{
  "abstract": "The European Southern Observatory's Extremely Large Telescope (ELT), the 39-m telescope under construction in Chile, forms its entrance pupil from 798 hexagonal segments that the six 0.5-m-wide spider arms fragment into six \"petals\". The low-wind / island effect, adaptive-optics residuals, and mechanical drift imprint an independent piston on each petal. These differential-piston (petal) modes remain largely undetected by the ELT's baseline continuous-pupil wavefront sensors, a major bottleneck for diffraction-limited, high-contrast imaging. This paper presents a complete theoretical model of a single-mode photonic discrete beam combiner (DBC) configured to sense the six petal pistons. The model constructs the coupled-mode description of a two-dimensional evanescently coupled waveguide lattice with six inputs and forty-five outputs and derives its visibility-to-pixel matrix (V2PM); treats the pupil remapping that routes one sub-aperture per petal into the six inputs; develops the five-dimensional petal-mode basis of the fragmented pupil; and propagates the petal modes through the DBC to quantify the sensitivity. Optimising the input-port spacing and interaction length by minimising the V2PM condition number yields a well-conditioned device (CN = 10.4). It recovers petal pistons with unit linear gain over the full +/-lambda/2 (+/-800 nm) unambiguous range and separates the five modes with negligible cross-talk (< 10^-3). For 1% photometric noise, the reconstructed-piston error is 4.7 nm rms at lambda_0 = 1.6 micron. Tested against petal amplitudes from end-to-end ELT simulations (~40-300 nm rms atmospheric residual; ~0.3-1 micron low-wind events), the DBC recovers each piston to a few nm rms at H band, with a two-wavelength extension capturing the larger events. The DBC is therefore a compact, chromatically robust petalometer for the fragmented ELT pupil.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13575",
  "author_total": 4,
  "authors": [
    {
      "name": "Kalaga V. Madhav"
    },
    {
      "name": "Abani Shankar Nayak"
    },
    {
      "name": "Lucas Labadie"
    },
    {
      "name": "Robert R. Thomson"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3ws12bf7wswwm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13575",
  "fulltext_url": null,
  "id": "3ws12bf7wswwm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13575",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "astro-ph.IM"
    ],
    [
      "arxiv",
      "physics.optics"
    ],
    [
      "openalex",
      "3107|Adaptive optics and wavefront sensing"
    ]
  ],
  "openalex": "W7213267789",
  "pdf_url": "https://arxiv.org/pdf/2609.13575",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3ws12bf7wswwm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:25Z",
      "native_id": "2609.13575",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13575"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.IM",
      "subfield": "instrumentation-methods"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.optics",
      "subfield": "optics-photonics"
    }
  ],
  "title": "Sensing ELT petal modes with a discrete beam combiner: an end-to-end theoretical model",
  "title_text": "Sensing ELT petal modes with a discrete beam combiner: an end-to-end theoretical model",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:25Z",
  "url": "https://research.draconitic.com/paper/3ws12bf7wswwm",
  "venue": "arXiv",
  "versions": []
}