Silicon photomultiplier signal readout and multiplexing techniques for positron emission tomography: a review

In recent years, silicon photomultiplier (SiPM) is replacing the photomultiplier tube (PMT) in positron emission tomography (PET) systems due to its superior properties, such as fast single-photon timing response, small gap between adjacent photosensitive pixels in the array, and insensitivity to magnetic fields. One of the technical challenges when developing SiPM-based PET systems or other position-sensitive radiation detectors is the large number of output channels coming from the SiPM array. Therefore, various signal multiplexing methods have been proposed to reduce the number of output channels and the load on the subsequent data acquisition (DAQ) system. However, the large PN-junction capacitance and quenching resistance of the SiPM yield undesirable resistance–capacitance delay when multiple SiPMs are combined, which subsequently causes the accumulation of dark counts and signal fluctuation of SiPMs. Therefore, without proper SiPM signal handling and processing, the SiPMs may yield worse timing characteristics than the PMTs. This article reviews the evolution of signal readout and multiplexing methods for the SiPM. In this review, we focus primarily on analog electronics for SiPM signal multiplexing, which allows for the reduction of DAQ channels required for the SiPM-based position-sensitive detectors used in PET and other radiation detector systems. Although the applications of most technologies described in the article are not limited to PET systems, the review highlights efforts to improve the physical performance (e.g. spatial, energy, and timing resolutions) of PET detectors and systems.


Introduction
Positron emission tomography (PET) is a biomedical imaging technique that allows for the quantitative evaluation of the metabolic processes and physiological activities of living bodies by visualizing the distribution of radiolabeled tracers [1][2][3][4]. To effectively detect the annihilation photons with relatively high energy of 511 keV, PET scanners are typically ring-shaped and consist of scintillation crystal-based radiation detector modules.
Conventionally, photomultiplier tubes (PMTs) have been widely used for scintillation detectors for radiation measurement and imaging owing to their robustness, high quantum efficiency, and high intrinsic gain [5][6][7][8][9][10][11][12][13][14]. However, clinical PET detectors based on PMT arrays have limited intrinsic spatial resolution owing to the large volume of PMTs [15]. In addition, the scintillation light loss due to the gap between the photosensitive areas of PMT array, the low quantum efficiency of the photocathode, and the large transit time jitter 1 3 of traveling electrons further limit the timing performance of PMT-based PET detectors [16][17][18][19][20].
With the advancement of semiconductor technology, solid-state photosensors have been actively investigated to achieve high photon detection efficiency and signal amplification gain with good noise characteristics suitable for various applications [21][22][23][24][25][26]. Insensitivity to the magnetic field is one of the advantages of solid-state photosensors; this characteristic has attracted considerable attention from the PET community for developing simultaneous PET/ MR imaging systems [27][28][29][30][31][32][33][34][35]. The avalanche photodiode (APD) is an early-generation solid-state photosensor that detects incoming photons in the depletion region between the P and N-doped semiconductors and has the high intrinsic amplification gain of electrical signals [36]. Also, the APD has attracted interest in various photon detection applications thanks to its small size and low bias voltage operation. However, conventional APDs have an intrinsic disadvantage of low avalanche multiplication gain [37]. Accordingly, the silicon photomultiplier (SiPM), also known as Geiger-mode APD (G-APD), has been developed by interconnecting a large number of small-sized APDs (i.e. single-photon avalanche diodes or SPADs) in parallel and operating them in Geiger-mode with a self-quenching circuit to stop avalanche ionization [38]. The development of SiPM has made it possible to detect extremely weak light at the photon-counting level with high efficiency.
One of the technical challenges when developing SiPMbased PET systems or other position-sensitive radiation detectors is the large number of output channels coming from the SiPM array. Therefore, various signal multiplexing methods have been proposed to reduce the number of output channels and the load on the subsequent data acquisition (DAQ) system. However, the large PN-junction capacitance and quenching resistance of SiPMs cause undesirable resistance-capacitance (RC) delay when multiple SiPM's are combined [55]. The combination causes accumulated dark counts that result in signal fluctuation. Therefore, without proper SiPM signal handling and processing, SiPMs may yield worse timing characteristics than PMTs which exhibit low detector capacitance and require no additional quenching resistors.
This article reviews the evolution of signal readout and multiplexing methods for SiPM-based detectors. We focus primarily on analog electronics for SiPM signal multiplexing, which allows for the reduction of DAQ channels that are required for SiPM-based position-sensitive detectors used in PET and other radiation detector systems. The first section reviews the basic principles of PET detector and crystal-photosensor coupling schemes. Next, various SiPM signal multiplexing methods and other technologies to improve the SiPM-based detector performance are introduced. It is worth noting that the signal readout and multiplexing techniques introduced in this review article can also be applied in other systems that utilize SiPM for detecting visible and invisible photons. Although the applications of most technologies described in the article are not limited to PET systems, the review highlights efforts to improve the physical performance (e.g. spatial, energy, and timing resolution) of PET detectors and systems.

