Large-Area SiPM Pixels (LASiPs): a cost-effective solution towards compact large SPECT cameras
D. Guberman, R. Paoletti, A. Rugliancich, C. Wunderlich, A. Passeri
LLarge-Area SiPM Pixels (LASiPs): a cost-effective solution towardscompact large SPECT cameras
D. Guberman a,b , R. Paoletti a,b , A. Rugliancich a , C. Wunderlich a,b , A. Passeri c a Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Pisa, I-56126 Pisa, Italy b Dipartimento di Scienze Fisiche, della Terra e dell’Ambiente, Universit`a di Siena, I-53100 Siena, Italy c Dipartimento di Scienze Biomediche Sperimentali e Cliniche (SBSC) Universit`a di Firenze, I-50134 Florence, Italy
Abstract
Single Photon Emission Computed Tomography (SPECT) scanners based on photomultiplier tubes (PMTs)are still largely employed in the clinical environment. A standard camera for full-body SPECT employs ∼ × . As a solution, we propose touse Large-Area SiPM Pixels (LASiPs), built by summing individual currents of several SiPMs into a singleoutput. We developed a LASiP prototype that has a sensitive area 8 times larger than a 6 × SiPM. Webuilt a proof-of-concept micro-camera consisting of a 40 × × NaI(Tl) crystal coupled to 4 LASiPs.We evaluated its performance in a central region of 15 ×
15 mm , where we were able to reconstruct imagesof a m Tc capillary with an intrinsic spatial resolution of ∼ ∼ .
6% at140 keV. We used these measurements to validate Geant4 simulations of the system. This can be extendedto simulate a larger camera with more and larger pixels, which could be used to optimize the implementationof LASiPs in large SPECT cameras. We provide some guidelines towards this implementation.
Keywords:
SPECT, silicon photomultiplier (SiPM), gamma camera, large-area SiPM
1. Introduction
Single-photon emission computed tomography (SPECT) is a nuclear imaging technique that has been usedin clinical environments since at least forty years. It provides high efficiency in diagnosing several diseases,like Alzheimer’s [1] and Parkinson [2].Most common clinical SPECT scanners are constituted by one or more gamma camera heads [3], roughlyconsisting of: (i) a lead collimator; (ii) a large ( ∼ × × ) scintillating crystal; (iii) an array of 50–100photomultiplier tubes (PMTs) of relatively large area (4–8 cm diameter). The whole camera (including atleast a part of the PMT electronic readout) is shielded by a ∼ ∼
10% at 140 keV and anintrinsic spatial resolution better than 5 mm . The intrinsic spatial resolution is a property of the scintillation Email address: [email protected] (D. Guberman) Preprint submitted to Physica Medica March 1, 2021 a r X i v : . [ phy s i c s . i n s - d e t ] F e b etector (scintillating crystal and photodetectors), that combined with the collimator resolution gives theextrinsic (total) spatial resolution of the system [4]. In most SPECT scans the extrinsic spatial resolutionis actually driven by the characteristics of the collimator [5] (with typical values going from 6 to 15 mmat a source-collimator distance of 10 cm). The clinical potential of SPECT relies on the compensation forqualitative and quantitative image degradation due to non-stationary experimental data, such as Comptonscattering, attenuation and geometrical system response, the latter representing the main source of blurringfor the system spatial resolution. The ability of the reconstruction algorithm to manage those effects plays akey-role in the final impact SPECT can have in the clinical practice [6]. Nonetheless, there is another pointof primary concern from the clinical point of view that is strictly related to the hardware: the possibilityof reducing the size, weight and cost of a SPECT scanner. A lighter and more compact system would besafer to operate, would give more flexibility both to the patient and the physician, and could be installed insmaller rooms (and would be easier to fit in smaller hospitals).Recently, SPECT scanners based on cadmium-zinc-telluride (CZT) technology have been introduced.With respect to traditional systems, they are characterized by a substantial improvement in both energy and(intrinsic) spatial resolution, while being lighter and more compact. The main limitation for a wider useof this technology in full-body SPECT is the camera price, which increases significantly with size [7]. Thefirst multi-purpose scanners became available very recently [8, 9, 10]. However, most CZT-SPECT systemsdeveloped in the last ten years were relatively small instruments, dedicated to image specific organs (e.g.,cardiac imaging, see [11] for a recent review). In these applications the organs to be scanned are close to thecollimator, thus making the improvement in intrinsic spatial resolution of primary value.A cost-effective approach to build lighter and more compact gamma cameras would be to replace thePMTs by silicon photomultipliers (SiPMs). Replacing PMTs by SiPMs would be beneficial for several reasons.They provide higher photodetection efficiency (PDE), do not require high-voltage operation and their costis trending down. Moreover, SiPMs are not sensitive to magnetic fields, which is particularly interestingfor combining SPECT and Magnetic Resonance Imaging [12]. Particularly, SiPMs are much more compactthan PMTs. A typical SPECT PMT is ∼
15 cm long (without electronics), which corresponds to more than50 % of the thickness of the camera (the millimeter thickness of a SiPM is negligible in comparison). ASPECT camera using compact photodetectors and electronics would be also much more compact. It wouldbe lighter because the amount of lead needed for the shielding would be reduced. And it would simplify theconstruction of the gantry, which could allow to also reduce the weight and size of the whole scanner.Probably the main obstacle for using SiPMs in full-body SPECT cameras is their limited pixel size: SiPMsare rarely commercially available in sizes larger than 6 × . A few thousand channels would be neededto fill a 50 ×
40 cm camera using SiPMs, dramatically increasing the cost and complexity of the system.This is one of the reasons why up to now almost all research in SiPMs for SPECT has been limited to smallcameras [12, 13, 14].Larger SiPMs are normally not built because their capacitance increases significantly with size. This isparticularly critical for many high-energy physics and astrophysics experiments where fast timing and closeto single-photoelectron resolution are needed. Several solutions have been developed in these fields to buildlarge SiPM pixels that keep their capacitance at a reasonable level [15, 16, 17, 18, 19]. Inspired by thesedevelopments, we performed a feasibility study on the implementation of Large Area SiPM Pixels (LASiPs) inSPECT, as a solution to use SiPM technology in large gamma cameras. In section 2 we introduce the LASiPconcept and present a prototype pixel we developed and characterized. We also describe the experimentsperformed with a NaI(Tl) crystal coupled to 4 of those LASiP prototypes and the Monte Carlo simulations2 a) (b) (c) Figure 1: Essential components of a LASiP prototype. (a)
SCT Matrix: only the 8 SiPMs marked in yellow are summed bythe MUSIC and are actually part of the pixel; (b) eMUSIC MiniBoard; (c)
A fully-assembled LASiP seen from the side: theSCT matrix is connected to the eMUSIC MiniBoard by a custom-made interface board. we performed to further study the system. The results of such experiments and simulations are shown insection 3. The impact of these results and the feasibility of developing large SPECT cameras equipped withLASiPs are discussed in section 4.
