Dual-Channel Cosmic-Ray Tomography

• The paper demonstrates that fusing dual cosmic-ray observables significantly enhances imaging resolution and material discrimination across varied applications.
• Dual-channel cosmic-ray tomography is a methodology that combines distinct detection channels—such as scattering and absorption—to address inverse problems by exploiting complementary physical signals.
• It offers practical benefits by reducing geometric ambiguities and achieving multi-sigma separation in scenarios like cargo verification, structural imaging, and atmospheric anisotropy mapping.

Dual-channel cosmic-ray tomography analysis denotes a class of reconstruction and inference methods that combine two physically distinct observables, detector streams, or emission pathways derived from cosmic rays in order to improve geometric recovery, material discrimination, or directional inference. In the volumetric-imaging literature, the most common pairings are multiple Coulomb scattering with absorption or transmission, scattering with energy-loss observables, and primary muon tracking with secondary-particle signatures; in other contexts, the same logic appears as dual-instrument sky reconstruction or dual-pulse radio analysis from geomagnetic and Askaryan emission (Georgadze, 2024, Zhao et al., 18 Jun 2026, Prada et al., 8 Aug 2025, collaboration et al., 2017, Ali et al., 17 Sep 2025). Across these formulations, the central premise is that no single channel fully constrains the inverse problem: scattering is sensitive to radiation length and hence to $Z$-dependent structure, absorption and energy loss encode stopping and $\rho Z/A$-related contrast, secondary production traces interaction topology, and multi-view or multi-vertex timing reduces geometric degeneracy (Georgadze, 2024, Dasgupta et al., 4 Apr 2026).

1. Conceptual scope and channel pairings

In current usage, “dual-channel” does not denote one fixed hardware architecture. Rather, it denotes the joint use of two complementary data channels that probe different aspects of the same target or sky. In cargo verification, the pairing is explicitly “multiple Coulomb scattering (MCS) with absorption/transmission analysis,” where angular deflection provides nuclear-charge sensitivity and stopped-muon information provides mass-density–dependent stopping (Georgadze, 2024). In Raw-Hit Muon Tomography, the pair is RHMT-S and RHMT-E: a scattering channel that reconstructs radiation-length contrast $\lambda = 1/X_0$ from hit residuals, and an energy-loss channel that reconstructs the electron-density-related contrast $s = \rho Z/A$ from per-muon log momentum loss (Zhao et al., 18 Jun 2026). In shower-aware learned reconstruction, the two streams are scattering kinematics and secondary electromagnetic shower multiplicity (Dasgupta et al., 4 Apr 2026). In shipping-container studies, the pairing is muon scattering tomography with secondary particle analysis, using photons, neutrons, and electrons generated inside the volume of interest (Prada et al., 8 Aug 2025). In atmospheric ray tomography for low-$Z$ media, the two modalities are cosmic muons and electrons, separated by Particle Track Filtering and combined in Multi-Modality Tomographic Reconstruction (Anbarjafari et al., 2021).

The same structural idea extends beyond material imaging. “Combined Analysis of Cosmic-Ray Anisotropy with IceCube and HAWC” treats the northern and southern hemisphere observatories as a dual-instrument tomographic system that shares a single sidereal relative-intensity field while fitting instrument-specific acceptances and isotropic rates (collaboration et al., 2017). The ARA Station-2 double-pulse candidate uses an early in-air geomagnetic pulse and a later in-ice Askaryan pulse as two reconstruction channels tied to different vertices and ray paths through air, firn, and ice (Ali et al., 17 Sep 2025). A related but distinct dual-use formulation appears in the RPC scattering experiment that uses the same scattering-angle observable for both cosmic-ray composition fitting and a muon-philic dark-matter search (Liu et al., 31 Jul 2025).

Channel pairing	Principal observables	Representative context
Scattering + absorption/transmission	angular deflection, stopped-muon rate, transmission ratio	cargo verification
Scattering + energy loss	hit-residual covariance, $\ln(p_{\rm in}/p_{\rm out})$	RHMT
Scattering + secondary signatures	PoCA or kinematics with photons/neutrons/electrons or shower multiplicity	cargo and structural imaging
Muons + electrons	scattering and transmission VDMs after Particle Track Filtering	low-$Z$ ART
Dual detector or dual emission pathways	shared sky intensity; geomagnetic + Askaryan timing	anisotropy mapping; ARA

This range of usage suggests that dual-channel analysis is best understood as a general inference strategy rather than a single algorithmic family.