Basic principle
A basic element of PET scanners is a detector module assembled with monolithic or pixelated scintillation crystal(s) and photosensor array (Fig. 2). In PET, the origin of radioactive sources is localized by performing image reconstruction that basically superimposes multiple line-of-responses (LORs) or segment-of-responses (SORs) incorporating TOF information. A true LOR (or SOR) is recorded when two 511 keV annihilation photons simultaneously interact with a pair of opposing PET detectors [56]. Based on the output signals from a photosensor array, we can estimate the position of interacted crystals, the arrival time difference, and the deposited energy of annihilation photons. Typically, the PET detector performance is characterized by floodmap quality, energy resolution, and coincidence time resolution (CTR: measurement uncertainty of the arrival time difference between two annihilation photons in terms of the full-width at half-maximum of time difference histogram) which reflect the position, energy, and precision of timing measurement, respectively. The performance of PET detectors is highly dependent on the crystal and photosensor configurations, as well as the front-end circuitry used for reading out the photosensor signals.

Crystal and SiPM coupling scheme
Fast and bright inorganic scintillation crystals with high density and effective atomic number are used to achieve good detector performance while effectively detecting annihilation photons with a relatively high energy of 511 keV. A sensitivity of PET system can be improved by extending the crystal thickness. However, the longer the crystal, the lower is the CTR performance. The collection efficiency and arrival time jitter of traveling scintillation photons are changed by the crystal surface treatment conditions (i.e. polished or unpolished), significantly affecting PET detector performance.
There are two different schemes for crystal and SiPM coupling: (1) one-to-one coupling and (2) light-sharing configuration. In the one-to-one crystal and SiPM coupling scheme, the dimensions of the crystal and SiPM elements are usually identical, and each crystal element is optically isolated by specular (e.g. enhanced specular reflector or ESR films) or diffusive reflectors (e.g. Teflon tape and BaSO 4 powder). In the light-sharing configuration, scintillation photons are dispersed in a monolithic crystal block or pixelated crystal array and then measured by multiple SiPMs. Using the light-sharing configuration, the number of DAQ channels in the PET system can be effectively reduced, and the fine intrinsic spatial resolution of the PET detector can reach a size smaller than that of the SiPM pixel. Light guides are typically used in the light-sharing configuration for pixelated crystal arrays to improve crystal positioning accuracy [57][58][59][60][61].

Single-ended readout
A standard approach for measuring scintillation photons emitted from a PET crystal block is to attach SiPM arrays to only the back or front surface of the crystal block, typically referred to as a single-ended readout configuration (Fig. 3a). In the single-ended readout configuration, all crystal block surfaces are covered with reflectors, so that scintillation photons are collected through only a single side of the crystal surface optically coupled with the SiPMs.

Dual-ended readout
Another approach is to collect scintillation photons from a PET crystal block using SiPM arrays placed on both (front and back) ends of the crystal block. This method is called a dual-ended readout configuration (Fig. 3b). At the expense of the doubled SiPM cost, the dual-ended readout method makes it possible to measure the depth-of-interaction (DOI) of annihilation photons. The DOI is determined by comparing the amount of scintillation photons collected by SiPMs placed on the opposite sides [62][63][64][65][66]. The DOI measurement enhances the PET image quality by mitigating parallax errors occurring at the periphery of the PET scanner's transverse field-of-view [67][68][69][70][71]. The timing resolution of PET detectors can be also improved by reducing DOI-dependent time measurement errors [72][73][74][75][76].

