Construction and On-site Performance of the LHAASO WFCTA Camera

The focal plane camera is the core component of the Wide Field-of-view Cherenkov/fluorescence Telescope Array (WFCTA) of the Large High-Altitude Air Shower Observatory (LHAASO). Because of the capability of working under moonlight without aging, silicon photomultipliers (SiPM) have been proven to be not only an alternative but also an improvement to conventional photomultiplier tubes (PMT) in this application. Eighteen SiPM-based cameras with square light funnels have been built for WFCTA. The telescopes have collected more than 100 million cosmic ray events and preliminary results indicate that these cameras are capable of working under moonlight. The characteristics of the light funnels and SiPMs pose challenges (e.g. dynamic range, dark count rate, assembly techniques). In this paper, we present the design features, manufacturing techniques and performances of these cameras. Finally, the test facilities, the test methods and results of SiPMs in the cameras are reported here.


Introduction
The energy spectrum of cosmic rays (CRs) exhibits several interesting features that provide a wealth of information about their origin, acceleration, and propagation processes. One of the major scientific goals of the Large High-Altitude Air Shower Observatory (LHAASO) [1,2] is to explore these physical processes [3,4] by measuring the energy spectrum and the composition of CRs. LHAASO consists of three ground-based detector arrays [5]: an array of scintillator detectors and muon detectors covering an area of about 1 km 2 (KM2A), a Water Cherenkov Detector Array (WCDA), and a Wide Field-ofview Cherenkov Telescope Array (WFCTA) consisting of eighteen telescopes.
Energetic primary CR particles that enter the atmosphere induce extensive air showers (EAS) [6]. EAS produce a large number of secondary photons which can be detected by the camera of the imaging atmosphere Cherenkov telescopes (IACT). The recorded image is then used to reconstruct the physical properties of the primary CR particles such as particle species, energy and incidence direction. The potential and efficiency of this method have been successfully demonstrated by previous experiments [7][8][9] and the WFCTA prototype experiment [10,11]. WFCTA aims at measuring the spectrum of CRs from 10 TeV up to 1 EeV and studying its composition [12]. WFCTA cannot be an effective gamma-ray detector compared to KM2A, but WFCTA, in conjunction with KM2A, provides cross calibration of the energy measurement of primary gamma-rays. WFCTA and KM2A adopt two independent methods to measure the energy of ultra-high energy gamma-rays in the energy range from 100 TeV to a few PeV, just as the AUGER experiment [13] provides two independent methods to measure ultra-high energy cosmic rays, namely the surface detector array [14] and the fluorescence detector [9].
The main information about the telescopes of WFCTA can be found in Sec. 2.
In Sec. 3, the WFCTA SiPM camera structure and main features are described.
The laboratory test facilities, test methods, results, and assembly techniques of the camera are reported in Sec. 4. Finally, on-site running performance and on-site test results of these cameras are discussed in Sec. 5.

The Telescope
Each telescope of WFCTA consists of a segmented spherical mirror of about 5 m 2 with a SiPM-based camera installed at its focal plane. The light induced by EAS is focused on the camera by the mirror. The focal plane camera which has a field of view (FoV) of 16 • × 16 • is composed by an array of 32×32 pixels, each with an angular size of 0.5 • × 0.5 • , featuring a SiPM coupled to a square light funnel. The telescopes are movable, and can be operated in Cherenkov or fluorescence mode during different observation phases by changing the locations and the directions of the telescopes.
Up to now, all of the telescopes have been deployed at the LHAASO site (E:100 • 03 , N:29 • 18 , 4410 m a.s.l.), which is located in Haizishan, Daocheng County, Sichuan Province, China. The photo of six telescopes is shown in Fig. 1.

