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

Beer's law is obeyed when the measured value of absorbance varies linearly with concentration in the absence of chemical effects. The absorbance range over which bands measured on any type of spectrometer obey Beer's law depends on the ratio of the resolution to the full width at half-height of the analytical band, often called the resolution parameter, ρ, and the instrument line shape (ILS) function of the spectrometer. Apodization functions are used widely in Fourier transform infrared (FT-IR) spectrometry to change the instrument line shape function. For Lorentzian bands, it is well known that when ρ is about 1 and the spectrum is computed with a triangular apodization function, there is a negative deviation from Beer's law when the true peak absorbance is high, whereas the use of boxcar truncation results in a positive deviation. In this paper, the possibility of extending the linear range of Beer's law by applying optimized apodization functions of the type proposed by Norton and Beer has been investigated. This theoretical study shows that the linear range of Beer's law plots for spectra measured at moderate resolution can be extended to peak absorbances greater than 2 with the use of any of the Norton Beer apodization functions. Linear plots of the apparent absorbance of a band against analyte concentration can be obtained even for bands of absorbance substantially greater than 3, although a nonzero intercept on the absorbance axis may be observed.