L1 ⚛ L1-138 ⊙ Testnet

CARS — Coherent Anti-Stokes Raman Scattering

Spectroscopy · Third-order nonlinear coherent vibrational microscopy

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⬇ L1-138.md

# ⚛ L1 Principle — CARS — Coherent Anti-Stokes Raman Scattering **ID:** `L1-138` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Spectroscopy — *Third-order nonlinear coherent vibrational microscopy* > **🎯 Problem class:** nonlinear inverse spectral · **🧮 Solution space:** concentration map > **📡 Carrier:** photon · **🌫 Noise:** shot poisson coherent > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554226 --- ## 🧠 1. Introduction **CARS — Coherent Anti-Stokes Raman Scattering** is a **nonlinear inverse spectral** whose unknown lives in **concentration map** space, within the **Third-order nonlinear coherent vibrational microscopy** sub-domain of **Spectroscopy**. Measurements consist of photons collected by an optical detector via a **coherent nonlinear** sensing mechanism. The forward operator applies, in order: L · beat · twocolor operator; S · nonlinear · chi3 operator; detector accumulates flux over the exposure window. Observations are corrupted by shot noise in a coherent detection regime. Well-posed for multiplex CARS with full spectrum + max-entropy phase retrieval; ill-posed for narrowband CARS contaminated by chi_NR (distortive interference with Lorentzian chi_R). ## ⚙ 2. Forward Model Physical chain: **x** → L · beat · twocolor → S · nonlinear · chi3 → Temporal integration → **y** (detector). ``` y = ∫_t dt `S.nonlinear.chi3` `L.beat.twocolor` x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.beat.twocolor` | L · beat · twocolor operator | | `S.nonlinear.chi3` | S · nonlinear · chi3 operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Spectroscopy | | Sub domain | Third-order nonlinear coherent vibrational microscopy | | Carrier | photon | | Problem class | nonlinear_inverse_spectral | | Solution space | concentration_map | | Noise model | shot_poisson_coherent | | Integration axis | spectral_and_temporal | | Difficulty delta | 5 | | L dag | 3 | ## 📡 4. Measurement Model Well-posed for multiplex CARS with full spectrum + max-entropy phase retrieval; ill-posed for narrowband CARS contaminated by chi_NR (distortive interference with Lorentzian chi_R). | Metric | Value | |---|---| | Metric | concentration_NMSE | | Secondary | SNR_dB | ## 📏 5. Operating Range (Ω) **Center problem class:** `multiplex_cars` · **Forward operator:** `cars_chi3_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 256 | | W | px | 256 | | Rho nr | — | 0.3 | | N omega | — | 300 | | Lambda p nm | nm | 800 | | Lambda s nm | nm | 1064 | | Pulse energy fluct | — | 0.05 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 64 – 1024 | | W | px | 64 – 1024 | | Rho nr | — | 0.0 – 5.0 | | N omega | — | 1 – 2048 | | Lambda p nm | nm | 750 – 1100 | | Lambda s nm | nm | 1000 – 1300 | | Focal volume error | — | 0.0 – 0.2 | | Pulse energy fluct | — | 0.0 – 0.3 | | Frequency drift cm1 | — | 0.0 – 20.0 | ## 🎯 6. Tolerance (ε) **Center tolerance:** NMSE 2e-2 | Metric | Range | |---|---| | Nmse | 0.001 – 0.5 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **concentration_NMSE**, with κ = `300` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x29235831ed94226fd6649d7716997998c214b53ab22d5e395c703c28837060c2` - **Chain tx hash:** `0x54723a83a9406ebfe78f1969e8bb0a8f5f0edee140e4a6d8044b52bd1438a51d` - **Chain block:** `41554226` --- ## File Mapping This bundle consists of: `L1-138.md`, `L1-138.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-138.md` | Source of truth — edit this | Human or LLM | | `L1-138.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 `L1-138`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-138.md).
Regenerate L1-138.json so every field matches the Markdown.
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Output each file in its own fenced code block tagged with the filename.

⌥ Hierarchy

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L2-138-001 CARS Multiplex Spec (broadband CARS family)

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📋 JSON metadata

{
  "artifact_id": "L1-138",
  "chain_block": 41554226,
  "chain_hash": "0x29235831ed94226fd6649d7716997998c214b53ab22d5e395c703c28837060c2",
  "chain_tx_hash": "0x54723a83a9406ebfe78f1969e8bb0a8f5f0edee140e4a6d8044b52bd1438a51d",
  "domain": "Spectroscopy",
  "hardness_fn": {
    "delta": 5,
    "kappa": 300,
    "metric": "concentration_NMSE",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "concentration_NMSE",
    "regime": "Well-posed for multiplex CARS with full spectrum + max-entropy phase retrieval; ill-posed for narrowband CARS contaminated by chi_NR (distortive interference with Lorentzian chi_R).",
    "secondary": "SNR_dB"
  },
  "physics_fingerprint": {
    "L_DAG": 3.0,
    "carrier": "photon",
    "difficulty_delta": 5,
    "domain": "Spectroscopy",
    "integration_axis": "spectral_and_temporal",
    "noise_model": "shot_poisson_coherent",
    "primitives": [
      "L.beat.twocolor",
      "S.nonlinear.chi3",
      "int.temporal"
    ],
    "problem_class": "nonlinear_inverse_spectral",
    "sensing_mechanism": "coherent_nonlinear",
    "solution_space": "concentration_map",
    "sub_domain": "Third-order nonlinear coherent vibrational microscopy",
    "title": "CARS \u2014 Coherent Anti-Stokes Raman Scattering"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "cars_chi3_forward",
      "single_freq_cars",
      "broadband_cars"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "N_omega",
      "lambda_p_nm",
      "lambda_s_nm",
      "rho_NR",
      "pulse_energy_fluct",
      "frequency_drift_cm1",
      "focal_volume_error"
    ],
    "allowed_problem_classes": [
      "multiplex_cars",
      "single_freq_cars",
      "blind_chi_R"
    ],
    "center_spec": {
      "epsilon_fn_center": "NMSE 2e-2",
      "forward_operator": "cars_chi3_forward",
      "input_format": "multiplex_cube_plus_library",
      "omega": {
        "H": 256,
        "N_omega": 300,
        "W": 256,
        "lambda_p_nm": 800,
        "lambda_s_nm": 1064,
        "pulse_energy_fluct": 0.05,
        "rho_NR": 0.3
      },
      "problem_class": "multiplex_cars"
    },
    "epsilon_bounds": {
      "nmse": [
        0.001,
        0.5
      ]
    },
    "omega_bounds": {
      "H": [
        64,
        1024
      ],
      "N_omega": [
        1,
        2048
      ],
      "W": [
        64,
        1024
      ],
      "focal_volume_error": [
        0.0,
        0.2
      ],
      "frequency_drift_cm1": [
        0.0,
        20.0
      ],
      "lambda_p_nm": [
        750,
        1100
      ],
      "lambda_s_nm": [
        1000,
        1300
      ],
      "pulse_energy_fluct": [
        0.0,
        0.3
      ],
      "rho_NR": [
        0.0,
        5.0
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Third-order nonlinear coherent vibrational microscopy",
  "title": "CARS \u2014 Coherent Anti-Stokes Raman Scattering"
}

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