The following paragraphs report results on the coincidence experiments conducted with the different setup configurations introduced above. Table 1 provides an overview over all results obtained, listing the CTRs achieved in:

Reference benchmarks in terms of CTR in \(\gamma\)-excitation experiments

With 2\(\times\)2\(\times\)3 mm\(^\) LYSO:Ce,Ca crystals and Broadcom NUV-MT SiPMs, the state-of-the-art version of the HF electronics read out by an oscilloscope shows CTRs of about 60 ps (FWHM) if tested without TOT discrimination. Using the TOFPET2c ASIC as an initial candidate as back-end electronics, a CTR of 120 ps was established as benchmark for the same crystals and NUV-MT SiPMs with standard TOFPET2 readout, excluding further signal amplification or discrimination prior to its input. The performance benchmarks can be found in Table 1 as well.

Fig. 8

CTR of individual channels of a detector block consisting of a \(4\times 4\) Broadcom NUV-MT SiPM arrays one-to-one coupled to a \(4\times 4\) LYSO:Ce,Ca crystal matrix at a bias voltage of 41.5 V and a discriminator threshold of \(\mathsf \)=  50. a DC readout at default TOFPET2 configuration with R\(_\textsf\) = 30 \(\Omega\). b DC readout with R\(_\textsf\) = 11 \(\Omega\). c Upscaled HF readout including TOT discrimination via a TLV3801 with a threshold of 90 mV

Impact of the TOT discrimination on the HF performance in \(\gamma\)-radiation experiments

With 2\(\times\)2\(\times\)3 mm\(^\) LYSO:Ce,Ca crystals and Broadcom NUV-MT SiPMs, compared to the reference measurement with CTRs of about 60 ps (FWHM) if tested without TOT discrimination (state-of-the-art HF readout), the initial single-channel board version read out by an oscilloscope shows CTRs of about 70 ps (FWHM) with the TLV3801 at low TLV thresholds (HF readout including TOT discrimination). Increasing the TLV threshold deteriorates the performance to 90±1 ps (FWHM) for a very high TLV threshold of 200 mV (c.f. Table 1), which corresponds to triggering on an amplitude of about 20 times the single-SPAD signal at an overvoltage of 9 V.

The HF circuit including TOT discrimination could not be operated at very low TLV thresholds lower than 40 mV in combination with the TOFPET2 ASIC due to instabilities (oscillations and feedback loops) as well as baseline shifts, which will be discussed in detail in Sect. "Single‑channel HF electronics without TOT discrimination featuring oscilloscope readout". For a threshold of 40 mV, the performance deteriorated from 70 ps (FWHM) with signal digitization via an oscilloscope to 118 ps (FWHM) with TOFPET2 readout. For a threshold of 90 mV, the performance deteriorated from 78 ps (FWHM) to 121 ps (FWHM), comparing the same types of measurements.

Comparing to the reference measurement without the HF readout circuit and TOT discrimination in front of the ASIC input stage, the same performance of about 120 ps (FWHM) is achieved.

Using crystals of clinical length (3\(\times\)3\(\times\)19 mm\(^\)), a CTR of 161 ps (FWHM) could be achieved with TOFPET2 readout and the HF circuit with a TLV threshold of 90 mV (c.f. Table 1), which resembles the performance of 157±1 ps (FWHM) achieved with standard TOFPET2 readout in prior studies [3].

Using 2\(\times\)2\(\times\)3 mm\(^\) BGO crystals on 3.8\(\times\)3.8 mm\(^\) NUV-MT SiPMs and digitizing the discriminated signals of the HF circuit via the TOFPET2 ASIC, the CTR was measured to 542 ps (FWHM), which is worse than a CTR of 480 ps (FWHM) achieved for DC coupling (c.f. Table 1). In comparison, a CTR of 359 ps is measured if the signals of the 16-channel HF readout are digitized via an oscilloscope (c.f. Table 1), which is worse than the results achieved for BGO and HF readout in prior studies [29]. This deterioration can be attributed to the considerably high TLV threshold applied (ranging from 40 mV to 90 mV) in comparison to a single-SPAD amplitude of about 10 mV.

Table 1 CTR achieved with Broadcom NUV-MT SiPMs and the HF readout circuit and different back-end electronics at optimum bias settings and trigger threshold settingsInvestigation on the performance of single channels in 16-channel HF electronics

