L1 ⚛ L1-089 ⊙ Testnet

Electron Backscatter Diffraction (EBSD) — crystallographic orientation mapping

Electron Microscopy · Kikuchi-pattern crystal orientation

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⬇ L1-089.md

# ⚛ L1 Principle — Electron Backscatter Diffraction (EBSD) — crystallographic orientation mapping **ID:** `L1-089` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Electron Microscopy — *Kikuchi-pattern crystal orientation* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** euler angle field > **📡 Carrier:** electron · **🌫 Noise:** shot poisson > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554184 --- ## 🧠 1. Introduction **Electron Backscatter Diffraction (EBSD) — crystallographic orientation mapping** is a **nonlinear inverse problem** whose unknown lives in **euler angle field** space, within the **Kikuchi-pattern crystal orientation** sub-domain of **Electron Microscopy**. Measurements consist of electrons collected by an electron detector via a **kikuchi diffraction pattern** sensing mechanism. The forward operator applies, in order: L · excitation · electron beam operator; L · diffraction kikuchi operator; L · pattern match operator; integration over the solid angle of incidence/emission. Observations are corrupted by Poisson shot noise from quantum-limited detection. Existence of the recovered euler angle field 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 ~= 25); pattern_center_drift dominates the stability cliff; band_contrast_degradation 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 · excitation · electron beam → L · diffraction kikuchi → L · pattern match → Angular integration → **y** (detector). ``` y = ∫dΩ `L.pattern_match` `L.diffraction_kikuchi` `L.excitation.electron_beam` x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.excitation.electron_beam` | L · excitation · electron beam operator | | `L.diffraction_kikuchi` | L · diffraction kikuchi operator | | `L.pattern_match` | L · pattern match operator | | `int.angular` | Integration over the solid angle of incidence/emission | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Electron Microscopy | | Sub domain | Kikuchi-pattern crystal orientation | | Carrier | electron | | Problem class | nonlinear_inverse | | Solution space | euler_angle_field | | Noise model | shot_poisson | | Integration axis | angular | | Difficulty delta | 5 | | L dag | 4 | ## 📡 4. Measurement Model Existence of the recovered euler angle field 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 ~= 25); pattern_center_drift dominates the stability cliff; band_contrast_degradation 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 | orientation_MAE_deg | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `ebsd_kikuchi` · **Forward operator:** `ebsd_kikuchi_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 1024 | | W | px | 1024 | | Kv | — | 20 | | Step nm | nm | 100 | | Peak electrons | — | 200 | | Pattern center drift | — | 0 | | Band contrast degradation | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 256 – 4096 | | W | px | 256 – 4096 | | Kv | — | 10 – 30 | | Step nm | nm | 10 – 1000 | | Peak electrons | — | 20 – 2000 | | Pattern center drift | — | 0.0 – 0.1 | | Grain boundary ambiguity | — | 0.0 – 0.3 | | Band contrast degradation | — | 0.0 – 0.5 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 0.5 | Metric | Range | |---|---| | Psnr db | 10.0 – 40.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **orientation_MAE_deg**, with κ = `500` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x552dd04e4f1654b0604973f09e411c7cb62855308209272563bafeac057db8f7` - **Chain tx hash:** `0xf705d315ca1c7fac5e4e647d8af9337dbf77876231e98acf65c0e826e4a5f5da` - **Chain block:** `41554184` --- ## File Mapping This bundle consists of: `L1-089.md`, `L1-089.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-089.md` | Source of truth — edit this | Human or LLM | | `L1-089.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 `L1-089`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-089-001 Electron Backscatter Diffraction (EBSD) — crystallographic orientation mapping Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41554184,
  "chain_hash": "0x552dd04e4f1654b0604973f09e411c7cb62855308209272563bafeac057db8f7",
  "chain_tx_hash": "0xf705d315ca1c7fac5e4e647d8af9337dbf77876231e98acf65c0e826e4a5f5da",
  "domain": "Electron Microscopy",
  "hardness_fn": {
    "delta": 5,
    "kappa": 500,
    "metric": "orientation_MAE_deg",
    "type": "epsilon_fn"
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      "license_hash": null,
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    "metric": "orientation_MAE_deg",
    "regime": "Existence of the recovered euler angle field 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 ~= 25); pattern_center_drift dominates the stability cliff; band_contrast_degradation 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": 5,
    "domain": "Electron Microscopy",
    "integration_axis": "angular",
    "noise_model": "shot_poisson",
    "primitives": [
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      "L.diffraction_kikuchi",
      "L.pattern_match",
      "int.angular"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "kikuchi_diffraction_pattern",
    "solution_space": "euler_angle_field",
    "sub_domain": "Kikuchi-pattern crystal orientation",
    "title": "Electron Backscatter Diffraction (EBSD) \u2014 crystallographic orientation mapping"
  },
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    "allowed_omega_dimensions": [
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      "W",
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      "step_nm",
      "peak_electrons",
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      "band_contrast_degradation",
      "pattern_center_drift",
      "band_contrast_degradation",
      "grain_boundary_ambiguity"
    ],
    "allowed_problem_classes": [
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    "center_spec": {
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      "input_format": "measurement_only",
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        "W": 1024,
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        "peak_electrons": 200,
        "step_nm": 100
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    "omega_bounds": {
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      "W": [
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        4096
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      "band_contrast_degradation": [
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        0.5
      ],
      "grain_boundary_ambiguity": [
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      ],
      "kV": [
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        30
      ],
      "pattern_center_drift": [
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        0.1
      ],
      "peak_electrons": [
        20,
        2000
      ],
      "step_nm": [
        10,
        1000
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Kikuchi-pattern crystal orientation",
  "title": "Electron Backscatter Diffraction (EBSD) \u2014 crystallographic orientation mapping"
}

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