Absolute calibration of the JEM-EUSO photodetection modules

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Introduction
Ultra-High-Energy Cosmic Rays (UHECRs) are the most energetic particles in the Universe with energies above 10 18 eV. Although ground-based installations have observed these energetic particles for decades, their source and acceleration mechanisms remain largely unknown, and their study is observationally challenging because of their extremely low flux at Earth's surface [1].
The goal of the JEM-EUSO (Joint Experiment Missions for Extreme Universe Space Observatory) international collaboration is to extend the study of UHECRs by operating for the first time an observatory from space, which allows us to observe a very large volume of atmosphere at once with one single instrument. A first attempt to measure UHECRs from orbit was carried out in the TUS experiment [2][3][4], now integrated in the global JEM-EUSO program. For a review and update on this program, see Parizot et al. [5](this conference).
The Extreme Universe Space Observatory on a Super Pressure Balloon 2 (EUSO-SPB2) [6] is the third and most advanced balloon mission undertaken by the JEM-EUSO collaboration. EUSO-SPB2 is built on the experience of previous stratosphere missions: EUSO-Balloon [7] and EUSO-SPB [8], and of the Mini-EUSO space mission currently active onboard the International Space Station (ISS) * e-mail: trofimov@apc.in2p3.fr [9]. It is particularly relevant in the context of future largescale orbital missions, such as the proposed K-EUSO [10] and POEMMA [11], of which EUSO-SPB2 can be considered a pathfinder.
While the EUSO-SPB2 payload is composed of two complementary instruments, namely a Fluorescence Telescope (FT) and a Cherenkov Telescope (CT), this paper focuses on the calibration of the former, which is expected to allow the detection of extensive air showers from ultrahigh-energy cosmic rays through fluorescence light for the first time. (See also Cummings et al. [12], this conference, for more details.)

Structure of the Fluorescence Telescope
The telescope is built according to the Schmidt scheme and has 6 mirror segments with a radius of curvature of 1659.8 mm and an effective focal length of 860 mm. The aperture is 1 m diameter, the field of view is 37.4 • ×11.4 • , for one pixel 0.2 • ×0.2 • and the direction of the FOV is nadir [13]. The FT camera consists of 3 photodetection modules (PDMs), each PDM contains 9 elementary cells (EC -units). A PDM and an EC-unit are shown in Figure 1. The main parts of each EC are 4 multi-anode photomultiplier tubes (MAPMTs) Hamamatsu type R11265 with 64 channels of registration. Thus each PDM has 64×4×9 = 2304 channels of registration. The MAPMT signals are read by SPACIROC3 specialized chips designed to count single photoelectron pulses for a certain time [14]. The basis of the chip is an amplitude discriminator.
An important task of the pre-flight preparation of the equipment is the pixel-by-pixel calibration of such a multichannel detector.

The method of pre-flight PDM calibration
The calibration uses a controlled light source, either in full illumination mode (all pixels at once) or in single pixel illumination mode (with a collimator). The first method provides pixel efficiency and allows us to determine the optimal value of the electronics threshold used to measure a single photoelectron pulse for each pixel (see Sect. 3.2), and the second is used in conjunction with a mechanical scanning procedure to determine response of the photosensitive area to local illumination, also allowing to estimate the actual borders of each pixel and its internal structure. The principle is shown in Figure 2: the PDM is placed in a black box, with negligible background. The PDM is connected to the computer, which also has connections to a power-meter for precise light intensity control and to an XY-movement system providing precise positioning of the light source in front of the PDM. The light control system uses an integrating sphere with three windows: one is used to received light from LED (input), another one to illuminate the PDM pixels (output), and the third one to measure the light intensity inside the sphere with a NIST photodiode (control). The output window is connected to a collimator, which allows us to illuminate a surface even smaller than one pixel. The intensity of the output light is in a constant ratio with the intensity of light on the control NIST. Thus, it can be precisely calibrated at high intensity, and then used at low intensity for detailed calibration in single photon counting mode.

