# ⚛  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._