260:
500:
157:
22:
524:
515:("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%.
1270:
547:); 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
1154:
785:
1121:, 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.
1213:
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
2271:
1191:
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
831:
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
427:
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
1161:
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
467:
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
1212:
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
1203:
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.
160:
Anti-reflective coatings are often used in camera lenses, giving lens elements distinctive colors. Such colors indicate the wavelength of visible light least affected by the antireflective properties of the coating. A variety of colors can be produced whose precise hue depends entirely on the
360:, 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
1086:
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.
352:
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".
410:
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.
1192:
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
429:
207:
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.
331:
One approach is to use graded-index (GRIN) anti-reflective coatings, that is, ones with nearly continuously varying indices of refraction. With these, it is possible to curtail reflection for a broad band of frequencies and incidence angles.
323:
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
1696:
Moghal, Jonathan; Kobler, Johannes; Sauer, Jürgen; Best, James; Gardener, Martin; Watt, Andrew A.R.; Wakefield, Gareth (2012). "High-performance, single-layer antireflective optical coatings comprising mesoporous silica nanoparticles".
551:
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.
1207:
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
2269:, "Verfahren zur Erhoehung der Lichtdurchlaessigkeit optischer Teile durch Erniedrigungdes Brechungsexponenten an den Grenzflaechen dieser optischen Teile", published 1935-11-01, assigned to Zeiss Carl FA
707:
1803:
946:, 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.
1375:
1855:
Boudoire, Florent; Toth, Rita; Heier, Jakob; Braun, Artur; Constable, Edwin C. (2014). "Photonic light trapping in self-organized all-oxide microspheroids impacts photoelectrochemical water splitting".
472:
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
1257:
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.
239:
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
165:
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
2205:
1011:
315:
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
124:
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
25:
Uncoated glasses lens (top) versus lens with anti-reflective coating. The reflection from the coated lens is tinted because the coating works better at some wavelengths than others.
319:
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
856:, 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
832:
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
1250:
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
584:, 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
1945:
1732:
2235:
1225:
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
1454:
2837:
487:
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
2067:
Hsu, Ching-Mei; Connor, Stephen T.; Tang, Mary X.; Cui, Yi (2008). "Wafer-scale silicon nanopillars and nanocones by
Langmuir–Blodgett assembly and etching".
1232:
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,
491:
to produce hydrogen. The structure consists of tungsten oxide spheroids several hundred micrometers in diameter, coated with a few nanometers of iron oxide.
188:
may recommend "anti-reflection lenses" because the decreased reflection enhances the cosmetic appearance of the lenses. Such lenses are often said to reduce
1094:
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 (
1090:
Practical anti-reflection coatings, however, rely on an intermediate layer not only for its direct reduction of reflection coefficient, but also use the
2213:
1243:
approximation: rays should be reflected many times before they are sent back toward the source. In this case the reflection can be calculated using
2389:
308:
1236:
can be used. To minimize reflection, various profiles of pyramids have been proposed, such as cubic, quintic or integral exponential profiles.
751:
2340:
1400:
Hemant Kumar Raut; V. Anand Ganesh; A. Sreekumaran Nair; Seeram
Ramakrishna (2011). "Anti-reflective coatings: A critical, in-depth review".
2001:
617:
136:
range must be specified when designing or ordering such coatings, but good performance can often be achieved for a relatively wide range of
161:
thickness of the coating. Color or cast can change radically when the coating is increased or decreased in thickness by tens of nanometers.
2284:
877:). The light ray now reflects twice: once from the surface between air and the thin layer, and once from the layer-to-glass interface.
192:, but the reduction is very slight. Eliminating reflections allows slightly more light to pass through, producing a slight increase in
2180:
384:
coatings are commonly used because they are cheap and durable. When the coatings are designed for a wavelength in the middle of the
259:
2357:
1883:
1319:
optics company. These coatings remained a German military secret for several years, until the Allies discovered the secret during
415:
can also be made with special characteristics, such as near-zero reflectance at multiple wavelengths, or optimal performance at
2862:
2658:
1428:
1233:
1147:
1091:
468:
works because the bumps are smaller than the wavelength of visible light, so the light sees the surface as having a continuous
1251:
2774:
2751:
1226:
101:
lenses that makes the eyes of the wearer more visible to others, or a coating to reduce the glint from a covert viewer's
2607:
1745:
1678:
1049:
The reflection loss of each interface is approximately 1.0% (with a combined loss of 2.0%), and an overall transmission
880:
From the equation above and the known refractive indices, reflectivities for both interfaces can be calculated, denoted
588:
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
2243:
1579:
1070:
The use of an intermediate layer to form an anti-reflection coating can be thought of as analogous to the technique of
824:) actually enters the glass, and the rest is reflected from the surface. The amount of light reflected is known as the
2382:
1962:
1461:
499:
416:
125:
1332:
1142:. Therefore, there is no reflection from the surface, and all the energy of the beam must be in the transmitted ray,
1584:
1062:
of approximately 98%. Therefore, an intermediate coating between the air and glass can halve the reflection loss.
