L1 ⚛ L1-245 ⊙ Testnet

Thin Film Interference — transfer-matrix optical design

Electromagnetics · Layered-stack optical transfer-matrix

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⬇ L1-245.md

# ⚛ L1 Principle — Thin Film Interference — transfer-matrix optical design **ID:** `L1-245` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Electromagnetics — *Layered-stack optical transfer-matrix* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** stack thickness and n > **📡 Carrier:** em · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41553989 --- ## 🧠 1. Introduction **Thin Film Interference — transfer-matrix optical design** is a **linear inverse problem** whose unknown lives in **stack thickness and n** space, within the **Layered-stack optical transfer-matrix** sub-domain of **Electromagnetics**. Measurements consist of electromagnetic field measurements via a **spectrophotometer** sensing mechanism. The forward operator applies, in order: L · transfer matrix operator; L · layer phase operator; L · boundary match operator; integration over a band of frequencies. Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds. ## ⚙ 2. Forward Model Physical chain: **x** → L · transfer matrix → L · layer phase → L · boundary match → Frequency integration → **y** (detector). ``` y = ∫dω `L.boundary_match` `L.layer_phase` `L.transfer_matrix` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.transfer_matrix` | L · transfer matrix operator | | `L.layer_phase` | L · layer phase operator | | `L.boundary_match` | L · boundary match operator | | `int.frequency` | Integration over a band of frequencies | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Electromagnetics | | Sub domain | Layered-stack optical transfer-matrix | | Carrier | em | | Problem class | linear_inverse | | Solution space | stack_thickness_and_n | | Noise model | gaussian | | Integration axis | frequency | | Difficulty delta | 3 | | L dag | 3 | ## 📡 4. Measurement Model Conditional stability; mismatch parameters dominate at Omega bounds. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `thin_film` · **Forward operator:** `thin_film_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | Snr db | dB | 40 | | N error | — | 0 | | N layers | — | 5 | | N wavelengths | — | 401 | | Substrate error | — | 0 | | Thickness error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Snr db | dB | 10 – 60 | | N error | — | 0.0 – 0.05 | | N layers | — | 1 – 100 | | N wavelengths | — | 11 – 10001 | | Substrate error | — | 0.0 – 0.05 | | Thickness error | — | 0.0 – 0.05 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 30.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 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:** `0xf8bc8ce7dd2a17826058979d41d0a62a7f1ea3668c55dd8e8ffba835184eb08e` - **Chain tx hash:** `0xa6622612b5410b7f67d069163195c3b096076b8c5602c1daddeaeccf759c61ff` - **Chain block:** `41553989` --- ## File Mapping This bundle consists of: `L1-245.md`, `L1-245.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-245.md` | Source of truth — edit this | Human or LLM | | `L1-245.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 `L1-245`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-245.md).
Regenerate L1-245.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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L2-245-001 Thin Film Interference — transfer-matrix optical design Mismatch-Only Spec

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📋 JSON metadata

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  "artifact_id": "L1-245",
  "chain_block": 41553989,
  "chain_hash": "0xf8bc8ce7dd2a17826058979d41d0a62a7f1ea3668c55dd8e8ffba835184eb08e",
  "chain_tx_hash": "0xa6622612b5410b7f67d069163195c3b096076b8c5602c1daddeaeccf759c61ff",
  "domain": "Electromagnetics",
  "hardness_fn": {
    "delta": 3,
    "kappa": 200,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
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      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "Conditional stability; mismatch parameters dominate at Omega bounds.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.0,
    "carrier": "em",
    "difficulty_delta": 3,
    "domain": "Electromagnetics",
    "integration_axis": "frequency",
    "noise_model": "gaussian",
    "primitives": [
      "L.transfer_matrix",
      "L.layer_phase",
      "L.boundary_match",
      "int.frequency"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "spectrophotometer",
    "solution_space": "stack_thickness_and_n",
    "sub_domain": "Layered-stack optical transfer-matrix",
    "title": "Thin Film Interference \u2014 transfer-matrix optical design"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "thin_film_forward"
    ],
    "allowed_omega_dimensions": [
      "N_layers",
      "N_wavelengths",
      "SNR_dB",
      "thickness_error",
      "n_error",
      "substrate_error",
      "thickness_error",
      "n_error",
      "substrate_error"
    ],
    "allowed_problem_classes": [
      "thin_film"
    ],
    "center_spec": {
      "epsilon_fn_center": "30.0",
      "forward_operator": "thin_film_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_layers": 5,
        "N_wavelengths": 401,
        "SNR_dB": 40,
        "n_error": 0.0,
        "substrate_error": 0.0,
        "thickness_error": 0.0
      },
      "problem_class": "thin_film"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "N_layers": [
        1,
        100
      ],
      "N_wavelengths": [
        11,
        10001
      ],
      "SNR_dB": [
        10,
        60
      ],
      "n_error": [
        0.0,
        0.05
      ],
      "substrate_error": [
        0.0,
        0.05
      ],
      "thickness_error": [
        0.0,
        0.05
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Layered-stack optical transfer-matrix",
  "title": "Thin Film Interference \u2014 transfer-matrix optical design"
}

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