# ⚛  L1 Principle — Lensless Imaging with Diffuser PSF (DiffuserCam)

**ID:** `L1-075` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Computational Photography — *Flat-form-factor lensless imaging*
> **🎯 Problem class:** linear inverse · **🧮 Solution space:** 2D spatial
> **📡 Carrier:** photon · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554170

---

## 🧠 1. Introduction

**Lensless Imaging with Diffuser PSF (DiffuserCam)** is a **linear inverse problem** whose unknown lives in **2D spatial** space, within the **Flat-form-factor lensless imaging** sub-domain of **Computational Photography**.

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

The forward operator applies, in order: K · psf · caustic operator; S · select operator; detector accumulates flux over the exposure window.

Observations are corrupted by additive Gaussian noise. Deconvolution with a wideband random PSF is well-conditioned over the non-zero OTF support (caustics have rich high-frequency content). Cropping by sensor extent introduces boundary ill-posedness (recoverable via TV + boundary-extension priors). Mismatch between calibrated PSF and actual PSF (temperature drift, mask rotation) dominates stability.

## ⚙ 2. Forward Model

Physical chain: **x** → K · psf · caustic → S · select → Temporal integration → **y** (detector).

```
y = ∫_t dt `S.select` `K.psf.caustic` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `K.psf.caustic` | K · psf · caustic operator |
| `S.select` | S · select operator |
| `int.temporal` | Detector accumulates flux over the exposure window |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Computational Photography |
| Sub domain | Flat-form-factor lensless imaging |
| Carrier | photon |
| Problem class | linear_inverse |
| Solution space | 2D_spatial |
| Noise model | gaussian |
| Integration axis | spatial |
| Difficulty delta | 3 |
| L dag | 2.6 |

## 📡 4. Measurement Model

Deconvolution with a wideband random PSF is well-conditioned over the non-zero OTF support (caustics have rich high-frequency content). Cropping by sensor extent introduces boundary ill-posedness (recoverable via TV + boundary-extension priors). Mismatch between calibrated PSF and actual PSF (temperature drift, mask rotation) dominates stability.

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

## 📏 5. Operating Range (Ω)

**Center problem class:** `lensless_deconvolution` · **Forward operator:** `diffuser_psf_convolution`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| H | px | 512 |
| W | px | 512 |
| Psf h | — | 256 |
| Psf w | — | 256 |
| Psf drift | — | 0 |
| Photon count | — | 1000 |
| Mask rotation | — | 0 |
| Chromatic aberration | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| H | px | 128 – 2048 |
| W | px | 128 – 2048 |
| Psf h | — | 64 – 512 |
| Psf w | — | 64 – 512 |
| Psf drift | — | 0.0 – 0.1 |
| Dark offset | — | 0.0 – 0.02 |
| Photon count | — | 10 – 10000 |
| Mask rotation | — | 0.0 – 0.02 |
| Chromatic aberration | — | 0.0 – 0.05 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 26.0 dB PSNR

| Metric | Range |
|---|---|
| Psnr db | 16.0 – 38.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `1800` and δ = `3`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0xc4485a83284e8cbceab5500ca8a35d229762019b1f189d97309edb29b45b999b`
- **Chain tx hash:** `0x730892a23b2706bd9f15ef50438f052f1e0f5bc22e35cb961fc706de88c87196`
- **Chain block:** `41554170`

---

## File Mapping

This bundle consists of: `L1-075.md`, `L1-075.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-075.md` | Source of truth — edit this | Human or LLM |
| `L1-075.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 `L1-075`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._