In ion beam therapy, the quality of dose and range calculations strongly depends on precise knowledge of the tissue composition inside the treated volume. Especially the relative stopping power (RSP) of the irradiated tissue has to be precisely known as it describes the ions energy loss per unit path length relative to the energy loss in water. Currently, RSP images are obtained via conventional x-ray computed tomography (CT), where the measured Hounsfield units (HU) have to be converted to the corresponding RSP values (Schneider et al 1996). This conversion process, however, represents a significant source of inaccuracy, resulting in RSP errors that directly influence uncertainties in estimated particle range (Yang et al 2012). For instance, Bär et al (2022) have investigated RSP errors in CT by measuring the mean absolute percentage error (MAPE) of the RSP using different porcine and bovine samples. Their findings revealed a MAPE of 2.06% for single-energy CT and 0.61% for more modern dual-energy CT.

An alternative imaging modality that aims at improving the accuracy of the RSP estimation is ion computed tomography (iCT). Unlike CT or DECT, iCT allows determining the RSP directly by measuring the particle path and energy loss of single ions travelling through the patient using a tracking system and a separate calorimeter (Schulte et al 2004). While recent iCT prototype scanners showed promising results (Johnson et al 2016, DeJongh et al 2021, Scaringella et al 2023) and also the potential to compete with modern DECT scanners (Dedes et al 2019, Bär et al 2022), no clinical iCT system exists so far. The main reason is that meeting all detector requirements of a clinically viable iCT system is quite challenging, especially the minimum required data acquisition rate of at least 10 MHz (Johnson 2017) to keep the acquisition time of the iCT scan comparable to CT ().

However, recent advances in 4D-tracking detectors, in particular the low gain avalanche diode (LGAD) technology, constitute a potential solution to this challenge. LGADs are silicon-based particle detectors, which allow to simultaneously measure the particle's position and time-of-arrival (ToA) with a spatial and time precision better than 100 μm and 100 ps, respectively (Sadrozinski et al 2017). Consequently, single-particle tracks can be resolved even at very high track densities, thus leading to much higher rate capabilities when compared to conventional silicon detectors. For instance, in a recent proton-proton production experiment with the high-acceptance dielectron spectrometer (HADES) at GSI, an LGAD-based start reaction time detector and beam monitor system was able to cope with a particle flux of 108 p s−1 cm2 (Krüger et al 2022). Besides this high rate performance, LGADs are also very radiation hard as they can withstand neutron equivalent fluences of up to ≈1015 neq/cm2 without significantly deteriorating their excellent 4D-tracking capability (Padilla et al 2020). All those detector properties, combined with a relatively low material budget () silicon), make LGADs a perfect detector candidate for high luminosity environments with many applications ranging from high energy physics to medical physics, e.g. iCT.

Building an iCT system based on LGADs could not only help to boost the scanner's rate capability, but it would also allow integrating time-of-flight (TOF) measurements into the imaging process itself, which is then referred to as TOF-iCT. In contrast to conventional iCT designs, a TOF-iCT system can be solely based on LGADs, as LGADs can be used for both the particle path and energy loss estimation. For instance, by measuring the TOF in air inside a TOF calorimeter placed downstream of the patient, the residual energy of the ion can be determined (Volz 2021, Krah et al 2022, Ulrich-Pur et al 2022). Alternatively, the energy and material-dependent increase in an ion's TOF through the scanned object can be used as an indirect measure for the energy loss, which is the so-called Sandwich TOF-iCT concept introduced in Ulrich-Pur et al (2023). The latter approach, unlike any other iCT system, does not require a dedicated residual energy detector downstream of the patient, which would make the scanner design much more compact and therefore easier to integrate into a clinical treatment room.

While recent Monte Carlo (MC) feasibility studies demonstrated the potential of both TOF-iCT (Krah et al 2022, Ulrich-Pur et al 2022) and Sandwich TOF-iCT (Ulrich-Pur et al 2023) to fulfil the requirements of a clinical iCT system, no TOF-iCT system exists so far. This study aims to fill this gap by providing the first experimental study of an LGAD-based iCT system, focussing on the novel Sandwich TOF-iCT method. This should serve both as an experimental proof-of-concept for Sandwich TOF-iCT as well as a guide for potential refinements in succeeding TOF-iCT designs and methods. For that purpose, we designed a compact Sandwich TOF-iCT prototype using single-sided LGAD strip sensors. The LGAD sensors were obtained from an R&D sensor production run at the Fondazione Bruno Kessler (FBK) and operated using a modified readout system from the LGAD-based start reaction time detector of the HADES experiment at GSI (Krüger et al 2022).

