State of the art timing in TOF-PET detectors with LuAG, GAGG and L(Y)SO scintillators of various sizes coupled to FBK-SiPMs

Time of flight (TOF) in positron emission tomography (PET) has experienced a revival of interest after its first introduction in the eighties. This is due to a significant progress in solid state photodetectors (SiPMs) and newly developed scintillators (LSO and its derivatives). Latest developments at Fondazione Bruno Kessler (FBK) lead to the NUV-HD SiPM with a very high photon detection efficiency of around 55%. Despite the large area of 4×4 mm2 it achieves a good single photon time resolution (SPTR) of 180±5ps FWHM. Coincidence time resolution (CTR) measurements using LSO:Ce codoped with Ca scintillators yield best values of 73±2ps FWHM for 2×2×3 mm3 and 117±3ps for 2×2×20 mm3 crystal sizes. Increasing the crystal cross-section from 2×2 mm2 to 3×3 mm2 a non negligible CTR deterioration of approximately 7ps FWHM is observed. Measurements with LSO:Ce codoped Ca and LYSO:Ce scintillators with various cross-sections (1×1 mm2 - 4×4 mm2) and lengths (3mm - 30mm) will be a basis for discussing on how the crystal geometry affects timing in TOF-PET. Special attention is given to SiPM parameters, e.g. SPTR and optical crosstalk, and their measured dependency on the crystal cross-section. Additionally, CTR measurements with LuAG:Ce, LuAG:Pr and GGAG:Ce samples are presented and the results are interpreted in terms of their scintillation properties, e.g. rise time, decay time, light yield and emission spectra.


Introduction
Scintillator based detectors for time-of-flight positron emission tomography (TOF-PET) are able to achieve very good timing approaching a coincidence time resolution (CTR) of 100ps FWHM, as shown in several publications [1,2]. This is due to a significant progress in solid state photodetectors, e.g the silicon photomultiplier (SiPM), which facilitates excellent timing properties and a high photon detection efficiency (PDE). Additionally to the advances in SiPMs, scintillator materials like Cerium-doped Lutetium Oxyorthosilicate (LSO:Ce) and its derivatives show a high light yield, fast decay and rise times and a very high effective atomic number. The progress made allows for very fast timing, keeping a high 511keV absorption coefficient with a high photoelectric fraction. NUV-HD SiPMs are the latest development of FBK (Fondazione Bruno Kessler), representing the state of the art in SiPM photodetector technology regarding photon detection efficiency (PDE) and single photon time resolution (SPTR). These photodetectors, if coupled to LYSO:Ce scintillators with 3 × 3 × 5 mm 3 dimensions are able to achieve ∼100ps FWHM, as was recently published in [3]. In this paper it will be shown that these good results can almost be retained (within 20%) if using -1 -

JINST 11 P08008
state of the art LSO:Ce codoped Ca crystals of 20mm length, particularly interesting for applications in TOF-PET.
In whole body PET the number of electronic channels is an important issue and should be reduced in order to keep complexity and cost low. Hence, an increase in the SiPM and crystal crosssection is anticipated. Measurements with various crystal cross-sections (1 × 1 mm 2 -4 × 4 mm 2 ) will be presented and interpreted within further complementary measurements and Monte Carlo simulations.
Furthermore, we present latest CTR values measured for different crystal compositions, i.e. LuAG and GAGG doped with Cerium. The effect of codoping with either Magnesium or Calcium is discussed as well [4][5][6]. Codoped scintillators are particularly interesting because of their faster scintillation rise times and decay times leading to improved timing [7]. Additionally, prompt photons have been seen and clearly separated from the scintillation signal in some compositions, e.g. LuAG:Pr [7]. These prompt photons are produced most likely by the Cherenkov effect, although some other contributions, for instance from hot-intraband-luminescence are not excluded [8]. The Cherenkov effect has already been studied in several publications and its potential influence to the CTR discussed [7,9,10]. However, until now there was no clear evaluation on how the CTR is affected by these prompt photons. We will show that prompt photons in LuAG:Pr and LuAG:Ce are important to estimate the CTR correctly. Additional comprehensive Monte Carlo simulations of the CTR will be evaluated with experimental data, using the measured prompt photon yield, scintillation light yield, rise-and decay-times.

