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An antireflective, antiglare or anti-reflection (AR) coating is a type of
optical coating An optical coating is one or more thin layers of material deposited on an optical component such as a lens, prism or mirror, which alters the way in which the optic reflects and transmits light. These coatings have become a key technology in th ...
applied to the surface of
lens A lens is a transmissive optical device which 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''), ...
es, other optical elements, and
photovoltaic cell A solar cell, or photovoltaic cell, is an electronic device that converts the energy of light directly into electricity by the photovoltaic effect, which is a physics, physical and Chemical substance, chemical phenomenon.reflection Reflection or reflexion may refer to: Science and technology * Reflection (physics), a common wave phenomenon ** Specular reflection, reflection from a smooth surface *** Mirror image, a reflection in a mirror or in water ** Signal reflection, in ...
. In typical imaging systems, this improves the efficiency since less
light Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 tera ...
is lost due to reflection. In complex systems such as
camera A camera is an Optics, optical instrument that can capture an image. Most cameras can capture 2D images, with some more advanced models being able to capture 3D images. At a basic level, most cameras consist of sealed boxes (the camera body), ...
s,
binoculars Binoculars or field glasses are two refracting telescopes mounted side-by-side and aligned to point in the same direction, allowing the viewer to use both eyes (binocular vision) when viewing distant objects. Most binoculars are sized to be held ...
,
telescope A telescope is a device used to observe distant objects by their emission, absorption, or reflection of electromagnetic radiation. Originally meaning only an optical instrument using lenses, curved mirrors, or a combination of both to observe ...
s, and
microscopes A microscope () is a laboratory instrument used to examine objects that are too small to be seen by the naked eye. Microscopy is the science of investigating small objects and structures using a microscope. Microscopic means being invisibl ...
the reduction in reflections also improves the contrast of the image by elimination of stray light. This is especially important in
planetary astronomy Planetary science (or more rarely, planetology) is the scientific study of planets (including Earth), celestial bodies (such as moons, asteroids, comets) and planetary systems (in particular those of the Solar System) and the processes of their ...
. In other applications, the primary benefit is the elimination of the reflection itself, such as a coating on
eyeglass Glasses, also known as eyeglasses or spectacles, are vision eyewear, with lenses (clear or tinted) mounted in a frame that holds them in front of a person's eyes, typically utilizing a bridge over the nose and hinged arms (known as temples or t ...
lenses that makes the eyes of the wearer more visible to others, or a coating to reduce the glint from a covert viewer's
binoculars Binoculars or field glasses are two refracting telescopes mounted side-by-side and aligned to point in the same direction, allowing the viewer to use both eyes (binocular vision) when viewing distant objects. Most binoculars are sized to be held ...
or
telescopic sight A telescopic sight, commonly called a scope informally, is an optical sighting device based on a refracting telescope. It is equipped with some form of a referencing pattern – known as a ''reticle'' – mounted in a focally appropriate po ...
. Many coatings consist of transparent
thin film A thin film is a layer of material ranging from fractions of a nanometer (monolayer) to several micrometers in thickness. The controlled synthesis of materials as thin films (a process referred to as deposition) is a fundamental step in many ap ...
structures with alternating layers of contrasting
refractive index In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, or ...
. Layer thicknesses are chosen to produce
destructive interference In physics, interference is a phenomenon in which two waves combine by adding their displacement together at every single point in space and time, to form a resultant wave of greater, lower, or the same amplitude. Constructive and destructive ...
in the beams reflected from the interfaces, and constructive interference in the corresponding transmitted beams. This makes the structure's performance change with wavelength and incident angle, so that color effects often appear at oblique angles. A
wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
range must be specified when designing or ordering such coatings, but good performance can often be achieved for a relatively wide range of
frequencies Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
: usually a choice of IR, visible, or UV is offered.


