SPHERE-3: Dual-Channel Cherenkov Detector

• SPHERE-3 is a high-energy cosmic-ray project using dual-channel Cherenkov detection to accurately measure primary cosmic-ray composition in the PeV range.
• It integrates a reflected-light telescope with a direct-light detector to jointly capture shower profiles, enhancing energy reconstruction and mass assignment.
• Key features include a Schmidt telescope design, advanced trigger algorithms, and extensive Monte Carlo simulations to drive precise calibration and performance modeling.

SPHERE-3 is the next stage of the SPHERE project in high-energy cosmic-ray physics, aimed at measuring the mass composition of primary cosmic rays through the registration of Cherenkov light from extensive air showers (EAS). In published descriptions, its scientific target spans the PeV domain from the “knee” region upward, with the central project framing given as $1\text{–}1000\ \mathrm{PeV}$, while some methodological papers focus on $1\text{–}100\ \mathrm{PeV}$ and event-by-event primary-mass assignment. The project builds on the balloon-borne SPHERE-2 experiment and develops a dual-channel technique in which Cherenkov light reflected from a snow surface is combined with direct Cherenkov light from the shower itself, with detector design, reconstruction, and performance estimation driven by large-scale Monte Carlo modeling (Galkin et al., 2024, Chernov et al., 21 Jul 2025).

1. Scientific context and project lineage

SPHERE-3 is motivated by the long-standing problem of primary cosmic-ray composition in the energy interval that includes the spectral “knee” and extends toward the region where a Galactic–extragalactic transition may occur. Published project papers identify this interval as central for testing rigidity-dependent Galactic acceleration, leakage from the Galaxy, and the onset of extragalactic components; they also emphasize that hadronic-interaction uncertainties remain substantial in this regime (Ivanov et al., 2024, Chernov et al., 21 Jul 2025).

The project continues the observational concept proposed by A. E. Chudakov: detection of atmospheric Cherenkov light after reflection from a snow-covered surface. SPHERE-1 and SPHERE-2 implemented this concept with balloon-borne detectors over snow or ice, and SPHERE-2 at Lake Baikal demonstrated the viability of the reflected-light method, produced an energy spectrum, and extracted the light $(p+\mathrm{He})$ component (Galkin et al., 2024, Chernov et al., 21 Jul 2025).

SPHERE-3 is presented as a qualitative extension of that program rather than a simple scale-up. Published descriptions explicitly state that the project is optimized for mass composition, not merely for energy spectrum and arrival direction, and that its defining novelty is a dual-depth or “3D detection” strategy in which the same EAS is observed both through reflected Cherenkov light from the snow surface and through direct Cherenkov light at flight altitude (Galkin et al., 21 Jul 2025, Bonvech et al., 10 May 2025).

2. Detection principle and dual-atmospheric measurement

The reflected-light channel uses a Schmidt-type optical system that looks down at a snow-covered surface. In this geometry, the snow acts as a “quasi-Lambertian, high-albedo screen,” and the focal-plane image encodes the lateral distribution of Cherenkov photons on the ground. Project papers describe this as a quasi-calorimetric method because the integrated Cherenkov photon density at ground scales nearly linearly with primary energy and is less dependent on interaction models than in classical ground arrays (Chernov et al., 21 Jul 2025).

The direct-light channel emerged from SPHERE-2 experience. During SPHERE-2 analysis, direct Cherenkov flashes entering through small gaps between mirror segments were identified as strongly sensitive to shower development and hence to primary mass. SPHERE-3 therefore incorporates direct-light registration as a deliberate subsystem rather than a parasitic effect (Chernov et al., 21 Jul 2025, Ivanov et al., 2024).

In the project’s methodological formulation, the reflected Cherenkov Light Telescope (RLT) and the Direct Light Detector (DLD) observe the same shower at two atmospheric depths. The RLT reconstructs the ground-projected lateral distribution and timing front; the DLD reconstructs an angular image of the shower at flight altitude. This two-depth observation is designed to disentangle geometry from shower-development effects and thereby improve primary-mass estimation (Galkin et al., 21 Jul 2025).

The dual-detection geometry is constrained. For a baseline case at 500 m flight altitude, the RLT requires the shower axis to hit the snow within $R<175$ m of the telescope projection, while the DLD is most effective for $100~\mathrm{m}<R<200~\mathrm{m}$ at flight level and zenith angles up to about $20^\circ\text{–}25^\circ$. Published modeling gives a joint-detection fraction of about one third of RLT-detected events at 500 m, with that fraction decreasing at larger altitude (Galkin et al., 21 Jul 2025).

3. Detector architecture and subsystem design

The current reflected-light telescope is described as a Schmidt system with an aspheric primary mirror of diameter $D = 2.2\ \mathrm{m}$, an aspheric corrector of diameter 850 mm, and a SiPM mosaic located 592 mm from the mirror. The effective entry window area is $1.92\ \mathrm{m}^2$, the field of view is $\pm 20^\circ$, and the camera comprises 2653 pixels arranged as 379 segments of 7 SiPMs each. In the status paper, the full detector weight is given as 100 kg and the maximum altitude as 1500 m on a heavy UAV platform (Chernov et al., 21 Jul 2025).