2938:
2638:
2559:
2449:
1906:"Photonic light trapping in self-organized all-oxide microspheroids impacts photoelectrochemical water splitting"
1178:
1083:
959:
380:
coatings perform much better on higher-index glasses, especially those with index of refraction close to 1.9. MgF
1239:
If wavelength is smaller than the textured size, the reflection reduction can be explained with the help of the
2539:
548:
121:
97:. In other applications, the primary benefit is the elimination of the reflection itself, such as a coating on
1970:
1829:
156:
1486:
Yet, Siew Ing (2004). "Investigation of UFO defect on DUV CAR and BARC process". In Silver, Richard M (ed.).
2902:
2643:
1324:
432:.) Absorbing ARCs often make use of unusual optical properties exhibited in compound thin films produced by
428:
be produced more cheaply, or at greater scale, than standard non-absorbing AR coatings. (See, for example,
2375:
2135:
1138:
are exactly equal, they will destructively interfere and cancel each other, since they are exactly out of
248:
1740:
2711:
2519:
2296:
1244:
469:
341:
1580:"Silicon nitride as antireflection coating to enhance the conversion efficiency of silicon solar cells"
21:
2206:"History of Camera Lenses from Carl Zeiss - 1935 - Olexander Smakula develops anti-reflection coating"
223:
lenses, as these reflect more light without the coating than a lower-index lens (a consequence of the
2867:
2741:
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2479:
2266:
2127:
2076:
2018:
1637:
1532:
1491:
1344:
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1214:
357:
62:
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523:
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laminated to a surface can be used to eliminate reflections. The polarizer transmits light with one
2887:
2809:
2731:
2706:
1193:
767:
540:
480:
uses the moth-eye technique in their Sub-Wavelength structure
Coating, which significantly reduces
94:
2332:
263:
An unmetallised heterojunction solar cell precursor. The blue colour arises from the dual-purpose
2794:
2716:
2464:
2454:
2118:
A. Deinega; et al. (2011). "Minimizing light reflection from dielectric textured surfaces".
2100:
2042:
1653:
1603:
1170:
1071:
508:
433:
361:
275:
82:
1884:"Photoelectrochemical Water Splitting Can Be Achieved with Self-Organized, All-Oxide Electrodes"
1905:
2907:
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2842:
2799:
2736:
2721:
2633:
2524:
2336:
2176:
2153:
2092:
2034:
1714:
1560:
1312:
589:
445:
392:
325:
224:
193:
86:
58:
219:, making them easier to keep clean. Anti-reflection coatings are particularly suited to high-
2663:
2653:
2648:
2418:
2145:
2084:
2026:
1865:
1783:
1706:
1645:
1593:
1550:
1540:
1499:
1409:
1240:
596:
585:
449:
437:
376:
on a crown glass surface gives a reflectance of about 1%, compared to 4% for bare glass. MgF
320:
287:
264:
236:
220:
117:
113:
106:
2857:
2852:
2701:
2597:
2569:
2554:
2549:
2544:
2504:
2474:
1927:
1349:
1328:
1177:) is often used, since this is hard-wearing and can be easily applied to substrates using
565:
488:
441:
412:
283:
279:
189:
166:
50:
2574:
2131:
2080:
2022:
1649:
1641:
1536:
1495:
274:
are often coated with an anti-reflective coating. Materials that have been used include
2819:
2789:
2784:
2299:. Southwest Museum of Engineering, Communications and Computation. 2007. Archived from
2009:
1555:
1518:
1200:(400–700 nm) with maximal reflectivity of less than 0.5% are commonly achievable.
950:
291:
1807:
1269:
2932:
2726:
2683:
2589:
2564:
2459:
2362:
2104:
1657:
1622:
1607:
1316:
1197:
1139:
1075:
853:
464:
385:
369:
348:
of the substrate's refractive index. In air, such a coating theoretically gives zero
340:
The simplest interference anti-reflective coating consists of a single thin layer of
244:
129:
54:
730:
varies from 0 (no reflection) to 1 (all light reflected) and is usually quoted as a
726:
are the refractive indices of the first and second media respectively. The value of
2892:
2847:
2804:
2494:
2469:
2423:
1320:
599:(perpendicularly to the surface), the intensity of light reflected is given by the
561:
398:
with refractive indices as low as 1.12, which function as antireflection coatings.
395:
1545:
1308:
of Cooke company developed a chemical method for producing such coatings in 1904.
1519:"Effect of obliquity of incident light on the performance of silicon solar cells"
2917:
2882:
2602:
2484:
1153:
784:
349:
345:
240:
170:
145:
137:
90:
1788:
1771:
531:
There are two separate causes of optical effects due to coatings, often called
2912:
2877:
2746:
2514:
2509:
1354:
1304:, natural index-matching "coatings" were discovered by Lord Rayleigh in 1886.