FBK NUV-HD SiPM
The NUV-HD (near ultraviolet -high density) SiPM is a new development done at FBK which implements a new microcell border structure similar to the technology utilized for the RGB-HD devices [3]. This allows to increase the fill factor of the device, despite a relatively small single avalanche photodiode (SPAD) size of 25 × 25 µm 2 , and hence increases the photon detection efficiency (PDE). The smaller cell size additionally allows for a higher operational bias overvoltage and thus boosts the PDE further. The higher overvoltage achievable is mainly explained by a decreased gain of smaller SPADs and thus a decreased optical crosstalk probability [11]. On the left hand side in figure 1 it can be seen that for the NUV-HD SiPM, with coupled crystal, the maximum applicable operational overvoltage is 13V before the bias current increases drastically. In our former publication [12] we showed that this exact behavior happens already at ∼6V for the NUV type SiPM. The right hand side of figure 1 shows the PDE of the NUV and NUV-HD SiPM plotted versus the wavelength. It can be seen that the NUV SiPM achieves a maximum PDE of 40% whilst the NUV-HD SiPM can reach values as high as 55%. PDE values were measured at 6V overvoltage and 13V overvoltage for the NUV and NUV-HD SiPM, respectively -representing the maximum possible operational overvoltages.

Coincidence time resolution measurements
The coincidence time resolution (CTR) was measured with our standard setup as described in [2] and shown in figure 2. For these measurements the scintillators were wrapped in Teflon, at least -2 -  The signals generated by the SiPM were readout by NINO [13], a low noise leading edge threshold discriminator amplifier, which delivered the time information and a voltage amplifier for energy discrimination. The splitting of the energy and timing signal is necessary in order to be able to optimize both channels independently for best performance, i.e. for energy and time resolution. The reason is that typically the leading edge discrimination is performed at very low threshold voltages in the order of the single cell signal amplitude of the SiPM (one SPAD signal), which needs amplification. On the other hand the energy signal amplitude is several orders of magnitude larger, calling for a different readout strategy with much lower amplification, sometimes even attenuation. The timing and energy signals were digitized and stored on disk by a fast -3 - oscilloscope (LeCroy DDA 735Zi with 3.5GHz bandwidth and 40Gs/s). In the offline data analysis we only selected events within the photopeak (−1.5σ to +2σ around the centroid µ), representing the whole energy of 511keV deposited in the crystal. We want to mention that studies on the photopeak-selection have shown that the width of valid events plays a minor (almost negligible) role in the obtained CTR. This is mainly explained by a sufficient energy resolution which allows for a clear cut between Compton and photoelectric events [14]. For the selected events within the photopeak we plotted the time delays in a histogram and applied a Gaussian fit on the data yielding the coincidence time resolution in full width at half maximum (FWHM), as described in [2]. The temperature was stabilized at 15 • C for all ensuing measurements.