Utilising this demonstrator, we generated a proton radiography (pRad) of a small aluminium stair phantom at the research and therapy centre MedAustron in Wiener Neustadt, Austria. Details about the calibration procedures of the Sandwich TOF-iCT system, encompassing both sensor and water-equivalent-thickness (WET) calibration, will be outlined in the following before delving into the specifics of the pRad experiment, its image reconstruction and analysis.

2.1. Sandwich TOF-iCT concept

The Sandwich TOF-iCT concept was first introduced in Ulrich-Pur et al (2023) and will be summarized briefly in the following.

2.1.1. Time-of-flight of ions in matter

As ions travel through matter, they lose energy and slow down, which leads to a material and energy-dependent TOF, calculated as

with m0 as the rest mass of the ion, c as the speed of light and and as the kinetic energy and corresponding velocity at position .

2.1.2. Slowing down power

While the TOF in equation (1) strongly depends on the tissue composition, beam energy and ion's path, it was shown that, for a small pathlength increment Δx inside the traversed tissue, the difference in TOF per unit pathlength with respect to the TOF in vacuum (TOFvac), i.e. without any energy loss, is directly related to the stopping power (SP) of the medium according to

with f(E) as a solely energy-dependent term, ΔTOF = TOF − TOFvac and SDP(E) as the so-called slowing-down power of the traversed medium at the beam energy E.

2.1.3. Relative slowing down power

Using equation (2), one can easily see that the relative slowing down power (RSDP), i.e. the SDP in matter (SDPmat) relative to the SDP in water () is equal to the RSP since f(E) cancels out and

with SPmat and denoting the SP in the material and water, respectively.

2.1.4. Imaging problem

In standard iCT, the RSP distribution inside the patient can be reconstructed by measuring the particle path of multiple ions travelling through the patient and the corresponding WETs, which are a measure for the total energy loss along the path (ΔE) for a given primary energy E0. The respective inverse problem reads as follows

with and denoting the RSP and RSDP at positon and L the total pathlength of the ion's trajectory inside the patient. Inserting equations (2) and (3) into the right-hand-side of equation (4) yields the following image reconstruction problem for Sandwich TOF-iCT

where is given as a function of . To obtain the relation between ΔTOF and E, and therefore , one can correlate the cumulative TOF increase in water for different water thicknesses and a given primary beam energy E0 to the corresponding residual energy using the initial condition . The correlation for water can be either obtained via MC simulations or analytically as described in Ulrich-Pur et al (2023). After determining and measuring the total increase in TOF (TOF − TOFvac) and the total pathlength L, one can reconstruct the RSP using standard iCT reconstruction algorithms, e.g. as defined in Rit et al (2013).

2.1.5. Alternative WET calibration approach

However, actually measuring the total increase in TOF requires prior knowledge of the velocity distribution along the particle path, which can only be estimated, e.g. via MC simulation. Therefore, as a first step, a much simpler approach was introduced in Ulrich-Pur et al (2023). Instead of estimating the true increase in TOF, the increase in TOF w.r.t the TOF in air (TOFair), i.e. the TOF through the scanner without the phantom, is determined. For each particle, the resulting TOF increase is then mapped to the corresponding WET of the traversed medium using a fifth-order polynomial

with ai (E0) as the fit parameters for an ion with primary beam energy E0. To obtain the fit parameters ai (E0), a calibration run has to be performed prior to the actual imaging experiment, where TOF − TOFair(WET, E0) has to be measured for a fixed beam energy E0 and different absorbers with known WET.

While this simplified calibration model is easy to implement, it also introduces a systematic dependence of the WET estimation on the system parameters of the used TOF-iCT system (Ulrich-Pur et al 2023). Thus, an optimized model should be developed to further advance this imaging modality. However, since the study presented here focuses mainly on the first experimental realisation of Sandwich TOF-iCT, improving the WET estimation algorithms for this modality was out of the scope. Therefore, the simplified WET calibration method described in equation (6) was also chosen for the pRad experiment conducted at MedAustron.