755:
731:
481:
477:
473:
271:
204:
174:
133:
102:
74:
2096:
1682:
372:, which can have indices as low as 1.30, but are more difficult to apply. MgF
2779:
2678:
2149:
527:
An anti-reflection coated window, shown at a 45° and a 0° angle of incidence
512:
200:
78:
2157:
2038:
1975:
1718:
1564:
463:' eyes have an unusual property: their surfaces are covered with a natural
1623:"Wide-angle and broadband graded-refractive-index antireflection coatings"
444:
are used in absorbing ARCs. These can be useful in applications requiring
2897:
2668:
2444:
2439:
2363:
Browser-based numerical calculator of single-layer thin film reflectivity
2030:
576:), some portion of the light is reflected from the surface (known as the
185:
141:
1598:
2617:
2367:
1869:
1523:
1413:
1162:
glass, since few useful substances have the required refractive index (
312:
98:
2088:
1710:
1503:
702:{\displaystyle R=\left({\frac {n_{0}-n_{S}}{n_{0}+n_{S}}}\right)^{2},}
227:). It is also generally easier and cheaper to coat high index lenses.
211:
Many anti-reflection lenses include an additional coating that repels
65:. In typical imaging systems, this improves the efficiency since less
2693:
2499:
1488:
Metrology, Inspection, and
Process Control for Microlithography XVIII
813:
is 0.04, or 4%, on a single reflection. So at most 96% of the light (
581:
580:) between the two media. This can be observed when looking through a
407:
311:
in 1886. The optical glass available at the time tended to develop a
70:
448:
enhancement or as a replacement for tinted glass (for example, in a
1311:
Interference-based coatings were invented and developed in 1935 by
1146:. In the calculation of the reflection from a stack of layers, the
539:
effects. Thick-film effects arise because of the difference in the
2612:
2579:
2529:
2413:
2398:
1152:
792:
For the simplified scenario of visible light travelling from air (
783:
569:
522:
498:
388:, they give reasonably good anti-reflection over the entire band.
258:
212:
155:
66:
2300:
1169:) that will make both reflected rays exactly equal in intensity.
1770:
Han, Z.W.; Wang, Z.; Feng, X.M.; et al. (14 October 2016).
1621:
Zhang, Jun-Chao; Xiong, Li-Min; Fang, Ming; He, Hong-Bo (2013).
460:
267:
anti-reflective coating, which also enhances emitter conduction.
235:
Antireflective coatings (ARC) are often used in microelectronic
2371:
307:
The simplest form of anti-reflective coating was discovered by
1264:
894:
respectively. The transmission at each interface is therefore
573:
216:
1429:"Anti-reflective Coating - American Academy of Ophthalmology"
788:
Reflection and transmission of an uncoated and coated surface
199:
Antireflective ophthalmic lenses should not be confused with
2297:"Carl Zeiss – A History of a Most Respected Name in Optics"
1433:
Anti-reflective
Coating - American Academy of Ophthalmology
1806:(Press release). Pro-talk. 3 December 2003. Archived from
406:
By using alternating layers of a low-index material like
2358:
Browser-based thin film design and optimization software
1772:"Antireflective surface inspired from biology: A review"
1210:
relative to the phase of the light immediately reflected
1281:
1157:
Interference in a quarter-wave anti-reflection coating
1113:
is the vacuum wavelength). The layer is then called a
568:
to another (for example, when light enters a sheet of
69:
is lost due to reflection. In complex systems such as
2285:
Camera Lens Anti-Reflection
Coatings: Magic Explained
1679:"Opstar AR fluoride coatings and application methods"
962:
620:
1331:
developed organic anti-reflection coatings known as
1117:. For this type of coating a normally incident beam
1074:
of electrical signals. (A similar method is used in
2828:
2760:
2692:
2626:
2588:
2432:
2406:
2000:Moreno, I.; Araiza, J.; Avendano-Alejo, M. (2005).
543:between the layers above and below the coating (or
1196:, broadband anti-reflection coatings covering the
1181:, even though its index is higher than desirable (
1005:
701:
116:structures with alternating layers of contrasting
926:. The total transmittance into the glass is thus
773:is incident on the surface, a beam of intensity
503:Reflections are blocked by a circular polarizer.
939:. Calculating this value for various values of
85:the reduction in reflections also improves the
1455:"Understanding bottom antireflective coatings"
2838:Conservation and restoration of glass objects
2383:
1376:"Anti-Reflection Coating Color | PVEducation"
8:
344:material with refractive index equal to the
1006:{\displaystyle n_{1}={\sqrt {n_{0}n_{S}}}.}
120:. Layer thicknesses are chosen to produce
2390:
2376:
2368:
1490:. Vol. 5375. SPIE. pp. 940–948.
2139:
1787:
1597:
1554:
1544:
992:
982:
976:
967:
961:
690:
677:
664:
652:
639:
632:
619:
356:The most common type of optical glass is
173:elements, and antireflective coatings on
1963:"Maximally flat antireflection coatings"
1950:. Society for Information Display. 2006.
1082:is sometimes used to temporarily defeat
844:. For glass in air, this is about 7.7%.
777:is reflected, and a beam with intensity
128:, so that color effects often appear at
20:
1367:
16:Optical coating that reduces reflection
2195:British Patent 29561, 31 December 1904
1699:ACS Applied Materials & Interfaces
595:When the light meets the interface at
1252:solving Maxwell equations numerically
112:Many coatings consist of transparent
7:
1124:If the intensities of the two beams
1036:), this optimal refractive index is
1830:"Canon Subwavelength Coating (SWC)"
1435:. American Academy of Ophthalmology
1427:Duffner, Lee R (27 February 2015).
