L1 ⚛ L1-140 ⊙ Testnet

FTIR Imaging — Fourier-Transform Infrared Hyperspectral Microscopy

Spectroscopy · Mid-IR vibrational absorption hyperspectral imaging

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⬇ L1-140.md

# ⚛ L1 Principle — FTIR Imaging — Fourier-Transform Infrared Hyperspectral Microscopy **ID:** `L1-140` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Spectroscopy — *Mid-IR vibrational absorption hyperspectral imaging* > **🎯 Problem class:** linear inverse absorption · **🧮 Solution space:** concentration map hyperspectral > **📡 Carrier:** photon · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554227 --- ## 🧠 1. Introduction **FTIR Imaging — Fourier-Transform Infrared Hyperspectral Microscopy** is a **linear inverse absorption** whose unknown lives in **concentration map hyperspectral** space, within the **Mid-IR vibrational absorption hyperspectral imaging** sub-domain of **Spectroscopy**. Measurements consist of photons collected by an optical detector via a **ir absorption interferometric** sensing mechanism. The forward operator applies, in order: L · modulate · interferometer operator; L · absorb · beerlambert operator; detector sums all spectral bands. Observations are corrupted by additive Gaussian noise. Linear Beer-Lambert inverse problem; conditioning depends on spectral-overlap of K species. Mismatch: Mie scattering induces resonant distortions (Kramers-Kronig-like baseline); water vapor spikes. ## ⚙ 2. Forward Model Physical chain: **x** → L · modulate · interferometer → L · absorb · beerlambert → Spectral integration → **y** (detector). ``` y = Σ_λ `L.absorb.beerlambert` `L.modulate.interferometer` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.modulate.interferometer` | L · modulate · interferometer operator | | `L.absorb.beerlambert` | L · absorb · beerlambert operator | | `int.spectral` | Detector sums all spectral bands | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Spectroscopy | | Sub domain | Mid-IR vibrational absorption hyperspectral imaging | | Carrier | photon | | Problem class | linear_inverse_absorption | | Solution space | concentration_map_hyperspectral | | Noise model | gaussian | | Integration axis | spectral | | Difficulty delta | 3 | | L dag | 2.7 | ## 📡 4. Measurement Model Linear Beer-Lambert inverse problem; conditioning depends on spectral-overlap of K species. Mismatch: Mie scattering induces resonant distortions (Kramers-Kronig-like baseline); water vapor spikes. | Metric | Value | |---|---| | Metric | concentration_NMSE | | Secondary | classification_accuracy | ## 📏 5. Operating Range (Ω) **Center problem class:** `ftir_hyperspectral_unmix` · **Forward operator:** `beerlambert_spectrum` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 128 | | K | — | 5 | | W | px | 128 | | N nu | — | 1000 | | Delta nu cm1 | — | 8 | | Baseline drift | — | 0.05 | | Mie scattering | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 32 – 1024 | | K | — | 1 – 20 | | W | px | 32 – 1024 | | N nu | — | 128 – 4096 | | Delta nu cm1 | — | 2 – 32 | | Baseline drift | — | 0.0 – 0.3 | | Mie scattering | — | 0.0 – 0.5 | | Water vapor spikes | — | 0.0 – 0.2 | | Pure component uncertainty | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 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:** `0x3a3be0c168ad589a37495dbc1b7654e759510a33b0dc48b46bdfad4fc060ab59` - **Chain tx hash:** `0x42d4585feaeb4591de1656307e4f509396c9b5deab1ac5235d935fb18a7d70d4` - **Chain block:** `41554227` --- ## File Mapping This bundle consists of: `L1-140.md`, `L1-140.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-140.md` | Source of truth — edit this | Human or LLM | | `L1-140.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 `L1-140`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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📋 JSON metadata

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  "chain_block": 41554227,
  "chain_hash": "0x3a3be0c168ad589a37495dbc1b7654e759510a33b0dc48b46bdfad4fc060ab59",
  "chain_tx_hash": "0x42d4585feaeb4591de1656307e4f509396c9b5deab1ac5235d935fb18a7d70d4",
  "domain": "Spectroscopy",
  "hardness_fn": {
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    "kappa": 200,
    "metric": "concentration_NMSE",
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    "metric": "concentration_NMSE",
    "regime": "Linear Beer-Lambert inverse problem; conditioning depends on spectral-overlap of K species. Mismatch: Mie scattering induces resonant distortions (Kramers-Kronig-like baseline); water vapor spikes.",
    "secondary": "classification_accuracy"
  },
  "physics_fingerprint": {
    "L_DAG": 2.7,
    "carrier": "photon",
    "difficulty_delta": 3,
    "domain": "Spectroscopy",
    "integration_axis": "spectral",
    "noise_model": "gaussian",
    "primitives": [
      "L.modulate.interferometer",
      "L.absorb.beerlambert",
      "int.spectral"
    ],
    "problem_class": "linear_inverse_absorption",
    "sensing_mechanism": "ir_absorption_interferometric",
    "solution_space": "concentration_map_hyperspectral",
    "sub_domain": "Mid-IR vibrational absorption hyperspectral imaging",
    "title": "FTIR Imaging \u2014 Fourier-Transform Infrared Hyperspectral Microscopy"
  },
  "size_tiers": {
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      "N_nu",
      "delta_nu_cm1",
      "K",
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      "baseline_drift",
      "water_vapor_spikes",
      "pure_component_uncertainty"
    ],
    "allowed_problem_classes": [
      "ftir_hyperspectral_unmix",
      "ftir_classification",
      "blind_ftir_demix"
    ],
    "center_spec": {
      "epsilon_fn_center": "NMSE 5e-3",
      "forward_operator": "beerlambert_spectrum",
      "input_format": "absorbance_cube_plus_library",
      "omega": {
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        "K": 5,
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        "W": 128,
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        "delta_nu_cm1": 8,
        "mie_scattering": 0.0
      },
      "problem_class": "ftir_hyperspectral_unmix"
    },
    "epsilon_bounds": {
      "nmse": [
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        0.1
      ]
    },
    "omega_bounds": {
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        1024
      ],
      "K": [
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        20
      ],
      "N_nu": [
        128,
        4096
      ],
      "W": [
        32,
        1024
      ],
      "baseline_drift": [
        0.0,
        0.3
      ],
      "delta_nu_cm1": [
        2,
        32
      ],
      "mie_scattering": [
        0.0,
        0.5
      ],
      "pure_component_uncertainty": [
        0.0,
        0.3
      ],
      "water_vapor_spikes": [
        0.0,
        0.2
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Mid-IR vibrational absorption hyperspectral imaging",
  "title": "FTIR Imaging \u2014 Fourier-Transform Infrared Hyperspectral Microscopy"
}

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