# ⚛  L1 Principle — Cathodoluminescence (CL) Imaging & Spectroscopy

**ID:** `L1-136` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Scientific Instrumentation — *Electron-beam-induced light emission at nm resolution*
> **🎯 Problem class:** linear inverse spectral emission · **🧮 Solution space:** emission center map
> **📡 Carrier:** electron · **🌫 Noise:** shot poisson
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554226

---

## 🧠 1. Introduction

**Cathodoluminescence (CL) Imaging & Spectroscopy** is a **linear inverse spectral emission** whose unknown lives in **emission center map** space, within the **Electron-beam-induced light emission at nm resolution** sub-domain of **Scientific Instrumentation**.

Measurements consist of electrons collected by an electron detector via a **electron induced luminescence** sensing mechanism.

The forward operator applies, in order: L · absorb · eBeam operator; S · emit · recombine operator; L · disperse · spectral operator; detector accumulates flux over the exposure window.

Observations are corrupted by Poisson shot noise from quantum-limited detection. Linear at low injection; saturation/beam-damage at high current. Carrier-diffusion blurs spatial resolution beyond geometric beam.

## ⚙ 2. Forward Model

Physical chain: **x** → L · absorb · eBeam → S · emit · recombine → L · disperse · spectral → Temporal integration → **y** (detector).

```
y = ∫_t dt `L.disperse.spectral` `S.emit.recombine` `L.absorb.eBeam` x,    measurements ~ Poisson(αy)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.absorb.eBeam` | L · absorb · ebeam operator |
| `S.emit.recombine` | S · emit · recombine operator |
| `L.disperse.spectral` | L · disperse · spectral operator |
| `int.temporal` | Detector accumulates flux over the exposure window |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Scientific Instrumentation |
| Sub domain | Electron-beam-induced light emission at nm resolution |
| Carrier | electron |
| Problem class | linear_inverse_spectral_emission |
| Solution space | emission_center_map |
| Noise model | shot_poisson |
| Integration axis | spectral_and_spatial |
| Difficulty delta | 3 |
| L dag | 3.5 |

## 📡 4. Measurement Model

Linear at low injection; saturation/beam-damage at high current. Carrier-diffusion blurs spatial resolution beyond geometric beam.

| Metric | Value |
|---|---|
| Metric | emission_center_NMSE |
| Secondary | spatial_resolution_nm |

## 📏 5. Operating Range (Ω)

**Center problem class:** `cl_hyperspectral_mapping` · **Forward operator:** `cl_emission_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| H | px | 256 |
| K | — | 5 |
| W | px | 256 |
| N lambda | — | 500 |
| Pixel nm | nm | 10 |
| Beam energy kev | — | 10 |
| Carrier diffusion length | — | 50 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| H | px | 32 – 2048 |
| K | — | 1 – 20 |
| W | px | 32 – 2048 |
| N lambda | — | 64 – 2048 |
| Pixel nm | nm | 1 – 500 |
| Beam drift | — | 0.0 – 0.2 |
| Beam energy kev | — | 1 – 30 |
| Self absorption | — | 0.0 – 0.3 |
| Electron beam damage | — | 0.0 – 0.5 |
| Carrier diffusion length | — | 1 – 500 |
| 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 **emission_center_NMSE**, with κ = `200` and δ = `3`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x6162bc1d5380c4abaa63dbb41c2e67f344abfb9c3574266073f0e220572cf825`
- **Chain tx hash:** `0x76a0b7caf81f0ed096f043f28262b7a8cf833174f570c9b197df4a7a43a23464`
- **Chain block:** `41554226`

---

## File Mapping

This bundle consists of: `L1-136.md`, `L1-136.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-136.md` | Source of truth — edit this | Human or LLM |
| `L1-136.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 `L1-136`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._