Applications

Anti-reflective coatings are used in a wide variety of applications where light passes through an optical surface, and low loss or low reflection is desired. Examples include anti-glare coatings on
corrective lens A corrective lens is a lens (i.e. a transmissive optical device) that is typically worn in front of the eye to improve daily vision. The most common use is to treat refractive errors: myopia, hypermetropia, astigmatism, and presbyopia. Glass ...
es and
camera lens A camera lens (also known as photographic lens or photographic objective) is an optical lens or assembly of lenses used in conjunction with a camera body and mechanism to make images of objects either on photographic film or on other media capab ...
elements, and antireflective coatings on
solar cell A solar cell, or photovoltaic cell, is an electronic device that converts the energy of light directly into electricity by the photovoltaic effect, which is a physical and chemical phenomenon.
s.


Corrective lenses

Optician An optician, or ''dispensing optician'', is a technical practitioner who designs, fits and dispenses lenses for the correction of a person's vision. Opticians determine the specifications of various ophthalmic appliances that will give the nec ...
s may recommend "anti-reflection lenses" because the decreased reflection enhances the cosmetic appearance of the lenses. Such lenses are often said to reduce glare, but the reduction is very slight. Eliminating reflections allows slightly more light to pass through, producing a slight increase in contrast and visual acuity. Antireflective ophthalmic lenses should not be confused with polarized lenses, which are found only in
sunglasses Sunglasses or sun glasses (informally called shades or sunnies; more names below) are a form of protective eyewear designed primarily to prevent bright sunlight and high-energy visible light from damaging or discomforting the eyes. They can s ...
and decrease (by absorption) the visible glare of sun reflected off surfaces such as sand, water, and roads. The term "antireflective" relates to the reflection from the surface of the lens itself, not the origin of the light that reaches the lens. Many anti-reflection lenses include an additional coating that repels
water Water (chemical formula ) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living organisms (in which it acts as a ...
and grease, making them easier to keep clean. Anti-reflection coatings are particularly suited to high-
index Index (or its plural form indices) may refer to: Arts, entertainment, and media Fictional entities * Index (''A Certain Magical Index''), a character in the light novel series ''A Certain Magical Index'' * The Index, an item on a Halo megastru ...
lenses, as these reflect more light without the coating than a lower-index lens (a consequence of the
Fresnel equations The Fresnel equations (or Fresnel coefficients) describe the reflection and transmission of light (or electromagnetic radiation in general) when incident on an interface between different optical media. They were deduced by Augustin-Jean Fresne ...
). It is also generally easier and cheaper to coat high index lenses.


Photolithography

Antireflective coatings (ARC) are often used in microelectronic
photolithography In integrated circuit manufacturing, photolithography or optical lithography is a general term used for techniques that use light to produce minutely patterned thin films of suitable materials over a substrate, such as a silicon wafer, to protect ...
to help reduce image distortions associated with reflections off the surface of the substrate. Different types of antireflective coatings are applied either before (Bottom ARC, or BARC) or after the
photoresist A photoresist (also known simply as a resist) is a light-sensitive material used in several processes, such as photolithography and photoengraving, to form a patterned coating on a surface. This process is crucial in the electronic industry. T ...
, and help reduce
standing wave In physics, a standing wave, also known as a stationary wave, is a wave that oscillates in time but whose peak amplitude profile does not move in space. The peak amplitude of the wave oscillations at any point in space is constant with respect ...
s,
thin-film interference Thin-film interference is a natural phenomenon in which light waves reflected by the upper and lower boundaries of a thin film interfere with one another, either enhancing or reducing the reflected light. When the thickness of the film is an ...
, and specular reflections.


Solar cells

Solar cell A solar cell, or photovoltaic cell, is an electronic device that converts the energy of light directly into electricity by the photovoltaic effect, which is a physical and chemical phenomenon.
s are often coated with an anti-reflective coating. Materials that have been used include
magnesium fluoride Magnesium fluoride is an inorganic compound with the formula MgF2. The compound is a white crystalline salt and is transparent over a wide range of wavelengths, with commercial uses in optics that are also used in space telescopes. It occurs natur ...
,
silicon nitride Silicon nitride is a chemical compound of the elements silicon and nitrogen. is the most thermodynamically stable and commercially important of the silicon nitrides, and the term "silicon nitride" commonly refers to this specific composition. It ...
,
silicon dioxide Silicon dioxide, also known as silica, is an oxide of silicon with the chemical formula , most commonly found in nature as quartz and in various living organisms. In many parts of the world, silica is the major constituent of sand. Silica is one ...
,
titanium dioxide Titanium dioxide, also known as titanium(IV) oxide or titania , is the inorganic compound with the chemical formula . When used as a pigment, it is called titanium white, Pigment White 6 (PW6), or CI 77891. It is a white solid that is insolubl ...
, and aluminum oxide.


