# ⚛  L1 Principle — Scanning Electron Microscopy (SEM) — secondary-electron surface imaging

**ID:** `L1-084` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Electron Microscopy — *Surface topography EM*
> **🎯 Problem class:** linear inverse · **🧮 Solution space:** 2D intensity
> **📡 Carrier:** electron · **🌫 Noise:** shot poisson
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554183

---

## 🧠 1. Introduction

**Scanning Electron Microscopy (SEM) — secondary-electron surface imaging** is a **linear inverse problem** whose unknown lives in **2D intensity** space, within the **Surface topography EM** sub-domain of **Electron Microscopy**.

Measurements consist of electrons collected by an electron detector via a **electron beam scanning** sensing mechanism.

The forward operator applies, in order: L · excitation · electron beam operator; ordered pixel-by-pixel sampling; D · secondary electron operator; detector accumulates flux over the exposure window.

Observations are corrupted by Poisson shot noise from quantum-limited detection. Existence of the recovered 2D intensity is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by the declared priors. Stability is well-conditioned (kappa_eff ~= 8); beam_drift dominates the stability cliff; charging_artifact and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) sets the irreducible data-fidelity floor, while mild Tikhonov or analytic inversion is sufficient at the nominal Omega point.

## ⚙ 2. Forward Model

Physical chain: **x** → L · excitation · electron beam → Raster scan → D · secondary electron → Temporal integration → **y** (detector).

```
y = ∫_t dt `D.secondary_electron` S_raster `L.excitation.electron_beam` x,    measurements ~ Poisson(αy)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.excitation.electron_beam` | L · excitation · electron beam operator |
| `S.scan.raster` | Ordered pixel-by-pixel sampling |
| `D.secondary_electron` | D · secondary electron operator |
| `int.temporal` | Detector accumulates flux over the exposure window |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Electron Microscopy |
| Sub domain | Surface topography EM |
| Carrier | electron |
| Problem class | linear_inverse |
| Solution space | 2D_intensity |
| Noise model | shot_poisson |
| Integration axis | temporal |
| Difficulty delta | 3 |
| L dag | 3 |

## 📡 4. Measurement Model

Existence of the recovered 2D intensity is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by the declared priors. Stability is well-conditioned (kappa_eff ~= 8); beam_drift dominates the stability cliff; charging_artifact and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) sets the irreducible data-fidelity floor, while mild Tikhonov or analytic inversion is sufficient at the nominal Omega point.

| Metric | Value |
|---|---|
| Metric | PSNR_dB |
| Secondary | SSIM |

## 📏 5. Operating Range (Ω)

**Center problem class:** `sem_se` · **Forward operator:** `sem_se_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| H | px | 2048 |
| W | px | 2048 |
| Kv | — | 5 |
| Spot nm | nm | 1.5 |
| Pixel nm | nm | 5 |
| Beam drift | — | 0 |
| Peak electrons | — | 100 |
| Charging artifact | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| H | px | 512 – 8192 |
| W | px | 512 – 8192 |
| Kv | — | 1 – 30 |
| Spot nm | nm | 0.5 – 10 |
| Pixel nm | nm | 0.5 – 100 |
| Beam drift | — | 0.0 – 2.0 |
| Beam damage | — | 0.0 – 0.5 |
| Peak electrons | — | 10 – 10000 |
| Charging artifact | — | 0.0 – 0.3 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 30.0

| Metric | Range |
|---|---|
| Psnr db | 10.0 – 40.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `160` and δ = `3`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0xcbcb6c80ecdbef26d5fe95eb5fc64a4e46ba20f8da890e3c0c765008e447d4e6`
- **Chain tx hash:** `0xf1e2014b8c0d1b745ecb106316da297ace1e4887957234a0b911ae7ca83db653`
- **Chain block:** `41554183`

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## File Mapping

This bundle consists of: `L1-084.md`, `L1-084.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-084.md` | Source of truth — edit this | Human or LLM |
| `L1-084.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 `L1-084`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._