2765:
1035:
2056:
20:
2897:
1115:
1655:
2805:
1085:
1077:
2785:
2982:." In 1923, C. W. Mason noted that the barbules in the peacock feather were made from very thin layers. Some of these layers were colored while others were transparent. He noticed that pressing the barbule would shift the color toward the blue, while swelling it with a chemical would shift it toward the red. He also found that bleaching the pigments from the feathers did not remove the iridescence. This helped to dispel the surface color theory and reinforce the structural color theory.
120:
2909:
128:
1097:
phase and constructively interfere (as depicted in the first figure). If the distance traveled by beam A is an odd integer multiple of the half wavelength of light in the film, the beams destructively interfere (as in the second figure). Thus, the film shown in these figures reflects more strongly at the wavelength of the light beam in the first figure, and less strongly at that of the beam in the second figure.
927:
623:
95:, but rather are a mixture of various wavelengths. Therefore, the colors observed are rarely those of the rainbow, but rather browns, golds, turquoises, teals, bright blues, purples, and magentas. Studying the light reflected or transmitted by a thin film can reveal information about the thickness of the film or the effective
2747:
due to thin-film layers is common in the natural world. The wings of many insects act as thin films because of their minimal thickness. This is clearly visible in the wings of many flies and wasps. In butterflies, the thin-film optics are visible when the wing itself is not covered by pigmented wing
1096:
The phase relationship of the two reflected beams depends on the relationship between the wavelength of beam A in the film, and the film's thickness. If the total distance beam A travels in the film is an integer multiple of the wavelength of the beam in the film, then the two reflected beams are in
1662:
In the case of a thin oil film, a layer of oil sits on top of a layer of water. The oil may have an index of refraction near 1.5 and the water has an index of 1.33. As in the case of the soap bubble, the materials on either side of the oil film (air and water) both have refractive indices that are
1067:
If the incident light is broadband, or white, such as light from the sun, interference patterns appear as colorful bands. Different wavelengths of light create constructive interference for different film thicknesses. Different regions of the film appear in different colors depending on the local
1092:
The figures show two incident light beams (A and B). Each beam produces a reflected beam (dashed). The reflections of interest are beam A’s reflection off of the lower surface and beam B’s reflection off of the upper surface. These reflected beams combine to produce a resultant beam (C). If the
235:
Consider light incident on a thin film and reflected by both the upper and lower boundaries. The optical path difference (OPD) of the reflected light must be calculated in order to determine the condition for interference. Referring to the ray diagram above, the OPD between the two waves is the
1046:
in nature, interference patterns appear as light and dark bands. Light bands correspond to regions at which constructive interference is occurring between the reflected waves and dark bands correspond to destructive interference regions. As the thickness of the film varies from one location to
1105:
The type of interference that occurs when light is reflected from a thin film is dependent upon the wavelength and angle of the incident light, the thickness of the film, the refractive indices of the material on either side of the film, and the index of the film medium. Various possible film
2069:
An anti-reflection coating eliminates reflected light and maximizes transmitted light in an optical system. A film is designed such that reflected light produces destructive interference and transmitted light produces constructive interference for a given wavelength of light. In the simplest
3019:, he could reduce the reflections on the surface. In 1819, after watching a layer of alcohol evaporate from a sheet of glass, Fraunhofer noted that colors appeared just before the liquid evaporated completely, deducing that any thin film of transparent material will produce colors.
190:
at a boundary depending on the refractive indices of the materials on either side of the boundary. This phase shift occurs if the refractive index of the medium the light is travelling through is less than the refractive index of the material it is striking. In other words, if
165:
between the two light waves depends on the difference in their phase. This difference in turn depends on the thickness of the film layer, the refractive index of the film, and the angle of incidence of the original wave on the film. Additionally, a phase shift of 180° or
231:
and the light is travelling from material 1 to material 2, then a phase shift occurs upon reflection. The pattern of light that results from this interference can appear either as light and dark bands or as colorful bands depending upon the source of the incident light.
2821:
takes advantage of thin film interference to selectively choose which wavelengths of light are allowed to transmit through the device. These films are created through deposition processes in which material is added to a substrate in a controlled manner. Methods include
922:{\displaystyle {\begin{aligned}OPD&=n_{2}\left({\frac {2d}{\cos(\theta _{2})}}\right)-2d\tan(\theta _{2})n_{2}\sin(\theta _{2})\\&=2n_{2}d\left({\frac {1-\sin ^{2}(\theta _{2})}{\cos(\theta _{2})}}\right)\\&=2n_{2}d\cos {\big (}\theta _{2})\\\end{aligned}}}
2812:. At a 45° angle the coating is slightly thicker to the incident light, causing the center wavelength to shift toward the red and reflections appear at the violet end of the spectrum. At 0°, for which this coating was designed, almost no reflection is observed.
1270:). Light that is transmitted at the upper air-film interface will continue to the lower film-air interface where it can be reflected or transmitted. The reflection that occurs at this boundary will not change the phase of the reflected wave because
1051:", demonstrates the interference pattern that results when light is reflected from a spherical surface adjacent to a flat surface. Concentric rings are observed when the surface is illuminated with monochromatic light. This phenomenon is used with
2635:
1428:
1960:
349:
439:
160:
provide a quantitative description of how much of the light will be transmitted or reflected at an interface. The light reflected from the upper and lower surfaces will interfere. The degree of constructive or destructive
1211:). The reflection that occurs at the upper boundary of the film (the air-film boundary) will introduce a 180° phase shift in the reflected wave because the refractive index of the air is less than the index of the film (
1093:
reflected beams are in phase (as in the first figure) the resultant beam is relatively strong. If, on the other hand, the reflected beams have opposite phase, the resulting beam is attenuated (as in the second figure).
