110:(bent) from their normal straight path. This is due to the variation of refractive index between the hot, less dense air at the surface of the road, and the denser cool air above it. The variation in temperature (and thus density) of the air causes a gradient in its refractive index, causing it to increase with height. This index gradient causes refraction of light rays (at a shallow angle to the road) from the sky, bending them into the eye of the viewer, with their apparent location being the road's surface.
282:– While point-by-point exposing the pre-designed structure an exposure dose is varied (scanning speed, laser power, etc.). This corresponds to spatially tunable monomer-to-polymer degree-of-conversion resulting to a different refractive index. The method is applicable to free-form micro-optical elements and multi-component optics.
301:, it involves a spherical index function and would be expected to be spherical in shape as well. This lens, however, is impractical to make and has little usefulness since only points on the surface and within the lens are sharply imaged and extended objects suffer from extreme aberrations. In 1905,
305:
used a dipping technique creating a gelatin cylinder with a refractive index gradient that varied symmetrically with the radial distance from the axis. Disk-shaped slices of the cylinder were later shown to have plane faces with radial index distribution. He showed that even though the faces of the
113:
The Earth's atmosphere acts as a GRIN lens, allowing observers to see the sun for a few minutes after it is actually below the horizon, and observers can also view stars that are below the horizon. This effect also allows for observation of electromagnetic signals from satellites after they have
160:
In imaging applications, GRIN lenses are mainly used to reduce aberrations. The design of such lenses involves detailed calculations of aberrations as well as efficient manufacture of the lenses. A number of different materials have been used for GRIN lenses including optical glasses, plastics,
319:
applications. Some years later several new techniques have been developed to fabricate lenses of the Wood type. Since then at least the thinner GRIN lenses can possess surprisingly good imaging properties considering their very simple mechanical construction, while thicker GRIN lenses found
314:
that focuses incident parallel rays of light onto a point on the opposite surface of the lens. This also limited the applications of the lens because it was difficult to use it to focus visible light; however, it had some usefulness in
600:
1052:
Zukauskas, Albertas; Matulaitiene, Ieva; Paipulas, Domas; Niaura, Gedinimas; Malinauskas, Mangirdas; Gadonas, Roaldas (2015). "Tuning the refractive index in 3D direct laser writing lithography: towards GRIN microoptics".
264:
ions in the glass are partially exchanged with lithium ones, with a larger amount of exchange occurring at the edge. Thus the sample obtains a gradient material structure and a corresponding gradient of the refractive
98:
of the lens varies from approximately 1.406 in the central layers down to 1.386 in less dense layers of the lens. This allows the eye to image with good resolution and low aberration at both short and long distances.
695:
612:
The refractive index gradient of GRIN lenses can be mathematically modelled according to the method of production used. For example, GRIN lenses made from a radial gradient index material, such as
306:
lens were flat, they acted like converging and diverging lens depending on whether the index was a decreasing or increasing relative to the radial distance. In 1964, a posthumous book of
455:
126:
The ability of GRIN lenses to have flat surfaces simplifies the mounting of the lens, which makes them useful where many very small lenses need to be mounted together, such as in
377:
609:
The light path integral is able to characterize the path of light through the lens in a qualitative manner, such that the lens may be easily reproduced in the future.
206:
An axial gradient lens has been used to concentrate sunlight onto solar cells, capturing as much as 90% of incident light when the sun is not at an optimal angle.
1744:
106:
of a pool of water appearing on a road on a hot day. The pool is actually an image of the sky, apparently located on the road since light rays are being
203:
Antireflection coatings are typically effective for narrow ranges of frequency or angle of incidence. Graded-index materials are less constrained.
474:
1296:
1031:
A digest of technical papers presented at the
Topical Meeting on Gradient Index Optical Imaging Systems, May 15-16, 1979, Rochester, New York
1235:
Flores-Arias, M.T.; Bao, C.; Castelo, A.; Perez, M.V.; Gomez-Reino, C. (2006-10-15). "Crossover interconnects in gradient-index planar optics".
1855:
1151:
1089:
231:– Involving the deposition of different glass with varying refractive indexes, onto a surface to produce a cumulative refractive change.
1211:
764:
812:
622:
74:
typical of traditional spherical lenses. Gradient-index lenses may have a refraction gradient that is spherical, axial, or radial.
