The proposed detector panel consists of an array of four-layered dual-readout detector towers. Photographs of the proposed detector panel and the readout electronics are presented in figure 1. The panel contains 12 detector towers arranged in a 4 × 3 grid along X and Z directions, respectively (figure 2(a)). The full panel measures 98.4 × 104.2 mm2 and the center-to-center distances between the towers are 26.8 mm and 37.1 mm, along the X and Z directions, respectively.

Figure 1. Photographs of the detector panel and its readout electronics. (a) Front view of the panel showing the crystal arrays. (b) Rear view of the panel showing the readout electronic cards. (c) A single readout electronic card with its main components highlighted.

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Figure 2. (a) Schematic illustration of the detector panel showing the arrangement of detector towers and the integrated readout electronics. (b) Layout of the 4 × 3 grid of detector towers on the panel, with center-to-center distances indicated. (c) Illustration of a single four-layer, dual-readout detector tower, highlighting the four directional readout groups (Northeast, Northwest, Southeast, and Southwest).

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Detector towers operate in side-irradiation configuration, enabling DOI measurement across the layers, while axial positioning is derived from the dual-ended readout. The detector towers employ Lutetium Fine Silicate (LFS) scintillator crystals, characterized by a density of 7.35 g cm−3, an attenuation length of 1.15 cm for 511 keV photons, and a refractive index of 1.81. Its light yield reaches approximately 80% of that of NaI(Tl), and a decay time of 36 ns, which is shorter than the 41 ns of more commonly used LYSO crystals (Doroud et al 2014). Supplementary table 1 summarizes the physical properties of LFS and LYSO crystals. A comparison of their CTR for 15 mm-long crystals, as reported in (Doroud et al 2014), showed that LFS achieved a CTR of 148 ps, outperforming LYSO, which recorded a CTR of 180 ps.

Each detector tower consists of a stack of 32 LFS crystals (figure 2(c)), forming a block with overall dimensions of 18 × 18 × 30 mm along the X, Y, and Z axes, respectively. The block is configured as an array of 8 crystals along the X axis, stacked in 4 layers along the Y axis. Each individual LFS crystal measures 2.05 × 4.4 × 30 mm. All surfaces are polished, and adjacent crystals are optically isolated using powdered barium sulfate (BaSO₄). Additionally, the four lateral surfaces are coated with BaSO₄ and an outer layer of E60 to enhance optical photon collection.

Two arrays of strip-shaped multi-pixel photon counter (SMPPC) silicon photomultipliers (SiPMs) (Hamamatsu, Japan) are attached to opposite sides of the detector (figure 1(c)) using EP601-LV epoxy glue (Polytec PT GmbH). Each SMPPC array consists of 16 strips mounted on a substrate, with a 0.08 mm gap between adjacent SMPPCs and a 0.25 mm gap between groups of four (layers). Each SMPPC features an active area of 18 × 1 mm2 with single-photon avalanche diodes (SPADs) of 50 × 50 μm2 and is read with 2 channels at its ends (Doroud et al 2021).

To simplify orientation and referencing, the sides of the detector tower are assigned directional (Dir) labels: the faces attached to the SMPPC arrays are referred to as North (N) and South (S), while the perpendicular ends of the SMPPCs are designated East (E) and West (W). Each layer (consequently each crystal) is attached to 4 SMPPCs at each end, thus read by 16 channels (each SMPPC is read by two channels) organized into four directional groups: NE, NW, SE, and SW.

Each SMPPC is read out from both ends with an ultra-fast amplifier discriminator, thus 64 channels are required to fully instrument a single detector tower. The power consumption is about 27 mW per channel. A closed loop water cooling system is used to dissipate this power. An onboard chip provides high-voltage power supply optimized for driving SMPPCs, which contains a temperature compensation function that constantly regulates the SMPPCs operation in environments with varying temperatures. All SMPPCs are operated at around 6 V overvoltage.

The readout operations are handled by the CAEN A5203B, part of the FERS-5200 (front-end readout system) electronics platform (figure 1(c)). It integrates two CERN picoTDC application-specific integrated circuits (ASICs) in a compact and scalable unit capable of high-resolution time of arrival (ToA) and time over threshold (ToT) measurements over 128 channels. A full detector panel requires 768 channels; therefore, it is readout with 6 A5203B cards.

