# ⚛  L1 Principle — LIBS — Laser-Induced Breakdown Spectroscopy imaging

**ID:** `L1-141` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Spectroscopy — *Atomic emission elemental imaging*
> **🎯 Problem class:** nonlinear inverse emission · **🧮 Solution space:** elemental concentration map
> **📡 Carrier:** photon · **🌫 Noise:** shot poisson
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554227

---

## 🧠 1. Introduction

**LIBS — Laser-Induced Breakdown Spectroscopy imaging** is a **nonlinear inverse emission** whose unknown lives in **elemental concentration map** space, within the **Atomic emission elemental imaging** sub-domain of **Spectroscopy**.

Measurements consist of photons collected by an optical detector via a **plasma emission** sensing mechanism.

The forward operator applies, in order: L · ablate · plasma operator; S · emit · atomic operator; L · disperse · spectral operator; detector accumulates flux over the exposure window.

Observations are corrupted by Poisson shot noise from quantum-limited detection. Plasma physics non-linear but under LTE the Saha-Boltzmann equation yields explicit calibration; self-absorption violates linearity; matrix-effect mismatch dominant uncertainty.

## ⚙ 2. Forward Model

Physical chain: **x** → L · ablate · plasma → S · emit · atomic → L · disperse · spectral → Temporal integration → **y** (detector).

```
y = ∫_t dt `L.disperse.spectral` `S.emit.atomic` `L.ablate.plasma` x,    measurements ~ Poisson(αy)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.ablate.plasma` | L · ablate · plasma operator |
| `S.emit.atomic` | S · emit · atomic 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 | Atomic emission elemental imaging |
| Carrier | photon |
| Problem class | nonlinear_inverse_emission |
| Solution space | elemental_concentration_map |
| Noise model | shot_poisson |
| Integration axis | spectral_and_temporal |
| Difficulty delta | 5 |
| L dag | 3 |

## 📡 4. Measurement Model

Plasma physics non-linear but under LTE the Saha-Boltzmann equation yields explicit calibration; self-absorption violates linearity; matrix-effect mismatch dominant uncertainty.

| Metric | Value |
|---|---|
| Metric | concentration_NMSE |
| Secondary | LOD_ppm |

## 📏 5. Operating Range (Ω)

**Center problem class:** `libs_elemental_mapping` · **Forward operator:** `libs_plasma_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| H | px | 256 |
| K | — | 5 |
| W | px | 256 |
| E p mj | — | 50 |
| Gate us | µs | 10 |
| N lambda | — | 2048 |
| Delay us | µs | 1 |
| Self absorption | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| H | px | 32 – 2048 |
| K | — | 1 – 30 |
| W | px | 32 – 2048 |
| E p mj | — | 5 – 500 |
| Gate us | µs | 0.1 – 100 |
| N lambda | — | 512 – 16384 |
| Delay us | µs | 0.1 – 100 |
| Matrix effects | — | 0.0 – 0.3 |
| Self absorption | — | 0.0 – 0.5 |
| Plasma temp drift | — | 0.0 – 0.3 |
| Shot to shot variability | — | 0.0 – 0.3 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** NMSE 0.05

| Metric | Range |
|---|---|
| Nmse | 0.001 – 0.5 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **concentration_NMSE**, with κ = `500` and δ = `5`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x18c79b747a6b87c142442621a12d8d71cffe88d33773615addd7d67f1d589354`
- **Chain tx hash:** `0xb4d33703da75b45bd14e81910462186fab474928d8ebb866b81ccea850497537`
- **Chain block:** `41554227`

---

## File Mapping

This bundle consists of: `L1-141.md`, `L1-141.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-141.md` | Source of truth — edit this | Human or LLM |
| `L1-141.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 `L1-141`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._