The Fourier Transform and Interferometer

Interferometer:

Interferometer in action: 

Interferometer (the last part of the video is most relevant for the FTIR):  The interferometer creates constructive and destructive interference of light waves.  The light in this video is a single wavelength (HeNe laser).  The FTIR spectrometer uses a laser for alignment, but data is collected using a light source that emits a large range of wavelengths.

https://youtu.be/j-u3IEgcTiQ 

Watch:

Fourier Transforms: (watch from beginning until 4:42)
Fourier transform allows us to collect data in the time domain (motion of the non-fixed mirror in the interferometer) and convert it to the frequency domain (proportional to wavenumbers).  We can collect an entire spectrum in one scan, instead of having to measure each frequency/wavenumber separately over the entire spectral range.  We have much faster data collection by using this math trick!

https://youtu.be/1JnayXHhjlg