L1 ⚛ L1-085 ⊙ Testnet

Transmission Electron Microscopy (TEM) — thin-section contrast imaging

Electron Microscopy · Phase-contrast electron transmission

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⬇ L1-085.md

# ⚛ L1 Principle — Transmission Electron Microscopy (TEM) — thin-section contrast imaging **ID:** `L1-085` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Electron Microscopy — *Phase-contrast electron transmission* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 2D phase > **📡 Carrier:** electron · **🌫 Noise:** shot poisson > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554183 --- ## 🧠 1. Introduction **Transmission Electron Microscopy (TEM) — thin-section contrast imaging** is a **linear inverse problem** whose unknown lives in **2D phase** space, within the **Phase-contrast electron transmission** sub-domain of **Electron Microscopy**. Measurements consist of electrons collected by an electron detector via a **electron transmission** sensing mechanism. The forward operator applies, in order: L · illumination · coherent beam operator; L · transmit sample operator; L · lens aberration operator; detector accumulates flux over the exposure window. Observations are corrupted by Poisson shot noise from quantum-limited detection. Existence of the recovered 2D phase 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 ~= 12); defocus_nm dominates the stability cliff; Cs_aberration 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 · illumination · coherent beam → L · transmit sample → L · lens aberration → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.lens_aberration` `L.transmit_sample` `L.illumination.coherent_beam` x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.illumination.coherent_beam` | L · illumination · coherent beam operator | | `L.transmit_sample` | L · transmit sample operator | | `L.lens_aberration` | L · lens aberration operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Electron Microscopy | | Sub domain | Phase-contrast electron transmission | | Carrier | electron | | Problem class | linear_inverse | | Solution space | 2D_phase | | Noise model | shot_poisson | | Integration axis | temporal | | Difficulty delta | 3 | | L dag | 3.3 | ## 📡 4. Measurement Model Existence of the recovered 2D phase 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 ~= 12); defocus_nm dominates the stability cliff; Cs_aberration 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:** `tem_ctf` · **Forward operator:** `tem_ctf_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 4096 | | W | px | 4096 | | Kv | — | 300 | | Cs mm | mm | 2.7 | | Pixel a | — | 1 | | Drift nm | nm | 0 | | Defocus nm | nm | -80 | | Peak electrons | — | 50 | | Envelope coherence | — | 1 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 1024 – 8192 | | W | px | 1024 – 8192 | | Kv | — | 80 – 300 | | Cs mm | mm | 0.01 – 5.0 | | Pixel a | — | 0.3 – 5.0 | | Drift nm | nm | 0.0 – 5.0 | | Defocus nm | nm | -2000 – 2000 | | Peak electrons | — | 1 – 1000 | | Envelope coherence | — | 0.5 – 1.0 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 26.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 40.0 | ## ⚖ 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:** `0xa8e36a2459d223c4be945625a2cf20aa0a8ceaef9882c2d56957e5ee4e75a21a` - **Chain tx hash:** `0x183d8ec5e79a28d11334bad4a73f79425b14cc08d42722d2b8c8f5371d63f511` - **Chain block:** `41554183` --- ## File Mapping This bundle consists of: `L1-085.md`, `L1-085.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-085.md` | Source of truth — edit this | Human or LLM | | `L1-085.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 `L1-085`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-085-001 Transmission Electron Microscopy (TEM) — thin-section contrast imaging Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-085",
  "chain_block": 41554183,
  "chain_hash": "0xa8e36a2459d223c4be945625a2cf20aa0a8ceaef9882c2d56957e5ee4e75a21a",
  "chain_tx_hash": "0x183d8ec5e79a28d11334bad4a73f79425b14cc08d42722d2b8c8f5371d63f511",
  "domain": "Electron Microscopy",
  "hardness_fn": {
    "delta": 3,
    "kappa": 240,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "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 phase 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 ~= 12); defocus_nm dominates the stability cliff; Cs_aberration 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": 3.3,
    "carrier": "electron",
    "difficulty_delta": 3,
    "domain": "Electron Microscopy",
    "integration_axis": "temporal",
    "noise_model": "shot_poisson",
    "primitives": [
      "L.illumination.coherent_beam",
      "L.transmit_sample",
      "L.lens_aberration",
      "int.temporal"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "electron_transmission",
    "solution_space": "2D_phase",
    "sub_domain": "Phase-contrast electron transmission",
    "title": "Transmission Electron Microscopy (TEM) \u2014 thin-section contrast imaging"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "tem_ctf_forward"
    ],
    "allowed_omega_dimensions": [
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      "W",
      "pixel_A",
      "kV",
      "Cs_mm",
      "defocus_nm",
      "peak_electrons",
      "drift_nm",
      "envelope_coherence",
      "defocus_nm",
      "Cs_aberration",
      "drift_nm",
      "envelope_coherence"
    ],
    "allowed_problem_classes": [
      "tem_ctf"
    ],
    "center_spec": {
      "epsilon_fn_center": "26.0",
      "forward_operator": "tem_ctf_forward",
      "input_format": "measurement_only",
      "omega": {
        "Cs_mm": 2.7,
        "H": 4096,
        "W": 4096,
        "defocus_nm": -80,
        "drift_nm": 0.0,
        "envelope_coherence": 1.0,
        "kV": 300,
        "peak_electrons": 50,
        "pixel_A": 1.0
      },
      "problem_class": "tem_ctf"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        40.0
      ]
    },
    "omega_bounds": {
      "Cs_mm": [
        0.01,
        5.0
      ],
      "H": [
        1024,
        8192
      ],
      "W": [
        1024,
        8192
      ],
      "defocus_nm": [
        -2000,
        2000
      ],
      "drift_nm": [
        0.0,
        5.0
      ],
      "envelope_coherence": [
        0.5,
        1.0
      ],
      "kV": [
        80,
        300
      ],
      "peak_electrons": [
        1,
        1000
      ],
      "pixel_A": [
        0.3,
        5.0
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Phase-contrast electron transmission",
  "title": "Transmission Electron Microscopy (TEM) \u2014 thin-section contrast imaging"
}

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