# ⚛  L1 Principle — Light-Field (Plenoptic) Imaging

**ID:** `L1-080` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Computational Optics — *4D plenoptic sampling*
> **🎯 Problem class:** linear inverse · **🧮 Solution space:** 4D light field
> **📡 Carrier:** photon · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554182

---

## 🧠 1. Introduction

**Light-Field (Plenoptic) Imaging** is a **linear inverse problem** whose unknown lives in **4D light field** space, within the **4D plenoptic sampling** sub-domain of **Computational Optics**.

Measurements consist of photons collected by an optical detector via a **plenoptic sampling** sensing mechanism.

The forward operator applies, in order: L · project · pupil operator; rotates source / detector to acquire different projections; F · shear operator; integration over the solid angle of incidence/emission.

Observations are corrupted by additive Gaussian noise. Well-posed when MLA is calibrated and scene lies within depth-of-field cone of each sub-aperture. Degrades at occlusion boundaries, specular highlights, and beyond the angular-resolution disparity limit; MLA misregistration couples spatial and angular dimensions.

## ⚙ 2. Forward Model

Physical chain: **x** → L · project · pupil → Angular scan → F · shear → Angular integration → **y** (detector).

```
y = ∫dΩ `F.shear` R(θ) `L.project.pupil` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.project.pupil` | L · project · pupil operator |
| `S.scan.angular` | Rotates source / detector to acquire different projections |
| `F.shear` | F · shear operator |
| `int.angular` | Integration over the solid angle of incidence/emission |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Computational Optics |
| Sub domain | 4D plenoptic sampling |
| Carrier | photon |
| Problem class | linear_inverse |
| Solution space | 4D_light_field |
| Noise model | gaussian |
| Integration axis | angular |
| Difficulty delta | 3 |
| L dag | 3.2 |

## 📡 4. Measurement Model

Well-posed when MLA is calibrated and scene lies within depth-of-field cone of each sub-aperture. Degrades at occlusion boundaries, specular highlights, and beyond the angular-resolution disparity limit; MLA misregistration couples spatial and angular dimensions.

| Metric | Value |
|---|---|
| Metric | LF_PSNR_dB |
| Secondary | refocus_PSNR_dB |

## 📏 5. Operating Range (Ω)

**Center problem class:** `lightfield_decoding` · **Forward operator:** `plenoptic_mla_capture`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| H | px | 625 |
| U | — | 9 |
| V | — | 9 |
| W | px | 434 |
| Mla offset | — | 0 |
| Mla rotation | — | 0 |
| Photon count | — | 1000 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| H | px | 128 – 2048 |
| U | — | 3 – 17 |
| V | — | 3 – 17 |
| W | px | 128 – 2048 |
| Mla offset | — | 0.0 – 2.0 |
| Mla rotation | — | 0.0 – 0.05 |
| Photon count | — | 50 – 10000 |
| Disparity range error | — | 0.0 – 2.0 |
| Vignetting per subaperture | — | 0.0 – 0.2 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 32.0 dB LF-PSNR

| Metric | Range |
|---|---|
| Psnr db | 20.0 – 44.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **LF_PSNR_dB**, with κ = `1500` and δ = `3`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x55191abc37624bb508f96979eab7ba1021ff0351dbcf59cd8c5159ffb7dfb32c`
- **Chain tx hash:** `0xc04066f8e6c6c7543ab3cfb1bee876ebe85343acb514e8882e1b59c19bfd8dc1`
- **Chain block:** `41554182`

---

## File Mapping

This bundle consists of: `L1-080.md`, `L1-080.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-080.md` | Source of truth — edit this | Human or LLM |
| `L1-080.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 `L1-080`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._