Editing Grating (section)

==Optical grating==
[[File:Moire2grd.png|thumb|Superimposed transparent gratings generating a [[Moiré pattern]]]]
[[File:Waveforms.svg|thumb|Graphs of [[sine wave|sine]], [[Square wave (waveform)|square]], [[triangle wave|triangle]], and [[sawtooth wave|sawtooth]] profiles.]]

As optical elements, optical gratings are images having the characteristic pattern of alternating, parallel lines. The lines alternate between high and low [[reflectance]] (black-white gratings) or high and low [[transmittance]] (transparent-opaque gratings). The grating profile is the function of the reflectance or transmittance perpendicular to the lines. This function is generally a [[Square wave (waveform)|square wave]], in that every transition between lines is abrupt. 

A grating can be defined by six parameters:
* ''[[Spatial frequency]]'' is the number of cycles occupying a particular distance (e.g. 10 line pairs per millimeter). The period of the grating is the inverse of the spatial frequency, measured in distance (e.g. 0.1 mm).
* ''[[Duty Cycle]]'' is the relative thickness of high and low lines. The duty cycle is the ratio of the width of the low line (black or opaque) to one whole grating period.
* ''[[Square wave (waveform)|Profile]]'' is the shape of the repeating pattern, which is typically a square wave but can also be any periodic pattern ([[sine wave]], [[triangle wave]], [[sawtooth wave]], etc.).
* ''[[contrast (vision)|Contrast]]'' is a measure of the difference in luminance between the high lines of the grating and the low lines. It is usually expressed as [[Michelson contrast]]:<ref>Michelson, A. A. (1891). On the application of interference methods to spectroscopic measurements. I. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Fifth Series, 31, 338-346 and Plate VII.</ref> the difference between maximum and minimum luminance divided by their sum.
* ''[[Orientation (geometry)|Orientation]]'' is the [[angle]] the grating makes with some reference orientation (such as the y-axis in a picture or of another grating). It is usually measured in degree or in radians.
* ''[[Phase (waves)|Phase]]'' is the position of the grating profile relative to some reference position. It is usually measured in [[degree (angle)|degree]]s (from 0 to 360 for one complete cycle) or in [[radian]]s (2π for one complete cycle). For example, two identical transparent gratings of 50% duty cycle and the same orientation will appear fully opaque only if the relative phase is π (180 degrees).

Gratings with sine wave profiles are used extensively in [[optics]] to determine the [[transfer function]]s of [[lens (optics)|lenses]]. A lens will form an image of a sine wave grating that is still sinusoidal, but with some reduction in its contrast depending on the spatial frequency and possibly some change in phase. The branch of mathematics dealing with this part of optics is [[Fourier analysis]] while the associated branch of study is [[Fourier optics]]. Gratings are also used extensively in research into [[visual perception]]. Campbell and Robson  promoted using sine-wave gratings by arguing that the human visual performs a Fourier analysis on retinal images.<ref>Campbell, F. W., & Robson, J. G. (1968). Application of Fourier analysis to the visibility of gratings. Journal of Physiology, 197, 551-566.</ref>

===Diffraction gratings===
{{main|Diffraction grating}}
Grating can also refer to a [[diffraction grating]]: a [[reflection (physics)|reflecting]] or [[transparency (optics)|transparent]] optical component on which there are many fine, [[parallel (geometry)|parallel]], equally spaced grooves. They [[Dispersion (optics)|disperse]] light, so are one of the main functional components in many kinds of [[spectrometer]]s, which decompose a light source into its constituent wavelength components.