1357:, which AR coating helps to reduce.
1301:
949:This optimal value is given by the
391:Researchers have produced films of
1886:. Materials Research Society. 2014
1402:Energy & Environmental Science
93:. This is especially important in
14:
1928:"HNCP Circular Polarizing Filter"
2175:(3rd ed.). CRC. p. 4.
1268:
953:of the two surrounding indices:
781:is transmitted into the medium.
2908:Radioactive waste vitrification
2863:Glass fiber reinforced concrete
1517:Rajinder Sharma (2 July 2019).
1234:effective medium approximations
766:. Thus if a beam of light with
89:of the image by elimination of
1804:"Novel film inspired by moths"
758:are neglected, then the value
57:, other optical elements, and
1:
2775:Chemically strengthened glass
1744:(2): 10. 2005. Archived from
1650:10.1088/1674-1056/22/4/044201
1546:10.1016/j.heliyon.2019.e01965
368:(with an index of 1.38), and
2608:Glass-ceramic-to-metal seals
1578:Rajinder Sharma (May 2018).
251:, and specular reflections.
2002:"Thin-film spatial filters"
1776:Biosurface and Biotribology
2955:
1932:www.visionteksystems.co.uk
1789:10.1016/j.bsbt.2016.11.002
1585:Turkish Journal of Physics
1315:, who was working for the
1016:For the example of glass (
799:≈ 1.0) into common glass (
203:, which are found only in
53:applied to the surface of
2639:Chemical vapor deposition
2560:Ultra low expansion glass
2450:Borophosphosilicate glass
2173:Thin Film Optical Filters
1974:(3–5): 53. Archived from
1733:"Nanostructured Surfaces"
1179:physical vapor deposition
1084:total internal reflection
572:after travelling through
470:refractive index gradient
336:Single-layer interference
2878:Glass-reinforced plastic
2540:Sodium hexametaphosphate
1971:Jemná Mechanika a Optika
1782:(4). Elsevier: 137–150.
740:transmission coefficient
402:Multi-layer interference
122:destructive interference
2770:Anti-reflective coating
2644:Glass batch calculation
2525:Photochromic lens glass
2150:10.1364/josaa.28.000770
2069:Applied Physics Letters
1333:Langmuir–Blodgett films
1325:Katharine Burr Blodgett
870:) and the glass (index
863:between the air (index
1158:
1148:transfer-matrix method
1007:
789:
703:
601:reflection coefficient
528:
504:
268:
249:thin-film interference
162:
140:: usually a choice of
26:
2903:Prince Rupert's drops
2752:Transparent materials
2712:Gradient-index optics
2520:Phosphosilicate glass
2171:MacLeod, H A (2001).
1961:Krepelka, J. (1992).
1836:. July–September 2009
1156:
1066:Interference coatings
1008:
787:
704:
526:
502:
262:
159:
24:
2868:Glass ionomer cement
2742:Photosensitive glass
2669:Liquidus temperature
2490:Fluorosilicate glass
2031:10.1364/OL.30.000914
1834:www.eos-magazine.com
1345:Anti-scratch coating
1306:Harold Dennis Taylor
1115:quarter-wave coating
960:
847:
618:
2888:Glass-to-metal seal
2810:Self-cleaning glass
2732:Optical lens design
2132:2011JOSAA..28..770D
2081:2008ApPhL..93m3109H
2048:on 19 February 2009
2023:2005OptL...30..914M
1947:Information Display
1810:on 13 December 2014
1741:Fraunhofer Magazine
1685:on 29 January 2011.
1642:2013ChPhB..22d4201Z
1599:10.3906/fiz-1801-28
1537:2019Heliy...501965S
1496:2004SPIE.5375..940Y
1380:www.pveducation.org
1335:in the late 1930s.
1078:research, where an
734:. Complementary to
541:index of refraction
430:US Patent 5,091,244
417:angles of incidence
196:and visual acuity.
95:planetary astronomy
2873:Glass microspheres
2795:Hydrogen darkening
2717:Hydrogen darkening
2465:Chalcogenide glass
2455:Borosilicate glass
2327:Hecht, E. (1987).
1981:on 12 January 2011
1870:10.1039/C4EE00380B
1858:Energy Environ Sci
1414:10.1039/c1ee01297e
1280:. You can help by
1171:Magnesium fluoride
1159:
1080:index-matching oil
1072:impedance matching
1003:
790:
699:
586:refractive indices
529:
509:circular polarizer
505:
495:Circular polarizer
434:sputter deposition
362:magnesium fluoride
276:magnesium fluoride
269:
243:, and help reduce
163:
59:photovoltaic cells
27:
2926:
2925:
2843:Glass-coated wire
2815:sol–gel technique
2800:Insulated glazing
2737:Photochromic lens
2722:Optical amplifier
2674:sol–gel technique
2342:978-0-201-11609-0
2246:on 1 January 2013
2216:on 8 October 2016
2089:10.1063/1.2988893
1711:10.1021/am201494m
1630:Chinese Physics B
1504:10.1117/12.535034
1408:(10): 3779–3804.
