Extending the Range of Beer's Law in FT-IR Spectrometry. Part II: Theoretical Study of Continuous Apodization Functions

Abstract

In the previous paper in this series, it was shown that deviations from Beer's law caused by limited resolution could be reduced through the application of Norton Beer apodization functions. The side lobes in the instrument line shape (ILS) function introduced by these functions converge quite slowly because of the discontinuities at the maximum optical retardation. It is possible that these side lobes may limit the range of peak absorbance for which linear Beer's law plots are observed. To check on this hypothesis, we have examined the effect of three continuous apodization functions (cosine, Bessel, and sinc squared), on the Beer's law behavior of Lorentzian bands. Despite the much smaller side-lobe amplitude away from the main lobe of the ILS function, the performance of these apodization functions is only slightly better than that of the Norton Beer functions for broad bands. Better adherence to Beer's law for strongly absorbing bands is obtained for spectra measured with a resolution parameter, ρ, of about 0.5.