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A grating (or diffraction grating) is a type of disperser, i.e., an optical device that defracts light, which bends it, the amount of the angle depending upon the wavelength. As such, it separates the light into colors or wavelengths to make an instrument that measures intensity by wavelength, a grating spectrometer. A "basic" optical grating consists of a bunch of evenly-spaced, identical "bars" in parallel (scaled down very small and close together), such that each slit opening between them has the same diffractive effect on light passing through. The same diffractive effect can be carried out with tiny reflective-strips, which are termed reflective gratings and the original kind can be termed transmissive gratings to distinguish them. Likely, the vast majority of gratings in today's research telescopes are reflective. Gratings are used in optics for infrared to X-ray electromagnetic radiation (EMR). They are generally flat, but curved gratings are useful in some situations.
A property of gratings is that they produce multiple images of the spectrum, each termed an order, that can overlap if the spectrum spans a large wavelength-range. There are design techniques to avoid or reduce the overlap, and techniques have been developed to (somewhat) untangle the resulting overlaps with post-processing.
An echelle grating is a particular kind of reflective grating with a low density of grooves, typically used as one of a pair of reflective gratings, in an echelle spectrometer. HARPS has one.
A blazed grating or echelette grating is optimized (blazed) for one wavelength.
A Littrow configuration is such that the blaze angle and incidence angle are identical, and in a reflection grating, the diffracted beam is in the direction of the incident beam.
A volume phase holographic grating (VPH grating) uses parallel strips with varying refractive index, embedded in gel between glass plates. The pattern is formed using laser diffraction patterns on a photosensitive gel.
A grism is a type of disperser that combines a grating and a prism.