L1 ⚛ L1-018 ⊙ Testnet

Differential Interference Contrast (DIC / Nomarski) Microscopy

Microscopy · Shear-interference phase-gradient imaging

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⬇ principle.md ⬇ principle.json

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⬇ L1-018.md ⬇ L1-018.json

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You are helping me submit a MODIFICATION of L1-018 (Differential Interference Contrast (DIC / Nomarski) Microscopy) to the PWM Protocol — a Principle (L1) artifact.

I will paste a Markdown template (or the current L1-018.md).
1. Rewrite the Markdown so the science is correct and clearly explained for my change.
2. Regenerate the sibling L1-018.json so EVERY field matches the Markdown.
3. Keep the schema in the "File Mapping" footer at the bottom of the MD.
4. Keep the parent reference unchanged unless I ask otherwise.
Rules: the Markdown is the source of truth; use SI units; do NOT invent benchmark scores.
Output each file in its own fenced code block tagged with the filename.

Here is my template:
[PASTE THE .md HERE]

⚙ Forward Model

y = ∫_t dt |·|² `L.add_coherent` `L.wollaston_shear` x + n,    n ~ 𝒩(0, σ²)

world state x (2D phase)

→

L · wollaston shear `L.wollaston_shear`

→

L · add coherent `L.add_coherent`

→

Magnitude-squared |·|²

→

Temporal integration ∫_t dt

→

observation y (photon detector)

Noise: additive Gaussian noise

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-018.md

# ⚛ L1 Principle — Differential Interference Contrast (DIC / Nomarski) Microscopy **ID:** `L1-018` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Microscopy — *Shear-interference phase-gradient imaging* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 2D phase > **📡 Carrier:** photon · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554156 --- ## 🧠 1. Introduction **Differential Interference Contrast (DIC / Nomarski) Microscopy** is a **nonlinear inverse problem** whose unknown lives in **2D phase** space, within the **Shear-interference phase-gradient imaging** sub-domain of **Microscopy**. Measurements consist of photons collected by an optical detector via a **shear interferometry** sensing mechanism. The forward operator applies, in order: L · wollaston shear operator; L · add coherent 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 ~= 12); shear_drift dominates the stability cliff; bias_retardation_error 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 · wollaston shear → L · add coherent → Magnitude-squared → Temporal integration → **y** (detector). ``` y = ∫_t dt |·|² `L.add_coherent` `L.wollaston_shear` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.wollaston_shear` | L · wollaston shear operator | | `L.add_coherent` | L · add coherent 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 | Shear-interference phase-gradient imaging | | Carrier | photon | | Problem class | nonlinear_inverse | | Solution space | 2D_phase | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 3 | | L dag | 3.5 | ## 📡 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 ~= 12); shear_drift dominates the stability cliff; bias_retardation_error 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:** `dic_nomarski` · **Forward operator:** `dic_nomarski_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 1024 | | W | px | 1024 | | Na | — | 1.4 | | Pixel nm | nm | 100 | | Shear nm | nm | 200 | | Shear drift | — | 0 | | Photon count | — | 1000 | | Theta bias deg | deg | 90 | | Bias retardation error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 256 – 4096 | | W | px | 256 – 4096 | | Na | — | 0.3 – 1.49 | | Pixel nm | nm | 50 – 300 | | Shear nm | nm | 50 – 500 | | Shear drift | — | 0.0 – 10.0 | | Photon count | — | 100 – 20000 | | Theta bias deg | deg | 30 – 150 | | Bias retardation error | — | 0.0 – 0.15 | | Condenser misalignment | — | 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 = `240` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xdaf5f3b45c8e21d94481ee3fe5ac7f9c56aa01956c90eb9f1aef59d777949c36` - **Chain tx hash:** `0x3c99a5af4af41dfa6ea357fea2201842d8decc2f9c47d78b2044f279c3012703` - **Chain block:** `41554156` --- ## File Mapping This bundle consists of: `L1-018.md`, `L1-018.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-018.md` | Source of truth — edit this | Human or LLM | | `L1-018.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 `L1-018`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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📋 JSON metadata

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  "chain_block": 41554156,
  "chain_hash": "0xdaf5f3b45c8e21d94481ee3fe5ac7f9c56aa01956c90eb9f1aef59d777949c36",
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  "domain": "Microscopy",
  "hardness_fn": {
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    "kappa": 240,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
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    "regime": "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 ~= 12); shear_drift dominates the stability cliff; bias_retardation_error 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.",
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  "physics_fingerprint": {
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      "int.temporal"
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    "sensing_mechanism": "shear_interferometry",
    "solution_space": "2D_phase",
    "sub_domain": "Shear-interference phase-gradient imaging",
    "title": "Differential Interference Contrast (DIC / Nomarski) Microscopy"
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      "condenser_misalignment": [
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      "photon_count": [
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        20000
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      "pixel_nm": [
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      ],
      "shear_drift": [
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      ],
      "shear_nm": [
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      ],
      "theta_bias_deg": [
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      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Shear-interference phase-gradient imaging",
  "title": "Differential Interference Contrast (DIC / Nomarski) Microscopy"
}

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