1313:Olexander Smakula
1298:
1297:
1227:Langmuir-Blodgett
1221:Textured coatings
998:
684:
590:Fresnel equations
549:add destructively
393:mesoporous silica
326:Fresnel equations
225:Fresnel equations
181:Corrective lenses
167:corrective lenses
2946:
2939:Thin-film optics
2664:Ion implantation
2419:Glass transition
2392:
2385:
2378:
2369:
2346:
2331:(2nd ed.).
2313:
2312:
2310:
2308:
2293:
2287:
2282:
2276:
2275:
2274:
2270:
2262:
2256:
2255:
2253:
2251:
2242:. Archived from
2232:
2226:
2225:
2223:
2221:
2212:. Archived from
2202:
2196:
2193:
2187:
2186:
2168:
2162:
2161:
2143:
2115:
2109:
2108:
2064:
2058:
2057:
2055:
2053:
2047:
2041:. Archived from
2006:
1997:
1991:
1990:
1988:
1986:
1980:
1967:
1958:
1952:
1951:
1942:
1936:
1935:
1924:
1918:
1917:
1915:
1913:
1902:
1896:
1895:
1893:
1891:
1880:
1874:
1873:
1864:(8): 2680–2688.
1852:
1846:
1845:
1843:
1841:
1826:
1820:
1819:
1817:
1815:
1800:
1794:
1793:
1791:
1767:
1761:
1760:
1758:
1756:
1750:
1737:
1729:
1723:
1722:
1693:
1687:
1686:
1681:. Archived from
1675:
1669:
1668:
1666:
1664:
1627:
1618:
1612:
1611:
1601:
1575:
1569:
1568:
1558:
1548:
1514:
1508:
1507:
1483:
1477:
1476:
1474:
1472:
1467:on 25 April 2012
1466:
1460:. Archived from
1459:
1451:
1445:
1444:
1442:
1440:
1424:
1418:
1417:
1397:
1391:
1390:
1388:
1386:
1372:
1293:
1290:
1272:
1265:
1241:geometric optics
1187:
1168:
1108:
1045:
1035:
1025:
1012:
1010:
1009:
1004:
999:
997:
996:
987:
986:
977:
972:
971:
925:
909:
843:
823:
809:), the value of
808:
708:
706:
705:
700:
695:
694:
689:
685:
683:
682:
681:
669:
668:
658:
657:
656:
644:
643:
633:
597:normal incidence
438:titanium nitride
413:Optical coatings
321:refractive index
288:titanium dioxide
265:indium tin oxide
237:photolithography
231:Photolithography
201:polarized lenses
118:refractive index
107:telescopic sight
2954:
2953:
2949:
2948:
2947:
2945:
2944:
2943:
2929:
2928:
2927:
2922:
2858:Glass electrode
2853:Glass databases
2830:
2824:
2762:
2756:
2688:
2622:
2598:Bioactive glass
2584:
2570:Vitreous enamel
2555:Thoriated glass
2550:Tellurite glass
2535:Soda–lime glass
2505:Gold ruby glass
2475:Cranberry glass
2428:
2402:
2396:
2354:
2349:
2343:
2326:
2322:
2317:
2316:
2306:
2304:
2303:on 27 June 2017
2295:
2294:
2290:
2283:
2279:
2272:
2265:
2263:
2259:
2249:
2247:
2234:
2233:
2229:
2219:
2217:
2204:
2203:
2199:
2194:
2190:
2183:
2170:
2169:
2165:
2141:10.1.1.716.4775
2117:
2116:
2112:
2066:
2065:
2061:
2051:
2049:
2045:
2004:
1999:
1998:
1994:
1984:
1982:
1978:
1965:
1960:
1959:
1955:
1944:
1943:
1939:
1926:
1925:
1921:
1911:
1909:
1908:. Authors. 2014
1904:
1903:
1899:
1889:
1887:
1882:
1881:
1877:
1854:
1853:
1849:
1839:
1837:
1828:
1827:
1823:
1813:
1811:
1802:
1801:
1797:
1769:
1768:
1764:
1754:
1752:
1751:on 10 June 2011
1748:
1735:
1731:
1730:
1726:
1695:
1694:
1690:
1677:
1676:
1672:
1662:
1660:
1625:
1620:
1619:
1615:
1577:
1576:
1572:
1516:
1515:
1511:
1485:
1484:
1480:
1470:
1468:
1464:
1457:
1453:
1452:
1448:
1438:
1436:
1426:
1425:
1421:
1399:
1398:
1394:
1384:
1382:
1374:
1373:
1369:
1364:
1350:Dichroic filter
1341:
1329:Irving Langmuir
1294:
1288:
1285:
1278:needs expansion
1263:
1223:
1182:
1176:
1163:
1137:
1130:
1112:
1106:
1099:
1095:
1068:
1061:
1055:
1043:
1037:
1033:
1027:
1023:
1017:
988:
978:
963:
958:
957:
945:
938:
932:
924:
917:
911:
908:
901:
895:
893:
886:
876:
869:
862:
852:As observed by
850:
848:Rayleigh's film
833:
826:reflection loss
814:
806:
800:
798:
725:
718:
673:
660:
659:
648:
635:
634:
628:
627:
616:
615:
564:moves from one
558:
521:
497:
489:splitting water
458:
442:niobium nitride
436:. For example,
425:
419:other than 0°.