Overview
The SiPM camera converts optical signals generated by EAS into electrical signals, and records or discards them according to triggering criteria. The photon flux received by the camera is determined by the energy of the primary particle and the shower core distance. In each observation phase, the target energy span is about two orders of magnitude. Each pixel of the camera is required to accommodate a dynamic range from about 10 photo-electrons (p.e.) to 32,000 p.e. according to the results of the shower and the telescope simulation.
A SiPM camera of WFCTA consists of 64 sub-clusters, a trigger board, four power distribution boards, an aluminium alloy backbone plate, and a steel housing. Each sub-cluster is composed of 16 light funnels, 16 SiPMs, a preamplifier board [15], two analog amplifier boards [16], a digitizer board [17], a bias voltage and temperature compensation loop board, a power regulator board and an aluminium alloy support frame. The camera is cooled by an air-cooling system.  The WFCTA electronics amplifies and digitizes the signals, and acts as the trigger system and the Ethernet interface. The front-end electronics has two stages. In the first stage, the SiPM current is converted into a voltage signal by a 3 Ω resistor, and then amplified in a low noise linear preamplifier [15] (OPA846, Texas Instruments) with a design gain of 10. In the second stage, the preamplifier output is fed in parallel into two linear amplifiers [16] (AD8012, Analog Devices) with different gains to cope with the large dynamic range. The first one, with a design gain of 14.1 (high gain), is used for signals with less than 800 p.e., while the second one, with a design gain of 0.64 (low gain), is used to cover the rest of the dynamic range. The width of the amplified signals is stretched to at least 80 ns to avoid sampling aliasing effects.
A 50 MHz, 12 bit analog-to-digital converter (ADC, AD 9249, Analog Devices) digitizes the amplified signals with a resolution of 0.5 mV/ADC-count, and feeds them to a field programmable gate array (FPGA, XC6SLX100T-FGG676, Xilinx) discriminating between signals and noise according to a given threshold. A single-pixel trigger is issued when the signal exceeds the threshold. In this case, the trigger is sent to the trigger board, while the data are buffered in a pipeline and readout only if a telescope trigger is issued by the trigger board. A telescope trigger is issued when the number of triggered pixels exceeds a threshold number and their distribution has a circular (for Cherenkov mode) or linear (for fluorescence mode) pattern in a time window of 1.92 µs.
When a telescope trigger is issued, the FPGA frames the waveform data of triggered pixels into a set of TCP/IP packets, stamps them with a White Rabbit time mark [18,19] and sends them to the data center. In the data center, a final shower-trigger decision is made based on triggers from other WFCTA telescopes and/or other LHAASO detectors. The waveform data of each pixel is composed of 28 points, and each point is the sum of 4 consecutive original sampling points with a sampling interval of 20 ns. The signal charge is obtained by integrating the waveform with a time window of 320 ns (one point before the pulse peak and two points after the peak) and subtracting the baseline of the waveform.

General Specifications
A SiPM consists of a large number of Geiger-mode avalanche photodiodes (G-APDs) [20], each of which is referred to as a cell. The SiPMs used in WFCTA are Hamamatsu S14466. The arrangement of the channels and the temperature sensor of the SiPMs were customized to comply with WFCTA requirements. This type of SiPM has a monolithic array of 3 × 3 channels. Each channel has 39,936 cells, and a size of 5 mm ×5 mm. Such a large number of cells are employed because of the dynamic range requirement (10 p.e.-32,000 p.e.). In our design, the output signals of nine channels are summed and read out together.
The main specifications of the SiPM are listed in Table 1. The photon detection efficiency (P DE) vs. wavelength characteristic of the SiPM is shown in Fig. 3.  The WFCTA camera is an upgrade of the original design based on PMTs [10,21]. This upgrade brings benefits and challenges. Conventional PMTs limit the duty cycle of Cherenkov telescopes [22,23], because bright light, such as the moon and stars light, significantly accelerates their aging. On the contrary, SiPMs can extend their duty cycle [24,25]  Array (CTA) have proven its feasibility and have provided us with many useful inspirations and application experiences.

