L1 ⚛ L1-013 ⊙ Testnet

Polarization Microscopy (Stokes / birefringence imaging)

Microscopy · Polarization-sensitive optical imaging

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⬇ L1-013.md

# ⚛ L1 Principle — Polarization Microscopy (Stokes / birefringence imaging) **ID:** `L1-013` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Microscopy — *Polarization-sensitive optical imaging* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** stokes triplet > **📡 Carrier:** photon · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554155 --- ## 🧠 1. Introduction **Polarization Microscopy (Stokes / birefringence imaging)** is a **linear inverse problem** whose unknown lives in **stokes triplet** space, within the **Polarization-sensitive optical imaging** sub-domain of **Microscopy**. Measurements consist of photons collected by an optical detector via a **polarization stokes** sensing mechanism. The forward operator applies, in order: L · polarizer operator; L · analyzer operator; detector accumulates flux over the exposure window. Observations are corrupted by additive Gaussian noise. Existence of the recovered stokes triplet is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by the declared priors. Stability is moderately conditioned (kappa_eff ~= 10); polarizer_alignment_error dominates the stability cliff; retarder_drift and the remaining mismatch parameters contribute higher-order bias terms. Additive gaussian thermal/electronic noise sets the irreducible data-fidelity floor, while mild Tikhonov or analytic inversion is sufficient at the nominal Omega point. ## ⚙ 2. Forward Model Physical chain: **x** → L · polarizer → L · analyzer → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.analyzer` `L.polarizer` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.polarizer` | L · polarizer operator | | `L.analyzer` | L · analyzer operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Microscopy | | Sub domain | Polarization-sensitive optical imaging | | Carrier | photon | | Problem class | linear_inverse | | Solution space | stokes_triplet | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 3 | | L dag | 3 | ## 📡 4. Measurement Model Existence of the recovered stokes triplet is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by the declared priors. Stability is moderately conditioned (kappa_eff ~= 10); polarizer_alignment_error dominates the stability cliff; retarder_drift and the remaining mismatch parameters contribute higher-order bias terms. Additive gaussian thermal/electronic noise sets the irreducible data-fidelity floor, while mild Tikhonov or analytic inversion is sufficient at the nominal Omega point. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `stokes_polarimetry` · **Forward operator:** `stokes_polarimetry_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 1024 | | W | px | 1024 | | Lambda nm | nm | 550 | | N pol states | — | 4 | | Photon count | — | 1000 | | Retarder drift | — | 0 | | Polarizer alignment error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 256 – 4096 | | W | px | 256 – 4096 | | Lambda nm | nm | 400 – 900 | | N pol states | — | 3 – 16 | | Photon count | — | 50 – 20000 | | Retarder drift | — | 0.0 – 0.1 | | Polarizer alignment error | — | 0.0 – 0.05 | | Intrinsic birefringence background | — | 0.0 – 0.2 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 30.0 | Metric | Range | |---|---| | Psnr db | 12.0 – 42.0 | ## ⚖ 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:** `0x292c76a6117a6e45e89cad4deccdf656e75696b3af1b876777256686c8e3163d` - **Chain tx hash:** `0xb3f658a839fe8570c99e066590e3c8c1ae1fd7e25a6fea11fea149220ca18649` - **Chain block:** `41554155` --- ## File Mapping This bundle consists of: `L1-013.md`, `L1-013.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-013.md` | Source of truth — edit this | Human or LLM | | `L1-013.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 `L1-013`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-013-001 Polarization Microscopy (Stokes / birefringence imaging) Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41554155,
  "chain_hash": "0x292c76a6117a6e45e89cad4deccdf656e75696b3af1b876777256686c8e3163d",
  "chain_tx_hash": "0xb3f658a839fe8570c99e066590e3c8c1ae1fd7e25a6fea11fea149220ca18649",
  "domain": "Microscopy",
  "hardness_fn": {
    "delta": 3,
    "kappa": 200,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
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      "name": "primary",
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    "regime": "Existence of the recovered stokes triplet is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by the declared priors. Stability is moderately conditioned (kappa_eff ~= 10); polarizer_alignment_error dominates the stability cliff; retarder_drift and the remaining mismatch parameters contribute higher-order bias terms. Additive gaussian thermal/electronic noise sets the irreducible data-fidelity floor, while mild Tikhonov or analytic inversion is sufficient at the nominal Omega point.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.0,
    "carrier": "photon",
    "difficulty_delta": 3,
    "domain": "Microscopy",
    "integration_axis": "temporal",
    "noise_model": "gaussian",
    "primitives": [
      "L.polarizer",
      "L.analyzer",
      "int.temporal"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "polarization_stokes",
    "solution_space": "stokes_triplet",
    "sub_domain": "Polarization-sensitive optical imaging",
    "title": "Polarization Microscopy (Stokes / birefringence imaging)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "stokes_polarimetry_forward"
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    "allowed_omega_dimensions": [
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      "W",
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      "lambda_nm",
      "photon_count",
      "polarizer_alignment_error",
      "retarder_drift",
      "polarizer_alignment_error",
      "retarder_drift",
      "intrinsic_birefringence_background"
    ],
    "allowed_problem_classes": [
      "stokes_polarimetry"
    ],
    "center_spec": {
      "epsilon_fn_center": "30.0",
      "forward_operator": "stokes_polarimetry_forward",
      "input_format": "measurement_only",
      "omega": {
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        "N_pol_states": 4,
        "W": 1024,
        "lambda_nm": 550,
        "photon_count": 1000,
        "polarizer_alignment_error": 0.0,
        "retarder_drift": 0.0
      },
      "problem_class": "stokes_polarimetry"
    },
    "epsilon_bounds": {
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        12.0,
        42.0
      ]
    },
    "omega_bounds": {
      "H": [
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        4096
      ],
      "N_pol_states": [
        3,
        16
      ],
      "W": [
        256,
        4096
      ],
      "intrinsic_birefringence_background": [
        0.0,
        0.2
      ],
      "lambda_nm": [
        400,
        900
      ],
      "photon_count": [
        50,
        20000
      ],
      "polarizer_alignment_error": [
        0.0,
        0.05
      ],
      "retarder_drift": [
        0.0,
        0.1
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Polarization-sensitive optical imaging",
  "title": "Polarization Microscopy (Stokes / birefringence imaging)"
}

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