SPHERE-3 Cherenkov Telescope

• SPHERE-3 is an airborne Cherenkov telescope that employs dual-depth detection using both snow-reflected and direct Cherenkov light to investigate cosmic-ray mass composition in the PeV range.
• The instrument features a modified Schmidt optical system for the reflected-light channel and evolving direct-light detector options to enhance energy, core, and directional reconstructions.
• Extensive simulation campaigns with tools like CORSIKA and Geant4 drive its design, reducing degeneracies among energy, geometry, and mass parameters for more precise event-by-event analysis.

SPHERE-3 is an airborne Cherenkov telescope project in the SPHERE series, developed to study primary cosmic rays in the PeV domain by combining two observational channels for the same extensive air shower: Cherenkov light reflected from a snow-covered surface and direct Cherenkov light registered at flight altitude. Across the current design papers, the instrument is described as a two-detector system intended for event-by-event primary-mass assignment, with the reflected-light channel providing robust energy, shower-core, and arrival-direction reconstruction, and the direct-light channel supplying additional mass-sensitive image information and improved directional constraints. The project builds on the SPHERE-2 heritage, uses Lake Baikal snow as the reflective screen in the Chudakov method, and is supported by large CORSIKA-based simulation campaigns on the Lomonosov-2 supercomputer (Galkin et al., 2024, Galkin et al., 21 Jul 2025, Ziva et al., 9 Mar 2026).

1. Scientific aims and project lineage

The central scientific objective of SPHERE-3 is to determine the mass composition of primary cosmic-ray nuclei in the PeV range, especially across the region of the all-particle spectrum commonly associated with the “knee.” In the project descriptions, this goal is formulated not merely as an ensemble-composition problem but as an event-by-event mass-assignment problem for individual extensive air showers. The stated motivation is that composition trends in the $1\text{–}100\ \mathrm{PeV}$ range constrain acceleration and propagation scenarios for Galactic cosmic rays, while some design and simulation papers frame the broader science target as $1\text{–}1000\ \mathrm{PeV}$ (Galkin et al., 2024, Ivanov et al., 2024).

SPHERE-3 is explicitly positioned as the successor to balloon-borne SPHERE-2. The earlier instrument established the viability of the reflected-Cherenkov technique over snow and produced results near $\sim 10\ \mathrm{PeV}$. SPHERE-3 retains that reflected-light capability but adds a second, upward-looking detector for direct light from the same shower. This dual registration is repeatedly described as a form of “3D detection,” because the shower is sampled at two distinct atmospheric depths: at the flight altitude and after reflection from the snow surface (Bonvech et al., 10 May 2025, Galkin et al., 21 Jul 2025).

A recurrent design principle is to construct mass-sensitive observables that depend weakly on hadronic-interaction-model details. In the reflected channel, this means using lateral-distribution and image-shape descriptors; in the direct channel, it means exploiting the morphology of the angular image. The combination is intended to reduce degeneracies among energy, geometry, and shower-development variables that limit single-modality composition measurements (Galkin et al., 2024, Bonvech et al., 23 Jul 2025).

2. Dual-depth detection principle

SPHERE-3 applies Chudakov’s method by observing Cherenkov light from charged particles in an extensive air shower after reflection from snow, while also recording Cherenkov light that reaches the payload directly. The reflected-light telescope looks downward toward the snow surface, and the direct-light detector looks upward. In the project notes, the reflective surface is the snow cover in the Lake Baikal area, with the snow level modeled at $455\ \mathrm{m}$ above sea level in one of the reconstruction studies (Bonvech et al., 23 Jul 2025).

The physical basis is standard Cherenkov emission. The Cherenkov condition and angle are written as

$$\beta n > 1, \qquad \cos \theta_c = \frac{1}{\beta n},$$

and the Frank–Tamm yield is given as

$$\frac{d^2N}{dx\,d\lambda} = 2\pi \alpha \left(1 - \frac{1}{\beta^2 n^2(\lambda)}\right)\frac{1}{\lambda^2}.$$

These relations determine the angular and spectral structure of the light field later processed by the two SPHERE-3 channels (Ivanov et al., 2024, Bonvech et al., 23 Jul 2025).

