# ⚛  L1 Principle — Brillouin Microscopy (acousto-optic inelastic scattering)

**ID:** `L1-142` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Spectroscopy — *Mechanical-property hyperspectral microscopy*
> **🎯 Problem class:** parametric spectral fit · **🧮 Solution space:** elastic modulus map
> **📡 Carrier:** photon · **🌫 Noise:** shot poisson
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554227

---

## 🧠 1. Introduction

**Brillouin Microscopy (acousto-optic inelastic scattering)** is a **parametric spectral fit** whose unknown lives in **elastic modulus map** space, within the **Mechanical-property hyperspectral microscopy** sub-domain of **Spectroscopy**.

Measurements consist of photons collected by an optical detector via a **acoustic phonon inelastic** 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. Lorentzian peak fitting well-posed at SNR > 10 dB; multi-component mixing requires broader-peak modeling. Mismatch: elastic anisotropy, thermal drift, refractive-index uncertainty.

## ⚙ 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 | Mechanical-property hyperspectral microscopy |
| Carrier | photon |
| Problem class | parametric_spectral_fit |
| Solution space | elastic_modulus_map |
| Noise model | shot_poisson |
| Integration axis | spectral_and_temporal |
| Difficulty delta | 3 |
| L dag | 2.7 |

## 📡 4. Measurement Model

Lorentzian peak fitting well-posed at SNR > 10 dB; multi-component mixing requires broader-peak modeling. Mismatch: elastic anisotropy, thermal drift, refractive-index uncertainty.

| Metric | Value |
|---|---|
| Metric | frequency_RMSE_MHz |
| Secondary | modulus_NMSE |

## 📏 5. Operating Range (Ω)

**Center problem class:** `brillouin_peak_fitting` · **Forward operator:** `brillouin_backscatter`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| H | px | 128 |
| W | px | 128 |
| Z | — | 64 |
| N f | — | 200 |
| Tau ms | ms | 100 |
| Lambda nm | nm | 532 |
| Thermal drift | — | 0 |
| Refractive index uncertainty | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| H | px | 32 – 1024 |
| W | px | 32 – 1024 |
| Z | — | 1 – 256 |
| N f | — | 50 – 1024 |
| Tau ms | ms | 1 – 10000 |
| Anisotropy | — | 0.0 – 0.2 |
| Thermal drift | — | 0.0 – 0.1 |
| Rayleigh leakage | — | 0.0 – 0.5 |
| Spectrometer drift | — | 0.0 – 50 |
| Refractive index uncertainty | — | 0.0 – 0.05 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 20 MHz RMSE

| Metric | Range |
|---|---|
| Freq rmse mhz | 1 – 500 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **frequency_RMSE_MHz**, with κ = `100` and δ = `3`.

## 💾 8. Reference Dataset

- **primary** · weight 1.0 · IPFS _(not pinned yet)_

## 9. On-chain Registration

- **Chain hash:** `0x862b2ac5fe4e69738b13b23d1697c64ac12a0caabc7ac29ccd6db3dd3f47ee72`
- **Chain tx hash:** `0x9011b9005ac81fdf6b1e064034c870b05cc840caa497eb328e5e2baa8c071fd5`
- **Chain block:** `41554227`

---

## File Mapping

This bundle consists of: `L1-142.md`, `L1-142.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-142.md` | Source of truth — edit this | Human or LLM |
| `L1-142.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 `L1-142`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._