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arxiv: 2606.26702 · v1 · pith:VLSMOU5Gnew · submitted 2026-06-25 · 🌌 astro-ph.IM · astro-ph.HE

Interferometric Analysis of Air-shower Radio Emission in the Near Field with an Information Field Theory Approach

Keito Watanabe , Karen Terveer , Sjoerd Bouma , Justin Bray , Stijn Buitink , Arthur Corstanje , Vital De Henau , Tim Huege
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Edwin Dickinson Vincent Eberle Torsten En{\ss}lin Brian Hare Haoning He J\"org H\"orandel Clancy James Philipp Laub Xingyu Li Hermann-Josef Mathes Katharine Mulrey Anna Nelles Subhadip Saha Felix Schl\"uter Olaf Scholten Ralph Spencer Christopher Sterpka Satyendra Thoudam Gia Trinh Paulina Turekova Darko Veberic Chao Zhang Pengfei Zhang Yi Zhang
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classification 🌌 astro-ph.IM astro-ph.HE
keywords air-shower radio emissionInformation Field Theorynear-field interferometrycosmic-ray detectionBayesian reconstructionSKA-Lowradio astronomy
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The pith

Information Field Theory extracts all signal information to enable holistic reconstruction of air-shower radio parameters and near-field interferometry.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that existing methods for reconstructing radio emission from cosmic-ray air showers are held back by high computational costs, simplified models, and incomplete use of the signal data. It presents Information Field Theory as a Bayesian framework that infers distributions of field-like quantities directly from the measurements. This approach supports reconstruction of every relevant parameter at once and permits interferometric analysis in the near field. The work reviews current implementations and notes their relevance for the SKA-Low array.

Core claim

Information Field Theory can extract every available piece of information from air-shower radio signals, infer distributions of field-like quantities, and thereby deliver complete parameter sets together with near-field interferometry, overcoming the limitations of prior reconstruction techniques.

What carries the argument

Information Field Theory (IFT), a Bayesian inference framework that reconstructs field-like quantities by using all information contained in the measured signals.

If this is right

  • All relevant air-shower parameters can be recovered in a single consistent reconstruction rather than through sequential approximations.
  • Near-field interferometry becomes feasible, allowing analysis of the emission geometry closer to the detector than far-field assumptions permit.
  • The same framework is directly applicable to the SKA-Low telescope for air-shower studies.
  • Bayesian uncertainty quantification on the inferred fields is obtained as a built-in output.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • IFT reconstructions could be run on existing radio-detector archives to test whether they recover known shower properties more completely than current pipelines.
  • The method may open a route to joint radio and particle-detector analyses that share a common field representation.
  • Computational scaling with array size will determine whether real-time or near-real-time use is practical for next-generation instruments.

Load-bearing premise

The IFT framework, already used for other imaging tasks, can be applied to the transient and complex radio signals from air showers without substantial loss of information or excessive computational demands.

What would settle it

Direct comparison of reconstruction accuracy, completeness of recovered parameters, and run time between IFT and standard methods on the same set of simulated or observed air-shower radio events.

Figures

Figures reproduced from arXiv: 2606.26702 by Anna Nelles, Arthur Corstanje, Brian Hare, Chao Zhang, Christopher Sterpka, Clancy James, Darko Veberic, Edwin Dickinson, Felix Schl\"uter, Gia Trinh, Haoning He, Hermann-Josef Mathes, J\"org H\"orandel, Justin Bray, Karen Terveer, Katharine Mulrey, Keito Watanabe, Olaf Scholten, Paulina Turekova, Pengfei Zhang, Philipp Laub, Ralph Spencer, Satyendra Thoudam, Sjoerd Bouma, Stijn Buitink, Subhadip Saha, Tim Huege, Torsten En{\ss}lin, Vincent Eberle, Vital De Henau, Xingyu Li, Yi Zhang.