The dual-depth concept is significant because the two channels weight the same shower differently. The direct-light detector measures the angular distribution of Cherenkov light at flight altitude, which is closely connected to shower longitudinal development and therefore to mass-sensitive quantities. The reflected-light telescope measures the snow-projected lateral distribution and the temporal structure across its mosaic, which are particularly useful for reconstructing primary energy, shower-core position, and arrival direction. The collaboration’s interpretation is that fitting both channels together reduces degeneracies among $E_0$, geometry, $X_{\max}$, and mass (Galkin et al., 21 Jul 2025).

A recurrent clarification in the SPHERE-3 literature concerns the phrase “direct Cherenkov.” In this project, direct light refers to Cherenkov emission from shower particles in the atmosphere, not to the pre-interaction Cherenkov emission of an unscathed primary nucleus. That distinction is stated explicitly, because the mass-sensitive signal used by SPHERE-3 in the PeV domain is tied to shower development rather than to the lower-energy primary-nucleus direct-Cherenkov technique (Galkin et al., 2024).

Channel	Observable	Reported role
Reflected-light telescope	Snow-reflected Cherenkov image and time structure	Energy, core position, arrival direction, first-pass mass-sensitive criterion
Direct-light detector	Angular image of direct Cherenkov light at flight altitude	Mass-sensitive image features and directional refinement
Dual registration	Same EAS at two depths	Reduced energy–geometry–mass degeneracy

3. Instrument architecture and evolving optical design

The system architecture consists of two synchronized instruments carried on the same airborne platform. Early concept papers describe a reflected-light telescope based on a classical mirror plus PMT mosaic and a direct-light telescope implemented as a compact lens+CCD camera. Later simulation and capability papers discuss a reflected-light Schmidt optical system with a correction lens and a segmented camera using SiPMs, while the direct-light telescope remains under study with several options considered. This suggests that the optical and photosensor implementation remains under optimization rather than being frozen in a single final configuration (Galkin et al., 2024, Ivanov et al., 2024, Bonvech et al., 23 Jul 2025).

For the reflected-light channel, the most developed optical description is a modified Schmidt system with an aspherical primary mirror and a corrector plate intended to suppress spherical aberration, with an entrance window described as an acrylic corrector plate of diameter $1700\ \mathrm{mm}$ and thickness $5\text{–}30\ \mathrm{mm}$. The same design note reports an SiPM mosaic with sensitive diameter $1\text{–}1000\ \mathrm{PeV}$0, overall mosaic diameter $1\text{–}1000\ \mathrm{PeV}$1, a target effective aperture area of at least $1\text{–}1000\ \mathrm{PeV}$2, and a current-geometry effective aperture of $1\text{–}1000\ \mathrm{PeV}$3 after accounting for shading by the mosaic and electronics. The field of view is stated as at least $1\text{–}1000\ \mathrm{PeV}$4, and the optical-resolution goal is at least 2000 pixels across the focal plane (Ivanov et al., 2024).

For the direct-light channel, the hardware remains less fixed. One project note uses current working assumptions of a lens+CCD camera with $1\text{–}1000\ \mathrm{PeV}$5 effective area, field of view $1\text{–}1000\ \mathrm{PeV}$6, and pixel angular size $1\text{–}1000\ \mathrm{PeV}$7. Another note specifies a zenith-pointing direct-light detector with a single-lens configuration of field-of-view radius $1\text{–}1000\ \mathrm{PeV}$8, an alternative 7-lens hexagonal mosaic with field-of-view radius $1\text{–}1000\ \mathrm{PeV}$9, and collecting area under consideration of $\sim 10\ \mathrm{PeV}$0 per lens for the single-lens configuration (Galkin et al., 2024, Galkin et al., 21 Jul 2025).

The airborne platform also evolved across the design sequence. Whereas SPHERE-1 and SPHERE-2 were balloon-borne, SPHERE-3 is described as UAV-borne or drone-borne in the dual-detection studies. The preferred flight altitudes emphasized in current performance estimates are $\sim 10\ \mathrm{PeV}$1, $\sim 10\ \mathrm{PeV}$2, and $\sim 10\ \mathrm{PeV}$3, with an initial simulation stage also including $\sim 10\ \mathrm{PeV}$4 (Bonvech et al., 10 May 2025, Bonvech et al., 23 Jul 2025).

