L1 ⚛ L1-002 ⊙ Testnet

Low-Dose Widefield Fluorescence (photon-starved Airy deconvolution)

Microscopy · Photon-limited epifluorescence

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⬇ L1-002.md

# ⚛ L1 Principle — Low-Dose Widefield Fluorescence (photon-starved Airy deconvolution) **ID:** `L1-002` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Microscopy — *Photon-limited epifluorescence* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 2D intensity > **📡 Carrier:** photon · **🌫 Noise:** poisson gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554153 --- ## 🧠 1. Introduction **Low-Dose Widefield Fluorescence (photon-starved Airy deconvolution)** is a **linear inverse problem** whose unknown lives in **2D intensity** space, within the **Photon-limited epifluorescence** sub-domain of **Microscopy**. Measurements consist of photons collected by an optical detector via a **fluorescence widefield** sensing mechanism. The forward operator applies, in order: convolution with the Airy disk of a circular aperture; detector accumulates flux over the exposure window. Observations are corrupted by Poisson shot noise plus Gaussian read-out noise. Existence of the recovered 2D intensity is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by the declared priors. Stability is well-conditioned (kappa_eff ~= 8); dz_nm dominates the stability cliff; sigma_bg and the remaining mismatch parameters contribute higher-order bias terms. Poisson signal noise + gaussian read noise sets the irreducible data-fidelity floor, while mild Tikhonov or analytic inversion is sufficient at the nominal Omega point. ## ⚙ 2. Forward Model Physical chain: **x** → Airy PSF convolution → Temporal integration → **y** (detector). ``` y = ∫_t dt K_Airy * x + n, Poisson + 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `K.psf.airy` | Convolution with the airy disk of a circular aperture | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Microscopy | | Sub domain | Photon-limited epifluorescence | | Carrier | photon | | Problem class | linear_inverse | | Solution space | 2D_intensity | | Noise model | poisson_gaussian | | Integration axis | temporal | | Difficulty delta | 3 | | L dag | 1 | ## 📡 4. Measurement Model Existence of the recovered 2D intensity is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by the declared priors. Stability is well-conditioned (kappa_eff ~= 8); dz_nm dominates the stability cliff; sigma_bg and the remaining mismatch parameters contribute higher-order bias terms. Poisson signal noise + gaussian read noise sets the irreducible data-fidelity floor, while mild Tikhonov or analytic inversion is sufficient at the nominal Omega point. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `airy_psf_low_dose` · **Forward operator:** `airy_psf_low_dose` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 512 | | W | px | 512 | | Na | — | 1.4 | | Dz nm | nm | 0 | | Pixel nm | nm | 65 | | Sigma bg | — | 0 | | Peak photons | photons | 50 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 128 – 4096 | | W | px | 128 – 4096 | | Na | — | 0.4 – 1.49 | | Dz nm | nm | 0.0 – 1500.0 | | Pixel nm | nm | 30 – 200 | | Sigma bg | — | 0.0 – 0.1 | | Peak photons | photons | 5 – 200 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 24.0 | Metric | Range | |---|---| | Psnr db | 12.0 – 42.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `160` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x1c2c8279a42465282fd5ead803d6357541d23506fbee53091a428728b2f8c79a` - **Chain tx hash:** `0x9cc700a9bcfb032addb8f17b4ea344e0893361cc4cfc7dae30cd2732c395199d` - **Chain block:** `41554153` --- ## File Mapping This bundle consists of: `L1-002.md`, `L1-002.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-002.md` | Source of truth — edit this | Human or LLM | | `L1-002.json` | Structured metadata for the registry | LLM regenerates from the sections above | **Prompt for your LLM after editing this Markdown:** > Read the attached Markdown. Regenerate the sibling `.json` so every field matches. > Preserve the schema documented in the rows above. > Output each file in its own fenced code block tagged with the filename. > Output only the JSON object. _This Markdown was auto-synthesized from the catalog row for `L1-002`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-002-001 Low-Dose Widefield Fluorescence (photon-starved Airy deconvolution) Mismatch-Only Spec

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📋 JSON metadata

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  "chain_tx_hash": "0x9cc700a9bcfb032addb8f17b4ea344e0893361cc4cfc7dae30cd2732c395199d",
  "domain": "Microscopy",
  "hardness_fn": {
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    "kappa": 160,
    "metric": "PSNR_dB",
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    "regime": "Existence of the recovered 2D intensity is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by the declared priors. Stability is well-conditioned (kappa_eff ~= 8); dz_nm dominates the stability cliff; sigma_bg and the remaining mismatch parameters contribute higher-order bias terms. Poisson signal noise + gaussian read noise sets the irreducible data-fidelity floor, while mild Tikhonov or analytic inversion is sufficient at the nominal Omega point.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
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    "carrier": "photon",
    "difficulty_delta": 3,
    "domain": "Microscopy",
    "integration_axis": "temporal",
    "noise_model": "poisson_gaussian",
    "primitives": [
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      "int.temporal"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "fluorescence_widefield",
    "solution_space": "2D_intensity",
    "sub_domain": "Photon-limited epifluorescence",
    "title": "Low-Dose Widefield Fluorescence (photon-starved Airy deconvolution)"
  },
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      "shot_noise_variance"
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      "input_format": "measurement_only",
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        "peak_photons": 50,
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    "epsilon_bounds": {
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        4096
      ],
      "NA": [
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      ],
      "W": [
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      ],
      "dz_nm": [
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      ],
      "peak_photons": [
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      ],
      "pixel_nm": [
        30,
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      ],
      "sigma_bg": [
        0.0,
        0.1
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Photon-limited epifluorescence",
  "title": "Low-Dose Widefield Fluorescence (photon-starved Airy deconvolution)"
}

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