---
title: "Fourier-transform infrared spectroscopy"
chunk: 3/5
source: "https://en.wikipedia.org/wiki/Fourier-transform_infrared_spectroscopy"
category: "reference"
tags: "science, encyclopedia"
date_saved: "2026-05-05T03:13:34.037453+00:00"
instance: "kb-cron"
---

The separation is the inverse of the maximum OPD. For example, a maximum OPD of 2 cm results in a separation of 0.5 cm−1. This is the spectral resolution in the sense that the value at one point is independent of the values at adjacent points. Most instruments can be operated at different resolutions by choosing different OPD's. Instruments for routine analyses typically have a best resolution of around 0.5 cm−1, while spectrometers have been built with resolutions as high as 0.001 cm−1, corresponding to a maximum OPD of 10 m. The point in the interferogram corresponding to zero path difference has to be identified, commonly by assuming it is where the maximum signal occurs. This so-called centerburst is not always symmetrical in real world spectrometers so a phase correction may have to be calculated. The interferogram signal decays as the path difference increases, the rate of decay being inversely related to the width of features in the spectrum. If the OPD is not large enough to allow the interferogram signal to decay to a negligible level there will be unwanted oscillations or sidelobes associated with the features in the resulting spectrum. To reduce these sidelobes the interferogram is usually multiplied by a function that approaches zero at the maximum OPD. This so-called apodization reduces the amplitude of any sidelobes and also the noise level at the expense of some reduction in resolution.
For rapid calculation the number of points in the interferogram has to equal a power of two. A string of zeroes may be added to the measured interferogram to achieve this. More zeroes may be added in a process called zero filling to improve the appearance of the final spectrum although there is no improvement in resolution. Alternatively, interpolation after the Fourier transform gives a similar result.

== Advantages ==
There are three principal advantages for an FT spectrometer compared to a scanning (dispersive) spectrometer.

The multiplex or Fellgett's advantage (named after Peter Fellgett). 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.
The throughput or Jacquinot's advantage (named after Pierre Jacquinot). 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. For a given resolution and wavelength this circular aperture allows more light through than a slit, resulting in a higher signal-to-noise ratio.
The wavelength accuracy or Connes's advantage (named after Janine Connes). 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.
Another minor advantage is less sensitivity to stray light, that is radiation of one wavelength appearing at another wavelength in the spectrum.  In dispersive instruments, this is the result of imperfections in the diffraction gratings and accidental reflections. In FT instruments there is no direct equivalent as the apparent wavelength is determined by the modulation frequency in the interferometer.

=== Resolution ===
The interferogram belongs in the length dimension. Fourier transform (FT) inverts the dimension, so the FT of the interferogram belongs in the reciprocal length dimension([L−1]), that is the dimension of wavenumber. The spectral resolution in cm−1 is equal to the reciprocal of the maximal OPD in cm. Thus a 4 cm−1 resolution will be obtained if the maximal OPD is 0.25 cm; this is typical of the cheaper FTIR instruments. Much higher resolution can be obtained by increasing the maximal OPD. This is not easy, as the moving mirror must travel in a near-perfect straight line. The use of corner-cube mirrors in place of the flat mirrors is helpful, as an outgoing ray from a corner-cube mirror is parallel to the incoming ray, regardless of the orientation of the mirror about axes perpendicular to the axis of the light beam.
A spectrometer with 0.001 cm−1 resolution is now available commercially. The throughput advantage is important for high-resolution FTIR, as the monochromator in a dispersive instrument with the same resolution would have very narrow entrance and exit slits.
In 1966 Janine Connes measured the temperature of the atmosphere of Venus by recording the vibration-rotation spectrum of Venusian CO2 at 0.1 cm−1 resolution. Michelson himself attempted to resolve the hydrogen Hα emission band in the spectrum of a hydrogen atom into its two components by using his interferometer. p25

== Motivation ==
FTIR is a method of measuring infrared absorption and emission spectra. For a discussion of why people measure infrared absorption and emission spectra, i.e. why and how substances absorb and emit infrared light, see the article: Infrared spectroscopy.

== Components ==