{
  "abstract": "Three-dimensional (3D) localization microscopy using rotational point spread functions (PSFs) is fundamentally challenged by limited axial range, poor PSF compactness, and depth-decoding ambiguity -- particularly in dense specimens with heavy PSF overlap. To address these limitations, we introduce a 3D localization approach based on tornado wave (ToW)-PSFs, combined with a convolutional neural network (CNN) designed to decode continuous rotational patterns and resolve multi-period axial ambiguity. Our engineered PSF encodes the 3D position of each nanoparticle into a compact double-lobe pattern whose orientation rotates with axial position. This design yields a clean, well-defined structural evolution across an unprecedented 15 um axial range, with an average rotation rate of 21.8 degrees/um, ensuring robust long-range depth encoding. To recover coordinates from overlapping emitters, we systematically benchmark a conventional matching-pursuit (MP) algorithm against our CNN. While MP performs adequately in sparse scenes, the CNN demonstrates exceptional robustness in dense fields, achieving a 70.24% localization accuracy at 20 particles per image-substantially outperforming MP's 22.52% -- while also significantly suppressing axial period-jump errors. Experimental validation on nanoparticles confirms reliable single- and multi-particle localization throughout the entire working range. Our results establish ToW-PSFs as a powerful and practical optical encoding strategy for high-density, extended-range 3D localization imaging.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15606",
  "author_total": 3,
  "authors": [
    {
      "name": "Lai Chen"
    },
    {
      "name": "Rui Wang"
    },
    {
      "name": "Li-Gang Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/es2036ygjrb5f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15606",
  "fulltext_url": null,
  "id": "es2036ygjrb5f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15606",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "physics.optics"
    ],
    [
      "openalex",
      "1304|Advanced Fluorescence Microscopy Techniques"
    ]
  ],
  "openalex": "W7221826348",
  "pdf_url": "https://arxiv.org/pdf/2610.15606",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/es2036ygjrb5f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:06Z",
      "native_id": "2610.15606",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15606"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.optics",
      "subfield": "optics-photonics"
    }
  ],
  "title": "Tornado Wave-Encoded Point Spread Functions for Multi-Period Three-Dimensional Localization Imaging",
  "title_text": "Tornado Wave-Encoded Point Spread Functions for Multi-Period Three-Dimensional Localization Imaging",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:06Z",
  "url": "https://research.draconitic.com/paper/es2036ygjrb5f",
  "venue": "arXiv",
  "versions": []
}