2. Materials and Methods
One way of building large SiPM pixels is summing the analog currents of several SiPMs into a singleoutput. SiPM signals are filtered and summed using custom-designed adder circuits based, for instance, onoperational or common-base transistor amplifiers. This way the pixel size can be increased by a factor equalto the number of SiPMs that are being summed, while keeping the capacitance at a reasonable level. Inthis solution, which has been successfully applied in Very High Energy (VHE) astrophysics [15, 16, 19], theadder circuits are typically built using discrete components. In our case, the sum is performed using anApplication-Specific Integrated Circuit (ASIC) named MUSIC (8 channel Multiple Use IC for SiPM anodereadout). The MUSIC was designed for multiple purposes, but mainly targeting the readout of SiPMs inCherenkov telescopes. One of its main functionalities is the possibility to sum up to 8 SiPMs using a currentswitch consisting of two common base transistors and an operational transconductance amplifier (see [20]for the details). Using an ASIC offers several advantages, including compactness and ease of reproductionon a large scale, which is particularly relevant for SPECT applications. The MUSIC offers many otherfunctionalities. Some of them will be described in section 2.2.
For the proof of concept we developed a LASiP prototype in which 8 SiPMs of ∼ × are summed,resulting in a single pixel of ∼ . (with an active area of ∼ . ). We used technology that wasalready available, that had been developed for VHE astrophysics applications: a single prototype employsone SCT matrix and one eMUSIC MiniBoard (see Figure 1).The SCT matrices were originally produced to equip the Schwarzschild-Couder medium-size Telescope After which the “SCT matrix” name is given. N(cid:20)(cid:19)(cid:19)Q 6L30+9 ’LIIHUHQWLDOWR(cid:3)VLQJOH(cid:3)HQGHGFRQYHUWHU (cid:23)&+’LJLWL]HU6XP(cid:16)6XP(cid:14)(cid:240)(cid:27) &RD[ 3&86%H0XVLF(cid:3)0LQL%RDUGWKH(cid:3)+9(cid:3)5&(cid:3)(cid:192)OWHUV(cid:3)DUHPRXQWHG(cid:3)QH[W(cid:3)WR(cid:3)WKH(cid:3)6L30V (cid:27)FK 086,&$6,&3=(cid:3)VKDSHUDQG(cid:3)VXPPHU ’LIIHUHQWLDOGULYHU
Figure 2: Scheme of the electronic readout including the summing stage. proposed for the Cherenkov Telescope Array [21]. A single matrix holds 16 FBK NUV-HD3 SiPMs of ∼ × (nominal chip size: 6 . × .
24 mm ), with a ∼ . ∼
60 % at ∼
350 nm and a dark count rate (DCR) of ∼ .
13 MHz / mm at 20 ◦ C when operated at ∼
33 V [22]. The LASiP prototype uses only 8 of the 16 SiPMs that the SCTmatrix holds. The limitation was imposed by the MUSIC, which can sum up to 8 channels.The eMUSIC MiniBoard (bought from SCIENTIFICA, S.L.U ) is an evaluation board for the MUSICchip (Figure 1b). It can be connected to up to 8 SiPMs and allows to program the MUSIC from the computer.The eMUSIC MiniBoard is a plug-and-play board that allows to exploit all the functionalities the MUSICprovides (see [20]). Those particularly relevant for our detector are: • An output with the sum of up to 8 SiPMs. • Enabling/disabling channels. The output signal of each individual SiPM can be accessed during cali-bration by disabling the remaining seven. • Applying individual offset values to the bias voltage of each SiPM (useful to equalize the gain). • Configure a filter with pole-zero cancellation to shape the pulse.A scheme of the electronic readout of a LASiP prototype can be found in Figure 2. The 8 individual SiPMsignals are shaped and summed by the MUSIC. The MUSIC outputs the sum of the signals in differentialmode. Then it is converted to single-ended and is sent to a digitizer or an oscilloscope for the acquisition.Using the SCT matrix and the eMUSIC MiniBoard was useful for the proof-of-concept and especiallyefficient in terms of time and cost. However, this constrained the size and geometry of the pixel we couldbuild. We decided to adopt the geometry shown in Figure 1a: in our LASiP prototype the SiPMs areorganized forming a square of ∼ × area, with a dead corner of ∼ × . We considered this wasthe best solution that would allow us to place four LASiPs near each other, building the micro-camera thatis described in the next section. The signal loss due to the pixel dead corner was studied with Monte Carlo(MC) simulations (see section 2.8). The 8 active SiPMs of the SCT matrix are connected to the eMUSICMiniBoard by means of a custom-made interface board (Figure 1c). igure 3: Scheme showing the different components of the micro-camera and setup employed. To test the feasibility of using LASiPs in SPECT we built a micro-camera consisting of a NaI(Tl) scintil-lation crystal coupled to an array of four LASiPs. This was the minimum number of LASiPs with which wecould achieve our aims: (i) evaluate the energy resolution when charge is shared between pixels and compareit with that of standard SPECT scanners, (ii) prove that we can reconstruct simple images with a reasonablespatial resolution and (iii) have a system that we could use to validate MC simulations that let us studywith further detail the impact of LASiPs in the performance of a gamma camera. We considered that thesethree goals were milestones that should be achieved before even considering to build a large SPECT camerabased on LASiPs (which would be significantly more complex and expensive since it would involve muchmore channels). In this sense, the micro-camera was envisioned as a test bench for evaluating the developedLASiPs: we did not aim to perform a full characterization of its performance, especially in view of its limitednumber of channels.An overview of the micro-camera and the setup employed is shown in Figure 3. The different componentsof the micro-camera are described in the next paragraphs.
Figure 4: Electronic readout of the micro-camera.
