L1 ⚛ L1-099 ⊙ Testnet

Flash LiDAR (single-shot 2D SPAD-array direct ToF)

Depth Imaging · Flash-illumination focal-plane-array dToF

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⬇ L1-099.md

# ⚛ L1 Principle — Flash LiDAR (single-shot 2D SPAD-array direct ToF) **ID:** `L1-099` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Depth Imaging — *Flash-illumination focal-plane-array dToF* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 2D depth map > **📡 Carrier:** photon · **🌫 Noise:** shot poisson > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41547812 --- ## 🧠 1. Introduction **Flash LiDAR (single-shot 2D SPAD-array direct ToF)** is a **linear inverse problem** whose unknown lives in **2D depth map** space, within the **Flash-illumination focal-plane-array dToF** sub-domain of **Depth Imaging**. Measurements consist of photons collected by an optical detector via a **flash pulse spad array** sensing mechanism. The forward operator applies, in order: L · emit · flash operator; L · reflect scene operator; D · spad histogram operator; detector accumulates flux over the exposure window. Observations are corrupted by Poisson shot noise from quantum-limited detection. Well-posed in high-SNR regime (photon_count_per_pixel >= 5). Under high ambient (sun-lit daytime), photon-efficient reconstruction (Kirmani, Shin) is required. Walk error (signal-ambient interference) shifts bin peaks; crosstalk between neighbouring SPAD pixels reduces effective resolution. ## ⚙ 2. Forward Model Physical chain: **x** → L · emit · flash → L · reflect scene → D · spad histogram → Temporal integration → **y** (detector). ``` y = ∫_t dt `D.spad_histogram` `L.reflect_scene` `L.emit.flash` x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.emit.flash` | L · emit · flash operator | | `L.reflect_scene` | L · reflect scene operator | | `D.spad_histogram` | D · spad histogram operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Depth Imaging | | Sub domain | Flash-illumination focal-plane-array dToF | | Carrier | photon | | Problem class | linear_inverse | | Solution space | 2D_depth_map | | Noise model | shot_poisson | | Integration axis | temporal | | Difficulty delta | 3 | | L dag | 3 | ## 📡 4. Measurement Model Well-posed in high-SNR regime (photon_count_per_pixel >= 5). Under high ambient (sun-lit daytime), photon-efficient reconstruction (Kirmani, Shin) is required. Walk error (signal-ambient interference) shifts bin peaks; crosstalk between neighbouring SPAD pixels reduces effective resolution. | Metric | Value | |---|---| | Metric | depth_RMSE_mm | | Secondary | outlier_fraction | ## 📏 5. Operating Range (Ω) **Center problem class:** `flash_spad_dtof` · **Forward operator:** `flash_pulse_spad_histogram` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 640 | | W | px | 480 | | N t | — | 1024 | | Tau tdc ps | — | 100 | | Walk error | — | 0 | | Dark count rate | — | 100 | | Ambient photon rate | — | 0 | | Photon count per pixel | — | 20 | | Crosstalk neighbour pixels | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 128 – 1280 | | W | px | 128 – 1280 | | N t | — | 128 – 4096 | | Tau tdc ps | — | 20 – 500 | | Walk error | — | 0.0 – 0.2 | | Dark count rate | — | 10 – 10000 | | Pile up saturation | — | 0.0 – 0.5 | | Ambient photon rate | — | 0.0 – 1000000 | | Photon count per pixel | — | 1 – 1000 | | Crosstalk neighbour pixels | — | 0.0 – 0.05 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 15.0 mm depth RMSE at 10 m | Metric | Range | |---|---| | Rmse mm | 2.0 – 200.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **depth_RMSE_mm**, with κ = `800` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xdaf7231b5da64bd629f1f5201361cdc13761ddfa9bd505b084aca7a6748c680c` - **Chain tx hash:** `0x9b50365487d4930a8928fb3d600621178c3b9d7d2acd12c14d3a6fec25cc8685` - **Chain block:** `41547812` --- ## File Mapping This bundle consists of: `L1-099.md`, `L1-099.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-099.md` | Source of truth — edit this | Human or LLM | | `L1-099.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 `L1-099`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-099.md).
Regenerate L1-099.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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L2-099-001 Flash-LiDAR SPAD-Array Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-099",
