The optical module of Baikal-GVD

In April 2015, the first cluster of Baikal-GVD was deployed in Lake Baikal and put into operation. It comprises eight strings. Each string consists of 24 optical modules. An optical module is a detection element of Baikal-GVD; it includes a Hamamatsu R7081-100 photomultiplier tube with a high quantum sensitivity. We describe the design of the optical module, the front-end electronics, and the laboratory characterization and calibration.


INTRODUCTION
The new-generation Baikal-GVD neutrino telescope is being created now in Lake Baikal on the basis of many year experience of НТ200 detector operation [1,2]. Its effective volume is about a cubic kilometer [3][4][5][6][7][8][9]. The telescope has a modular structure formed by 12 stand-alone systems-clusters of vertical strings of optical modules. The modular structure of the telescope allows data acquisition already at early stages of the deployment; provides for scalability; and, if changing scientific priorities, the adaptation of the telescope structure to new requirements.
An optical module (OM) is the key component of the telescope recording system. A R7081-100 (Hamamatsu) photomultiplier tube (PMT) is a photodetector in an OM. Along with OM electronics, it is placed inside a high-pressure resistant glass case. A PMT records Vavilov-Cherenkov radiation generated by charged particles in water. The data (photon recording time and the number of photoelectrons (p.e.)) from a section of OMs serve as the basis for the retrieval of the event type (single muon, group of muons, and cascade shower), the track direction, and the interaction energy.
The strings are integrated into clusters. Each cluster of the telescope is a stand-along detector capable of operating as part of the integrated setup and independently. In April 2015, the first Baikal-GVD cluster DUBNA was deployed in Lake Baikal and started continuous operation. The cluster configuration is shown in Fig. 1. The cluster consists of eight strings of 24 OMs spaced by 40 m.
The work describes the optical modules: design, principle of operation, and the results of the study of its parameters.

PECULIARITIES OF BAIKAL-GVD DATA
ACQUISITION SYSTEM An OM section is the main structural unit of the Baikal-GVD data acquisition system [10][11][12]. The section is an independent detection unit; it includes systems for radiation recording, signal processing, cal- † Deceased.

PHYSICS OF PARTICLES AND NUCLEI LETTERS
Vol. 13 No. 6 2016 AVRORIN et al. ibration, trigger formation, and data transmission. The organization of the data acquisition system of a section allows different OM configurations. OMs can be fixed at different distances from each other individ-ually or pairwise. Several OM sections can be mounted on one string. The section configuration (Fig. 2) is now the basis for the setup creation. The section consists of 12 OMs located with a step of 15 m   [13]. Synchronization, power supply, and data-transmission channels of the sections are combined in a string communication module and are connected by a cable line ~1200 m long to the cluster control center. The above approach to the construction of the Baikal-GVD data-acquisition system determines the composition of OM electronic components, their functionality, and some design features of deepwater modules of the telescope.
OM DESIGN AND ANGULAR PARAMETERS The first optical modules for deepwater neutrino telescopes were designed within the DUMAND project [14]. The approach was developed in the IceCube [15,16], ANTARES [17], and KM3NeT [18] projects. A Baikal-GVD optical module is shown in Fig. 3. A PMT with a semispherical photocathode is placed inside a deepwater VITROVEX glass sphere (Nautilus Marine Service GmbH, Germany) made of borosilicate glass 42 cm in diameter. An optical contact between the photocathode and the glass sphere is supported with a transparent (refractive index is 1.404) two-component silicone gel SilGel 612A/B (Wacker-Chemie GmbH, Germany). It reliably fixes the PMT in the deepwater case and ensures the required elasticity. To decrease the effect of the terrestrial magnetic field on PMT operation, it is protected with a screen (mesh) of annealed permalloy, which decreases the magnetic field effect on the PMT signal from ~20 to 5-8% during rotation (depending on the photocathode exposure position: central part or periphery).
A deepwater connector is mounted on the OM case, as is a vacuum port used for OM pumping out to a pressure of ~0.7 atm, which is sufficient for the reliable connection of two hemispheres of the deepwater case. A SubConn LPBH5FSS panel-mount deepwater low-profiled female five-point connector made of stainless steel in a neoprene case is intended for the PMT analog signal transmission, OM operation control, and supply with power. The OM electronics is mounted directly at the PMT base. An OM is fixed to a string with the help of a special frame (Fig. 3).
A Hamamatsu R7081-10010-dynode PMT (Japan) with a semispherical photocathode 25 cm in diameter is used as a photodetector. Main PMT specifications are given in Table 1.
The PMT photocathode shape and OM design determine the angular dependence of the OM response to irradiation. The dependence of OM response on the angle of light incidence on PMT photocathode is used for simulating the detector response. This parameter was measured at an automated test bench, which rotates an OM to a preset angle with a step motor. The test bench was located in a light-protected room. An OM was placed in a water tank to exclude the distortion of the angular characteristic by light reflection and refraction and kept in the dark for no less than 12 h. The PMT photocathode was illuminated by a plane-parallel light flux from an isotropic light source based on a pulsed (pulse length is ~5 ns) Kingbright L7113 blue LED (wavelength of 470 nm) spaced 3 m apart from the module under study. The charge of PMT pulses induced by LED flares was measured. To estimate the systematic error, which could be connected with instable LED intensity, the measurements were carried out for three successive complete rotations relative to the light source and the   Fig. 4. For maximal OM rotation angles (the photocathode is oriented in the direction opposite to the light source), the measurement accuracy is affected by the reflection from light-absorbing material on the tank wall the farthest from the light source (up to 10% of the signal measured).