28:
469:
are used, this equation is modified to incorporate the change in arc length for a spherical gradient, to each physical dimension:
828:
1769:
1565:
225:-rich glass is bombarded with neutrons to cause a change in the boron concentration, and thus the refractive index of the lens.
295:
suggested a lens whose refractive index distribution would allow for every region of space to be sharply imaged. Known as the
200:, in that all modes of the GRIN fibres propagate at the same speed, allowing for a higher temporal bandwidth for the fibre.
1681:
1658:
1514:
1289:
399:
relative to its value for any nearby curve joining the two points. The light path integral is given by the equation
1105:
228:
1001:
Keck D B and
Olshansky R, "Optical Waveguide Having Optimal Index Gradient," U.S. Patent 3,904,268 (9 Sept. 1975).
1545:
1466:
1356:
1029:
Mohr, R K; Wilder, J A; Macedo, P B; Gupta, P K (1979). "Graded index lenses by the molecular stuffing process".
197:
965:
1446:
185:
1019:
Hensler J R, "Method of
Producing a Refractive Index Gradient in Glass," U.S. Patent 3,873,408 (25 Mar. 1975).
405:
1809:
1676:
1550:
1282:
1126:
1010:
Moore R S, "Plastic
Optical Element Having Refractive Index Gradient," U.S. Patent 3,718,383 (Feb. 1973).
1850:
1426:
380:
1774:
1648:
1396:
1386:
1244:
1062:
931:
466:
332:
An inhomogeneous gradient-index lens possesses a refractive index whose change follows the function
279:
193:
1721:
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1441:
852:
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1638:
1613:
292:
181:
272:
separation of a specific glass causes pores to form, which can later be filled using a variety of
1701:
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1371:
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885:
735:
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177:
71:
335:
1814:
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1217:
1207:
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808:
770:
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243:
180:) are made with a radially-varying refractive index profile; this design strongly reduces the
115:
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188:. The radial variation in refractive index allows for a sinusoidal height distribution of
170:
150:
1481:
1248:
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83:
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67:
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154:
17:
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Shirk J S, Sandrock M, Scribner D, Fleet E, Stroman R, Baer E, Hiltner A. (2006)
1824:
1789:
1509:
1391:
127:
134:. The flat surface also allows a GRIN lens to be easily optically aligned to a
1819:
1784:
1653:
1421:
1416:
1161:
803:
Tsiboulia, A B (2003). "Gradient Index (GRIN) Lenses". In Ronald G. Driggers.
1264:
1038:
595:{\displaystyle L=\int _{S_{o}}^{S}n(x,y,z){\sqrt {x'^{2}+y'^{2}+z'^{2}}}\,ds}
1686:
1585:
774:
316:
257:
162:
143:
107:
91:
1221:
1188:
1175:
Marchand, E.W. (1976). "Third-order aberrations of the photographic Wood".
1074:
966:"Pyramid lenses catch light from any angle to boost solar cell efficiency"
917:"Wide-angle and broadband graded-refractive-index antireflection coatings"
1804:
1575:
1351:
1346:
901:
379:
of the coordinates of the region of interest in the medium. According to
59:
1524:
1274:
253:
239:
218:
90:
is the most obvious example of gradient-index optics in nature. In the
829:"Gradient Index Lenses Selection Guide: Types, Features, Applications"
31:
A gradient-index lens with a parabolic variation of refractive index (
27:
1600:
1406:
261:
103:
55:
1090:"Solutions of problems: (prob. 3, vol. VIII. p. 188)"
1519:
1486:
1436:
1320:
1305:
222:
26:
102:
Another example of gradient index optics in nature is the common
39:). The lens focuses light in the same way as a conventional lens.
915:
Zhang, Jun-Chao; Xiong, Li-Min; Fang, Ming; He, Hong-Bo (2013).
1278:
1033:. paper WA1. Washington, D C: Optical Society of America.
196:. This differs from traditional optical fibres, which rely on
87:
759:(2nd ed.). Reading, Mass.: Addison-Wesley. p. 178.
690:{\displaystyle n_{r}=n_{o}\left(1-{\frac {Ar^{2}}{2}}\right)}
66:
of a material. Such gradual variation can be used to produce
192:
within the fibre, preventing the rays from leaving the
625:
477:
408:
338:
276:
or concentration of salts to give a varying gradient.