2. Physical observables and forward models

The dominant volumetric channel in muography remains multiple Coulomb scattering. For cargo tomography, the Highland approximation is written as

$$\sigma_\theta(x) \approx \frac{13.6\,{\rm MeV}}{\beta c p}\sqrt{\frac{x}{X_0}}\left[1 + 0.038 \ln\!\left(\frac{x}{X_0}\right)\right],$$

with $\beta \approx 1$ for cosmic muons, $p$ the momentum, $\rho Z/A$0 the traversed path length, and $\rho Z/A$1 the radiation length (Georgadze, 2024). In related formulations, the scattering-density parameter is

$\rho Z/A$2

with $\rho Z/A$3 taken as nominal in the cargo study (Georgadze, 2024). The same physics underlies the silicon-strip scattering tracker, the dry-cask $\rho Z/A$4CT studies, and the RHMT scattering channel (Keizer et al., 2018, Liu, 2018, Zhao et al., 18 Jun 2026).

Absorption and transmission form a second major channel. In the combined cargo analysis, stopped muons are represented by a line-of-response model,

$\rho Z/A$5

where $\rho Z/A$6 is the predicted number of absorbed muons in line of response $\rho Z/A$7, $\rho Z/A$8 is the path length through voxel $\rho Z/A$9, and $\lambda = 1/X_0$0 is the stopping power (Georgadze, 2024). In P$\lambda = 1/X_0$1MA, transmission is encoded geometrically rather than through an explicit attenuation fit: each muon defines a transmission point on an imaging plane, and the transmission ratio is

$\lambda = 1/X_0$2

with the reference taken either from a “without sample” run or from incident points in four-detector mode (Qin et al., 18 Dec 2025). That work states explicitly that the TP-to-IP ratio “is not equal to the physical transmissivity,” although it “monotonically encodes areal density under matched conditions” (Qin et al., 18 Dec 2025).

Secondary-particle channels exploit information that standard muography often discards. In the shipping-container simulation, photons, neutrons, and electrons are back-traced linearly from detector intercepts through the volume of interest to form voxel-wise density scores after subtraction of an empty-container background (Prada et al., 8 Aug 2025). In “Revealing Secondary Particle Signatures in PoCA-Based Muography,” PoCA points reconstructed at detector planes are interpreted as signatures of secondary particles produced in detectors and surrounding materials, especially the roof, rather than as mere noise (Zhang et al., 5 Jul 2025). In SA-DSVN, the secondary channel is formalized as 40 voxelized shower-multiplicity features, including per-plane electron, positron, gamma, shower-energy, spatial-spread, and time-spread information (Dasgupta et al., 4 Apr 2026).

Other domains use different physical pairings. In ARA, the two channels are radio pulses generated by distinct mechanisms: an in-air geomagnetic pulse and an in-ice Askaryan pulse. Ray propagation is modeled by

$\lambda = 1/X_0$3

which makes the dual-pulse delay field sensitive both to shower geometry and to firn/ice refractive structure (Ali et al., 17 Sep 2025). In all-sky anisotropy analysis, the target quantity is the relative-intensity field

$\lambda = 1/X_0$4

expanded in spherical harmonics with angular power spectrum $\lambda = 1/X_0$5, where partial-sky coverage produces pseudo-$\lambda = 1/X_0$6 mode coupling through the window function (collaboration et al., 2017).