Left:
Top-view of the micro-camera interface board holding 4 SCT matrices.As an example, the top-left matrix is delimited in black and the 8 SiPMs that are used to build a LASiP, in yellow. Themicro-camera (in blue) uses 4 LASiPs. The 32 outermost SiPMs are not used.
Center:
The 4 eMUSIC MiniBoards seen fromthe back.
Right:
Side-view of the photodetectors and electronic boards. igure 5: Left:
The NaI(Tl) crystal and the custom-designed holder, seen from below, before mounting the electronic readout.
Center:
Two different views of the micro-camera and
Coll 1 fixed in a rail during measurements in the lab.
Right:
Micro-camera and
Coll 2 mounted in the positioning platform at Careggi Hospital (Firenze, Italy). In this image a capillary was filledwith a solution containing m Tc and was placed close to the collimator.
Electronic readout
The electronic readout of the micro-camera consists of 4 SCT matrices, 4 eMUSIC MiniBoards (one ofeach per LASiP) and an interface board (see Figure 4). The micro-camera interface board is designed to hold4 LASiPs together and, in the frame of a single LASiP, connect the 8 SiPMs of each SCT matrix to theircorresponding eMUSIC MiniBoard. The eMUSIC MiniBoard takes care of distributing the power supply toall SiPMs (applying individual offsets to each of them), shape each SiPM signal and sum all of them intoa single output that is later sent to a digitizer. A common bias voltage ( V b ) of 33 V was supplied to the 4eMUSIC MiniBoards, which was chosen as a balance between PDE, DCR and the possibility to resolve thesingle-photoelectron (phe) pulse during the calibration. The pole-zero configuration was optimized to achievea relatively high gain and short pulse tails that also facilitated the identification of the single-phe pulse. Theindividual offsets were adjusted until the conversion factor from charge to phes in all SiPMs were within 5%. Scintillation crystal, collimator and mechanics
A NaI(Tl) crystal of 40 × × bought from OST Photonics was coupled to the 4 LASiPs withSS-988 optical gel (refractive index 1.47, above 99% transmission between 300 and 600 nm) from SiliconeSolutions . According to the manufacturer, the crystal, which is sealed in an aluminum housing, is surroundedby an MgO diffuse reflector and has a 3 mm thick fused silica glass exit window (see Figure 5). Crystal,LASiPs and the electronic readout boards were mounted in a 3D-printed holder that was designed to beattached to two different lead collimators. The first one, Coll 1 had a hole diameter d (cid:39) . a (cid:39) Coll 2 was a clinical LEUHR collimator ( d (cid:39) . a (cid:39) https://siliconesolutions.com/ss-988.html ata acquisition A CAEN DT5720 digitizer was used for the acquisition (250 MS/s). Individual discriminator thresholdswere set to each channel, optimized to minimize the triggering by dark count events. For each event, a 2 µ swaveform was acquired on each channel. The charge was integrated offline in a 600 ns window. The widthand position of the integration window were both optimized aiming to maximize energy resolution. Thelonger the integration window, the larger the number of collected photons, but also the number of integrateddark counts. The optimal integration time depends on the SiPM bias voltage, since it affects both PDEand DCR. The Pole-Zero shaper may also have an impact the optimal integration time, although we did notstudy in detail such eventual dependence. The total charge Q collected in an event is defined as the sum of the charges collected by each LASiP.With all the values of Q obtained during a measurement we built a histogram where we could identify thephotopeak corresponding to the energy of the gamma rays emitted by the radioactive source employed. Onlyevents with an energy within ±
15% of the photopeak position were used for the image reconstruction (seesection 2.5).
The method used to reconstruct the position of an event begins with a simple centroid method. Spatiallinearity and uniformity corrections are later applied to produce the final image [23]. More complex image-reconstruction algorithms exist (most of them also start from the centroid method) and have the potential toprovide better spatial resolution (see for instance [24, 25, 26]). However, testing other methods was beyondthe scope of this work.
In the centroid method, the coordinates ( x c , y c ) of an event are reconstructed as x c = (cid:80) i =1 x i q i (cid:80) i =1 q i ; y c = (cid:80) i =1 y i q i (cid:80) i =1 q i (1)where q i is the charge measured by the i -th pixel that has its center in ( x i , y i ). This method, althoughfast and simple, has several limitations. Events cannot be reconstructed outside the region delimited bythe ( x i , y i ) of the four pixels. This is true even in the ideal case in which the crystal surfaces are perfectlypolished and all scintillation photons are carrying information of their initial direction. In a more realisticscenario, events contain also a diffuse component. For instance, due to diffuse reflections in the crystal walls,as in our case. As a result, with the centroid method events are reconstructed within an area that is muchsmaller than the one delimited by the center of the four pixels. To recover spatial linearity we followed a similar method to what was described in [14]. A radioactivesource was fixed near the micro-camera and, using the positioning platform, the camera was moved to scanthe field of view (FOV). In our case, the size of the FOV after corrections was limited by the range of themoving platform (15 mm).We built a grid of measurements in which the relative position between source and detector was known.For each measurement we mapped the mean position reconstructed with the centroid method ( x recc , y recc ) to7 igure 6: Setup employed to characterize LASiP noise. its known position ( x truec , y truec ). This map can be interpolated so that each event reconstructed with thecentroid method can be corrected to recover spatial linearity.A uniformity correction map was generated by taking a long-exposure flood-field irradiation: a m Tcsource was placed far (more than 50 cm away) from the micro-camera. The image was reconstructed with thecentroid method and corrected by spatial linearity. The inverse of this image was the uniformity correctionmap, which was applied to every reconstructed image.
