L1 ⚛ L1-081 ⊙ Testnet

Integral Photography (Lippmann-style MLA capture + reconstruction)

Computational Optics · Microlens-array 3D imaging

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⬇ L1-081.md

# ⚛ L1 Principle — Integral Photography (Lippmann-style MLA capture + reconstruction) **ID:** `L1-081` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Computational Optics — *Microlens-array 3D imaging* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 4D light field > **📡 Carrier:** photon · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554183 --- ## 🧠 1. Introduction **Integral Photography (Lippmann-style MLA capture + reconstruction)** is a **linear inverse problem** whose unknown lives in **4D light field** space, within the **Microlens-array 3D imaging** sub-domain of **Computational Optics**. Measurements consist of photons collected by an optical detector via a **microlens array sampling** sensing mechanism. The forward operator applies, in order: L · project · pupil operator; an unspecified linear measurement operator; L · rearrange operator; pixel-level spatial averaging on the detector. Observations are corrupted by additive Gaussian noise. Well-conditioned when MLA is rigidly calibrated and angular/spatial trade-off is sufficient (N_ml * L_x >= scene bandwidth). Fourier-mode integral photography trades angular for spatial resolution; reconstruction is linear with known MLA geometry. ## ⚙ 2. Forward Model Physical chain: **x** → L · project · pupil → Generic linear operator → L · rearrange → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.rearrange` A `L.project.pupil` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.project.pupil` | L · project · pupil operator | | `L.linear_op` | An unspecified linear measurement operator | | `L.rearrange` | L · rearrange operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Computational Optics | | Sub domain | Microlens-array 3D imaging | | Carrier | photon | | Problem class | linear_inverse | | Solution space | 4D_light_field | | Noise model | gaussian | | Integration axis | angular | | Difficulty delta | 3 | | L dag | 3 | ## 📡 4. Measurement Model Well-conditioned when MLA is rigidly calibrated and angular/spatial trade-off is sufficient (N_ml * L_x >= scene bandwidth). Fourier-mode integral photography trades angular for spatial resolution; reconstruction is linear with known MLA geometry. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | disparity_MAE_px | ## 📏 5. Operating Range (Ω) **Center problem class:** `integral_photography_decoding` · **Forward operator:** `mla_integral_photo_capture` **Center point:** | Parameter | Unit | Value | |---|---|---| | H s | s | 2048 | | L x | — | 20 | | L y | — | 20 | | W s | s | 2048 | | N ml x | — | 100 | | N ml y | — | 100 | | Mla rotation | — | 0 | | Photon count | — | 1000 | | Mla pitch drift | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H s | s | 512 – 8192 | | L x | — | 5 – 50 | | L y | — | 5 – 50 | | W s | s | 512 – 8192 | | N ml x | — | 20 – 400 | | N ml y | — | 20 – 400 | | Mla rotation | — | 0.0 – 0.05 | | Photon count | — | 50 – 10000 | | Mla pitch drift | — | 0.0 – 0.02 | | Vignetting residual | — | 0.0 – 0.2 | | Sensor mla gap error | — | 0.0 – 0.1 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 30.0 dB PSNR | Metric | Range | |---|---| | Psnr db | 18.0 – 42.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `1200` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x00ab86129a33565e3b06e8e802fe23bdd57111cfbc628a9caad9e9fd038eeb31` - **Chain tx hash:** `0x88644c9580ab3fb4e37108cca886c94625a2f61e1f7ae8d91fdea89e231a4b73` - **Chain block:** `41554183` --- ## File Mapping This bundle consists of: `L1-081.md`, `L1-081.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-081.md` | Source of truth — edit this | Human or LLM | | `L1-081.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 `L1-081`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-081.md).
Regenerate L1-081.json so every field matches the Markdown.
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📋 JSON metadata

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  "chain_tx_hash": "0x88644c9580ab3fb4e37108cca886c94625a2f61e1f7ae8d91fdea89e231a4b73",
  "domain": "Computational Optics",
  "hardness_fn": {
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    "kappa": 1200,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
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    "metric": "PSNR_dB",
    "regime": "Well-conditioned when MLA is rigidly calibrated and angular/spatial trade-off is sufficient (N_ml * L_x \u003e= scene bandwidth). Fourier-mode integral photography trades angular for spatial resolution; reconstruction is linear with known MLA geometry.",
    "secondary": "disparity_MAE_px"
  },
  "physics_fingerprint": {
    "L_DAG": 3.0,
    "carrier": "photon",
    "difficulty_delta": 3,
    "domain": "Computational Optics",
    "integration_axis": "angular",
    "noise_model": "gaussian",
    "primitives": [
      "L.project.pupil",
      "L.linear_op",
      "L.rearrange",
      "int.spatial"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "microlens_array_sampling",
    "solution_space": "4D_light_field",
    "sub_domain": "Microlens-array 3D imaging",
    "title": "Integral Photography (Lippmann-style MLA capture + reconstruction)"
  },
  "size_tiers": {
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      "mla_integral_photo_capture",
      "fourier_integral_photo",
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      "W_s",
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      "mla_rotation",
      "mla_pitch_drift",
      "sensor_mla_gap_error",
      "vignetting_residual"
    ],
    "allowed_problem_classes": [
      "integral_photography_decoding",
      "mla_super_resolution"
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    "center_spec": {
      "epsilon_fn_center": "30.0 dB PSNR",
      "forward_operator": "mla_integral_photo_capture",
      "input_format": "raw_sensor_mosaic_plus_mla_calibration",
      "omega": {
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        "L_x": 20,
        "L_y": 20,
        "N_ml_x": 100,
        "N_ml_y": 100,
        "W_s": 2048,
        "mla_pitch_drift": 0.0,
        "mla_rotation": 0.0,
        "photon_count": 1000
      },
      "problem_class": "integral_photography_decoding"
    },
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        42.0
      ]
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      "L_x": [
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      "L_y": [
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      "N_ml_x": [
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      "N_ml_y": [
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      "W_s": [
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        8192
      ],
      "mla_pitch_drift": [
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        0.02
      ],
      "mla_rotation": [
        0.0,
        0.05
      ],
      "photon_count": [
        50,
        10000
      ],
      "sensor_mla_gap_error": [
        0.0,
        0.1
      ],
      "vignetting_residual": [
        0.0,
        0.2
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Microlens-array 3D imaging",
  "title": "Integral Photography (Lippmann-style MLA capture + reconstruction)"
}

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