Optical crosstalk, Afterpulse and Dark Count Rate
The optical crosstalk [28][29][30][31] and the afterpulse [32,33] are considered as the correlated noises of incident optical signals, and their effects need to be evaluated quantitatively in the shower reconstruction. The optical crosstalk and afterpulses have been studied by a variety of experimental and theoretical methods [34][35][36][37][38], and the mathematical models [39][40][41][42] have been proposed. According to the measurement results of 120 SiPM samples of type S14466, the crosstalk probability is 3.9%±0.4%, while the afterpulse probability In order to understand the optical crosstalk and afterpulses in detail, a Monte Carlo simulation is conducted based on the measured probability and the models reported in [40,41]. Providing that the '8 nearest neighbors' model is valid for the SiPM used, considering crosstalk cascades up to 5, and an average crosstalk probability of 3.9%, the Monte Carlo simulation results indicate that crosstalk will introduce a relative error of 4% and a relative RMS fluctuation of 6.5% when the number of initial fired cells (N f ) is 10. Due to the saturation effect of crosstalk [40], the relative error introduced by crosstalk decreases slightly for N f ¿2,000, and reduces to 3.2% for N f =32,000. This saturation effect introduces a non-linearity of −0.8% for N f =32,000. The time interval between the initial pulse and the afterpulse is a single exponential distribution, the average 1/e-amplitude time constant of afterpulses measured for five SiPM samples is approximately 69 ns. There will be 99% of the afterpulse charge in the integration time window of 320 ns. An average afterpulse probability of 4.6% introduces a relative error of 4.4% and a relative RMS fluctuation of 6.3% for N f =10. The relative error introduced by afterpulses gradually approaches 4.6% with increasing N f . The relative errors introduced by crosstalk and afterpulses can be considered as a measurement bias, which can be eliminated by the calibration of the camera. The relative RMS fluctuations introduced by crosstalk and afterpulses decrease almost exponentially with increasing N f . Although they increase the measurement uncertainty of small signals, the relative uncertainty will decrease with the accumulation of events. In addition, the measurement uncertainty of small signals is dominated by the Poisson fluctuation of the night sky background (NSB), not by crosstalk and afterpulses.
The SiPM generates pulses in dark environments due to thermally generated carriers in the sensitive area. Usually, spuriously triggered breakdowns with an amplitude larger than 0.5 p.e. are considered as dark counts. The number of dark counts per unit time is referred to as the dark count rate (DCR), which increases with increasing operating voltage, temperature and area of SiPMs.
For the S14466 SiPM, the DCR changes by about a factor 10 for every 25 • C change in temperature. Fig. 4 shows the DCR distribution for the pixels of the first eight cameras.
It can be seen from Fig. 4   distribution. This is mainly because these SiPMs come from different silicon wafer lots. Different wafer lots have subtle differences in their production process that affect the DCR. DCR of the applied SiPM is 4 MHz to 18 MHz, while the count rate induced by the diffuse NSB light is usually greater than 50 MHz.
Therefore, in actual observations, DCR becomes a negligible factor compared with NSB.

Temperature Effects and Compensation Loop
The basic SiPM input-output characteristic, without considering the effects of non-linearity, crosstalk and afterpulses, can be expressed as where Q is the SiPM output charge, N p is the number of incident photons, and e is the charge of the electron. g is the gain of the SiPM, and can be formulated where C j is the junction capacitance of the SiPM cell. V ov is the overvoltage, and V ov = V bias − V bd , where V bias is the bias voltage provided by the power supply, and V bd is the breakdown voltage of the cell. P DE is affected by V ov .
Consequently, the output charge Q can be formulated as The breakdown voltage V bd increases almost linearly with the temperature increasing [43][44][45]. So, providing that N p and V bias are constant, V ov and then Q will decrease with the temperature increasing. The compensation applied is based on the on-site measured compensation voltage of each pixel. Fig. 6 shows the distribution of the compensation voltage for the 1024 pixels of the first camera.