2.2. TOF-iCT demonstrator

The TOF-iCT demonstrator utilizes an adapted version of the readout system for the LGAD-based HADES start-reaction time (T0) detector developed at GSI (Krüger et al 2022). A brief description of all components of the TOF-iCT demonstrator, including the LGAD sensors, corresponding front-end electronics (FEE) and data-acquisition (DAQ) system, is given in the following.

2.2.1. LGAD sensors

Four single-sided LGAD strip sensors were used for the TOF-iCT demonstrator, each measuring ≈1 × 1 cm2 and containing 86 strips with a strip length of 8.6 mm and a pitch of 100 μm (figure 1(a)). Similar to the HADES T0 detector, which stems from the same R&D production run as the LGADs used within this work, all sensors underwent a thinning procedure to reduce the overall material budget of the detector, resulting in a total sensor thickness of 200 μm.

Figure 1. Components of the LGAD-based 4D-tracking module. (a) 1 × 1 cm2 LGAD strip sensor with 86 channels wire-bonded to the discrete front-end electronics. (b) Two single-sided LGAD strip sensor modules were mounted perpendicular to each other to form a full 4D-tracking layer. (c) Schematic of a single-sided LGAD strip sensor module.

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Standard image High-resolution image 2.2.2. LGAD module

In order to bias and read out each sensor, four detector modules were developed. As shown in figure 1(c), each module was designed with a centrally located rectangular cut-out in which a 3D-printed plastic grid was placed (dark green grid). The sensor was then glued onto this grid and connected to the discrete FEE consisting of a two-stage pre-amplifier indicated as dark blue strips and the corresponding low-voltage (LV) power lines to drive the pre-amplifiers as well as high-voltage (HV) power lines for biasing the LGAD. The pre-amplified signals were then forwarded to custom FPGA-based time-to-digital converter (TDC) boards (DiRICH5s1 boards), which also feature another amplification stage and a leading edge discriminator (indicated as pink strips) as well as an optical link for the readout (highlighted in yellow) and low voltage differential signal (LVDS) lines for triggering (grey connectors). Using the DiRICH5s1, the leading and falling edge of the amplified LGAD signal could be determined, which allowed measuring the time-of-arrival (ToA) of the particle as well as the time-over-threshold (ToT), i.e. a measure of the signal duration and therefore also signal height. While each DiRICH5s1 has 32 readout channels, the channel configuration inside the discrete FEE required four of those FPGA-based TDC boards to read out all 86 channels of a single LGAD sensor. However, constraints related to the number of available DiRICH5s1 boards, which was 14 in total, meant that only every second channel in the final LGAD was effectively connected. This still allowed full particle tracking inside the last sensor as the cluster size, i.e. the number of fired strips per particle, was mostly greater than 3 for the used proton beam energies, and therefore, this sensor required a minor adaptation of the 4D-cluster finder algorithm, which will be briefly outlined in section 2.4.1.

2.2.3. 4D-tracking layer

Given that an individual LGAD module can measure just one spatial coordinate, we paired two of the aforementioned modules orthogonally to each other to create a single 4D-tracking layer. Since mechanical constraints prohibited mounting the LGADs in close proximity, they were installed at a distance of 1.64 cm between the individual LGAD sensors. For each sensor, an additional light-tight enclosure was constructed using a 3D-printed plastic holder featuring a circular aperture with an area greater than the LGAD size. This cutout was subsequently sealed with light-tight tape to ensure total light isolation. An image of a completely assembled 4D-tracking layer can be seen in figure 1(b).

2.2.4. TOF-iCT demonstrator layout

Figure 2 illustrates the structural design of the TOF-iCT demonstrator, which consists of two 4D-tracking layers separated by a distance of d4D−stations = 27 cm. While dLGAD denotes the previously mentioned spacing between the individual LGAD sensors per 4D-tracking layer, dtape describes the gap between the sensor and the light-tight tape. The latter was determined by the dimensions of the light-tight enclosure, measuring 0.5 cm.