To investigate the functionality of the 16-channel board, additional measurements have been performed using the 4\(\times\)4 NUV-MT SiPM array, biasing all 16 SiPMs, but only coupling one 2\(\times\)2\(\times\)3 mm\(^\) LYSO:Ce,Ca crystal to one of the SiPMs, ruling out a deterioration solely due to electronic crosstalk between channels or the implementation of the 16-channel HF circuit. For a direct connection to the TOFPET2 ASIC, these measurements resulted in the same CTR as actual single-channel coincidence experiments. For an HF connection to the TOFPET2 ASIC, the performance was deteriorated by approximately 10 ps to 131 ps (FWHM) compared to the single-channel version with a CTR of to 121 ps (FWHM) (c.f. Table 1). Only operating the timing channels, the CTR decreased to 175 ps, which is again based on filtering on a raw energy value spectrum that corresponds to the TOT of the TLV3801 signal. A similar investigation was performed using oscilloscope readout for one channel of the multi-channel HF board. Here, the CTR was 79 ps for a 2\(\times\)2\(\times\)3 mm\(^\) LYSO:Ce,Ca crystal and 137 ps for a 3.88\(\times\)3.88\(\times\)19 mm\(^\) LYSO:Ce,Ca crystal coupled to one of the SiPMs, respectively (c.f. Table 1). The deterioration between the values is similar to the deterioration in comparable configurations with TOFPET2 readout. Additionally, the CTR of a single channel of the 16-channel, one-to-one coupled detector block was measured with HF readout and digitization via the oscilloscope and is 173 ps (FHWM) as reported in Table 1.

16-channel HF electronics with a one-to-one coupled LYSO:Ce,Ca detector block

Moving to a 4\(\times\)4 matrix of one-to-one coupled, isolated 3.8\(\times\)3.8\(\times\)19 mm\(^\) LYSO:Ce,Ca crystals, an average CTR of 252±15 ps (FWHM) (default configuration, R\(_\textsf\) = 11 \(\Omega\), c.f. Fig. 8a) and 219±24 ps (FWHM) (optimized configuration, c.f. Fig. 8b) was measured using a DC connection to the TOFPET2 ASIC. This is a deterioration of 60 ps to 80 ps compared to prior single-channel experiments, where a CTR of about 160 ps (FWHM) was measured (c.f. Table 1). Incorporating the 16-channel HF electronics including TOT discrimination in the signal path, an average CTR of 240±14 ps (FWHM) was achieved configuring a TLV threshold of 90 mV and 242±27 ps (FWHM) with a TLV threshold of 40 mV (c.f. Fig. 8c), which is, within its errors, in accordance with the aforementioned performance of the DC readout. Reducing the gain \(\mathsf \) of the transimpedance amplifier in the timing branch to diminish effects of noise on the timing trigger did not improve the CTR any further, as also seen in measurements exposing the SiPMs to laser pulses. The latter performance at a TLV threshold of 40 mV was evaluated only on the timing channels of the circuit, meaning the digitized raw energy values correspond to the TOT of the TLV3801 signal. Disconnecting the energy channels (originally connected of the ASIC front-end board (FEB/A) to the SiPM anodes) significantly reduced the instabilities and oscillations observed, which were even stronger than in single-channel experiments, and enabled this measurement at a TLV threshold of 40 mV. This hints at a feedback loop between the FEB/A and the 16-channel HF readout, which can be improved by capacitive decoupling. Consequently, adapting the filter parameters in the signal paths of the timing and energy channels improved the achievable CTR to 223±17 ps with a TLV threshold of 40 mV due to an improved energy resolution, which is the same as for a direct connection of the TOFPET2 input. Again, a higher threshold deteriorated the CTR, as seen for single-channel experiments, to 235±16 ps with a TLV threshold of 90 mV (c.f. Table 1 and Fig. 13).

Fig. 9

Channel raw energy value spectrum for a 2\(\times\)2 \(\times\)3 mm\(^\) LYSO:Ce,Ca crystal read out via one Broadcom NUV-MT SiPM channel of a 4 \(\times\) 4 SiPM array connected to the 16-channel HF readout board at an overvoltage of 6 V and 9 V. Raw energy values were digitized via the TOFPET2 ASIC operated in qdc mode

Fig. 10

Multi-photon coincidence time resolution of the different SiPM-ASIC channel combinations illuminated with optical photons at 406 nm and at different frequencies. Data were acquired using Broadcom NUV-MT SiPMs and the TOFPET2 ASIC with an ASIC threshold of \(\mathsf = 20\). a One SiPM channel coupled to two ASIC channels of the same ASIC. b Two SiPM channels on one SiPM array each coupled to one ASIC channel of the same ASIC. c Comparison between different combinations and readout electronics at an overvoltage of 9 V

Fig. 11

Coincidence multi-photon time resolution of the different SiPM-ASIC channel combinations illuminated with optical photons at 406 nm and a pulse frequency of 10 kHz and triggering at different TOFPET2 ASIC thresholds \(\mathsf \). Data were acquired using Broadcom NUV-MT SiPMs and a DC connection to the TOFPET2 ASIC

