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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Fourier-transform spectroscopy | 1/2 | https://en.wikipedia.org/wiki/Fourier-transform_spectroscopy | reference | science, encyclopedia | 2026-05-05T10:04:36.785085+00:00 | kb-cron |
Fourier-transform spectroscopy (FTS) is a measurement technique whereby spectra are collected based on measurements of the coherence of a radiative source, using time-domain or space-domain measurements of the radiation, electromagnetic or not. It can be applied to a variety of types of spectroscopy including optical spectroscopy, infrared spectroscopy (FTIR, FT-NIRS), nuclear magnetic resonance (NMR) and magnetic resonance spectroscopic imaging (MRSI), mass spectrometry and electron spin resonance spectroscopy. There are several methods for measuring the temporal coherence of the light (see: field-autocorrelation), including the continuous-wave and the pulsed Fourier-transform spectrometer or Fourier-transform spectrograph. The term "Fourier-transform spectroscopy" reflects the fact that in all these techniques, a Fourier transform is required to turn the raw data into the actual spectrum, and in many of the cases in optics involving interferometers, is based on the Wiener–Khinchin theorem.
== Conceptual introduction ==
=== Measuring an emission spectrum ===
One of the most basic tasks in spectroscopy is to characterize the spectrum of a light source: how much light is emitted at each different wavelength. The most straightforward way to measure a spectrum is to pass the light through a monochromator, an instrument that blocks all of the light except the light at a certain wavelength (the un-blocked wavelength is set by a knob on the monochromator). Then the intensity of this remaining (single-wavelength) light is measured. The measured intensity directly indicates how much light is emitted at that wavelength. By varying the monochromator's wavelength setting, the full spectrum can be measured. This simple scheme in fact describes how some spectrometers work. Fourier-transform spectroscopy is a less intuitive way to get the same information. Rather than allowing only one wavelength at a time to pass through to the detector, this technique lets through a beam containing many different wavelengths of light at once, and measures the total beam intensity. Next, the beam is modified to contain a different combination of wavelengths, giving a second data point. This process is repeated many times. Afterwards, a computer takes all this data and works backwards to infer how much light there is at each wavelength. To be more specific, between the light source and the detector, there is a certain configuration of mirrors that allows some wavelengths to pass through but blocks others (due to wave interference). The beam is modified for each new data point by moving one of the mirrors; this changes the set of wavelengths that can pass through. As mentioned, computer processing is required to turn the raw data (light intensity for each mirror position) into the desired result (light intensity for each wavelength). The processing required turns out to be a common algorithm called the Fourier transform (hence the name, "Fourier-transform spectroscopy"). The raw data is sometimes called an "interferogram". Because of the existing computer equipment requirements, and the ability of light to analyze very small amounts of substance, it is often beneficial to automate many aspects of the sample preparation. The sample can be better preserved and the results are much easier to replicate. Both of these benefits are important, for instance, in testing situations that may later involve legal action, such as those involving drug specimens.
=== Measuring an absorption spectrum ===
The method of Fourier-transform spectroscopy can also be used for absorption spectroscopy. The primary example is "FTIR Spectroscopy", a common technique in chemistry. In general, the goal of absorption spectroscopy is to measure how well a sample absorbs or transmits light at each different wavelength. Although absorption spectroscopy and emission spectroscopy are different in principle, they are closely related in practice; any technique for emission spectroscopy can also be used for absorption spectroscopy. First, the emission spectrum of a broadband lamp is measured (this is called the "background spectrum"). Second, the emission spectrum of the same lamp shining through the sample is measured (this is called the "sample spectrum"). The sample will absorb some of the light, causing the spectra to be different. The ratio of the "sample spectrum" to the "background spectrum" is directly related to the sample's absorption spectrum. Accordingly, the technique of "Fourier-transform spectroscopy" can be used both for measuring emission spectra (for example, the emission spectrum of a star), and absorption spectra (for example, the absorption spectrum of a liquid).
== Continuous-wave Michelson or Fourier-transform spectrograph ==
The Michelson spectrograph is similar to the instrument used in the Michelson–Morley experiment. Light from the source is split into two beams by a half-silvered mirror, one is reflected off a fixed mirror and one off a movable mirror, which introduces a time delay—the Fourier-transform spectrometer is just a Michelson interferometer with a movable mirror. The beams interfere, allowing the temporal coherence of the light to be measured at each different time delay setting, effectively converting the time domain into a spatial coordinate. By making measurements of the signal at many discrete positions of the movable mirror, the spectrum can be reconstructed using a Fourier transform of the temporal coherence of the light. Michelson spectrographs are capable of very high spectral resolution observations of very bright sources. The Michelson or Fourier-transform spectrograph was popular for infra-red applications at a time when infra-red astronomy only had single-pixel detectors. Imaging Michelson spectrometers are a possibility, but in general have been supplanted by imaging Fabry–Pérot instruments, which are easier to construct.
=== Extracting the spectrum === The intensity as a function of the path length difference (also denoted as retardation) in the interferometer
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