404:
383:
379:
375:
367:
338:
305:
300:
284:silicon dioxide
280:silicon nitride
257:
233:
183:
154:
51:optical coating
39:anti-reflection
17:
12:
11:
5:
2952:
2950:
2942:
2941:
2931:
2930:
2924:
2923:
2921:
2920:
2915:
2910:
2905:
2900:
2895:
2890:
2885:
2880:
2875:
2870:
2865:
2860:
2855:
2850:
2845:
2840:
2834:
2832:
2826:
2825:
2823:
2822:
2820:Tempered glass
2817:
2812:
2807:
2802:
2797:
2792:
2790:DNA microarray
2787:
2785:Dealkalization
2782:
2777:
2772:
2766:
2764:
2758:
2757:
2755:
2754:
2749:
2744:
2739:
2734:
2729:
2724:
2719:
2714:
2709:
2704:
2698:
2696:
2690:
2689:
2687:
2686:
2681:
2676:
2671:
2666:
2661:
2659:Glass modeling
2656:
2651:
2646:
2641:
2636:
2630:
2628:
2624:
2623:
2621:
2620:
2615:
2610:
2605:
2600:
2594:
2592:
2590:Glass-ceramics
2586:
2585:
2583:
2582:
2577:
2572:
2567:
2562:
2557:
2552:
2547:
2542:
2537:
2532:
2530:Silicate glass
2527:
2522:
2517:
2512:
2507:
2502:
2497:
2492:
2487:
2482:
2477:
2472:
2467:
2462:
2457:
2452:
2447:
2442:
2436:
2434:
2430:
2429:
2427:
2426:
2421:
2416:
2410:
2408:
2404:
2403:
2401:science topics
2397:
2395:
2394:
2387:
2380:
2372:
2366:
2365:
2360:
2353:
2352:External links
2350:
2348:
2347:
2341:
2333:Addison–Wesley
2323:
2321:
2318:
2315:
2314:
2288:
2277:
2257:
2236:"Lens coating"
2227:
2197:
2188:
2181:
2163:
2110:
2075:(13): 133109.
2059:
2017:(8): 914–916.
2010:Optics Letters
1992:
1953:
1937:
1919:
1897:
1875:
1847:
1821:
1795:
1762:
1724:
1705:(2): 854–859.
1688:
1670:
1613:
1592:(4): 350–355.
1570:
1509:
1478:
1446:
1419:
1392:
1366:
1365:
1363:
1360:
1359:
1358:
1352:
1347:
1340:
1337:
1296:
1295:
1275:
1273:
1262:
1259:
1222:
1219:
1174:
1135:
1128:
1110:
1104:
1097:
1067:
1064:
1059:
1053:
1041:
1031:
1021:
1014:
1013:
1002:
995:
991:
985:
981:
975:
970:
966:
951:geometric mean
943:
936:
930:
922:
915:
906:
899:
891:
884:
874:
867:
860:
849:
846:
804:
796:
762:is always 1 −
723:
716:
710:
709:
698:
693:
688:
680:
676:
672:
667:
663:
655:
651:
647:
642:
638:
631:
626:
623:
557:
554:
520:
517:
496:
493:
465:nanostructured
457:
454:
424:
421:
403:
400:
381:
377:
373:
370:fluoropolymers
365:
337:
334:
304:
303:Index-matching
301:
299:
296:
292:aluminum oxide
256:
253:
245:standing waves
232:
229:
182:
179:
153:
150:
144:, visible, or
130:oblique angles
126:incident angle
31:antireflective
15:
13:
10:
9:
6:
4:
3:
2:
2951:
2940:
2937:
2936:
2934:
2919:
2916:
2914:
2911:
2909:
2906:
2904:
2901:
2899:
2896:
2894:
2891:
2889:
2886:
2884:
2881:
2879:
2876:
2874:
2871:
2869:
2866:
2864:
2861:
2859:
2856:
2854:
2851:
2849:
2846:
2844:
2841:
2839:
2836:
2835:
2833:
2827:
2821:
2818:
2816:
2813:
2811:
2808:
2806:
2803:
2801:
2798:
2796:
2793:
2791:
2788:
2786:
2783:
2781:
2778:
2776:
2773:
2771:
2768:
2767:
2765:
2759:
2753:
2750:
2748:
2745:
2743:
2740:
2738:
2735:
2733:
2730:
2728:
2727:Optical fiber
2725:
2723:
2720:
2718:
2715:
2713:
2710:
2708:
2705:
2703:
2700:
2699:
2697:
2695:
2691:
2685:
2684:Vitrification
2682:
2680:
2677:
2675:
2672:
2670:
2667:
2665:
2662:
2660:
2657:
2655:
2654:Glass melting
2652:
2650:
2649:Glass forming
2647:
2645:
2642:
2640:
2637:
2635:
2632:
2631:
2629:
2625:
2619:
2616:
2614:
2611:
2609:
2606:
2604:
2601:
2599:
2596:
2595:
2593:
2591:
2587:
2581:
2578:
2576:
2573:
2571:
2568:
2566:
2565:Uranium glass
2563:
2561:
2558:
2556:
2553:
2551:
2548:
2546:
2545:Soluble glass
2543:
2541:
2538:
2536:
2533:
2531:
2528:
2526:
2523:
2521:
2518:
2516:
2513:
2511:
2508:
2506:
2503:
2501:
2498:
2496:
2493:
2491:
2488:
2486:
2483:
2481:
2478:
2476:
2473:
2471:
2468:
2466:
2463:
2461:
2460:Ceramic glaze
2458:
2456:
2453:
2451:
2448:
2446:
2443:
2441:
2438:
2437:
2435:
2431:
2425:
2422:
2420:
2417:
2415:
2412:
