Performance comparison of depth-encoding detectors based on dual-ended readout and different SiPMs for high-resolution PET applications

Schematics and photographs of the four SiPM arrays that were tested are shown in figure 1, whilst the characteristics of the SiPM arrays are listed in table 1. The reported PDEs of the SiPM arrays are shown in figure 2. The SensL SiPM array and the KETEK SiPM array both have a pitch size of 3.36 mm, whilst the two Hamamatsu SiPM arrays have a pitch size of 3.2 mm. The PDE, provided by the manufacturers, were measured at room temperature, but at different over-voltages (OV, voltage above the breakdown voltage).

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To evaluate the SiPM arrays for high-resolution PET applications, four dual-ended readout detector modules were fabricated. Each detector module was assembled using two of the same SiPM arrays coupled to both ends of the same 24  ×  24 array of 0.945  ×  0.945  ×  20 mm³ polished LYSO crystals (Crystal Photonics, Inc., FL). The pitch size of the LYSO array was 1.0 mm and Toray lumirror E60 film (Toray Industries Inc., Japan) was used as the inter-crystal reflector (James et al 2009, Kuang et al 2018, Yang et al 2011). The crystal array was coupled to the SiPM arrays using BC-630 optical grease (Saint-Gobain, S.A.) and clear acrylic sheets with a thickness of 1.0 mm were used as light guides. The BC-630 and the acrylic sheet have a refractive index of 1.465 and 1.49, respectively.

Each DOI detector module has two 8  ×  8 SiPM arrays with 128 SiPM pixels/signals. To simplify the readout electronics, for each array, the 64 SiPM signals were amplified individually using transimpedance amplifiers based on AD8045 chips, and the amplified SiPM signals were summed into rows and columns, generating 8 row and 8 column signals. The row/column signals were weighted by applying a gain to each row and column proportional to its location along each axis, generating four signals (X⁺, X⁻ and Y⁺, Y⁻) for position information (Popov 2011). Figure 3 shows the signal multiplexing boards. Each board can handle the 64 signals from each 8  ×  8 SiPM array, and the two stacked boards multiplex the 128 SiPM signals from each DOI detector module into nine signals, eight for position information and one for timing information. The timing signal was created from the sum of the 16 row and 16 column signals. The eight signals for position information were further shaped by a CAEN spectroscopy amplifier (N586B, CAEN S.p.A., Italy) and digitized by a PowerDAQ board (PD2MFS, United Electronic Industries, Inc., USA) (Du et al 2018).

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The gamma photon interaction position (x, y ), deposited energy (E) and DOI information were calculated as follows (Du et al 2016, 2016):

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle x=\frac{1}{2}(\frac{X_{1}^{+}-X_{1}^{-}}{X_{1}^{+}+X_{1}^{-}}+\frac{X_{2}^{+}-X_{2}^{-}}{X_{2}^{+}+X_{2}^{-}}),\quad y=\frac{1}{2}(\frac{Y_{1}^{+}-Y_{1}^{-}}{Y_{1}^{+}+Y_{1}^{-}}+\frac{Y_{2}^{+}-Y_{2}^{-}}{Y_{2}^{+}+Y_{2}^{-}})\nonumber \end{align} \tag{ 1 }$$

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle E={{E}_{1}}+{{E}_{2}}\nonumber \end{align} \tag{ 2 }$$

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {\rm DOI}=a(\frac{{{E}_{1}}-{{E}_{2}}}{{{E}_{1}}+{{E}_{2}}})+b\nonumber \end{align} \tag{ 3 }$$

where ${{E}_{1}}=X_{1}^{+}+X_{1}^{-}+Y_{1}^{+}+Y_{1}^{-}$ and ${{E}_{2}}=X_{2}^{+}+X_{2}^{-}+Y_{2}^{+}+Y_{2}^{-}$ were the two energies detected by the two SiPM arrays coupled at opposite ends of the LYSO array. $X_{i}^{+}$, $X_{i}^{-}$, $Y_{i}^{+}$, $Y_{i}^{-}$ (i  =  1, 2) were the position signals from SiPM array i. a and b were constants used to model the relationship between the ratio of the two energies and the DOI.

Identifying the optimal bias voltage for measuring the flood histogram is essential to achieve the best performance for high-resolution detectors (Du et al 2016, 2018), hence, the crystal identification ability (flood histogram) of the detector modules was evaluated at different bias voltages (with an 0.5 V interval) and at four different temperatures (table 2), whilst the energy, timing, and DOI resolution were evaluated at the optimal bias voltage found for each SiPM array for the flood histogram (table 3). The detector module being evaluated, along with the electronics boards (figure 3), were placed in a light-tight black box and cooled using cold, dry air. The detector's temperature was monitored by a thermocouple attached to the back side of the SiPM array. A 0.25 mm diameter, 30 uCi ²²Na point source was used to irradiate the LYSO array, and a 350–750 keV energy window was applied to each crystal to select events.