Scintillator materials
We tested different scintillator materials activated with Cerium, i.e. LSO:Ce and LSO:Ce codoped with 0.2%Ca or 0.4%Ca from the producer Agile, LYSO:Ce from the producer CPI, LuAG:Ce and LuAG:Ce codoped Ca produced in Ashtarak (Ashot Petrosyan) [4], GAGG:Ce and GAGG:Ce codoped Mg produced in Prague (Martin Nikl) [5]. Additionally we measured LuAG activated with Praseodymium (Pr) produced in Ashtarak [4]. The emission spectra of the tested materials can be seen in figure 3. The measured emission of LuAG:Ce codoped Ca or GAGG:Ce codoped Mg have an identical spectra with respect to LuAG:Ce or GAGG:Ce, and hence are not depicted in figure 3. The same applies for LYSO:Ce and LSO:Ce codoped Ca.
In table 1 measurements of the scintillation characteristics of the tested materials are summarized, i.e. rise time, decay times, relative light yield and scintillation light detection probability (PDE·LTE). The detection probability (PDE·LTE) describes the PDE weighted with the emission spectra of the scintillator, taking into account the Meltmount transmission, multiplied with the light transfer efficiency (LTE) of the crystal. In our following Monte Carlo simulations we used these values and took an intrinsic light yield value of 40kph/MeV for LYSO:Ce [15].
-4 - Table 1. Measured scintillation properties of the tested materials. Values are partly taken from our previous measurements published in [5,7]. Light output (LO) measurements were performed with 2 × 2 × 10 mm 3 crystals (and 2×2×8 mm 3 for LuAG) wrapped in Teflon and optically coupled with Rhodorsil 47V (n = 1.42). A Hamamatsu PMT R2059 was used for the relative light output measurements, normalized to LYSO:Ce. The relative error of the LY and decay time measurements is in the order of ±5%, whereas the statistical uncertainty of the rise time is stated in the table. Note: the light output value for LuAG:Pr underlies a higher uncertainty due to its emission in the UV together with uncertainties in the transmittance of the used Rhodorsil 47V grease. As can be seen in figure 3 the chosen Meltmount glue with a refractive index of n = 1.68 has a cut-off around 400nm which unfortunately is unfavorable for LuAG:Pr and halves the detected scintillation light as compared to LuAG:Ce. The light transfer efficiency, defined as the ratio of scintillation light reaching the photodetector and the total amount of light produced, was estimated by Monte Carlo simulations [2,12] to be ∼61% for LYSO:Ce scintillators with 2 × 2 × 10 mm 3 size coupled to the FBK NUV-HD SiPM with Meltmount (n = 1.68). This value does not take into account the transmittance of the Meltmount glue, which is included in the effective PDE (column PDE·LTE in table 1). Similar LTE values were taken for LuAG and GAGG crystals. For LuAG crystals this is justified, because of the almost similar refractive index. In fact other influences, like small differences in diffusivity, e.g. surface or edge polishing, tendentiously can have a larger influence on the light transfer efficiency [16]. For GAGG crystals the exact determination of the LTE value is still subject to investigation, as the index of refraction, magnitude of bulk absorption and amount of re-absorption still need further evaluation. However, for the following CTR simulations this uncertainty in LTE is accounted for in the relative LO measurements, as shown in column 7 of table 1.
On the left hand side of figure 4 we show transmission measurements of 2 × 2 × 10 mm 3 sized LYSO:Ce, LSO:Ce codoped 0.2%Ca and LSO:Ce codoped 0.4%Ca crystals. Whereas on the right hand side of figure 4 similar measurements for 2 × 2 × 20 mm 3 crystals are shown. We observe that with increasing crystal length the transmission becomes significantly worse in LSO:Ce codoped 0.4%Ca crystals as compared to LYSO:Ce and LSO:Ce codoped 0.2%Ca. However, it should be mentioned that the Agile LSO:Ce:0.4%Ca samples are from an older production batch (2011) as compared to the Agile LSO:Ce:0.2%Ca and LYSO:Ce crystals (2016). Therefore, it might be possible that the observed increase in re-absorption is a feature of our particular samples and not generally valid.