246:
at varying intensities to give a refractive gradient.
616:, have a refractive index that varies according to:
1735:
1667:
1599:
1533:
1495:
1339:
1313:
70:with flat surfaces, or lenses that do not have the
807:, Volume 1. New York, NY: Marcel Dekker. 675-683.
689:
594:
449:
371:
823:
821:
1110:. New York: Dover Publications. pp. 76–79.
1745:Conservation and restoration of glass objects
1290:
1094:The Cambridge and Dublin Mathematical Journal
853:"In Vivo Calcium Imaging: The Ultimate Guide"
721:is the design index on the optical axis, and
8:
1146:. Berkeley: University of California Press.
1107:The scientific papers of James Clerk Maxwell
252:– Glass is immersed into a liquid melt with
214:GRIN lenses are made by several techniques:
1297:
1283:
1275:
1131:. New York; London: Macmillan. p. 71.
1177:Journal of the Optical Society of America
670:
660:
643:
630:
624:
585:
576:
558:
540:
530:
500:
493:
488:
476:
440:
431:
424:
419:
407:
337:
450:{\displaystyle L=\int _{S_{o}}^{S}n\,ds}
879:
877:
875:
873:
871:
869:
747:
706:is the refractive index at a distance,
573:
555:
537:
58:covering optical effects produced by a
310:was published in which he described a
1104:Nivin, William Davidson, ed. (1890).
755:Hecht, Eugene; Zając, Alfred (1987).
7:
799:
797:
805:Encyclopedia of Optical Engineering
465:is the arc length of the curve. If
114:descended below the horizon, as in
25:
886:"Gradient-index optics: a review"
142:output, making it applicable for
1815:Radioactive waste vitrification
1770:Glass fiber reinforced concrete
242:is partially polymerized using
1142:Luneburg, Rudolf Karl (1964).
964:Irving, Michael (2022-06-28).
605:where prime corresponds to d/d
527:
509:
366:
348:
1:
1856:Glass engineering and science
1682:Chemically strengthened glass
1144:Mathematical Theory of Optics
1088:Maxwell, James Clerk (1854).
1055:Laser & Photonics Reviews
944:10.1088/1674-1056/22/4/044201
1515:Glass-ceramic-to-metal seals
1257:10.1016/j.optcom.2006.05.049
1206:. New York: Academic Press.
461:is the refractive index and
391:joining any two points of a
1202:Marchand, Erich W. (1978).
383:, the light path integral (
1872:
1125:, Robert Williams (1905).
372:{\displaystyle n=f(x,y,z)}
229:Chemical vapour deposition
1546:Chemical vapor deposition
1467:Ultra low expansion glass
1357:Borophosphosilicate glass
884:Moore, Duncan T. (1980).
198:total internal reflection
1785:Glass-reinforced plastic
1447:Sodium hexametaphosphate
186:multi-mode optical fiber
176:Certain optical fibres (
35:) with radial distance (
1677:Anti-reflective coating
1551:Glass batch calculation
1432:Photochromic lens glass
725:is a positive constant.
155:optogenetic stimulation
1189:10.1364/JOSA.66.001326
1075:10.1002/lpor.201500170
691:
596:
451:
373:
40:
1810:Prince Rupert's drops
1659:Transparent materials
1619:Gradient-index optics
1427:Phosphosilicate glass
1237:Optics Communications
1204:Gradient index optics
692:
597:
467:Cartesian coordinates
452:
374:
256:ions. As a result of
30:
1775:Glass ionomer cement
1649:Photosensitive glass
1576:Liquidus temperature
1397:Fluorosilicate glass
902:10.1364/AO.19.001035
623:
475:
406:
336:
320:application e.g. in
298:Maxwell fisheye lens
280:Direct laser writing
1795:Glass-to-metal seal
1717:Self-cleaning glass
1639:Optical lens design
1249:2006OptCo.266..490F
1067:2015LPRv....9..706Z
936:2013ChPhB..22d4201Z
505:
436:
178:graded-index fibres
18:Gradient index lens
1780:Glass microspheres
1702:Hydrogen darkening
1624:Hydrogen darkening
1372:Chalcogenide glass
1362:Borosilicate glass
736:Graded-index fiber
687:
592:
484:
447:
415:
381:Fermat's principle
369:
41:
1833:
1832:
1750:Glass-coated wire
1722:sol–gel technique
1707:Insulated glazing
1644:Photochromic lens
1629:Optical amplifier
1581:sol–gel technique
1183:(12): 1326–1330.
