L1 ⚛ L1-075 ⊙ Testnet

Lensless Imaging with Diffuser PSF (DiffuserCam)

Computational Photography · Flat-form-factor lensless imaging

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⬇ L1-075.md

# ⚛ L1 Principle — Lensless Imaging with Diffuser PSF (DiffuserCam) **ID:** `L1-075` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Computational Photography — *Flat-form-factor lensless imaging* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 2D spatial > **📡 Carrier:** photon · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554170 --- ## 🧠 1. Introduction **Lensless Imaging with Diffuser PSF (DiffuserCam)** is a **linear inverse problem** whose unknown lives in **2D spatial** space, within the **Flat-form-factor lensless imaging** sub-domain of **Computational Photography**. Measurements consist of photons collected by an optical detector via a **diffuser caustic imaging** sensing mechanism. The forward operator applies, in order: K · psf · caustic operator; S · select operator; detector accumulates flux over the exposure window. Observations are corrupted by additive Gaussian noise. Deconvolution with a wideband random PSF is well-conditioned over the non-zero OTF support (caustics have rich high-frequency content). Cropping by sensor extent introduces boundary ill-posedness (recoverable via TV + boundary-extension priors). Mismatch between calibrated PSF and actual PSF (temperature drift, mask rotation) dominates stability. ## ⚙ 2. Forward Model Physical chain: **x** → K · psf · caustic → S · select → Temporal integration → **y** (detector). ``` y = ∫_t dt `S.select` `K.psf.caustic` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `K.psf.caustic` | K · psf · caustic operator | | `S.select` | S · select operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Computational Photography | | Sub domain | Flat-form-factor lensless imaging | | Carrier | photon | | Problem class | linear_inverse | | Solution space | 2D_spatial | | Noise model | gaussian | | Integration axis | spatial | | Difficulty delta | 3 | | L dag | 2.6 | ## 📡 4. Measurement Model Deconvolution with a wideband random PSF is well-conditioned over the non-zero OTF support (caustics have rich high-frequency content). Cropping by sensor extent introduces boundary ill-posedness (recoverable via TV + boundary-extension priors). Mismatch between calibrated PSF and actual PSF (temperature drift, mask rotation) dominates stability. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `lensless_deconvolution` · **Forward operator:** `diffuser_psf_convolution` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 512 | | W | px | 512 | | Psf h | — | 256 | | Psf w | — | 256 | | Psf drift | — | 0 | | Photon count | — | 1000 | | Mask rotation | — | 0 | | Chromatic aberration | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 128 – 2048 | | W | px | 128 – 2048 | | Psf h | — | 64 – 512 | | Psf w | — | 64 – 512 | | Psf drift | — | 0.0 – 0.1 | | Dark offset | — | 0.0 – 0.02 | | Photon count | — | 10 – 10000 | | Mask rotation | — | 0.0 – 0.02 | | Chromatic aberration | — | 0.0 – 0.05 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 26.0 dB PSNR | Metric | Range | |---|---| | Psnr db | 16.0 – 38.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `1800` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xc4485a83284e8cbceab5500ca8a35d229762019b1f189d97309edb29b45b999b` - **Chain tx hash:** `0x730892a23b2706bd9f15ef50438f052f1e0f5bc22e35cb961fc706de88c87196` - **Chain block:** `41554170` --- ## File Mapping This bundle consists of: `L1-075.md`, `L1-075.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-075.md` | Source of truth — edit this | Human or LLM | | `L1-075.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 `L1-075`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-075-001 DiffuserCam Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-075",
  "chain_block": 41554170,
  "chain_hash": "0xc4485a83284e8cbceab5500ca8a35d229762019b1f189d97309edb29b45b999b",
  "chain_tx_hash": "0x730892a23b2706bd9f15ef50438f052f1e0f5bc22e35cb961fc706de88c87196",
  "domain": "Computational Photography",
  "hardness_fn": {
    "delta": 3,
    "kappa": 1800,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
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      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
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  "layer": "L1",
  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "Deconvolution with a wideband random PSF is well-conditioned over the non-zero OTF support (caustics have rich high-frequency content). Cropping by sensor extent introduces boundary ill-posedness (recoverable via TV + boundary-extension priors). Mismatch between calibrated PSF and actual PSF (temperature drift, mask rotation) dominates stability.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 2.6,
    "carrier": "photon",
    "difficulty_delta": 3,
    "domain": "Computational Photography",
    "integration_axis": "spatial",
    "noise_model": "gaussian",
    "primitives": [
      "K.psf.caustic",
      "S.select",
      "int.temporal"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "diffuser_caustic_imaging",
    "solution_space": "2D_spatial",
    "sub_domain": "Flat-form-factor lensless imaging",
    "title": "Lensless Imaging with Diffuser PSF (DiffuserCam)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "diffuser_psf_convolution",
      "pbar_psf",
      "mla_lenslet_psf"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "psf_H",
      "psf_W",
      "photon_count",
      "psf_drift",
      "mask_rotation",
      "chromatic_aberration",
      "dark_offset"
    ],
    "allowed_problem_classes": [
      "lensless_deconvolution",
      "flat_cam_recovery"
    ],
    "center_spec": {
      "epsilon_fn_center": "26.0 dB PSNR",
      "forward_operator": "diffuser_psf_convolution",
      "input_format": "raw_sensor_image_plus_calibrated_psf",
      "omega": {
        "H": 512,
        "W": 512,
        "chromatic_aberration": 0.0,
        "mask_rotation": 0.0,
        "photon_count": 1000,
        "psf_H": 256,
        "psf_W": 256,
        "psf_drift": 0.0
      },
      "problem_class": "lensless_deconvolution"
    },
    "epsilon_bounds": {
      "psnr_db": [
        16.0,
        38.0
      ]
    },
    "omega_bounds": {
      "H": [
        128,
        2048
      ],
      "W": [
        128,
        2048
      ],
      "chromatic_aberration": [
        0.0,
        0.05
      ],
      "dark_offset": [
        0.0,
        0.02
      ],
      "mask_rotation": [
        0.0,
        0.02
      ],
      "photon_count": [
        10,
        10000
      ],
      "psf_H": [
        64,
        512
      ],
      "psf_W": [
        64,
        512
      ],
      "psf_drift": [
        0.0,
        0.1
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Flat-form-factor lensless imaging",
  "title": "Lensless Imaging with Diffuser PSF (DiffuserCam)"
}

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