Optical optimization has already affected the design. Geant4 modeling of the reflected-light detector showed that, before optimization, about $\sim 10\ \mathrm{PeV}$5 of detected light originated outside the nominal field of view and up to $\sim 10\ \mathrm{PeV}$6 of mosaic segments responded even when light was incident from one sector. Absorbers added around each pixel suppressed parasitic reflections and out-of-field light, after which the carpet pattern was correctly reproduced and parasitic temporal lines were strongly reduced (Bonvech et al., 23 Jul 2025).

4. Simulation framework, databases, and high-performance computing

SPHERE-3 development is simulation-driven. The software chain combines CORSIKA for air-shower generation, custom photon-selection and mapping code, Geant4 for optical transport through the detector, and Python-based orchestration for automated production. The chain is modular: CORSIKA generates shower and Cherenkov-photon outputs; a specialized FORTRAN application selects photons relevant for photoelectron production and maps them to the telescope aperture; Geant4 propagates photons through optics and materials; and a Python co-routine supervises parameter sweeps, job submission, integrity checks, and aggregation (Ivanov et al., 2024).

The simulation domain spans multiple primary species, energies, observation altitudes, hadronic models, and atmospheric profiles. One design paper uses $\sim 10\ \mathrm{PeV}$7, He, N, Al, S, and Fe primaries at $\sim 10\ \mathrm{PeV}$8, $\sim 10\ \mathrm{PeV}$9, $455\ \mathrm{m}$0, and $455\ \mathrm{m}$1, zenith angles $455\ \mathrm{m}$2 in $455\ \mathrm{m}$3 steps, and the U.S. Standard, AT223, AT511, and South Pole MSIS-90-E atmospheric profiles, with QGSJET01 and QGSJETII-04. A later capability paper reports CORSIKA runs with QGSJET01, QGSJETII-04, and SIBYLL 2.3, five atmosphere models, and a current Open Refined Cherenkov Image Database containing more than 100,000 unique images (Ivanov et al., 2024, Bonvech et al., 23 Jul 2025).

The recorded observables are tailored to SPHERE-3 geometry. At snow level, the simulations store spatial-temporal distributions of photoelectrons on a $455\ \mathrm{m}$4 grid with $455\ \mathrm{m}$5 spatial steps and $455\ \mathrm{m}$6 time resolution. At instrument altitudes of $455\ \mathrm{m}$7, $455\ \mathrm{m}$8, and $455\ \mathrm{m}$9, they store angular, spatial, and temporal distributions of Cherenkov photons, with the angular resolution upgraded from $$\beta n > 1, \qquad \cos \theta_c = \frac{1}{\beta n},$$0 to $$\beta n > 1, \qquad \cos \theta_c = \frac{1}{\beta n},$$1, spatial resolution $$\beta n > 1, \qquad \cos \theta_c = \frac{1}{\beta n},$$2, and temporal structure in 13 bins of $$\beta n > 1, \qquad \cos \theta_c = \frac{1}{\beta n},$$3 each (Bonvech et al., 23 Jul 2025).

The database scale is correspondingly large. The parallel-CORSIKA paper reports single-event binary results of about $$\beta n > 1, \qquad \cos \theta_c = \frac{1}{\beta n},$$4, compressible to less than $$\beta n > 1, \qquad \cos \theta_c = \frac{1}{\beta n},$$5, and a curated database already exceeding $$\beta n > 1, \qquad \cos \theta_c = \frac{1}{\beta n},$$6 events and roughly $$\beta n > 1, \qquad \cos \theta_c = \frac{1}{\beta n},$$7. In the event-production chain, each unique event can be cloned 100 times by shifting the shower axis relative to the telescope axis to extend statistics for detector-response studies (Ziva et al., 9 Mar 2026, Bonvech et al., 23 Jul 2025).