Types


Index-matching

The simplest form of anti-reflective coating was discovered by
Lord Rayleigh John William Strutt, 3rd Baron Rayleigh, (; 12 November 1842 – 30 June 1919) was an English mathematician and physicist who made extensive contributions to science. He spent all of his academic career at the University of Cambridge. Amo ...
in 1886. The optical glass available at the time tended to develop a
tarnish Tarnish is a thin layer of corrosion that forms over copper, brass, aluminum, magnesium, neodymium and other similar metals as their outermost layer undergoes a chemical reaction. Tarnish does not always result from the sole effects of oxygen in ...
on its surface with age, due to chemical reactions with the environment. Rayleigh tested some old, slightly tarnished pieces of glass, and found to his surprise that they transmitted ''more'' light than new, clean pieces. The tarnish replaces the air-glass interface with two interfaces: an air-tarnish interface and a tarnish-glass interface. Because the tarnish has a
refractive index In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, or ...
between those of glass and air, each of these interfaces exhibits less reflection than the air-glass interface did. In fact, the total of the two reflections is less than that of the "naked" air-glass interface, as can be calculated from the
Fresnel equations The Fresnel equations (or Fresnel coefficients) describe the reflection and transmission of light (or electromagnetic radiation in general) when incident on an interface between different optical media. They were deduced by Augustin-Jean Fresne ...
. One approach is to use graded-index (GRIN) anti-reflective coatings, that is, ones with nearly continuously varying index of refraction. With these, it is possible to curtail reflection for a broad band of frequencies and incidence angles.


Single-layer interference

The simplest interference anti-reflective coating consists of a single thin layer of
transparent Transparency, transparence or transparent most often refer to: * Transparency (optics), the physical property of allowing the transmission of light through a material They may also refer to: Literal uses * Transparency (photography), a still, ...
material with refractive index equal to the
square root In mathematics, a square root of a number is a number such that ; in other words, a number whose ''square'' (the result of multiplying the number by itself, or  ⋅ ) is . For example, 4 and −4 are square roots of 16, because . E ...
of the substrate's refractive index. In air, such a coating theoretically gives zero
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 ...
for light with wavelength (in the coating) equal to four times the coating's thickness. Reflectance is also decreased for wavelengths in a broad band around the center. A layer of thickness equal to a quarter of some design wavelength is called a "quarter-wave layer". The most common type of optical glass is crown glass, which has an index of refraction of about 1.52. An optimal single-layer coating would have to be made of a material with an index of about 1.23. There are no solid materials with such a low refractive index. The closest materials with good physical properties for a coating are
magnesium fluoride Magnesium fluoride is an inorganic compound with the formula MgF2. The compound is a white crystalline salt and is transparent over a wide range of wavelengths, with commercial uses in optics that are also used in space telescopes. It occurs natur ...
, MgF2 (with an index of 1.38), and
fluoropolymer A fluoropolymer is a fluorocarbon-based polymer with multiple carbon–fluorine bonds. It is characterized by a high resistance to solvents, acids, and bases. The best known fluoropolymer is polytetrafluoroethylene under the brand name "Teflon ...
s, which can have indices as low as 1.30, but are more difficult to apply. MgF2 on a crown glass surface gives a reflectance of about 1%, compared to 4% for bare glass. MgF2 coatings perform much better on higher-index glasses, especially those with index of refraction close to 1.9. MgF2 coatings are commonly used because they are cheap and durable. When the coatings are designed for a wavelength in the middle of the visible band, they give reasonably good anti-reflection over the entire band. Researchers have produced films of
mesoporous silica Mesoporous silica is a form of silica that is characterised by its mesoporous structure, that is, having pores that range from 2 nm to 50 nm in diameter. According to IUPAC's terminology, mesoporosity sits between microporous (50  ...
nanoparticle A nanoparticle or ultrafine particle is usually defined as a particle of matter that is between 1 and 100 nanometres (nm) in diameter. The term is sometimes used for larger particles, up to 500 nm, or fibers and tubes that are less than 1 ...
s with refractive indices as low as 1.12, which function as antireflection coatings.


