L1 ⚛ L1-088 ⊙ Testnet

4D-STEM — pixelated-detector scanning diffraction imaging

Electron Microscopy · Momentum-resolved electron ptychography

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⬇ L1-088.md

# ⚛ L1 Principle — 4D-STEM — pixelated-detector scanning diffraction imaging **ID:** `L1-088` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Electron Microscopy — *Momentum-resolved electron ptychography* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** complex 2D > **📡 Carrier:** electron · **🌫 Noise:** shot poisson > **⚖ Difficulty (δ):** 10 · **⛓ Block:** 41554184 --- ## 🧠 1. Introduction **4D-STEM — pixelated-detector scanning diffraction imaging** is a **nonlinear inverse problem** whose unknown lives in **complex 2D** space, within the **Momentum-resolved electron ptychography** sub-domain of **Electron Microscopy**. Measurements consist of electrons collected by an electron detector via a **4d stem diffraction** sensing mechanism. The forward operator applies, in order: L · illumination · convergent probe operator; ordered pixel-by-pixel sampling; L · diffraction operator; phase is lost; only intensity is measured; pixel-level spatial averaging on the detector. Observations are corrupted by Poisson shot noise from quantum-limited detection. Existence of the recovered complex 2D 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 ~= 40); 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 → L · diffraction → Magnitude-squared → Spatial integration → **y** (detector). ``` y = ∫_A dA |·|² `L.diffraction` 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 | | `L.diffraction` | L · diffraction operator | | `L.modulus_squared` | Phase is lost; only intensity is measured | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Electron Microscopy | | Sub domain | Momentum-resolved electron ptychography | | Carrier | electron | | Problem class | nonlinear_inverse | | Solution space | complex_2D | | Noise model | shot_poisson | | Integration axis | angular | | Difficulty delta | 10 | | L dag | 4.5 | ## 📡 4. Measurement Model Existence of the recovered complex 2D 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 ~= 40); 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_ptychography` · **Forward operator:** `stem_ptychography_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 128 | | W | px | 128 | | Kv | — | 200 | | N q | — | 128 | | Pixel a | — | 0.3 | | Dose e per a2 | — | 10000 | | Scan distortion | — | 0 | | Probe aberration | — | 0 | | Partial coherence | — | 1 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 32 – 1024 | | W | px | 32 – 1024 | | Kv | — | 60 – 300 | | N q | — | 32 – 1024 | | Pixel a | — | 0.1 – 2.0 | | Dose e per a2 | — | 100 – 100000 | | Scan distortion | — | 0.0 – 0.05 | | Probe aberration | — | 0.0 – 0.3 | | Partial coherence | — | 0.6 – 1.0 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 24.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 40.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `800` and δ = `10`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x7cd537f25ca9dedbb219a2a693607d677a0daf6fe75a8b693c8b436e3fa150cf` - **Chain tx hash:** `0x0a49debd1fc8f2593e9823c630231c10af5a8eca5c4863f0cfd0dacee167530b` - **Chain block:** `41554184` --- ## File Mapping This bundle consists of: `L1-088.md`, `L1-088.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-088.md` | Source of truth — edit this | Human or LLM | | `L1-088.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 `L1-088`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-088-001 4D-STEM — pixelated-detector scanning diffraction imaging Mismatch-Only Spec

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📋 JSON metadata

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  "chain_tx_hash": "0x0a49debd1fc8f2593e9823c630231c10af5a8eca5c4863f0cfd0dacee167530b",
  "domain": "Electron Microscopy",
  "hardness_fn": {
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    "kappa": 800,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
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    "regime": "Existence of the recovered complex 2D 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 ~= 40); 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": {
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    "carrier": "electron",
    "difficulty_delta": 10,
    "domain": "Electron Microscopy",
    "integration_axis": "angular",
    "noise_model": "shot_poisson",
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      "S.scan.raster",
      "L.diffraction",
      "L.modulus_squared",
      "int.spatial"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "4d_stem_diffraction",
    "solution_space": "complex_2D",
    "sub_domain": "Momentum-resolved electron ptychography",
    "title": "4D-STEM \u2014 pixelated-detector scanning diffraction imaging"
  },
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      "scan_distortion",
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      "partial_coherence"
    ],
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        "N_q": 128,
        "W": 128,
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        "kV": 200,
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        "pixel_A": 0.3,
        "probe_aberration": 0.0,
        "scan_distortion": 0.0
      },
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    "epsilon_bounds": {
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      "N_q": [
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      "W": [
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      ],
      "dose_e_per_A2": [
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        100000
      ],
      "kV": [
        60,
        300
      ],
      "partial_coherence": [
        0.6,
        1.0
      ],
      "pixel_A": [
        0.1,
        2.0
      ],
      "probe_aberration": [
        0.0,
        0.3
      ],
      "scan_distortion": [
        0.0,
        0.05
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Momentum-resolved electron ptychography",
  "title": "4D-STEM \u2014 pixelated-detector scanning diffraction imaging"
}

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