One of the main limitations to increase the number of SiPMs that are summed to build a pixel is thedegradation of the single-phe resolution. The noise of all the SiPMs that build a LASiP are summed, whichdegrades the timing performance and single-phe resolution of a pixel. The noise (e.g., DCR, optical cross-talk) of a single FBK NUV-HD3 SiPM has been studied in [22]. Here we focused on the additional noiseintroduced by the summing stage. We studied in particular two forms of noise that could have a significantimpact in the performance of a SPECT system: the single-phe resolution (the ability to resolve differencesof a few photons, which depends on the amplitude of the measured signal) and uncorrelated noise, whichincludes SiPM dark counts, electronic and digitizer noise and is independent of the measured signal.The setup employed for noise measurements is shown in Figure 6. LASiPs were placed inside a dark boxwhere they could be illuminated by ∼ . ∼
380 nm generated by a PicoQuant PDL 800-B LEDdriver. To study the degradation of the single-phe resolution introduced by the summing stage, we turnedon the LED driver, set a pulse frequency of 1 kHz, and recorded the waveforms with an oscilloscope. Werepeated the measurement eight times, changing the number of SiPMs summed by the MUSIC from 1 to 8.The LED intensity was regulated in each measurement to keep the mean number of detected photons at thelevel of a few phes to facilitate the identification of the single-phe peak. We obtained the charge spectrum foreach of these measurements and fitted them with eq. 2 of [17], a multi-peak fit function that includes opticalcross-talk and is standard for describing SiPM charge spectra: f ( x ) ∼ P (0 | µ ) G ( x − x , , σ ) + N (cid:88) n =1 n (cid:88) m =1 p n,m ( p XT ) P ( m | µ ) G ( x − x , n, σ t ) (2) P ( m | µ ) is the Poisson probability of having m cells fired given a mean number of interacting photons µ and G ( x, n, σ ) is a Gaussian function of expected value n and variance σ . The optical cross-talk probability8 XT is modeled by a binomial function p n,m (see eq. 1 of [17]). x is measured in phe and x is the positionof the pedestal peak. σ t = (cid:112) σ + nσ gives the width of the n -th peak, where σ is defined as the pedestalnoise and σ is typically associated to SiPM cell-to-cell gain fluctuations. The lower σ t ( n ) is, the better isthe SiPM resolution of the n -th peak. Both p XT and σ t ( n ) introduce uncertainties in the measured photonflux that could have an impact on the energy resolution of the system.To study the impact of uncorrelated noise we recorded events in the absence of visible-light or radioactivesources (with all eight channels enabled for the sum). Random-triggered events were acquired with thedigitizer in the same conditions than during standard measurements with the micro-camera. Charge wasintegrated in the same 600 ns window employed for the charge extraction. We fitted the charge distributionwith a Gaussian function of variance σ UN , which was used as input for the simulations described in section 2.8. We evaluated the energy and spatial resolution of the micro-camera in a small region around the FOVcenter. We limited our measurements to this region aiming to be as far as possible from the dead corners.The performance closer to the edges would be naturally worse because in the micro-camera all 4 pixels are outer-most pixels , but especially because of the proximity to the pixel dead corners. Then it would not bevery representative of what may occur in a large camera equipped with “proper” LASiPs (i.e., without deadcorners). The central region was the only place in which we could obtain results that could eventually be usedto undesrtand how LASiPs would perform in a larger camera. For the measurements we employed the setupof Figure 3. We used a sealed source of
Am (which we assumed to be point-like) and a liquid radioactivesolution of m Tc, embedded into a glass capillary (0.5 mm inner diameter, 100 mm long).The energy resolution was measured employing m Tc, using two different setups. In the first setup, thecapillary was completely filled with the radioactive solution (total activity of ∼ µ C) and placed in differentpositions, near the collimator. In the second setup the collimator was removed and the capillary was filled fora length not exceeding 2 mm. Its active volume was positioned at a distance of ∼
500 mm from the camera,with its longitudinal axis perpendicular to the camera plane. This way we produced a flood-field irradiationof the detector.Spatial resolution was evaluated with both
Am and m Tc sources. First, the
Am source was imagedat a distance h (cid:39)
15 mm from the camera using
Coll 1 . We fitted the reconstructed image by a 2D-gaussianand defined the extension R of the image as the FWHM of the function that resulted from the fit. Then thecapillary was fully-filled with the m Tc solution and was imaged at a distance h (cid:39)
20 mm from the camerausing
Coll 2 . In this case we define R as the FWHM of the projection of the reconstructed image in the axisperpendicular to the capillary orientation. In both cases, with the source fixed, the micro-camera was movedin the detector plane to acquire data from different regions of the FOV.The measured R results from the contribution of the source diameter R src (negligible for the point-likesource), the collimator resolution R c and the intrinsic detector resolution R d as: R = (cid:113) R d + R c + R src (3)The collimator resolution depends on the hole diameter d , the distance h between source and collimator andthe effective collimator thickness a eff as R c ( h ) = d a eff + ha eff (4)where a eff = a − /µ , with a the collimator thickness and µ the linear attenuation coefficient ( µ − = 0 .
37 mmat 140 keV in lead). 9 igure 7: Overview of the simulated system.
Left:
The different components of the simulated system (side view).
Center:
Theback part of 36 the simulated SiPMs are shown. The output from the SiPMs in the corner (in red) can be enabled/disabled tostudy the impact of the LASiP dead corner.
Right:
A representation showing different gamma rays approaching the detector.A few of them are able to go through the collimator and produce scintillation photons inside the crystal.