Figure 2. Schematic representation of the TOF-iCT demonstrator setup at MedAustron, highlighting only components directly irradiated by the beam and positioned in the field of view of the LGAD sensors, thus influencing the experimental outcome.

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Standard image High-resolution image 2.2.5. Data acquisition system

The DAQ system of the TOF-iCT demonstrator (figure 3) is a modified version of the HADES DAQ system (Michel et al 2011). Central to this system is the TrbNet (Michel et al 2013), a custom FPGA-based network protocol used for triggering, data transfer and slow control of the FEE of the individual detectors, e.g. the DiRICH5s1 boards on the LGAD modules. The main hardware component of the DAQ system is the FPGA-based multi-purpose trigger and readout board version 3 (TRB3), which houses five FPGAs (Neiser et al 2013). One of these FPGAs acts as the central controller and the other four establish the optical connections to the LGAD modules using supplementary adapter boards equipped with small form-factor pluggable (SFP) modules. While the synchronisation, data transfer and slow control operations are carried out through these optical links, additional LVDS connections provide the physical trigger to the DiRICH5s1 boards. Both the synchronisation and triggering are managed by the so-called central triggering system (CTS), which is also integrated into the central controller FPGA. Leveraging the capability of the CTS to accept external trigger inputs, an auxiliary FPGA-based logic board (i.e. the Trb3sc) was utilized to set the trigger condition for the readout. A logical OR across all channels of the third LGAD was chosen for this purpose, meaning that a trigger was initiated and forwarded to the CTS inside the TRB3 via LVDS whenever the signal in any channel of the third LGAD exceeded the threshold set in the corresponding leading-edge discriminators. The CTS then generated an output trigger, which was synchronously dispatched to all the LGAD modules through a fan-out board linked to the TRB3. Once an event was triggered, all incoming signals that fell within a predefined time window were sent from the DiRICH5s1 boards to the main FPGA and then to the readout PC via ethernet. For this experiment, the time window was set to 250 ns prior to and 50 ns after the trigger's arrival to account for the different delays in the readout chain and to guarantee the simultaneous measurement of a single particle in all detector modules. On the readout PC, the C++-based data acquisition backbone core framework (DABC) and Go4 analysis framework (Go4) were running to combine the data streams and build complete events, perform online monitoring and store the pre-processed data to disk. A more detailed description of the HADES DAQ and all used components and protocols can be found on the TRB Homepage (trb.gsi.de).

Figure 3. Sketch of the TOF-iCT demonstrator DAQ system.

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Standard image High-resolution image 2.3. Sensor calibration

Prior to recording the pRad, the LGAD sensors had to be calibrated. The calibration procedures, which will be outlined in the following sections, were first tested and optimized in the detector laboratory at GSI using a Sr-90 source. Given that the Sr-90 electrons produce signals similar to minimum-ionizing particles (MIPs), it was necessary to repeat the calibration for each of the used proton beam energies at MedAustron to cover the full signal height spectrum. Since the used beam energies varied between 83 and 800 MeV, the signal heights were anticipated to exceed that of MIPs by a factor ranging between 1.14 and 4.03.

2.3.1. TDC calibration and threshold scan

First, each TDC had to be calibrated using internal calibration pulses issued from the CTS. Details about the FPGA-based TDC calibration can be found on the TRB Homepage (trb.gsi.de). Then, the thresholds in each leading-edge discriminator were set to a fixed value above the noise level (≈20 mV), which was low enough to capture the smaller, capacitively-coupled signals (Pietraszko et al 2020) in the strips adjacent to the actual strip hit by the particle. Since the noise level was assumed to be constant for the entire experiment, the thresholds were only set at the beginning of the experiment.

2.3.2. Time-over-threshold re-scaling

However, slight variations in the effective threshold levels, attributed to different noise levels, and differences in signal amplification across individual LGAD channels could still be expected. Given that these factors can significantly impact the signal response, especially the obtained ToT, normalizing the ToT measurement for each channel was essential to maintain a uniform response across all sensors. Therefore, each 4D-tracking module was irradiated with protons of a fixed beam energy E0 and the corresponding ToT distributions were recorded in both sensors of every 4D-tracking module. First, to estimate the position of the main signal peak, the most probable ToT value () was determined for each LGAD channel. This was done by fitting a Gaussian to the maximum of the obtained ToT distributions using only the ToT values in the vicinity of the ToT peak. Then, the ToT spectra were normalized by setting the to 20 ns in every LGAD channel using the following re-scaling function

Here, ToTraw(i, j) and ToT(i, j) denote the raw and the corresponding normalized ToT value measured in channel i of LGAD j.

