Abstract

An analysis of binary mixtures of hydroxyl compound by Attenuated Total Reflection Fourier transform infrared spectroscopy (ATR FT-IR) and classical least squares (CLS) yield large model error due to the presence of unmodeled components such as H-bonded components. To accommodate these spectral variations, polynomial-based least squares (LSP) and polynomial-based total least squares (TLSP) are proposed to capture the nonlinear absorbance-concentration relationship. LSP is based on assuming that only absorbance noise exists; while TLSP takes both absorbance noise and concentration noise into consideration. In addition, based on different solving strategy, two optimization algorithms (limited-memory Broyden–Fletcher–Goldfarb–Shanno (LBFGS) algorithm and Levenberg–Marquardt (LM) algorithm) are combined with TLSP and then two different TLSP versions (termed as TLSP-LBFGS and TLSP-LM) are formed. The optimum order of each nonlinear model is determined by cross-validation. Comparison and analyses of the four models are made from two aspects: absorbance prediction and concentration prediction. The results for water-ethanol solution and ethanol-ethyl lactate solution show that LSP, TLSP-LBFGS, and TLSP-LM can, for both absorbance prediction and concentration prediction, obtain smaller root mean square error of prediction than CLS. Additionally, they can also greatly enhance the accuracy of estimated pure component spectra. However, from the view of concentration prediction, the Wilcoxon signed rank test shows that there is no statistically significant difference between each nonlinear model and CLS.

© 2016 The Author(s)

Chemical visualization of individual chondrocytes in articular cartilage by attenuated-total-reflection Fourier Transform Infrared Microimaging

Jianhua Yin and Yang Xia
Biomed. Opt. Express 2(4) 937-945 (2011)

Use of attenuated total reflectance Fourier transform infrared spectroscopy to monitor the development of lipid aggregate structures

Mateo R. Hernandez, Elyse N. Towns, Terry C. Ng, Brian C. Walsh, Richard Osibanjo, Atul N. Parikh, and Donald P. Land
Appl. Opt. 51(15) 2842-2846 (2012)

Dispersion effects on infrared spectra in attenuated total reflection

Rabah Belali, Jean-Marie Vigoureux, and Joseph Morvan
J. Opt. Soc. Am. B 12(12) 2377-2381 (1995)

One-step fluorescence photoacoustic tomography with the optical radiative transfer model

Prabodh Kumar Pandey, Jampu Bharadwaj, Naren Naik, and Hari Om Aggrawal
J. Opt. Soc. Am. A 37(7) 1175-1192 (2020)

Least-Squares Polynomial Filtering of Images by Convolution

Peter A. Jansson
J. Opt. Soc. Am. 62(2) 195-198 (1972)