Experimental methods followed the methods we have previously developed and published and are only briefly summarized here (Du et al 2016, 2016).

2.3.1. Flood histograms.

2.3.2. Energy resolution.

2.3.3. Signal-to-noise ratio (SNR)

2.3.4. DOI measurements.

The detector module was irradiated from the side at five fixed depths (2 to 18 mm, in 4 mm intervals) by using a reference detector (based on 25 mm diameter Hamamatsu R13449-10 PMT and a 0.5  ×  20  ×  20 mm³ LYSO plate wrapped with Teflon) in coincidence (Du et al 2018). The distance from the ²²Na source to the reference detector was 100 mm and the distance from the ²²Na source to the dual-ended readout detector was 80 mm. Data was collected at different depths and DOI was calculated by comparing the two energy signals detected by the two SiPM arrays with appropriate calibration (equation (3)). The FWHM of the DOI distribution was used as a measure of the DOI resolution (Du et al 2018). Because only some of the LYSO elements were efficiently irradiated due to the geometry, and the fact that the signal drops off quickly with distance from the side entrance face (figure 4), only the 12  ×  12 LYSO elements shown in the white rectangle in figure 4 were used to compute the DOI resolution.

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2.3.5. Timing measurements

Figure 5 shows the best flood histogram obtained using the different SiPM arrays at 0 °C. All the LYSO crystals can be clearly identified except some crystals in the last two rows and columns in the flood histograms obtained using the Hamamatsu SiPM arrays. As explained earlier, this is because the LYSO array extends closer to the edges of the Hamamatsu arrays due to their slightly smaller area, making it difficult to identify the outermost crystals using light sharing. The flood histogram quality metric, calculated using the central 20  ×  20 LYSO elements and the method described in Du et al (2016), is shown in figure 6. The flood histogram quality generally increases and then decreases with increasing bias voltage, however, the responses of the SiPMs are quite different. While the Hamamatsu arrays can yield the highest values, the values also show a larger dependence on the bias voltage than these obtained using the SensL and the KETEK SiPM arrays. Better flood histogram quality was obtained at lower temperature, as expected, due to the lower SiPM noise (Piemonte et al 2013).

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The highest flood histogram quality values obtained using different SiPM arrays at different temperatures are shown in figure 7 and the corresponding bias voltages are listed in table 3. The best flood histogram was obtained using the Hamamatsu S13361 SiPM arrays. Table 3 and figure 6 show that the optimal bias voltage for the flood histogram at different temperatures varies little for the SensL and KETEK SiPM arrays, but increases with increasing temperature for the Hamamatsu SiPM arrays.

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The average energy resolution calculated using the central 20  ×  20 LYSO elements are shown in figure 8. The average energy resolution obtained using different SiPM arrays are comparable and does not change much with increasing temperature. The average energy resolution measured here, 25%–27%, is poorer than other reports in the literature (Borghi et al 2018, Choe et al 2017), because the LYSO arrays (reflector and surface treatment) were optimized to obtain good DOI information. These LYSO arrays exhibit a strong depth dependence of the 511 keV photopeak position (Ren et al 2014).

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The average signal, noise and average SNR across the central 20  ×  20 LYSO elements are shown in figure 9. They were obtained at the optimal bias voltage for the flood histogram (shown in table 3). Better SNR was obtained at lower temperatures, as expected. The best SNR was obtained using the Hamamatsu S13361 SiPMs. Interestingly, the Hamamatsu S13361, despite having slightly higher noise, gives better SNR than the Hamamatsu S14161 at these settings. This is because the working over-voltage of the Hamamatsu S13361 SiPM for the optimal flood histogram is higher than that of the S14161 SiPM, and the increase in signal at this over-voltage outweighs the higher noise levels.

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The average DOI resolution across the selected crystals (figure 4) and all the five depths are shown in figure 10. The average DOI resolution degrades slightly with increasing temperature. The average value of the DOI resolution obtained using different SiPM arrays are comparable, with slightly better DOI resolution obtained using the SensL and the Hamamatsu S13361 SiPM arrays.

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The CTR (test detector in coincidence with reference detector) averaged across the central 20  ×  20 LYSO elements and obtained at different temperatures is shown in figure 11. The timing resolution obtained using different SiPM arrays degrades with increasing temperature, and the best timing resolution was consistently obtained using the Hamamatsu S14161 SiPM arrays.

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