2851:
is a technique that is often used to measure properties of thin films. In a typical ellipsometry experiment polarized light is reflected off a film surface and is measured by a detector. The complex reflectance ratio,
2523:
2903:
colors are produced when steel is heated and a thin film of iron oxide forms on the surface. The color indicates the temperature the steel reached, which made this one of the earliest practical uses of thin-film
2216:
525:
155:
range. As light strikes the surface of a film, it is either transmitted or reflected at the upper surface. Light that is transmitted reaches the bottom surface and may once again be transmitted or reflected. The
2816:
Thin films are used commercially in anti-reflection coatings, mirrors, and optical filters. They can be engineered to control the amount of light reflected or transmitted at a surface for a given wavelength. A
2733:, the reflected waves will be completely out of phase and will destructively interfere. Further reduction in reflection is possible by adding more layers, each designed to match a specific wavelength of light.
1512:
2041:
1744:
616:
1021:
2432:
628:
2919:
caused by thin-film interference is a commonly observed phenomenon in nature, being found in a variety of plants and animals. One of the first known studies of this phenomenon was conducted by
2764:
2358:
1862:
2287:
1327:
1268:
1800:
1209:
2692:
2118:
2731:
1165:
1577:
229:
1604:
1644:
950:
2870:
184:
2533:
1624:
1539:
2872:, of the system is measured. A model analysis is then conducted, in which the information is used to determine film layer thicknesses and refractive indices.
1335:
1870:
242:
2960:
360:
2951:, who helped to establish the wave theory of light in 1816. However, very little explanation could be made of the iridescence until the 1870s, when
2993:, first described the process of thin-film interference as an explanation for the iridescence. The first examination of iridescent feathers by an
2784:
2440:
2947:
provided the first explanation of constructive and destructive interference. Young's contribution went largely unnoticed until the work of
2126:
445:
2878:
is an emerging technique for measuring refractive index and thickness of molecular scale thin films and how these change when stimulated.
2120:
is a quarter-wavelength of the incident light and its refractive index is greater than the index of air and less than the index of glass.
3359:
1438:
1970:
2845:
of a thin-film features distinct oscillations and the extrema of the spectrum can be used to calculate the thickness of the thin-film.
1666:
57:
2974:, as some form of surface color, such as a dye or pigment that might alter the light when reflected from different angles. In 1919,
3055:
537:
2943:, that the iridescence in a peacock feather was due to the fact that the transparent layers in the feather were so thin. In 1801,
958:
2978:
proposed that the bright, changing colors were not caused by dyes or pigments, but by microscopic structures, which he termed "
2754:
butterfly. The glossy appearance of buttercup flowers is also due to a thin film as well as the shiny breast feathers of the
932:
Interference will be constructive if the optical path difference is equal to an integer multiple of the wavelength of light,
2841:, that aids in light collecting. The effects of thin-film interference can also be seen in oil slicks and soap bubbles. The
123:
Demonstration of the optical path length difference for light reflected from the upper and lower boundaries of a thin film.
2363:
2295:
49:
and decreasing it at others. When white light is incident on a thin film, this effect produces colorful reflections.
1805:
2222:
1273:
1214:
1749:
2875:
1047:
another, the interference may change from constructive to destructive. A good example of this phenomenon, termed "
3065:
162:
42:
3170:
2964:
3090:
Stavenga, D. G. (2014). "Thin Film and
Multilayer Optics Cause Structural Colors of Many Insects and Birds".
2694:
is equal to a quarter-wavelength of the incident light and if the light strikes the film at normal incidence
2292:
A 180° phase shift will be induced upon reflection at both the top and bottom interfaces of the film because
3214:
3169:
Van Der Kooi, C. J.; Wilts, B. D.; Leertouwer, H. L.; Staal, M.; Elzenga, J. T. M.; Stavenga, D. G. (2014).
3022:
Little advancement was made in thin-film coating technology until 1936, when John Strong began evaporating
1170:
2647:
2073:
3375:
3215:"Dramatic colour changes in a bird of paradise caused by uniquely structured breast feather barbules"
2827:
2823:
2697:
1129:
1038:
Gasoline on water shows a pattern of bright and dark fringes when illuminated with 589nm laser light.
2818:
1544:
194:
2944:
2055:
1056:
1034:
2970:
In much of the early work, scientists tried to explain iridescence, in animals like peacocks and
2064:
1582:
187:
100:
2900:
65:
1629:
1026:
This condition may change after considering possible phase shifts that occur upon reflection.
935:
2967:, in 1899, the mechanisms of thin-film interference could be demonstrated on a larger scale.
2891:
2744:
1106:
configurations and the related equations are explained in more detail in the examples below.
3004:, in 1942, revealed an extremely tiny array of thin-film structures on the nanometer scale.
