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Related Experiment Video

Updated: May 27, 2026

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis

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Published on: August 19, 2021

Reducing Non-Linearity in Spectral Evaluation via a Modified Lorentz-Lorenz Relation.

Thomas G Mayerhöfer^1,2, Isao Noda³, Jürgen Popp^1,2

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.

Keywords:

2D-COS Two-dimensional correlation spectroscopy chemometrics complex refractive index liquid mixtures

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Measurement of Scattering Nonlinearities from a Single Plasmonic Nanoparticle

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Published on: January 3, 2016

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.