Multi-layer interference

By using alternating layers of a low-index material like
silica Silicon dioxide, also known as silica, is an oxide of silicon with the chemical formula , most commonly found in nature as quartz and in various living organisms. In many parts of the world, silica is the major constituent of sand. Silica is one ...
and a higher-index material, it is possible to obtain reflectivities as low as 0.1% at a single wavelength. Coatings that give very low reflectivity over a broad band of frequencies can also be made, although these are complex and relatively expensive.
Optical coating An optical coating is one or more thin layers of material deposited on an optical component such as a lens, prism or mirror, which alters the way in which the optic reflects and transmits light. These coatings have become a key technology in th ...
s can also be made with special characteristics, such as near-zero reflectance at multiple wavelengths, or optimal performance at angles of incidence other than 0°.


Absorbing

An additional category of anti-reflection coatings is the so-called "absorbing ARC". These coatings are useful in situations where high transmission through a surface is unimportant or undesirable, but low reflectivity is required. They can produce very low reflectance with few layers, and can often be produced more cheaply, or at greater scale, than standard non-absorbing AR coatings. (See, for example
US Patent 5,091,244
) Absorbing ARCs often make use of unusual optical properties exhibited in compound thin films produced by
sputter deposition Sputter deposition is a physical vapor deposition (PVD) method of thin film deposition by the phenomenon of sputtering. This involves ejecting material from a "target" that is a source onto a "substrate" such as a silicon wafer. Resputtering is re ...
. For example,
titanium nitride Titanium nitride (TiN; sometimes known as Tinite) is an extremely hard ceramic material, often used as a physical vapor deposition (PVD) coating on titanium alloys, steel, carbide, and aluminium components to improve the substrate's surface prope ...
and
niobium nitride Niobium nitride is a compound of niobium and nitrogen (nitride) with the chemical formula NbN. At low temperatures (about 16 K) NbN becomes a superconductor, and is used in detectors for infrared light. Uses *Niobium nitride's main use is as a ...
are used in absorbing ARCs. These can be useful in applications requiring contrast enhancement or as a replacement for tinted glass (for example, in a
CRT display CRT or Crt may refer to: Science, technology, and mathematics Medicine and biology * Calreticulin, a protein * Capillary refill time, for blood to refill capillaries * Cardiac resynchronization therapy and CRT defibrillator (CRT-D) * Catheter- ...
).


Moth eye

Moth Moths are a paraphyletic group of insects that includes all members of the order Lepidoptera that are not butterflies, with moths making up the vast majority of the order. There are thought to be approximately 160,000 species of moth, many of w ...
s' eyes have an unusual property: their surfaces are covered with a natural
nanostructure A nanostructure is a structure of intermediate size between microscopic and molecular structures. Nanostructural detail is microstructure at nanoscale. In describing nanostructures, it is necessary to differentiate between the number of dimens ...
d film, which eliminates reflections. This allows the moth to see well in the dark, without reflections to give its location away to predators. The structure consists of a hexagonal pattern of bumps, each roughly 200 nm high and spaced on 300 nm centers. This kind of antireflective coating works because the bumps are smaller than the wavelength of visible light, so the light sees the surface as having a continuous refractive index gradient between the air and the medium, which decreases reflection by effectively removing the air-lens interface. Practical anti-reflective films have been made by humans using this effect; this is a form of
biomimicry Biomimetics or biomimicry is the emulation of the models, systems, and elements of nature for the purpose of solving complex human problems. The terms "biomimetics" and "biomimicry" are derived from grc, βίος (''bios''), life, and μίμησ ...
.
Canon Canon or Canons may refer to: Arts and entertainment * Canon (fiction), the conceptual material accepted as official in a fictional universe by its fan base * Literary canon, an accepted body of works considered as high culture ** Western ca ...
uses the moth-eye technique in their Sub-Wavelength structure Coating, which significantly reduces
lens flare A lens flare happens when light is scattered or flared in a lens system, often in response to a bright light, producing a sometimes undesirable artifact in the image. This happens through light scattered by the imaging mechanism itself, for e ...
. Such structures are also used in photonic devices, for example, moth-eye structures grown from tungsten oxide and iron oxide can be used as photoelectrodes for splitting water to produce hydrogen. The structure consists of tungsten oxide spheroids several hundred micrometers in diameter, coated with a few nanometers of iron oxide.