The scale of this simulation program led directly to modifications of the underlying CORSIKA production workflow. At primary energies above about $$\beta n > 1, \qquad \cos \theta_c = \frac{1}{\beta n},$$8 and slightly below $$\beta n > 1, \qquad \cos \theta_c = \frac{1}{\beta n},$$9, single-core runs on the Lomonosov-2 supercomputer often exceeded queue time limits and were killed before completion. To address this, the collaboration developed a multithreaded master–slave version of CORSIKA-7 with Cherenkov output tailored to SPHERE-3. The sequential stage tracks the primary and then the “leader,” defined as the most energetic secondary, until the leader energy falls to approximately $$\frac{d^2N}{dx\,d\lambda} = 2\pi \alpha \left(1 - \frac{1}{\beta^2 n^2(\lambda)}\right)\frac{1}{\lambda^2}.$$0 of the primary or a high-energy gamma appears in the stack; at that point the particle stack is partitioned among slave threads or processes and Cherenkov outputs are aggregated into multidimensional histograms at the snow and at $$\frac{d^2N}{dx\,d\lambda} = 2\pi \alpha \left(1 - \frac{1}{\beta^2 n^2(\lambda)}\right)\frac{1}{\lambda^2}.$$1 (Ziva et al., 9 Mar 2026).

On an AMD Ryzen 9 5950X development host with 16 cores and 128 GB RAM, the reported wall-clock time for $$\frac{d^2N}{dx\,d\lambda} = 2\pi \alpha \left(1 - \frac{1}{\beta^2 n^2(\lambda)}\right)\frac{1}{\lambda^2}.$$2 proton events decreased from about 20 hours in the sequential version to about 7.5 hours in the parallel version, corresponding to $$\frac{d^2N}{dx\,d\lambda} = 2\pi \alpha \left(1 - \frac{1}{\beta^2 n^2(\lambda)}\right)\frac{1}{\lambda^2}.$$3, with overall speedups $$\frac{d^2N}{dx\,d\lambda} = 2\pi \alpha \left(1 - \frac{1}{\beta^2 n^2(\lambda)}\right)\frac{1}{\lambda^2}.$$4. The same study reports physical validation through lateral distribution functions consistent with the serial version within expected statistical fluctuations and mean Cherenkov-photon-count differences of $$\frac{d^2N}{dx\,d\lambda} = 2\pi \alpha \left(1 - \frac{1}{\beta^2 n^2(\lambda)}\right)\frac{1}{\lambda^2}.$$5 for protons and $$\frac{d^2N}{dx\,d\lambda} = 2\pi \alpha \left(1 - \frac{1}{\beta^2 n^2(\lambda)}\right)\frac{1}{\lambda^2}.$$6 for iron across $$\frac{d^2N}{dx\,d\lambda} = 2\pi \alpha \left(1 - \frac{1}{\beta^2 n^2(\lambda)}\right)\frac{1}{\lambda^2}.$$7, attributed to intrinsic shower fluctuations and sample-size differences (Ziva et al., 9 Mar 2026).

5. Reconstruction methods and quantitative performance

The reflected-light telescope is treated as the main reconstruction instrument. Its image and time structure are used to estimate the shower axis on the snow, the arrival direction, the primary energy, and a first mass-sensitive observable. In one reconstruction study, the shower core is estimated from the projection of the time-integrated signal and an axial-symmetric fit around the maximum; for events whose axis lies within the field of view, the reported core-position resolution is $$\frac{d^2N}{dx\,d\lambda} = 2\pi \alpha \left(1 - \frac{1}{\beta^2 n^2(\lambda)}\right)\frac{1}{\lambda^2}.$$8 at $$\frac{d^2N}{dx\,d\lambda} = 2\pi \alpha \left(1 - \frac{1}{\beta^2 n^2(\lambda)}\right)\frac{1}{\lambda^2}.$$9 altitude and $E_0$0 at $E_0$1. The arrival direction from the reflected channel, obtained from the time structure projected onto the snow and fitted by a quadratic function, reaches an accuracy of about $E_0$2 (Bonvech et al., 23 Jul 2025).