3. Statistical reconstruction and data-fusion strategies

A defining characteristic of dual-channel analysis is that the channels are fused at the level of a likelihood, a statistical classifier, or a shared latent representation. In the HAWC+IceCube anisotropy analysis, the expected counts are modeled as

$\lambda = 1/X_0$7

with $\lambda = 1/X_0$8 the isotropic rate term, $\lambda = 1/X_0$9 the detector acceptance, and $s = \rho Z/A$0 the sky relative intensity in local coordinates. The likelihood

$s = \rho Z/A$1

is generalized to the product over both datasets, sharing a single sky $s = \rho Z/A$2 while fitting independent acceptances and isotropic-rate terms for HAWC and IceCube (collaboration et al., 2017). This directly addresses partial-sky mode coupling, summarized by

$s = \rho Z/A$3

In rapid cargo verification, the scatter–absorption pair is fused through a two-component Gaussian Mixture Model in the feature vector $s = \rho Z/A$4, with

$s = \rho Z/A$5

and classification based on a log-likelihood ratio

$s = \rho Z/A$6

The study defines its reported “$s = \rho Z/A$7 accuracy” from the largest non-overlapping confidence ellipse between the fitted Gaussians in the $s = \rho Z/A$8 plane (Georgadze, 2024).

RHMT adopts a measurement-domain formulation. RHMT-S projects out the unknown straight track and models the residuals with a Fermi–Eyges covariance; marginalizing the unknown scattering scale gives a blank-calibrated Student-$s = \rho Z/A$9-type likelihood

$Z$0

while RHMT-E models

$Z$1

and reconstructs $Z$2 with a convex Huber objective and total-variation regularization (Zhao et al., 18 Jun 2026). The paper also writes a unified objective,

$Z$3

making explicit the additive combination of the two channels (Zhao et al., 18 Jun 2026).

Learned dual-stream fusion is exemplified by SA-DSVN, which processes a $Z$4 scattering tensor and a $Z$5 shower tensor through independent encoders and fuses them through four-head cross-attention at the bottleneck (Dasgupta et al., 4 Apr 2026). Atmospheric ray tomography uses a less formal but still structured fusion: PTF isolates muon-dominated and electron-dominated track populations, and MMTR constructs multiple volume density maps from scattering and transmission before edge detection and connected-component labeling (Anbarjafari et al., 2021). Shipping-container dual-channel fusion uses normalization, Gaussian sharpening, 3D smoothing, threshold-based segmentation, volumetric center alignment, and voxel-wise summation of segmented secondary and MST maps (Prada et al., 8 Aug 2025).

These methods differ algorithmically, but they share a common statistical idea: each channel constrains a different nuisance structure, and fused inference is more stable than any single-channel summary.

4. Detector architectures, geometry, and calibration requirements

Dual-channel tomography has been implemented on detector systems ranging from large shipping-container portals to compact RPC and silicon trackers. In the cargo scatter–absorption study, the Muon Tomography Station uses two tracking modules above and below the container; each module has two planes of plastic scintillator of dimension $Z$6, plane spacing $Z$7, and upper-to-lower module separation $Z$8. Simulations assume $Z$9 detector efficiency and Gaussian hit smearing with FWHM values $\ln(p_{\rm in}/p_{\rm out})$0, $\ln(p_{\rm in}/p_{\rm out})$1, and $\ln(p_{\rm in}/p_{\rm out})$2 (Georgadze, 2024). P$\ln(p_{\rm in}/p_{\rm out})$3MA reduces the hardware burden further: its minimal two-detector setup places RPC1 at $\ln(p_{\rm in}/p_{\rm out})$4 and RPC2 at $\ln(p_{\rm in}/p_{\rm out})$5, each with $\ln(p_{\rm in}/p_{\rm out})$6 sensitive area and $\ln(p_{\rm in}/p_{\rm out})$7 single-plane spatial resolution, while four-detector variants add incident-track and angle-gating capability (Qin et al., 18 Dec 2025).

Compact RPC systems support other dual-channel uses. The four-layer RPC stack for composition and muon-philic dark-matter searches has inter-layer spacings $\ln(p_{\rm in}/p_{\rm out})$8, $\ln(p_{\rm in}/p_{\rm out})$9, and $Z$0, active area $Z$1, fiducial scattering volume $Z$2, and $Z$3 per-hit spatial resolution (Liu et al., 31 Jul 2025). The secondary-signature PoCA study uses the same fixed detector-plane $Z$4 positions, $Z$5, $Z$6, $Z$7, and $Z$8, and shows that energy-deposition-weighted centroids can improve effective spatial resolution while simultaneously making the system sensitive to secondary-particle contamination (Zhang et al., 5 Jul 2025).