Circular polarizer

A
circular polarizer A polarizer or polariser is an optical filter that lets light waves of a specific polarization pass through while blocking light waves of other polarizations. It can filter a beam of light of undefined or mixed polarization into a beam of wel ...
laminated to a surface can be used to eliminate reflections. The polarizer transmits light with one
chirality Chirality is a property of asymmetry important in several branches of science. The word ''chirality'' is derived from the Greek (''kheir''), "hand", a familiar chiral object. An object or a system is ''chiral'' if it is distinguishable from ...
("handedness") of circular polarization. Light reflected from the surface after the polarizer is transformed into the opposite "handedness". This light cannot pass back through the circular polarizer because its chirality has changed (e.g. from right circular polarized to left circularly polarized). A disadvantage of this method is that if the input light is unpolarized, the transmission through the assembly will be less than 50%.


Theory

There are two separate causes of optical effects due to coatings, often called ''thick-film'' and ''thin-film'' effects. Thick-film effects arise because of the difference in the
index of refraction In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, or ...
between the layers above and below the coating (or ''film''); in the simplest case, these three layers are the air, the coating, and the glass. Thick-film coatings do not depend on how thick the coating is, so long as the coating is much thicker than a wavelength of light. Thin-film effects arise when the thickness of the coating is approximately the same as a quarter or a half a wavelength of light. In this case, the reflections of a steady source of light can be made to add destructively and hence reduce reflections by a separate mechanism. In addition to depending very much on the thickness of the film and the wavelength of light, thin-film coatings depend on the angle at which the light strikes the coated surface.


