# ⚛  L1 Principle — Flash LiDAR (single-shot 2D SPAD-array direct ToF)

**ID:** `L1-099` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Depth Imaging — *Flash-illumination focal-plane-array dToF*
> **🎯 Problem class:** linear inverse · **🧮 Solution space:** 2D depth map
> **📡 Carrier:** photon · **🌫 Noise:** shot poisson
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41547812

---

## 🧠 1. Introduction

**Flash LiDAR (single-shot 2D SPAD-array direct ToF)** is a **linear inverse problem** whose unknown lives in **2D depth map** space, within the **Flash-illumination focal-plane-array dToF** sub-domain of **Depth Imaging**.

Measurements consist of photons collected by an optical detector via a **flash pulse spad array** sensing mechanism.

The forward operator applies, in order: L · emit · flash operator; L · reflect scene operator; D · spad histogram operator; detector accumulates flux over the exposure window.

Observations are corrupted by Poisson shot noise from quantum-limited detection. Well-posed in high-SNR regime (photon_count_per_pixel >= 5). Under high ambient (sun-lit daytime), photon-efficient reconstruction (Kirmani, Shin) is required. Walk error (signal-ambient interference) shifts bin peaks; crosstalk between neighbouring SPAD pixels reduces effective resolution.

## ⚙ 2. Forward Model

Physical chain: **x** → L · emit · flash → L · reflect scene → D · spad histogram → Temporal integration → **y** (detector).

```
y = ∫_t dt `D.spad_histogram` `L.reflect_scene` `L.emit.flash` x,    measurements ~ Poisson(αy)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.emit.flash` | L · emit · flash operator |
| `L.reflect_scene` | L · reflect scene operator |
| `D.spad_histogram` | D · spad histogram operator |
| `int.temporal` | Detector accumulates flux over the exposure window |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Depth Imaging |
| Sub domain | Flash-illumination focal-plane-array dToF |
| Carrier | photon |
| Problem class | linear_inverse |
| Solution space | 2D_depth_map |
| Noise model | shot_poisson |
| Integration axis | temporal |
| Difficulty delta | 3 |
| L dag | 3 |

## 📡 4. Measurement Model

Well-posed in high-SNR regime (photon_count_per_pixel >= 5). Under high ambient (sun-lit daytime), photon-efficient reconstruction (Kirmani, Shin) is required. Walk error (signal-ambient interference) shifts bin peaks; crosstalk between neighbouring SPAD pixels reduces effective resolution.

| Metric | Value |
|---|---|
| Metric | depth_RMSE_mm |
| Secondary | outlier_fraction |

## 📏 5. Operating Range (Ω)

**Center problem class:** `flash_spad_dtof` · **Forward operator:** `flash_pulse_spad_histogram`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| H | px | 640 |
| W | px | 480 |
| N t | — | 1024 |
| Tau tdc ps | — | 100 |
| Walk error | — | 0 |
| Dark count rate | — | 100 |
| Ambient photon rate | — | 0 |
| Photon count per pixel | — | 20 |
| Crosstalk neighbour pixels | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| H | px | 128 – 1280 |
| W | px | 128 – 1280 |
| N t | — | 128 – 4096 |
| Tau tdc ps | — | 20 – 500 |
| Walk error | — | 0.0 – 0.2 |
| Dark count rate | — | 10 – 10000 |
| Pile up saturation | — | 0.0 – 0.5 |
| Ambient photon rate | — | 0.0 – 1000000 |
| Photon count per pixel | — | 1 – 1000 |
| Crosstalk neighbour pixels | — | 0.0 – 0.05 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 15.0 mm depth RMSE at 10 m

| Metric | Range |
|---|---|
| Rmse mm | 2.0 – 200.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **depth_RMSE_mm**, with κ = `800` and δ = `3`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0xdaf7231b5da64bd629f1f5201361cdc13761ddfa9bd505b084aca7a6748c680c`
- **Chain tx hash:** `0x9b50365487d4930a8928fb3d600621178c3b9d7d2acd12c14d3a6fec25cc8685`
- **Chain block:** `41547812`

---

## File Mapping

This bundle consists of: `L1-099.md`, `L1-099.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-099.md` | Source of truth — edit this | Human or LLM |
| `L1-099.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 `L1-099`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._