Earlier simulation work described the optical concept in slightly more generic terms as a modified Schmidt telescope with an aspherical mirror, an acrylic corrector plate, effective aperture $1.9\ \mathrm{m}^2$, optical resolution of at least 2000 pixels, and a field of view of at least $1\text{–}100\ \mathrm{PeV}$0. That paper also modeled shading by the sensor mosaic and mechanical structure in Geant4 because those effects alter photon transport and image formation (Ivanov et al., 2024).

A prototype system has already been built. The prototype is described with a mirror diameter of 0.8 m, effective area $1\text{–}100\ \mathrm{PeV}$1, 259 pixels, maximum altitude 500 m, and total UAV-borne weight 15 kg. It is used to test SiPM segments, FADC boards, trigger electronics, cooling, and data-exchange algorithms with UAV platforms (Chernov et al., 21 Jul 2025).

Several direct-light detector options have been explored. Two early variants were abandoned: a coded-aperture pinhole design because photon statistics per pixel were too low and large pinholes degraded reflected-light performance, and a small central lens sharing the main camera because the angular resolution was insufficient. Two remaining options are under detailed study. Option C uses a single lens with collecting area $1\text{–}100\ \mathrm{PeV}$2, focal length $1\text{–}100\ \mathrm{PeV}$3, and field-of-view half-angle $1\text{–}100\ \mathrm{PeV}$4. Option D uses seven such lenses in a hexagonal arrangement, total area $1\text{–}100\ \mathrm{PeV}$5, focal length $1\text{–}100\ \mathrm{PeV}$6, and optical resolution $1\text{–}100\ \mathrm{PeV}$7 (Chernov et al., 21 Jul 2025).

The trigger and readout design is already part of the published project architecture. For reflected light, SPHERE-3 uses a two-stage trigger: a topological trigger that searches for neighboring pixels above an adaptive threshold, followed by a convolutional neural network that classifies short time–space buffers to reject spurious SiPM cross-talk events. For direct light, the trigger is based on photon counts per pixel in a time bin; for Option C the night-sky background estimate is parameterized as

$1\text{–}100\ \mathrm{PeV}$8

with $1\text{–}100\ \mathrm{PeV}$9, $(p+\mathrm{He})$0, $(p+\mathrm{He})$1, and $(p+\mathrm{He})$2 (Chernov et al., 21 Jul 2025).

4. Simulation infrastructure and computational workflow

The SPHERE-3 literature gives unusual prominence to simulation as a primary project component. A 2024 software paper described a computational complex linking primary type, energy, direction, interaction model, atmosphere, and observation geometry to final Cherenkov images on the focal plane. Its workflow is CORSIKA for EAS development and Cherenkov production, a post-processing stage for photon distributions and event cloning, Geant4 for optical transport through the telescope, and Python orchestration for automated production (Ivanov et al., 2024).

Later work reformulated this as a multi-level parallel pipeline with four named stages: shower generation in CORSIKA, event decoding and cloning in C++/OpenMP, ray tracing in Geant4 MT, and image approximation in Python with multiprocessing and iminuit. The key design property is “natural atomicity”: each event is processed independently at every stage, which permits near-linear scaling under parallel execution while keeping shared data read-only and mutable state isolated per worker (Ivanov et al., 9 Mar 2026).

The simulation bank itself is large and heterogeneous. Published ORCHID datasets include multiple hadronic interaction models—QGSJET01, QGSJETII-04, and Sibyll 2.3—together with five CORSIKA atmospheric models. One detailed capability study reports more than 100,000 unique Cherenkov-light distributions, with simulated energies at $(p+\mathrm{He})$3, primaries including $(p+\mathrm{He})$4, and cloning of each distribution 100 times by shifting the shower axis relative to the telescope (Bonvech et al., 23 Jul 2025). Another pipeline paper reports simulation grids including $(p+\mathrm{He})$5, nuclei $(p+\mathrm{He})$6, and 100 base showers per parameter point (Ivanov et al., 9 Mar 2026).

The computational cost of Cherenkov-enabled EAS simulation is high enough that a dedicated parallel version of CORSIKA was developed for the project. That paper reports that on a $(p+\mathrm{He})$7 proton shower, the sequential version required about 20 hours per event, while the parallel version with master plus 10 slaves reduced this to about 7.5 hours, corresponding to a speedup of about 2.7; across tested energies and primaries the speedup ranged from 2.2 to 3.6. The same paper states that the collaboration’s event database already contains about $(p+\mathrm{He})$8 events and occupies about 100 TB, with individual event files of about 6 GB uncompressed and less than 1 GB compressed (Ziva et al., 9 Mar 2026).