2.3.3. Time-walk and offset correction

Since both the ToA and the ToT are determined using a predefined, fixed threshold, their measured values strongly depend on the actual amplitude of the physical signal. This amplitude-dependence of the ToA, also known as the time-walk effect, can lead to ToA variations in the order of several nanoseconds, depending on the used readout electronics and resulting signal shape. As those variations can significantly deteriorate the precision of the time measurement, correcting for the time-walk effect is essential. The time-walk correction in each 4D-tracking layer was done in two steps using the data sets recorded for the ToT normalisation (section 2.3.2). First, to obtain the time-walk trend, the time difference spectra between every channel on one LGAD and a reference channel on the other LGAD of a single 4D-tracking layer were determined with respect to the corresponding signal amplitudes on the first LGAD, given via the related ToT of those signals. A 4D-clustering procedure (section 2.4.1) in addition to a ToT cut to the signals in the reference channels was applied to avoid redundancy by selecting only hits, which stem from the actual particle and not from noise events or capacitive-coupling between the neighbouring strips. Then, to estimate the time walk trend in each LGAD strip, the corresponding time difference vs ToT spectrum was divided into 50 ps × 50 ps bins and the most probable time difference value (TDiff,MPV(ToT)) was obtained for each ToT bin using a Gaussian fit. The obtained TDiff,MPV(ToT) values were then stored in a look-up-table (LUT) and used to remove the signal amplitude dependence of the measured ToA in this channel. This was done by determining the TDiff,MPV(ToT) for the measured ToT and subtracting it from the corresponding ToA (ToAmeas(ToT)) according to

with ToAcorr as the time-walk corrected ToA. After calibrating every channel inside the first LGAD, the same procedure was applied to the second LGAD of the same 4D-tracking layer by choosing one channel in the first LGAD as the reference channel.

While the previously mentioned time-walk calibration procedure removes any ToT dependence of the measured ToA, it also has the advantageous effect of synchronising the time measurement across the entire 4D-tracking layer. By subtracting TDiff,MPV(ToT) from the measured ToA, the mean time difference between the calibrated channel on the one LGAD and corresponding reference channel on the second LGAD of the same 4D-tracking layer will always be zero for the same beam energy. Since the same reference channel on one LGAD is used to calculate TDiff,MPV(ToT) for calibrating all channels on its partner LGAD, the mean time difference between all those channels and the corresponding reference channel is also zero. This also means that no offset in the measured ToA between the individual LGAD channels caused e.g. different signal propagation times inside the individual channels or the non-zero propagation time of the particles travelling between the sensors should remain. Consequently, for the same beam energy, all channels inside the 4D-tracking layer should measure precisely the same mean ToA with the ToA of the reference channel defining the global reference time. However, since the time-walk calibration procedure has to be done once for one LGAD and once for the partnering LGAD of the same 4D-tracking layer, it is important to carefully choose the order of the calibration as this will define the final reference ToA for the entire 4D-tracking layer. For instance, if LGAD1 (figure 2) is calibrated after LGAD2, the reference channel in LGAD1 defines the final reference ToA of the corresponding 4D-tracking layer. For all following experiments, one central strip in LGAD2 and one central strip LGAD3 were used to define the final reference ToAs.