OM OPERATION PRINCIPLE
OM electronics includes high-voltage power supply, a voltage divider, a PMT signal amplifier, a controller, and an LED calibration system. The electronic unit is shown in Fig. 5 and its block diagram is in Fig. 6.
The TRACO POWER PHV12-2.0K2500P highvoltage power supply (Japan) provides the PMT divider with positive polarity voltage (the maximal output current is 1 mA). This supply has a low noise level (8 mV peak-peak, ~20 MHz frequency band) and highly stable output voltage (0.05%); the value of the latter can be varied in the range from 0 to 2.5 kV by the controlling voltage in the 0-2.5 V range with a step of 1 mV. This ensures the accuracy of the PMT working voltage selection no worse than 1 V. Field tests showed the high reliability of these units. The PMT interdynode voltages were selected according to the manufacturer's recommendations. The total resistance of the divider is 18 MOhm. The voltage divider circuit is shown in Fig. 7.    The PMT gain coefficient can be set equal to 10 7 by choosing the divider voltage. For a single photoelectronic signal to attain a required magnitude, the signal is additionally amplified in PMT. The amplifier is mounted at one board with the PMT voltage divider and has two channels. The first channel is used for measurements and amplifies single photoelectronic signals by ~14 times up to ~25 mV. The second channel amplifies PMT signals fed to the OM controller noise pulse counter by about 21 times to provide a constant load of the measuring channel, which determines the rate of operation of the detector trigger. Its maximal value is limited by the capacity of the data acquisition and transmission system. Local variations in the Baikal water fluorescence intensity can increase the counting rate of individual channels 5-10 times. The monitoring of the counting rate of the channels allows the rapid correction of the trigger system parameters (the number of coincidences and the channel recording thresholds), up to exclusion of a channel from the triggering procedure.
For temporal and amplitude calibration of the measuring channel, there are two Kingbright L7113 blue LEDs in an OM, with a wavelength at the radiation maximum of 470 nm and a pulse length of ~5 ns. The possibility of independent control of the LED intensity and quite low crosstalks between LED channels (<1%) allow checking the measuring channel linearity. The technique used for the channel linearity check does not require light sources with linear characteristics. The parameters Q(L1 + L2)/(Q(L1) + Q(L2)) are used for the check, where Q is the signal charges measured during PMT illumination by the first and the second LEDS in turn and by both LEDs simultaneously. This approach significantly simplifies the OM electronics and allows controlling the channel linearity during OM operation within the telescope. The OM control system has been designed by SNIIP-Aunis company, Ltd. (Russia) on the basis of a SiLabs C8051F121 microcontroller. It controls the PMT voltage, frequency and intensity of calibration LEDs, and other parameters of the electronic unit. An OM is controlled through a communication (control) line based on the RS-485 interface.
A 90-m hybrid deepwater cable KST (RK50 + 9 × 0.15) (Pskovgeokabel, Russia) is an important part of the OM measuring channel, which connects an OM and the central module of a section. The cable includes RK50 coaxial conductor and nine wires for power supply and OM operation control.
The OM output signal shape is determined by parameters of PMT, amplifier, and coaxial cable. Figure 8 shows typical shapes of pulses that arrived from an OM, which corresponds to signals of ~1, ~22, 48, and ~1140 p.e. The mean values of pulse parameters from this OM are presented in Table 2. In the linear region, the OM pulse shape is mainly determined by propagation through the long coaxial cable, which, in addition, acts as a natural filter increasing the PMT signal length (FWHM) from ~10 to ~30 ns. This signal width is optimal for its following digitizing in an ADC with a sampling rate of 200 MHz (~10 points per pulse). In the nonlinear region of measuring channel operation >10 2 p.e., the signal shape is distorted due to  the saturation of the PMT anode current and restriction of the signal amplitude amplifier by 3 V. PMT signal attenuation in the cable is ~30%. The gain factor the OM measuring channel is 10 8 with consideration for signal attenuation in the cable at a PMT dynode system gain factor of ~10 7 and an amplifier gain factor of ~14.