Silicon-strip and scintillating-fiber systems emphasize precision tracking. The semiconductor MST tracker uses ATLAS SCT modules with $Z$9 pitch, module spacing $$\sigma_\theta(x) \approx \frac{13.6\,{\rm MeV}}{\beta c p}\sqrt{\frac{x}{X_0}}\left[1 + 0.038 \ln\!\left(\frac{x}{X_0}\right)\right],$$0, station separation $$\sigma_\theta(x) \approx \frac{13.6\,{\rm MeV}}{\beta c p}\sqrt{\frac{x}{X_0}}\left[1 + 0.038 \ln\!\left(\frac{x}{X_0}\right)\right],$$1, and precision mechanics at $$\sigma_\theta(x) \approx \frac{13.6\,{\rm MeV}}{\beta c p}\sqrt{\frac{x}{X_0}}\left[1 + 0.038 \ln\!\left(\frac{x}{X_0}\right)\right],$$2, achieving a scattering-angle resolution compatible with $$\sigma_\theta(x) \approx \frac{13.6\,{\rm MeV}}{\beta c p}\sqrt{\frac{x}{X_0}}\left[1 + 0.038 \ln\!\left(\frac{x}{X_0}\right)\right],$$3 at the $$\sigma_\theta(x) \approx \frac{13.6\,{\rm MeV}}{\beta c p}\sqrt{\frac{x}{X_0}}\left[1 + 0.038 \ln\!\left(\frac{x}{X_0}\right)\right],$$4 average cosmic-ray muon energy (Keizer et al., 2018). The ART proof-of-concept uses plastic scintillating fiber arrays with $$\sigma_\theta(x) \approx \frac{13.6\,{\rm MeV}}{\beta c p}\sqrt{\frac{x}{X_0}}\left[1 + 0.038 \ln\!\left(\frac{x}{X_0}\right)\right],$$5 fiber core diameter, $$\sigma_\theta(x) \approx \frac{13.6\,{\rm MeV}}{\beta c p}\sqrt{\frac{x}{X_0}}\left[1 + 0.038 \ln\!\left(\frac{x}{X_0}\right)\right],$$6 pitch, and reports $$\sigma_\theta(x) \approx \frac{13.6\,{\rm MeV}}{\beta c p}\sqrt{\frac{x}{X_0}}\left[1 + 0.038 \ln\!\left(\frac{x}{X_0}\right)\right],$$7 spatial resolution and $$\sigma_\theta(x) \approx \frac{13.6\,{\rm MeV}}{\beta c p}\sqrt{\frac{x}{X_0}}\left[1 + 0.038 \ln\!\left(\frac{x}{X_0}\right)\right],$$8 angular resolution in track reconstruction (Anbarjafari et al., 2021). A triple-GEM detector adds a different kind of channel separation by rise-time gating: with drift/transfer/induction gaps of $$\sigma_\theta(x) \approx \frac{13.6\,{\rm MeV}}{\beta c p}\sqrt{\frac{x}{X_0}}\left[1 + 0.038 \ln\!\left(\frac{x}{X_0}\right)\right],$$9, Ar/CO$\beta \approx 1$0 $\beta \approx 1$1, and full waveform digitization, a $\beta \approx 1$2 rise-time threshold discriminated cosmic muons from $\beta \approx 1$3Fe x-rays at about $\beta \approx 1$4 in both directions (Hui-Yin et al., 2015).

Calibration and alignment recur as dominant systematics. The RPC dark-matter study reports a fitted data/MC normalization ratio of $\beta \approx 1$5, validating geometry, material budget, and resolution modeling (Liu et al., 31 Jul 2025). The PoCA-secondary study attributes residual discrepancies to uncalibrated particle-dependent RPC efficiencies and generator-plane geometry (Zhang et al., 5 Jul 2025). ART reports mechanical alignment tolerance $\beta \approx 1$6, fiber positioning tolerance $\beta \approx 1$7, and mat orthogonality $\beta \approx 1$8 (Anbarjafari et al., 2021). The ARA dual-pulse analysis emphasizes timing calibration, antenna positions, and refractive-index modeling $\beta \approx 1$9 as dominant uncertainties for dual-channel timing and polarization fits (Ali et al., 17 Sep 2025).