Reflection

Whenever a ray of light moves from one
medium Medium may refer to: Science and technology Aviation *Medium bomber, a class of war plane *Tecma Medium, a French hang glider design Communication * Media (communication), tools used to store and deliver information or data * Medium of ...
to another (for example, when light enters a sheet of
glass Glass is a non-crystalline, often transparent, amorphous solid that has widespread practical, technological, and decorative use in, for example, window panes, tableware, and optics. Glass is most often formed by rapid cooling (quenching) of ...
after travelling through
air The atmosphere of Earth is the layer of gases, known collectively as air, retained by Earth's gravity that surrounds the planet and forms its planetary atmosphere. The atmosphere of Earth protects life on Earth by creating pressure allowing f ...
), some portion of the light is reflected from the surface (known as the ''interface'') between the two media. This can be observed when looking through a
window A window is an opening in a wall, door, roof, or vehicle that allows the exchange of light and may also allow the passage of sound and sometimes air. Modern windows are usually glazed or covered in some other transparent or translucent materia ...
, for instance, where a (weak) reflection from the front and back surfaces of the window glass can be seen. The strength of the reflection depends on the ratio of the
refractive indices In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, or ...
of the two media, as well as the angle of the surface to the beam of light. The exact value can be calculated using the
Fresnel equations The Fresnel equations (or Fresnel coefficients) describe the reflection and transmission of light (or electromagnetic radiation in general) when incident on an interface between different optical media. They were deduced by Augustin-Jean Fresne ...
. When the light meets the interface at
normal incidence The angle of incidence, in geometric optics, is the angle between a ray incident on a surface and the line perpendicular (at 90 degree angle) to the surface at the point of incidence, called the normal. The ray can be formed by any waves, such as o ...
(perpendicularly to the surface), the intensity of light reflected is given by the ''reflection coefficient'', or ''reflectance'', ''R'': :R = \left( \frac \right)^2, where ''n''0 and ''n''S are the refractive indices of the first and second media respectively. The value of ''R'' varies from 0 (no reflection) to 1 (all light reflected) and is usually quoted as a
percentage In mathematics, a percentage (from la, per centum, "by a hundred") is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also us ...
. Complementary to ''R'' is the ''transmission coefficient'', or ''transmittance'', ''T''. If
absorption Absorption may refer to: Chemistry and biology * Absorption (biology), digestion **Absorption (small intestine) *Absorption (chemistry), diffusion of particles of gas or liquid into liquid or solid materials *Absorption (skin), a route by which ...
and
scattering Scattering is a term used in physics to describe a wide range of physical processes where moving particles or radiation of some form, such as light or sound, are forced to deviate from a straight trajectory by localized non-uniformities (including ...
are neglected, then the value ''T'' is always 1 − ''R''. Thus if a beam of light with
intensity Intensity may refer to: In colloquial use *Strength (disambiguation) *Amplitude * Level (disambiguation) * Magnitude (disambiguation) In physical sciences Physics *Intensity (physics), power per unit area (W/m2) *Field strength of electric, ma ...
''I'' is incident on the surface, a beam of intensity ''RI'' is reflected, and a beam with intensity ''TI'' is transmitted into the medium. For the simplified scenario of visible light travelling from air (''n''0 ≈ 1.0) into common glass (), the value of ''R'' is 0.04, or 4%, on a single reflection. So at most 96% of the light () actually enters the glass, and the rest is reflected from the surface. The amount of light reflected is known as the ''reflection loss''. In the more complicated scenario of multiple reflections, say with light travelling through a window, light is reflected both when going from air to glass and at the other side of the window when going from glass back to air. The size of the loss is the same in both cases. Light also may bounce from one surface to another multiple times, being partially reflected and partially transmitted each time it does so. In all, the combined reflection coefficient is given by . For glass in air, this is about 7.7%.


Rayleigh's film

As observed by
Lord Rayleigh John William Strutt, 3rd Baron Rayleigh, (; 12 November 1842 – 30 June 1919) was an English mathematician and physicist who made extensive contributions to science. He spent all of his academic career at the University of Cambridge. Amo ...
, a thin film (such as tarnish) on the surface of glass can reduce the reflectivity. This effect can be explained by envisioning a thin layer of material with refractive index ''n''1 between the air (index ''n''0) and the glass (index ''n''S). The light ray now reflects twice: once from the surface between air and the thin layer, and once from the layer-to-glass interface. From the equation above and the known refractive indices, reflectivities for both interfaces can be calculated, denoted ''R''01 and ''R''1S respectively. The transmission at each interface is therefore and . The total transmittance into the glass is thus ''T''1S''T''01. Calculating this value for various values of ''n''1, it can be found that at one particular value of optimal refractive index of the layer, the transmittance of both interfaces is equal, and this corresponds to the maximal total transmittance into the glass. This optimal value is given by the
geometric mean In mathematics, the geometric mean is a mean or average which indicates a central tendency of a set of numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum). The geometric mean is defined as the ...
of the two surrounding indices: :n_1 = \sqrt. For the example of glass () in air (), this optimal refractive index is . The reflection loss of each interface is approximately 1.0% (with a combined loss of 2.0%), and an overall transmission ''T''1S''T''01 of approximately 98%. Therefore, an intermediate coating between the air and glass can halve the reflection loss.