STUDY OF OM PARAMETERS
A series of tests is planned to be carried out before OM mounting in Lake Baikal to ensure their reliable and long operation as part of the neutrino telescope.
The tests include checking the functionality of individual OM elements, checking OM electronics under a high temperature, and a complex check for OM in all operation modes. The OM testing and calibration were carried out at a test bench based on a four-channel digital oscillograph LeCroy HDO4034 (passband is 300 MHz, sampling rate is up to 2.5 GHz). OMs were placed in a light-protected housing shielded from the electromagnetic radiation of a (50 Hz) power main. The housing includes up to four OMs simultaneously. The OMs were connected to the oscillograph entries by 90 m deepwater cables used in the telescope. LEDs mounted in OMs served as calibrating light sources. The test bench operation is completely automated. The software is based on Windows OC.
During the first step of the testing, the PMT divider voltage was selected so as to ensure amplification of the OM measuring channels (hereinafter, the channel) up to ~10 8 . This, as is mentioned above, corresponds to a gain factor of the OMT dynode system of ~10 7 . The channel amplification was determined from measurements of single-photoelectron (s.p.e.) charge distributions of PMTs in the LED s.p.e. illumination mode (the signal recording probability was ~10% at a recording threshold of 0.2. pulse amplitude). For the measurements, the oscillograph was triggered by the LED pulse generator of the OM controller. The base magnitude and channel noise contribution were estimated at switch-off LEDs when triggering also by the pulse generator. Figure 9 shows a characteristics s.p.e. spectrum and OM distribution over the s.p.e. resolution. The first peak on the s.p.e. spectrum corresponds to the base distribution measured at the switch-off LED and the second peak corresponds to the distribution of the single-electron PMT pulses distinguished while recording LED-generated flares. The s.p.e. resolution is defined as the ratio of the standard deviation of the distribution to the mean. It should be noted that the contribution of multiphotoelectronic pulses overestimates the s.p.e. resolution by ~20%. Figure 10 shows the dependence of the channel gain factors on the PMT divider voltage and the channel distribution over the selected gain coefficient. The amplification at a level of ~10 8 is attained at the voltage from 1150 to 1750 V for the PMTs studied.
The OM temporal resolution was also measured in s.p.e. and defined as the standard deviation of the s.p.e. signal recording time distribution (during the Signal, mV Time, ns signal recording, a sliding threshold equal to a half of pulse amplitude was used). Figure 11 shows a typical time spectrum for an OM (left) and OM distribution over the temporal resolution (right).
The linearity range is an important parameter of a channel. Two main sources of channel nonlinearity could be mentioned: limitation of the maximal signal amplitude by the channel amplifier and PMT saturation, which changes the signal shape at the PMT exit. To study the form of the channel nonlinearity function, PMTs were illuminated by LED flares of different brightnesses. The variable S = Q/(N pe × Q pe ) (Q is the measured pulse charge, Q pe is the s.p.e. pulse charge, and N pe is the number of p.e. that form a pulse) was used as a parameter that determines the degree of the channel nonlinearity. To estimate the number of p.e., data on the magnitude of s.p.e. charge were used, as was the technique for PMT illumination by two independent sources capable of illuminating a photocathode both individually and together. Successive doubling of the light flare intensity allows the extrapolation of the channel conversion ratio measurements to the nonlinear region of channel operation. For this, an iterative method is used for matching the light flare intensity of each LED to the channel response measured under conditions of joint operation of LEDs. Thus, a combination of light signals from two LEDs under different combinations of flare intensities allows the generation of pulses with a preset number of p.e. The dependence S of the number of p.e. (saturation curves) are shown in Fig. 12 for 87 OMs. The linearity   The PMT saturation effect not only limits the range of channel linearity, but also affects the measurement accuracy of the recording time of high-amplitude pulses. The pulse recording time is fixed at the instant where the signal magnitude attains a half of its maximum. In the nonlinear region of channel operation, the pulse recording time at half maximum starts depending on the signal amplitude. The time-amplitude dependence is charac-terized by the parameter Δt, i.e., the deviation of the recording time from the rated value. Figure 13 shows the characteristic dependence of Δt on the number of pulseforming p.e.; Δt does not exceed 1 ns in the channel linearity range. The OM distribution over the threshold number of p.e., for which Δt < 1 ns, is shown in the right part of Fig. 13.
The coincidence in time of signals from neighbor OMs with the thresholds ~0.5 and 3 p.e. is one of the main trigger conditions for the hardware discrimination of physical events in a Baikal-GVD cluster. From this point of view, the fraction of high-amplitude signals in OMT noises is an important PMT parameter. The high-amplitude component of PMT noises is caused by after-pulses [19], which are formed by ions that originate from electron-residual gas interactions and are accelerated in the PMT dynode system. The contribution of the after-pulses in a PMT signal was estimated with the use of short LED flares (~5 ns). The total charge of the after-pulses N pe afterpulse was measured 30 ns to 50 μs after the initial pulse with a step of 500 ns for flares of different brightnesses. The after-pulse charge increases near linearly with the flare brightness. The fraction of after-pulses is characterized by the parameter R = N pe afterpulse /N pe initial pulse × 100%. The characteristic dependence of R on the time after the initial pulse is shown in Fig. 14.
The OM distribution over the total after-pulse charge in the range from 0.3 to 50 μs is shown in Fig. 15. The fraction of after-pulses is 10-15% for most OMs. Today, 80 tested OMs are mounted in Lake Baikal within the Baikal-GVD cluster. All the modules of the OMs mounted operate correctly. In situ measurements of the after-pulse effect on the counting rate of the trigger system are carried out. These measurements are to be the basis for the formulation of the after-pulse fraction criterion for PMT selection for use in the telescope.

