Question

(A) Explain what a Fourier Transform (FT) does in plain English.

(B) Explain the advantages of a FT instrument over a constant wavelength diffuse instrument.

Answer 1

Fourier-transform spectroscopy is a measurement technique in which spectra are collected based on measurements of the coherence of a radiative source, using time or space measurements of the electromagnetic radiation or other type of radiation.

There are several methods for measuring the temporal coherence of the light, including the continuous wave Michelson or Fourier-transform spectrometer and the pulsed Fourier-transform spectrograph which is more sensitive and has a much shorter sampling time than conventional spectroscopic techniques, but applicable only in Laboratory environment.

Hence a Fourier transform is required to turn the raw data into the actual spectrum.

The Fourier theorem states that any waveform can be duplicated by the superposition of a series of sine and cosine waves.

The term Fourier-transform infrared spectroscopy originates from the fact that a Fourier transform (a mathematical process) is required to convert the raw data into the actual spectrum.

There are three principal advantages for an FT spectrometer compared to a scanning (dispersive) spectrometer.^[1]

1. The multiplex or Fellgett's advantage. This arises from the fact that information from all wavelengths is collected simultaneously. It results in a higher signal-to-noise ratio for a given scan-time for observations limited by a fixed detector noise contribution (typically in the thermal infrared spectral region where a photodetector is limited by generation-recombination noise). For a spectrum with m resolution elements, this increase is equal to the square root of m. Alternatively, it allows a shorter scan-time for a given resolution. In practice multiple scans are often averaged, increasing the signal-to-noise ratio by the square root of the number of scans.
2. The throughput or Jacquinot's advantage. This results from the fact that in a dispersive instrument, the monochromator has entrance and exit slits which restrict the amount of light that passes through it. The interferometer throughput is determined only by the diameter of the collimated beam coming from the source. Although no slits are needed, FTIR spectrometers do require an aperture to restrict the convergence of the collimated beam in the interferometer. This is because convergent rays are modulated at different frequencies as the path difference is varied. Such an aperture is called a Jacquinot stop.^[1] For a given resolution and wavelength this circular aperture allows more light through than a slit, resulting in a higher signal-to-noise ratio.
3. The wavelength accuracy or Connes' advantage. The wavelength scale is calibrated by a laser beam of known wavelength that passes through the interferometer. This is much more stable and accurate than in dispersive instruments where the scale depends on the mechanical movement of diffraction gratings. In practice, the accuracy is limited by the divergence of the beam in the interferometer which depends on the resolution.