Lateral side-readout
In the lateral side-readout configuration, a lateral side of each crystal element is covered by SiPMs (Fig. 3c). The lateral side-readout results in the improvement of light collection efficiency and reduction in the transit time variation of scintillation photons; this improves the overall timing performance of PET detectors [77][78][79][80]. This method also allows for the 3D measurement of each position of high energy photon interaction (Compton scattering or photo-electric absorption) within a pixelated crystal array, enabling the inter-crystal scatter (ICS) event identification and recovery [81,82]. The ICS event recovery increases PET system sensitivity and improves image quality [83,84]. However, the lateral side-readout configuration requires a substantially increased number of photosensors and thus suffers from a high readout complexity and manufacturing costs.

Sparse SiPM arrangement
Utilizing sparsely arranged SiPM arrays coupled to scintillation crystal arrays allows the detector manufacturing cost to be reduced, at the expense of light collection efficiency degradation [85] (Fig. 4a). Optimizing the sparse SiPM layout to resolve crystal elements smaller than the SiPM pitch is a major research interest. Detector performance degradation due to the sparse SiPM arrangement should also be minimized.
Recently, there has been a growing interest in sparsely arranged detector configurations for total-body PET applications. The total-body PET scanner provides dynamic PET data for whole-body kinetic analysis and parametric imaging. However, the high material cost for a large number of many scintillation detectors still hinders the widespread use of this new technology. Therefore, various cost-effective long axial field-of-view PET scanner designs based on the sparse arrangement of PET detectors in axial [86][87][88] or transverse [85,89] directions have been proposed, which

SiPM signal readout and multiplexing
As mentioned above, SiPM is contributing to improved imaging performance and replacing PMT in modern PET system [15, 33, 48-51, 53, 90-94]. This section introduces SiPM signal readout and multiplexing methods that may be useful for developing SiPM-based PET detectors and systems.

Individual readout scheme
A simple way to achieve superior SiPM-based PET detector performance is to manage each SiPM signal from the PET detector with an individual readout scheme. In terms of circuitry, the individual readout scheme is simply implemented by connecting the SiPM signals (or pre-amplified SiPM signals) from the PET detector to the subsequent DAQ system. In principle, the individual readout of SiPM signals may lead to the best achievable PET system performance. This is because individual readout allows us to avoid the accumulation of detector capacitance and the baseline fluctuation caused by interference between SiPM channels (e.g. dark noises).
However, the individual readout scheme requires a large number of high-speed DAQ channels. This results in a lack of scalability, which is required to configure a full-ring PET system. The lack of scalability greatly increases the design complexity and manufacturing costs of PET systems. A practical solution for the individual SiPM signal readout is to use application-specific integrated circuits (ASICs) that can individually handle large numbers of SiPM signals with a small footprint and low power consumption [95]. Recently, various research groups developed and evaluated their own ASICs that feature the number of input channels ranging from 8 to 144 . For example, the STiC ASIC developed for a multimodal system combining TOF-PET and ultrasound endoscopy (EndoTOFPET-US) [100,101,114] yielded an average CTR of 233 ps at the system level for a total of 128 channels. PETA series [104,105,108,111] utilize a charge integration method for energy estimation that covers up to 144 channels in a compact size, being employed for HYPERImage and SUBLIMA projects. A more detailed description of the various ASICs and their usages can be found in Calo et al. [118].

Multiplexing readout scheme
Signal multiplexing techniques are widely used to reduce the number of DAQ channels required in PET systems.
Reducing the readout channel number while minimizing performance degradation is an important research topic in PET hardware development. Multiplexing methods described below were summarized in Table 1.

