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The descriptions of the achromat lens designs mention advantages of designs that do not produce "ghost" images. Historically, this was indeed a driving concern for lens makers up to the 19th century and a primary criterion for early optical designs. However, in the mid 20th century, the development
1750:
required by the achromat design. Other adjustable lens parameters include the thickness of each lens and the space between the two, all constrained only by the two required focal lengths. Normally, the free parameters are adjusted to minimize non-color-related optical aberrations.
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have a wide air space between the two elements. They were originally devised in the 19th century to allow much smaller flint glass elements down stream since flint glass was hard to produce and expensive. They are also lenses where the elements can not be cemented because
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remains after spherical and chromatic aberrations are corrected. In order to correct other aberrations, the front and back curvatures of each of the two lenses remain free parameters, since the color correction design only prescribes the net focal length of each lens,
1767:
Lens designs more complex than achromatic can improve the precision of color images by bringing more wavelengths into exact focus, but require more expensive types of glass, and more careful shaping and spacing of the combination of simple lenses:
182:, who understood their potential and was able to reproduce their design. Dollond applied for and was granted a patent on the technology in 1758, which led to bitter fights with other opticians over the right to make and sell achromatic doublets.
1369:
1254:
85:. Achromatic lenses are corrected to bring two wavelengths (typically red and blue) into focus on the same plane. Wavelengths in between these two then have better focus error than could be obtained with a simple lens.
119:
such as BK7, which has lower dispersion. The lens elements are mounted next to each other, often cemented together, and shaped so that the chromatic aberration of one is counterbalanced by that of the other.
1000:{\displaystyle {\begin{aligned}{\frac {1}{\ f_{1}\ }}+{\frac {1}{\ f_{2}\ }}&={\frac {1}{\ f_{\mathsf {dblt}}\ }}\ ,\\{\frac {1}{\ f_{1}\ V_{1}\ }}+{\frac {1}{\ f_{2}\ V_{2}\ }}&=0\ ;\end{aligned}}}
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715:
1813:); several of those lenses can be made with different types of glass, with slightly altered curvatures, in order to bring more colors into focus. The constraint is extra manufacturing cost, and
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201:
Several different types of achromat have been devised. They differ in the shape of the included lens elements as well as in the optical properties of their glass (most notably in their
171:. He realized the two components were for the same client and, after fitting the two parts together, noted the achromatic properties. Hall used the achromatic lens to build the first
620:, is a flint-first doublet. In contrast to the Fraunhofer doublet, it has a negative lens first followed by a positive lens. It needs stronger curvature than the Fraunhofer doublet.
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of the crown lens element is not quite equalled by the negative power of the flint lens element. Together they form a weak positive lens that will bring two different
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are mounted close, but not quite in contact. This design yields more degrees of freedom (one more free radius, length of the air space) to correct for
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1853:
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Early Clark lenses follow the
Fraunhofer design. After the late 1860s, they changed to the Littrow design, approximately equiconvex crown,
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1966:
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are positive-valued, the power of the second element in the doublet is negative when the first element is positive, and vice-versa.
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lenses to two different opticians, Edward
Scarlett and James Mann. They in turn sub-contracted the work to the same person,
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Theoretical considerations of the feasibility of correcting chromatic aberration were debated in the 18th century following
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281:
for the most part has eliminated the issue of ghost images, and modern optical designs are preferred for other merits.
717:
of the doublet and the two glasses to use. The choice of glass gives the mean refractive index, often written as
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148:
1941:– A review of the events of the invention of the achromatic doublet with emphasis on the roles of Hall, Bass,
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41:
Chromatic aberration of a single lens causes different wavelengths of light to have differing focal lengths.
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This leaves a continuum of different combinations of front and back lens curvatures for design tweaks (
159:. Hall wished to keep his work on the achromatic lenses a secret and contracted the manufacture of the
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denotes the first lens surface counted from the object. A doublet lens has four surfaces with radii
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The use of oil between the crown and flint eliminates the effect of ghosting, particularly where
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brings red and blue light to the same focus, and is the earliest example of an achromatic lens.
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1364:{\displaystyle \ {\frac {f_{2}}{\ f_{\mathsf {dblt}}\ }}={\frac {-V_{1}+V_{2}\;}{V_{2}}}~.}
778:). To make the linear dispersion of the system zero, the system must satisfy the equations
720:
2130:
278:
61:
In an achromatic lens, two wavelengths are brought into the same focus, here red and blue.
1249:{\displaystyle {\frac {f_{1}}{\ f_{\mathsf {dblt}}\ }}={\frac {+V_{1}-V_{2}\;}{V_{1}}}\ }
151:). Credit for the invention of the first achromatic doublet is often given to an English
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135:. Negative doublets, in which the negative-power element predominates, are also made.
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It can also increase light transmission slightly and reduce the impact of errors in
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Scientific
Instruments of the Seventeenth and Eighteenth Centuries and Their Makers
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Focus error for four types of lens, over the visible and near infrared spectrum.