S-curve measurements
When a photon hits the photocathode of the MAPMT, it generates an internal electron cascade which results in a signal on the anode. This signal is read by an ASIC (SPACIROC3) which counts one pulse if the signal amplitude is above a given threshold, adjustable through a DAC value. The so-called "S-curve" is the curve giving the number of counts as a function of that threshold or DAC. S-curves were studied in details for the Mini-EUSO project previously [15]. At low threshold (high DAC), the ASIC essentially counts electronic noise (pedestal). At higher thresholds (lower DAC), it counts only real photoelectrons, with an efficiency given by the number of counts per incoming photons. If the threshold increases, the number of counts decreases (i.e. some photoelectrons are missed). The ASIC can adjust its threshold through a combination of two DAC values: a "DAC-10" (10 bits, from 0 to 1023), set at the level of the MAPMT (for all pixels) and a "DAC-7" (7 bits, from 0 to 127), set at the level of individual pixels (before the pedestal). Figure 3 (left) demonstrates the S-curve for one pixel in DAC-10 mode. The dashed line is the S-curve derivative, i.e. amplitude distribution of single photoelectron pulses (at DAC-10 ≈ 370). In the right Figure 3 S-curve plots for all 2304 pixels in DAC-10 mode with individual DAC-7 thresholds adjusted so that all pedestals appear around the same DAC-10 value.

PDM scans
After setting individual thresholds, the full scans for each PDM were obtained. Each full scan has a resolution 200 × 200 points, it allows us to see details in the internal structure of the pixel (Figure 4). Full scans were made for all PDMs using 2 LEDs with 375 nm or 405 nm wavelengths, and with 2 different values of cathode high voltage: with a normal one around 1 kV and a reduced one for bright events. Precise scans were obtained for several MAPMTs with a resolution of 100 × 100 points revealing additional details on the internal structure of the photocathode, down to sub-pixel resolution. The left panel of Figure 5 shows a response map of a MAPMT where, for each position, the sum photon count of the 4 brightest pixels were used to derive the total detection efficiency at that position ("top-4 channel response map"). In the right panel of Figure 5 there is the "maximum response map" (photon count rate of the brightest pixel only). This figure reveals that border pixels are larger than the central ones -causing "border effects" in full illumination mode (Figure 8).
It is interesting to note that the structure of the pixel's efficiency depends on the direction of scanning (vertically or horizontally). It is demonstrated in Figure 6. On the right panel (horizontal scan) the shape of the curve for each pixel is smooth with one maximum. On the left figure (vertical scan) there is a dip in the efficiency in the center of each pixel.

Pixel sizes accounting
The size of a pixel is an important parameter of the photodetector and should be investigated and taken into account because of the possible nonuniformity of the MAPMT. Area of the pixel is included in the formula for calculating the number of photons during calibrations: where N ph is the average number of photon received and counted in one Gate Time Unit = 1 µs (GTU), c cross is the cross calibration coefficient (ratio of two NIST photodiodes measurements), λ -wavelength of light source,   (equal for each pixel), on the right panel, renormalized efficiency, taking into account the individual pixel areas is demostrated. The efficiency map appears more uniform.

Pile-up effect
For high light intensity the superimposition of pulses begins to play a significant role (so called "pile-up" effect) because the time interval between consecutive photoelectrons is smaller than the time resolution of the ASIC (a few ns). The number of counts thus saturates and eventually decreases as the photon rate increases (more and more photons being missed). Figure 9 shows saturation and consequtive decrease of number of counts/GTU as a function of incoming photons/GTU. On the left panel the results of simulations are shown. The expected average number of counts per GTU is defined by the following expression: N p.e. = εN ph × exp(−εN ph δt/t GT U ) (2) where N ph is the average number of photon received and counted in one GTU, ε is the detection efficiency, δt is the double pulse resolution (dead time) and t GT U is GTU. The source of photons is assumed as poissonian. The right panel shows a measured pile-up curve in the relatively low incoming photon flux, which corresponds to the left part of the simulated curve.

Summary
All three PDMs of the EUSO-SPB2 fluorescence telescope have been calibrated with high precision in differ-ent modes. Detailed information about the size and efficiency of each pixel will be used in the analyses of extensive air showers and other events detected during the mission, which is expected to be launched in spring 2023 from Wanaka (New-Zealand). The calibration methods presented here will also be useful for the future missions of the JEM-EUSO Collaboration and can be applied more generally to any instrument using MAPMTs.
D.T. acknowledges the support by the French space agency CNES, the Vernadski program (BGF scolarship) and the Interdisciplinary Scientific and Educational School of Moscow University "Fundamental and Applied Space Research"