L1 ⚛ L1-021 ⊙ Testnet

Second Harmonic Generation (SHG) Microscopy

Microscopy · Chi-2 non-centrosymmetric NLO imaging

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⬇ L1-021.md

# ⚛ L1 Principle — Second Harmonic Generation (SHG) Microscopy **ID:** `L1-021` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Microscopy — *Chi-2 non-centrosymmetric NLO imaging* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 2D intensity > **📡 Carrier:** photon · **🌫 Noise:** shot poisson > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554168 --- ## 🧠 1. Introduction **Second Harmonic Generation (SHG) Microscopy** is a **nonlinear inverse problem** whose unknown lives in **2D intensity** space, within the **Chi-2 non-centrosymmetric NLO imaging** sub-domain of **Microscopy**. Measurements consist of photons collected by an optical detector via a **second harmonic nlo** sensing mechanism. The forward operator applies, in order: L · excitation · nonlinear chi2 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 2D 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 ~= 15); 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 mild Tikhonov or analytic inversion is sufficient at the nominal Omega point. ## ⚙ 2. Forward Model Physical chain: **x** → L · excitation · nonlinear chi2 → Raster scan → Temporal integration → **y** (detector). ``` y = ∫_t dt S_raster `L.excitation.nonlinear_chi2` x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.excitation.nonlinear_chi2` | L · excitation · nonlinear chi2 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 | Chi-2 non-centrosymmetric NLO imaging | | Carrier | photon | | Problem class | nonlinear_inverse | | Solution space | 2D_intensity | | Noise model | shot_poisson | | Integration axis | temporal | | Difficulty delta | 5 | | L dag | 3.5 | ## 📡 4. Measurement Model Existence of the recovered 2D 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 ~= 15); 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 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:** `shg` · **Forward operator:** `shg_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 512 | | W | px | 512 | | Na | — | 1 | | Pixel nm | nm | 500 | | Lambda ex nm | nm | 920 | | Peak photons | photons | 100 | | Pulse width fs | — | 100 | | Sample scattering | — | 0 | | Quasi phase mismatch | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 128 – 2048 | | W | px | 128 – 2048 | | Na | — | 0.6 – 1.1 | | Pixel nm | nm | 200 – 1000 | | Lambda ex nm | nm | 800 – 1100 | | Peak photons | photons | 10 – 2000 | | Pulse width fs | — | 50 – 500 | | Sample scattering | — | 0.0 – 0.5 | | Quasi phase mismatch | — | 0.0 – 0.3 | ## 🎯 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 = `300` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x27555a14a99c9b9b5d4eeadcf0a413c93b7e0ff95a6de4e24740c491919146aa` - **Chain tx hash:** `0x835cc7a436d59b7909b3aed2559bed9119295e641e2885093301ba1efddbcd0f` - **Chain block:** `41554168` --- ## File Mapping This bundle consists of: `L1-021.md`, `L1-021.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-021.md` | Source of truth — edit this | Human or LLM | | `L1-021.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 `L1-021`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-021.md).
Regenerate L1-021.json so every field matches the Markdown.
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L2-021-001 Second Harmonic Generation (SHG) Microscopy Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41554168,
  "chain_hash": "0x27555a14a99c9b9b5d4eeadcf0a413c93b7e0ff95a6de4e24740c491919146aa",
  "chain_tx_hash": "0x835cc7a436d59b7909b3aed2559bed9119295e641e2885093301ba1efddbcd0f",
  "domain": "Microscopy",
  "hardness_fn": {
    "delta": 5,
    "kappa": 300,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
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      "license_hash": null,
      "name": "primary",
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    }
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  "layer": "L1",
  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "Existence of the recovered 2D 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 ~= 15); 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 mild Tikhonov or analytic inversion is sufficient at the nominal Omega point.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.5,
    "carrier": "photon",
    "difficulty_delta": 5,
    "domain": "Microscopy",
    "integration_axis": "temporal",
    "noise_model": "shot_poisson",
    "primitives": [
      "L.excitation.nonlinear_chi2",
      "S.scan.raster",
      "int.temporal"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "second_harmonic_nlo",
    "solution_space": "2D_intensity",
    "sub_domain": "Chi-2 non-centrosymmetric NLO imaging",
    "title": "Second Harmonic Generation (SHG) Microscopy"
  },
  "size_tiers": {
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    "allowed_omega_dimensions": [
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      "W",
      "pixel_nm",
      "NA",
      "lambda_ex_nm",
      "peak_photons",
      "pulse_width_fs",
      "sample_scattering",
      "quasi_phase_mismatch",
      "pulse_compression_drift",
      "sample_scattering",
      "quasi_phase_mismatch"
    ],
    "allowed_problem_classes": [
      "shg"
    ],
    "center_spec": {
      "epsilon_fn_center": "24.0",
      "forward_operator": "shg_forward",
      "input_format": "measurement_only",
      "omega": {
        "H": 512,
        "NA": 1.0,
        "W": 512,
        "lambda_ex_nm": 920,
        "peak_photons": 100,
        "pixel_nm": 500,
        "pulse_width_fs": 100,
        "quasi_phase_mismatch": 0.0,
        "sample_scattering": 0.0
      },
      "problem_class": "shg"
    },
    "epsilon_bounds": {
      "psnr_db": [
        12.0,
        42.0
      ]
    },
    "omega_bounds": {
      "H": [
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        2048
      ],
      "NA": [
        0.6,
        1.1
      ],
      "W": [
        128,
        2048
      ],
      "lambda_ex_nm": [
        800,
        1100
      ],
      "peak_photons": [
        10,
        2000
      ],
      "pixel_nm": [
        200,
        1000
      ],
      "pulse_width_fs": [
        50,
        500
      ],
      "quasi_phase_mismatch": [
        0.0,
        0.3
      ],
      "sample_scattering": [
        0.0,
        0.5
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Chi-2 non-centrosymmetric NLO imaging",
  "title": "Second Harmonic Generation (SHG) Microscopy"
}

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