To better understand the system behavior we performed Geant4 simulations [27] of a system with similarcharacteristics to the micro-camera. We did not aim to perfectly match the micro-camera response, but tomodel a system in which we could study the impact that LASiP noise and the pixel dead corner had on theoverall performance.The simulated system features a 40 × × NaI(Tl) crystal coupled to 36 SiPMs of ∼ × (Figure 7). A 140 keV capillary source of 0.5 mm diameter and 40 mm long was also simulated. Theoptical photons generated by scintillation inside the crystal were tracked until they were absorbed, escaped ordetected by one of the SiPMs. An MgO reflector surrounding the crystal was also included in the simulations.We used the Geant4 RoughTeflon LUT Davis model [28] for describing the interaction of optical photons inthe crystal-reflector interface. It was the one that was better reproducing the relative charge distributionbetween pixels observed in the micro-camera, at least compared to the other models we tested:
Glisur (withseveral surface roughness) and
Unified (with different surface finish like groundteflonair and etchedteflonair ).A 3 mm fused silica glass exit window was placed between SiPMs and crystal. Lead collimators with thesame geometrical characteristics of
Coll1 and
Coll2 could be placed in front of the camera.The 36 SiPMs were distributed in the same way as in the micro-camera. The number of scintillationphotons detected by each SiPM were recorded independently. Then they were summed in groups of 8 tomimic a micro-camera LASiP or in groups of 9 to study the performance degradation introduced by the deadcorner (see Figure 7). The PDE of the SiPMs was not simulated. Instead, we scaled the scintillation lightoutput so that the total number of photons was comparable to what we estimated from the measurementswith the micro-camera. According to the manufacturer, the NaI(Tl) crystal employed in the micro-cameracoupled to a PMT exhibits an energy resolution of ∼
8% at 662 keV. In the simulations we scaled (and fixed)the scintillation light-yield to achieve an energy resolution of ∼
9% at 140 keV when all 36 SiPMs are enabledand no noise is added.We also did not simulate the LASiP pulse shape or the waveforms acquired with the digitizer. Instead,we injected noise in three steps. In a simulated event in which N scintillation photons hit a single LASiP we:1. Simulate cross-talk events: we add ∆ N artificial counts, that are randomly generated with a Poisson10istribution with mean µ ( N, p XT ), where p XT is the cross-talk probability. At the end of this step N is replaced by N (cid:48) = N + ∆ N
2. Simulate the finite resolution of the detector: we build a Gaussian distribution with expected value N (cid:48) and variance σ t ( σ , σ , N (cid:48) ) (see definition in section 2.6). At the end of this step N (cid:48) is replaced by arandom number N (cid:48)(cid:48) generated with this Gaussian distribution.3. Simulate uncorrelated noise: ∆ N (cid:48)(cid:48) random counts are generated with a Gaussian distribution of variance σ UN . σ UN is the standard deviation of the charge distribution collected in the absence of signal (seedefinition in section 2.6). At the end of this step N (cid:48)(cid:48) is replaced by N (cid:48)(cid:48)(cid:48) = N (cid:48)(cid:48) + ∆ N (cid:48)(cid:48) .Note that four parameters should be input to simulate the noise: p XT , σ , σ and σ UN . The referencevalues for these parameters were estimated from the LASiP noise measurements described in section 2.6.Then we could vary them to study the individual impact of the different forms of noise in the micro-cameraperformance.A charge histogram is finally built with the sum of the noise-corrected charge measured in each pixel.This charge histogram is later used to evaluate the energy resolution and to extract the acceptance windowfor the image reconstruction, the same way it was done with the micro-camera (section 2.4). Since we wantedto study the specific impact of the LASiP noise in the performance, the rest of the detector components(crystal, reflector, coupling material, exit window) were treated as ideal objects. Simulations do not includebackground effects that are present in the data like Iodine escape peak or scattering in other materials thatare not those belonging to the micro-camera.
3. Results
Figure 8 shows the single-phe spectra obtained when flashing a LASiP with a pulsed LED as describedin section 2.6. The single-phe resolution degrades as the number of summed SiPMs increases. We were ableto fit all spectra using eq. 2, except for the case in which we summed 8 SiPMs in which it was impossibleto identify peaks. The fit parameters p XT and σ , were reasonably constant in all seven cases, with valuesof ∼
25% and ∼ .
07 phe respectively. As expected, σ increased as √ N SiP M , with N SiP M the number ofsummed SiPMs. This can be seen in Figure 9a, where we fitted the points in the range between 1 and 7SiPMs as σ = p + p √ N SiP M , with p = (0 . ± .
02) phe and p = (0 . ± .
01) phe. The fitting functioncan be evaluated to estimate σ ( N SiP M = 8) (cid:39) .
53 phe.Figure 9b shows the charge distribution obtained using the digitizer for the acquisition, for a LASiPsumming 8 SiPMs in the absence of sources (uncorrelated noise measurements). The distribution was fittedby a Gaussian of σ UN = 186 ADC counts, which corresponds to ∼ .
6% of the mean position of the photopeak(see section 3.3).From the results reported in this section we defined the reference values of the input parameters forsimulating the pixel noise (see section 2.8). These values are shown in Table 1. The MC images shown insections 3.2 to 3.4 contain noise simulated with those values. p XT [%] σ [phe] σ [phe] σ UN [Q]25 0.53 0.07 6.e-3 Table 1: Reference input noise parameters of the simulations. Note that σ UN is given in units of the total charge Q collectedin the four pixels at the photopeak. harge [phe] − E v en t s sum of 1 SiPMs Charge [phe] − E v en t s sum of 2 SiPMs Charge [phe] − E v en t s sum of 3 SiPMs Charge [phe] − E v en t s sum of 4 SiPMs Charge [phe] − E v en t s sum of 5 SiPMs Charge [phe] − E v en t s sum of 6 SiPMs Charge [phe] − E v en t s sum of 7 SiPMs Charge [phe] − E v en t s sum of 8 SiPMs Figure 8: From left to right and top to bottom: evolution of the single-phe spectrum as the number of summed SiPMs increases.In red the fit performed using eq. 2. The data were acquired with an oscilloscope.
Figure 10 shows the image of a flood-field image before and after spatial linearity and uniformity correc-tions, both for the experimental measurements and the MC simulations. As mentioned in section 2.5 the rawimages reconstructed with the centroid method appear “collapsed” in the center of the FOV (Figures 10aand 10b). The response of the real micro-camera is not uniform all across the FOV, probably caused by acombination of several factors including a non-homogeneous crystal response due to the presence of impuri-ties, a non-uniform crystal-LASiP coupling or a non-perfect SiPM gain equalization. These inhomogeneitieswere not simulated, which explains why Figure 10b seems to have a rotation symmetry that Figure 10a doesnot have. However, the bulk of this effect is corrected after spatial linearity and uniformity corrections, ascan be seen in Figure 10c and as it will be shown in the reconstructed images of section 3.4. After correctionsthe FOV is also enlarged. Note that in the simulations we limited the FOV to an area of 15 ×
15 mm aimingto emulate the conditions of the laboratory measurements.Figure 10e shows the raw-reconstructed position (before corrections) of a capillary source that was orientedparallel to the x axis as a function of its true (measured) position in the y axis, both for experimental data andMC simulations. The agreement between the experimental and the simulated curves is good enough for thescope of this work, which illustrates that the RoughTeflon LUT DAVIS model employed in the simulationsreproduces accurately enough the light distribution inside the crystal. There is an acceptable disagreementbetween the two curves near the edges that should not affect the conclusions derived in the next sections.
