L1 ⚛ L1-020 ⊙ Testnet

Lattice Light Sheet Microscopy (LLSM) — Bessel-lattice 3D imaging

Microscopy · High-resolution 3D live imaging via optical lattice

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⬇ L1-020.md

# ⚛ L1 Principle — Lattice Light Sheet Microscopy (LLSM) — Bessel-lattice 3D imaging **ID:** `L1-020` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Microscopy — *High-resolution 3D live imaging via optical lattice* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 3D intensity > **📡 Carrier:** photon · **🌫 Noise:** poisson gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554168 --- ## 🧠 1. Introduction **Lattice Light Sheet Microscopy (LLSM) — Bessel-lattice 3D imaging** is a **linear inverse problem** whose unknown lives in **3D intensity** space, within the **High-resolution 3D live imaging via optical lattice** sub-domain of **Microscopy**. Measurements consist of photons collected by an optical detector via a **lattice illumination** sensing mechanism. The forward operator applies, in order: L · illumination · lattice operator; K · psf · detection operator; S · scan · axial operator; detector accumulates flux over the exposure window. Observations are corrupted by Poisson shot noise plus Gaussian read-out noise. Existence of the recovered 3D 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 moderately conditioned (kappa_eff ~= 18); lattice_registration dominates the stability cliff; dithering_phase_error and the remaining mismatch parameters contribute higher-order bias terms. Poisson signal noise + gaussian read noise sets the irreducible data-fidelity floor, while TV / wavelet-sparsity / deep priors stabilise recovery at the ill-conditioned end of Omega. ## ⚙ 2. Forward Model Physical chain: **x** → L · illumination · lattice → K · psf · detection → S · scan · axial → Temporal integration → **y** (detector). ``` y = ∫_t dt `S.scan.axial` `K.psf.detection` `L.illumination.lattice` x + n, Poisson + 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.illumination.lattice` | L · illumination · lattice operator | | `K.psf.detection` | K · psf · detection operator | | `S.scan.axial` | S · scan · axial operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Microscopy | | Sub domain | High-resolution 3D live imaging via optical lattice | | Carrier | photon | | Problem class | linear_inverse | | Solution space | 3D_intensity | | Noise model | poisson_gaussian | | Integration axis | axial | | Difficulty delta | 5 | | L dag | 3.8 | ## 📡 4. Measurement Model Existence of the recovered 3D 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 moderately conditioned (kappa_eff ~= 18); lattice_registration dominates the stability cliff; dithering_phase_error and the remaining mismatch parameters contribute higher-order bias terms. Poisson signal noise + gaussian read noise sets the irreducible data-fidelity floor, while TV / wavelet-sparsity / deep priors stabilise recovery at the ill-conditioned end of Omega. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `llsm` · **Forward operator:** `llsm_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 2048 | | W | px | 512 | | Z | — | 100 | | Na det | — | 1.1 | | Na illum | — | 0.6 | | Peak photons | photons | 200 | | Lattice pitch nm | nm | 1500 | | Lattice registration | — | 0 | | Dithering phase error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 512 – 4096 | | W | px | 256 – 2048 | | Z | — | 32 – 512 | | Na det | — | 0.8 – 1.2 | | Na illum | — | 0.3 – 0.8 | | Peak photons | photons | 30 – 2000 | | Lattice pitch nm | nm | 600 – 3000 | | Lattice registration | — | 0.0 – 0.1 | | Dithering phase error | — | 0.0 – 0.2 | | Sample induced aberration | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 28.5 | Metric | Range | |---|---| | Psnr db | 12.0 – 42.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `360` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x5e1bbdd7f64417cf30eb12955afe6c6bc58dfcdbc5e8a77537b40926f17389b6` - **Chain tx hash:** `0x7d009b5ece6f1a1570af66a425cbd9edae78ba5990d88498df65b33dad323f8a` - **Chain block:** `41554168` --- ## File Mapping This bundle consists of: `L1-020.md`, `L1-020.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-020.md` | Source of truth — edit this | Human or LLM | | `L1-020.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 `L1-020`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Regenerate L1-020.json so every field matches the Markdown.
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L2-020-001 Lattice Light Sheet Microscopy (LLSM) — Bessel-lattice 3D imaging Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41554168,
  "chain_hash": "0x5e1bbdd7f64417cf30eb12955afe6c6bc58dfcdbc5e8a77537b40926f17389b6",
  "chain_tx_hash": "0x7d009b5ece6f1a1570af66a425cbd9edae78ba5990d88498df65b33dad323f8a",
  "domain": "Microscopy",
  "hardness_fn": {
    "delta": 5,
    "kappa": 360,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
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      "license_hash": null,
      "name": "primary",
      "weight": 1.0
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  "observable_profile": {
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    "regime": "Existence of the recovered 3D 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 moderately conditioned (kappa_eff ~= 18); lattice_registration dominates the stability cliff; dithering_phase_error and the remaining mismatch parameters contribute higher-order bias terms. Poisson signal noise + gaussian read noise sets the irreducible data-fidelity floor, while TV / wavelet-sparsity / deep priors stabilise recovery at the ill-conditioned end of Omega.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.8,
    "carrier": "photon",
    "difficulty_delta": 5,
    "domain": "Microscopy",
    "integration_axis": "axial",
    "noise_model": "poisson_gaussian",
    "primitives": [
      "L.illumination.lattice",
      "K.psf.detection",
      "S.scan.axial",
      "int.temporal"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "lattice_illumination",
    "solution_space": "3D_intensity",
    "sub_domain": "High-resolution 3D live imaging via optical lattice",
    "title": "Lattice Light Sheet Microscopy (LLSM) \u2014 Bessel-lattice 3D imaging"
  },
  "size_tiers": {
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    "allowed_omega_dimensions": [
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      "NA_det",
      "NA_illum",
      "peak_photons",
      "lattice_registration",
      "dithering_phase_error",
      "lattice_registration",
      "dithering_phase_error",
      "sample_induced_aberration"
    ],
    "allowed_problem_classes": [
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    "center_spec": {
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      "forward_operator": "llsm_forward",
      "input_format": "measurement_only",
      "omega": {
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        "NA_det": 1.1,
        "NA_illum": 0.6,
        "W": 512,
        "Z": 100,
        "dithering_phase_error": 0.0,
        "lattice_pitch_nm": 1500,
        "lattice_registration": 0.0,
        "peak_photons": 200
      },
      "problem_class": "llsm"
    },
    "epsilon_bounds": {
      "psnr_db": [
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        42.0
      ]
    },
    "omega_bounds": {
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        4096
      ],
      "NA_det": [
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        1.2
      ],
      "NA_illum": [
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        0.8
      ],
      "W": [
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        2048
      ],
      "Z": [
        32,
        512
      ],
      "dithering_phase_error": [
        0.0,
        0.2
      ],
      "lattice_pitch_nm": [
        600,
        3000
      ],
      "lattice_registration": [
        0.0,
        0.1
      ],
      "peak_photons": [
        30,
        2000
      ],
      "sample_induced_aberration": [
        0.0,
        0.3
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "High-resolution 3D live imaging via optical lattice",
  "title": "Lattice Light Sheet Microscopy (LLSM) \u2014 Bessel-lattice 3D imaging"
}

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