Hybrid 2D Correlation-Based Loss Function for the Correction of Systematic Errors.

Area of Science:

• Spectroscopy
• Materials Science
• Data Analysis

Background:

• Spectroscopic data analysis often suffers from systematic multiplicative errors, particularly when using substrates like gold.
• These errors can lead to unphysical spectral data, such as reflectance values greater than unity.
• Existing correction methods may not fully address these systematic inaccuracies.

Purpose of the Study:

• To derive and validate a novel correlation-based loss function for spectroscopic data analysis.
• To address non-linear inverse problems affected by systematic multiplicative errors.
• To improve the accuracy and physical meaningfulness of spectroscopic data, especially from challenging substrates.

Main Methods:

• Derivation of a new loss function based on symmetry rules of synchronous and asynchronous two-dimensional correlation maps.
• Application of dispersion analysis and band fitting to spectroscopic data of poly(methyl methacrylate) films.
• Validation using spectra from substrates like gold, calcium fluoride (CaF2), and silicon (Si).

Main Results:

• The novel loss function is insensitive to systematic multiplicative errors common in spectroscopy.
• Accurate spectral fitting and correction of unphysical data (reflectance > 1) were achieved for poly(methyl methacrylate) on gold.
• The method demonstrated superior performance compared to conventional correction techniques.

Conclusions:

• The developed correlation-based loss function offers a robust solution for analyzing spectroscopic data with systematic errors.
• It enables the retrieval of physically meaningful spectra, enhancing the reliability of spectroscopic measurements.
• This approach is particularly valuable for spectral data obtained from substrates that induce experimental artifacts.