Charge modulation-based multiplexing
A useful way to reduce the number of readout channels from the PET detector is to modulate the input charge collected from the SiPM arrays based on charge division (or charge sharing) multiplexing networks. The charge division multiplexing network steers the input charge toward output channels, and the amount of input charge is divided by the impedance between the input channel and each of the multiplexed output channels. This allows the interacted crystal position and photon energy information from the PET detectors to be encoded. The charge division multiplexing method can be used not only for one-to-one coupled crystal arrays but also for light-sharing crystal arrays. Typically, the charge division multiplexing network is implemented based on resistive chains, followed by signal shaping and amplification stages at the front-end electronics module.
An early version of the charge division multiplexing network was developed by Hal Anger and used in his gamma cameras. In 1958, Anger [119] proposed a position-sensitive readout circuit that reduced the initially large number of PMT array outputs into only four output channels (Fig. 5). He deployed a set of four resistors for each PMT, and the value of resistor sets was chosen to individually encode the interacted position (i.e. Anger logic) within the PMT array. The Anger logic-based multiplexing network is well-established and has shown excellent position decoding accuracy within photosensor arrays [120]. However, it is difficult to implement compact PET detector modules based on the Anger logic-based multiplexing network because such a network requires four passive electronic components for each photosensor elements.
A more commonly used charge division multiplexing network in PET detectors is the discretized positioning circuit (DPC) [121][122][123][124][125][126][127][128][129][130]. The DPC network was originally developed to collect radiation signals from position-sensitive proportional counters in nuclear science applications and was later applied to PET detectors [61,131]. DPC utilizes a two-dimensional (2D) resistive chain throughout the multiplexing network, where the 2D resistor chain allows the different amounts of input charge to be steered at each DPC node (i.e., the input node of photosensor outputs) toward each of the four output channels (Fig. 6a). In each row, all DPC nodes are connected by a 1D resistor chain. The twoterminal signals of each row are then fed respectively into two 1D resistor chains arranged in a column direction. The split signals by the resister chains in the column direction are collected by four amplifiers at the corner of the multiplexing network. The DPC is also called a four-corner readout circuit because it generates output signals at four corners. The DPC requires fewer passive electronic components than Anger logic to reduce the number of output signals from the photosensor arrays, making it more suitable for developing compact PET detector modules with a simple circuit design. However, unlike PMT-based detectors, DPC combined with a SiPM array suffers from undesirable RC delay in the fourcorner output signals due to the relatively large terminal capacitance of SiPM [132]. The RC-filtered SiPM signals by the DPC circuit increase the measurement uncertainty of photon arrival time when the leading-edge discrimination (LED) method is applied [133].
To further improve the performance of the DPC, Park et al. [134] investigated and demonstrated a hybrid DPC implemented by cascading the parallel combination of a resistor and capacitor throughout the DPC network (Fig. 6b). Compared with the conventional DPC, the hybrid DPC exhibits an improved timing performance of the PET detector and an excellent pulse shape uniformity that does not depend on the position of the interacted crystals within the PET detectors.
A row-column summing readout circuit is also widely utilized in various PET detectors [135][136][137]. This features a small form factor when designing the charge division multiplexing network. This makes them suitable for compact high-resolution PET detector implementation. The row-column summing readout circuit is implemented by splitting the SiPM signal (either anode or cathode) into two branches through resistors, capacitors, or diodes (Fig. 7). Subsequently, one branch is used for multiplexing the signals in the row direction of the SiPM array. The other is used for multiplexing the signals in the column direction of the SiPM array. The row-column summing readout circuit features a multiplexing ratio that is lower than that of a DPC network. However, PET detectors based on the row-column summing readout circuits generally outperform DPC-based ones. This is because undesirable crosstalk between SiPM channels is better avoided with row-column summing readout at the expense of using more preamplifiers and readout channels. Recently, an improved row-column summing readout was proposed to minimize the crosstalk between adjacent SiPM channels caused by leakage currents [138]. In this method, the resistors in the conventional row-column summing circuits were replaced by diodes that prevent the charge from flowing back into the adjacent channels by their rectifying function.
The symmetric charge division (SCD) network corresponds to a hybrid approach that combines the row-column summing readout circuit and a one-dimensional (1D) resistive chain. Row and column signals from the row-column summing circuit are further multiplexed into four position-encoded signals using 1D resistive chains (Fig. 8a) or  (Fig. 8b). The additional use of 1D resistive chains or weighted summing circuits further reduces the number of the row-column summing readout circuit output channels; however, there is, a trade-off between readout complexity and PET count-rate performance (e.g. pulse pile-up and dead time) [139][140][141].
Various studies have been conducted to improve the performance of the charge division multiplexing network by using capacitors instead of resistors. The capacitor-based multiplexing methods have a better high-frequency response. As such, they can achieve a faster and more accurate timing performance of PET systems than resistor-based methods [142]. Sun et al. [143] improved the PET detector performance by modifying the conventional row-column summing readout circuit. This was done by simply replacing resistors with capacitors throughout the multiplexing network (Fig. 9a). Olcott et al. [144] proposed the concept of cross-strip capacitive multiplexing; each SiPM anode and cathode is individually modulated using linearly-weighted splitting capacitor pairs and summed in the row and column directions, respectively (Fig. 9b). Consequently, the crossstrip capacitive multiplexing network generates four output signals (i.e., two signals for row direction and two signals for column direction) from the SiPM array. Here, the sum of all the independent capacitor pairs for each SiPM element is designed to be constant. Simplified capacitor-based Anger logic methods have been proposed and applied to a 2 × 2 position-sensitive solid-state photomultiplier array and a 4 × 4 SiPM array [145,146]. In this method, each of detector anodes is split into two branches using a set of weighting capacitors and generates a four-set of position signals by summing the nine-branched signals close to each corner of the photomultiplier array (Fig. 9c).

