L1 ⚛ L1-137 ⊙ Testnet

Raman Imaging (spontaneous inelastic photon scattering)

Spectroscopy · Vibrational hyperspectral microscopy

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⬇ L1-137.md

# ⚛ L1 Principle — Raman Imaging (spontaneous inelastic photon scattering) **ID:** `L1-137` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Spectroscopy — *Vibrational hyperspectral microscopy* > **🎯 Problem class:** linear inverse spectral unmix · **🧮 Solution space:** concentration map hyperspectral > **📡 Carrier:** photon · **🌫 Noise:** shot poisson > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554226 --- ## 🧠 1. Introduction **Raman Imaging (spontaneous inelastic photon scattering)** is a **linear inverse spectral unmix** whose unknown lives in **concentration map hyperspectral** space, within the **Vibrational hyperspectral microscopy** sub-domain of **Spectroscopy**. Measurements consist of photons collected by an optical detector via a **inelastic scattering** sensing mechanism. The forward operator applies, in order: S · scatter · inelastic operator; L · disperse · spectral operator; detector accumulates flux over the exposure window. Observations are corrupted by Poisson shot noise from quantum-limited detection. Linear inverse problem mapping concentration to spectral signal; conditioning governed by spectral overlap (correlation of pure-component spectra). Mismatch: fluorescence background, wavenumber drift, laser-power fluctuation. ## ⚙ 2. Forward Model Physical chain: **x** → S · scatter · inelastic → L · disperse · spectral → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.disperse.spectral` `S.scatter.inelastic` x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `S.scatter.inelastic` | S · scatter · inelastic operator | | `L.disperse.spectral` | L · disperse · spectral operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Spectroscopy | | Sub domain | Vibrational hyperspectral microscopy | | Carrier | photon | | Problem class | linear_inverse_spectral_unmix | | Solution space | concentration_map_hyperspectral | | Noise model | shot_poisson | | Integration axis | spectral_and_spatial | | Difficulty delta | 3 | | L dag | 2.7 | ## 📡 4. Measurement Model Linear inverse problem mapping concentration to spectral signal; conditioning governed by spectral overlap (correlation of pure-component spectra). Mismatch: fluorescence background, wavenumber drift, laser-power fluctuation. | Metric | Value | |---|---| | Metric | concentration_NMSE | | Secondary | SNR_dB | ## 📏 5. Operating Range (Ω) **Center problem class:** `raman_hyperspectral_unmix` · **Forward operator:** `raman_disperse_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 256 | | K | — | 5 | | W | px | 256 | | Tau ms | ms | 100 | | N lambda | — | 512 | | Lambda l nm | nm | 785 | | Laser power fluct | — | 0 | | Wavenumber drift cm1 | — | 0 | | Fluorescence background | — | 0.1 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 64 – 2048 | | K | — | 1 – 20 | | W | px | 64 – 2048 | | Tau ms | ms | 10 – 10000 | | N lambda | — | 128 – 2048 | | Lambda l nm | nm | 488 – 1064 | | Laser power fluct | — | 0.0 – 0.3 | | Wavenumber drift cm1 | — | 0.0 – 10.0 | | Fluorescence background | — | 0.0 – 10.0 | | Pure component uncertainty | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** concentration NMSE 5e-3 | Metric | Range | |---|---| | Nmse | 0.0001 – 0.1 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **concentration_NMSE**, with κ = `200` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x44940adf96f90059f1837abd88cfb2a23d1e28fccaf6239067857825c2cf8eb3` - **Chain tx hash:** `0xc5001d6d607000195a04a69bbfa72c2e05a0f18dedcafdc6c337128549d157ba` - **Chain block:** `41554226` --- ## File Mapping This bundle consists of: `L1-137.md`, `L1-137.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-137.md` | Source of truth — edit this | Human or LLM | | `L1-137.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 `L1-137`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-137.md).
Regenerate L1-137.json so every field matches the Markdown.
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L2-137-001 Raman Imaging Hyperspectral Unmixing Spec

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📋 JSON metadata

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  "artifact_id": "L1-137",
  "chain_block": 41554226,
  "chain_hash": "0x44940adf96f90059f1837abd88cfb2a23d1e28fccaf6239067857825c2cf8eb3",
  "chain_tx_hash": "0xc5001d6d607000195a04a69bbfa72c2e05a0f18dedcafdc6c337128549d157ba",
  "domain": "Spectroscopy",
  "hardness_fn": {
    "delta": 3,
    "kappa": 200,
    "metric": "concentration_NMSE",
    "type": "epsilon_fn"
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      "license_hash": null,
      "name": "primary",
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    "metric": "concentration_NMSE",
    "regime": "Linear inverse problem mapping concentration to spectral signal; conditioning governed by spectral overlap (correlation of pure-component spectra). Mismatch: fluorescence background, wavenumber drift, laser-power fluctuation.",
    "secondary": "SNR_dB"
  },
  "physics_fingerprint": {
    "L_DAG": 2.7,
    "carrier": "photon",
    "difficulty_delta": 3,
    "domain": "Spectroscopy",
    "integration_axis": "spectral_and_spatial",
    "noise_model": "shot_poisson",
    "primitives": [
      "S.scatter.inelastic",
      "L.disperse.spectral",
      "int.temporal"
    ],
    "problem_class": "linear_inverse_spectral_unmix",
    "sensing_mechanism": "inelastic_scattering",
    "solution_space": "concentration_map_hyperspectral",
    "sub_domain": "Vibrational hyperspectral microscopy",
    "title": "Raman Imaging (spontaneous inelastic photon scattering)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "raman_disperse_forward",
      "raman_mosaic_scan",
      "hyperspectral_line_scan"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "N_lambda",
      "tau_ms",
      "lambda_L_nm",
      "K",
      "fluorescence_background",
      "wavenumber_drift_cm1",
      "laser_power_fluct",
      "pure_component_uncertainty"
    ],
    "allowed_problem_classes": [
      "raman_hyperspectral_unmix",
      "raman_classification",
      "blind_raman_demixing"
    ],
    "center_spec": {
      "epsilon_fn_center": "concentration NMSE 5e-3",
      "forward_operator": "raman_disperse_forward",
      "input_format": "hyperspectral_cube_plus_library",
      "omega": {
        "H": 256,
        "K": 5,
        "N_lambda": 512,
        "W": 256,
        "fluorescence_background": 0.1,
        "lambda_L_nm": 785,
        "laser_power_fluct": 0.0,
        "tau_ms": 100,
        "wavenumber_drift_cm1": 0.0
      },
      "problem_class": "raman_hyperspectral_unmix"
    },
    "epsilon_bounds": {
      "nmse": [
        0.0001,
        0.1
      ]
    },
    "omega_bounds": {
      "H": [
        64,
        2048
      ],
      "K": [
        1,
        20
      ],
      "N_lambda": [
        128,
        2048
      ],
      "W": [
        64,
        2048
      ],
      "fluorescence_background": [
        0.0,
        10.0
      ],
      "lambda_L_nm": [
        488,
        1064
      ],
      "laser_power_fluct": [
        0.0,
        0.3
      ],
      "pure_component_uncertainty": [
        0.0,
        0.3
      ],
      "tau_ms": [
        10,
        10000
      ],
      "wavenumber_drift_cm1": [
        0.0,
        10.0
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Vibrational hyperspectral microscopy",
  "title": "Raman Imaging (spontaneous inelastic photon scattering)"
}

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