2896:
19:
3348:
2855:
2630:{\displaystyle 2n_{\rm {coating}}d\cos(\theta _{2})=\left(m-{\frac {1}{2}}\right)\lambda }
1126:, light travels through air and strikes a soap film. The air has a refractive index of 1 (
169:
8:
3039:
2994:
2952:
88:
87:
The reflection from a thin film is typically not individual wavelengths as produced by a
3352:
3239:
3146:
3121:
2755:
1609:
1524:
1423:{\displaystyle 2n_{\rm {film}}d\cos(\theta _{2})=\left(m-{\frac {1}{2}}\right)\lambda }
1114:
3026:
in order to make anti-reflection coatings on glass. During the 1930s, improvements in
2997:
occurred in 1939, revealing complex thin-film structures, while an examination of the
1955:{\displaystyle 2n_{\rm {oil}}d\cos(\theta _{2})=\left(m-{\frac {1}{2}}\right)\lambda }
3244:
3195:
3151:
3031:
3008:
1048:
157:
2833:
Thin films are also found in nature. Many animals have a layer of tissue behind the
2070:
implementation of such a coating, the film is created so that its optical thickness
1654:
344:{\displaystyle OPD=n_{2}({\overline {AB}}+{\overline {BC}})-n_{1}({\overline {AD}})}
3234:
3226:
3185:
3141:
3133:
3099:
3060:
2979:
2948:
2804:
132:
96:
80:
of the incident light, then the interference pattern will be washed out due to the
77:
3360:
Thin film and multilayer optics cause structural colors of many insects and birds
2838:
1084:
1076:
52:
Thin-film interference explains the multiple colors seen in light reflected from
3103:
3007:
The first production of thin-film coatings occurred quite by accident. In 1817,
434:{\displaystyle {\overline {AB}}={\overline {BC}}={\frac {d}{\cos(\theta _{2})}}}
3120:
Van Der Kooi, C. J.; Elzenga, J.T.M.; Dijksterhuis, J.; Stavenga, D.G. (2017).
2998:
2986:
2956:
2809:
531:
108:
92:
2736:
Interference of transmitted light is completely constructive for these films.
1746:. There will be a phase shift upon reflection from the upper boundary because
3369:
3171:"Iridescent flowers? Contribution of surface structures to optical signaling"
2975:
3248:
3230:
3199:
3155:
3137:
2971:
2934:
2933:
feathers was caused by thin, alternating layers of plate and air. In 1704,
2925:
2920:
2848:
2842:
1052:
99:
of the film medium. Thin films have many commercial applications including
2908:
3027:
3016:
2916:
2887:
1123:
119:
73:
53:
3213:
Stavenga, D. G.; Leertouwer, H. L.; Marshall, N. J.; Osorio, D. (2010).
3119:
3043:
3035:
1043:
46:
35:
3290:
By Hugh Angus
Macleod – Institute of Physics Publishing 2001 Pages 1–4
3190:
2518:{\displaystyle 2n_{\rm {coating}}d\cos {\big (}\theta _{2})=m\lambda }
3001:
2791:
2771:
2750:
2211:{\displaystyle n_{\rm {air}}<n_{\rm {coating}}<n_{\rm {glass}}}
1329:. The condition for interference for a soap bubble is the following:
520:{\displaystyle {\overline {AD}}=2d\tan(\theta _{2})\sin(\theta _{1})}
148:
144:
81:
39:
3302:
By Shūichi
Kinoshita - World Scientific Publishing 2008 Page 165-167
3023:
1507:{\displaystyle 2n_{\rm {film}}d\cos {\big (}\theta _{2})=m\lambda }
2036:{\displaystyle 2n_{\rm {oil}}d\cos {\big (}\theta _{2})=m\lambda }
127:
3271:
By Shūichi
Kinoshita – World Scientific Publishing 2008 pages 3–6
2939:
2930:
1739:{\displaystyle n_{\rm {air}}<n_{\rm {water}}<n_{\rm {oil}}}
69:
3212:
3168:
2991:
A Spectrophotometric Study of
Certain Cases of Structural Color
2834:
152:
136:
104:
3012:
2434:. The equations for interference of the reflected light are:
1802:
but no shift upon reflection from the lower boundary because
1606:
is the angle of incidence of the wave on the lower boundary,
611:{\displaystyle n_{1}\sin(\theta _{1})=n_{2}\sin(\theta _{2})}
61:
24:
3038:, possible. In 1939, Walter H. Geffcken created the first
1016:{\displaystyle 2n_{2}d\cos {\big (}\theta _{2})=m\lambda }
2748:
scales, which is the case in the blue wing spots of the
3316:
3219:
Proceedings of the Royal
Society B: Biological Sciences
76:. If the thickness of the film is much larger than the
2858:
2700:
2650:
2536:
2443:
2366:
2298:
2225:
2129:
2076:
2059:
Light incident on an anti-reflection coating on glass
1973:
1873:
1808:
1752:
1669:
1632:
1612:
1585:
1547:
1527:
1441:
1338:
1276:
1217:
1173:
1132:
961:
938:
626:
540:
448:
363:
245:
197:
172:
3362:
Materials today: Proceedings, 1S, 109 – 121 (2014).
2427:{\displaystyle n_{\rm {coating}}<n_{\rm {glass}}}
3283:
3281:
3279:
3277:
1864:. The equations for interference will be the same.
1167:) and the film has an index that is larger than 1 (
3345:Optics of Thin Films; An Optical Multilayer Theory
2864:
2725:
2686:
2629:
2517:
2426:
2353:{\displaystyle n_{\rm {air}}<n_{\rm {coating}}}
2352:
2281:
2210:
2112:
2035:
1954:
1856:
1794:
1738:
1638:
1618:
1598:
1571:
1533:
1506:
1422:
1321:
1262:
1203:
1159:
1015:
944:
921:
610:
519:
433:
343:
223:
178:
147:is a layer of material with thickness in the sub-
64:. It is also the mechanism behind the action of
38:reflected by the upper and lower boundaries of a
3367:
3274:
3264:
3262:
3260:
3258:
1965:for constructive interference of reflected light
1857:{\displaystyle n_{\rm {oil}}>n_{\rm {water}}}
1433:for constructive interference of reflected light
45:with one another, increasing reflection at some
3122:"Functional optics of glossy buttercup flowers"
2282:{\displaystyle d=\lambda /(4n_{\rm {coating}})}
2046:for destructive interference of reflected light
1517:for destructive interference of reflected light
1322:{\displaystyle n_{\rm {film}}>n_{\rm {air}}}
1263:{\displaystyle n_{\rm {air}}<n_{\rm {film}}}
1795:{\displaystyle n_{\rm {air}}<n_{\rm {oil}}}
3255:
2912:Iridescent interference colors in an oil film
2488:
2006:
1477:
986:
897:
3324:
3115:
3113:
2929:, Hooke postulated that the iridescence in
2050:
3325:Greivenkamp, John (1995), "Interference",
3085:
3083:
3081:
3238:
3189:
3145:
2794:flowers is due to thin-film interference.