Time modulation-based multiplexing
Signal multiplexing can also be achieved by modulating the time intervals of propagating signals; this is called the time modulation-based multiplexing method. Compared to the charge modulation-based methods, the time modulationbased method typically features a simpler multiplexing network design and yields higher quality multiplexed output signals that are not significantly affected by RC delays as the multiplexing ratio increases. Therefore, time modulationbased multiplexing could be useful for TOF PET detectors because it overcomes the limitation of resistor-based charge division multiplexing methods. In addition, the time modulation-based multiplexing method can be further combined with a time-over-threshold (TOT) technique, which allows   simple energy measurement by recording the time duration above certain thresholds of SiPM signals, thanks to good signal integrity with minimal shape distortion.
Several useful time modulation-based multiplexing approaches have been proposed. Kim et al. [147] proposed a scalable multiplexing solution of SiPM signals using a strip-line readout scheme. The principle of the proposed method is based on measuring the time difference of arrival (TDOA), which is generally used in global positioning system (GPS) applications. The strip-line readout collects two propagating SiPM signals at both ends of signal traces without requiring any passive electronic components for multiplexing SiPM arrays. The position of fired SiPM elements can be uniquely identified using the time difference of two propagated output signals. The non-uniform response of the multiplexed SiPM elements should be considered to achieve a good PET detector performance. In addition, PCB design parameters should be carefully optimized depending on multiplexing ratio. Won et al. [148] proposed a 2D TDOA-based multiplexing approach: the so-called delay grid multiplexing method (Fig. 10). The proposed method also does not require any additional passive electronic components for multiplexing SiPM signals and only connects the adjacent signal pins of the SiPM array. Therefore, the delay grid method is implemented in a printed circuit board (PCB) where SiPM elements along the row direction of the SiPM array are connected, and both ends of the row traces are subsequently connected to the two column traces. The fired SiPM element can be identified by measuring the time difference of signal propagation from the SiPM element to each readout channel at the corners. Similar to the stripline multiplexing method mentioned above, PCB design parameters, including the PCB materials, the dielectric  constant, the width of the signal trace, and the PCB height width with respect to the reference plane, should be carefully optimized.
Vinke et al. [149] proposed an electrical delay line multiplexing method (Fig. 11). In this method, the SiPM signal is split into two branches using an RF splitter. One branch is connected to an N-to-1 RF combiner (i.e. first multiplexer), and the other branch is fed into another N-to-1 RF combiner (i.e. second multiplexer). The input signals to the second multiplexer have different time delays. The fired SiPM element in PET detectors is identified by measuring the arrival time difference between two multiplexed output signals. The proposed method can be also used for identifying ICS events by arranging the multiplexing network in a checkerboard pattern, but the further demonstration is required. The trigger level of SiPM signals should be chosen carefully because it affects the performance of SiPM identification and timing performance of PET detectors. The use of coaxial cables is not a practical solution for time delays because of their bulkiness. Therefore, delay chips are used in the subsequent investigations based on the delay line multiplexing methods [81,84,150].