Light Funnel
In order to minimize the dead space between the photosensitive area of SiPMs and to reduce stray light coming from outside the mirror of the telescope, square light funnels are designed to be as close as possible to the ideal Winston cone [46,47], and coupled with the SiPMs. The shape selection of the funnel is constrained by the arrangement of pixels, while it is also a trade-off between the simplicity of implementation and the ideal optical performance. The funnels have an entrance area of 24.4 mm×24.4 mm to match the optical spot size [48], and have an exit area of 15 mm×15 mm to match the size of the SiPM. The sidewall thickness of the funnel is 0.5±0.2 mm. The clearance between the side walls of the light funnel is 0.2 mm (design value). Therefore, the physical area occupied by each pixel is 25.8 mm × 25.8 mm. The funnels were designed for a cut-off angle of 35 • . The inner surface of the funnels has a roughness of 50 nm, and is coated with an aluminium layer and a dichroic layer (Al+R) [49]. This coating has a reflectivity of about 90% in the wavelength range from 300 nm to 700 nm, and is provided by Thin Film Physics 1 . Fig. 7 shows how the funnels and the SiPMs are coupled in a pixel. The collection efficiency for the parallel beams of light with different incidence angles is shown in Fig. 8, which is obtained from a ray tracing simulation based on the physical parameters mentioned above, and assuming an ideal sur-

Test Facilities
In order to perform a massive test on the performances of SiPMs and subclusters, two dedicated facilities have been built. One is called Temp-System, which is used for the temperature dependent characteristics inspection of a small amount of samples (5% of the total), such as the gain, the response vs. voltage, and DCR. Another is called 1D-System, which is used for the massive batch test on the response vs. voltage, the non-linearity and the signal resolution.
The scheme of Temp-System is shown in Fig. 9. The scheme of the set-up of 1D-System is shown in Fig. 10. More detailed information about this system and the test method can be found in Ref. [21].

Response Charge vs. Voltage Characteristic
In different observation phases of WFCTA, the responsivity to the optical signal of each pixel is adjusted individually according to different observation requirements. Therefore, the response charge vs. the bias voltage characteristic of each pixel should be known. Hamamatsu provides the bias voltage (V 0 ) of all SiPMs for the gain of 1.1 × 10 6 (g 0 ). Here, the gain calculated by the following equation is defined as the nominal gain (g).
where Q is the response charge for a certain bias voltage. at which this curve is measured is also recorded, so that it can be used for the compensation of the effect of the temperature. The response charge is the integration value of the signal pulse in a time window of 320 ns, in which crosstalk and afterpulses are included. Because the probabilities of them also increase with increasing the bias voltage [44], the response charge-voltage curve is slightly upturned. Fig. 12 shows the operation voltage distribution of the SiPMs in eighteen WFCTA cameras for g = 8 × 10 5 and 1.1 × 10 6 .

Non-linearity and Signal Resolution
In order to correctly reconstruct physical parameters of CRs, the relation between the flux of photons from a shower (input) and the camera signal charge (output) should be known. To this end, the non-linearity in dynamic range of each pixel is measured and simulated. The measurement setup is shown in Fig. 10, and the double-pulse method is used, which can be found in [15,21,51].
The non-linear behavior of the camera pixels is related to the following three factors: the binomial response of the SiPM to incident photons, the non-uniform photon distribution on the SiPM coming from the pattern induced by the funnel, and the readout electronics non-linearity (N L elec ).
The binomial response of the SiPM originates from the fact that there is always a certain probability that two or more photons entering the same cell at an interval shorter than the cell recovery time. In this case, the cell is still not fully recharged, and thus the second and succeeding photons will not produce a full amplitude output. The pulse width used in our test is 20 ns, which is less than the SiPM recovery time of 32 ns. And the ratio of the number of fired cells to the number of total cells is lower than 11%, so the following equation can be used to approximately describe the binomial response for the uniformly illuminated SiPM [52,53] where N f is the number of fired cells, P DE is the photon detection efficiency, N 0 is the total number of cells, and N p is the number of incident photons.
N p · P DE can be considered as the number of photo-electrons (N pe ) that should be measured without the binomial response. N f is calculated from the signal charge Q, and by using the following equation where g is the gain of the SiPM, and adjusted to 8 × 10 5 in the test. g elec is the gain of the readout electronics, and e is the charge of the electron. The non-linearity of the uniformly illuminated SiPM (N L SiP M ) can be calculated by In order to understand the effects of the non-uniform photon distribution, are not considered, because these factors have no significant effect on the nonlinearity. Fig. 13 shows the non-linearity obtained through the measurement, the calculation and the simulation. The discrepancy between the measurement and the simulation results is less than ±1% over the dynamic range. We attribute this discrepancy to N L elec and the measurement method. N L elec is required to be less than ±2% within the dynamic range from 10 p.e to 32,000 p.e. In order to avoid introducing a systematic bias into the reconstruction of showers, an off-line correction is applied according to the results of the telescope simulation.
Optical signals will fluctuate after being converted and amplified by SiPMs where σ Q is the standard deviation of signal distribution, and Q is the mean value of signals. Fig. 14

