# ⚛  L1 Principle — Streak Camera — picosecond 1D time-resolved imaging

**ID:** `L1-149` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Ultrafast Imaging — *1D time-resolved photoelectron streaking*
> **🎯 Problem class:** linear inverse · **🧮 Solution space:** 1D time trace
> **📡 Carrier:** photon · **🌫 Noise:** shot poisson
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554229

---

## 🧠 1. Introduction

**Streak Camera — picosecond 1D time-resolved imaging** is a **linear inverse problem** whose unknown lives in **1D time trace** space, within the **1D time-resolved photoelectron streaking** sub-domain of **Ultrafast Imaging**.

Measurements consist of photons collected by an optical detector via a **streak tube time resolved** sensing mechanism.

The forward operator applies, in order: L · photocathode operator; L · sweep voltage operator; D · streaked phosphor operator; detector accumulates flux over the exposure window.

Observations are corrupted by Poisson shot noise from quantum-limited detection. Existence of the recovered 1D time trace 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 moderately conditioned (kappa_eff ~= 12); sweep_nonlinearity dominates the stability cliff; photocathode_jitter 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 · photocathode → L · sweep voltage → D · streaked phosphor → Temporal integration → **y** (detector).

```
y = ∫_t dt `D.streaked_phosphor` `L.sweep_voltage` `L.photocathode` x,    measurements ~ Poisson(αy)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.photocathode` | L · photocathode operator |
| `L.sweep_voltage` | L · sweep voltage operator |
| `D.streaked_phosphor` | D · streaked phosphor operator |
| `int.temporal` | Detector accumulates flux over the exposure window |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Ultrafast Imaging |
| Sub domain | 1D time-resolved photoelectron streaking |
| Carrier | photon |
| Problem class | linear_inverse |
| Solution space | 1D_time_trace |
| Noise model | shot_poisson |
| Integration axis | temporal |
| Difficulty delta | 5 |
| L dag | 3.3 |

## 📡 4. Measurement Model

Existence of the recovered 1D time trace 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 moderately conditioned (kappa_eff ~= 12); sweep_nonlinearity dominates the stability cliff; photocathode_jitter 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:** `streak_camera` · **Forward operator:** `streak_camera_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| N t | — | 1024 |
| N x | — | 1024 |
| Sweep ps | — | 100 |
| Afterglow | — | 0 |
| Photon count | — | 500 |
| Space charge | — | 0 |
| Sweep nonlinearity | — | 0 |
| Photocathode jitter | — | 0.5 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| N t | — | 128 – 4096 |
| N x | — | 128 – 4096 |
| Sweep ps | — | 1 – 1000 |
| Afterglow | — | 0.0 – 0.3 |
| Photon count | — | 10 – 10000 |
| Space charge | — | 0.0 – 0.3 |
| Sweep nonlinearity | — | 0.0 – 0.3 |
| Photocathode jitter | — | 0.0 – 5.0 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 26.0

| Metric | Range |
|---|---|
| Psnr db | 5.0 – 40.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `240` and δ = `5`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0xabe8402be261e624237347f71c511f7b48021b9c295bb2b2becf6765775d6ce9`
- **Chain tx hash:** `0xe170b82b27c15c7df9bf0e446671249f2f9bef84cf7eec561bb358281f568022`
- **Chain block:** `41554229`

---

## File Mapping

This bundle consists of: `L1-149.md`, `L1-149.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-149.md` | Source of truth — edit this | Human or LLM |
| `L1-149.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 `L1-149`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._