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Reducing Non-Linearity in Spectral Evaluation via a Modified Lorentz-Lorenz Relation
Thomas G Mayerhöfer1,2, Isao Noda3, Jürgen Popp1,2
1Leibniz Institute of Photonic Technology (IPHT), Albert-Einstein-Str. 9, D-07745 Jena, Germany.
Applied Spectroscopy
|May 26, 2026
Summary
This study introduces a modified Lorentz-Lorenz transformation to improve linearity in quantitative infrared spectroscopy of liquid mixtures. This physics-informed approach significantly enhances prediction accuracy for chemical analysis.
Area of Science:
- Analytical Chemistry
- Spectroscopy
- Physical Chemistry
Background:
- Quantitative infrared spectroscopy of liquids commonly assumes linear Beer-Lambert behavior.
- Intrinsic nonlinearities arise from local-field interactions and dipole-dipole coupling in liquid mixtures.
Purpose of the Study:
- To investigate a modified Lorentz-Lorenz relation for restoring linearity in binary liquid mixtures.
- To evaluate the effectiveness of this transformation in improving quantitative spectral analysis.
Main Methods:
- Utilized benzene-toluene and benzene-cyclohexane as model systems.
- Assessed linearity using RMSE metrics, 2D-correlation analysis, and complex-valued classical least squares (CLS) regression.
- Employed a modified Lorentz-Lorenz transformation within the CLS regression framework.
Main Results:
- Correlation-based methods offered qualitative insights but failed to reliably identify optimal linearization parameters.
- CLS regression in the Lorentz-Lorenz-transformed domain, with error correction, significantly improved prediction accuracy.
- Mean absolute errors were reduced by over a factor of three compared to the Beer-Lambert domain.
Conclusions:
- The modified Lorentz-Lorenz transformation provides a physics-informed chemometric domain that enhances spectral linearity for mixtures.
- This approach offers a pathway to improve quantitative mixture analysis by extending regression techniques into the transformed domain.
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