The measured energy resolution at 140 keV slightly depends on the measuring position. The averagevalue was 11.6%, ranging from a minimum value of 10.9% to a maximum of 12.7%. The variations of thephotopeak position measured in different parts of the FOV were below 5%. Figure 11a shows the chargehistograms obtained during a flood-field irradiation with m Tc. Figure 11b, the charge histograms obtainedwhen imaging the capillary using
Coll 2 . The green histograms contain all the events reconstructed inside a12 umber of summed channels0 1 2 3 4 5 6 7 8 9 [ phe ] σ (a) Charge [ADC counts}800 − − − − E v en t s (b) Figure 9:
Left:
Values of σ obtained from the fits performed in Figure 8 as a function of the number of summed SiPMs. In redthe fit described in the text. Right:
Charge distribution recorded with the digitizer for a single LASiP summing 8 SiPMs inthe absence of visible-light or radioactive sources. In red the Gaussian fit performed from which we obtained σ UN (cid:39)
186 ADCcounts. x [mm]0 5 10 15 20 25 30 35 40 y [ mm ] (a) Data: raw reconstruction x [mm]20 − − − − y [ mm ] − − − − − (b) MC: raw reconstruction x [mm]0 5 10 15 20 25 30 35 40 y [ mm ] − (c) Data: after corrections x [mm]20 − − − − y [ mm ] − − − − − − (d) MC: after corrections true y [mm]6 − − − r a w r e c on s t r u c t ed y [ mm ] − − − − DataMC (e)
Figure 10: (a)–(d)
Flood-field images obtained in the laboratory with the micro-camera and Monte Carlo simulations, before(raw-reconstructed with the centroid method) and after spatial linearity and uniformity corrections. (e) raw-reconstructedposition in the y axis for a capillary oriented parallel to the x axis as a function of its true position, both for data and MC. harge [ADC counts]0 10000 20000 30000 40000 N o r m a li z ed c oun t s (a) Data: flood-field Charge [ADC counts]0 10000 20000 30000 40000 N o r m a li z ed c oun t s (b) Data: capillary Figure 11: Charge histograms obtained during: (a) a flood-field irradiation with m Tc (corresponding image in Figure 10); (b) a capillary fully-filled with m Tc, placed at 20 cm from
Coll2 (corresponding image in Figure 13). Green histograms containall the events in the UFOV. Black histograms only those reconstructed in a 6 × region around the camera center. Thepeak corresponds to 140 keV. Vertical red lines show the limits of the acceptance window used for image reconstruction. ×
13 mm region around the camera center (i.e., the full FOV excluding 1 mm at the edges). The blackhistograms include only those events that were reconstructed in a 6 × region around the camera center.The green histograms exhibit wider peaks, which was expected since they are more sensitive to a non-uniformcharge collection across the crystal area, especially close to the crystal corners where light is not detected.In fact, as it will be shown in section 3.5, simulations suggest that the LASiP dead corners could degradesignificantly the energy resolution and be the main responsible for the second peak at 22000 ADC countsthat appears in Figure 11a. The non-uniform light collection across the whole crystal area also explains whythe photopeaks are broader in Figure 11a than in Figure 11b. While in the first case all parts of the FOVequally contribute to the charge histogram, in the second one most of the histogram counts come from thespecific region in which the capillary was imaged, which was close to the camera center and far from thecorners. For the same reason the mean of the photopeak in Figure 11b is slightly higher than in Figure 11a.As it will be shown in section 3.5, the dead corner does not only impact the width of the photopeak, but alsothe mean collected charge. Images of the
Am source were taken with the micro-camera in different test positions. Their positionswere reconstructed with an accuracy better than 0.3 mm. Three of those images are shown in Figure 12. Theextension R point of the reconstructed images obtained from the 2D-Gaussian fit was on average (2 . ± .
1) mm.Removing the collimator resolution (see 3) we obtained an intrinsic spatial resolution of R d = (2 . ± .
2) mm.Figure 13 compares the reconstruction of two images of the m Tc capillary from laboratory measurementsand simulations. To obtain the MC images we simulated the same conditions of the experiments: sameorientation of the capillary, geometrical characteristics of the collimator and the capillary, and source-to-detector distance. As a reference the projection in one of the main axis of the detector plane are also shown.We consider that the agreement between data and simulations is good enough to use the simulations as a14 [mm]0 5 10 15 20 25 30 35 40 y [ mm ] y [ mm ] y [ mm ] x [mm]0 5 10 15 20 25 30 35 40 N o r m a li z ed c oun t s N o r m a li z ed c oun t s N o r m a li z ed c oun t s Figure 12:
Top:
Images of a
Am point source, taken with the micro-camera and
Coll 1 . Bottom:
Projection of the imagesin the x axis. [mm]0 5 10 15 20 25 30 35 40 y [ mm ] x [mm]20 − − − − y [ mm ] − − − − y [mm] − − − − N o r m a li z ed c oun t s DataMC x [mm]0 5 10 15 20 25 30 35 40 y [ mm ] (a) Data x [mm]20 − − − − y [ mm ] − − − − (b) MC x [mm] − − − − N o r m a li z ed c oun t s DataMC (c) Projection
Figure 13:
Left:
Images of a capillary fully-field with a m Tc solution, taken with the micro-camera and
Coll 2 . Center:
MCimages obtained when the same experimental conditions were simulated.
Right:
Projection of the left and center images in theaxis y (top) and x axis (bottom). test-probe to study with more detail the impact of the LASiP characteristics in the system performance (seesection 3.5).The capillary was imaged in different positions in the two orientations of Figure 13. The mean width ofthe capillary measured in the experiments was R cyl = (2 . ± .
2) mm. Removing the source diameter andthe collimator resolution we obtained R d = (1 . ± .
4) mm.
