page_title: Fourier-transform spectroscopy
section_title: Continuous-wave Michelson or Fourier-transform spectrograph
hierarchical_section_title: Fourier-transform spectroscopy / Continuous-wave Michelson or Fourier-transform spectrograph
caption_attribution_description: English: A Fourier transform spectrometer comprises a Michelson interferometer with a movable mirror. A Fourier transform converts the interferogram into the actual spectrum.
context_page_description: Fourier-transform spectroscopy 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 electromagnetic radiation or other type of radiation. It can be applied to a variety of types of spectroscopy including optical spectroscopy, infrared spectroscopy, nuclear magnetic resonance and magnetic resonance spectroscopic imaging, mass spectrometry and electron spin resonance spectroscopy. 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.
  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.
context_section_description: 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.
caption: The Fourier-transform spectrometer is just a Michelson interferometer, but one of the two fully reflecting mirrors is movable, allowing a variable delay (in the travel time of the light) to be included in one of the beams.
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