Precision Refractive Index Measurement at 1762 nm

This repository contains the complete dataset and analysis code for the research paper "Precision Refractive Index Measurement at 1762 nm", which demonstrates precision refractive index measurement using dual-wavelength interferometry traceable to quantum frequency standards.

📖 Abstract

This work establishes a wavelength-specific metrological framework for precision refractive index measurement at 1762 nm. Using quantum-referenced interferometry traceable to a single trapped barium ion, we analyze 149,243 measurements to determine the refractive index coefficients of air with part-per-billion precision. The study identifies a 17.2% enhanced humidity sensitivity at 1762 nm relative to standard atmospheric models, consistent with Kramers-Kronig predictions near water absorption lines.

🚀 Key Features

• Precision Refractometry: Experimental determination of refractive index coefficients for air at 1762 nm with part-per-billion (ppb) precision
• Quantum-Traceable Metrology: Direct linkage to atomic frequency standards enables SI-traceable environmental monitoring
• Enhanced Humidity Sensitivity: Identification of 17.2% enhanced humidity sensitivity at 1762 nm
• Model Validation: Comprehensive comparison with established atmospheric models (Ciddor, Edlén, Mathar)
• Open Data: Complete synchronized dataset of environmental parameters and interferometric measurements

📊 Dataset

The dataset includes 145784 synchronized measurements from January to August 2025, which includes synchronized measurements of temperature, humidity, pressure, and dual-wavelength interferometric data.

Data Format

Each processed CSV file contains:

• time: UTC timestamp
• temperature: Temperature in °C
• humidity: Relative humidity in %
• pressure: Atmospheric pressure in hPa
• counts_ratio: Interference pattern counts ratio
• n_1762: Measured refractive index at 1762 nm

📈 Key Results

Refractive Index Coefficients at 1762 nm

Parameter	Coefficient	HAC Standard Error	Precision
Temperature (αₜ)	-8.8474 × 10⁻⁷ °C⁻¹	2.7967 × 10⁻¹⁰	0.28 ppb/°C
Humidity (αₕ)	-1.3152 × 10⁻⁸ %⁻¹	2.2435 × 10⁻¹⁰	0.22 ppb/%
Pressure (αₚ)	+2.5949 × 10⁻⁷ hPa⁻¹	1.8632 × 10⁻¹⁰	0.19 ppb/hPa

Model Performance

• Model Fit: R² = 0.996
• Residual Precision: σₙ = 1.837 × 10⁻⁷
• Enhanced Humidity Sensitivity: 17.2% relative to standard models (v.s. Mathar@1762nm: -1.122 × 10⁻⁸ %⁻¹)
• Kramers-Kronig Prediction: -1.4361 × 10⁻⁸ %⁻¹ (v.s. experimental -1.3152 × 10⁻⁸ %⁻¹)

Bootstrap Confidence Intervals (95%)

• Temperature: [-8.8513, -8.8437] × 10⁻⁷ °C⁻¹
• Humidity: [-1.3464, -1.2859] × 10⁻⁸ %⁻¹
• Pressure: [2.5925, 2.5973] × 10⁻⁷ hPa⁻¹

📁 Repository Structure

zenodo/
├── README.md                  
├── LICENSE.txt                
├── CITATION.cff              
├── data/
│   ├── raw/
│   │   ├── interferometer/
│   │   │   └── counts_ratio_data_{date}.csv
│   │   └── environmental/
│   │       ├── humidity_data_{date}.csv
│   │       ├── temperature_data_{date}.csv
│   │       └── pressure_data_{date}.csv
│   ├── processed/
│   │   ├── training_data.csv
│   │   └── validation_data.csv
│   └── derived/
│       ├── figures/
│       │   ├── data_preview.pdf
│       │   ├── deviation_validation.pdf
│       │   └── kramers_kronig.pdf
│       └── models/
│           └── hitran
│               ├── H2O.data
│               └── H2O.header
├── code/
│   ├── data_processing/
│   │   └── preprocess_data.ipynb
│   ├── analysis/              
│   │   ├── refractive_index_model.ipynb
│   │   ├── model_validation.ipynb
│   │   ├── regression_results.json
│   │   └── kramers_kronig.ipynb
│   └── models/              
│       ├── hitran
│       │   └── hapi.py
│       ├── mathar
│       │   └── Mathar2007.py
│       └── nist
│           └── refractive_index.py
└── manuscript/
    ├── manuscript.tex                  
    └── manuscript.pdf   

🔬 Scientific Context

This work addresses the critical need for wavelength-specific refractive index measurements, particularly at 1762 nm where standard atmospheric models show limitations. The research demonstrates:

1. Part-per-billion precision in environmental coefficient determination
2. Enhanced humidity sensitivity near water absorption lines at 1762 nm
3. Quantum-traceable metrology enabling SI-traceable atmospheric monitoring
4. Comprehensive validation against independent datasets and theoretical predictions

📜 License

This project is dual-licensed under:

• Code: MIT License - See LICENSE for details
• Data: Creative Commons Attribution 4.0 International (CC BY 4.0) - See LICENSE-CC-BY-4.0.txt for details

🔗 Related Resources

• Zenodo Data Repository
• Qsim Group in Freiburg
• EU Quantum Flagship

📧 Contact

• Wei Wu: wei.wu@physik.uni-freiburg.de
• Ulrich Warring: ulrich.warring@physik.uni-freiburg.de

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This research was supported by the European Research Council, Deutsche Forschungsgemeinschaft, QUSTEC Programme, and the Georg H. Endress Foundation.