Assembly Techniques of the Camera
The assembly process includes four steps: the gluing of the two halves of the funnel, the gluing of the funnels and a preamplifier board (PAB), the assembly of sub-clusters, and the assembly of the camera. To prevent the clearances between the side wall of light funnels from exceeding 0.2 mm, the RMS deviations of length (L C ) and width (W C ) of the funnels are required to be less than ±0.1 mm, and the height differences induced by the tilt of funnels to be less than ±0.6 mm. If the assembly processes do not meet the requirements, the collection efficiency will be degraded. Particular care is needed in three of the assembly steps: the correct gluing of the two halves of the funnels to guarantee the same dimensions for all of them, the gluing of the funnels on PAB to ensure the perfect planarity of the funnels' entrance, and the sub-cluster assembly to ensure that all of them have the same height to guarantee the planarity of the whole camera focal plane.
In order to address the challenges, two kinds of assembling jigs were designed and fabricated by using 3D printing technology. Fig. 15 shows the funnel gluing jig where funnels are positioned while the glue is drying. The measurement results of 550 randomly selected light funnel samples demonstrate that L C and W C can be kept within ±0.07 mm by this method. Fig. 16 shows the funnels-PAB gluing jig, which is similar to a 'box' with a removable cover. When the funnels and a PAB are slotted in the jig, the funnels are covered with an acrylic sheet, and then the jig together with the components are turned upside down for gluing. In this way, the entrances of the funnels will be constrained by gravity to lie on the surface of the acrylic sheet. In addition, for every sub-cluster, the height is measured and adjusted until it meets the required tolerance. With this method, the camera focal plane can achieve a flatness of ±0.3 mm. Fig. 17 shows a sub-cluster and a camera in the telescope.

Running information
The layout of eighteen WFCTA telescopes is shown in Fig. 18. The first SiPM-based WFCTA telescope started its operation at the end of January 2019 Two of them started operation in January 2020 and ten in April 2021. Events measured by WFCTA are sent to an off-line event filter, which collects them together with events from WCDA or other detectors of LHAASO by using White Rabbit time stamps with a time precision of less than 0.5 ns [54] for time coincidence. More than 50 million coincidence events of the telescopes and the first pond of WCDA were collected by February 2020. One of the coincidence events is shown in Fig. 19(a) and Fig. 19(b).