  "chain_block": 41547812,
  "chain_hash": "0xdaf7231b5da64bd629f1f5201361cdc13761ddfa9bd505b084aca7a6748c680c",
  "chain_tx_hash": "0x9b50365487d4930a8928fb3d600621178c3b9d7d2acd12c14d3a6fec25cc8685",
  "domain": "Depth Imaging",
  "hardness_fn": {
    "delta": 3,
    "kappa": 800,
    "metric": "depth_RMSE_mm",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
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      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
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  "layer": "L1",
  "observable_profile": {
    "metric": "depth_RMSE_mm",
    "regime": "Well-posed in high-SNR regime (photon_count_per_pixel \u003e= 5). Under high ambient (sun-lit daytime), photon-efficient reconstruction (Kirmani, Shin) is required. Walk error (signal-ambient interference) shifts bin peaks; crosstalk between neighbouring SPAD pixels reduces effective resolution.",
    "secondary": "outlier_fraction"
  },
  "physics_fingerprint": {
    "L_DAG": 3.0,
    "carrier": "photon",
    "difficulty_delta": 3,
    "domain": "Depth Imaging",
    "integration_axis": "temporal",
    "noise_model": "shot_poisson",
    "primitives": [
      "L.emit.flash",
      "L.reflect_scene",
      "D.spad_histogram",
      "int.temporal"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "flash_pulse_spad_array",
    "solution_space": "2D_depth_map",
    "sub_domain": "Flash-illumination focal-plane-array dToF",
    "title": "Flash LiDAR (single-shot 2D SPAD-array direct ToF)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "flash_pulse_spad_histogram",
      "gated_iccd",
      "sipm_array_tof"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "N_t",
      "tau_tdc_ps",
      "photon_count_per_pixel",
      "ambient_photon_rate",
      "dark_count_rate",
      "crosstalk_neighbour_pixels",
      "walk_error",
      "pile_up_saturation"
    ],
    "allowed_problem_classes": [
      "flash_spad_dtof",
      "photon_efficient_lidar",
      "nlos_flash"
    ],
    "center_spec": {
      "epsilon_fn_center": "15.0 mm depth RMSE at 10 m",
      "forward_operator": "flash_pulse_spad_histogram",
      "input_format": "per_pixel_histograms_plus_calibration",
      "omega": {
        "H": 640,
        "N_t": 1024,
        "W": 480,
        "ambient_photon_rate": 0.0,
        "crosstalk_neighbour_pixels": 0.0,
        "dark_count_rate": 100,
        "photon_count_per_pixel": 20,
        "tau_tdc_ps": 100,
        "walk_error": 0.0
      },
      "problem_class": "flash_spad_dtof"
    },
    "epsilon_bounds": {
      "rmse_mm": [
        2.0,
        200.0
      ]
    },
    "omega_bounds": {
      "H": [
        128,
        1280
      ],
      "N_t": [
        128,
        4096
      ],
      "W": [
        128,
        1280
      ],
      "ambient_photon_rate": [
        0.0,
        1000000
      ],
      "crosstalk_neighbour_pixels": [
        0.0,
        0.05
      ],
      "dark_count_rate": [
        10,
        10000
      ],
      "photon_count_per_pixel": [
        1,
        1000
      ],
      "pile_up_saturation": [
        0.0,
        0.5
      ],
      "tau_tdc_ps": [
        20,
        500
      ],
      "walk_error": [
        0.0,
        0.2
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Flash-illumination focal-plane-array dToF",
  "title": "Flash LiDAR (single-shot 2D SPAD-array direct ToF)"
}

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