# ⚛  L1 Principle — Radiometric Sensor Calibration

**ID:** `L1-473` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Geodesy — *Sensor calibration*
> **🎯 Problem class:** parameter estimation · **🧮 Solution space:** calibration coefficient vector
> **📡 Carrier:** photon · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555299

---

## 🧠 1. Introduction

**Radiometric Sensor Calibration** is a **parameter-estimation problem** whose unknown lives in **calibration coefficient vector** space, within the **Sensor calibration** sub-domain of **Geodesy**.

Measurements consist of photons collected by an optical detector via a **absolute radiometric calibration** sensing mechanism.

The forward operator applies, in order: S · calibration · vicarious operator; operator inherits structure from a graph (mesh, network); O · least squares · calibration operator.

Observations are corrupted by additive Gaussian noise. Existence of the recovered calibration_coefficient_vector is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 20); sensor_degradation_drift_percent_yr dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor.

## ⚙ 2. Forward Model

Physical chain: **x** → S · calibration · vicarious → Structured graph operator → O · least squares · calibration → **y** (detector).

```
y = `O.least_squares.calibration` G `S.calibration.vicarious` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `S.calibration.vicarious` | S · calibration · vicarious operator |
| `G.structured` | Operator inherits structure from a graph (mesh, network) |
| `O.least_squares.calibration` | O · least squares · calibration operator |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Geodesy |
| Sub domain | Sensor calibration |
| Carrier | photon |
| Problem class | parameter_estimation |
| Solution space | calibration_coefficient_vector |
| Noise model | gaussian |
| Integration axis | temporal_vicarious |
| Difficulty delta | 3 |
| L dag | 2.5 |

## 📡 4. Measurement Model

Existence of the recovered calibration_coefficient_vector is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 20); sensor_degradation_drift_percent_yr dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor.

| Metric | Value |
|---|---|
| Metric | radiometric_calibration_uncertainty_percent |
| Secondary | reflectance_RMSE |

## 📏 5. Operating Range (Ω)

**Center problem class:** `parameter_estimation` · **Forward operator:** `absolute_radiometric_calibration`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| N bands | bands | 10 |
| N cal sites | — | 20 |
| Degradation percent yr | — | 0.5 |
| Aerosol uncertainty aod | — | 0.02 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| N bands | bands | 1 – 100 |
| N cal sites | — | 5 – 100 |
| Degradation percent yr | — | 0.0 – 2.0 |
| Aerosol uncertainty aod | — | 0.005 – 0.1 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 2.0 radiometric_calibration_uncertainty_percent

| Metric | Range |
|---|---|
| Radiometric calibration uncertainty percent | 0.5 – 10.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **radiometric_calibration_uncertainty_percent**, with κ = `500` and δ = `3`.

## 💾 8. Reference Dataset

- **primary** · weight 1.0 · IPFS _(not pinned yet)_

## 9. On-chain Registration

- **Chain hash:** `0xaed9702d7418006fe1eceeffbcfb63696eb1a130cda9788d7e1bfbca17b9e189`
- **Chain tx hash:** `0x1af13fbf67e41defa9f5cf19a2f3965c96e4123095dda29b4f143d72f9f79ea9`
- **Chain block:** `41555299`

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## File Mapping

This bundle consists of: `L1-473.md`, `L1-473.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-473.md` | Source of truth — edit this | Human or LLM |
| `L1-473.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 `L1-473`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._