Time resolution with LSO:Ce codoped with 0,4%Ca and LYSO:Ce
We measured the coincidence time resolution with LSO:Ce codoped with 0.4%Ca crystals from the producer Agile and LYSO:Ce from the producer CPI with the measurement details already discussed in section 2.2. In figure 5 the CTR versus the bias overvoltage and NINO threshold voltage is shown for 2 × 2 × 3 mm 3 LSO:Ce:0.4%Ca crystals coupled to the NUV-HD SiPM. A best CTR value of 73±2ps FWHM is achieved at an overvoltage of 12.5V and a NINO threshold voltage of ∼120mV, which corresponds to 1 SiPM single cell signal amplitude (SPAD signal amplitude). However, it should be noted that the number of photoelectrons contributing to the leading edge time estimation is much higher and more in the order of several photoelectrons [2,17]. A clear improvement in CTR with bias overvoltage is observed, which is explained by an increase in PDE plus a decrease in SPTR value for higher overvoltages. On the right hand side of figure 5 it can be seen that for low threshold values electronic noise worsens the time resolution and that for higher threshold values photonstatistics leads to worse CTR, hence, resulting in the optimum NINO threshold voltage at around 120mV [1,2,17]. The CTR improvement as compared to our former publication with the NUV SiPM (85±4ps FWHM with 2 × 2 × 3 mm 3 LSO:Ce codoped 0.4%Ca) [12] can be entirely explained by the higher PDE the NUV-HD SiPM achieves, as was discussed in section 2.1. We additionally performed measurements with various lengths of the codoped 0.4%Ca LSO:Ce crystals, ranging from 3mm to 20mm, the results of which are shown in figure 6. A deterioration in CTR for longer crystals is observed, due to an increased photon travel spread (PTS) and decreased light transfer efficiency (LTE) [18]. CTR values for 2 × 2 × 20 mm 3 crystal sizes are measured to reach values as low as 122±3ps FWHM.
In addition to LSO:Ce:0,4%Ca we used standard LYSO:Ce crystals from the producer CPI and compared the best CTR values achievable, as can be seen on the left hand side of figure 7. For shorter crystals of 2 × 2 × 3 mm 3 size the best CTR achieved for LYSO:Ce is 87±3ps FWHM,   (see table 1). However, if the crystal length is increased up to 20mm, we observe that LYSO:Ce gives almost the same performance of 130±3ps FWHM as compared to 122±3ps FWHM for LSO:Ce:0.4%Ca. This we could explain by a lower light absorption observed in LYSO:Ce than in LSO:Ce:0.4%Ca, to be seen on the right hand side of figure 7 and in figure 4. Increasing the LYSO:Ce crystal length even further, to 30mm, we obtain a CTR of 142±3ps FWHM.

Limitations of the electronics and acquisition system
In order to test the limitations of the electronics (NINO) and acquisition system (oscilloscope) we tested our measurement setup by splitting one SiPM signal (with coupled 2 × 2 × 3 mm 3 LSO:Ce codoped with 0.4%Ca crystal) and feeding it into two NINO chips. This gives the "intrinsic CTR", which represents the electronic noise influence on the leading edge discrimination with the correct signal generated from the SIPM+crystal plus the independent time jitter of the oscilloscope. In figure 8 the outcome of this measurement is shown, where threshold values are corrected for the slightly lower single cell amplitude due to the lower input impedance in this setup. The CTR "intrinsic" value decreases with increasing leading edge NINO threshold voltage and saturates at a value of 12ps FWHM. The saturation at 12ps is defined by the noise floor of NINO plus the oscilloscope and the dV/dt of the NINO output pulse recorded. The rise in CTR for lower threshold voltages is explained by the shape of the NINO input signal being a sum of single cell pulses and its dV/dt together with the NINO electronic noise and bandwidth filtering. In full generality it can be fitted with 532/(V Threshold ) 0.79 for 12.5V overvoltage, as expressed by the green dotted line in figure 8.
As already mentioned, this term represents the ratio of the electronic noise in the first stage of NINO divided by the dV/dt of the signal in this stage, i.e. u noise /(dV /dt) = 532/(V Threshold ) 0.79 for 12.5V. Supposing a noise level of u noise = 0.01mV and a NINO threshold setting of V Threshold = 100mV we would obtain an input stage slew rate of dV /dt = 0.7mV /ns for the SiPM signal with multiple photoelectrons piled-up already. However, it should be mentioned that the slew rate is rather complex to estimate and depends not only on the electronics but as well on the scintillator photonemission and SiPM properties. Nonetheless, figure 8 shows one important conclusion; if very low leading edge thresholds are needed, e.g. for the detection of prompt photons like Cherenkov or in the case of low SPTR values, electronic noise can potentially limit the best achievable time resolution [7]. In these circumstances a digital approach might be viable [7,17].
-8 - Figure 8. "Intrinsic" CTR of the electronics plus acquisition system. A 2 × 2 × 3 mm 3 LSO:Ce:0.4%Ca crystal was coupled to a NUV-HD SiPM. The SiPM signal was split and fed into two NINO chips, measuring the delay times as in a standard CTR setup. This plot represents the lowest CTR FWHM achievable with the current electronics and data acquisition system.