Frequency modulation-based multiplexing
Frequency modulation techniques are widely used in various applications, including computing, telecommunication, radio broadcasting, and radiation detecting fields [151]. The frequency modulation typically uses a carrier wave with varying frequency to encode information-of-interest. Wonders et al. [152] introduced a novel multiplexing method for SiPM-based PET detectors that utilize mixed sinusoidal waves. The proposed multiplexing method requires a single sinusoid source per each SiPM channel and a pair of Schottky diodes to prevent signal interference between the multiplexed SiPM signals (Fig. 12). The sinusoid pulse serves as a tagging signal and is used for pulse shape discrimination. The initial energy and timing performances of the proposed method were demonstrated using a PET-like coincidence measurement setup, showing a potential to be used for SiPM-based PET systems. Although this method allows the readout of multiple SiPMs using a single channel, the requirement for a single sinusoid source for each SiPM limits its scalability. Another major drawback of this multiplexing method is that about half of the signal is lost while splitting the charge between the two diodes. If an adequate modulation to the effective impedance to steer more charge to the forward direction is applied, this method can be one

Polarity modulation-based multiplexing
There are multiplexing approaches that modulate PET data based on the polarity of SiPM signals. An analog bipolar multiplexing method was proposed by Yoon et al. [153] to further reduce the readout burden on a DAQ system for DPC output signals. In this approach, four DPC output signals were further encoded with different polarity combinations. The proposed method requires only four differential amplifiers and one summing amplifier for the multiple DPC-based PET detectors before the multiplexed signals are fed to the subsequent DAQ system (Fig. 13). The proposed method achieves a 50-75% channel reduction in the DAQ module, depending on a multiplexing ratio [33,35]. The multiplexing ratio of this approach should be carefully chosen considering the tradeoff between the multiplexing ratio and the PET count rate performance. The polarity modulation can be also applied to the TOT circuit [154]. In this approach, each of four multiplexed output signals generated from the DPC network is subsequently converted into a bipolar signal using a preamplifier, an active capacitor-resistor (CR)-shaping filter, two comparators, and an OR logic gate (Fig. 14). The proposed method improved the energy linearity of the conventional TOT method and yielded a performance similar to the data collection based on free-running analog-to-digital converters (ADCs). Careful parameter optimization of the CR-shaping filter and threshold sweep would be required to achieve optimal PET detector performance at a system level.