Table 2 summarizes the impact of the different input noise parameters in the detector energy resolutionmeasured in the center of the FOV (6 × region around the camera center, as defined in section 3.3) fora flood-field irradiation. Except for p XT , the input noise parameters are given in units of the noise referencevalues (n.r.v) of Table 1 and were varied to better understand their individual contribution. The obtainedenergy resolution is shown both for the case in which all 36 SiPMs are enabled (each pixel summing 9 SiPMs)and for the case in which each LASiP sums 8 SiPMs, as in the laboratory measurements. The first entryin the table shows the energy resolution when no noise is simulated. Entry nr. 12 represents the closestsituation to our laboratory measurements (when the input noise parameters are exactly those of Table 1).Even if the energy resolution that was obtained with the 8-SiPM simulated LASiPs is slightly better thanwhat was obtained in section 3.3 (expected due to the simplification of the simulations), we considered it tobe close enough to the values measured with the micro-camera, at least for the scope of studying how energy16r p XT σ σ σ UN (cid:15) (8-SiPM LASiP) (cid:15) (9-SiPM LASiP)[%] [ × n.r.v.] [ × n.r.v.] [ × n.r.v.] [%] [%]1 - - - - 9.7 9.12 - - - 9.8 9.13 - - - 10.0 9.34 - - - 10.1 9.45 - - - 10.4 9.76 - - 9.8 9.17 -
10 1 - 10.2 9.58 - - 10.2 9.59 - - - Table 2: Simulations performed with Geant4 to study the impact of LASiP noise in the micro-camera energy resolution. p XT , σ , σ and σ UN were defined in section 2.6 and their noise reference values (n.r.v) were listed in Table 1. The energy resolution (cid:15) was calculated assuming LASiPs built by summing 8 SiPMs (same geometry of the LASiP prototype) and 9 SiPMs (no deadcorners). resolution changes when we modify the input noise parameters.As anticipated in section 3.3, the LASiP dead corners affect significantly the detector performance, ascan be seen in all entries of Table 2. This suggests that we expect to achieve a significantly better energyresolution in a camera in which LASiPs are built without dead corners, fully covering the crystal surface.The effect of the dead corner can also be seen in Figure 14, that shows the obtained charge spectra for entrynr. 12. The green histograms contain all the events reconstructed inside a 13 ×
13 mm region around thecamera center. The black histograms include only those events that were reconstructed in the center of theFOV. In Figure 14a a second peak left to the main peak can be seen that does not appear in Figure 14b. Itis more pronounced in the green histogram that includes events that were reconstructed closer to the cameracorners. The dead corner impacts both the mean position and width of the photopeak.It would seem that optical cross-talk has a minor impact on the energy resolution of the system (entriesnr. 2–5 in Table 2), although not very critical: the results suggest that reducing p XT to ∼
10% (typicallyachievable at the expense of a lower PDE) would not provide a significant improvement. The parameters σ and σ that describe the finite single-phe resolution of the SiPMs must be increased by a factor of 5or 10 (which is rather unlikely to occur) with respect to their reference measured values to give a non-negligible contribution (entries nr. 6–8). Energy resolution seems to be much more sensitive to an increasein uncorrelated noise, likely dominated by dark counts (entries nr. 9–11). The noise level measured in themicro-camera LASiPs (relative to their mean signals) seems to be adequate if we compare entries 9 and 1.However, an increase in σ UN by a factor 2 (which is not so unlikely, for instance if using noisier SiPMs)already degrades significantly the energy resolution (entry nr. 10). This must be taken into account whendesigning a large camera with several and larger LASiPs.Concerning spatial resolution, we found that it was 10% worse in the images of the capillary simulatedwith the n.r.v. than in the case in which no noise was added. This difference would not be very significantin the context of full-body SPECT, where the collimator contribution typically dominates spatial resolution.17 harge [phe]0 200 400 600 800 1000 1200 N o r m a li z ed c oun t s Energy resolution 12.0Entire FOVEnergy resolution 10.7Center of the FOV (a) MC: 8-SiPM LASiPs
Charge [phe]0 200 400 600 800 1000 1200 N o r m a li z ed c oun t s Energy resolution 10.4Entire FOVEnergy resolution 9.9Center of the FOV (b) MC: 9-SiPM LASiPs
Figure 14: Charge histograms obtained with Monte Carlo simulations (entry nr. 12 in Table 2) during a flood-field irradiationwith m Tc when: (a) the SiPMs in the corners are switched-off (each LASiP is the sum of 8 SiPMs, as in the micro-camera); (b) all 36 SiPMs are enabled (each LASiP is the sum of 9 SiPMs).
However, we note that the impact of noise on the detector spatial resolution should be studied in camerasholding more pixels, where the relative weight of noise will be high in pixels showing low (or no) signal. Suchcase should also require an optimization of the trigger settings, which is far beyond the scope of this work.
4. Discussion
In the previous sections we introduced the concept of LASiP and performed a series of experimentsand simulations to study the feasibility of employing these pixels in large gamma cameras for SPECT. Wewere able to reconstruct simple images with a simple system like the proof-of-concept micro-camera, whichsupports the idea that LASiPs can be used in SPECT.The measured energy resolution of the micro-camera was ∼ .
6% at 140 keV, which is equivalent to typicalvalues from both clinical SPECT systems based on PMTs and small SPECT cameras using SiPMs [12]. Themeasured value was affected by the LASiP prototype dead corner (as it was shown in the simulations).Hence we expect an improvement in an optimized design in which photodetectors cover the entire crystal exitwindow. Energy resolution is affected by all the detector components: scintillation crystal, reflective surfacesurrounding the crystal, photodetectors, coupling between crystal and photodetectors. From the LASiP side,the energy resolution could be improved by using SiPMs with higher PDE, reducing the pixel noise andincreasing the photodetector active area. A better performance should be achieved using modern SiPMswith peak sensitivity at the 420 nm where NaI(Tl) scintillation light peaks. Some of them provide a PDEhigher than 50%, with cross-talk probability of ∼
10% and a DCR of ∼
70 kHz (half the DCR of the SiPMsused in the micro-camera) [29]. The photodetector active area could be increased if reducing the dead spacebetween the SiPMs that build the LASiP.In our simulations we found that uncorrelated noise (DCR and electronic noise) is the dominant noisecomponent affecting energy resolution. The impact of dark counts in the performance of gamma camerasemploying silicon-based photodetectors had been studied in different works. In [30] it was shown that a18elatively high dark count rate (400 kHz/mm at 20 ◦ ) could significantly degrade energy resolution of acamera using SiPMs with a ∼
30% PDE in the wavelength of interest. In fact, the detector module thatwas under study (later developed in [12]) was cooled down to ∼ ◦ C to reduce the DCR. For the samereason, a cooling system was also employed in the camera of [13], which was equipped with digital photoncounters. With the micro-camera we were able to reconstruct images and achieve a reasonable energyresolution operating the LASiPs at room temperature. However, it should be noted that in the micro-cameraall four pixels always exhibit a relatively large signal and hence achieve a high signal-to-noise (SNR) ratio.In a larger camera the situation could be different, as it will be discussed afterwards.We were able to reconstruct the images produced by a Tc capillary and by a
Am point-like source.Even if using only four pixels, we could produce simple images that support the idea that LASiPs couldbe an alternative for building compact SPECT cameras. The intrinsic spatial resolution measured close tothe micro-camera center was ∼ The micro-camera was useful to prove that LASiPs could be used to reconstruct simple images in thecenter of a gamma-camera and to validate the MC simulations that we used to understand the contribution ofthe LASiP noise to the overall performance. This was a necessary step towards the ultimate goal, which is toapply the proposed solution in a large camera (e.g., a camera of a full-body SPECT scanner). Extrapolatingthe performance evaluated with the micro-camera to a larger camera is not straightforward and it requiresa dedicated study that is left for a future work. We would like to highlight that we have developed twokey components for such a study: validated MC simulations that can be extended to a larger camera anda characterization of the LASiP noise as a function of the number of summed SiPMs, which let us modelthe noise in larger pixels. Nevertheless, in the next paragraphs we briefly discuss a few aspects that will beparticularly relevant in a large camera in which a few thousand SiPMs may be employed.