5. Representative applications and reported performance

Recent studies show that dual-channel analysis is not merely conceptual; it changes measurable performance.

Study	Dual channels	Reported result
Cargo verification (Georgadze, 2024)	scattering density + stopped-muon rate	tobacco vs paper towel rolls separated at $p$0, $p$1, and $p$2 for $p$3, $p$4, and $p$5 FWHM in a 10-second scan
P$p$6MA (Qin et al., 18 Dec 2025)	transmission occupancy + scattering-induced projection shift	$p$7 lead knife-edge: KEW $p$8 for P$p$9MA4 and $\rho Z/A$00 with near-vertical selection; $\rho Z/A$01 copper letters resolved in $\rho Z/A$02–3 days
SA-DSVN (Dasgupta et al., 4 Apr 2026)	scattering kinematics + shower multiplicity	$\rho Z/A$03 voxel accuracy, defect Dice $\rho Z/A$04–$\rho Z/A$05, and $\rho Z/A$06 volume-level detection sensitivity
RHMT (Zhao et al., 18 Jun 2026)	scattering + energy loss	RHMT-S mean ROC-AUC $\rho Z/A$07–$\rho Z/A$08 versus $\rho Z/A$09 for ASR; RHMT-E mean AUC $\rho Z/A$10
Composition/DM RPC study (Liu et al., 31 Jul 2025)	shared $\rho Z/A$11 channel for composition + DM search	electron fraction resolved at $\rho Z/A$12 total uncertainty; $\rho Z/A$13 at $\rho Z/A$14 CL for $\rho Z/A$15 slow DM
HAWC + IceCube (collaboration et al., 2017)	northern + southern sky coverage	large-scale anisotropy amplitude $\rho Z/A$16; small-scale residuals at the $\rho Z/A$17 level; significant power up to $\rho Z/A$18

In cargo inspection, the key empirical result is that the one-dimensional scattering-only and absorption-only projections overlap, whereas the joint $\rho Z/A$19 plane yields multi-$\rho Z/A$20 separation in the modeled tobacco-smuggling scenario (Georgadze, 2024). In P$\rho Z/A$21MA, the gain is not only contrast but resolution: under matched simulations, conventional MST and MSTC produced KEW values around $\rho Z/A$22–$\rho Z/A$23, while P$\rho Z/A$24MA variants achieved millimeter-scale edge widths and resolved thin copper letters that MSTC failed to render in 12 days (Qin et al., 18 Dec 2025).

In structural tomography, the learned dual-stream result is notable because the ablation study attributes most discriminative power to the shower-multiplicity stream: defect-mean Dice rises from $\rho Z/A$25 for scattering only to $\rho Z/A$26 for shower only, while the full SA-DSVN reaches $\rho Z/A$27 voxel accuracy on fresh validation volumes (Dasgupta et al., 4 Apr 2026). This materially changes the interpretation of secondaries. The PoCA-secondary RPC study had already shown a strong positive correlation between roof thickness and the detector-plane PoCA integral ratio, with $\rho Z/A$28, and a monotonic increase from $\rho Z/A$29 at $\rho Z/A$30 lead to $\rho Z/A$31 at $\rho Z/A$32 lead (Zhang et al., 5 Jul 2025). The learned model extends that insight by treating secondary shower multiplicity as a first-class imaging signal rather than an after-the-fact diagnostic (Dasgupta et al., 4 Apr 2026).

In non-imaging contexts, dual-channel methods similarly sharpen inference. The HAWC+IceCube all-sky map recovered a stronger dipole than direct 24 h integration and reduced cross-talk among low-order multipoles through near-full-sky coverage (collaboration et al., 2017). The ARA dual-pulse candidate showed per-channel delays and reconstructed directions consistent with a downward, inclined cosmic-ray shower with a proton primary at nominal $\rho Z/A$33, with HPol/VPol power ratios of $\rho Z/A$34 for the first pulse and $\rho Z/A$35 for the second (Ali et al., 17 Sep 2025). This suggests that dual-channel timing and polarization can function as a tomographic constraint on both event geometry and refractive structure.

