Fourier Transformation and FT-Spectroscopy

Abstract

In this chapter we present some basic properties of Fourier transformation and applications of Fourier transform spectroscopy. A simple example of an application of Fourier transformation is the determination of the frequencies one needs to compose a function f (x), presenting a rectangular pulse. Such a pulse may be generated by superposition of many monochromatic waves with many different wavelengths and amplitudes. The input data to Fourier transformation are the space coordinates of f (x). The result of Fourier transformation is the frequency spectrum corresponding to the different wavelengths used to compose f (x). A more complicated application is the analysis of the interferogram obtained from incident light traversing an absorbing material. The Fourier transformation of the interferogram will calculate the absorption spectrum of the material.