Energy resolution with and without linearized TOT

Currently, the multi-channel HF readout approach suggests the digitization of the signal’s energy via a separate channel, leading to an increase in the number of required readout channels, which could be considered problematic on system level in terms of form factor and power consumption. Two example energy spectra are shown in Fig. 9. Digitizing the energy via a TOT of the discriminated signal might deteriorate the energy resolution, which for a separate energy channel should remain as high as reported in [25]. A linearized TOT has therefore been tested in this initial design, which allows to improve the linearity ratio of the energy spectrum from 0.97 to 0.89. The energy resolution obtained in linearized TOT mode is 15.7 %, convolved with the TOFPET2 TDC resolution, compared to 10.1 % in TOFPET2 charge integration mode, both measured at an overvoltage of 9 V. Even without linearization, the quality of the raw energy value spectra acquired using only the timing channels allows to reliably separate Compton-scattered events from true coincidences and maintains the selection of events \(\pm 2\sigma\) around the photopeak. As Fig. 9 shows that the peak separability decreases for higher overvoltages, each detector configuration requires at least a bias scan to evaluate the optimum point of performance with respect to peak separability and achievable timing performance.

Timing limits with optical illumination using a pulsed picosecond laser

With a Broadcom AFBR-S4N33C013 SiPM coupled to an LYSO crystal (EPIC Crystal; 2\(\times\)2\(\times\)3 mm\(^\)) connected to two channels of the same ASIC, as shown in Fig. 5a, the intrinsic CTR of the TOFPET2 ASIC was measured to be on average CTR\(_\textsf\)=58 ps (FWHM) at a threshold of \(\mathsf = 20\) over the whole bias range scanned [25]. Illuminating an NUV-MT SiPM (c.f. Fig. 5b) with the laser, a value of MPCTR\(_\textsf\)=55 ps (FWHM) could be confirmed for several pulse frequencies in a range of 0.1 kHz to 100 kHz and bias voltages applied to the SiPM from 36.5 V to 45.5 V (corresponding to overvoltage 4 V to 13 V; c.f. Figure 10a). Connecting each of two SiPM channels to one ASIC channel on the same ASIC, as shown in Fig. 5c, slightly elevated the MPCTR value to about 65 ps to 70 ps (FWHM) measured with the standard readout with the TOFPET2 ASIC (c.f. Fig. 10b). The CTR shows a strong dependency on the overvoltage over the whole range of investigated frequencies. Reaching an MPCTR close to the intrinsic performance limit CTR\(_\textsf\) at 4 V suggests a severe problem with baseline shifts at the TOFPET2 input stage limiting the ASIC’s performance at optimum SiPM operation point, i.e., a higher overvoltage. This results in a contribution of up to more than 80 ps (FWHM) to the overall CTR, depending on the chosen overvoltage. Additionally, the contribution of the front end was measured for the multi-channel HF readout board using TLV thresholds of 40 mV and 90 mV (c.f. Fig. 10c), which shows the same limitation as for the DC TOFPET2 readout at a fixed overvoltage of 9 V. A comparison of the achieved MPCTR\(_\textsf\) and MPCTR over a range of TOFPET2 trigger thresholds is provided in Fig. 11. Here, it becomes evident that configuring sufficiently high trigger threshold (starting from \(\mathsf = 20\)) allows to converge to a MPCTR closer to the intrinsic timing limits of the TOFPET2 ASIC and reduce the contribution of the electronic front end to the overall MPCTR.

Switching to the 16-channel HF readout electronics including TOT discrimination prior to the TOFPET2 front end pushes the MPCTR of the 4\(\times\)4 NUV-MT SiPM array illuminated with a laser toward the intrinsic timing limit and results in about the same contribution of the front end of 70 ps (FWHM) over the entire frequency range, but reduces the deterioration at higher frequencies and higher overvoltages (c.f. Fig. 10c).

Fig. 12

Channel coincidence time difference spectrum for the detector block read out via the TOFPET2 ASIC (left) and for the detector block read out via the 16-channel HF readout board including TOT discrimination with the TOFPET2 ASIC emulating the TDC (right) at an overvoltage of 9 V

Fig. 13

TOFPET2 performance of a detector block consisting of a \(4\times 4\) Broadcom NUV-MT SiPM arrays one-to-one coupled to a \(4\times 4\) LYSO:Ce,Ca crystal matrix in comparison with exposing the SiPMs to laser pulses (406 nm) of an SiPM array. The performance with default configuration and DC readout can be optimized (1), (2), while laser pulses reveal timing limitations of the front end (3). Reducing the applied bias leads to a better intrinsic resolution (4), which is why baseline shifts are thought to be the cause of the problem. Pulse amplification and discrimination via a TLV3801, i.e., 16-channel HF electronics, are employed (5), delivering the same intrinsic timing resolution at higher overvoltages. Switching back to a full detector block with a scintillator, the performance is still limited by a high TLV threshold, which is needed due to unstable baselines at lower thresholds. (6). Adapting signal filters in the timing and energy signal paths reduces this noise and improve the CTR to DC level (7), which shows that the adapted HF readout board does not worsen the CTR and, hence, could be a good candidate for readout with the picoTDC