Interference coatings

The use of an intermediate layer to form an anti-reflection coating can be thought of as analogous to the technique of
impedance matching In electronics, impedance matching is the practice of designing or adjusting the input impedance or output impedance of an electrical device for a desired value. Often, the desired value is selected to maximize power transfer or minimize signal ...
of electrical signals. (A similar method is used in
fibre optic An optical fiber, or optical fibre in Commonwealth English, is a flexible, transparent fiber made by drawing glass (silica) or plastic to a diameter slightly thicker than that of a human hair. Optical fibers are used most often as a means to ...
research, where an ''index-matching oil'' is sometimes used to temporarily defeat
total internal reflection Total internal reflection (TIR) is the optical phenomenon in which waves arriving at the interface (boundary) from one medium to another (e.g., from water to air) are not refracted into the second ("external") medium, but completely reflected b ...
so that light may be coupled into or out of a fiber.) Further reduced reflection could in theory be made by extending the process to several layers of material, gradually blending the refractive index of each layer between the index of the air and the index of the substrate. Practical anti-reflection coatings, however, rely on an intermediate layer not only for its direct reduction of reflection coefficient, but also use the
interference Interference is the act of interfering, invading, or poaching. Interference may also refer to: Communications * Interference (communication), anything which alters, modifies, or disrupts a message * Adjacent-channel interference, caused by extr ...
effect of a thin layer. Assume the layer's thickness is controlled precisely, such that it is exactly one quarter of the wavelength of light in the layer (, where λ0 is the vacuum wavelength). The layer is then called a ''quarter-wave coating''. For this type of coating a normally incident beam ''I'', when reflected from the second interface, will travel exactly half its own wavelength further than the beam reflected from the first surface, leading to destructive interference. This is also true for thicker coating layers (3λ/4, 5λ/4, etc.), however the anti-reflective performance is worse in this case due to the stronger dependence of the reflectance on wavelength and the angle of incidence. If the intensities of the two beams ''R''1 and ''R''2 are exactly equal, they will destructively interfere and cancel each other, since they are exactly out of
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 mathematic ...
. Therefore, there is no reflection from the surface, and all the energy of the beam must be in the transmitted ray, ''T''. In the calculation of the reflection from a stack of layers, the
transfer-matrix method In statistical mechanics, the transfer-matrix method is a mathematical technique which is used to write the partition function into a simpler form. It was introduced in 1941 by Hans Kramers and Gregory Wannier. In many one dimensional lattice m ...
can be used. Real coatings do not reach perfect performance, though they are capable of reducing a surface reflection coefficient to less than 0.1%. Also, the layer will have the ideal thickness for only one distinct wavelength of light. Other difficulties include finding suitable materials for use on ordinary glass, since few useful substances have the required refractive index () that will make both reflected rays exactly equal in intensity.
Magnesium fluoride Magnesium fluoride is an inorganic compound with the formula MgF2. The compound is a white crystalline salt and is transparent over a wide range of wavelengths, with commercial uses in optics that are also used in space telescopes. It occurs natur ...
(MgF2) is often used, since this is hard-wearing and can be easily applied to substrates using
physical vapor deposition Physical vapor deposition (PVD), sometimes called physical vapor transport (PVT), describes a variety of vacuum deposition methods which can be used to produce thin films and coatings on substrates including metals, ceramics, glass, and polym ...
, even though its index is higher than desirable (). Further reduction is possible by using multiple coating layers, designed such that reflections from the surfaces undergo maximal destructive interference. One way to do this is to add a second quarter-wave thick higher-index layer between the low-index layer and the substrate. The reflection from all three interfaces produces destructive interference and anti-reflection. Other techniques use varying thicknesses of the coatings. By using two or more layers, each of a material chosen to give the best possible match of the desired refractive index and
dispersion Dispersion may refer to: Economics and finance *Dispersion (finance), a measure for the statistical distribution of portfolio returns *Price dispersion, a variation in prices across sellers of the same item *Wage dispersion, the amount of variatio ...
, broadband anti-reflection coatings covering the visible range (400–700 nm) with maximal reflectivity of less than 0.5% are commonly achievable. The exact nature of the coating determines the appearance of the coated optic; common AR coatings on eyeglasses and photographic lenses often look somewhat bluish (since they reflect slightly more blue light than other visible wavelengths), though green and pink-tinged coatings are also used. If the coated optic is used at non-normal incidence (that is, with light rays not perpendicular to the surface), the anti-reflection capabilities are degraded somewhat. This occurs because the phase accumulated in the layer ''relative to the phase of the light immediately reflected'' decreases as the angle increases from normal. This is counterintuitive, since the ray experiences a greater total phase shift in the layer than for normal incidence. This paradox is resolved by noting that the ray will exit the layer spatially offset from where it entered and will interfere with reflections from incoming rays that had to travel further (thus accumulating more phase of their own) to arrive at the interface. The net effect is that the relative phase is actually reduced, shifting the coating, such that the anti-reflection band of the coating tends to move to shorter wavelengths as the optic is tilted. Non-normal incidence angles also usually cause the reflection to be polarization-dependent.


