L1 ⚛ L1-019 ⊙ Testnet

Darkfield Microscopy (oblique-illumination scattering imaging)

Microscopy · Scattering-only contrast via annular condenser

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⬇ L1-019.md

# ⚛ L1 Principle — Darkfield Microscopy (oblique-illumination scattering imaging) **ID:** `L1-019` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Microscopy — *Scattering-only contrast via annular condenser* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 2D intensity > **📡 Carrier:** photon · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 1 · **⛓ Block:** 41554156 --- ## 🧠 1. Introduction **Darkfield Microscopy (oblique-illumination scattering imaging)** is a **linear inverse problem** whose unknown lives in **2D intensity** space, within the **Scattering-only contrast via annular condenser** sub-domain of **Microscopy**. Measurements consist of photons collected by an optical detector via a **oblique scattering** sensing mechanism. The forward operator applies, in order: L · oblique illumination operator; L · scatter operator; detector accumulates flux over the exposure window. Observations are corrupted by additive Gaussian 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 ~= 5); condenser_angle_error dominates the stability cliff; stray_light and the remaining mismatch parameters contribute higher-order bias terms. Additive gaussian thermal/electronic 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 · oblique illumination → L · scatter → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.scatter` `L.oblique_illumination` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.oblique_illumination` | L · oblique illumination operator | | `L.scatter` | L · scatter operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Microscopy | | Sub domain | Scattering-only contrast via annular condenser | | Carrier | photon | | Problem class | linear_inverse | | Solution space | 2D_intensity | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 1 | | L dag | 2.2 | ## 📡 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 ~= 5); condenser_angle_error dominates the stability cliff; stray_light and the remaining mismatch parameters contribute higher-order bias terms. Additive gaussian thermal/electronic 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:** `darkfield` · **Forward operator:** `darkfield_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 1024 | | W | px | 1024 | | Na obj | — | 0.75 | | Na cond | — | 0.95 | | Pixel nm | nm | 200 | | Stray light | — | 0 | | Photon count | — | 500 | | Condenser angle error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 256 – 4096 | | W | px | 256 – 4096 | | Na obj | — | 0.3 – 1.3 | | Na cond | — | 0.6 – 1.4 | | Pixel nm | nm | 100 – 500 | | Stray light | — | 0.0 – 0.2 | | Photon count | — | 50 – 10000 | | Specimen absorption | — | 0.0 – 0.5 | | Condenser angle error | — | 0.0 – 0.05 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 26.0 | Metric | Range | |---|---| | Psnr db | 12.0 – 42.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `100` and δ = `1`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xa2dd03b62319dd7b0500dffd0b70abbf537b73a2a2d2661f264a8deb4fa6ca66` - **Chain tx hash:** `0x3b87ae09e57e3bf7e3bd2c345c15340c7a432d15fbd78f01495fe8dbb1819b61` - **Chain block:** `41554156` --- ## File Mapping This bundle consists of: `L1-019.md`, `L1-019.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-019.md` | Source of truth — edit this | Human or LLM | | `L1-019.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 `L1-019`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-019-001 Darkfield Microscopy (oblique-illumination scattering imaging) Mismatch-Only Spec

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📋 JSON metadata

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  "domain": "Microscopy",
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    "secondary": "SSIM"
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  "physics_fingerprint": {
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    "integration_axis": "temporal",
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      "L.scatter",
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    ],
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    "sensing_mechanism": "oblique_scattering",
    "solution_space": "2D_intensity",
    "sub_domain": "Scattering-only contrast via annular condenser",
    "title": "Darkfield Microscopy (oblique-illumination scattering imaging)"
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    "center_spec": {
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      "input_format": "measurement_only",
      "omega": {
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      ],
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      "photon_count": [
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      "specimen_absorption": [
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      "stray_light": [
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      ]
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  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Scattering-only contrast via annular condenser",
  "title": "Darkfield Microscopy (oblique-illumination scattering imaging)"
}

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