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Lens that is designed to limit the effects of chromatic and spherical aberration
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such as F2, which has relatively high dispersion, and the other is a positive (
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positive is a convex first surface); negative radii curve toward the object (
152:
2013:. Press monograph. Vol. 163 (illustrated ed.). SPIE. p. 38.
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658:
The first-order design of an achromat involves choosing the overall power
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wavelengths into focus and must be manufactured with even more expensive
563:, thereby avoiding ghosting caused by reflections within the airspace.
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The first lens has positive refractive power, the second negative.
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because the lens surfaces of the two lenses have the same radii.
30:"Achromat" redirects here. For the form of color blindness, see
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other than just color are present in all lenses. For example,
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wavelengths into a common focus and requires costly materials
1454:{\displaystyle \ f_{1}=-f_{2}\ {\frac {\ V_{2}\ }{V_{1}}}\ ,}
175:, but his invention did not become widely known at the time.
1901:
Astronomy; A history of man's investigation of the universe
255:. Surfaces with positive radii curve away from the object (
321:
and a complementary-curved second flint glass lens (with
2010:
Optics Made Clear: The nature of light and how We Use it
440:. In a Fraunhofer doublet, the dissimilar curvatures of
147:'s statement that such a correction was impossible (see
710:{\displaystyle \ {\frac {1}{\ f_{\mathsf {dblt}}\ }}\ }
95:, which is composed of two individual lenses made from
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1958:
Techniques in microscopy for biomedical applications
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A Littrow doublet can produce a ghost image between
178:In the late 1750s, Bass mentioned Hall's lenses to
2053:. Bellingham, WA: SPIE Press. p. 174 ff.
1801:In theory, the process can continue indefinitely:
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2034:Warner, Deborah Jean; Ariail, Robert B. (1995).
1684:for lens 2) that will all produce the same
1809:typically have six or more simple lenses (e.g.
1873:Stargazer: the life and times of the telescope
123:In the most common type (shown), the positive
8:
2038:(2nd ed.). Willmann-Bell. p. 174.
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193:, an improvement on the achromat, in 1763.
2070:. Cambridge University Press. p. 55.
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289:Uses an equiconvex crown glass lens (i.e.
2036:Alvan Clark & Sons, Artists In Optics
1955:Dokland, Terje; Ng, Mary Mah-Lee (2006).
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376:Fraunhofer doublet (Fraunhofer objective)
340:The back of the flint glass lens is flat
77:that is designed to limit the effects of
1930:Museum of the History of Science, Oxford
103:. Typically, one element is a negative (
88:The most common type of achromat is the
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1876:. Allen & Unwin. pp. 140–55.
1797:and to considerably tighter tolerances
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1048:{\displaystyle \ {\frac {1}{\ f\ }}\ }
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273:negative is a concave first surface).
1922:"Peter Dollond answers Jesse Ramsden"
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2093:Basic Optics and Optical Instruments
545:to create a focus mismatch between
224:that define the optically relevant
1817:of improved image for the effort.
1078:. Solving these two equations for
616:The Steinheil doublet, devised by
25:
774:(for the reciprocal of the glass
744:(for the refractive index at the
2108:
650:have different absolute values.
527:By about 1880, Clark lenses had
1848:, Portman Books, London 1989
228:lens surfaces. By convention,
1:
749:"d" spectral line wavelength
155:and amateur optician named
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2051:Fundamental Optical Design
2007:Wolfe, William L. (2007).
1469:Removing other aberrations
536:set slightly shorter than
99:with different amounts of
29:
1743:{\displaystyle \ f_{2}\ }
1710:{\displaystyle \ f_{1}\ }
1677:{\displaystyle \ R_{4}\ }
1644:{\displaystyle \ R_{3}\ }
1611:{\displaystyle \ R_{2}\ }
1578:{\displaystyle \ R_{1}\ }
1545:{\displaystyle \ f_{2}~.}
1509:{\displaystyle \ f_{1}\ }
1137:{\displaystyle \ f_{2}\ }
1104:{\displaystyle \ f_{1}\ }
618:Carl August von Steinheil
2064:Manly, Peter L. (1995).
1903:, Rathbone Books, 1962,
1755:Further color correction
430:is usually greater than
149:History of the telescope
1987:Encyclopædia Britannica
1785:superachromatic lenses
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2049:Kidger, M.J. (2002).
1870:Watson, Fred (2007).
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737:{\displaystyle n_{d}}
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131:of light to a common
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2117:at Wikimedia Commons
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173:achromatic telescope
83:spherical aberration
1983:"Chester Moor Hall"
1815:diminishing returns
1773:apochromatic lenses
1474:Optical aberrations
461:optical aberrations
2067:Unusual Telescopes
1844:Daumas, Maurice,
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567:Oil-spaced doublet
212:In the following,
203:optical dispersion
157:Chester Moore Hall
115:) element made of
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51:achromatic doublet
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18:Achromatic doublet
2115:Achromatic lenses
2113:Media related to
2077:978-0-521-48393-3
1883:978-1-74175-383-7
1854:978-0-7134-0727-3
1811:double-Gauss lens
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2103:External links
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1961:. p. 23.