2411:
2409:
2405:
2400:
2393:
2388:
2386:
2381:
2379:
2374:
2373:
2370:
2364:
2361:
2359:
2356:
2355:
2351:
2344:
2338:
2334:
2330:
2325:
2324:
2319:
2302:
2298:
2292:
2289:
2286:
2281:
2278:
2268:
2261:
2258:
2245:
2241:
2237:
2231:
2228:
2215:
2211:
2207:
2201:
2198:
2192:
2189:
2184:
2182:9780750306881
2178:
2174:
2167:
2164:
2159:
2155:
2151:
2147:
2142:
2137:
2133:
2129:
2125:
2121:
2114:
2111:
2106:
2102:
2098:
2094:
2090:
2086:
2082:
2078:
2074:
2070:
2063:
2060:
2044:
2040:
2036:
2032:
2028:
2024:
2020:
2016:
2012:
2011:
2003:
1996:
1993:
1977:
1973:
1972:
1964:
1957:
1954:
1949:
1948:
1941:
1938:
1933:
1929:
1923:
1920:
1907:
1901:
1898:
1885:
1879:
1876:
1871:
1867:
1863:
1859:
1851:
1848:
1835:
1831:
1825:
1822:
1809:
1805:
1799:
1796:
1790:
1785:
1781:
1777:
1773:
1766:
1763:
1747:
1743:
1742:
1734:
1728:
1725:
1720:
1716:
1712:
1708:
1704:
1700:
1692:
1689:
1684:
1680:
1674:
1671:
1659:
1655:
1651:
1647:
1643:
1639:
1636:(4): 044201.
1635:
1631:
1624:
1617:
1614:
1609:
1605:
1600:
1595:
1591:
1587:
1586:
1581:
1574:
1571:
1566:
1562:
1557:
1552:
1547:
1542:
1538:
1534:
1531:(7): e01965.
1530:
1526:
1525:
1520:
1513:
1510:
1505:
1501:
1497:
1493:
1489:
1482:
1479:
1463:
1456:
1450:
1447:
1434:
1430:
1423:
1420:
1415:
1411:
1407:
1403:
1396:
1393:
1381:
1377:
1371:
1368:
1361:
1356:
1353:
1351:
1348:
1346:
1343:
1342:
1338:
1336:
1334:
1330:
1326:
1322:
1318:
1314:
1309:
1307:
1303:
1300:As mentioned
1292:
1283:
1279:
1276:This section
1274:
1271:
1267:
1266:
1260:
1258:
1255:
1253:
1248:
1246:
1242:
1237:
1235:
1230:
1228:
1220:
1218:
1216:
1211:
1205:
1201:
1199:
1198:visible range
1195:
1189:
1185:
1180:
1172:
1166:
1155:
1151:
1150:can be used.
1149:
1145:
1141:
1134:
1127:
1122:
1120:
1116:
1103:
1093:
1088:
1085:
1081:
1077:
1073:
1065:
1063:
1058:
1052:
1047:
1040:
1030:
1020:
1000:
993:
989:
983:
979:
973:
968:
964:
956:
955:
954:
952:
947:
942:
935:
929:
921:
914:
905:
898:
890:
883:
878:
873:
866:
859:
855:
854:Lord Rayleigh
845:
841:
837:
829:
827:
821:
817:
812:
803:
795:
786:
782:
780:
776:
772:
769:
765:
761:
757:
753:
749:
745:
744:transmittance
741:
737:
733:
729:
722:
715:
696:
691:
686:
678:
674:
670:
665:
661:
653:
649:
645:
640:
636:
629:
624:
621:
614:
613:
612:
610:
606:
602:
598:
593:
591:
587:
583:
579:
575:
571:
567:
563:
555:
553:
550:
546:
542:
538:
534:
525:
518:
516:
514:
510:
501:
494:
492:
490:
485:
483:
479:
475:
471:
466:
462:
455:
453:
451:
447:
443:
439:
435:
431:
422:
420:
418:
414:
409:
401:
399:
397:
396:nanoparticles
394:
389:
387:
371:
363:
359:
354:
351:
347:
343:
335:
333:
329:
327:
322:
318:
314:
310:
309:Lord Rayleigh
302:
297:
295:
293:
289:
285:
281:
277:
273:
266:
261:
254:
252:
250:
246:
242:
238:
230:
228:
226:
222:
218:
214:
209:
206:
202:
197:
195:
191:
187:
180:
178:
176:
172:
168:
158:
151:
149:
147:
143:
139:
135:
131:
127:
123:
119:
115:
110:
108:
104:
100:
96:
92:
88:
84:
80:
76:
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49:is a type of
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2893:Porous glass
2848:Safety glass
2805:Porous glass
2769:
2763:modification
2575:Wood's glass
2495:Fused quartz
2470:Cobalt glass
2424:Supercooling
2328:
2305:. Retrieved
2301:the original
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2248:. Retrieved
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1379:
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1321:World War II
1310:
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1289:January 2013
1286:
1282:adding to it
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1256:
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1224:
1217:-dependent.
