L1 ⚛ L1-074 ⊙ Testnet

Talbot-Lau Grating Interferometry (X-ray phase-contrast imaging)

Coherent Imaging · Grating-based phase and dark-field imaging

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⬇ L1-074.md

# ⚛ L1 Principle — Talbot-Lau Grating Interferometry (X-ray phase-contrast imaging) **ID:** `L1-074` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Coherent Imaging — *Grating-based phase and dark-field imaging* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** triplet 2D fields > **📡 Carrier:** x_ray · **🌫 Noise:** shot poisson > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554170 --- ## 🧠 1. Introduction **Talbot-Lau Grating Interferometry (X-ray phase-contrast imaging)** is a **linear inverse problem** whose unknown lives in **triplet 2D fields** space, within the **Grating-based phase and dark-field imaging** sub-domain of **Coherent Imaging**. Measurements consist of X-ray photons transmitted through (or scattered by) the sample via a **grating interferometry** sensing mechanism. The forward operator applies, in order: K · transmit · grating operator; F · propagation · fresnel operator; L · modulation · analyzer operator; pixel-level spatial averaging on the detector. Observations are corrupted by Poisson shot noise from quantum-limited detection. Well-conditioned linear Fourier extraction of three contrast channels from K phase-stepped frames (K >= 3 required; K = 8 typical for noise averaging). Stability dominated by grating alignment and vibration; dark-field channel degrades when visibility V < 0.15. ## ⚙ 2. Forward Model Physical chain: **x** → K · transmit · grating → F · propagation · fresnel → L · modulation · analyzer → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.modulation.analyzer` `F.propagation.fresnel` `K.transmit.grating` x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `K.transmit.grating` | K · transmit · grating operator | | `F.propagation.fresnel` | F · propagation · fresnel operator | | `L.modulation.analyzer` | L · modulation · analyzer operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Coherent Imaging | | Sub domain | Grating-based phase and dark-field imaging | | Carrier | x_ray | | Problem class | linear_inverse | | Solution space | triplet_2D_fields | | Noise model | shot_poisson | | Integration axis | temporal | | Difficulty delta | 3 | | L dag | 3.4 | ## 📡 4. Measurement Model Well-conditioned linear Fourier extraction of three contrast channels from K phase-stepped frames (K >= 3 required; K = 8 typical for noise averaging). Stability dominated by grating alignment and vibration; dark-field channel degrades when visibility V < 0.15. | Metric | Value | |---|---| | Metric | phase_PSNR_dB | | Secondary | darkfield_SNR | ## 📏 5. Operating Range (Ω) **Center problem class:** `grating_phase_contrast_imaging` · **Forward operator:** `talbot_lau_three_grating` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 1024 | | W | px | 1024 | | K steps | — | 8 | | V center | — | 0.3 | | E mean kev | — | 40 | | Alignment tilt | — | 0 | | Grating period um | µm | 4.8 | | Grating period drift | — | 0 | | Photon count per pixel | — | 10000 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 256 – 4096 | | W | px | 256 – 4096 | | K steps | — | 3 – 16 | | V center | — | 0.05 – 0.6 | | E mean kev | — | 10.0 – 120.0 | | Alignment tilt | — | 0.0 – 0.02 | | Grating period um | µm | 1.0 – 10.0 | | Phase step jitter | — | 0.0 – 0.1 | | Grating period drift | — | 0.0 – 0.05 | | Source coherence loss | — | 0.0 – 0.5 | | Photon count per pixel | — | 100 – 1000000 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 30.0 dB phase PSNR | Metric | Range | |---|---| | Psnr db | 18.0 – 42.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **phase_PSNR_dB**, with κ = `400` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x0ba11dfeb8a6b1207f64364b2c77952da6b41f189d4405907b04d3c6973de6f1` - **Chain tx hash:** `0xacbb7730764cd90afc9010534172c04ecfbee959079c125f5f74cd721093ab9a` - **Chain block:** `41554170` --- ## File Mapping This bundle consists of: `L1-074.md`, `L1-074.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-074.md` | Source of truth — edit this | Human or LLM | | `L1-074.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 `L1-074`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-074.md).
Regenerate L1-074.json so every field matches the Markdown.
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Output each file in its own fenced code block tagged with the filename.

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L2-074-001 Talbot-Lau 3-Grating Mismatch-Only Spec

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📋 JSON metadata

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  "chain_tx_hash": "0xacbb7730764cd90afc9010534172c04ecfbee959079c125f5f74cd721093ab9a",
  "domain": "Coherent Imaging",
  "hardness_fn": {
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    "kappa": 400,
    "metric": "phase_PSNR_dB",
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    "metric": "phase_PSNR_dB",
    "regime": "Well-conditioned linear Fourier extraction of three contrast channels from K phase-stepped frames (K \u003e= 3 required; K = 8 typical for noise averaging). Stability dominated by grating alignment and vibration; dark-field channel degrades when visibility V \u003c 0.15.",
    "secondary": "darkfield_SNR"
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  "physics_fingerprint": {
    "L_DAG": 3.4,
    "carrier": "x_ray",
    "difficulty_delta": 3,
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    "integration_axis": "temporal",
    "noise_model": "shot_poisson",
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    "sensing_mechanism": "grating_interferometry",
    "solution_space": "triplet_2D_fields",
    "sub_domain": "Grating-based phase and dark-field imaging",
    "title": "Talbot-Lau Grating Interferometry (X-ray phase-contrast imaging)"
  },
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    "allowed_problem_classes": [
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      "forward_operator": "talbot_lau_three_grating",
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      "phase_step_jitter": [
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      "photon_count_per_pixel": [
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      ],
      "source_coherence_loss": [
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      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Grating-based phase and dark-field imaging",
  "title": "Talbot-Lau Grating Interferometry (X-ray phase-contrast imaging)"
}

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