A concentrator board works as bridge and synchronization module for all channels, providing data readout, synchronization between the units and broadcasting of commands (e.g. triggers, time resets, etc.). This is carried out using Janus, an open-source software platform tailored for such modular systems. In Janus, each event is encoded as a 32-bit data word (for each channel). The lowest 8 bits contain the ToT information, with a least significant bit (LSB) corresponding to 1.6 ns. The following 19 bits encode the ToA, with a LSB of 3.125 ps. Consequently, the ToA measurement rolls over after 219 × 3.125 = 1.64 µs which necessitates the introduction of a frame counter. The timing resolution can reach approximately 7 ps root mean squared (RMS) under stable input amplitude, and around 20 ps RMS when input signal amplitudes vary (Venturini et al 2024).

Spontaneous firing of SPADs can cause dark counts and noise in the output signal. To suppress these dark counts, an acceptance threshold was applied on the ToT values whether to record the SMPPC hit or to suppress it. This threshold was set far enough from the 511 keV photopeak to ensure full efficiency. Furthermore, ToT-based corrections are applied in software to compensate for amplitude-dependent timing shifts (walk effect), thus removing the need for hardware-based constant fraction discriminators (Venturini et al 2024).

The following section explains how the ToT and ToA values are used to infer the energy deposition, timestamp, and spatial coordinates of the incident annihilation photon.

A flood illumination phantom was constructed using two plexiglass plates sealed together, forming a fillable cavity with 2 mm thickness. A schematic of the phantom is shown in figure 3. The phantom was filled with 18F-FDG to uniformly irradiate the detector panel. For the TOF measurements, the same phantom was positioned midway between the two detector panels, separated by a distance of 30 cm. The activity rate during data acquisition was below the saturation point of the setup to avoid the effects of deadtime. Data acquired from these scans were used for detector calibration.

Figure 3. Schematic of the flood illumination phantom used for calibrating the detector panel. The phantom consists of two plexiglass plates enclosing a 2 mm thick fillable cavity, uniformly irradiating the detector surface when filled with 18F.

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Layer detection (DOI): Event reconstruction begins with identifying the layer in which the interaction occurred. This is defined as the layer where all its 16 channels register a signal (non-zero ToT). The DOI is then assigned to the geometric center of the identified layer. If, within a single time frame (1.64 µs), more than one layer satisfies this activation condition, each would go through further processing as an independent event: In cases of inter-layer scattering, the events would typically get rejected by the energy window due to insufficient deposited energy; Conversely, if the multi-layer activation is due to arrival of more than one annihilation photon during the time frame, each layer whose energy falls within the 511 keV energy window, will be recorded as a separate event.

Time: Differences in cable lengths and PCB trace lengths among the SMPPC-ASIC channels introduce relative timing offsets. These offsets were corrected among the four channels within each directional group (i.e. NE, NW, SE, SW) of a detector layer. For this purpose, the Gaussian mean of the ToA difference between each channel and the average ToA of its directional group was calculated and applied as a constant correction factor.

After aligning channels’ timing within each directional group, a single ToA value was computed to represent that group. It is given in equation (1),

with Dir indicating the directional group (NE, NW, SE, or SW) and the indices 1-4 referring to the detection times sorted in ascending order. The higher weights assigned to earlier channels reflect the statistical nature of photon arrival times, which approximately follow a Poisson distribution in which the variance equals the mean. Under this model, earlier photon detections carry lower temporal uncertainty, justifying their preferential weighting. The weighting coefficients were determined experimentally and yielded a marginal improvement in CTR. The final event timestamp (t) was then determined as the average of the four directional group ToAs (equation (2)),

To calibrate the TOF, timing offsets were calculated at the layer-to-layer level for each corresponding detector tower pair. A Gaussian function was fitted to the distribution of coincidence time differences, and the mean used to correct the TOF offset. Importantly, TOF offsets were computed after applying the energy window (as described in the energy calibration section) on events to minimize time walk effects.