Figure 1
Figure 1. Figure 1: Example of simulated electric field traces from a cosmic ray with primary energy 𝐸 = 1016 eV and zenith angle of 15◦ at an antenna 𝑑core = 101 m (left) and 138 m (right) from the shower core. The traces are shown for varying values of 𝑋max, indicated by the colorbar. The top and bottom figure show the 𝑥 and 𝑦 polarizations of the electric field trace, respectively. Traces are band-pass filtered to [50, 350… view at source ↗
Figure 2
Figure 2. Figure 2: An example of the air shower reconstruction for a proton primary with an electromagnetic energy (𝐸rad) of 6.61 × 105 eV and a shower maximum (𝑋max) at 731.6 g cm−2 . The shower arrived from a zenith angle of 37.0 ◦ and an azimuth of 52.4 ◦ , with its core at (21.5 m, 7.7 m). The event had a peak signal￾to-noise ratio (SNR) of 3.5. The top row displays the input data and compares the true CoREAS radio footp… view at source ↗
Figure 3
Figure 3. Figure 3: Fluence-based reconstruction performance for shower maximum (top row) and radiation energy (bottom row). For each parameter, the left plot shows the reconstructed vs. Monte Carlo true value, with an inset detailing the pull distribution. The right plot shows the resolution, with the distribution of reconstruction errors (top) and the mean reconstruction uncertainty per bin (bottom). The unconnected dots in… view at source ↗
Figure 4
Figure 4. Figure 4: Performance of the radiation energy 𝐸rad and 𝑋max reconstruction on CoREAS simulations. The left side displays both the reconstructed values compared to the CoREAS truth for all 390 successful reconstructions, as well as the pull from the reconstruction. The right side of the plots show histograms of the reconstruction errors at the top and how the reconstruction uncertainties correlate with reconstruction… view at source ↗
Figure 5
Figure 5. Figure 5: The longitudinal shower development parameterized using the Gaisser-Hillas function in the L-R-formalism. We take 𝑋max = 500 g cm−2 and normalise the function by 𝑁max. informative priors to describe the posterior without explicitly including information. However, as a first step, we use relationships known from current studies of air shower physics and encode these into the prior. Previous studies have sho… view at source ↗
Figure 6
Figure 6. Figure 6: Corner plot of the truncated multivariate normal distribution used as our prior distribution (blue). We also overlay the true distribution obtained from CORSIKA simulations (red). The mean value from the fit are also shown. The contours represent the 1, 2, and 3𝜎 confidence level for a 2-D Gaussian distribution. Figure generated using corner.py (Foreman-Mackey, 2016). The core idea of SMIET lies in the con… view at source ↗
Figure 7
Figure 7. Figure 7: The electric field traces obtained from SMIET (dashed) and from CoREAS (orange) in the geomagnetic and charge-excess components. The traces are band pass filtered to 30 - 500 MHz. The traces were generated by using the same longitudinal profile (in orange). The longitudinal profile and electric field trace of the origin shower (in purple) used to generate the synthesised trace is also shown. 4.2 Antenna Re… view at source ↗
Figure 8
Figure 8. Figure 8: An example of an event reconstruction from this model with 𝐸 = 2 × 1017 eV, 𝜃 = 28◦ , 𝜙 = 84◦ , and 𝑋 truth max = 602 g cm−2 . For each plot, we show the posterior mean and standard deviation (blue), true values from the CoREAS simulation (red, dashed), and each posterior sample used in the inference (gray). Top Left: The reconstructed longitudinal profile. The profile from the origin shower used in the te… view at source ↗
Figure 9
Figure 9. Figure 9: Distribution of the bias of the shower parameters 𝑋max, log10 (𝑁max), 𝐿 and 𝑅 for all events considered in this work. The contours show the 0.5, 1, 1.5, and 2𝜎 values following a 2-D Gaussian distribution. The point where the bias is zero is indicated by the black lines and dots. Figure generated using corner.py (Foreman-Mackey, 2016). ≤ 19 g cm−2 . We further notice that the values for log10 (𝑁max) are sl… view at source ↗
Figure 10
Figure 10. Figure 10: Left: Radio footprint (at ground) from a simulated air shower generated by a cosmic ray (with energy 𝐸 = 3.8 × 1017 eV, zenith angle 𝜃 = 4 ◦ , and azimuthal angle 𝜙 = 151◦ ), where the signal is observed in the idealized star-shape antenna layout. Right: Same simulated cosmic ray as the left figure, but for the SKA-Low AA∗ antenna layout. The shower core is shifted to (-100, 100) m to showcase an event th… view at source ↗
read the original abstract

