EXTENDING THE RANGE OF BEERS-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 line arly with concentration in the absence of chemical effects. The absorb ance 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 param eter, rho, and the instrument line shape (ILS) function of the spectro meter. Apodization functions are used widely in Fourier transform infr ared (FT-IR) spectrometry to change the instrument line shape function . For Lorentzian bands, it is well known that when rho 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 d eviation. In this paper, the possibility of extending the linear range of Beer's law by applying optimized apodization functions of the type proposed hy Norton and Beer has been investigated. This theoretical s tudy shows that the linear range of Beer's law plots for spectra measu red 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 conc entration can be obtained even for bands of absorbance substantially g reater than 3, although a nonzero intercept on the absorbance axis may be observed.