How an Interferogram Becomes a Spectrum

As about mentioned, an interferogram is Fourier transformed to yield a spectrum. However, we have said nothing about how the Fourier transform (FT) works. A detailed discussion of the mathematics of the FT and its use in spectroscopy is available in ref [4]. Here we will use words and pictures to give the reader a feeling for the qualitative aspects of how a Fourier transform works. 

FIGURE 2.13 An illustration of the relationship between the spectrum of an idealized laser line and its interferogram. The Fonrier transform of a line is a cosine wave, and the Fourier transform of a cosine wave is a line. Note that the x-axis units of the interferogram are transformed from cm to cm when the spectrum is calculated. 

FIGURE 2.14 When an interferogram is Fourier transformed it produces a single beam spectrum. 

FIGURE 2.15 An example of a background spectrum, a single beam spectrum measured with no sample present. 

FIGURE 2.16 A typical background spectrum with the contributions of the instrument response function noted. 

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