L1 ⚛ L1-241 ⊙ Testnet

Fresnel Diffraction — paraxial wave propagation

Electromagnetics · Paraxial (Fresnel) diffraction integral

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⬇ L1-241.md

# ⚛ L1 Principle — Fresnel Diffraction — paraxial wave propagation **ID:** `L1-241` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Electromagnetics — *Paraxial (Fresnel) diffraction integral* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** complex 2D field > **📡 Carrier:** em · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41553988 --- ## 🧠 1. Introduction **Fresnel Diffraction — paraxial wave propagation** is a **linear inverse problem** whose unknown lives in **complex 2D field** space, within the **Paraxial (Fresnel) diffraction integral** sub-domain of **Electromagnetics**. Measurements consist of electromagnetic field measurements via a **intensity camera** sensing mechanism. The forward operator applies, in order: L · paraxial propagate operator; L · fresnel convolve operator; L · intensity capture operator; pixel-level spatial averaging on the detector. Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds. ## ⚙ 2. Forward Model Physical chain: **x** → L · paraxial propagate → L · fresnel convolve → L · intensity capture → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.intensity_capture` `L.fresnel_convolve` `L.paraxial_propagate` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.paraxial_propagate` | L · paraxial propagate operator | | `L.fresnel_convolve` | L · fresnel convolve operator | | `L.intensity_capture` | L · intensity capture operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Electromagnetics | | Sub domain | Paraxial (Fresnel) diffraction integral | | Carrier | em | | Problem class | linear_inverse | | Solution space | complex_2D_field | | Noise model | gaussian | | Integration axis | spatial | | Difficulty delta | 3 | | L dag | 3 | ## 📡 4. Measurement Model Conditional stability; mismatch parameters dominate at Omega bounds. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `fresnel` · **Forward operator:** `fresnel_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 512 | | W | px | 512 | | Z m | m | 1 | | Snr db | dB | 30 | | Lambda nm | nm | 633 | | Z dist error | — | 0 | | Aperture error | — | 0 | | Wavelength error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 64 – 4096 | | W | px | 64 – 4096 | | Z m | m | 0.001 – 1000 | | Snr db | dB | 0 – 40 | | Lambda nm | nm | 1 – 10000 | | Z dist error | — | 0.0 – 0.05 | | Aperture error | — | 0.0 – 0.1 | | Wavelength error | — | 0.0 – 0.02 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 26.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `200` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x962286a8a0878837f180eb1ef49a26fe3456eebd93ac875ffe3719696c0450a3` - **Chain tx hash:** `0x400affcdc98972afee3a3617b38912e3d4e9ebff2a355d392f5c059b51da9e51` - **Chain block:** `41553988` --- ## File Mapping This bundle consists of: `L1-241.md`, `L1-241.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-241.md` | Source of truth — edit this | Human or LLM | | `L1-241.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 `L1-241`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-241.md).
Regenerate L1-241.json so every field matches the Markdown.
Preserve the schema documented in the File Mapping footer at the bottom of the MD.
Output each file in its own fenced code block tagged with the filename.

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L2-241-001 Fresnel Diffraction — paraxial wave propagation Mismatch-Only Spec

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📋 JSON metadata

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  "artifact_id": "L1-241",
  "chain_block": 41553988,
  "chain_hash": "0x962286a8a0878837f180eb1ef49a26fe3456eebd93ac875ffe3719696c0450a3",
  "chain_tx_hash": "0x400affcdc98972afee3a3617b38912e3d4e9ebff2a355d392f5c059b51da9e51",
  "domain": "Electromagnetics",
  "hardness_fn": {
    "delta": 3,
    "kappa": 200,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
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      "name": "primary",
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  "layer": "L1",
  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "Conditional stability; mismatch parameters dominate at Omega bounds.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.0,
    "carrier": "em",
    "difficulty_delta": 3,
    "domain": "Electromagnetics",
    "integration_axis": "spatial",
    "noise_model": "gaussian",
    "primitives": [
      "L.paraxial_propagate",
      "L.fresnel_convolve",
      "L.intensity_capture",
      "int.spatial"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "intensity_camera",
    "solution_space": "complex_2D_field",
    "sub_domain": "Paraxial (Fresnel) diffraction integral",
    "title": "Fresnel Diffraction \u2014 paraxial wave propagation"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "fresnel_forward"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "lambda_nm",
      "z_m",
      "SNR_dB",
      "z_dist_error",
      "aperture_error",
      "wavelength_error",
      "z_dist_error",
      "aperture_error",
      "wavelength_error"
    ],
    "allowed_problem_classes": [
      "fresnel"
    ],
    "center_spec": {
      "epsilon_fn_center": "26.0",
      "forward_operator": "fresnel_forward",
      "input_format": "measurement_only",
      "omega": {
        "H": 512,
        "SNR_dB": 30,
        "W": 512,
        "aperture_error": 0.0,
        "lambda_nm": 633,
        "wavelength_error": 0.0,
        "z_dist_error": 0.0,
        "z_m": 1.0
      },
      "problem_class": "fresnel"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "H": [
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        4096
      ],
      "SNR_dB": [
        0,
        40
      ],
      "W": [
        64,
        4096
      ],
      "aperture_error": [
        0.0,
        0.1
      ],
      "lambda_nm": [
        1,
        10000
      ],
      "wavelength_error": [
        0.0,
        0.02
      ],
      "z_dist_error": [
        0.0,
        0.05
      ],
      "z_m": [
        0.001,
        1000
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Paraxial (Fresnel) diffraction integral",
  "title": "Fresnel Diffraction \u2014 paraxial wave propagation"
}

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