Performance
The total power consumption of a camera is about 720 W. Each camera is cooled by two 750 W air blowers. The temperature of SiPMs near the air inlet is lower than that of SiPMs near the air outlet. A typical temperature distribution in the camera is shown in Fig. 20. The gradient between the SiPM with the highest and lowest temperature never exceeds 16 • C when two air   by the internal resistance of the SiPM causes its temperature to rise by 6 • C above normal conditions. In the maximum current limiting output state, the HV power supply works in constant current mode and the output voltage is not constant. Although the camera can not be damaged in this condition, the HV power supply is required to be turned off according to the present telescope operation strategy. Therefore, if the angular distance between the edge of the telescope FoV and the moon is less than 1 • , the HV power supply will be turned off automatically to avoid exposing the camera to the direct moonlight, which may lead to the power supply working in the maximum current limiting output state.
The SiPM signals are read out by using a direct current (DC) coupled electronics system. Thus, the baseline amplitude of SiPM output varies with the light intensity of NSB, such as a bright star or the moon passing through the FoV of a pixel in the camera. A higher NSB light intensity generates a higher DC output in the SiPM and then a higher baseline amplitude. The NSB is calculated off-line by the following equation where BL open and BL close stand for the open-shutter and closed-shutter baseline amplitudes, respectively. The amount of moonlight collected by the telescope depends on the moon phase, the atmospheric conditions, the elevation angle of the moon and the angular distance of the moon to the FoV.
The WFCTA telescopes were operated under the full moon on the clear night of January 11, 2020. The elevation angle of the moon as a function of time is shown in Fig. 21(a). The moonlight is scattered by molecules (Rayleigh scattering) and aerosols (Mie scattering), and absorbed in the atmosphere, before it enters the telescope [56,57]. Therefore, the measured NSB correlates with the moonlight slant depth in the atmosphere (the elevation angle of the moon). As an example, the NSB measured by one pixel in a camera as a function of time is shown in Fig. 21(b). The shorter the slant depth (higher elevation angle of the moon), the more moonlight is collected by the telescope. The influence of the moon on the SiPM-based Cherenkov telescope has already been measured and studied in FACT [43]. The moonlight induces a continuous photo-current in the SiPM, and leads to an additional voltage drop on the bias resistor. Accordingly, the bias voltage, and then the gain, P DE, DCR, the crosstalk probability, the afterpulse probability of the SiPM, varies with the intensity of NSB light [58].
The continuous photo-current can also generate additional heat on the SiPM. SiPM itself, because the heat can be transmitted through the air, the funnel or the connector on the SiPM backside. Although, it is not easy to study these effects cause by the NSB item by item, the overall effects are discussed in the following.
As is shown in Fig. 22, the output charge ratio of a SiPM with and without NSB, that is, the relative SiPM response charge, is linearly related to the NSB. at the maximum NSB shown in Fig. 22, the dynamic range of Cherenkov light measurement will be reduced by about 3.4%. Due to the increase of the NSB noise on the moon night, the threshold value of each pixel is correspondingly increased to discriminate the signal from the noise. As a result, the energy threshold of the telescope is increased, e.g. the energy threshold is about 50 TeV on the full moon night. The energy threshold can be further reduced by optimizing the trigger algorithm for the moon night, which is in progress.

Conclusions
Eighteen cameras were assembled and tested in a laboratory of Yunnan University, and mounted to telescopes that have been operated for months. As a major component of the LHAASO experiment, the preliminary on-site performance was studied for all the cameras. The most significant improvement of the SiPM-based camera, versus the traditional PMT-based camera is that all of the cameras can be operated even during a full-moon night. The gains of all SiPMs are stabilized within 2% by bias voltage adjustment and temperature compensation over a typical range of 18 • C. The camera pixels are optimized for maximizing the photon collection area by using the relative smaller SiPMs coupled with square-shaped funnels which fully fill up the FoV of the camera.
To achieve the desired performance, tools and jigs were designed and produced to enable successful assembly. Before putting all assembled sub-clusters together as the whole camera, the features of all pixels are calibrated and tested, including the temperature response, the response charge vs. bias voltage, the non-linearity over dynamic range, the signal resolution and DCR. Characterization and construction procedures and corresponding test facilities, such as the 1D-System and the Temp-System, were established. The characterized parameters of all pixels are recorded in a database used in on-line operation and off-line analysis.
Through the past few observational seasons, eighteen telescopes have collected about 100 million cosmic ray events that will be used to measure the energy spectra of cosmic ray protons and other species around 1 PeV. The telescopes can also provide cross calibration of the energy measurement of primary gamma-rays to KM2A in the energy range from 100 TeV to a few PeV.
The success summarized here, and the fact that 18,432 SiPMs have been operated regularly, will eventually establish the large-scale application of SiPMs in IACTs.
Foundation of China (U1738211, 11675204 and 11905240), Yunnan University, and Grant RTA 6280002 from Thailand Science Research and Innovation. We give thanks to the Swiss Foundation Ernst and Lucie Schmidheiney for having provided the light funnels of the first camera, which were produced according to a technique developed by the University of Geneva. We wish to express our gratitude to the students who helped us fabricating, testing, and operating the SiPM cameras and WFCTA.