2.4. Hit reconstruction and 4D-tracking2.4.1. Hit reconstruction

As discussed in Pietraszko et al (2020), a particle hit inside the used LGADs results in a signal above the discriminator threshold across a cluster of strips mainly due to capacitive coupling between the individual detector channels. While the strip closest to the actual particle hit position yields the highest signal (highest ToT), the neighbouring strips detect a reduced signal, depending on the capacitive properties of the LGAD strip detector. To estimate the actual hit position for each particle, those clusters have to be identified and analyzed. For that purpose, a 4D cluster finder algorithm was implemented, which will be summarized briefly in the following. For every hit inside the LGAD, coincident signals within a given time window (±15 ns before and ±1 ns after the time-walk calibration) and strip distance to the strip position of the corresponding hit (±12 strips) were determined. For LGAD1, LGAD2 and LGAD3 (figure 2), where all channels could be read out, a cluster was found if the strips of those coincident hits were consecutive in space. For the last LGAD (LGAD4), where only every second channel was connected, a cluster was found if the coincident hits where within the previously described time window and strip range. Once a 4D cluster was found, the true ToA and hit position of the particle hit inside the LGAD were estimated using the strip signal inside the cluster with the largest ToT, i.e. closest to the actual particle position.

2.4.2. 4D-track selection

After applying the 4D cluster finder procedure to the calibrated data and estimating the corresponding particle hit positions and ToAs for each cluster, the 4D-particle tracks inside the TOF-iCT demonstrator could be reconstructed using a custom 4D-tracking algorithm. However, given that the TOF-iCT demonstrator consists of two 4D-tracking layers, only a straight-line track model could be utilised. First, a track candidate was identified if every LGAD had at least one cluster within a triggered event. Then, to simplify the 4D-tracking finding procedure, only events with exactly one cluster per layer were selected for the subsequent analysis to guarantee that only one particle passed through the TOF-iCT demonstrator.

2.4.3. Detector alignment and position measurement

In order to align the 4D-tracking layers of the TOF-iCT demonstrator, an available laser-positioning system at MedAustron was utilised. Following this, a more accurate, software-based detector alignment technique similar to the pre-alignment procedure defined in Dannheim et al (2021) was applied. For that purpose, the TOF-iCT demonstrator was irradiated with 800 MeV protons and the hit positions were recorded on both 4D-tracking layers using the 4D-track candidates described in section 2.4.2. Then, the lateral displacement rx and ry between the first and second 4D-tracking layer were calculated for each particle according to

with xfront, yfront, xback, yback denoting the x and y hit position in the first and second 4D-tracking layer, respectively. Any lateral misalignment of the layers would then manifest as a non-zero mean in the distributions of rx and ry since the average trajectory of all particles should theoretically be a straight line. To mitigate this misalignment, the first 4D-tracking layer was designated as the reference layer and the second layer's hit positions were adjusted by subtracting the mean offsets and , which were obtained by fitting a 1D Gaussian to both the rx and ry distributions.

2.4.4. TOF measurement

Using the calibrated and aligned TOF-iCT demonstrator, the TOF through the scanner could be determined. For all of the following experiments, the TOF was defined as the difference between the mean ToA per 4D-tracking layer using

with ToAcorr(j) as the calibrated ToA measured in LGAD j. As detailed in section 2.3, the reference ToA channels for the offsets correction between the individual LGAD layers were chosen such, that the measured TOF in equation (10) reflects the TOF between LGAD2 and LGAD3 (figure 2).

2.5. Performance of the TOF-iCT demonstrator2.5.1. Energy and position dependence of the TOF

In order to assess the homogeneity of the TOF measurement for the entire active area of the TOF-iCT demonstrator, the position dependence of the TOF was investigated using different proton beams with energies ranging from 83 MeV to 800 MeV. This was done by projecting the TOF of every particle (equation (10)) onto the last 4D-tracking layer by combining all 86 LGAD channels per sensor to 86 × 86 pixels. For each pixel, the TOF distribution was recorded and the corresponding most probable value and standard deviation were estimated using a Gaussian fit. The resulting TOF values were then compared to the theoretical TOF through vacuum for the same flight path length and primary beam energy to assess the accuracy of the TOF measurement.

2.5.2. Energy and position dependence of the intrinsic time resolution

Using the same data set as obtained in section 2.5.1, the intrinsic time resolution per LGAD channel was estimated for all of the employed beam energies. This was done by calculating the time difference

between every channel i in LGADj and a reference channel iref on LGADk≠ j of the same 4D-tracking layer (figure 2). A Gaussian was then fitted to the resulting TDiff(i, j) distributions to estimate the corresponding standard deviations . Finally, to approximate the intrinsic time resolution for every LGAD channel (σToA(i, j)), the obtained was divided by since , which can be derived from a Gaussian error propagation of equation (11) and assuming a similar time-resolution in each LGAD (σToA(i, j) ≈ σToA) for a fixed beam energy.