3300:Structural colors in the realm of nature
3269:Structural colors in the realm of nature
3110:
3089:
3056:Reflectometric interference spectroscopy
2907:
2895:
2803:
2054:
1653:
1113:
1083:
1075:
1033:
126:
118:
18:
3078:
1029:
23:Thin-film interference caused by water-
3368:
3342:
3334:Hecht, Eugene (2002), "Interference",
3315:
3126:Journal of the Royal Society Interface
1658:Light incident on an oil film on water
3333:
1579:is the refractive index of the film,
2778:) are due to thin-film interference.
1118:Light incident on a soap film in air
1071:
2961:the electromagnetic nature of light
1204:{\displaystyle n_{\rm {film}}>1}
1062:
13:
3309:
2687:{\displaystyle dn_{\rm {coating}}}
2678:
2675:
2672:
2669:
2666:
2663:
2660:
2564:
2561:
2558:
2555:
2552:
2549:
2546:
2471:
2468:
2465:
2462:
2459:
2456:
2453:
2418:
2415:
2412:
2409:
2406:
2391:
2388:
2385:
2382:
2379:
2376:
2373:
2344:
2341:
2338:
2335:
2332:
2329:
2326:
2311:
2308:
2305:
2270:
2267:
2264:
2261:
2258:
2255:
2252:
2202:
2199:
2196:
2193:
2190:
2175:
2172:
2169:
2166:
2163:
2160:
2157:
2142:
2139:
2136:
2113:{\displaystyle dn_{\rm {coating}}}
2104:
2101:
2098:
2095:
2092:
2089:
2086:
1989:
1986:
1983:
1889:
1886:
1883:
1848:
1845:
1842:
1839:
1836:
1821:
1818:
1815:
1786:
1783:
1780:
1765:
1762:
1759:
1730:
1727:
1724:
1709:
1706:
1703:
1700:
1697:
1682:
1679:
1676:
1663:less than the index of the film.
1563:
1560:
1557:
1554:
1460:
1457:
1454:
1451:
1357:
1354:
1351:
1348:
1313:
1310:
1307:
1292:
1289:
1286:
1283:
1254:
1251:
1248:
1245:
1230:
1227:
1224:
1189:
1186:
1183:
1180:
1145:
1142:
1139:
14:
3387:
188:may be introduced upon reflection
131:Thin-film interference caused by
34:is a natural phenomenon in which
2876:Dual polarisation interferometry
2783:
2763:
3066:Transfer-matrix method (optics)
3011:discovered that, by tarnishing
2799:
2726:{\displaystyle (\theta _{2}=0)}
1160:{\displaystyle n_{\rm {air}}=1}
3293:
3206:
3162:
2720:
2701:
2592:
2579:
2503:
2276:
2240:
2021:
1917:
1904:
1572:{\displaystyle n_{\rm {film}}}
1492:
1385:
1372:
1109:
1080:Constructive phase interaction
1001:
912:
853:
840:
829:
816:
761:
748:
729:
716:
691:
678:
605:
592:
570:
557:
514:
501:
492:
479:
425:
412:
338:
320:
304:
268:
224:{\displaystyle n_{1}<n_{2}}
1:
3318:Introduction to Modern Optics
3071:
2963:. After the invention of the
2770:The blue wing patches of the
2528:for constructive interference
1088:Destructive phase interaction
3092:Materials Today: Proceedings
2739:
2640:for destructive interference
1646:is the wavelength of light.
459:
392:
374:
333:
299:
281:
7:
3104:10.1016/j.matpr.2014.09.007
3049:
1649:
1599:{\displaystyle \theta _{2}}
1100:
10:
3392:
2965:Fabry–Perot interferometer
2885:
2881:
2772:European peacock butterfly
2062:
3288:Thin-film optical filters
2828:physical vapor deposition
2824:chemical vapor deposition
2808:An antireflection-coated
2644:If the optical thickness
1055:to measure the shape and
135:defrosting coating on an
114:
2051:Anti-reflection coatings
1639:{\displaystyle \lambda }
1042:Where incident light is
945:{\displaystyle \lambda }
101:anti-reflection coatings
3343:Knittl, Zdeněk (1976),
2065:Anti-reflective coating
1541:is the film thickness,
66:antireflection coatings
3231:10.1098/rspb.2010.2293
3138:10.1098/rsif.2016.0933
2913:
2905:
2866:
2813:
2727:
2688:
2631:
2519:
2428:
2354:
2283:
2212:
2114:
2060:
2037:
1956:
1858:
1796:
1740:
1659:
1640:
1620:
1600:
1573:
1535:
1508:
1424:
1323:
1264:
1205:
1161:
1119:
1089:
1081:
1039:
1017:
946:
923:
612:
521:
435:
345:
225:
180:
140:
124:
32:Thin-film interference
28:
2911:
2899:
2892:structural coloration
2886:Further information:
2867:
2865:{\displaystyle \rho }
2807:
2745:Structural coloration
2728:
2689:
2632:
2520:
2429:
2355:
2284:
2213:
2115:
2058:
2038:
1957:
1859:
1797:
1741:
1657:
1641:
1621:
1601:
1574:
1536:
1509:
1425:
1324:
1265:
1206:
1162:
1117:
1087:
1079:
1037:
1018:
947:
924:
613:
522:
436:
346:
226:
181:
130:
122:
84:of the light source.