Crystal cross-section influence on the time resolution
One possible way to reduce the number of electronic channels in a whole body TOF-PET machine is to increase the crystal cross-section, typically up to 4 × 4 mm 2 comparable to the resolution of commercially produced systems, e.g. [19]. In figures 9 and 10 we investigated how the time resolution is changing with increasing crystal cross-section, from 1 × 1 mm 2 up to 4 × 4 mm 2 .
All measurements shown are done with NUV-HD SiPMs from FBK which have a device area of 4 × 4 mm 2 . As already discussed in section 2.2 the crystals were wrapped in Teflon (at least 5 layers) and coupled to the SiPM with Meltmount (n = 1.68). All six surfaces of the scintillators were polished. We observe that an increase of crystal cross-section from 2 × 2 mm 2 to 3 × 3 mm 2 leads to an average CTR deterioration of ∼7ps FWHM, consistent for 3mm and 20mm long crystals (as can be seen on the left hand side of figures 9 and 10). Coupling crystals with 4 × 4 mm 2 cross-section leads to an even higher CTR deterioration. However, for this crystal area additional light loss at the crystal edges due to the SiPM wire bonds prohibiting a 1:1 coupling could have been the main reason for the observed CTR deterioration and, therefore, further tests will not consider this crystal cross-section anymore. On the other hand the CTR performance is similar with a crystal cross-section of 1 × 1 mm 2 and 2 × 2 mm 2 , for 3mm and 20mm long crystals, as can be seen on the right hand side of figures 9 and 10. Larger CTR fluctuations for the 1 × 1 mm 2 cross-section measurements are caused by a lower measurement statistics due to a smaller solid angle of 511keV gamma collection.
A summary of the measured CTR with different crystal cross-sections for various lengths can be seen in table 2 and 3, measured at 12.5V overvoltage and optimum threshold. We consistently observe a CTR deterioration of around 7ps FWHM if the crystal cross-section increases from -9 -2016 JINST 11 P08008 2 × 2 mm 2 to 3 × 3 mm 2 for 3mm, 5mm and 20mm long LYSO:Ce crystals (as can be seen in table 2 and in figures 9 and 10). Table 3 confirms this observation for LSO:Ce codoped with 0.2%Ca crystals from the producer Agile. For LSO:Ce:0.2%Ca it is worth to notice that the best CTR measured for 2 × 2 × 20 mm 3 crystals is 117±3ps FWHM. A slightly better value compared to LSO:Ce:0.4%Ca of 122±3ps FWHM, which could be explained by a smaller light absorption in LSO:Ce:0.2%Ca crystals, as can be seen on the right hand side of figure 4. This assumption -10 -  If we investigate the CTR deterioration with increasing crystal cross-section as a function of SiPM bias voltage, as can be seen in figure 11, we observe that the relative time resolution deterioration worsens with increasing bias voltage. This could be a hint that the increasing gain and, hence, the increasing optical crosstalk probability in the SiPM could explain at least part of the observed CTR deterioration.

Time resolution with GAGG:Ce and codoped with Mg
Apart from TOF-PET, the natural radioactivity of Lutetium could be a problem in some applications where timing is crucial. For this reason, newly developed GAGG:Ce crystals codoped with Mg can be a valid option to replace Lutetium based scintillators [5]. In order to study the potential of this crystal in terms of timing we measured the CTR of GAGG:Ce and GAGG:Ce codoped with Mg coupled to NUV-HD SiPMs, as can be seen in figure 12.
The best CTR value achieved with GAGG:Ce is 480±45ps FWHM, whereas we achieve a CTR of 200±18ps FWHM with the same crystal compound if codoped with Mg. This improvement in time resolution can be explained by a much faster scintillation rise time and faster scintillation decay time with codoped Mg crystals, as can be seen in table 1 and in [5]. The crystal dimensions where 2 × 2 × 10 mm 3   CPI and the same dimensions we measured a CTR of 113±3ps FWHM (as can be seen in figure 7). We further are able to estimate the measured CTR with comprehensive Monte-Carlo simulations (described in [2]), taking into account the independently measured scintillation properties, as shown in table 1, which is represented by the green solid lines in figure 12.