X-position: The X-position of the event (crystal identification) is estimated using the difference of ToA values () between East and West side of the layer, i.e. opposite sides of the SMPPCs (equation (3)). This is performed using directional ToA values () calculated in equation (1),

A layer specific look-up-table (LUT) was extracted to map the values to the X-positions. As shown in figure 4, histograms were calculated separately for each layer. Eight peaks are visible in the histogram which corresponds to the center of the 8 crystals in each layer. A peak detection algorithm identified the peaks. The LUTs were calculated to map the value to X-positions while aligning the peaks ( value) with the known crystal-center positions (physical X-coordinates). Based on the resulting X-positions, events in each crystal were grouped to enable further crystal-specific calibration.

Figure 4. Histogram of the values (used for X-positioning) for layers 1–4 obtained from the flood irradiation. The stars show the identified peaks corresponding to the center of the crystals.

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Energy: The deposited energy of events is estimated using the average of the 16 ToT values form the SMPPC-ASIC channels reading the corresponding layer (equation (4)),

Energy calibration was performed at the crystal level. Using the flood data, the histogram was calculated for each crystal, and a peak detection algorithm identified the peak corresponding to the 511 keV photopeak. A Gaussian function was fitted to the peak, and the full width at tenth maximum (FWTM) window was used as the accepting energy window for each crystal.

Z-Position: Two sources of information were used for Z-position estimation. Due to the attenuation of scintillation light as it propagates along the crystal length, an inverse relationship exists between the signal amplitude (ToT value) recorded by SMPPCs and their distance from the interaction point of the incident annihilation photon. This provides the first source of information, defined as the difference in ToT values measured at the North and South ends of the crystal. This difference, denoted as , was calculated by subtracting the average ToT value of the North side (averaged across the eight corresponding channels) from that of the South side (equation (5)),

However, the relationship between the ToT value and the event-to-SMPPC distance breaks down at short distances due to saturation of the SMPPCs. This effect is illustrated in figure 5(a), which shows the histogram for events in a single crystal obtained from the flood illumination data. Under uniform irradiation, a uniform histogram would be expected. Instead, the histogram exhibits sharp peaks at both extremes, indicating reduced responsiveness of to changes in interaction position near the crystal ends. This diminished positional responsiveness leads to degraded spatial resolution in these regions.

Figure 5. (a) Histogram of for events in a single crystal obtained from flood irradiation data. Sharp peaks are evident at both extremes, indicating reduced spatial responsiveness of for interactions occurring near the crystal ends. (b) Schematic illustration of the total internal reflection at the crystal-SMPPC interface. Photons emitted from an event close to crystal end and incident at angles larger than the critical angle are reflected back into the crystal rather than transmitted toward the SMPPC array. This leads to uneven light distribution across the four SMPPCs. (c) plotted against the [—]. At the extremes of , corresponding to events at the crystal ends, the absolute value of [ —] increases, while away from crystal ends, no trend is visible. (d) Histogram of . The fitted Gaussian mixture model to distinguish between events occurring near the North side (tail) and rest of events (main body), is shown on the plot. (e) Histogram of the . The dynamic range of the signal is increased at the ends of the crystal. The regions shown with dashed lines are approximate. (f) the histogram of the Z-positions mapped from using the calibration LUT.

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To mitigate this limitation, a second source of information was introduced for Z-position estimation. When scintillation light reaches the interface between the crystal (n = 1.82) and the crystal-SMPPC coupling epoxy glue layer (n = 1.53), part of it is reflected back into the crystal because of the refractive index mismatch. Photons striking the interface at angles larger than the critical angle are totally internally reflected rather than transmitted toward the SMPPC array (figure 5(b)). This effect becomes significant when an interaction occurs near the crystal end. As shown in figure 5(b) this will cause the four SMPPCs to receive unequal numbers of scintillation photons and therefore record different ToT values. The magnitude of this inequality increases progressively as the interaction point approaches the crystal end.

This information was utilized as the difference between the maximum and minimum ToT values among the four SMPPCs located at North (denoted as ) or South (denoted as ) end of the crystal (equation (6)),

With , and i = 1 (minimum ToT) or 4 (maximum ToT). was computed analogously.

However, and are only informative for events occurring near the crystal ends. When the interaction point is located farther from the ends, the scintillation light is more uniformly distributed across the four SMPPCs, and variations in their ToT values arise mainly from statistical fluctuations rather than spatial dependence on the interaction point. This is better shown in figure 5(c), which presents plotted against ( —). At the extremes of , representing interactions near the North and South crystal ends, the absolute value of ( —) increases, indicating elevated near the North side and near the South side. In contrast, for events occurring away from the crystal edges, ( —) shows no positional trend, confirming that it is not sensitive to depth for interactions away from crystal ends.

