L1 ⚛ L1-087 ⊙ Testnet

Scanning TEM (STEM) — HAADF / BF imaging with convergent beam

Electron Microscopy · Atom-resolution Z-contrast imaging

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⬇ L1-087.md

# ⚛ L1 Principle — Scanning TEM (STEM) — HAADF / BF imaging with convergent beam **ID:** `L1-087` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Electron Microscopy — *Atom-resolution Z-contrast imaging* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 2D intensity > **📡 Carrier:** electron · **🌫 Noise:** shot poisson > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554184 --- ## 🧠 1. Introduction **Scanning TEM (STEM) — HAADF / BF imaging with convergent beam** is a **linear inverse problem** whose unknown lives in **2D intensity** space, within the **Atom-resolution Z-contrast imaging** sub-domain of **Electron Microscopy**. Measurements consist of electrons collected by an electron detector via a **convergent electron probe** sensing mechanism. The forward operator applies, in order: L · illumination · convergent probe operator; ordered pixel-by-pixel sampling; D · annular detector 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 moderately conditioned (kappa_eff ~= 18); probe_aberration dominates the stability cliff; scan_distortion and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) sets the irreducible data-fidelity floor, while TV / wavelet-sparsity / deep priors stabilise recovery at the ill-conditioned end of Omega. ## ⚙ 2. Forward Model Physical chain: **x** → L · illumination · convergent probe → Raster scan → D · annular detector → Temporal integration → **y** (detector). ``` y = ∫_t dt `D.annular_detector` S_raster `L.illumination.convergent_probe` x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.illumination.convergent_probe` | L · illumination · convergent probe operator | | `S.scan.raster` | Ordered pixel-by-pixel sampling | | `D.annular_detector` | D · annular detector operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Electron Microscopy | | Sub domain | Atom-resolution Z-contrast imaging | | Carrier | electron | | Problem class | linear_inverse | | Solution space | 2D_intensity | | Noise model | shot_poisson | | Integration axis | temporal | | Difficulty delta | 5 | | L dag | 3.5 | ## 📡 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 moderately conditioned (kappa_eff ~= 18); probe_aberration dominates the stability cliff; scan_distortion and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) sets the irreducible data-fidelity floor, while TV / wavelet-sparsity / deep priors stabilise recovery at the ill-conditioned end of Omega. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `stem_haadf` · **Forward operator:** `stem_haadf_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 2048 | | W | px | 2048 | | Kv | — | 200 | | Pixel a | — | 0.5 | | Beam damage | — | 0 | | Peak electrons | — | 200 | | Scan distortion | — | 0 | | Probe aberration | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 512 – 8192 | | W | px | 512 – 8192 | | Kv | — | 60 – 300 | | Pixel a | — | 0.1 – 5.0 | | Beam damage | — | 0.0 – 0.5 | | Peak electrons | — | 5 – 5000 | | Scan distortion | — | 0.0 – 0.05 | | Probe aberration | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 28.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 40.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `360` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x3de9b42148752d3c7d632cad5be3635229b880185b8c96446c341163a0c20627` - **Chain tx hash:** `0xad87a307345cbf69d564079e654446cd8b23316152b5bf0e7c765061f715d570` - **Chain block:** `41554184` --- ## File Mapping This bundle consists of: `L1-087.md`, `L1-087.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-087.md` | Source of truth — edit this | Human or LLM | | `L1-087.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 `L1-087`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-087-001 Scanning TEM (STEM) — HAADF / BF imaging with convergent beam Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41554184,
  "chain_hash": "0x3de9b42148752d3c7d632cad5be3635229b880185b8c96446c341163a0c20627",
  "chain_tx_hash": "0xad87a307345cbf69d564079e654446cd8b23316152b5bf0e7c765061f715d570",
  "domain": "Electron Microscopy",
  "hardness_fn": {
    "delta": 5,
    "kappa": 360,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
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  "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 moderately conditioned (kappa_eff ~= 18); probe_aberration dominates the stability cliff; scan_distortion and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) sets the irreducible data-fidelity floor, while TV / wavelet-sparsity / deep priors stabilise recovery at the ill-conditioned end of Omega.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.5,
    "carrier": "electron",
    "difficulty_delta": 5,
    "domain": "Electron Microscopy",
    "integration_axis": "temporal",
    "noise_model": "shot_poisson",
    "primitives": [
      "L.illumination.convergent_probe",
      "S.scan.raster",
      "D.annular_detector",
      "int.temporal"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "convergent_electron_probe",
    "solution_space": "2D_intensity",
    "sub_domain": "Atom-resolution Z-contrast imaging",
    "title": "Scanning TEM (STEM) \u2014 HAADF / BF imaging with convergent beam"
  },
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      "kV",
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      "peak_electrons",
      "beam_damage",
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    "allowed_problem_classes": [
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    "center_spec": {
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      "input_format": "measurement_only",
      "omega": {
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        "W": 2048,
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        "peak_electrons": 200,
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        "scan_distortion": 0.0
      },
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      ]
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    "omega_bounds": {
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        8192
      ],
      "W": [
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        8192
      ],
      "beam_damage": [
        0.0,
        0.5
      ],
      "kV": [
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      ],
      "peak_electrons": [
        5,
        5000
      ],
      "pixel_A": [
        0.1,
        5.0
      ],
      "probe_aberration": [
        0.0,
        0.3
      ],
      "scan_distortion": [
        0.0,
        0.05
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Atom-resolution Z-contrast imaging",
  "title": "Scanning TEM (STEM) \u2014 HAADF / BF imaging with convergent beam"
}

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