L1 ⚛ L1-072 ⊙ Testnet

Coherent Diffraction Imaging (CDI) — lensless phase retrieval

Coherent Imaging · Single-shot lensless diffraction

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⬇ L1-072.md

# ⚛ L1 Principle — Coherent Diffraction Imaging (CDI) — lensless phase retrieval **ID:** `L1-072` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Coherent Imaging — *Single-shot lensless diffraction* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** complex 2D > **📡 Carrier:** photon · **🌫 Noise:** shot poisson > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554170 --- ## 🧠 1. Introduction **Coherent Diffraction Imaging (CDI) — lensless phase retrieval** is a **nonlinear inverse problem** whose unknown lives in **complex 2D** space, within the **Single-shot lensless diffraction** sub-domain of **Coherent Imaging**. Measurements consist of photons collected by an optical detector via a **coherent diffraction** sensing mechanism. The forward operator applies, in order: B · support operator; F · fourier 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. Strongly non-convex phaseless recovery. Hayes ambiguity (global phase, conjugate flip, sub-pixel translation) resolved by support compactness. Oversampling sigma >= 2 in each dimension is necessary; beam-stop inpainting and partial coherence further degrade conditioning. ## ⚙ 2. Forward Model Physical chain: **x** → B · support → F · fourier → Magnitude-squared → Spatial integration → **y** (detector). ``` y = ∫_A dA |·|² `F.fourier` `B.support` x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `B.support` | B · support operator | | `F.fourier` | F · fourier 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 | Coherent Imaging | | Sub domain | Single-shot lensless diffraction | | Carrier | photon | | Problem class | nonlinear_inverse | | Solution space | complex_2D | | Noise model | shot_poisson | | Integration axis | angular | | Difficulty delta | 5 | | L dag | 3.5 | ## 📡 4. Measurement Model Strongly non-convex phaseless recovery. Hayes ambiguity (global phase, conjugate flip, sub-pixel translation) resolved by support compactness. Oversampling sigma >= 2 in each dimension is necessary; beam-stop inpainting and partial coherence further degrade conditioning. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | R_factor | ## 📏 5. Operating Range (Ω) **Center problem class:** `phase_retrieval_cdi` · **Forward operator:** `far_field_intensity` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 512 | | W | px | 512 | | Photon count | — | 1000 | | Partial coherence | — | 1 | | Oversampling sigma | — | 3 | | Support mask error | — | 0 | | Beam stop radius px | — | 10 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 128 – 4096 | | W | px | 128 – 4096 | | Background | — | 0.0 – 0.05 | | Photon count | — | 10 – 100000 | | Partial coherence | — | 0.7 – 1.0 | | Oversampling sigma | — | 2.0 – 8.0 | | Support mask error | — | 0.0 – 0.3 | | Beam stop radius px | — | 0 – 50 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 25.0 dB PSNR | Metric | Range | |---|---| | Psnr db | 12.0 – 38.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `10000` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xe5148708a1786a8563612751bf0e19c17ea4c0cd9ca8fccdd71195f2b4e9d8a1` - **Chain tx hash:** `0x121db49d84508bb8b11f18d19599ce791df9cb7eb8bb41038738df1cca87720d` - **Chain block:** `41554170` --- ## File Mapping This bundle consists of: `L1-072.md`, `L1-072.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-072.md` | Source of truth — edit this | Human or LLM | | `L1-072.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 `L1-072`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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📋 JSON metadata

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  "chain_block": 41554170,
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  "domain": "Coherent Imaging",
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    "kappa": 10000,
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    "regime": "Strongly non-convex phaseless recovery. Hayes ambiguity (global phase, conjugate flip, sub-pixel translation) resolved by support compactness. Oversampling sigma \u003e= 2 in each dimension is necessary; beam-stop inpainting and partial coherence further degrade conditioning.",
    "secondary": "R_factor"
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    "integration_axis": "angular",
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    "sensing_mechanism": "coherent_diffraction",
    "solution_space": "complex_2D",
    "sub_domain": "Single-shot lensless diffraction",
    "title": "Coherent Diffraction Imaging (CDI) \u2014 lensless phase retrieval"
  },
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      "input_format": "diffraction_intensity_plus_support_prior",
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      "W": [
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      ],
      "background": [
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      ],
      "beam_stop_radius_px": [
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      "oversampling_sigma": [
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      ],
      "partial_coherence": [
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      "photon_count": [
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      ],
      "support_mask_error": [
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      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Single-shot lensless diffraction",
  "title": "Coherent Diffraction Imaging (CDI) \u2014 lensless phase retrieval"
}

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