Digital modulation-based multiplexing
Early digitization of SiPM signals may allow for a better performance of the SiPM-based PET system by effectively preventing the accumulation of undesirable noises (i.e., dark count, after pulse, and optical crosstalk) and interference between the multiplexed SiPM elements [155][156][157]. In addition, the digital multiplexing based on field-programmable gate array (FPGA)-only signal digitization method [141,158,159] reduces the manufacturing cost of DAQ modules by eliminating waveform sampling-based DAQ that uses ADCs. However, a limited number of available FPGA input/ output (I/O) ports should be considered when developing the DAQ module that incorporates the FPGA-only signal digitization method.
The usefulness of digital SiPM multiplexing for PET detectors has been demonstrated in several studies. A scalable multiplexing method based on digital pulse sequence generation was proposed by Cates et al. [160] with the goal of reducing DAQ channels while maintaining good timing performance. In this method, 16 SiPM signals are multiplexed into 2 output channels: one provides timing information with fast comparators, and the other generates a digital pulse sequence. The digital pulse sequence is generated using delay chips for both energy and position information encoding (Fig. 15). For energy and position encoding, 16 signals from a 4 × 4 SiPM array were reduced to 4 Anger logic outputs, which were passed to comparators to encode energy information into TOT pulses. TOT pulses were then combined into a single readout line after delaying 3 TOT pulses using active delay chips with an increasing delay in 500 ns increments. The energy was estimated by summing the total width of the digital pulse sequence based on a TOT method. The proposed method achieves the multiplexing ratio of 16:2.
The digital delay encoding technique was also useful in the development of a PET detector with ICS event identification capability [84]. The proposed method serializes 16 one-to-one coupled SiPM anode signals into 4 digital pulse sequences, in which time delays in 250-ns increment were introduced (Fig. 16). Energy information was estimated by the TOT method and position information was decoded by analyzing pre-defined time delays and pulse train output channels. A nearly fourfold reduction of readout channels was achieved for a 4 × 4 PET detector module while maintaining the ICS event identification capability of an individual signal readout scheme with TOF capability.
The pulse-tagging method proposed for a single transmission-line readout is a kind of semi-digital multiplexing approach that allows for readout channel reduction without compromising detector performance [161]. In this method, a square tagging pulse is attached ahead of an analog SiPM signal. The position information of the PET detector is encoded into a specific width and height of the tag signal, and timing information is extracted from the rising edge of the tag signal (Fig. 17a). This method requires only a single readout channel to acquire data from a 4 × 4 PET detector module without degrading timing performance as the multiplexing ratio increases. Encoding DOI information with phoswich scintillation crystals [70,[162][163][164] is also possible with this approach because it preserves the pulse shape information in the multiplexed output signals. Recently, a fully time-based single transmission-line readout method has been also proposed [165]. In this method, an L-shaped tagging pulse was used instead of the square pulse, and a 2D gamma-ray interaction position was encoded in the upper and bottom widths of the L-shaped tag (Fig. 17b). The dual-threshold TOT method applied to the tagged SiPM pulses allows for the simultaneous estimation of position and energy only based on time measurements.

Temperature compensation
One of the technical challenges of maintaining the performance of SiPM-based PET detectors and systems is the temperature-dependent gain variation of SiPM. Various temperature compensation methods have been proposed because the breakdown voltage and intrinsic gain of the SiPM drift with the changes in the operating temperature [166]. Bias voltage modulation technique which is based on temperature-voltage lookup tables (LUTs) implemented in the FPGA, microcontroller unit, or personal computer is a widely used method [50,167,168]. Although this method allows for an accurate gain drift compensation in real time, constructing a LUT for each SIPM or multiplexed SiPM array is a time-consuming and laborious task. Therefore, several automatic gain drift compensation methods that do not require LUTs have also been proposed. Licciulli et al. [169,170] proposed an automatic compensation method using a dark pulse amplitude of a "blind" SiPM, which should be approximately proportional to the gain of the operating SiPM. In this method, owing to the negative feedback configuration, it is possible to achieve constant SiPM gain without an accurate knowledge of the detector sensitivity to temperature variation; however, this is at the expense of an additional SiPM. Application specific customized temperature sensors based on thermometers and p-n diodes were Fig. 15 Digital modulation-based multiplexing using active delay chips also developed for the automatic gain drift compensation with LUT [171,172]. These sensors provide output voltage linearly proportional to the temperature, allowing effective gain drift compensation with simple circuitry. It was also shown that off-the-shelf temperature sensors can be used for the same purpose [173] (Fig. 18).

Fast timing
The various signal multiplexing methods introduced in this review can significantly reduce the signal readout channels. However, the signal multiplexing accumulates the intrinsic capacitance and dark current of the SiPM. The undesirable parasitic detector capacitance of the SiPM not only degrades the SNR of detector signal output by providing a sinking path to the ground, but also retards the slope of the rising edge, which degrades the timing performance of SiPMbased detectors [40]. Baseline fluctuation due to the dark counts is another source of timing performance degradation.

Analog high pass filters
High-pass filtering of timing signals is a simple but effective method to improve the timing and count-rate performances of SiPM-based PET detectors. High-pass filters with polezero cancellation applied to the SiPM are useful for reducing the baseline fluctuation and pulse width of SiPM output signals; this led to improvements in the timing and count-rate performance [161,174]. The usefulness of high-pass filtering for developing high-performance PET detectors while multiplexing SiPM signals was also demonstrated [94,175].

