# ⚛  L1 Principle — Scanning LiDAR (pulsed direct Time-of-Flight)

**ID:** `L1-096` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Depth Imaging — *Direct ToF ranging*
> **🎯 Problem class:** linear inverse · **🧮 Solution space:** 3D point cloud
> **📡 Carrier:** photon · **🌫 Noise:** shot poisson
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41547811

---

## 🧠 1. Introduction

**Scanning LiDAR (pulsed direct Time-of-Flight)** is a **linear inverse problem** whose unknown lives in **3D point cloud** space, within the **Direct ToF ranging** sub-domain of **Depth Imaging**.

Measurements consist of photons collected by an optical detector via a **pulsed dtof scan** sensing mechanism.

The forward operator applies, in order: S · emit · pulse operator; L · reflect scene operator; D · timestamp operator; integration over the solid angle of incidence/emission.

Observations are corrupted by Poisson shot noise from quantum-limited detection. Well-posed when returned pulse SNR > 10 dB. Atmospheric attenuation alpha_atm(d) = exp(-gamma * d) cuts range quadratically at rain/fog; retroreflective surfaces saturate the receiver; motion distortion (rolling-shutter of scan) biases point cloud during ego-motion.

## ⚙ 2. Forward Model

Physical chain: **x** → S · emit · pulse → L · reflect scene → D · timestamp → Angular integration → **y** (detector).

```
y = ∫dΩ `D.timestamp` `L.reflect_scene` `S.emit.pulse` x,    measurements ~ Poisson(αy)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `S.emit.pulse` | S · emit · pulse operator |
| `L.reflect_scene` | L · reflect scene operator |
| `D.timestamp` | D · timestamp operator |
| `int.angular` | Integration over the solid angle of incidence/emission |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Depth Imaging |
| Sub domain | Direct ToF ranging |
| Carrier | photon |
| Problem class | linear_inverse |
| Solution space | 3D_point_cloud |
| Noise model | shot_poisson |
| Integration axis | temporal |
| Difficulty delta | 3 |
| L dag | 3 |

## 📡 4. Measurement Model

Well-posed when returned pulse SNR > 10 dB. Atmospheric attenuation alpha_atm(d) = exp(-gamma * d) cuts range quadratically at rain/fog; retroreflective surfaces saturate the receiver; motion distortion (rolling-shutter of scan) biases point cloud during ego-motion.

| Metric | Value |
|---|---|
| Metric | point_cloud_RMSE_m |
| Secondary | detection_recall_at_range |

## 📏 5. Operating Range (Ω)

**Center problem class:** `pulsed_dtof_lidar` · **Forward operator:** `pulsed_scanning_lidar`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| N ch | — | 64 |
| F scan hz | Hz | 10 |
| Lambda nm | nm | 905 |
| Max range m | m | 200 |
| Tau pulse ns | ns | 5 |
| Motion distortion | — | 0 |
| Photon count per beam | — | 500 |
| Atmospheric extinction | — | 0 |
| Retroreflector saturation | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| N ch | — | 16 – 256 |
| F scan hz | Hz | 5 – 30 |
| Lambda nm | nm | 850 – 1550 |
| Max range m | m | 30 – 500 |
| Tau pulse ns | ns | 0.5 – 10 |
| Beam walk error | — | 0.0 – 0.01 |
| Motion distortion | — | 0.0 – 0.5 |
| Photon count per beam | — | 10 – 5000 |
| Atmospheric extinction | — | 0.0 – 2.0 |
| Crosstalk neighbour beams | — | 0.0 – 0.05 |
| Retroreflector saturation | — | 0.0 – 0.2 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 0.05 m point RMSE at 100 m

| Metric | Range |
|---|---|
| Rmse m | 0.01 – 1.0 |

## ⚖ 7. Hardness Function

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

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x1e40777b65932f4f482483408e2e456e7e6c6ec14eac5d24f72266a9b27b20be`
- **Chain tx hash:** `0x9c61c56323795b056cd1503e8bea10e7f3dcfa9106f71743c4afc98efbcf7deb`
- **Chain block:** `41547811`

---

## File Mapping

This bundle consists of: `L1-096.md`, `L1-096.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-096.md` | Source of truth — edit this | Human or LLM |
| `L1-096.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 `L1-096`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._