L1 ⚛ L1-017 ⊙ Testnet

Zernike Phase-Contrast Microscopy

Microscopy · Label-free phase visualization

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⬇ L1-017.md

# ⚛ L1 Principle — Zernike Phase-Contrast Microscopy **ID:** `L1-017` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Microscopy — *Label-free phase visualization* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 2D phase > **📡 Carrier:** photon · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554156 --- ## 🧠 1. Introduction **Zernike Phase-Contrast Microscopy** is a **nonlinear inverse problem** whose unknown lives in **2D phase** space, within the **Label-free phase visualization** sub-domain of **Microscopy**. Measurements consist of photons collected by an optical detector via a **phase plate interference** sensing mechanism. The forward operator applies, in order: L · phase plate operator; phase is lost; only intensity is measured; detector accumulates flux over the exposure window. Observations are corrupted by additive Gaussian noise. Existence of the recovered 2D phase 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 ~= 10); phase_plate_alignment dominates the stability cliff; halo_artifact 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 · phase plate → Magnitude-squared → Temporal integration → **y** (detector). ``` y = ∫_t dt |·|² `L.phase_plate` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.phase_plate` | L · phase plate operator | | `L.modulus_squared` | Phase is lost; only intensity is measured | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Microscopy | | Sub domain | Label-free phase visualization | | Carrier | photon | | Problem class | nonlinear_inverse | | Solution space | 2D_phase | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 3 | | L dag | 3 | ## 📡 4. Measurement Model Existence of the recovered 2D phase 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 ~= 10); phase_plate_alignment dominates the stability cliff; halo_artifact 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:** `zernike_phase_contrast` · **Forward operator:** `zernike_phase_contrast_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 1024 | | W | px | 1024 | | Na | — | 0.75 | | Pixel nm | nm | 200 | | Lambda nm | nm | 550 | | Photon count | — | 1000 | | Halo artifact | — | 0 | | Phase plate alignment | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 256 – 4096 | | W | px | 256 – 4096 | | Na | — | 0.3 – 1.0 | | Pixel nm | nm | 100 – 500 | | Lambda nm | nm | 400 – 700 | | Photon count | — | 100 – 20000 | | Halo artifact | — | 0.0 – 0.5 | | Phase plate alignment | — | 0.0 – 0.1 | | Annulus diaphragm drift | — | 0.0 – 0.1 | ## 🎯 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 = `200` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x1b4eb6666c67f5c4e1571bc63c21db808107cb1ff8c67434532bb4406d0781a1` - **Chain tx hash:** `0x12e1be1ad2428759b396576db622ae6d08d17aaf56deca84ab2f0c5acf40ce0d` - **Chain block:** `41554156` --- ## File Mapping This bundle consists of: `L1-017.md`, `L1-017.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-017.md` | Source of truth — edit this | Human or LLM | | `L1-017.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 `L1-017`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-017.md).
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L2-017-001 Zernike Phase-Contrast Microscopy Mismatch-Only Spec

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📋 JSON metadata

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  "domain": "Microscopy",
  "hardness_fn": {
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    "secondary": "SSIM"
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  "physics_fingerprint": {
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    "integration_axis": "temporal",
    "noise_model": "gaussian",
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    "sensing_mechanism": "phase_plate_interference",
    "solution_space": "2D_phase",
    "sub_domain": "Label-free phase visualization",
    "title": "Zernike Phase-Contrast Microscopy"
  },
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      "annulus_diaphragm_drift"
    ],
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    "center_spec": {
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      "forward_operator": "zernike_phase_contrast_forward",
      "input_format": "measurement_only",
      "omega": {
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        "NA": 0.75,
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        "halo_artifact": 0.0,
        "lambda_nm": 550,
        "phase_plate_alignment": 0.0,
        "photon_count": 1000,
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      "W": [
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      "annulus_diaphragm_drift": [
        0.0,
        0.1
      ],
      "halo_artifact": [
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        0.5
      ],
      "lambda_nm": [
        400,
        700
      ],
      "phase_plate_alignment": [
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        0.1
      ],
      "photon_count": [
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        20000
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      "pixel_nm": [
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        500
      ]
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  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Label-free phase visualization",
  "title": "Zernike Phase-Contrast Microscopy"
}

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