L1 ⚛ L1-008 ⊙ Testnet

Fourier Ptychographic Microscopy (FPM)

Microscopy · Synthetic-aperture low-NA wide-FOV microscopy

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⬇ L1-008.md

# ⚛ L1 Principle — Fourier Ptychographic Microscopy (FPM) **ID:** `L1-008` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Microscopy — *Synthetic-aperture low-NA wide-FOV microscopy* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** complex 2D > **📡 Carrier:** photon · **🌫 Noise:** shot poisson > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554154 --- ## 🧠 1. Introduction **Fourier Ptychographic Microscopy (FPM)** is a **nonlinear inverse problem** whose unknown lives in **complex 2D** space, within the **Synthetic-aperture low-NA wide-FOV microscopy** sub-domain of **Microscopy**. Measurements consist of photons collected by an optical detector via a **angular illumination scan** sensing mechanism. The forward operator applies, in order: S · scan · led angle operator; L · fourier aperture operator; phase is lost; only intensity is measured; integration over the solid angle of incidence/emission. Observations are corrupted by Poisson shot noise from quantum-limited detection. Existence of the recovered complex 2D is guaranteed within the declared Omega bounds. Uniqueness is local rather than global (non-convex landscape); convergence depends on initialisation and priors. Stability is ill-conditioned (kappa_eff ~= 80); LED_position_error dominates the stability cliff; LED_intensity_variation and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) sets the irreducible data-fidelity floor, while TV / wavelet-sparsity / deep priors stabilise recovery at the ill-conditioned end of Omega. ## ⚙ 2. Forward Model Physical chain: **x** → S · scan · led angle → L · fourier aperture → Magnitude-squared → Angular integration → **y** (detector). ``` y = ∫dΩ |·|² `L.fourier_aperture` `S.scan.led_angle` x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `S.scan.led_angle` | S · scan · led angle operator | | `L.fourier_aperture` | L · fourier aperture operator | | `L.modulus_squared` | Phase is lost; only intensity is measured | | `int.angular` | Integration over the solid angle of incidence/emission | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Microscopy | | Sub domain | Synthetic-aperture low-NA wide-FOV microscopy | | Carrier | photon | | Problem class | nonlinear_inverse | | Solution space | complex_2D | | Noise model | shot_poisson | | Integration axis | angular | | Difficulty delta | 5 | | L dag | 4 | ## 📡 4. Measurement Model Existence of the recovered complex 2D is guaranteed within the declared Omega bounds. Uniqueness is local rather than global (non-convex landscape); convergence depends on initialisation and priors. Stability is ill-conditioned (kappa_eff ~= 80); LED_position_error dominates the stability cliff; LED_intensity_variation and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) sets the irreducible data-fidelity floor, while TV / wavelet-sparsity / deep priors stabilise recovery at the ill-conditioned end of Omega. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `fpm` · **Forward operator:** `fpm_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 512 | | W | px | 512 | | N led | — | 169 | | Na obj | — | 0.1 | | Overlap | — | 0.65 | | Peak photons | photons | 1000 | | Partial coherence | — | 1 | | Led position error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 256 – 4096 | | W | px | 256 – 4096 | | N led | — | 49 – 625 | | Na obj | — | 0.05 – 0.3 | | Overlap | — | 0.35 – 0.85 | | Peak photons | photons | 50 – 10000 | | Partial coherence | — | 0.7 – 1.0 | | Led position error | — | 0.0 – 2.0 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 26.0 | Metric | Range | |---|---| | Psnr db | 12.0 – 42.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `1600` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x9beaa2d1b5a6dee00726849542f6ce3cfde09620cc9e6c20a0344ac5dc09c199` - **Chain tx hash:** `0x0e226b8e0395a1ee955c02b8fd4f7c033631ca2c65f9b86acf2193e789e729f0` - **Chain block:** `41554154` --- ## File Mapping This bundle consists of: `L1-008.md`, `L1-008.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-008.md` | Source of truth — edit this | Human or LLM | | `L1-008.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 `L1-008`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-008-001 Fourier Ptychographic Microscopy (FPM) Mismatch-Only Spec

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📋 JSON metadata

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  "chain_tx_hash": "0x0e226b8e0395a1ee955c02b8fd4f7c033631ca2c65f9b86acf2193e789e729f0",
  "domain": "Microscopy",
  "hardness_fn": {
    "delta": 5,
    "kappa": 1600,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
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    "metric": "PSNR_dB",
    "regime": "Existence of the recovered complex 2D is guaranteed within the declared Omega bounds. Uniqueness is local rather than global (non-convex landscape); convergence depends on initialisation and priors. Stability is ill-conditioned (kappa_eff ~= 80); LED_position_error dominates the stability cliff; LED_intensity_variation and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) sets the irreducible data-fidelity floor, while TV / wavelet-sparsity / deep priors stabilise recovery at the ill-conditioned end of Omega.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 4.0,
    "carrier": "photon",
    "difficulty_delta": 5,
    "domain": "Microscopy",
    "integration_axis": "angular",
    "noise_model": "shot_poisson",
    "primitives": [
      "S.scan.led_angle",
      "L.fourier_aperture",
      "L.modulus_squared",
      "int.angular"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "angular_illumination_scan",
    "solution_space": "complex_2D",
    "sub_domain": "Synthetic-aperture low-NA wide-FOV microscopy",
    "title": "Fourier Ptychographic Microscopy (FPM)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "fpm_forward"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "N_LED",
      "NA_obj",
      "overlap",
      "peak_photons",
      "LED_position_error",
      "partial_coherence",
      "LED_position_error",
      "LED_intensity_variation",
      "partial_coherence"
    ],
    "allowed_problem_classes": [
      "fpm"
    ],
    "center_spec": {
      "epsilon_fn_center": "26.0",
      "forward_operator": "fpm_forward",
      "input_format": "measurement_only",
      "omega": {
        "H": 512,
        "LED_position_error": 0.0,
        "NA_obj": 0.1,
        "N_LED": 169,
        "W": 512,
        "overlap": 0.65,
        "partial_coherence": 1.0,
        "peak_photons": 1000
      },
      "problem_class": "fpm"
    },
    "epsilon_bounds": {
      "psnr_db": [
        12.0,
        42.0
      ]
    },
    "omega_bounds": {
      "H": [
        256,
        4096
      ],
      "LED_position_error": [
        0.0,
        2.0
      ],
      "NA_obj": [
        0.05,
        0.3
      ],
      "N_LED": [
        49,
        625
      ],
      "W": [
        256,
        4096
      ],
      "overlap": [
        0.35,
        0.85
      ],
      "partial_coherence": [
        0.7,
        1.0
      ],
      "peak_photons": [
        50,
        10000
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Synthetic-aperture low-NA wide-FOV microscopy",
  "title": "Fourier Ptychographic Microscopy (FPM)"
}

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