Hence, before utilizing and , we aimed to neutralize them for events away from the crystal ends. Figure 5(d) shows the histogram for events in a crystal obtained from flood-illumination data. The distribution is approximately Gaussian, with an extended tail. The tail corresponds to interactions near the North end of the crystal, while the main body of the distribution corresponds to events occurring elsewhere in the crystal, where differences in are primarily statistical. To isolate the tail, a Gaussian mixture model (GMM) was fitted to the distributions as shown on the plot in figure 5(d). The intersection point of the two components of the GMM fit (denoted as ) was used as a threshold on the , activating it only for events close to the North end of crystal (equation (7)):

While the negative values are set to zero, and it is scaled by a factor of 2 to match the dynamic range of prior to combination. Same procedure was applied to the .

Eventually, as shown in equation (8), the two sources of information were combined into a single variable, denoted as . Due to the thresholds applied on the and (equation (7)), the will be reduced to for events away from both ends; will be equal to for events at the North end; and equal to for events at the South end. Thus, the dynamic range of is effectively increased at the ends of the crystal compared to alone. Figure 5(e) shows the histogram of for events in a crystal under flood uniform irradiation. As shown, the dynamic range of the signal is increased at the ends of the crystal,

The next step included mapping the values to Z-positions. The objective was to divide the range into segments, with each segment corresponding to a specific Z-position along the crystal’s length. Assuming uniform irradiation from the flood phantom, if each segment contains an equal number of events, the segments can be associated with equally spaced physical positions along the crystal. Accordingly, the values from the calibration data were partitioned so that all segments contained an equal number of events. The boundaries of these segments were then used to construct a LUT that maps values to physical Z-positions. Figure 5(f) shows the histogram of the Z-positions (mapped using the calibration LUT) for events in a crystal under uniform irradiation. As expected, the distribution of events across segments is approximately uniform.

An additional flood illumination data was acquired to evaluate the detectors’ performance. This acquisition was performed at a different time throughout the day, with the detectors being restarted between sessions to assess the stability of the system under varying temperature conditions and repeated power cycles. In addition, a radiolucent carbon fiber bed was placed between the detector panel and the flood irradiation source to account for the scattering impact of the bed. Key performance metrics including energy resolution, and CTR were measured, and the stability of the detectors across acquisitions was assessed.

To report the energy resolution, we performed a full spectrum energy calibration on one detector. The is a non-linear function of the interactions’ deposited energy and must be corrected before accurate energy resolution calculation. To this end, we irradiated a detector tower with various isotopes having different gamma peaks. The isotopes and their photopeak energies included: 131I (364 keV), 22Na (511 keV and 1274 keV), and 137Cs (662 keV) and the intrinsic gamma peaks from 176Lu present in the LFS crystals, at 202 keV and 307 keV. A 3rd order polynomial function was fitted to the photopeak positions and their corresponding ToT values for each crystal in the detector tower. The result was then applied to the flood irradiation data to extract corrected energy spectrum and calculate the energy resolution. A Gaussian function was fitted on the 511 keV photopeak, and energy resolution was calculated as the full-width-half-maximum (FWHM) of the Gaussian divided by the photopeak.

An additional experiment was conducted to evaluate the detector’s Z-positioning performance. One of the detector towers was irradiated using a sub-millimeter slit positioned at multiple locations along the 30 mm length of the crystals. The slit was formed by two laterally arranged lead blocks, with a syringe containing 1⁸F placed on top as the radiation source. Measurements were taken at 19 discrete positions. The slit was placed on top of a radiolucent carbon-fiber bed (7 mm thickness) with the detector underneath affixed to a motorized translation motor capable of 0.1 mm positioning accuracy. The total distance from the slit to the detector surface was 22 mm. The acquired data were used to assess both the linearity and spatial resolution of the detector’s Z-positioning capability. For each step, a Gaussian function was fitted to the resulting Z-positions distribution, with the mean value representing the estimated Z-position and the FWHM reported as the spatial resolution.