# ⚛  L1 Principle — Ghost Imaging (correlated-photon imaging)

**ID:** `L1-153` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Quantum Imaging — *Imaging via photon-pair correlations between bucket and reference*
> **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 2D intensity
> **📡 Carrier:** photon · **🌫 Noise:** shot poisson
> **⚖ Difficulty (δ):** 10 · **⛓ Block:** 41554241

---

## 🧠 1. Introduction

**Ghost Imaging (correlated-photon imaging)** is a **nonlinear inverse problem** whose unknown lives in **2D intensity** space, within the **Imaging via photon-pair correlations between bucket and reference** sub-domain of **Quantum Imaging**.

Measurements consist of photons collected by an optical detector via a **photon correlation imaging** sensing mechanism.

The forward operator applies, in order: L · photon pair source operator; D · bucket detector operator; D · reference imaging operator; L · correlation operator; detector accumulates flux over the exposure window.

Observations are corrupted by Poisson shot noise from quantum-limited detection. Existence of the recovered 2D intensity is guaranteed within the declared Omega bounds. Uniqueness is local rather than global (non-convex landscape); convergence depends on initialisation and priors. Stability is moderately conditioned (kappa_eff ~= 30); photon_pair_rate dominates the stability cliff; accidental_coincidences and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) sets the irreducible data-fidelity floor, while TV / wavelet-sparsity / deep priors stabilise recovery at the ill-conditioned end of Omega.

## ⚙ 2. Forward Model

Physical chain: **x** → L · photon pair source → D · bucket detector → D · reference imaging → L · correlation → Temporal integration → **y** (detector).

```
y = ∫_t dt `L.correlation` `D.reference_imaging` `D.bucket_detector` `L.photon_pair_source` x,    measurements ~ Poisson(αy)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.photon_pair_source` | L · photon pair source operator |
| `D.bucket_detector` | D · bucket detector operator |
| `D.reference_imaging` | D · reference imaging operator |
| `L.correlation` | L · correlation operator |
| `int.temporal` | Detector accumulates flux over the exposure window |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Quantum Imaging |
| Sub domain | Imaging via photon-pair correlations between bucket and reference |
| Carrier | photon |
| Problem class | nonlinear_inverse |
| Solution space | 2D_intensity |
| Noise model | shot_poisson |
| Integration axis | temporal |
| Difficulty delta | 10 |
| L dag | 4.2 |

## 📡 4. Measurement Model

Existence of the recovered 2D intensity is guaranteed within the declared Omega bounds. Uniqueness is local rather than global (non-convex landscape); convergence depends on initialisation and priors. Stability is moderately conditioned (kappa_eff ~= 30); photon_pair_rate dominates the stability cliff; accidental_coincidences and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) sets the irreducible data-fidelity floor, while TV / wavelet-sparsity / deep priors stabilise recovery at the ill-conditioned end of Omega.

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

## 📏 5. Operating Range (Ω)

**Center problem class:** `ghost_imaging` · **Forward operator:** `ghost_imaging_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| H | px | 128 |
| W | px | 128 |
| N pairs | — | 100000 |
| Bucket snr db | dB | 10 |
| Photon pair rate | — | 1 |
| Reference calibration | — | 1 |
| Accidental coincidences | — | 0.1 |
| Environmental decoherence | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| H | px | 32 |
| W | px | 32 |
| N pairs | — | 1000 – 100000000 |
| Bucket snr db | dB | 0.0 – 30.0 |
| Photon pair rate | — | 0.1 – 10.0 |
| Reference calibration | — | 0.3 – 1.0 |
| Accidental coincidences | — | 0.0 – 0.5 |
| Environmental decoherence | — | 0.0 – 0.5 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 18.0

| Metric | Range |
|---|---|
| Psnr db | 5.0 – 40.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `600` and δ = `10`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0xb06391d95e4843afb8624a137b2b120388b1074027095e55a1dbb3f498d016ef`
- **Chain tx hash:** `0x69513649625e504ee17741b4df3ab31017e91ac64380a6bb2596f338396eb455`
- **Chain block:** `41554241`

---

## File Mapping

This bundle consists of: `L1-153.md`, `L1-153.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-153.md` | Source of truth — edit this | Human or LLM |
| `L1-153.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 `L1-153`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._