Novel, Fourier Filtering Method that Reuses Interference-Patterned Spectra to Extend the Calibration Set for Thickness Determination
Abstract:Determining the thickness of plastic sheets on the basis of near-infrared spectra by building a multivariate calibration model requires a relatively large sample set. In the thickness region, where just a few non-interference-patterned samples are available, it is a waste of information if interference-patterned spectra are excluded. After eliminating the interference pattern from the spectra (filtering), the calibration set can be extended with these filtered spectra. Fourier transformation of an interference-patterned spectrum versus wavenumber leads to a Fourier spectrum as a function of the optical path length containing an easily recognizable interference peak. Unfortunately, this peak coincides with components of the spectral information of absorbance, on which multivariate calibration is based. Hence, replacing the interference peak is a cardinal step of the filtering process. Since the Fourier spectrum versus optical path length function is not known, it has been shown that interpolated data over the remaining Fourier components can be substituted for the missing part of the spectrum. In this paper, a novel method is proposed that uses a linear approximation between the Fourier spectra and the thickness values so that the regression coefficients are calculated on components of all but the interference-patterned Fourier spectra and the corresponding thicknesses, and then the deleted components in the filtered spectrum are replaced. This latter method yields more detailed Fourier spectra. Reducing the disturbing effect of scattering is also discussed. The effectiveness of the filtering was tested on low-density polyethylene sheets. The performance of different calibration models with or without filtering was compared by significance tests on standard error of prediction values. Application of the new Fourier type filtering technique led to significant improvements in the calibration performance.
Document Type: Research Article
Affiliations: Department of Atomic Physics, Budapest University of Technology and Economics, Budafoki 8, H-1111 Budapest, Hungary
Publication date: February 1, 2006
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