L1 ⚛ L1-533 ⊙ Testnet

Confocal Z-Stack (3D axial deconvolution)

Microscopy · 3D confocal volume imaging

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⬇ L1-533.md

# ⚛ L1 Principle — Confocal Z-Stack (3D axial deconvolution) **ID:** `L1-533` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Microscopy — *3D confocal volume imaging* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 3D intensity > **📡 Carrier:** photon · **🌫 Noise:** poisson gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555318 --- ## 🧠 1. Introduction **Confocal Z-Stack (3D axial deconvolution)** is a **linear inverse problem** whose unknown lives in **3D intensity** space, within the **3D confocal volume imaging** sub-domain of **Microscopy**. Measurements consist of photons collected by an optical detector via a **confocal laser scan** sensing mechanism. The forward operator applies, in order: K · psf · confocal operator; ordered pixel-by-pixel sampling; 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 ~= 12); z_step_error dominates the stability cliff; pinhole_size_AU 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** → K · psf · confocal → Raster scan → S · scan · axial → Temporal integration → **y** (detector). ``` y = ∫_t dt `S.scan.axial` S_raster `K.psf.confocal` x + n, Poisson + 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `K.psf.confocal` | K · psf · confocal operator | | `S.scan.raster` | Ordered pixel-by-pixel sampling | | `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 | 3D confocal volume imaging | | Carrier | photon | | Problem class | linear_inverse | | Solution space | 3D_intensity | | Noise model | poisson_gaussian | | Integration axis | axial | | Difficulty delta | 3 | | L dag | 3 | ## 📡 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 ~= 12); z_step_error dominates the stability cliff; pinhole_size_AU 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:** `confocal_zstack` · **Forward operator:** `confocal_zstack_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 512 | | W | px | 512 | | Z | — | 64 | | Na | — | 1.3 | | Pixel nm | nm | 100 | | Z step nm | nm | 500 | | Peak photons | photons | 300 | | Z step error | — | 0 | | Spherical aberration | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 128 – 2048 | | W | px | 128 – 2048 | | Z | — | 16 – 512 | | Na | — | 0.8 – 1.45 | | Pixel nm | nm | 50 – 300 | | Z step nm | nm | 100 – 2000 | | Peak photons | photons | 20 – 2000 | | Z step error | — | 0.0 – 0.2 | | Spherical aberration | — | 0.0 – 0.5 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 26.0 | Metric | Range | |---|---| | Psnr db | 12.0 – 42.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `240` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x8fb81af730c6cf0ab826ec31b982cd4a423af54d396ba24ed8d92e07919687a2` - **Chain tx hash:** `0x02ac23e9cd29edbd06e8ab741973836afd7559346f6366e73dd4caa9cf7cb0cf` - **Chain block:** `41555318` --- ## File Mapping This bundle consists of: `L1-533.md`, `L1-533.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-533.md` | Source of truth — edit this | Human or LLM | | `L1-533.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 `L1-533`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-533.md).
Regenerate L1-533.json so every field matches the Markdown.
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L2-533-001 Confocal Z-Stack (3D axial deconvolution) Mismatch-Only Spec

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📋 JSON metadata

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  "chain_tx_hash": "0x02ac23e9cd29edbd06e8ab741973836afd7559346f6366e73dd4caa9cf7cb0cf",
  "domain": "Microscopy",
  "hardness_fn": {
    "delta": 3,
    "kappa": 240,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
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    "metric": "PSNR_dB",
    "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 ~= 12); z_step_error dominates the stability cliff; pinhole_size_AU 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": {
    "L_DAG": 3.0,
    "carrier": "photon",
    "difficulty_delta": 3,
    "domain": "Microscopy",
    "integration_axis": "axial",
    "noise_model": "poisson_gaussian",
    "primitives": [
      "K.psf.confocal",
      "S.scan.raster",
      "S.scan.axial",
      "int.temporal"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "confocal_laser_scan",
    "solution_space": "3D_intensity",
    "sub_domain": "3D confocal volume imaging",
    "title": "Confocal Z-Stack (3D axial deconvolution)"
  },
  "size_tiers": {
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      "W",
      "Z",
      "pixel_nm",
      "z_step_nm",
      "NA",
      "peak_photons",
      "z_step_error",
      "spherical_aberration",
      "z_step_error",
      "pinhole_size_AU",
      "spherical_aberration"
    ],
    "allowed_problem_classes": [
      "confocal_zstack"
    ],
    "center_spec": {
      "epsilon_fn_center": "26.0",
      "forward_operator": "confocal_zstack_forward",
      "input_format": "measurement_only",
      "omega": {
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        "NA": 1.3,
        "W": 512,
        "Z": 64,
        "peak_photons": 300,
        "pixel_nm": 100,
        "spherical_aberration": 0.0,
        "z_step_error": 0.0,
        "z_step_nm": 500
      },
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    },
    "epsilon_bounds": {
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        42.0
      ]
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      ],
      "NA": [
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      ],
      "W": [
        128,
        2048
      ],
      "Z": [
        16,
        512
      ],
      "peak_photons": [
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        2000
      ],
      "pixel_nm": [
        50,
        300
      ],
      "spherical_aberration": [
        0.0,
        0.5
      ],
      "z_step_error": [
        0.0,
        0.2
      ],
      "z_step_nm": [
        100,
        2000
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "3D confocal volume imaging",
  "title": "Confocal Z-Stack (3D axial deconvolution)"
}

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