In optics, grating is a component with a surface covered by regular
pattern, often just parallel lines. For practical applications, most
gratings have grooves on their surface. Such gratings can be either
transparent or reflective. Gratings can be flat or concave addionally
they may be blazed or not, depending on the groove profile. For a given
grating, light with a larger wavelength generally has a larger
diffraction angle. Because of their ability of splitting light into
different wavelengths, gratings are commonly used in monochromators and
polychromtors. Gratings are characterised by their resolving power and
angular dispersion.

The resolving power is given by

where 'l' is the wavelength, dl is the difference in wavelength between two spectral lines of equal intensity, '*N*' stands for the total number of grooves on the grating and '*k'*
is the diffraction order. Resolution is then the ability of the
instrument to separate adjacent spectral lines. Two peaks are
considered resolved if the distance between them is such that the
maximum of one falls on the first minimum of the other. This is called
the Rayleigh criterion. It may be shown that

with '*W*' as the illuminated width of the grating, 'a' and 'b'
incident and exiting angles (angles of incidence and of diffraction).
Consequently, the resolving power of a grating is dependent on the
width of the grating, the centre wavelength to be resolved and the
geometry of the used conditions. The numerical resolving power '*R*'
should not be confused with the resolution or bandpass of an
instrument system. Angular dispersion is the variation of the
dispersion angle with wavelength and is defined as follows:

In principle a diffraction grating is only marginally more complicated
than Young's experiment.

A reflection diffraction grating consists of a flat or curved surface
with a series of **regular grooves**. In holographic gratings
the grooves in a master grating are formed by first exposing a photosensitive
material on the surface to the pattern formed by the interference
of light and then etching the surface.

This means that for a given diffraction angle *i'*,
constructive interference can occur for wavelengths: l, l/2, l/3,
etc., corresponding to orders 1, 2, 3, etc. The spectrum produced
by a grating is therefore complex, as it consists of several superimposed
orders.

Further, there is a zero order, which is not
scattered. For * k* = 0, the grating equation requires the angle of reflection to be equal and opposite to the angle
of incidence. In zero order, the grating behaves as a mirror. Order
zero represents about 40% of the total energy.

The rest of the energy is distributed amongst
the various orders. Generally, the higher the order, the lower the
brightness of its spectrum. The highest orders carry almost no energy.
In practice, only the first and second orders are usable.

**Further reading**:

- R Guenther,
*Modern
Optics*, John Wiley & Sons, New York (1990); - H Haken,
*Light, Vol. 1, Waves, Photons, Atoms*, North Holland,
Amsterdam (1981) - M Garbuny,
*Optical Physics*, Academic
Press, New York (1965).

First published on the web: 15 February 2000 by Richard Payling

revised and extended 19.11.2007

Authors: Aranka Derzsi and Giovanni Lotito. The text is based on a lecture given by Thomas Nelis at the first Gladnet training course in Antwerp Sept. 2007