1153:978-0-5203-2826-6
988:Sinai P, (1970).
924:Chinese Physics B
680:
583:
387:), taken along a
244:ultraviolet light
116:radio occultation
54:is the branch of
16:(Redirected from
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1571:Ion implantation
1326:Glass transition
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896:(7): 1035–1038.
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614:SELFOC Microlens
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182:modal dispersion
96:refractive index
64:refractive index
21:
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1870:
1866:
1865:
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1836:
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1834:
1829:
1765:Glass electrode
1760:Glass databases
1737:
1731:
1669:
1663:
1595:
1529:
1505:Bioactive glass
1491:
1477:Vitreous enamel
1462:Thoriated glass
1457:Tellurite glass
1442:Soda–lime glass
1412:Gold ruby glass
1382:Cranberry glass
1335:
1309:
1303:
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1229:
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1128:Physical Optics
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1103:
1102:(reprinted by:
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855:. Mightex. 2019
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334:
333:
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289:
268:Ion stuffing –
212:
171:sodium chloride
151:calcium imaging
146:as well as for
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15:
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1727:Tempered glass
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1699:
1697:DNA microarray
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1692:Dealkalization
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1566:Glass modeling
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1497:Glass-ceramics
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1308:science topics
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1243:(2): 490–494.
1227:
1213:978-0124707504
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1080:
1061:(6): 706–712.
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990:Applied Optics
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890:Applied Optics
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833:Engineering360
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766:978-0201116090
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308:R. K. Luneburg
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277:
266:
247:
236:polymerisation
232:
226:
221:irradiation –
211:
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123:
120:
118:measurements.
79:
76:
44:Gradient-index
24:
14:
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1634:Optical fiber
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1591:Vitrification
1589:
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1561:Glass melting
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1556:Glass forming
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1472:Uranium glass
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1452:Soluble glass
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1851:Fiber optics
1800:Porous glass
1755:Safety glass
1712:Porous glass
1670:modification
1618:
1482:Wood's glass
1402:Fused quartz
1377:Cobalt glass
1331:Supercooling
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122:Applications
112:
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1825:Glass fiber
1790:Glass cloth
1534:Preparation
1510:CorningWare
1392:Flint glass
1387:Crown glass
1340:Formulation
710:, from the
322:Selfoc rods
293:J C Maxwell
210:Manufacture
72:aberrations
1840:Categories
1820:Windshield
1654:Refraction
1614:Dispersion
1422:Milk glass
1417:Lead glass
1162:1149437946
975:2022-06-28
859:2021-07-11
838:2021-07-11
789:NRL Review
742:References
397:stationary
303:R. W. Wood
157:in brain.
140:collimated
1687:Corrosion
1586:Viscosity
1541:Annealing
1265:0030-4018
1039:489755284
970:New Atlas
658:−
486:∫
417:∫
317:microwave
291:In 1854,
258:diffusion
163:germanium
144:endoscopy
108:refracted
92:human eye
78:In nature
1805:Pre-preg
1609:Achromat
1352:Bioglass
1347:AgInSbTe
791:pp 53–61
775:13761389
730:See also
697:, where
574:′
556:′
538:′
457:, where
234:Partial
132:scanners
60:gradient
1736:Diverse
1668:Surface
1525:Zerodur
1245:Bibcode
1222:4497777
1100:: 9–11.
1063:Bibcode
932:Bibcode
287:History
254:lithium
240:monomer
219:Neutron
148:in vivo
86:of the
62:of the
1846:Optics
1738:topics
1601:Optics
1407:GeSbTe
1314:Basics
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393:medium
328:Theory
265:index.
262:sodium
169:, and
104:mirage
94:, the
68:lenses
56:optics
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1487:ZBLAN
1321:Glass
1306:Glass
920:(PDF)
395:, is
274:salts
270:Phase
223:Boron
184:of a
136:fiber
1261:ISSN
1218:OCLC
1208:ISBN
1158:OCLC
1148:ISBN
1123:Wood
1035:OCLC
951:2016
809:ISBN
771:OCLC
761:ISBN
312:lens
194:core
190:rays
153:and
130:and
84:lens
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48:GRIN
1253:doi
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