A grating is any regularly spaced collection of essentially identical,

parallel Parallel may refer to: Mathematics * Parallel (geometry), two lines in the Euclidean plane which never intersect * Parallel (operator), mathematical operation named after the composition of electrical resistance in parallel circuits Science a ...

, elongated elements. Gratings usually consist of a single set of elongated elements, but can consist of two sets, in which case the second set is usually

perpendicular In geometry, two geometric objects are perpendicular if they intersect at right angles, i.e. at an angle of 90 degrees or π/2 radians. The condition of perpendicularity may be represented graphically using the '' perpendicular symbol'', � ...

to the first (as illustrated). When the two sets are perpendicular, this is also known as a

grid Grid, The Grid, or GRID may refer to: Space partitioning * Regular grid, a tessellation of space with translational symmetry, typically formed from parallelograms or higher-dimensional analogs ** Grid graph, a graph structure with nodes connec ...

(as in

grid paper Graph paper, coordinate paper, grid paper, or squared paper is writing paper that is printed with fine lines making up a regular grid. It is available either as loose leaf paper or bound in notebooks or graph books. It is commonly found in mathe ...

) or a

mesh Medical Subject Headings (MeSH) is a comprehensive controlled vocabulary for the purpose of indexing journal articles and books in the life sciences. It serves as a thesaurus of index terms that facilitates searching. Created and updated by th ...

As filters

A grating covering a drain (as illustrated) can be a collection of iron bars (the identical, elongated elements) held together (to ensure the bars are parallel and regularly spaced) by a lighter iron frame. Gratings over drains and air vents are used as filters, to block movement of large solids (e.g. people) and to allow movement of liquids. A

register Register or registration may refer to: Arts, entertainment, and media Music * Register (music), the relative "height" or range of a note, melody, part, instrument, etc. * ''Register'', a 2017 album by Travis Miller * Registration (organ), ...

is a type of grating used in

heating, ventilation, and air conditioning Heating, ventilation, and air conditioning (HVAC ) is the use of various technologies to control the temperature, humidity, and purity of the air in an enclosed space. Its goal is to provide thermal comfort and acceptable indoor air quality. H ...

, which transmits air, while stopping solid objects. File:Vindobona Hoher Markt-71.JPG, Grating - drain cover,

ancient Roman architecture Ancient Roman architecture adopted the external language of classical ancient Greek architecture for the purposes of the ancient Romans, but was different from Greek buildings, becoming a new architectural style. The two styles are often consi ...

Vindobona Vindobona (; from Gaulish ''windo-'' "white" and ''bona'' "base/bottom") was a Roman military camp (or ) in the province of Pannonia, located on the site of the modern city of Vienna in Austria. The settlement area took on a new name in the 13 ...

Austria Austria, formally the Republic of Austria, is a landlocked country in Central Europe, lying in the Eastern Alps. It is a federation of nine Federal states of Austria, states, of which the capital Vienna is the List of largest cities in Aust ...

. File:Montreal Sewer Cover.jpg, Sewer grating (

manhole cover A manhole cover is a removable plate forming the lid over the opening of a manhole, an opening large enough for a person to pass through that is used as an access point for an underground vault or pipe. It is designed to prevent anyone or anythi ...

) that can be driven on despite letting water pass through File:Tree grating, Washington, D. C. (3678939694).jpg, Tree grating that can be walked on despite letting water pass through

As decking

Grating can also come in panels that are often used for decks on

bridge A bridge is a structure built to Span (engineering), span a physical obstacle (such as a body of water, valley, road, or railway) without blocking the path underneath. It is constructed for the purpose of providing passage over the obstacle, whi ...

footbridge A footbridge (also a pedestrian bridge, pedestrian overpass, or pedestrian overcrossing) is a bridge designed solely for pedestrians.''Oxford English Dictionary'' While the primary meaning for a bridge is a structure which links "two points at a ...

s and catwalks. Grating can be made of materials such as

steel Steel is an alloy of iron and carbon that demonstrates improved mechanical properties compared to the pure form of iron. Due to steel's high Young's modulus, elastic modulus, Yield (engineering), yield strength, Fracture, fracture strength a ...

aluminum Aluminium (or aluminum in North American English) is a chemical element; it has chemical symbol, symbol Al and atomic number 13. It has a density lower than that of other common metals, about one-third that of steel. Aluminium has ...

fiberglass Fiberglass (American English) or fibreglass (English in the Commonwealth of Nations, Commonwealth English) is a common type of fibre-reinforced plastic, fiber-reinforced plastic using glass fiber. The fibers may be randomly arranged, flattened i ...

. Fiberglass grating is also known as FRP grating. They are used to optimize bending stiffness while minimizing weight. File:Grating at the historic John Street Roundhouse, Toronto.jpg, Close up view of anti-slip grating File:Puente rejilla.jpg, Bridge showing deck grating driving surface File:Stahlbau mit Gitterrosten.JPG, Walkway gratings at a power plant

Optical grating

As optical elements, optical gratings are images having the characteristic pattern of alternating, parallel lines. The lines alternate between high and low

reflectance The reflectance of the surface of a material is its effectiveness in reflecting radiant energy. It is the fraction of incident electromagnetic power that is reflected at the boundary. Reflectance is a component of the response of the electronic ...