The energy estimator in the reflected channel is based on an axially symmetric lateral distribution function. The capability study states that the integral of the best-fit LDF and the distance from the telescope to the shower axis are compared to precomputed model dependencies; if the mass is known, energy is estimated from mass-specific dependencies, otherwise from a combined set. For a sample of 13,500 events consisting of $E_0$3, N, and Fe at $E_0$4, $E_0$5, and $E_0$6, the mean energy error is reported as $E_0$7 for unknown mass and $E_0$8 for known mass before axis-containment selection, and $E_0$9 for unknown mass and $X_{\max}$0 for known mass after applying the plane-versus-axial-symmetric $X_{\max}$1-selection together with removal of events reconstructed on the two outer pixel layers (Bonvech et al., 23 Jul 2025).

False-maximum rejection is a notable part of the reflected-light reconstruction logic. A related study defines

$X_{\max}$2

where $X_{\max}$3 and $X_{\max}$4 quantify plane and axially symmetric fits and $X_{\max}$5, $X_{\max}$6 are their degrees of freedom. In a 200-event test with 100 true and 100 false maxima, this filtering removed $X_{\max}$7 of false maxima with only $X_{\max}$8 loss of true maxima, while the average energy error improved from $X_{\max}$9 to $1700\ \mathrm{mm}$0 (Bonvech et al., 10 May 2025).

For mass classification, the reflected-light channel uses LDF-shape information. One paper defines a criterion

$1700\ \mathrm{mm}$1

optimized over $1700\ \mathrm{mm}$2 and $1700\ \mathrm{mm}$3, while another paper reports one-dimensional separation using an integral-shape parameter. Quantitatively, for $1700\ \mathrm{mm}$4 showers at zenith $1700\ \mathrm{mm}$5, the reflected-only misclassification rates are reported as $1700\ \mathrm{mm}$6 of protons misclassified as nitrogen at the $1700\ \mathrm{mm}$7-vs-$1700\ \mathrm{mm}$8 boundary and $1700\ \mathrm{mm}$9 of iron showers misclassified as nitrogen at the $5\text{–}30\ \mathrm{mm}$0-vs-$5\text{–}30\ \mathrm{mm}$1 boundary (Bonvech et al., 23 Jul 2025).

The direct-light detector uses the angular image rather than the snow footprint. A central feature is the major-axis length $5\text{–}30\ \mathrm{mm}$2, treated as a Hillas-style parameter. Direct-image studies show that, for $5\text{–}30\ \mathrm{mm}$3 and $5\text{–}30\ \mathrm{mm}$4 showers at a core distance of $5\text{–}30\ \mathrm{mm}$5 and observation heights of $5\text{–}30\ \mathrm{mm}$6, $5\text{–}30\ \mathrm{mm}$7, and $5\text{–}30\ \mathrm{mm}$8, classification using $5\text{–}30\ \mathrm{mm}$9 yields $1\text{–}1000\ \mathrm{PeV}$00-$1\text{–}1000\ \mathrm{PeV}$01 and $1\text{–}1000\ \mathrm{PeV}$02-$1\text{–}1000\ \mathrm{PeV}$03 misclassification probabilities in the range $1\text{–}1000\ \mathrm{PeV}$04, with a trend in which higher observation levels favor separation among heavier nuclei and lower altitudes favor light–intermediate separation (Galkin et al., 2024).

More advanced direct-channel processing conditions the criterion on geometry. By using a grid over instrument–axis distance and azimuth, together with distance-dependent absolute photon-count thresholds per pixel, the reported direct-only misclassification errors improve to $1\text{–}1000\ \mathrm{PeV}$05. The same study reports direct-light direction estimates from image asymmetry: for $1\text{–}1000\ \mathrm{PeV}$06 showers at $1\text{–}1000\ \mathrm{PeV}$07 instrument–axis distance, the residual angular error is approximately $1\text{–}1000\ \mathrm{PeV}$08 using the intensity maximum and $1\text{–}1000\ \mathrm{PeV}$09 using the center of gravity for ideal angular-distribution input, and approximately $1\text{–}1000\ \mathrm{PeV}$10 and $1\text{–}1000\ \mathrm{PeV}$11, respectively, for realistic camera images, assuming the axis distance is known (Bonvech et al., 23 Jul 2025).

