L1 ⚛ L1-084 ⊙ Testnet

Scanning Electron Microscopy (SEM) — secondary-electron surface imaging

Electron Microscopy · Surface topography EM

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⬇ L1-084.md

# ⚛ L1 Principle — Scanning Electron Microscopy (SEM) — secondary-electron surface imaging **ID:** `L1-084` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Electron Microscopy — *Surface topography EM* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 2D intensity > **📡 Carrier:** electron · **🌫 Noise:** shot poisson > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554183 --- ## 🧠 1. Introduction **Scanning Electron Microscopy (SEM) — secondary-electron surface imaging** is a **linear inverse problem** whose unknown lives in **2D intensity** space, within the **Surface topography EM** sub-domain of **Electron Microscopy**. Measurements consist of electrons collected by an electron detector via a **electron beam scanning** sensing mechanism. The forward operator applies, in order: L · excitation · electron beam operator; ordered pixel-by-pixel sampling; D · secondary electron operator; detector accumulates flux over the exposure window. Observations are corrupted by Poisson shot noise from quantum-limited detection. 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); beam_drift dominates the stability cliff; charging_artifact and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) 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 · electron beam → Raster scan → D · secondary electron → Temporal integration → **y** (detector). ``` y = ∫_t dt `D.secondary_electron` S_raster `L.excitation.electron_beam` x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.excitation.electron_beam` | L · excitation · electron beam operator | | `S.scan.raster` | Ordered pixel-by-pixel sampling | | `D.secondary_electron` | D · secondary electron operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Electron Microscopy | | Sub domain | Surface topography EM | | Carrier | electron | | Problem class | linear_inverse | | Solution space | 2D_intensity | | Noise model | shot_poisson | | Integration axis | temporal | | Difficulty delta | 3 | | L dag | 3 | ## 📡 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); beam_drift dominates the stability cliff; charging_artifact and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) 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:** `sem_se` · **Forward operator:** `sem_se_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 2048 | | W | px | 2048 | | Kv | — | 5 | | Spot nm | nm | 1.5 | | Pixel nm | nm | 5 | | Beam drift | — | 0 | | Peak electrons | — | 100 | | Charging artifact | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 512 – 8192 | | W | px | 512 – 8192 | | Kv | — | 1 – 30 | | Spot nm | nm | 0.5 – 10 | | Pixel nm | nm | 0.5 – 100 | | Beam drift | — | 0.0 – 2.0 | | Beam damage | — | 0.0 – 0.5 | | Peak electrons | — | 10 – 10000 | | Charging artifact | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 30.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 40.0 | ## ⚖ 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:** `0xcbcb6c80ecdbef26d5fe95eb5fc64a4e46ba20f8da890e3c0c765008e447d4e6` - **Chain tx hash:** `0xf1e2014b8c0d1b745ecb106316da297ace1e4887957234a0b911ae7ca83db653` - **Chain block:** `41554183` --- ## File Mapping This bundle consists of: `L1-084.md`, `L1-084.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-084.md` | Source of truth — edit this | Human or LLM | | `L1-084.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 `L1-084`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-084-001 Scanning Electron Microscopy (SEM) — secondary-electron surface imaging Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41554183,
  "chain_hash": "0xcbcb6c80ecdbef26d5fe95eb5fc64a4e46ba20f8da890e3c0c765008e447d4e6",
  "chain_tx_hash": "0xf1e2014b8c0d1b745ecb106316da297ace1e4887957234a0b911ae7ca83db653",
  "domain": "Electron Microscopy",
  "hardness_fn": {
    "delta": 3,
    "kappa": 160,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
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      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
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  "layer": "L1",
  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "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); beam_drift dominates the stability cliff; charging_artifact and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) sets the irreducible data-fidelity floor, while mild Tikhonov or analytic inversion is sufficient at the nominal Omega point.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.0,
    "carrier": "electron",
    "difficulty_delta": 3,
    "domain": "Electron Microscopy",
    "integration_axis": "temporal",
    "noise_model": "shot_poisson",
    "primitives": [
      "L.excitation.electron_beam",
      "S.scan.raster",
      "D.secondary_electron",
      "int.temporal"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "electron_beam_scanning",
    "solution_space": "2D_intensity",
    "sub_domain": "Surface topography EM",
    "title": "Scanning Electron Microscopy (SEM) \u2014 secondary-electron surface imaging"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "sem_se_forward"
    ],
    "allowed_omega_dimensions": [
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      "W",
      "pixel_nm",
      "kV",
      "spot_nm",
      "peak_electrons",
      "beam_drift",
      "charging_artifact",
      "beam_drift",
      "charging_artifact",
      "beam_damage"
    ],
    "allowed_problem_classes": [
      "sem_se"
    ],
    "center_spec": {
      "epsilon_fn_center": "30.0",
      "forward_operator": "sem_se_forward",
      "input_format": "measurement_only",
      "omega": {
        "H": 2048,
        "W": 2048,
        "beam_drift": 0.0,
        "charging_artifact": 0.0,
        "kV": 5,
        "peak_electrons": 100,
        "pixel_nm": 5,
        "spot_nm": 1.5
      },
      "problem_class": "sem_se"
    },
    "epsilon_bounds": {
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        40.0
      ]
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    "omega_bounds": {
      "H": [
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        8192
      ],
      "W": [
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        8192
      ],
      "beam_damage": [
        0.0,
        0.5
      ],
      "beam_drift": [
        0.0,
        2.0
      ],
      "charging_artifact": [
        0.0,
        0.3
      ],
      "kV": [
        1,
        30
      ],
      "peak_electrons": [
        10,
        10000
      ],
      "pixel_nm": [
        0.5,
        100
      ],
      "spot_nm": [
        0.5,
        10
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Surface topography EM",
  "title": "Scanning Electron Microscopy (SEM) \u2014 secondary-electron surface imaging"
}

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