Radiography with cosmic-ray and compact accelerator muons: Exploringinner-structure of large-scale objects and landforms.
Proceedings of the Japan Academy, Series B ,92(8):265–289, 2016.[14] R. Sehgal. Simulations and Track Reconstruction for Muon Tomography using Resistive PlateChambers.
DAE Symposium in Nuclear Physics , 61:1034–1035, 2016.[15] F. Fehr et al. Density imaging of volcanos with atmospheric muons.
Journal of Physics: ConferenceSeries , 375(5):052019, 2012.[16] S. Bouteille et al. A micromegas-based telescope for muon tomography: The WatTo experiment.
Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers,Detectors and Associated Equipment , 834:223–228, oct 2016.[17] L. Oláh et al. High-definition and low-noise muography of the sakurajima volcano with gaseoustracking detectors.
Scientific Reports , 8(1), feb 2018.[18] K. Nagamine et al. Method of probing inner-structure of geophysical substance with the horizontalcosmic-ray muons and possible application to volcanic eruption prediction.
Nuclear Instruments andMethods in Physics Research Section A: Accelerators, Spectrometers, Detectors and AssociatedEquipment , 356(2-3):585–595, mar 1995.[19] P. Aguiar et al. Geant4-GATE simulation of a large plastic scintillator for muon radiography.
IEEETransactions on Nuclear Science , 62(3):1233–1238, jun 2015.[20] S. W. Tang et al. A large area plastic scintillation detector with 4-corner-readout.
Chinese Physics C ,40(5):056001, may 2016.[21] S. Procureur. Muon imaging: Principles, technologies and applications.
Nuclear Instruments andMethods in Physics Research Section A: Accelerators, Spectrometers, Detectors and AssociatedEquipment , 878:169–179, jan 2018.[22] C. Grupen and B. Shwartz.
Particle Detectors (Cambridge Monographs on Particle Physics, NuclearPhysics and Cosmology) . Cambridge University Press, 2008.[23] F. Ambrosino et al. The MU-RAY project: detector technology and first data from mt. vesuvius.
Journal of Instrumentation , 9(02):C02029–C02029, February 2014.[24] A. Vesga-Ramírez et al. Muon tomography sites for colombian volcanoes.
Annals of Geophysics ,63(6), December 2020.[25] Saint-Gobain Ceramics and Plastics.
Plastic Scintillating Fibers , 2017. Rev. 1.[26] Hamamatsu.
MPPCs for precision measurement , 5 2018. Rev. 1.[27] J. Peña Rodríguez et al. Calibration and first measurements of MuTe: a hybrid Muon Telescope forgeological structures. In , volume 36 of
International Cosmic Ray Conference , page 381, July 2019.[28] H. Asorey et al. minimute: A muon telescope prototype for studying volcanic structures with cosmicray flux.
Scientia et technica , 23(3):386–390, 2018.[29] A. Vásquez-Ramírez et al. Simulated response of MuTe, a hybrid muon telescope.
Journal ofInstrumentation , 15(08):P08004–P08004, August 2020.[30] G. Georgiev, V. Kozhuharov, and L. Tsankov. Design and performance of a low intensity LED driverfor detector study purposes. In
RAD Conference Proceedings . RAD Association, 2016.[31] G. Eigen. Gain stabilization of SiPMs and afterpulsing.
Journal of Physics: Conference Series ,1162:012013, January 2019. – 14 –
32] F. Nagy et al. A model based DC analysis of SiPM breakdown voltages.
Nuclear Instruments andMethods in Physics Research Section A: Accelerators, Spectrometers, Detectors and AssociatedEquipment , 849:55–59, March 2017.[33] F. Acerbi and S. Gundacker. Understanding and simulating SiPMs.
Nuclear Instruments and Methodsin Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment ,926:16–35, May 2019.[34] L. Baudis et al. Characterisation of silicon photomultipliers for liquid xenon detectors.
Journal ofInstrumentation , 13(10):P10022–P10022, October 2018.[35] H. Xu et al. Design and characterization of a p+/n-well SPAD array in 150nm CMOS process.
OpticsExpress , 25(11):12765, May 2017.[36] M. Ramilli. Characterization of SiPM: Temperature dependencies. In . IEEE, October 2008.[37] J. Peña-Rodríguez et al. Design and construction of MuTe: a hybrid muon telescope to studycolombian volcanoes.
Journal of Instrumentation , 15(09):P09006–P09006, September 2020.[38] J. Pena-Rodriguez.
Diseño y calibración de un telescopio de muones híbrido para estudiosvulcanológicos . PhD thesis, Universidad Industrial de Santander, 2021.. PhD thesis, Universidad Industrial de Santander, 2021.