Wavenumber resolution spectrometry

Since FT-IR spectrometry is based on the interference of waves of light (or radiation), first an account of this phenomenon is briefly given, before explaining the Fourier transform method by which an infrared spectrum is obtained from a measured interferogram. Some characteristics of FT-IR spectrometry, namely, wavenumber resolution, measurable wavenumber region, and accurate determination of wavenumbers are discussed. To facilitate the understanding of the description, which inevitably requires some mathematical formulations, many illustrations are provided. 

In this section, characteristics of FT-IR spectrometry, that is, wavenumber resolution, measurable spectral region, and accurate determination of wavenumbers, are discussed. As mentioned in Section 3.2.2, the term wavenumber resolution is used in this book instead of the commonly used terminology of just resolution. ... 

Although a brief introduction to the wavenumber resolution in FT-IR spectrometry was given in Section 3.2.2, this subject is discussed here in greater detail. 

Deconvolution in spectroscopy means a mathematical operation for enhancing apparent wavenumber resolution by narrowing bandwidths. Deconvolution is useful for separating overlapping bands and thereby determining the number of the overlapping bands and their peak wavenumbers. Although a few methods of deconvolution exist, only FSD, which is closely associated with FT-IR spectrometry, is described here. 

To compute the convolution of these two functions, Eq. 2.19 requires that/(v) be reversed left to right [which is trivial in this case, since/(v) is an even function], after which the two functions are multiplied point by point along the wavenumber axis. The resulting points are then integrated, and the process is repeated for all possible displacements, v, of/( relative to B v). One particular example of convolution may be familiar to spectroscopists who use grating instruments (see Chapter 8). When a low-resolution spectrum is measured on a monochromator, the true spectrum is convolved with the triangular slit function of the monochromator. The situation with Fourier transform spectrometry is equivalent, except that the true spectrum is convolved with the sine function/(v). Since the Fourier transform spectrometer does not have any slits,/(v) has been variously called the instrument line shape (ILS) Junction, the instrument function, or the apparatus function, of which we prefer the term ILS function. 

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