# ⚛  L1 Principle — Holographic Reconstruction — wavefront from interference

**ID:** `L1-246` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Electromagnetics — *Digital holography reconstruction*
> **🎯 Problem class:** linear inverse · **🧮 Solution space:** complex 2D field
> **📡 Carrier:** em · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41553989

---

## 🧠 1. Introduction

**Holographic Reconstruction — wavefront from interference** is a **linear inverse problem** whose unknown lives in **complex 2D field** space, within the **Digital holography reconstruction** sub-domain of **Electromagnetics**.

Measurements consist of electromagnetic field measurements via a **ccd** sensing mechanism.

The forward operator applies, in order: L · interference operator; L · fft reconstruct operator; L · demultiplex operator; pixel-level spatial averaging on the detector.

Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds.

## ⚙ 2. Forward Model

Physical chain: **x** → L · interference → L · fft reconstruct → L · demultiplex → Spatial integration → **y** (detector).

```
y = ∫_A dA `L.demultiplex` `L.fft_reconstruct` `L.interference` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.interference` | L · interference operator |
| `L.fft_reconstruct` | L · fft reconstruct operator |
| `L.demultiplex` | L · demultiplex operator |
| `int.spatial` | Pixel-level spatial averaging on the detector |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Electromagnetics |
| Sub domain | Digital holography reconstruction |
| Carrier | em |
| Problem class | linear_inverse |
| Solution space | complex_2D_field |
| Noise model | gaussian |
| Integration axis | spatial |
| Difficulty delta | 3 |
| L dag | 3 |

## 📡 4. Measurement Model

Conditional stability; mismatch parameters dominate at Omega bounds.

| Metric | Value |
|---|---|
| Metric | PSNR_dB |
| Secondary | SSIM |

## 📏 5. Operating Range (Ω)

**Center problem class:** `holo_recon` · **Forward operator:** `holo_recon_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| H | px | 1024 |
| W | px | 1024 |
| Z m | m | 0.1 |
| Snr db | dB | 30 |
| Lambda nm | nm | 633 |
| Z focus error | — | 0 |
| Twin image error | — | 0 |
| Ref beam tilt error | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| H | px | 128 – 4096 |
| W | px | 128 – 4096 |
| Z m | m | 0.001 – 10 |
| Snr db | dB | 0 – 40 |
| Lambda nm | nm | 100 – 10000 |
| Z focus error | — | 0.0 – 0.05 |
| Twin image error | — | 0.0 – 0.3 |
| Ref beam tilt error | — | 0.0 – 0.1 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 27.0

| Metric | Range |
|---|---|
| Psnr db | 10.0 – 45.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `240` and δ = `3`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x35de961792cda4d255ec9ccf0a19c1ce44171c2983ee7c7ab5dcaf8f9dd76058`
- **Chain tx hash:** `0xfa9f79900a4a9d80660866a020442ee88231cf7478533f642bf6320b2158e623`
- **Chain block:** `41553989`

---

## File Mapping

This bundle consists of: `L1-246.md`, `L1-246.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-246.md` | Source of truth — edit this | Human or LLM |
| `L1-246.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 `L1-246`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._