Textured coatings

Reflection can be reduced by texturing the surface with 3D pyramids or 2D grooves (gratings). These kind of textured coating can be created using for example the Langmuir-Blodgett method. If wavelength is greater than the texture size, the texture behaves like a gradient-index film with reduced reflection. To calculate reflection in this case,
effective medium approximations In materials science, effective medium approximations (EMA) or effective medium theory (EMT) pertain to analytical or theoretical modeling that describes the macroscopic properties of composite materials. EMAs or EMTs are developed from averagi ...
can be used. To minimize reflection, various profiles of pyramids have been proposed, such as cubic, quintic or integral exponential profiles. If wavelength is smaller than the textured size, the reflection reduction can be explained with the help of the
geometric optics Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ca ...
approximation: rays should be reflected many times before they are sent back toward the source. In this case the reflection can be calculated using ray tracing. Using texture reduces reflection for wavelengths comparable with the feature size as well. In this case no approximation is valid, and reflection can be calculated by solving Maxwell equations numerically. Antireflective properties of textured surfaces are well discussed in literature for a wide range of size-to-wavelength ratios (including long- and short-wave limits) to find the optimal texture size.


History

As mentioned above, natural index-matching "coatings" were discovered by Lord Rayleigh in 1886.
Harold Dennis Taylor Harold Dennis Taylor (10 July 1862, in Huddersfield – 26 February 1943) was a British optical designer and inventor, chiefly famous for the invention of the Cooke Triplet, although he was granted about 50 other patents. He was born in 18 ...
of Cooke company developed a chemical method for producing such coatings in 1904. Interference-based coatings were invented and developed in 1935 by
Olexander Smakula Olexander Smakula ( uk, Олександр Теодорович Смакула) (1900 in Dobrovody, Austria-Hungary, today Ukraine – 17 May 1983 in Auburn, Massachusetts, USA) was a Ukrainian physicist known for the invention of anti-reflecti ...
, who was working for the
Carl Zeiss Carl Zeiss (; 11 September 1816 – 3 December 1888) was a German scientific instrument maker, optician and businessman. In 1846 he founded his workshop, which is still in business as Carl Zeiss AG. Zeiss gathered a group of gifted practica ...
optics company. These coatings remained a German military secret for several years, until the Allies discovered the secret during
World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...
.
Katharine Burr Blodgett Katharine Burr Blodgett (January 10, 1898 – October 12, 1979) was an American physicist and chemist known for her work on surface chemistry, in particular her invention of "invisible" or nonreflective glass while working at General Electric. S ...
and
Irving Langmuir Irving Langmuir (; January 31, 1881 – August 16, 1957) was an American chemist, physicist, and engineer. He was awarded the Nobel Prize in Chemistry in 1932 for his work in surface chemistry. Langmuir's most famous publication is the 1919 art ...
developed organic anti-reflection coatings known as Langmuir–Blodgett films in the late 1930s.


See also

*
Anti-scratch coating Anti-scratch coating is a type of protective coating or film applied to an object's surface for mitigation against scratches. Scratches are small surface-level cuts left on a surface following interaction with a sharper object. Anti-scratch coatings ...
*
Dichroic filter A dichroic filter, thin-film filter, or interference filter is a color filter used to selectively pass light of a small range of colors while reflecting other colors. By comparison, dichroic mirrors and dichroic reflectors tend to be characteriz ...
*
Lens flare A lens flare happens when light is scattered or flared in a lens system, often in response to a bright light, producing a sometimes undesirable artifact in the image. This happens through light scattered by the imaging mechanism itself, for e ...
, which AR coating helps to reduce.


References


Sources

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External links


Browser-based thin film design and optimization software

Browser-based numerical calculator of single-layer thin film reflectivity
{{Glass science Thin-film optics