Page "Fourier transform spectroscopy" Paragraph 26

One of the most important advantages of Fourier transform spectroscopy was shown by P. B.

Fellgett, an early advocate of the method.

The Fellgett advantage, also known as the multiplex principle, states that when obtaining a spectrum when measurement noise is dominated by detector noise ( which is independent of the power of radiation incident on the detector ), a multiplex spectrometer such as a Fourier transform spectrometer will produce a relative improvement in signal-to-noise ratio, compared to an equivalent scanning monochromator, of the order of the square root of m, where m is the number of sample points comprising the spectrum.

However if the detector is shot noise dominated, the noise will be proportional to the square root of the power, thus for a broad boxcar spectrum ( continuous broadband source ), the noise is proportional to the square root of m, thus precisely offset the Fellgett's advantage.

Shot noise is the main reason Fourier Transform Spectrometry was never popular for UV and visible spectrum.