# ⚛  L1 Principle — Integral Photography (Lippmann-style MLA capture + reconstruction)

**ID:** `L1-081` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Computational Optics — *Microlens-array 3D imaging*
> **🎯 Problem class:** linear inverse · **🧮 Solution space:** 4D light field
> **📡 Carrier:** photon · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554183

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## 🧠 1. Introduction

**Integral Photography (Lippmann-style MLA capture + reconstruction)** is a **linear inverse problem** whose unknown lives in **4D light field** space, within the **Microlens-array 3D imaging** sub-domain of **Computational Optics**.

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

The forward operator applies, in order: L · project · pupil operator; an unspecified linear measurement operator; L · rearrange operator; pixel-level spatial averaging on the detector.

Observations are corrupted by additive Gaussian noise. Well-conditioned when MLA is rigidly calibrated and angular/spatial trade-off is sufficient (N_ml * L_x >= scene bandwidth). Fourier-mode integral photography trades angular for spatial resolution; reconstruction is linear with known MLA geometry.

## ⚙ 2. Forward Model

Physical chain: **x** → L · project · pupil → Generic linear operator → L · rearrange → Spatial integration → **y** (detector).

```
y = ∫_A dA `L.rearrange` A `L.project.pupil` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.project.pupil` | L · project · pupil operator |
| `L.linear_op` | An unspecified linear measurement operator |
| `L.rearrange` | L · rearrange operator |
| `int.spatial` | Pixel-level spatial averaging on the detector |

## 🔬 3. Physics Fingerprint

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

## 📡 4. Measurement Model

Well-conditioned when MLA is rigidly calibrated and angular/spatial trade-off is sufficient (N_ml * L_x >= scene bandwidth). Fourier-mode integral photography trades angular for spatial resolution; reconstruction is linear with known MLA geometry.

| Metric | Value |
|---|---|
| Metric | PSNR_dB |
| Secondary | disparity_MAE_px |

## 📏 5. Operating Range (Ω)

**Center problem class:** `integral_photography_decoding` · **Forward operator:** `mla_integral_photo_capture`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| H s | s | 2048 |
| L x | — | 20 |
| L y | — | 20 |
| W s | s | 2048 |
| N ml x | — | 100 |
| N ml y | — | 100 |
| Mla rotation | — | 0 |
| Photon count | — | 1000 |
| Mla pitch drift | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| H s | s | 512 – 8192 |
| L x | — | 5 – 50 |
| L y | — | 5 – 50 |
| W s | s | 512 – 8192 |
| N ml x | — | 20 – 400 |
| N ml y | — | 20 – 400 |
| Mla rotation | — | 0.0 – 0.05 |
| Photon count | — | 50 – 10000 |
| Mla pitch drift | — | 0.0 – 0.02 |
| Vignetting residual | — | 0.0 – 0.2 |
| Sensor mla gap error | — | 0.0 – 0.1 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 30.0 dB PSNR

| Metric | Range |
|---|---|
| Psnr db | 18.0 – 42.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `1200` and δ = `3`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x00ab86129a33565e3b06e8e802fe23bdd57111cfbc628a9caad9e9fd038eeb31`
- **Chain tx hash:** `0x88644c9580ab3fb4e37108cca886c94625a2f61e1f7ae8d91fdea89e231a4b73`
- **Chain block:** `41554183`

---

## File Mapping

This bundle consists of: `L1-081.md`, `L1-081.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-081.md` | Source of truth — edit this | Human or LLM |
| `L1-081.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 `L1-081`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._