22:
3040:interference filters
2937:stated in his book,
2856:
2843:reflectance spectrum
2698:
2648:
2534:
2441:
2364:
2296:
2223:
2127:
2074:
1971:
1871:
1806:
1750:
1667:
1630:
1610:
1583:
1545:
1525:
1439:
1336:
1274:
1215:
1171:
1130:
1030:Monochromatic source
959:
936:
624:
538:
446:
361:
243:
195:
179:{\displaystyle \pi }
170:
3353:1976otf..book.....K
2995:electron microscope
1626:is an integer, and
89:diffraction grating
3327:Handbook of Optics
3225:(1715): 2098–104.
2959:helped to explain
2914:
2906:
2862:
2819:Fabry–Pérot etalon
2814:
2723:
2684:
2627:
2515:
2424:
2350:
2279:
2208:
2110:
2061:
2033:
1952:
1854:
1792:
1736:
1660:
1636:
1616:
1596:
1569:
1531:
1504:
1420:
1319:
1260:
1201:
1157:
1120:
1090:
1082:
1040:
1013:
942:
919:
917:
608:
517:
431:
341:
221:
176:
141:
125:
29:
16:Optical phenomenon
3191:10.1111/nph.12808
3132:(127): 20160933.
3032:vacuum deposition
3009:Joseph Fraunhofer
2980:structural colors
2617:
1942:
1619:{\displaystyle m}
1534:{\displaystyle d}
1410:
1122:In the case of a
1072:Phase interaction
857:
695:
462:
429:
395:
377:
336:
302:
284:
158:Fresnel equations
3383:
3376:Thin-film optics
3355:
3339:
3338:, Addison Wesley
3330:
3321:
3303:
3297:
3291:
3285:
3272:
3266:
3253:
3252:
3242:
3210:
3204:
3203:
3193:
3175:
3166:
3160:
3159:
3149:
3117:
3108:
3107:
3087:
3061:Thin-film optics
2949:Augustin Fresnel
2871:
2869:
2868:
2863:
2787:
2767:
2756:bird of paradise
2732:
2730:
2729:
2724:
2713:
2712:
2693:
2691:
2690:
2685:
2683:
2682:
2681:
2639:
2636:
2634:
2633:
2628:
2623:
2619:
2618:
2610:
2591:
2590:
2569:
2568:
2567:
2527:
2524:
2522:
2521:
2516:
2502:
2501:
2492:
2491:
2476:
2475:
2474:
2433:
2431:
2430:
2425:
2423:
2422:
2421:
2396:
2395:
2394:
2359:
2357:
2356:
2351:
2349:
2348:
2347:
2316:
2315:
2314:
2288:
2286:
2285:
2280:
2275:
2274:
2273:
2239:
2217:
2215:
2214:
2209:
2207:
2206:
2205:
2180:
2179:
2178:
2147:
2146:
2145:
2119:
2117:
2116:
2111:
2109:
2108:
2107:
2045:
2042:
2040:
2039:
2034:
2020:
2019:
2010:
2009:
1994:
1993:
1992:
1964:
1961:
1959:
1958:
1953:
1948:
1944:
1943:
1935:
1916:
1915:
1894:
1893:
1892:
1863:
1861:
1860:
1855:
1853:
1852:
1851:
1826:
1825:
1824:
1801:
1799:
1798:
1793:
1791:
1790:
1789:
1770:
1769:
1768:
1745:
1743:
1742:
1737:
1735:
1734:
1733:
1714:
1713:
1712:
1687:
1686:
1685:
1645:
1643:
1642:
1637:
1625:
1623:
1622:
1617:
1605:
1603:
1602:
1597:
1595:
1594:
1578:
1576:
1575:
1570:
1568:
1567:
1566:
1540:
1538:
1537:
1532:
1516:
1513:
1511:
1510:
1505:
1491:
1490:
1481:
1480:
1465:
1464:
1463:
1432:
1429:
1427:
1426:
1421:
1416:
1412:
1411:
1403:
1384:
1383:
1362:
1361:
1360:
1328:
1326:
1325:
1320:
1318:
1317:
1316:
1297:
1296:
1295:
1269:
1267:
1266:
1261:
1259:
1258:
1257:
1235:
1234:
1233:
1210:
1208:
1207:
1202:
1194:
1193:
1192:
1166:
1164:
1163:
1158:
1150:
1149:
1148:
1068:film thickness.