5. Reconstruction methods and projected performance

The reflected-light reconstruction chain proceeds from a spatio-temporal image on the mosaic to a corrected lateral distribution on the snow, then to an axially symmetric LDF fit. In the conceptual dual-detection paper, this RLT-only chain is credited with primary-energy resolution of 15–20%, shower-core uncertainty of about 5 m on the snow at 500 m flight altitude, arrival-direction uncertainty of $(p+\mathrm{He})$9, and three-group mass misclassification of about 0.30 (Galkin et al., 21 Jul 2025).

The direct-light detector primarily refines geometry and mass. A key direct-light observable is the Hillas-like image length $R<175$0, or major-axis length, which is strongly sensitive to primary mass but also depends on the detector–axis distance $R<175$1 and the azimuth $R<175$2. Using RLT-based geometry as input, the DLD is described as improving the arrival-direction uncertainty to about $R<175$3 in the dual reconstruction scheme (Galkin et al., 21 Jul 2025).

In the status paper, dual mass classification is formulated in a two-parameter space consisting of the direct-light image major-axis length and a reflected-light inner/outer integral ratio. With simple linear boundaries, preliminary per-class errors are reported as 0.22 and 0.15 for $R<175$4–$R<175$5 separation, and 0.19 and 0.14 for $R<175$6–Fe separation when both channels are combined; the corresponding reflected-only and direct-only errors are larger (Chernov et al., 21 Jul 2025).

A separate 2025 performance paper gives more granular capability estimates. For reflected light alone, energy reconstruction based on the LDF integral and core distance yields average errors of about 34% when the primary mass is unknown and 27% when it is known, before removing bad-axis events. After applying analytic axis-quality cuts, those values improve to about 15% and 8%, respectively. The same paper gives direct-light directional accuracies of $R<175$7 using the image maximum and $R<175$8 using the center of gravity for a 10 PeV shower at 100 m core distance, and reports combined direct-plus-reflected mass misclassification in the range 14–22% (Bonvech et al., 23 Jul 2025).

That paper also introduces an explicit quality parameter for rejecting events whose axis lies outside the field of view:

$R<175$9

where $100~\mathrm{m}<R<200~\mathrm{m}$0 and $100~\mathrm{m}<R<200~\mathrm{m}$1 are fit-quality measures for planar and axially symmetric approximations and $100~\mathrm{m}<R<200~\mathrm{m}$2 are the corresponding degrees of freedom. In the reported study, the combined rejection criteria eliminate 99% of events with erroneously placed axes on the mosaic, at the cost of removing 24–40% of otherwise valid events (Bonvech et al., 23 Jul 2025).

6. Project status, limitations, and outlook

As of the 2025 status paper, the optical and mechanical design of the main reflected-light detector is described as essentially complete, the prototype telescope has been built, the direct-light detector design has been narrowed to Options C and D, and the trigger and DAQ algorithms have been implemented and tested in simulations. The same paper states that the CNN-based second-level reflected-light trigger reduces false triggers by “several orders of magnitude” in Monte Carlo (Chernov et al., 21 Jul 2025).

At the same time, the published record makes clear that SPHERE-3 remains a development-stage project. The 2024 software paper notes that the then-current simulation chain mainly stopped at photon-to-pixel hits and that realistic electronics and reconstruction layers were still planned. It also notes that the base CORSIKA sample per configuration was modest—100 events—so the framework relied on cloning or transposition of showers to increase effective statistics, with the associated assumption of translational reuse of Cherenkov patterns over the snow surface (Ivanov et al., 2024).

Several limitations recur across the literature. Detailed calibration procedures are not yet fully documented. The direct-light detector is still under optimization, including the unresolved issue of suitable UV-sensitive sensors for Option C. Some simulation studies treat parts of the detector response in simplified form, including idealized photon detection or partial electronics modeling. The dual-detection fraction decreases with altitude, so the gain from a larger footprint must be balanced against the reduced number of jointly reconstructable events (Chernov et al., 21 Jul 2025, Galkin et al., 21 Jul 2025).

The project’s planned next steps are well defined. Published outlook sections describe full integration of the reflected and direct detectors on a heavy UAV capable of $100~\mathrm{m}<R<200~\mathrm{m}$3, commissioning flights over snow-covered surfaces, validation of PSF and alignment across the field of view, timing calibration and synchronization between detectors, and development of more advanced multivariate or machine-learning reconstruction methods that use the full information content of both images rather than simple two-parameter classifiers (Chernov et al., 21 Jul 2025, Galkin et al., 21 Jul 2025).

Taken together, these publications define SPHERE-3 as a simulation-driven, dual-channel Cherenkov project aimed at high-quality measurements of primary cosmic-ray composition around and above the knee. Its distinctive claim is not merely greater optical throughput than SPHERE-2, but the attempt to combine quasi-calorimetric reflected-light energy estimation with direct-light sensitivity to shower development in a unified reconstruction framework (Galkin et al., 21 Jul 2025, Chernov et al., 21 Jul 2025).