Fellgett Advantage in Spectroscopy

The Fellgett advantage (also called the multiplex advantage) states that a Fourier transform spectrometer achieves a signal-to-noise ratio improvement of over a scanning monochromator, where is the number of spectral elements.

This arises because the Fourier transform spectrometer measures all wavelengths simultaneously — each detector sample contains information about every spectral channel. In contrast, a scanning instrument measures one channel at a time, wasting photons at all other wavelengths.

Connection to OCT

The same principle explains the sensitivity advantage of Fourier-domain OCT over time-domain OCT. In FD-OCT, the spectral interferogram encodes all depth points simultaneously, while TD-OCT scans one depth at a time. The result is a 20–30 dB sensitivity improvement — see Optical Coherence Tomography Fundamentals for the full context.

Limitations

The Fellgett advantage assumes detector-noise-limited operation. When the dominant noise source is photon shot noise (which scales with total detected power), the multiplex advantage is reduced or eliminated. This is relevant for high-power swept-source OCT systems.

Still developing my understanding of how this interacts with relative intensity noise (RIN) in swept-source lasers — this may be a case where the Fellgett advantage is partially negated by the excess noise of the broadband source.