Bootstrapping
To address this timing performance degrading problem, capacitance compensation or "bootstrapping" techniques have been investigated. In passive bootstrapping compensation circuits [176][177][178] (Fig. 19a), the cathode and anode of the SiPM are connected to one end of a balun transformer, the other end of which is connected to a high-bandwidth amplifier. The balanced-to-unbalanced connection of the transformer with a 1:1 turn ratio should result in a twofold amplified signal output, yet the signal maximum amplitude was measured to be ~ 3.5, owing to a decreased effective terminal capacitance of the SiPM [176,179]. However, the use of balun transformers and the high-power consumption of the high-speed amplifiers remain challenges in the implementation of this technique on an ASIC. Miller effect was exploited to implement an active bootstrapping technique [180,181]. A unity gain amplifier, or so called "bootstrapping" amplifier, was placed between the cathode and anode of the SiPM (Fig. 19b). With this "bootstrapping" amplifier, the feedback factor can be modeled as C C C D /(C C + C D ). If the DC blocking capacitor C C is sufficiently larger than the detector capacitance C D , the feedback factor is approximately equal to C D . Then according to the Miller effect, the input capacitance C in can be reformed as C D (1−A) which will be zero if a unity gain amplifier is used as the "bootstrapping" amplifier. So, the effective detector capacitance seen in the following front-end circuit was then reduced by the Miller effect while preventing any undesirable voltage signal or noise signal from entering the following circuits.

Cherenkov photon readout
Recent efforts to detect fast prompt photons, such as Cherenkov photons, have pushed the limits of timing performance in SiPM-based TOF PET detectors [178,179,[182][183][184][185][186]. When estimating the interaction time of gamma rays based on the prompt photons, the following two points should be considered [184]: (1) SiPM and subsequent readout electronics Fig. 18 Automatic gain driftcompensation for SiPM: a conventional SiPM biasing and b SiPM biasing using a temperature sensor with current driving capability Fig. 19 Bootstrapping methods for SiPM capacitance compensation: a passive method using a balun transformer and b active method using a bootstrapping amplifier should have a single-photon timing resolution that is as low as possible and a − 3 dB bandwidth with > 1 GHz sampling rate [178,187], respectively; (2) Low noise level should be sufficiently low to avoid false triggers caused by the threshold equivalent to a few photon level [188]. Gundacker et al. [178] implemented a high-frequency readout electronics that utilize passive capacitance compensation and RF amplifiers to take full advantage of the SiPM with low single-photon timing resolution. The fast readout electronics with a − 3 dB bandwidth and ~ 1.5 GHz sampling rate yielded CTR values of 58 ± 2 ps and 98 ± 3 ps, respectively, by employing faint Cherenkov light from 2 × 2 × 3 mm to 2 × 2 × 20 mm LSO:Ce:Ca crystals coupled to FBK NUV-HD SiPMs. BGO crystals with dimensions of 2 × 2 × 3 mm also yielded a remarkable CTR value of 158 ± 3 ps. In other investigations with 3 × 3 × 3 mm BGO crystals [179,183,184], the capacitance compensated high-frequency SiPM readout electronics for measuring fast Cherenkov photons achieved timing resolution of 105-200 ps.

Summary and conclusions
This paper provides a systematic review of the signal readout schemes for PET detectors based on SiPMs. Several different crystal-to-SiPM coupling and visible light photon readout schemes were introduced, and various signal multiplexing techniques that reduce the readout complexity of highperformance PET systems were reviewed. Technologies to improve the stability and timing performance of SiPM-based PET detectors were also discussed.
Most readout schemes for SiPM-based PET detectors have trade-offs between various factors (e.g. spatial, energy, and timing resolutions, signal crosstalk, manufacturing cost, size and complexity of the readout circuitry, etc.). As described throughout this review, recent research interest is not to focus on one factor, but rather to overcome the trade-offs and improve the imaging quality and overall performance of PET detectors.

Declarations
Conflict of interest Haewook Park declares that he has no conflict of interest. Minseok Yi declares that he has no conflict of interest. Jae Sung Lee is the editor in chief of Biomedical Engineering Letters.
Ethical approval This article does not contain any studies with human participants or animals performed by any of the authors.
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