L1 ⚛ L1-012 ⊙ Testnet

Total Internal Reflection Fluorescence (TIRF)

Microscopy · Evanescent-field surface-selective imaging

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⬇ L1-012.md

# ⚛ L1 Principle — Total Internal Reflection Fluorescence (TIRF) **ID:** `L1-012` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Microscopy — *Evanescent-field surface-selective imaging* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 2D intensity > **📡 Carrier:** photon · **🌫 Noise:** poisson gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554155 --- ## 🧠 1. Introduction **Total Internal Reflection Fluorescence (TIRF)** is a **linear inverse problem** whose unknown lives in **2D intensity** space, within the **Evanescent-field surface-selective imaging** sub-domain of **Microscopy**. Measurements consist of photons collected by an optical detector via a **evanescent field excitation** sensing mechanism. The forward operator applies, in order: L · excitation · evanescent operator; convolution with the Airy disk of a circular aperture; detector accumulates flux over the exposure window. Observations are corrupted by Poisson shot noise plus Gaussian read-out noise. Existence of the recovered 2D intensity 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 well-conditioned (kappa_eff ~= 8); coverslip_angle_drift dominates the stability cliff; penetration_depth_error and the remaining mismatch parameters contribute higher-order bias terms. Poisson signal noise + gaussian read 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 · excitation · evanescent → Airy PSF convolution → Temporal integration → **y** (detector). ``` y = ∫_t dt K_Airy * `L.excitation.evanescent` x + n, Poisson + 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.excitation.evanescent` | L · excitation · evanescent operator | | `K.psf.airy` | Convolution with the airy disk of a circular aperture | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Microscopy | | Sub domain | Evanescent-field surface-selective imaging | | Carrier | photon | | Problem class | linear_inverse | | Solution space | 2D_intensity | | Noise model | poisson_gaussian | | Integration axis | temporal | | Difficulty delta | 3 | | L dag | 2.5 | ## 📡 4. Measurement Model Existence of the recovered 2D intensity 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 well-conditioned (kappa_eff ~= 8); coverslip_angle_drift dominates the stability cliff; penetration_depth_error and the remaining mismatch parameters contribute higher-order bias terms. Poisson signal noise + gaussian read 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:** `tirf` · **Forward operator:** `tirf_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 512 | | W | px | 512 | | Na | — | 1.49 | | D p nm | nm | 100 | | Pixel nm | nm | 100 | | Peak photons | photons | 500 | | Coverslip angle drift | — | 0 | | Background volume fluorescence | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 128 – 4096 | | W | px | 128 – 4096 | | Na | — | 1.4 – 1.49 | | D p nm | nm | 50 – 300 | | Pixel nm | nm | 50 – 300 | | Peak photons | photons | 50 – 5000 | | Coverslip angle drift | — | 0.0 – 0.5 | | Penetration depth error | — | 0.0 – 0.3 | | Background volume fluorescence | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 28.0 | Metric | Range | |---|---| | Psnr db | 12.0 – 42.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `160` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x6ea9b2675c3428287b42549754b99265fe3644e22a2ffc7338f9c6a9563c846a` - **Chain tx hash:** `0x6f7b2f941284af69ef41dac81758049fa90e84f27599413413a5c2a1d94f1a23` - **Chain block:** `41554155` --- ## File Mapping This bundle consists of: `L1-012.md`, `L1-012.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-012.md` | Source of truth — edit this | Human or LLM | | `L1-012.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 `L1-012`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-012.md).
Regenerate L1-012.json so every field matches the Markdown.
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L2-012-001 Total Internal Reflection Fluorescence (TIRF) Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-012",
  "chain_block": 41554155,
  "chain_hash": "0x6ea9b2675c3428287b42549754b99265fe3644e22a2ffc7338f9c6a9563c846a",
  "chain_tx_hash": "0x6f7b2f941284af69ef41dac81758049fa90e84f27599413413a5c2a1d94f1a23",
  "domain": "Microscopy",
  "hardness_fn": {
    "delta": 3,
    "kappa": 160,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
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      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "Existence of the recovered 2D intensity 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 well-conditioned (kappa_eff ~= 8); coverslip_angle_drift dominates the stability cliff; penetration_depth_error and the remaining mismatch parameters contribute higher-order bias terms. Poisson signal noise + gaussian read 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": 2.5,
    "carrier": "photon",
    "difficulty_delta": 3,
    "domain": "Microscopy",
    "integration_axis": "temporal",
    "noise_model": "poisson_gaussian",
    "primitives": [
      "L.excitation.evanescent",
      "K.psf.airy",
      "int.temporal"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "evanescent_field_excitation",
    "solution_space": "2D_intensity",
    "sub_domain": "Evanescent-field surface-selective imaging",
    "title": "Total Internal Reflection Fluorescence (TIRF)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "tirf_forward"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "pixel_nm",
      "NA",
      "d_p_nm",
      "peak_photons",
      "coverslip_angle_drift",
      "background_volume_fluorescence",
      "coverslip_angle_drift",
      "penetration_depth_error",
      "background_volume_fluorescence"
    ],
    "allowed_problem_classes": [
      "tirf"
    ],
    "center_spec": {
      "epsilon_fn_center": "28.0",
      "forward_operator": "tirf_forward",
      "input_format": "measurement_only",
      "omega": {
        "H": 512,
        "NA": 1.49,
        "W": 512,
        "background_volume_fluorescence": 0.0,
        "coverslip_angle_drift": 0.0,
        "d_p_nm": 100,
        "peak_photons": 500,
        "pixel_nm": 100
      },
      "problem_class": "tirf"
    },
    "epsilon_bounds": {
      "psnr_db": [
        12.0,
        42.0
      ]
    },
    "omega_bounds": {
      "H": [
        128,
        4096
      ],
      "NA": [
        1.4,
        1.49
      ],
      "W": [
        128,
        4096
      ],
      "background_volume_fluorescence": [
        0.0,
        0.3
      ],
      "coverslip_angle_drift": [
        0.0,
        0.5
      ],
      "d_p_nm": [
        50,
        300
      ],
      "peak_photons": [
        50,
        5000
      ],
      "penetration_depth_error": [
        0.0,
        0.3
      ],
      "pixel_nm": [
        50,
        300
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Evanescent-field surface-selective imaging",
  "title": "Total Internal Reflection Fluorescence (TIRF)"
}

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