TEMPORAL CALIBRATION OF CHANNELS
Physical events recorded by the telescope are retrieved from the pulse amplitudes and recording times in the detector channels. The calibration of the amplitude parameters of the channels is based o n the PMT s.p.e. spectra measurements by the technique described above. The temporal calibration of the channels is carried out using two complementary approaches [20]. The first approach is based on the measurements of delays between pulses of neighbor OMs initiated by LED flares in one of them. The data on OM position inside the telescope is used for the temporal calibration. The second approach is based on the measurements of individual signal delays in PMT and cable communications. The second approach can be used during OM tests and calibration in laboratory conditions.
To measure PMT delays, the operation mode is provided in the OM electronic unit, where the LED triggering is synchronized with the generation of a check pulse in the controller. This pulse arrives at the entry to the PMT amplifier along with a LED flareinduced signal (Fig. 16). In this case, the measurements were carried out in two sessions: with a check pulse and with a LED pulse. However, when OM operates within the telescope, another operation mode is used: a LED signal is delayed to a fixed time of about 200 ns (one of the functions of the OM controller), and the delay between two pulses in one event is measured. The PMT delay is defined as the difference between LED pulse and check pulses. In addition to PMT delay (60-80 ns), the pulse delay includes the delays between the check pulse and LED driver trigger signals (~2 ns), the photon-transit time from a LET to the photocathode surface (~2 ns), the amplifying path delay (~16 ns), and the delay in OM cable communications (~3 ns). These delays are time-independent and approximately equal for all OMs. Figure 17 shows the dependence of the signal delays of 87 OMs on the high PMT voltage that corresponds to a gain factor of the dynode system of ~10 7 . It is seen that the pulse delay is mainly determined by PMT divider voltage.
As is mentioned above, an OM channel includes a 90-m deepwater cable for analog signal transmission. Different lengths of the cables results in a spread in the time delays in the channels. Figure 18 shows the cali-   bration results for time delays of deepwater cables. The mean spread in the delays is ~1 ns. However, it should be noted that the results are presented for a lot of deepwater cables. The delays in different lots of the cables systematically differ by up to 5 ns.

CONCLUSIONS
Baikal-GVD OMs were designed in view of requirements for reliability and ergonomics of operation: maximal simplicity of assembling and mounting. An automated test bench was used during the stage of preparation for industrial production for OM verification; complex laboratory tests were carried out for a lot of 87 OMs. The test program included the analysis of s.p.e. spectra and temporal resolution, the behavior of time and amplitude parameters of the channel when recording high-intensity light pulses (up to 3 × 10 3 p.e.), and the probability of origination of PMT after-pulses. The resulting data are required for a detail simulation of the Baikal-GVD response.
Our study allows a conclusion about a quite complete correspondence of the OM parameters to requirements for telescope photodetectors. The OM output signal linearly depends on the light flare brightness in the signal region up to ~50 p.e. (this region determines the accuracy of retrieval of the parameters of tracks of particles detected). In addition, the signalrecording time delay is independent of the signal amplitude in this range. For high-intensity signals, a technique is developed that allows consideration for the channel saturation effect and retrieval of the light flare brightness with accuracy no worse that 10% in the region up to 10 3 p.e. The tests showed that ~10% of PMTs have a high fraction of after-pulse charge. At present, in situ studies of the after-pulse effect on the operation of the telescope trigger system is carried out, which will be the basis for the development of criteria for selecting PMTs for the neutrino telescope.