Current reconstruction techniques for air-shower radio emission generated by cosmic rays have shown great success, having been applied to several radio detectors over the last decade. Nevertheless, they are limited by their high computational cost, simplified approximations, and signal information used for reconstruction. As such, advanced analyses are required to not only be able to perform a holistic reconstruction of all parameters, but also to conduct near-field interferometry of the air shower. This can be achieved through Information Field Theory (IFT), an imaging reconstruction framework based on Bayesian inference that can extract all available information within the signal to infer distributions of field-like quantities. In this chapter, we highlight current novel approaches that use IFT for air shower reconstruction, and the potential of their applicability towards SKA-Low.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The manuscript claims that Information Field Theory (IFT), a Bayesian imaging framework, can overcome limitations of existing air-shower radio reconstruction methods (high computational cost, simplified approximations, incomplete signal information) by extracting all available information to infer field-like quantities, thereby enabling holistic reconstruction of all parameters and near-field interferometry of cosmic-ray air-shower emission, with highlighted novel approaches and potential applicability to SKA-Low.

Significance. If the IFT adaptation can be shown to preserve phase, polarization, and transient information while remaining computationally tractable, the result would be significant for radio detection of cosmic rays, offering a more complete Bayesian treatment that could improve parameter estimation and support interferometric analyses at scale with instruments such as SKA-Low.

major comments (1)
  1. [Abstract] Abstract: the central claim that IFT enables holistic reconstruction and near-field interferometry by extracting all available signal information rests on the premise that existing IFT response operators and priors (developed for other imaging tasks) can be instantiated for short-duration, broadband, near-field transients without information loss or prohibitive cost; however, no likelihood derivation, explicit near-field Green's function, or scaling test is supplied, leaving the load-bearing adaptation step unverified.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting the need for precision in the abstract's claims. We address the single major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that IFT enables holistic reconstruction and near-field interferometry by extracting all available signal information rests on the premise that existing IFT response operators and priors (developed for other imaging tasks) can be instantiated for short-duration, broadband, near-field transients without information loss or prohibitive cost; however, no likelihood derivation, explicit near-field Green's function, or scaling test is supplied, leaving the load-bearing adaptation step unverified.

    Authors: The manuscript is structured as an overview chapter that highlights existing and emerging IFT-based approaches for air-shower radio reconstruction rather than presenting a self-contained derivation of the full likelihood or response operator. Foundational IFT likelihood constructions and Green's functions for transient signals appear in the cited IFT literature; the novelty emphasized here lies in their targeted application to near-field cosmic-ray emission and SKA-Low relevance. We agree that the abstract phrasing could be read as implying a complete verification within this work. We will therefore revise the abstract to state explicitly that the adaptation builds on prior IFT response operators and that computational feasibility is supported by referenced implementations, while removing any implication that new derivations are supplied here. A dedicated scaling test is outside the scope of this conceptual overview but can be noted via citation to existing IFT benchmarks. revision: yes

Circularity Check

0 steps flagged

No derivation chain or equations presented; circularity cannot be assessed

full rationale

The abstract and provided context introduce the application of Information Field Theory (IFT) to air-shower radio emission but contain no equations, response operators, likelihood derivations, Green's functions, or explicit reconstruction steps. Without any load-bearing derivation that could reduce to fitted inputs or self-citations by construction, no circularity is identifiable. The central claim of holistic reconstruction via IFT remains unexamined for self-referential reduction because no mathematical chain is supplied.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract supplies no information on free parameters, axioms, or invented entities.

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discussion (0)

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Reference graph

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