1063:Broadband source
1022:
1020:
1019:
1014:
1000:
999:
990:
989:
974:
973:
951:
949:
948:
943:
928:
926:
925:
920:
918:
911:
910:
901:
900:
885:
884:
866:
862:
858:
856:
852:
851:
832:
828:
827:
812:
811:
795:
786:
785:
767:
760:
759:
741:
740:
728:
727:
700:
696:
694:
690:
689:
670:
662:
656:
655:
617:
615:
614:
609:
604:
603:
585:
584:
569:
568:
550:
549:
526:
524:
523:
518:
513:
512:
491:
490:
463:
458:
450:
440:
438:
437:
432:
430:
428:
424:
423:
401:
396:
391:
383:
378:
373:
365:
350:
348:
347:
342:
337:
332:
324:
319:
318:
303:
298:
290:
285:
280:
272:
267:
266:
230:
228:
227:
222:
220:
219:
207:
206:
185:
183:
182:
177:
97:refractive index
78:coherence length
3391:
3390:
3386:
3385:
3384:
3382:
3381:
3380:
3366:
3365:
3358:D.G. Stavenga,
3312:
3310:Further reading
3307:
3306:
3298:
3294:
3286:
3275:
3267:
3256:
3211:
3207:
3178:New Phytologist
3173:
3167:
3163:
3118:
3111:
3088:
3079:
3074:
3052:
2989:, in his paper
2894:
2884:
2857:
2854:
2853:
2839:Tapetum lucidum
2802:
2795:
2788:
2779:
2768:
2742:
2708:
2704:
2699:
2696:
2695:
2659:
2658:
2654:
2649:
2646:
2645:
2637:
2609:
2602:
2598:
2586:
2582:
2545:
2544:
2540:
2535:
2532:
2531:
2525:
2497:
2493:
2487:
2486:
2452:
2451:
2447:
2442:
2439:
2438:
2405:
2404:
2400:
2372:
2371:
2367:
2365:
2362:
2361:
2325:
2324:
2320:
2304:
2303:
2299:
2297:
2294:
2293:
2251:
2250:
2246:
2235:
2224:
2221:
2220:
2189:
2188:
2184:
2156:
2155:
2151:
2135:
2134:
2130:
2128:
2125:
2124:
2085:
2084:
2080:
2075:
2072:
2071:
2067:
2053:
2043:
2015:
2011:
2005:
2004:
1982:
1981:
1977:
1972:
1969:
1968:
1962:
1934:
1927:
1923:
1911:
1907:
1882:
1881:
1877:
1872:
1869:
1868:
1835:
1834:
1830:
1814:
1813:
1809:
1807:
1804:
1803:
1779:
1778:
1774:
1758:
1757:
1753:
1751:
1748:
1747:
1723:
1722:
1718:
1696:
1695:
1691:
1675:
1674:
1670:
1668:
1665:
1664:
1652:
1631:
1628:
1627:
1611:
1608:
1607:
1590:
1586:
1584:
1581:
1580:
1553:
1552:
1548:
1546:
1543:
1542:
1526:
1523:
1522:
1514:
1486:
1482:
1476:
1475:
1450:
1449:
1445:
1440:
1437:
1436:
1430:
1402:
1395:
1391:
1379:
1375:
1347:
1346:
1342:
1337:
1334:
1333:
1306:
1305:
1301:
1282:
1281:
1277:
1275:
1272:
1271:
1244:
1243:
1239:
1223:
1222:
1218:
1216:
1213:
1212:
1179:
1178:
1174:
1172:
1169:
1168:
1138:
1137:
1133:
1131:
1128:
1127:
1112:
1103:
1074:
1065:
1032:
995:
991:
985:
984:
969:
965:
960:
957:
956:
937:
934:
933:
916:
915:
906:
902:
896:
895:
880:
876:
864:
863:
847:
843:
833:
823:
819:
807:
803:
796:
794:
790:
781:
777:
765:
764:
755:
751:
736:
732:
723:
719:
685:
681:
671:
663:
661:
657:
651:
647:
640:
627:
625:
622:
621:
599:
595:
580:
576:
564:
560:
545:
541:
539:
536:
535:
508:
504:
486:
482:
451:
449:
447:
444:
443:
419:
415:
405:
400:
384:
382:
366:
364:
362:
359:
358:
325:
323:
314:
310:
291:
289:
273:
271:
262:
258:
244:
241:
240:
215:
211:
202:
198:
196:
193:
192:
171:
168:
167:
139:cockpit window.
117:
109:optical filters
17:
12:
11:
5:
3389:
3379:
3378:
3364:
3363:
3356:
3340:
3331:
3322:
3311:
3308:
3305:
3304:
3292:
3273:
3254:
3205:
3161:
3109:
3076:
3075:
3073:
3070:
3069:
3068:
3063:
3058:
3051:
3048:
3034:methods, like
2987:Ernest Merritt
2972:scarab beetles
2957:Heinrich Hertz
2883:
2880:
2861:
2810:optical window
2801:
2798:
2797:
2796:
2789:
2782:
2780:
2769:
2762:
2741:
2738:
2722:
2719:
2716:
2711:
2707:
2703:
2680:
2677:
2674:
2671:
2668:
2665:
2662:
2657:
2653:
2642:
2641:
2626:
2622:
2616:
2613:
2608:
2605:
2601:
2597:
2594:
2589:
2585:
2581:
2578:
2575:
2572:
2566:
2563:
2560:
2557:
2554:
2551:
2548:
2543:
2539:
2529:
2514:
2511:
2508:
2505:
2500:
2496:
2490:
2485:
2482:
2479:
2473:
2470:
2467:
2464:
2461:
2458:
2455:
2450:
2446:
2420:
2417:
2414:
2411:
2408:
2403:
2399:
2393:
2390:
2387:
2384:
2381:
2378:
2375:
2370:
2346:
2343:
2340:
2337:
2334:
2331:
2328:
2323:
2319:
2313:
2310:
2307:
2302:
2290:
2289:
2278:
2272:
2269:
2266:
2263:
2260:
2257:
2254:
2249:
2245:
2242:
2238:
2234:
2231:
2228:
2218:
2204:
2201:
2198:
2195:
2192:
2187:
2183:
2177:
2174:
2171:
2168:
2165:
2162:
2159:
2154:
2150:
2144:
2141:
2138:
2133:
2106:
2103:
2100:
2097:
2094:
2091:
2088:
2083:
2079:
2063:Main article:
2052:
2049:
2048:
2047:
2032:
2029:
2026:
2023:
2018:
2014:
2008:
2003:
2000:
1997:
1991:
1988:
1985:
1980:
1976:
1966:
1951:
1947:
1941:
1938:
1933:
1930:
1926:
1922:
1919:
1914:
1910:
1906:
1903:
1900:
1897:
1891:
1888:
1885:
1880:
1876:
1850:
1847:
1844:
1841:
1838:
1833:
1829:
1823:
1820:
1817:
1812:
1788:
1785:
1782:
1777:
1773:
1767:
1764:
1761:
1756:
1732:
1729:
1726:
1721:
1717:
1711:
1708:
1705:
1702:
1699:
1694:
1690:
1684:
1681:
1678:
1673:
1651:
1648:
1635:
1615:
1593:
1589:
1565:
1562:
1559:
1556:
1551:
1530:
1519:
1518:
1503:
1500:
1497:
1494:
1489:
1485:
1479:
1474:
1471:
1468:
1462:
1459:
1456:
1453:
1448:
1444:
1434:
1419:
1415:
1409:
1406:
1401:
1398:
1394:
1390:
1387:
1382:
1378:
1374:
1371:
1368:
1365:
1359:
1356:
1353:
1350:
1345:
1341:
1315:
1312:
1309:
1304:
1300:
1294:
1291:
1288:
1285:
1280:
1256:
1253:
1250:
1247:
1242:
1238:
1232:
1229:
1226:
1221:
1200:
1197:
1191:
1188:
1185:
1182:
1177:
1156:
1153:
1147:
1144:
1141:
1136:
1111:
1108:
1102:
1099:
1073:
1070:
1064:
1061:
1049:Newton's rings
1031:
1028:
1024:
1023:
1012:
1009:
1006:
1003:
998:
994:
988:
983:
980:
977:
972:
968:
964:
941:
930:
929:
914:
909:
905:
899:
894:
891:
888:
883:
879:
875:
872:
869:
867:
865:
861:
855:
850:
846:
842:
839:
836:
831:
826:
822:
818:
815:
810:
806:
802:
799:
793:
789:
784:
780:
776:
773:
770:
768:
766:
763:
758:
754:
750:
747:
744:
739:
735:
731:
726:
722:
718:
715:
712:
709:
706:
703:
699:
693:
688:
684:
680:
677:
674:
669:
666:
660:
654:
650:
646:
643:
641:
639:
636:
633:
630:
629:
607:
602:
598:
594:
591:
588:
583:
579:
575:
572:
567:
563:
559:
556:
553:
548:
544:
528:
527:
516:
511:
507:
503:
500:
497:
494:
489:
485:
481:
478:
475:
472:
469:
466:
461:
457:
454:
441:
427:
422:
418:
414:
411:
408:
404:
399:
394:
390:
387:
381:
376:
372:
369:
352:
351:
340:
335:
331:
328:
322:
317:
313:
309:
306:
301:
297:
294:
288:
283:
279:
276:
270:
265:
261:
257:
254:
251:
248:
218:
214:
210:
205:
201:
175:
116:
113:
15:
9:
6:
4:
3:
2:
3388:
3377:
3374:
3373:
3371:
3361:
3357:
3354:
3350:
3346:
3341:
3337:
3332:
3329:, McGraw–Hill
3328:
3323:
3319:
3314:
3313:
3301:
3296:
3289:
3284:
3282:
3280:
3278:
3270:
3265:
3263:
3261:
3259:
3250:
3246:
3241:
3236:
3232:
3228:
3224:
3220:
3216:
3209:
3201:
3197:
3192:
3187:
3184:(2): 667–73.
3183:
3179:
3172:
3165:
3157:
3153:
3148:
3143:
3139:
3135:
3131:
3127:
3123:
3116:
3114:
3105:
3101:
3097:
3093:
3086:
3084:
3082:
3077:
3067:
3064:
3062:
3059:
3057:
3054:
3053:
3047:
3045:
3041:
3037:
3033:
3029:
3025:
3020:
3018:
3014:
3010:
3005:
3003:
3000:
2996:
2992:
2988:
2983:
2981:
2977:
2976:Lord Rayleigh
2973:
2968:
2966:
2962:
2958:
2954:
2953:James Maxwell
2950:
2946:
2942:
2941:
2936:
2932:
2928:
2927:
2922:
2918:
2910:
2904:interference.
2902:
2898:
2893:
2889:
2879:
2877:
2873:
2859:
2850:
2846:
2844:
2840:
2836:
2831:
2829:
2825:
2820:
2811:
2806:
2793:
2790:The gloss of
2786:
2781:
2777:
2773:
2766:
2761:
2760:
2759:
2757:
2753:
2752:
2746:
2737:
2734:
2717:
2714:
2709:
2705:
2655:
2651:
2624:
2620:
2614:
2611:
2606:
2603:
2599:
2595:
2587:
2583:
2576:
2573:
2570:
2541:
2537:
2530:
2512:
2509:
2506:
2498:
2494:
2483:
2480:
2477:
2448:
2444:
2437:
2436:
2435:
2401:
2397:
2368:
2321:
2317:
2300:
2247:
2243:
2236:
2232:
2229:
2226:
2219:
2185:
2181:
2152:
2148:
2131:
2123:
2122:
2121:
2081:
2077:
2066:
2057:
2030:
2027:
2024:
2016:
2012:
2001:
1998:
1995:
1978:
1974:
1967:
1949:
1945:
1939:
1936:
1931:
1928:
1924:
1920:
1912:
1908:
1901:
1898:
1895:
1878:
1874:
1867:
1866:
1865:
1831:
1827:
1810:
1775:
1771:
1754:
1719:
1715:
1692:
1688:
1671:
1656:
1647:
1633:
1613:
1591:
1587:
1549:
1528:
1501:
1498:
1495:
1487:
1483:
1472:
1469:
1466:
1446:
1442:
1435:
1417:
1413:
1407:
1404:
1399:
1396:
1392:
1388:
1380:
1376:
1369:
1366:
1363:
1343:
1339:
1332:
1331:
1330:
1302:
1298:
1278:
1240:
1236:
1219:
1198:
1195:
1175:
1154:
1151:
1134:
1125:
1116:
1107:
1098:
1094:
1086:
1078:
1069:
1060:
1059:of surfaces.