LASiP size and geometry
The 8-SiPM LASiP prototype was a cost-effective solution that was adopted as the first step to studythe feasibility of using LASiP in SPECT. We do not intend to install pixels with such geometry in a camerahosting several tens to a few hundred pixels. As a minimum requirement, a more symmetric LASiP with nodead corners should be employed (e.g., building LASiPs of 9 SiPMs).Using LASiPs of ∼ × like the prototype we developed, about 500 pixels would be needed tocover a 50 ×
40 cm SPECT camera. This is a significant improvement with respect to the thousand ofpixels that would be needed if commercial SiPMs were used, although still high if compared to the 50–100PMTs of a standard clinical camera. The proposed solution of building large SiPM pixels by summing SiPMsignals, and in particular the MUSIC chip, were thought for VHE astrophysics. In these applications thephotosensors must be sensitive to fluxes close to the single-phe level and provide a time resolution of ∼ Dark counts and their impact on the trigger settings
In a large SPECT camera the scintillation photons will be distributed over a larger number of SiPMsthan in the micro-camera. To illustrate this situation, we simulated a perfectly collimated beam of 140 keVdirected into a NaI(Tl) crystal with similar characteristics to the one described in Section 2.8, but witha size of 500 × × . . The crystal was equipped with 4636 SiPMs of 6 × arranged in ahoneycomb geometry and the charge of each SiPM was readout individually. The spatial distribution of themean charge collected by the SiPMs is shown in Figure 15a. If more SiPMs are used to collect the charge,more dark counts will be integrated and this will degrade the performance of the system. One could limit thetrigger area (i.e., the number of SiPMs used to measure the charge of an event) or set individual SiPM/pixelthresholds to reduce the impact of dark counts. However, if the trigger area is too small or the threshold toohigh many scintillation photons will be lost. Figure 15b shows the evolution of the relative charge collectedby the N SiPMs with the highest signal as a function of N (for the events simulated to build Figure 15a).In the example ∼
200 ( ∼ ∼
60% ( ∼ .
13 MHz / mm and an integration time of 0 . µ s. Since both signal and dark counts increase with the number of SiPMsemployed to measure the charge, there should be an optimal trigger area that maximizes the SNR.With a similar reasoning, the integration time will also have to be optimized to maximize the SNR.The temporal distribution of the detected photons is dominated by the scintillation emission, which followsan exponential decay with a characteristic time τ = 240 ns. Dark counts, on the other hand, increaselinearly with time. As in the micro-camera, there will be an optimal integration time that maximizes energyresolution. However, this effect will be more relevant in a large camera employing more SiPMs to collect thecharge. It is then clear that in a larger LASiP-based camera not only the pixel size and geometry must beoptimized, but also the trigger conditions. The optimal trigger conditions (trigger area and integration time)20 [mm]200 − − y [ mm ] − − − − − − (a) Number of SiPMs1000 2000 3000 4000 5000 C o ll e c t ed c ha r ge / T o t a l c ha r ge [ % ] N u m b e r o f D a r k c oun t s [ kc t s ] (b) Figure 15: (a) × for a gamma-ray collimated beam of140 keV directed into a NaI(Tl) crystal of 500 × × . . The black star marks the position of the beam in the (x,y) plane. (b) Percentage of the total charge collected as a function of the number of SiPMs employed for the trigger. The expectednumber of integrated dark counts (DCR = 0 .
13 MHz / mm , integration time = 0 . µ s) is shown in red. will differ depending on the crystal thickness and the pixel size, but also on the SiPM PDE and the DCR. Final considerations
Following the arguments exposed in the previous paragraphs, it is hard to estimate how LASiPs wouldperform in a full-body SPECT camera without a dedicated study. We may expect some degradation of theenergy resolution due to a higher number of integrated dark counts. Depending on how large that degradationis, it may justify the use of a cooling system to lower the SiPM temperature and thus reduce the DCR. Itis also reasonable to expect that the spatial resolution would degrade if the pixel size increases, althoughat the same time using more than 4 pixels to reconstruct the events would probably help. Also applying abetter resolving algorithm during the image reconstruction should provide an improvement in this sense. Theresults of this work can be used as input for studying in detail the performance of a large SPECT camerabased on LASiP through Monte Carlo simulations.Undoubtedly the main advantage of replacing PMTs by SiPM-based pixels in SPECT is the reductionof the size and weight of the camera. The photodetectors would no longer be the main contributors to thecamera volume, which could be reduced by ∼ . Conclusions We studied for the first time the feasibility of using large SiPM pixels in SPECT, as a novel approachto build compact large-area SPECT cameras. We developed a LASiP prototype of ∼ . area ( ∼ . active area) and evaluated its impact on the performance of a gamma camera through laboratorymeasurements and MC simulations. With a proof-of-concept micro-camera using 4 LASiP prototypes wewere able to reconstruct simple images in a central region of 15 ×
15 mm , with an energy resolution of ∼ .
6% at 140 keV and an intrinsic spatial resolution of ∼ Acknowledgments
This work would not have been possible without the support from L. Stiaccini, who designed and built themechanics of the holder. We would also like to acknowledge E. Fiandrini and V. Vagelli for kindly providingthe SCT matrices we used for building the LASiPs. We would like to thank the ICCUB team (D. Gasc´on, S.G´omez, D. S´anchez) for the fruitful discussions and M. G. Bisogni for taking her time to go through the draft.This research has been carried on in the framework of the CompTo-NM project led by Imaginalis s.r.l. andfinanced by Regione Toscana - POR CREO FESR 2014-2020. The work of A. Rugliancich has been partiallysupported by the Tuscany Government, POR FSE 2014-2020, through the INFN-RT2 172800 Project.
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