# ⚛  L1 Principle — Total Internal Reflection Fluorescence (TIRF)

**ID:** `L1-012` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Microscopy — *Evanescent-field surface-selective imaging*
> **🎯 Problem class:** linear inverse · **🧮 Solution space:** 2D intensity
> **📡 Carrier:** photon · **🌫 Noise:** poisson gaussian
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554155

---

## 🧠 1. Introduction

**Total Internal Reflection Fluorescence (TIRF)** is a **linear inverse problem** whose unknown lives in **2D intensity** space, within the **Evanescent-field surface-selective imaging** sub-domain of **Microscopy**.

Measurements consist of photons collected by an optical detector via a **evanescent field excitation** sensing mechanism.

The forward operator applies, in order: L · excitation · evanescent operator; convolution with the Airy disk of a circular aperture; detector accumulates flux over the exposure window.

Observations are corrupted by Poisson shot noise plus Gaussian read-out noise. Existence of the recovered 2D intensity is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by the declared priors. Stability is well-conditioned (kappa_eff ~= 8); coverslip_angle_drift dominates the stability cliff; penetration_depth_error and the remaining mismatch parameters contribute higher-order bias terms. Poisson signal noise + gaussian read noise sets the irreducible data-fidelity floor, while mild Tikhonov or analytic inversion is sufficient at the nominal Omega point.

## ⚙ 2. Forward Model

Physical chain: **x** → L · excitation · evanescent → Airy PSF convolution → Temporal integration → **y** (detector).

```
y = ∫_t dt K_Airy * `L.excitation.evanescent` x + n,    Poisson + 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.excitation.evanescent` | L · excitation · evanescent operator |
| `K.psf.airy` | Convolution with the airy disk of a circular aperture |
| `int.temporal` | Detector accumulates flux over the exposure window |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Microscopy |
| Sub domain | Evanescent-field surface-selective imaging |
| Carrier | photon |
| Problem class | linear_inverse |
| Solution space | 2D_intensity |
| Noise model | poisson_gaussian |
| Integration axis | temporal |
| Difficulty delta | 3 |
| L dag | 2.5 |

## 📡 4. Measurement Model

Existence of the recovered 2D intensity is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by the declared priors. Stability is well-conditioned (kappa_eff ~= 8); coverslip_angle_drift dominates the stability cliff; penetration_depth_error and the remaining mismatch parameters contribute higher-order bias terms. Poisson signal noise + gaussian read noise sets the irreducible data-fidelity floor, while mild Tikhonov or analytic inversion is sufficient at the nominal Omega point.

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

## 📏 5. Operating Range (Ω)

**Center problem class:** `tirf` · **Forward operator:** `tirf_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| H | px | 512 |
| W | px | 512 |
| Na | — | 1.49 |
| D p nm | nm | 100 |
| Pixel nm | nm | 100 |
| Peak photons | photons | 500 |
| Coverslip angle drift | — | 0 |
| Background volume fluorescence | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| H | px | 128 – 4096 |
| W | px | 128 – 4096 |
| Na | — | 1.4 – 1.49 |
| D p nm | nm | 50 – 300 |
| Pixel nm | nm | 50 – 300 |
| Peak photons | photons | 50 – 5000 |
| Coverslip angle drift | — | 0.0 – 0.5 |
| Penetration depth error | — | 0.0 – 0.3 |
| Background volume fluorescence | — | 0.0 – 0.3 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 28.0

| Metric | Range |
|---|---|
| Psnr db | 12.0 – 42.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `160` and δ = `3`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x6ea9b2675c3428287b42549754b99265fe3644e22a2ffc7338f9c6a9563c846a`
- **Chain tx hash:** `0x6f7b2f941284af69ef41dac81758049fa90e84f27599413413a5c2a1d94f1a23`
- **Chain block:** `41554155`

---

## File Mapping

This bundle consists of: `L1-012.md`, `L1-012.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-012.md` | Source of truth — edit this | Human or LLM |
| `L1-012.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 `L1-012`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._