The project’s distinctive performance claim is the benefit of dual classification. For events seen by both detectors, two features are combined: the major-axis length from the direct image and the ratio of inner-to-outer integrals from the reflected image. An optimized linear separator in the two-dimensional feature space reduces the reported misclassification to $1\text{–}1000\ \mathrm{PeV}$12 under the specified $1\text{–}1000\ \mathrm{PeV}$13-altitude geometry constraints. A related dual-depth note summarizes the same trend more compactly as misclassification of about $1\text{–}1000\ \mathrm{PeV}$14 for $1\text{–}1000\ \mathrm{PeV}$15-$1\text{–}1000\ \mathrm{PeV}$16 and $1\text{–}1000\ \mathrm{PeV}$17-$1\text{–}1000\ \mathrm{PeV}$18 with the $1\text{–}1000\ \mathrm{PeV}$19 combination (Bonvech et al., 23 Jul 2025, Galkin et al., 21 Jul 2025).

6. Geometry, systematics, and current status

The geometry of dual detection is restrictive and strongly shapes the design. At $1\text{–}1000\ \mathrm{PeV}$20 altitude, the direct-light detector is most useful for shower-axis distances in the $1\text{–}1000\ \mathrm{PeV}$21 ring at flight level; at smaller distances the images become too compact, and at larger distances the photon density becomes too low for the assumed collecting area. Simultaneously, the shower axis on the snow must lie within the visible region of the reflected-light telescope. Under these constraints, the reported dual-detection fraction is about $1\text{–}1000\ \mathrm{PeV}$22 or about one-third at $1\text{–}1000\ \mathrm{PeV}$23, decreasing with altitude. This is the stated reason that $1\text{–}1000\ \mathrm{PeV}$24 is preferred in the current optimization (Bonvech et al., 10 May 2025, Galkin et al., 21 Jul 2025).

Atmospheric and surface effects are among the dominant systematic sources. The studies explicitly identify atmospheric transparency and aerosol content, snow albedo and BRDF, instrumental calibration and alignment, optical aberrations, and pixel-response nonuniformity as key limitations. Several design decisions are framed as mitigations: the use of multiple atmospheric profiles in CORSIKA, the emphasis on shape parameters rather than absolute light yield, optical baffling to suppress parasitic reflections, and dual-mode consistency checks between direct and reflected observables (Galkin et al., 2024, Bonvech et al., 23 Jul 2025).

At the formal level, the dual-depth framework is often written through separate direct and reflected forward models, with snow reflectivity $1\text{–}1000\ \mathrm{PeV}$25 entering only the reflected channel. One note expresses this schematically as

$1\text{–}1000\ \mathrm{PeV}$26

$1\text{–}1000\ \mathrm{PeV}$27

with the interpretive point that the two channels constrain the same shower through different path weights. A plausible implication is that the direct channel can help decorrelate atmospheric-transmission and surface-reflectivity uncertainties that are otherwise entangled in reflected-light-only reconstruction (Galkin et al., 21 Jul 2025).

A second misconception addressed by the project literature concerns the maturity of the hardware. Several critical quantities are still not fixed across the current papers: exact direct-light optical parameters, pixel pitch, final $1\text{–}1000\ \mathrm{PeV}$28, wavelength band, trigger logic, detailed electronics shaping, exact concurrency framework in the HPC code, and explicit snow reflectance parameterization. Effective area, trigger efficiency, event rates, dynamic range, and full end-to-end waveform realism are also not yet reported in the design notes. The published results are therefore best read as simulation-backed capability estimates for an instrument under active optimization rather than as the final specifications of an already frozen apparatus (Ivanov et al., 2024, Bonvech et al., 23 Jul 2025, Ziva et al., 9 Mar 2026).

Within those limits, the current SPHERE-3 concept is defined by a stable core: a mobile airborne system above snow, dual Cherenkov registration at two atmospheric depths, simulation-guided optimization on Lomonosov-2, and reconstruction strategies that combine reflected-light robustness with direct-light mass sensitivity. In that sense, SPHERE-3 advances the SPHERE program from single-depth reflected-light observation to a dual-depth Cherenkov methodology aimed at event-by-event cosmic-ray composition in the PeV domain (Bonvech et al., 10 May 2025, Galkin et al., 21 Jul 2025).