Fourier transform spectroscopy measures an interferogram as a function of optical path length difference. Its Fourier transform recovers the spectrum. An imaging implementation obtains an interferogram at every detector pixel, but a scanned cube is not simultaneous at all wavelengths.
A spectrograph records the optical spectrum dispersed by an instrument. Its spectral resolving power describes which nearby wavelengths it separates.
An integral field spectrograph records a spectrum for each of many spatial elements across a two-dimensional field, producing a spectral data cube. Field reformatters include lenslet arrays, optical fibers and image slicers.
An image slicer divides a two-dimensional image into narrow strips and optically rearranges them into a long pseudo-slit. A spectrograph then disperses each strip while preserving its position along the slit.
A spectral data cube stores intensity with two spatial coordinates and one spectral coordinate. The third coordinate is wavelength, not an additional spatial dimension.
Spectral resolving power is , where is the wavelength separation just resolved under the specified instrumental and source conditions.
A cross-dispersed echelle spectrograph uses an echelle grating for strong dispersion and a cross-disperser in the perpendicular direction to separate overlapping diffraction orders. It records many orders simultaneously in an echellogram.
A cross-disperser is a second dispersing element, often an optical prism or diffraction grating, oriented to separate optical spectra perpendicular to their principal dispersion direction.
An echellogram is the two-dimensional detector pattern of separated diffraction orders from a cross-dispersed echelle spectrograph.
A multi-object spectrograph records optical spectra of many selected objects simultaneously. The main designs are multi-slit spectrographs and fiber-fed spectrographs. The ESO instrumentation overview describes both arrangements.
A multi-slit spectrograph puts separate slits at target positions in the focal plane. Each slit transmits the target plus nearby sky; dispersion places its spatially resolved optical spectrum on the detector.
A fiber-fed spectrograph places optical fibers on selected targets and reformats their output into a common entrance slit. Dedicated sky fibers sample sky brightness. Fiber coupling, transmission, and output beam spreading affect throughput and resolution.

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A spectrometer is an analytical instrument used to measure and analyze the properties of light across a specific portion of the electromagnetic spectrum. It can be used to identify materials, determine their concentration, and analyze the structure of molecules by observing their interaction with light. Spectrometers work by dispersing light into its component wavelengths (spectrum) and measuring the intensity of light at each wavelength.