1058:
1054:
1053:optical flats
1050:
1045:
1044:monochromatic
1036:
1027:
1010:
1007:
1004:
996:
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981:
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966:
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939:
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837:
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733:
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667:
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631:
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533:
509:
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455:
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397:
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329:
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216:
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150:
146:
143:In optics, a
138:
134:
129:
121:
112:
110:
106:
102:
98:
94:
90:
85:
83:
79:
75:
74:camera lenses
71:
67:
63:
59:
55:
50:
48:
44:
41:
37:
33:
26:
21:
3344:
3335:
3326:
3317:
3299:
3295:
3287:
3268:
3222:
3218:
3208:
3181:
3177:
3164:
3129:
3125:
3095:
3091:
3028:vacuum pumps
3021:
3006:
2990:
2984:
2969:
2945:Thomas Young
2938:
2935:Isaac Newton
2926:Micrographia
2924:
2923:in 1665. In
2921:Robert Hooke
2915:
2874:
2849:Ellipsometry
2847:
2832:
2830:techniques.
2826:and various
2815:
2800:Applications
2775:
2749:
2743:
2735:
2643:
2291:
2068:
1661:
1520:
1121:
1104:
1095:
1091:
1066:
1041:
1025:
931:
529:
353:
234:
163:interference
142:
86:
54:soap bubbles
51:
31:
30:
3098:: 109–121.
3017:nitric acid
2917:Iridescence
2888:iridescence
1124:soap bubble
1110:Soap bubble
532:Snell's law
236:following:
47:wavelengths
36:light waves
3072:References
3046:coatings.
3044:dielectric
3036:sputtering
3347:, Wiley,
3002:butterfly
2985:In 1925,
2901:Tempering
2860:ρ
2792:buttercup
2776:Aglais io
2751:Aglais io
2740:In nature
2706:θ
2625:λ
2607:−
2584:θ
2577:
2513:λ
2495:θ
2484:
2233:λ
2031:λ
2013:θ
2002:
1950:λ
1932:−
1909:θ
1902:
1634:λ
1588:θ
1502:λ
1484:θ
1473:
1418:λ
1400:−
1377:θ
1370:
1011:λ
993:θ
982:
940:λ
904:θ
893:
845:θ
838:
821:θ
814:
801:−
753:θ
746:
721:θ
714:
702:−
683:θ
676:
597:θ
590:
562:θ
555:
506:θ
499:
484:θ
477:
460:¯
417:θ
410:
393:¯
375:¯
334:¯
308:−
300:¯
282:¯
174:π
149:nanometer
145:thin film
82:linewidth
58:oil films
43:interfere
40:thin film
3370:Category
3249:21159676
3200:24713039
3156:28228540
3050:See also
3024:fluorite
1650:Oil film
1101:Examples
1057:flatness
186:radians
68:used on
27:boundary
3349:Bibcode
3320:, Dover
3240:3107630
3147:5332578
2940:Opticks
2931:peacock
2882:History
354:Where,
105:mirrors
70:glasses
3336:Optics
3247:
3237:
3198:
3154:
3144:
3042:using
2999:morpho
2837:, the
2835:retina
2638:
2526:
2044:
1963:
1521:Where
1515:
1431:
530:Using
153:micron
137:Airbus
115:Theory
107:, and
3174:(PDF)
3030:made
3015:with
3013:glass
93:prism
62:water
25:lipid
3245:PMID
3196:PMID
3152:PMID
2955:and
2890:and
2398:<
2360:and
2318:<
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1828:>
1772:<
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72:and
56:and
3235:PMC
3227:doi
3223:278
3186:doi
3182:203
3142:PMC
3134:doi
3100:doi
2574:cos
2481:cos
1999:cos
1899:cos
1470:cos
1367:cos
979:cos
890:cos
835:cos
805:sin
743:sin
711:tan
673:cos
587:sin
552:sin
496:sin
474:tan
407:cos
151:to
133:ITO
91:or
60:on
3372::
3276:^
3257:^
3243:.
3233:.
3221:.
3217:.
3194:.
3180:.
3176:.
3150:.
3140:.
3130:14
3128:.
3124:.
3112:^
3094:.
3080:^
2758:.
952:.
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111:.
103:,
3351::
3251:.
3229::
3202:.
3188::
3158:.
3136::
3106:.
3102::
3096:1
2774:(
2721:)
2718:0
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2710:2
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2679:g
2676:n
2673:i
2670:t
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2007:(
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1925:(
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1467:d
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1414:)
1408:2
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1393:(
1389:=
1386:)
1381:2
1373:(
1364:d
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1355:l
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1340:2
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1199:1
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1152:=
1146:r
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1140:a
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1008:m
1005:=
1002:)
997:2
987:(
976:d
971:2
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963:2
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887:d
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874:2
871:=
860:)
854:)
849:2
841:(
830:)
825:2
817:(
809:2
798:1
792:(
788:d
783:2
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775:2
772:=
762:)
757:2
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725:2
717:(
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692:)
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668:d
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645:=
638:D
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632:O
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574:=
571:)
566:1
558:(
547:1
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510:1
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488:2
480:(
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465:=
456:D
453:A
426:)
421:2
413:(
403:d
398:=
389:C
386:B
380:=
371:B
368:A
339:)
330:D
327:A
321:(
316:1
312:n
305:)
296:C
293:B
287:+
278:B
275:A
269:(
264:2
260:n
256:=
253:D
250:P
247:O
217:2
213:n
204:1
200:n
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