2.6. Sandwich TOF proton radiography at MedAustron

After calibrating and testing the performance of the TOF-iCT demonstrator, two Sandwich TOF pRad images of a 1 cm3 aluminium stair phantom (figure 4(a)) were recorded at MedAustron using 83 and 100.4 MeV protons. A beam with a reduced particle rate (Ulrich-Pur et al 2021) close to the maximum trigger rate of the TRB DAQ system (≈105 p s−1) was chosen to reduce the probability of multiple particle hits per LGAD for every triggered event. However, this also meant that the full potential of the rate capability of LGADs (≈108 p s−1 cm−2) was not exploited for this experiment. The main reason for that was to obtain clean 4D particle tracks and avoid any ambiguities caused by e.g. detection inefficiencies in one of the LGADs, which would then require a more sophisticated 4D-tracking algorithm. The latter was out of the scope, as the main focus of this study was the first experimental realisation of Sandwich TOF pRad, for which a clean particle track and, therefore, simpler 4D-tracking methods were preferred.

Figure 4. Calibration phantom and object to be imaged. (a) Al stair phantom mounted on a rotating table. The imaged part of the phantom is highlighted as a red region of interest (ROI). (b) WET calibration phantom consisting of 10 × 10 cm2 PMMA slabs with a thickness of 1.65 mm each.

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Standard image High-resolution image 2.6.1. WET calibration

First, a calibration curve according to section 2.1.5 was recorded for each beam energy. This involved irradiating 1.65 mm thick PMMA slabs (figure 4(b)) with an RSP of 1.012 and measuring the corresponding TOF per pixel inside the TOF-iCT demonstrator as detailed in section 2.5.1. Then, the median over those TOF per pixel values was calculated and used to determine the calibration parameters ai (E0) (see equation (6)).

As shown in figure 5(a), the calibration phantom was mounted in front of the third LGAD. It was placed adjacent to the light-tight enclosure covering the LGAD to minimize the energy loss in air between the phantom and the last 4D-tracking station.

Figure 5. Sandwich TOF-iCT demonstrator system consisting of 4 single-sided LGAD strip sensors. Only every second channel of LGAD3 was connected to the readout electronics. (a) Schematic representation of the WET calibration setup at MedAustron. (b) Image of the TOF-pCT setup at MedAustron. The Al stair phantom was mounted on a rotating table and placed in front of the second 4D-tracking station marked as LGAD '3 + 4'.

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Standard image High-resolution image 2.6.2. TOF-based proton radiography

After determining the WET calibration curves, the pRads of the aluminium stair phantom were recorded. For that purpose, the phantom was mounted on a rotating table and placed 1.9 cm in front of the third LGAD (figure 5(b)). However, given that each LGAD consisted of 86 strips with a strip pitch of 100 μm, only a partial section of the phantom could be imaged. The specific area imaged is delineated in figure 4(a) by the red region of interest (ROI).

In order to acquire the pRad image for each beam energy, the TOF through the scanner was measured and projected onto the last 4D-tracking layer as outlined in section 2.5.1. A pixel size of 2 × 2 strips was selected for the pRad images, which is equivalent to an area of 200 μm × 200 μm per pixel. For each pixel, the MPV of the TOF, i.e. TOFMPV(x, y), was obtained by applying a Gaussian fit to the resulting TOF distributions. Using the WET calibration curves as determined in section 2.6.1, the collected TOFMPV(x, y) values were converted into the corresponding WET.

2.6.3. Image quality analysis

To assess the pRad image quality with respect to the WET accuracy, the WET values, which were obtained according to section 2.6.2, were collected inside the centre of the aluminium stair phantom using a square-shaped ROI with a size of 24 × 24 pixels. Based on the resulting WET distribution, the median WET (WETmedian) was calculated for that ROI. Then, to evaluate the WET accuracy, the relative WET error (WET) was determined as follows

using WETtheo as the theoretical WET for a 1 cm thick aluminium layer, which, according to the NIST PSTAR database (Berger et al