L1 ⚛ L1-073 ⊙ Testnet

Optical Diffraction Tomography (ODT) — 3D refractive-index imaging

Coherent Imaging · Multi-angle coherent tomography

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⬇ L1-073.md

# ⚛ L1 Principle — Optical Diffraction Tomography (ODT) — 3D refractive-index imaging **ID:** `L1-073` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Coherent Imaging — *Multi-angle coherent tomography* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 3D refractive index > **📡 Carrier:** photon · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554170 --- ## 🧠 1. Introduction **Optical Diffraction Tomography (ODT) — 3D refractive-index imaging** is a **linear inverse problem** whose unknown lives in **3D refractive index** space, within the **Multi-angle coherent tomography** sub-domain of **Coherent Imaging**. Measurements consist of photons collected by an optical detector via a **multi angle coherent holography** sensing mechanism. The forward operator applies, in order: rotates source / detector to acquire different projections; F · propagation · helmholtz operator; L · projection · ewald cap operator; integration over the solid angle of incidence/emission. Observations are corrupted by additive Gaussian noise. Ill-posed along the missing-cone axis (cone of k-space unreachable by finite-NA illumination). Regularized inversion (TV, deep priors) fills the cone with smoothness assumptions. Non-linear Beyond-Born solvers (LS-LT, SEAGLE) handle multiple scattering but become strongly non-convex. ## ⚙ 2. Forward Model Physical chain: **x** → Angular scan → F · propagation · helmholtz → L · projection · ewald cap → Angular integration → **y** (detector). ``` y = ∫dΩ `L.projection.ewald_cap` `F.propagation.helmholtz` R(θ) x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `S.scan.angular` | Rotates source / detector to acquire different projections | | `F.propagation.helmholtz` | F · propagation · helmholtz operator | | `L.projection.ewald_cap` | L · projection · ewald cap operator | | `int.angular` | Integration over the solid angle of incidence/emission | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Coherent Imaging | | Sub domain | Multi-angle coherent tomography | | Carrier | photon | | Problem class | linear_inverse | | Solution space | 3D_refractive_index | | Noise model | gaussian | | Integration axis | angular | | Difficulty delta | 5 | | L dag | 3.8 | ## 📡 4. Measurement Model Ill-posed along the missing-cone axis (cone of k-space unreachable by finite-NA illumination). Regularized inversion (TV, deep priors) fills the cone with smoothness assumptions. Non-linear Beyond-Born solvers (LS-LT, SEAGLE) handle multiple scattering but become strongly non-convex. | Metric | Value | |---|---| | Metric | 3D_PSNR_dB | | Secondary | refractive_index_L2 | ## 📏 5. Operating Range (Ω) **Center problem class:** `3d_refractive_index_recovery` · **Forward operator:** `rytov_ewald_cap` **Center point:** | Parameter | Unit | Value | |---|---|---| | D | — | 128 | | H | px | 512 | | W | px | 512 | | N 0 | — | 1.33 | | K angles | — | 90 | | Na illum | — | 1 | | Delta n max | — | 0.02 | | Wavelength nm | nm | 532 | | Illumination angle error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | D | — | 32 – 512 | | H | px | 128 – 2048 | | W | px | 128 – 2048 | | N 0 | — | 1.0 – 1.5 | | K angles | — | 30 – 360 | | Na illum | — | 0.4 – 1.4 | | Delta n max | — | 0.001 – 0.1 | | Wavelength nm | nm | 400 – 800 | | Aberration zernike | — | 0.0 – 0.5 | | Limited angle range | — | 90 – 360 | | Illumination angle error | — | 0.0 – 2.0 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 27.0 dB 3D PSNR | Metric | Range | |---|---| | Psnr db | 15.0 – 38.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **3D_PSNR_dB**, with κ = `6000` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xeeaf2db215d84a2c5cda06002d3890c1437abd73213fae9bb2ff76b241ff699d` - **Chain tx hash:** `0x1a84c7012fb789e01e13ef7d96b01b540866eff455a10fd61c1837ba13f316f5` - **Chain block:** `41554170` --- ## File Mapping This bundle consists of: `L1-073.md`, `L1-073.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-073.md` | Source of truth — edit this | Human or LLM | | `L1-073.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 `L1-073`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-073.md).
Regenerate L1-073.json so every field matches the Markdown.
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L2-073-001 ODT Rytov-Regime Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41554170,
  "chain_hash": "0xeeaf2db215d84a2c5cda06002d3890c1437abd73213fae9bb2ff76b241ff699d",
  "chain_tx_hash": "0x1a84c7012fb789e01e13ef7d96b01b540866eff455a10fd61c1837ba13f316f5",
  "domain": "Coherent Imaging",
  "hardness_fn": {
    "delta": 5,
    "kappa": 6000,
    "metric": "3D_PSNR_dB",
    "type": "epsilon_fn"
  },
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      "license_hash": null,
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    "regime": "Ill-posed along the missing-cone axis (cone of k-space unreachable by finite-NA illumination). Regularized inversion (TV, deep priors) fills the cone with smoothness assumptions. Non-linear Beyond-Born solvers (LS-LT, SEAGLE) handle multiple scattering but become strongly non-convex.",
    "secondary": "refractive_index_L2"
  },
  "physics_fingerprint": {
    "L_DAG": 3.8,
    "carrier": "photon",
    "difficulty_delta": 5,
    "domain": "Coherent Imaging",
    "integration_axis": "angular",
    "noise_model": "gaussian",
    "primitives": [
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      "F.propagation.helmholtz",
      "L.projection.ewald_cap",
      "int.angular"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "multi_angle_coherent_holography",
    "solution_space": "3D_refractive_index",
    "sub_domain": "Multi-angle coherent tomography",
    "title": "Optical Diffraction Tomography (ODT) \u2014 3D refractive-index imaging"
  },
  "size_tiers": {
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      "n_0",
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    ],
    "allowed_problem_classes": [
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      "odt_beyond_born",
      "tomographic_phase_imaging"
    ],
    "center_spec": {
      "epsilon_fn_center": "27.0 dB 3D PSNR",
      "forward_operator": "rytov_ewald_cap",
      "input_format": "K_complex_fields_plus_angle_list",
      "omega": {
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        "H": 512,
        "K_angles": 90,
        "NA_illum": 1.0,
        "W": 512,
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        "n_0": 1.33,
        "wavelength_nm": 532
      },
      "problem_class": "3d_refractive_index_recovery"
    },
    "epsilon_bounds": {
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        38.0
      ]
    },
    "omega_bounds": {
      "D": [
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      "H": [
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      ],
      "NA_illum": [
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      "W": [
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        2048
      ],
      "aberration_zernike": [
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        0.5
      ],
      "delta_n_max": [
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        0.1
      ],
      "illumination_angle_error": [
        0.0,
        2.0
      ],
      "limited_angle_range": [
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        360
      ],
      "n_0": [
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        1.5
      ],
      "wavelength_nm": [
        400,
        800
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Multi-angle coherent tomography",
  "title": "Optical Diffraction Tomography (ODT) \u2014 3D refractive-index imaging"
}

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