Time resolution with LuAG:Pr, LuAG:Ce and codoped with Ca
Recently it was shown that the scintillation properties of LuAG:Ce crystals can be improved substantially by codoping with divalent ions such as Mg 2+ and Ca 2+ [4,6,7]. Because of the faster -12 - scintillation rise-and decay times observed in LuAG:Ce codoped with Ca together with a large suppression of long tailed decay-components the CTR measurements with LuAG:Ce:Ca yield much better results as compared to LuAG:Ce, as can be seen in figure 13. For LuAG:Ce we measured a CTR of 530±28ps which improves to 230±15ps FWHM if codoped with Calcium, measurements were performed with 2 × 2 × 8 mm 3 sized crystals. Standard LuAG:Pr achieves a CTR of 300±20ps FWHM, however, it should be mentioned that the chosen Meltmount coupling with its cut-off at around 400nm is not beneficial for the LuAG:Pr emission in the near ultraviolet. In figure 13 the green solid lines represent comprehensive Monte Carlo simulations (as described in our former publication [2]), which are able to estimate the CTR as a function of the threshold voltage. We want to point out that in order to simulate correctly it is important to include Cherenkov photons in the Monte Carlo simulations, i.e. 3.4 photoelectrons detected for LuAG:Pr and 1.7 photoelectrons detected for LuAG:Ce [7]. In figure 13 the solid green lines represent the MC simulations including the estimated Cherenkov photon yields, whereas the dotted green lines show simulations with the number of Cherenkov photons set to zero. From this test we indeed infer that the inclusion of prompt photons (Cherenkov) produced in the scintillator is important to fully understand the CTR as a function of the leading edge discrimination threshold.

Scintillator light output with different cross-sections
One reason for the observed worsening of the CTR with increasing crystal cross-section could be a changed light output of the crystals. In order to test this we measured the light output of our samples -13 - versus the crystal cross-section for 3mm and 20mm long crystals, as can be seen in figure 14. The crystals were wrapped in Teflon (minimum 5 layers) and coupled to the used PMT R2059 with Rhodorsil 47V (n = 1.42) grease.
No significant difference in light output is observed apart from the 1 × 1 × 20 mm 3 crystals, which show a slightly lower value. The difference in light output for 1 × 1 × 20 mm 3 crystals can be explained by the higher amount of diffusive reflections (edge diffusion) due to the larger aspect ratio, resulting in a higher absorption or loss [16]. Nevertheless, it should be noted that light emitted in a small angle directly towards the photodetector is undergoing total internal reflection on the side walls and therefore being transfered rather efficiently, despite multiple reflections. This light, in fact, determines the CTR largely and therefore smaller cross-section crystals perform very similar in timing as compared to crystals with larger cross-sections, as can be seen in figures 9 and 10.

