L1 ⚛ L1-095 ⊙ Testnet

Amplitude-Modulated Continuous-Wave Time-of-Flight (AMCW-ToF) Depth

Depth Imaging · Indirect ToF via phase

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⬇ L1-095.md

# ⚛ L1 Principle — Amplitude-Modulated Continuous-Wave Time-of-Flight (AMCW-ToF) Depth **ID:** `L1-095` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Depth Imaging — *Indirect ToF via phase* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 2D depth map > **📡 Carrier:** photon · **🌫 Noise:** shot poisson > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41547811 --- ## 🧠 1. Introduction **Amplitude-Modulated Continuous-Wave Time-of-Flight (AMCW-ToF) Depth** is a **nonlinear inverse problem** whose unknown lives in **2D depth map** space, within the **Indirect ToF via phase** sub-domain of **Depth Imaging**. Measurements consist of photons collected by an optical detector via a **amcw modulated illumination** sensing mechanism. The forward operator applies, in order: L · modulate · amcw operator; L · reflect scene operator; L · demodulate operator; detector accumulates flux over the exposure window. Observations are corrupted by Poisson shot noise from quantum-limited detection. Well-posed with multi-frequency unwrap (3 f_mod sufficient for Chinese Remainder Theorem unwrap). Precision sigma_d ~ c / (4*pi*f_mod * sqrt(SNR)). Multipath interference (MPI) at concave corners and translucent surfaces biases depth; motion during 4-bucket integration causes phase artifacts. ## ⚙ 2. Forward Model Physical chain: **x** → L · modulate · amcw → L · reflect scene → L · demodulate → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.demodulate` `L.reflect_scene` `L.modulate.amcw` x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.modulate.amcw` | L · modulate · amcw operator | | `L.reflect_scene` | L · reflect scene operator | | `L.demodulate` | L · demodulate operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Depth Imaging | | Sub domain | Indirect ToF via phase | | Carrier | photon | | Problem class | nonlinear_inverse | | Solution space | 2D_depth_map | | Noise model | shot_poisson | | Integration axis | temporal | | Difficulty delta | 3 | | L dag | 3.2 | ## 📡 4. Measurement Model Well-posed with multi-frequency unwrap (3 f_mod sufficient for Chinese Remainder Theorem unwrap). Precision sigma_d ~ c / (4*pi*f_mod * sqrt(SNR)). Multipath interference (MPI) at concave corners and translucent surfaces biases depth; motion during 4-bucket integration causes phase artifacts. | Metric | Value | |---|---| | Metric | depth_RMSE_mm | | Secondary | depth_MAE_mm | ## 📏 5. Operating Range (Ω) **Center problem class:** `amcw_tof_depth` · **Forward operator:** `four_bucket_tof_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 424 | | W | px | 512 | | N freq | — | 3 | | T int ms | ms | 10 | | K buckets | — | 4 | | F mod mhz | MHz | 80 | | Photon count | — | 500 | | Ambient light | — | 0 | | Motion jitter | — | 0 | | Multipath interference | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 240 – 1080 | | W | px | 320 – 1920 | | N freq | — | 1 – 5 | | T int ms | ms | 1 – 100 | | K buckets | — | 3 – 9 | | F mod mhz | MHz | 10 – 200 | | Photon count | — | 20 – 5000 | | Ambient light | — | 0.0 – 50000 | | Motion jitter | — | 0.0 – 0.05 | | Temperature drift | — | 0.0 – 0.05 | | Mixed pixels at edges | — | 0.0 – 0.1 | | Multipath interference | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 8.0 mm RMSE | Metric | Range | |---|---| | Depth rmse mm | 2.0 – 100.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **depth_RMSE_mm**, with κ = `700` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x69287c38a8582f25577dd3476514ee4e1c4751cf7707a96c9107a986c6779138` - **Chain tx hash:** `0xb790c39792c2ac236327e21a9896c3e70db6c3e5137b11b4861a93756237fd5d` - **Chain block:** `41547811` --- ## File Mapping This bundle consists of: `L1-095.md`, `L1-095.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-095.md` | Source of truth — edit this | Human or LLM | | `L1-095.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 `L1-095`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-095.md).
Regenerate L1-095.json so every field matches the Markdown.
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Output each file in its own fenced code block tagged with the filename.

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L2-095-001 AMCW-ToF Depth Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41547811,
  "chain_hash": "0x69287c38a8582f25577dd3476514ee4e1c4751cf7707a96c9107a986c6779138",
  "chain_tx_hash": "0xb790c39792c2ac236327e21a9896c3e70db6c3e5137b11b4861a93756237fd5d",
  "domain": "Depth Imaging",
  "hardness_fn": {
    "delta": 3,
    "kappa": 700,
    "metric": "depth_RMSE_mm",
    "type": "epsilon_fn"
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    "regime": "Well-posed with multi-frequency unwrap (3 f_mod sufficient for Chinese Remainder Theorem unwrap). Precision sigma_d ~ c / (4*pi*f_mod * sqrt(SNR)). Multipath interference (MPI) at concave corners and translucent surfaces biases depth; motion during 4-bucket integration causes phase artifacts.",
    "secondary": "depth_MAE_mm"
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  "physics_fingerprint": {
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    "carrier": "photon",
    "difficulty_delta": 3,
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    "integration_axis": "temporal",
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      "L.reflect_scene",
      "L.demodulate",
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    ],
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    "sensing_mechanism": "amcw_modulated_illumination",
    "solution_space": "2D_depth_map",
    "sub_domain": "Indirect ToF via phase",
    "title": "Amplitude-Modulated Continuous-Wave Time-of-Flight (AMCW-ToF) Depth"
  },
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      "multipath_interference",
      "motion_jitter",
      "ambient_light",
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      "temperature_drift"
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      "input_format": "K_bucket_frames_plus_modulation_params",
      "omega": {
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        "motion_jitter": 0.0,
        "multipath_interference": 0.0,
        "photon_count": 500
      },
      "problem_class": "amcw_tof_depth"
    },
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      "W": [
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      "f_mod_MHz": [
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      "mixed_pixels_at_edges": [
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      "motion_jitter": [
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      "multipath_interference": [
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      ],
      "photon_count": [
        20,
        5000
      ],
      "temperature_drift": [
        0.0,
        0.05
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Indirect ToF via phase",
  "title": "Amplitude-Modulated Continuous-Wave Time-of-Flight (AMCW-ToF) Depth"
}

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