1215:polarization
1209:
1206:
1202:
1190:
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1092:interference
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562:ray of light
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386:visible band
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152:Applications
148:is offered.
111:
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30:
28:
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2918:Glass fiber
2883:Glass cloth
2627:Preparation
2603:CorningWare
2485:Flint glass
2480:Crown glass
2433:Formulation
1245:ray tracing
1076:fibre optic
605:reflectance
560:Whenever a
450:CRT display
358:crown glass
350:reflectance
346:square root
342:transparent
272:Solar cells
255:Solar cells
241:photoresist
175:solar cells
171:camera lens
138:frequencies
91:stray light
83:microscopes
2913:Windshield
2747:Refraction
2707:Dispersion
2515:Milk glass
2510:Lead glass
2307:9 February
1439:22 January
1385:2 December
1362:References
1355:Lens flare
1317:Carl Zeiss
1194:dispersion
1026:) in air (
756:scattering
752:absorption
732:percentage
556:Reflection
533:thick-film
482:lens flare
474:biomimicry
205:sunglasses
134:wavelength
103:binoculars
79:telescopes
75:binoculars
63:reflection
61:to reduce
2780:Corrosion
2679:Viscosity
2634:Annealing
2267:DE 685767
2240:Zeiss.com
2210:Zeiss.com
2136:CiteSeerX
2105:123191151
2097:0003-6951
1658:250840321
1608:139899251
1109:, where λ
768:intensity
646:−
578:interface
537:thin-film
513:chirality
423:Absorbing
186:Opticians
114:thin film
35:antiglare
2933:Category
2898:Pre-preg
2702:Achromat
2445:Bioglass
2440:AgInSbTe
2158:21532687
2039:15865397
1719:22188238
1565:31317080
1339:See also
1229:method.
456:Moth eye
446:contrast
194:contrast
99:eyeglass
87:contrast
2829:Diverse
2761:Surface
2618:Zerodur
2320:Sources
2264:Patent
2250:15 June
2220:15 June
2128:Bibcode
2077:Bibcode
2052:26 June
2019:Bibcode
1985:17 June
1890:24 July
1840:24 July
1814:17 June
1755:17 June
1638:Bibcode
1556:6611928
1533:Bibcode
1524:Heliyon
1492:Bibcode
1471:25 June
1261:History
1096:λ/4 = λ
1044:≈ 1.225
738:is the
313:tarnish
71:cameras
47:coating
2831:topics
2694:Optics
2500:GeSbTe
2407:Basics
2339:
2329:Optics
2273:
2179:
2156:
2138:
2120:JOSA A
2103:
2095:
2037:
1717:
1663:13 May
1656:
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1167:≈ 1.23
918:= 1 −
902:= 1 −
838:/(1 +
822:= 0.96
818:= 1 −
712:where
582:window
566:medium
519:Theory
408:silica
290:, and
217:grease
81:, and
55:lenses
2613:Macor
2580:ZBLAN
2414:Glass
2399:Glass
2101:S2CID
2046:(PDF)
2005:(PDF)
1979:(PDF)
1966:(PDF)
1912:1 May
1749:(PDF)
1736:(PDF)
1654:S2CID
1626:(PDF)
1604:S2CID
1465:(PDF)
1458:(PDF)
1302:above
1140:phase
1034:≈ 1.0
1024:≈ 1.5
807:≈ 1.5
750:. If
742:, or
603:, or
570:glass
478:Canon
461:Moths
364:, MgF
298:Types
221:index
213:water
190:glare
132:. A
67:light
2337:ISBN
2309:2007
2252:2013
2222:2013
2177:ISBN
2154:PMID
2093:ISSN
2054:2007
2035:PMID
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1914:2014
1892:2014
1842:2019
1816:2009
1757:2009
1715:PMID
1665:2016
1561:PMID
1473:2012
1441:2016
1387:2023
1327:and
1173:(MgF
1131:and
910:and
887:and
754:and
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545:film
535:and
440:and
317:more
215:and
169:and
2146:doi
2085:doi
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