Single photon time resolution
The single photon time resolution (SPTR) of the NUV-HD SiPM was measured with a 420nm PiLas picosecond laser from the producer Advanced Laser Diode Systems A.L.S. GmbH. The light intensity was reduced with optical filters to the extent that the photons detected by the SiPM were at the level of a single photon for each pulse. In addition we selected in the offline data analysis only events corresponding to single photoelectrons. This was done by splitting and recording the SiPM amplitude separately from the NINO signal, similar to the CTR measurements discussed in section 2.2. The used PiLas laser has a pulse width of around 42ps FWHM, which is small enough to be negligible for the ensuing SPTR measurements. In figure 15 we show the SPTR in FWHM measured with the NUV-HD SiPM (4 × 4 mm 2 and 25µm SPAD size).
We investigated different areas of illumination, i.e. the whole SiPM illuminated uniformly by the incoming picosecond pulsed laser light ("No Mask"), a "2mm Mask" only illuminating an area of 2 × 2 mm 2 centered in the middle of the SiPM, a "500µm Mask" illuminating a 0.5 × 0 .5mm 2 area and the laser beam being focused in the center of a single SPAD with a spot size smaller 10µm ("Focussed"). There is only a small SPTR difference observed for the SiPM being illuminated with different mask sizes, having slightly better values if the illuminated area is getting smaller. This is explained by a decreased signal transfer time spread of the electrical signals for smaller areas [20]. However, the NUV-HD SiPM is already optimized to reduce this effect largely. If the laser light is focussed within one SPAD we observe a significant improvement in the SPTR value to 150ps FWHM. We could explain this improvement by "border effects" in the SPAD worsening the SPTR, which are not observed if the laser spot is focussed in the middle of one SPAD.
It is important to mention that the measured SPTR of 180ps FWHM (illuminating a 2 × 2 mm 2 area) is influenced by electronic noise [21]. We estimated the electronic noise influence to the SPTR with measurements similar to the method described in section 3.2. Deconvolving the measured electronic noise contribution, the "real" SiPM SPTR is lower and around 115ps FWHM.
As already mentioned, there is only a slight change in the SPTR with different mask sizes (at maximum 20ps FWHM for 13V overvoltage), as shown in figure 15. A worse SPTR for larger active SiPM areas is indeed an important factor in order to explain the observed CTR deterioration with increasing crystal cross-section. However, from Monte Carlo simulations (described in [2]) we estimated that the measured change in SPTR can only account partially for the measured CTR deterioration. This can be seen in figure 16, which shows simulations of the CTR for LSO:Ce:0.2%Ca with 2 × 2 × 3 mm 3 size as a function of the SPTR in FWHM. The MC data can be fitted with √ SPT R 1.556 + 63 2 , shown as red solid line in figure 16. With this fit-function we can evaluate that a SPTR change of 20ps FWHM (as can be deduced from figure 15) leads to a CTR change of only 3ps and, hence, can only account to maximum half the measured CTR deterioration with increasing crystal cross-section. This can be understood by the photon travel spread in the crystal, which has a similar magnitude as the SPTR [18], leading to a smaller sensitivity of SPTR -15 - changes on the CTR. Additionally, electronic noise (discussed in section 3.2) leads to a worse CTR if the leading edge threshold for best timing is low, as in the case of a low SPTR [2].

Baseline shift influence
Another possible reason for a deterioration of the CTR with a larger crystal cross-section could be an increased noise floor (either due to dark counts or a larger crosstalk probability) and, hence, amplified baseline shifts. In order to estimate the baseline-shift influence on the CTR we measured the timing with different filters coupling the SiPM signal to NINO. On the left hand side of figure 17 it can be seen that different high-pass filters (100pF and 10pF) do not significantly change the best achieved CTR, where the crystal size is 3×3×3 mm 3 . Even a more rigorous pole-zero compensation technique [22] does not improve the CTR, as can be seen on the right hand side of figure 17. Similar results were obtained for longer crystals, i.e. 3 × 3 × 20 mm 3 , as can be seen in figure 18. From these measurements we are confident that baseline-shifts do not influence the CTR significantly, at least for the given NUV-HD SiPM and electronics.

