Applications of Vibrational Techniques

The basis of Fourier transform infrared (FT-IR) spectroscopy is the two-beam interferometer, designed by Michelson in 1891 [28]. and shown 

The resolution of an interferometer depends mainly on two factors firstly, the distance x the moving mirror travels or the maximum optical path difference A = 2x (Fig. 1), and secondly, the apodization function used in computing the spectrum. 

The first point is derived from the Rayleigh criterion of resolution, which states that to resolve two spectral lines separated by a distance d, the interferogram must be measured to an optical path length of at least Md 29]. 

The second factor is related to the fact that in real life the interferogram is truncated at finite optical path difference. In addition, in the fast Fourier transform (FFT) algorithm, according to Cooley and TTikey [30], which is used to perform the Fourier transform faster than the classical method, certain assumptions and simplifications are made. The result is that the FFT of a monochromatic source is not an infinitely narrow line. 

To explain the origins of a vibrational spectrum the vibration of a diatomic molecule is considered first. This can be illustrated by a molecular model in which the atomic nuclei are represented by two point masses mi and m2, and the inter- 

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