6. Limits, recurring misconceptions, and future directions

A recurrent misconception is that a second channel simply adds redundancy. The cited work shows the opposite: channels often fail differently. In dense cargo, spectrum hardening removes low-momentum muons, so scattering contrast decreases because $\rho Z/A$36, while the absorption channel becomes more discriminating (Georgadze, 2024). In P$\rho Z/A$37MA, transmission occupancy sharpens edges through scattering-induced redistribution, but the reported transmission ratio is explicitly not the physical transmissivity (Qin et al., 18 Dec 2025). In ground-based sky anisotropy, near-full-sky coverage greatly reduces multipole coupling, yet the arrays remain insensitive to purely declination-dependent anisotropy, so the dipole is reconstructed only as its projection onto the equatorial plane (collaboration et al., 2017). In limited-angle muon imaging, column images are often better constrained than full depth-resolved volumes, and stronger anisotropic regularization is required (Zhao et al., 18 Jun 2026).

A second misconception is that secondary signatures are merely nuisance structure. Several studies directly contradict that view. Detector-plane PoCA clusters encode local secondary-particle production and can be used to infer roof thickness or to gate contaminated events out of the primary reconstruction (Zhang et al., 5 Jul 2025). SA-DSVN finds that shower multiplicity alone outperforms scattering alone for reinforced-concrete defect segmentation (Dasgupta et al., 4 Apr 2026). Shipping-container fusion studies report that secondary maps regularize ASR’s $\rho Z/A$38-elongation and improve Chamfer distance for mid-$\rho Z/A$39 materials (Prada et al., 8 Aug 2025). These results suggest that “noise” and “signal” are channel-dependent categories rather than intrinsic properties of the data.

The literature also identifies unresolved practical issues. Several systems rely on idealized detector efficiency, perfect particle identification, or simulation-only validation (Georgadze, 2024, Prada et al., 8 Aug 2025, Dasgupta et al., 4 Apr 2026). Residual energy-spectrum and mass-composition differences between HAWC and IceCube remain under evaluation (collaboration et al., 2017). ART reconstructions show vertical elongation from limited-angle coverage (Anbarjafari et al., 2021). Dry-cask $\rho Z/A$40CT studies emphasize long measurement times, insufficiently accurate path models, and the inability to precisely measure muon momentum (Liu, 2018). ARA dual-pulse analyses remain limited by event rarity, firn-model uncertainty, and amplitude systematics (Ali et al., 17 Sep 2025).

Future directions in the cited work are correspondingly diverse. They include longer HAWC exposure and inclusion of additional air-shower arrays for energy-dependent anisotropy studies (collaboration et al., 2017); empirical libraries of joint $\rho Z/A$41 distributions for operational cargo inspection (Georgadze, 2024); larger-area RPC stacks, improved hit and angle resolution, and energy-tagging for combined composition and dark-matter searches (Liu et al., 31 Jul 2025); multi-event dual-pulse tomography for firn modeling and station calibration in radio arrays (Ali et al., 17 Sep 2025); automated threshold and fusion-weight selection, momentum-aware MST, and experimental validation of secondary-particle efficiencies in shipping-container tomography (Prada et al., 8 Aug 2025); and domain-randomized, physics-informed learning systems that bridge simulation and field data (Dasgupta et al., 4 Apr 2026).

Taken together, these developments define dual-channel cosmic-ray tomography analysis as a broad methodological shift: from single-observable inversion toward coordinated inference over complementary channels whose failures, biases, and sensitivities are explicitly different. That shift is already visible in maximum-likelihood sky mapping, raw-hit muography, cargo verification, structural inspection, low-$\rho Z/A$42 atmospheric-ray tomography, and radio reconstruction, and it consistently yields either better-constrained inverse problems or access to material and geometric contrasts that are weak or ambiguous in any one channel alone (collaboration et al., 2017, Zhao et al., 18 Jun 2026, Georgadze, 2024).