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Related Concept Videos

Infrared (IR) Spectroscopy: Overview01:09

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There are two main infrared (IR) spectrophotometers: dispersive IR spectrometers and Fourier transform infrared (FTIR) spectrometers. In a dispersive IR spectrometer, a beam of infrared radiation produced by a hot wire is divided into two parallel equal-intensity beams using mirrors. One beam passes through the sample, while another is a reference beam. The beams then move through the monochromator, which separates the radiations into a continuous spectrum of different frequencies. The...
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Selective Weighted Least Squares Method for Fourier Transform Infrared Quantitative Analysis.

Xin Wang1,2, Yan Li2, Haoyun Wei2

  • 11 College of Mechanical Engineering and Applied Electronics Technology, Beijing University of Technology, Beijing, China.

Applied Spectroscopy
|November 1, 2016
PubMed
Summary

Classical least squares (CLS) and weighted least squares (WLS) regression methods were compared for Fourier transform infrared (FT-IR) quantitative analysis. A new selective weighted least squares (SWLS) method improves accuracy by adapting to spectral noise and bias errors.

Keywords:
CLSFT-IRFourier transform infraredSWLSWLSbaseline errorclassical least squaresnoiseselective weighted least squaresweighted least squares

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Area of Science:

  • Analytical Chemistry
  • Spectroscopy
  • Chemometrics

Background:

  • Classical least squares (CLS) regression is widely used for quantitative analysis in Fourier transform infrared (FT-IR) spectrometry.
  • FT-IR spectral noise is often heteroscedastic, potentially limiting the performance of CLS, which assumes uncorrelated residual errors.
  • Bias errors, such as baseline drift, can also impact the accuracy of regression models.

Purpose of the Study:

  • To compare the performance of CLS and weighted least squares (WLS) regression in FT-IR quantitative analysis under varying noise and bias error conditions.
  • To introduce and evaluate a novel selective weighted least squares (SWLS) regression method that optimizes quantitative analysis by adaptively applying CLS or WLS based on spectral characteristics.
  • To investigate the factors influencing the optimal threshold value (OTV) for the SWLS method.

Main Methods:

  • Comparative analysis of CLS and WLS regression models using simulated and experimental FT-IR spectral data.
  • Development and implementation of the selective weighted least squares (SWLS) regression algorithm, incorporating an absorbance threshold for method selection.
  • Numerical simulations to study the impact of noise, bias error, concentration, and analyte type on the optimal threshold value (OTV).
  • Application and evaluation of CLS, WLS, and SWLS methods for quantitative analysis of methane and methane/toluene gas mixtures using FT-IR spectrometry.

Main Results:

  • For wavenumbers with low absorbance, CLS outperformed WLS due to significant bias error, while at high absorbance, WLS was superior due to dominant noise.
  • SWLS demonstrated improved accuracy, yielding the lowest standard error of prediction (SEP) and residual sum of squares (RSS) in methane gas analysis.
  • A modified SWLS effectively addressed bias errors from interfering components in mixture analysis, reducing bias and RSS compared to CLS, particularly for minor components.

Conclusions:

  • SWLS offers a robust approach for FT-IR quantitative analysis by adaptively selecting between CLS and WLS based on absorbance levels, outperforming both individually.
  • The optimal threshold value (OTV) in SWLS is primarily determined by the ratio of bias error to noise standard deviation, with minimal influence from concentration or analyte type.
  • Modified SWLS provides enhanced accuracy and reduced bias in complex mixtures, making it a valuable tool for quantitative FT-IR applications.