Increased optical crosstalk probability due to a coupled scintillator
In figures 9 and 10 we have measured a ∼7ps FWHM deterioration in CTR with increasing crystal cross-section (2×2 mm 2 to 3×3 mm 2 ). This deterioration was confirmed with different crystal types and renewed coupling and wrapping, allowing us to exclude a systematic bias from these effects. We showed that the light output of the crystal and baseline-fluctuations are not the reason for the observed CTR degradation. Furthermore, we have partly excluded an increase of the SPAD signal transfer time spread and thus SPTR with increased illuminated area of the SiPM being the whole reason for the seen CTR deterioration, because it could not account for the complete amount seen. Another possibility to explain the CTR deterioration with increasing crystal cross-section could be an increase in optical crosstalk probability caused by the scintillator acting as a reflector [11]. Figure 19 shows staircase plots for 12.5V overvoltage measured with various configurations; no crystal coupled to the SiPM or with coupled 3mm or 20mm long crystals and different crosssections, i.e. 1 × 1 mm 2 , 2 × 2 mm 2 and 3 × 3 mm 2 . It can be seen that the crosstalk probability rises with increasing crystal cross-section, as the crystal acts as a reflector for the generated optical photons in the SiPM within an avalanche. In figure 20 similar measurements are shown, now performed with an overvoltage of 6.5V. Reducing the overvoltage from 12.5V to 6.5V the crosstalk probability reduces, mainly because of a lower gain.
Besides the increase in baseline fluctuations, which we excluded to be the reason for the CTR degradation, this increase in crosstalk induces as well an excess noise factor in the scintillation statistics and thus leads to a worsening of the CTR [23]. In order to qualitatively investigate this influence we performed Monte Carlo simulations as described in [2]. In these simulations we set the i th crosstalk probability to P i = exp (−i/τ XT ), where τ XT can be seen as a crosstalk "decay" parameter, i.e. the smaller τ XT the smaller the crosstalk probability and less consecutive (additive) -17 - events. If the parameter i equals zero (i = 0), the probability P i is one (P i = 1), which in this case represents the normal photon detection. We suppose that each crosstalk event has an increased time smearing (σ = SPT R · √ i + 1) and an additional time delay (µ = µ 0 + SPT R · √ i) with µ 0 being the time delay of the detected photoelectron (i = 0). The outcome of this simulation study can be seen in figure 21. One can see that for high crosstalk probabilities in the order of > 65% (1/τ XT < 0.44) the CTR starts to deteriorate. This is consistent with the crosstalk probabilities deduced from the staircase plots shown in figure 19, as we can fit the parameter 1/τ XT to 0.53 for 1 × 1 mm 2 , 0.44 for 2 × 2 mm 2 and 0.34 for 3 × 3 mm 2 crystal cross section and 12.5V overvoltage.
The lower observed crosstalk probability for lower bias overvoltages would in this simple model lead to no observable CTR deterioration. This is confirmed by the lower CTR deterioration with increasing crystal cross-section observed for lower SiPM bias overvoltages as compared to higher bias overvoltages, which can be seen in figure 11. In this model the remaining CTR deterioration -18 - Only for very high crosstalk probabilities a CTR deterioration in the order of 10ps FWHM is observed. with higher crystal cross-sections at lower bias overvoltages could be explained by an increased SPTR due to an increased signal transfer time spread with a larger active SiPM area, as was discussed in section 4.2. We want to mention that the simple toy-model described above certainly does not represent the real time structure of crosstalk events, which by definition are not independently distributed. Simply because the n th crosstalk event depends on the (n − 1) th event. This simple model should merely show that there can be a possible influence of direct crosstalk events to the CTR, if the crosstalk probability is high enough. In summary, we have to conclude that a precise measurement and modeling (including the crystal) of the time structure of crosstalk events for various overvoltages has to be anticipated in future, in order to give a more precise insight on how crosstalk events could deteriorate the CTR in analog-SiPM based TOF-PET systems.

Conclusions
We have shown that the newest SiPM technology from FBK, i.e. the NUV-HD, can achieve a coincidence time resolution of 73±2ps FWHM if coupled to 2 × 2 × 3 mm 3 LSO:Ce codoped 0.4%Ca crystals. In PET a high 511keV detection efficiency is important, which calls for the need of longer crystals. In this respect LSO:Ce codoped 0.2%Ca crystals with a size of 2 × 2 × 20 mm 3 are able to achieve a best CTR of 117±3ps FWHM. Using more standard LYSO:Ce this value would be 130±3ps FWHM for similar scintillator sizes. Increasing the crystal cross-section leads to a deterioration in the CTR which we attributed partly to an increased single photon time resolution of the SiPM due to an increased signal transfer time spread seen with larger active SiPM areas. Another factor deteriorating the CTR for larger crystal cross-sections might be an increased optical crosstalk due to the crystal itself acting as a reflector for optical photons generated in the avalanche. However, further studies in this direction are necessary (e.g. with 6 × 6 mm 2 sized SiPMs) to fully conclude on the exact size of these different contributions. Finally, we tested GAGG:Ce and LuAG:Ce and confirmed that codoping with Magnesium or Calcium can improve significantly the scintillation properties and therefore the achievable time resolution.