Fourier transform spectrometry

Fourier transform spectrometry is a technique in which the spectrum of a light source is estimated by taking the following steps:

• Modulate the light with an interferometer of the Michelson type (or any variant).
• Record the light intensity at the output port as the optical path difference between the two arms of the interferometer varies to form the so-called interferogram.
• By the Wiener-Khinchine-Einstein theorems, the spectrum of a wide-sense stationary random process is given by the Fourier transform of its autocorrelation function. Which is the interferogram, since the Michelson interferometer is in fact nothing else than an autocorrelator.

An interferometer that can generate a large optical path difference will allow a high physical resolution in the spectrum domain. Since a Michelson interferometer cannot produce an infinite optical path difference, the autocorrelation signal produced will always be truncated, that is, multiplied by a rectangle (or boxcar) function. Since the interferogram is Fourier-transformed, this means that all the spectrum gets convoluted with a sinc function. The greater the optical path difference, the larger is the rectangle and the narrower the sinc is.

The Jacquinot (or throughput, or étendue) advantage of the Fourier transform spectrometers (over dispersive spectrometers) is the fact that information is multiplexed in a FTS so that no spatial dimension is lost to retrieve it. For a given measure time and physical resolution, a FTS will always get more photons on the detector.