L1 ⚛ L1-023 ⊙ Testnet

Three-Photon Microscopy (chi-5 deep-tissue imaging)

Microscopy · Higher-order NLO microscopy for thick scattering tissue

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⬇ L1-023.md

# ⚛ L1 Principle — Three-Photon Microscopy (chi-5 deep-tissue imaging) **ID:** `L1-023` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Microscopy — *Higher-order NLO microscopy for thick scattering tissue* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 3D intensity > **📡 Carrier:** photon · **🌫 Noise:** shot poisson > **⚖ Difficulty (δ):** 10 · **⛓ Block:** 41554169 --- ## 🧠 1. Introduction **Three-Photon Microscopy (chi-5 deep-tissue imaging)** is a **nonlinear inverse problem** whose unknown lives in **3D intensity** space, within the **Higher-order NLO microscopy for thick scattering tissue** sub-domain of **Microscopy**. Measurements consist of photons collected by an optical detector via a **three photon nlo** sensing mechanism. The forward operator applies, in order: L · excitation · nonlinear chi5 operator; ordered pixel-by-pixel sampling; detector accumulates flux over the exposure window. Observations are corrupted by Poisson shot noise from quantum-limited detection. Existence of the recovered 3D intensity is guaranteed within the declared Omega bounds. Uniqueness is local rather than global (non-convex landscape); convergence depends on initialisation and priors. Stability is moderately conditioned (kappa_eff ~= 22); pulse_compression_drift dominates the stability cliff; sample_scattering and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) 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 · excitation · nonlinear chi5 → Raster scan → Temporal integration → **y** (detector). ``` y = ∫_t dt S_raster `L.excitation.nonlinear_chi5` x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.excitation.nonlinear_chi5` | L · excitation · nonlinear chi5 operator | | `S.scan.raster` | Ordered pixel-by-pixel sampling | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Microscopy | | Sub domain | Higher-order NLO microscopy for thick scattering tissue | | Carrier | photon | | Problem class | nonlinear_inverse | | Solution space | 3D_intensity | | Noise model | shot_poisson | | Integration axis | temporal | | Difficulty delta | 10 | | L dag | 3.8 | ## 📡 4. Measurement Model Existence of the recovered 3D intensity is guaranteed within the declared Omega bounds. Uniqueness is local rather than global (non-convex landscape); convergence depends on initialisation and priors. Stability is moderately conditioned (kappa_eff ~= 22); pulse_compression_drift dominates the stability cliff; sample_scattering and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) 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:** `three_photon` · **Forward operator:** `three_photon_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 512 | | W | px | 512 | | Z | — | 100 | | Na | — | 1 | | Pixel nm | nm | 400 | | Lambda ex nm | nm | 1300 | | Peak photons | photons | 30 | | Pulse width fs | — | 60 | | Sample scattering | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 128 – 2048 | | W | px | 128 – 2048 | | Z | — | 16 – 512 | | Na | — | 0.5 – 1.1 | | Pixel nm | nm | 200 – 1000 | | Lambda ex nm | nm | 1200 – 1700 | | Peak photons | photons | 5 – 500 | | Pulse width fs | — | 30 – 300 | | Sample scattering | — | 0.0 – 0.8 | | Long wavelength absorption | — | 0.0 – 0.5 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 22.0 | Metric | Range | |---|---| | Psnr db | 12.0 – 42.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `440` and δ = `10`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x6006f879b51c8780e420c3954e99bc17c13956a58980560d0d0fe2508eaa644a` - **Chain tx hash:** `0xe772075299607a0c14e359f93aad3b5b4757c04e22c383ee8a3054094792b0e2` - **Chain block:** `41554169` --- ## File Mapping This bundle consists of: `L1-023.md`, `L1-023.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-023.md` | Source of truth — edit this | Human or LLM | | `L1-023.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 `L1-023`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-023.md).
Regenerate L1-023.json so every field matches the Markdown.
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L2-023-001 Three-Photon Microscopy (chi-5 deep-tissue imaging) Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41554169,
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  "domain": "Microscopy",
  "hardness_fn": {
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    "kappa": 440,
    "metric": "PSNR_dB",
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    "regime": "Existence of the recovered 3D intensity is guaranteed within the declared Omega bounds. Uniqueness is local rather than global (non-convex landscape); convergence depends on initialisation and priors. Stability is moderately conditioned (kappa_eff ~= 22); pulse_compression_drift dominates the stability cliff; sample_scattering and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) sets the irreducible data-fidelity floor, while TV / wavelet-sparsity / deep priors stabilise recovery at the ill-conditioned end of Omega.",
    "secondary": "SSIM"
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  "physics_fingerprint": {
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    "difficulty_delta": 10,
    "domain": "Microscopy",
    "integration_axis": "temporal",
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    ],
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    "sensing_mechanism": "three_photon_nlo",
    "solution_space": "3D_intensity",
    "sub_domain": "Higher-order NLO microscopy for thick scattering tissue",
    "title": "Three-Photon Microscopy (chi-5 deep-tissue imaging)"
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        "Z": 100,
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      "NA": [
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      "W": [
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      "Z": [
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      "long_wavelength_absorption": [
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      ],
      "peak_photons": [
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      ],
      "pixel_nm": [
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      ],
      "pulse_width_fs": [
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      ],
      "sample_scattering": [
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      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Higher-order NLO microscopy for thick scattering tissue",
  "title": "Three-Photon Microscopy (chi-5 deep-tissue imaging)"
}

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