# ⚛  L1 Principle — XRF Tomography — X-ray Fluorescence CT

**ID:** `L1-134` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Scientific Instrumentation — *Elemental 3D tomography via fluorescence detection*
> **🎯 Problem class:** linear tomographic inverse · **🧮 Solution space:** 3d elemental concentration
> **📡 Carrier:** photon · **🌫 Noise:** shot poisson
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554214

---

## 🧠 1. Introduction

**XRF Tomography — X-ray Fluorescence CT** is a **linear tomographic reconstruction** whose unknown lives in **3d elemental concentration** space, within the **Elemental 3D tomography via fluorescence detection** sub-domain of **Scientific Instrumentation**.

Measurements consist of photons collected by an optical detector via a **xray fluorescence yield** sensing mechanism.

The forward operator applies, in order: L · absorb · innerShell operator; S · emit · fluor operator; L · project · pencilbeam operator; pixel-level spatial averaging on the detector.

Observations are corrupted by Poisson shot noise from quantum-limited detection. Linear at low concentration; self-absorption breaks linearity (must be corrected iteratively). Limited-angle geometry adds ill-posedness.

## ⚙ 2. Forward Model

Physical chain: **x** → L · absorb · innerShell → S · emit · fluor → L · project · pencilbeam → Spatial integration → **y** (detector).

```
y = ∫_A dA `L.project.pencilbeam` `S.emit.fluor` `L.absorb.innerShell` x,    measurements ~ Poisson(αy)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.absorb.innerShell` | L · absorb · innershell operator |
| `S.emit.fluor` | S · emit · fluor operator |
| `L.project.pencilbeam` | L · project · pencilbeam operator |
| `int.spatial` | Pixel-level spatial averaging on the detector |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Scientific Instrumentation |
| Sub domain | Elemental 3D tomography via fluorescence detection |
| Carrier | photon |
| Problem class | linear_tomographic_inverse |
| Solution space | 3d_elemental_concentration |
| Noise model | shot_poisson |
| Integration axis | projection |
| Difficulty delta | 3 |
| L dag | 3 |

## 📡 4. Measurement Model

Linear at low concentration; self-absorption breaks linearity (must be corrected iteratively). Limited-angle geometry adds ill-posedness.

| Metric | Value |
|---|---|
| Metric | concentration_NMSE |
| Secondary | spatial_resolution_um |

## 📏 5. Operating Range (Ω)

**Center problem class:** `xrf_tomography` · **Forward operator:** `xrf_ct_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| H | px | 500 |
| K | — | 10 |
| W | px | 500 |
| N view | — | 360 |
| Pixel um | µm | 1 |
| E exc kev | — | 20 |
| Self absorption | — | 0.1 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| H | px | 64 – 2048 |
| K | — | 1 – 30 |
| W | px | 64 – 2048 |
| N view | — | 10 – 1000 |
| Pixel um | µm | 0.1 – 100 |
| E exc kev | — | 5 – 50 |
| Self absorption | — | 0.0 – 0.8 |
| Pileup correction | — | 0.0 – 0.2 |
| Detector live time | — | 0.1 – 1.0 |
| Scatter background | — | 0.0 – 0.3 |
| Beam position jitter | — | 0.0 – 2 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** NMSE 0.02

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

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **concentration_NMSE**, with κ = `500` and δ = `3`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x36c1be9356697935b503381c1fdbe41727da9974932e724504afc3a9507a8e22`
- **Chain tx hash:** `0x320e79fa04307dea821f7da23ff521db7302e8a4375bb608ad14cd0b8d38552e`
- **Chain block:** `41554214`

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## File Mapping

This bundle consists of: `L1-134.md`, `L1-134.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-134.md` | Source of truth — edit this | Human or LLM |
| `L1-134.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 `L1-134`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._