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Smart Error Sum Based on Hybrid Two-Trace Two-Dimensional (2T2D) Correlation Analysis.

Thomas G Mayerhöfer1,2, Marie Richard-Lacroix1, Susanne Pahlow1,2

  • 1Leibniz Institute of Photonic Technology (IPHT), Jena, Germany.

Applied Spectroscopy
|January 27, 2022
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Summary
This summary is machine-generated.

A new "smart error sum" method improves nonlinear inverse problem solving for optical spectra. This advanced technique accurately analyzes individual spectra, overcoming limitations of traditional methods.

Keywords:
2D-COSDispersion analysisIRinfrared spectroscopyloss functionresidual sum of squaressum of squared errorstwo-dimensional correlation analysis

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Area of Science:

  • Spectroscopy
  • Materials Science
  • Data Analysis

Background:

  • Nonlinear inverse problems in spectroscopy are challenging.
  • Conventional methods struggle with systematic errors in spectral data.
  • Existing loss functions may not adequately handle spectral correlations.

Purpose of the Study:

  • To extend the "smart error sum" for analyzing individual spectra.
  • To introduce hybrid two-trace two-dimensional (2T2D) correlation analysis for spectral fitting.
  • To validate the new method against conventional approaches.

Main Methods:

  • Development of a "smart error sum" loss function based on hybrid 2D correlation analysis.
  • Application of hybrid two-trace two-dimensional (2T2D) correlation analysis.
  • Analysis of experimental transflection spectra of polymethyl methacrylate (PMMA) layers.

Main Results:

  • The 2T2D smart error sum effectively analyzes individual spectra.
  • The new method successfully marginalizes multiplicative systematic errors.
  • Results show improved accuracy compared to conventional fitting methods.

Conclusions:

  • The 2T2D smart error sum is a robust and valid approach for spectral analysis.
  • This method enhances the determination of optical constants and oscillator parameters.
  • The approach offers a significant advancement over traditional sum of squared errors.