(black-white gratings) or high and low

transmittance Electromagnetic radiation can be affected in several ways by the medium in which it propagates. It can be Scattering, scattered, Absorption (electromagnetic radiation), absorbed, and Fresnel equations, reflected and refracted at discontinui ...

(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 Square wave may refer to: *Square wave (waveform) A square wave is a non-sinusoidal waveform, non-sinusoidal periodic waveform in which the amplitude alternates at a steady frequency between fixed minimum and maximum values, with the same ...

, in that every transition between lines is abrupt. A grating can be defined by six parameters: * ''

Spatial frequency In mathematics, physics, and engineering, spatial frequency is a characteristic of any structure that is periodic across position in space. The spatial frequency is a measure of how often sinusoidal components (as determined by the Fourier tra ...

'' 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 A duty cycle or power cycle is the fraction of one period in which a signal or system is active. Duty cycle is commonly expressed as a percentage or a ratio. A period is the time it takes for a signal to complete an on-and-off cycle. As a for ...

'' 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. * '' Profile'' is the shape of the repeating pattern, which is typically a square wave but can also be any periodic pattern (

sine wave A sine wave, sinusoidal wave, or sinusoid (symbol: ∿) is a periodic function, periodic wave whose waveform (shape) is the trigonometric function, trigonometric sine, sine function. In mechanics, as a linear motion over time, this is ''simple ...

triangle wave A triangular wave or triangle wave is a non-sinusoidal waveform named for its triangular shape. It is a periodic, piecewise linear, continuous real function. Like a square wave, the triangle wave contains only odd harmonics. However, t ...

sawtooth wave The sawtooth wave (or saw wave) is a kind of non-sinusoidal waveform. It is so named based on its resemblance to the teeth of a plain-toothed saw with a zero rake angle. A single sawtooth, or an intermittently triggered sawtooth, is called a ...

, etc.). * '' 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: the difference between maximum and minimum luminance divided by their sum. * ''

Orientation Orientation may refer to: Positioning in physical space * Map orientation, the relationship between directions on a map and compass directions * Orientation (housing), the position of a building with respect to the sun, a concept in building des ...

'' is the

angle In Euclidean geometry, an angle can refer to a number of concepts relating to the intersection of two straight Line (geometry), lines at a Point (geometry), point. Formally, an angle is a figure lying in a Euclidean plane, plane formed by two R ...

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 Phase or phases may refer to: Science *State of matter, or phase, one of the distinct forms in which matter can exist *Phase (matter), a region of space throughout which all physical properties are essentially uniform *Phase space, a mathematica ...

'' is the position of the grating profile relative to some reference position. It is usually measured in degrees (from 0 to 360 for one complete cycle) or in

radian The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. It is defined such that one radian is the angle subtended at ...

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 Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of optical instruments, instruments that use or Photodetector, detect it. Optics usually describes t ...

to determine the

transfer function In engineering, a transfer function (also known as system function or network function) of a system, sub-system, or component is a function (mathematics), mathematical function that mathematical model, models the system's output for each possible ...

s of

lenses A lens is a transmissive optical device that focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (''elements''), ...

. 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 In mathematics, Fourier analysis () is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Joseph Fo ...

while the associated branch of study is

Fourier optics Fourier optics is the study of classical optics using Fourier transforms (FTs), in which the waveform being considered is regarded as made up of a combination, or '' superposition'', of plane waves. It has some parallels to the Huygens–Fresnel pr ...

. Gratings are also used extensively in research into

visual perception Visual perception is the ability to detect light and use it to form an image of the surrounding Biophysical environment, environment. Photodetection without image formation is classified as ''light sensing''. In most vertebrates, visual percept ...

. Campbell and Robson promoted using sine-wave gratings by arguing that the human visual performs a Fourier analysis on retinal images.Campbell, F. W., & Robson, J. G. (1968). Application of Fourier analysis to the visibility of gratings. Journal of Physiology, 197, 551-566.

Diffraction gratings

Grating can also refer to a

diffraction grating In optics, a diffraction grating is an optical grating with a periodic structure that diffraction, diffracts light, or another type of electromagnetic radiation, into several beams traveling in different directions (i.e., different diffractio ...

: a reflecting or transparent optical component on which there are many fine,

, equally spaced grooves. They disperse light, so are one of the main functional components in many kinds of

spectrometer A spectrometer () is a scientific instrument used to separate and measure Spectrum, spectral components of a physical phenomenon. Spectrometer is a broad term often used to describe instruments that measure a continuous variable of a phenomeno ...

s, which decompose a light source into its constituent wavelength components.

References

* Palmer, Christopher, ''Diffraction Grating Handbook'', 8th edition, MKS Newport (2020)

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As filters

As decking

Optical grating

Diffraction gratings

See also

References