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992:
986:
983:
980:
978:
968:
964:
955:
951:
943:
938:
927:
923:
914:
910:
902:
897:
896:
893:
878:
875:
872:
869:
864:
856:
851:
848:
846:
836:
832:
824:
819:
808:
804:
796:
791:
790:
763:
731:
727:
694:
691:
688:
685:
680:
672:
655:
652:
646:
637:
629:Dialyte lenses
625:
622:
613:
610:
604:
595:
584:
577:
568:
565:
559:
550:
541:
532:
521:
514:
503:
496:
484:
477:
468:
465:
455:
446:
436:
426:
417:
407:
398:
386:
377:
374:
368:
359:
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334:
327:
315:
308:
295:
286:
283:
269:
260:
251:
242:
233:
198:
195:
185:Dollond's son
140:
137:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
2148:
2137:
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2132:
2129:
2128:
2126:
2116:
2111:
2107:
2106:
2102:
2094:
2087:
2084:
2079:
2073:
2069:
2068:
2060:
2057:
2052:
2045:
2042:
2037:
2030:
2027:
2022:
2020:9780819463074
2016:
2012:
2011:
2003:
2000:
1988:
1984:
1978:
1975:
1970:
1968:981-256-434-9
1964:
1960:
1959:
1951:
1948:
1944:
1931:
1927:
1923:
1916:
1913:
1910:
1906:
1902:
1898:
1893:
1890:
1885:
1879:
1875:
1874:
1866:
1864:
1862:
1858:
1855:
1851:
1847:
1841:
1838:
1832:
1828:
1825:
1824:
1820:
1818:
1816:
1812:
1808:
1804:
1796:
1792:
1788:
1786:
1783:
1780:
1776:
1774:
1771:
1770:
1769:
1761:
1754:
1752:
1732:
1728:
1699:
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1666:
1662:
1633:
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1600:
1596:
1567:
1563:
1539:
1531:
1527:
1498:
1494:
1481:
1480:
1475:
1468:
1466:
1464:
1448:
1438:
1434:
1424:
1420:
1405:
1401:
1397:
1394:
1389:
1385:
1358:
1348:
1344:
1336:
1332:
1328:
1323:
1319:
1315:
1309:
1283:
1273:
1269:
1236:
1232:
1224:
1220:
1216:
1211:
1207:
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1157:
1147:
1146:
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1126:
1122:
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1058:
1033:
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1013:
990:
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979:
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609:
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576:
566:
564:
558:
549:
540:
531:
520:
513:
502:
495:
483:
476:
467:Clark doublet
466:
464:
462:
454:
445:
435:
425:
416:
406:
397:
385:
375:
373:
367:
358:
346:
333:
326:
314:
307:
294:
284:
282:
280:
274:
268:
259:
250:
241:
232:
227:
223:
219:
210:
208:
204:
196:
194:
192:
189:invented the
188:
183:
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176:
174:
170:
166:
162:
158:
154:
150:
146:
138:
136:
134:
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118:
114:
110:
106:
102:
98:
94:
93:
86:
84:
80:
76:
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33:
32:achromatopsia
19:
2092:
2086:
2066:
2059:
2050:
2044:
2035:
2029:
2009:
2002:
1990:. Retrieved
1986:
1977:
1957:
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1943:John Dollond
1935:November 27,
1933:. Retrieved
1925:
1915:
1900:
1892:
1872:
1845:
1840:
1800:
1790:
1778:
1766:
1478:
1472:
1463:Abbe numbers
1373:
1057:focal length
1009:
657:
643:
634:
627:
615:
601:
592:
581:
574:
570:
556:
547:
538:
529:
518:
511:
500:
493:
481:
474:
470:
452:
443:
433:
423:
414:
404:
395:
383:
379:
365:
356:
344:
331:
324:
312:
305:
292:
288:
277:of advanced
275:
266:
257:
248:
239:
230:
216:denotes the
211:
200:
184:
180:John Dollond
177:
142:
122:
89:
87:
70:
66:
64:
50:
1992:16 February
1945:and others.
1827:Barlow lens
753:Abbe number
751:), and the
207:Abbe number
169:George Bass
129:wavelengths
117:crown glass
109:flint glass
90:achromatic
2125:Categories
1897:Fred Hoyle
1833:References
1012:lens power
1010:where the
776:dispersion
746:Fraunhofer
226:refracting
191:apochromat
101:dispersion
1926:Sphaera 8
1920:J. A. B.
1398:−
1316:−
1217:−
153:barrister
79:chromatic
1909:62-14108
1821:See also
1805:used in
1461:and the
246:through
71:achromat
1807:cameras
624:Dialyte
222:spheres
220:of the
139:History
105:concave
97:glasses
92:doublet
2131:Lenses
2074:
2017:
1965:
1907:
1880:
1852:
1789:bring
1777:bring
1738:
1725:
1705:
1692:
1672:
1659:
1639:
1626:
1606:
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1573:
1560:
1537:
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1430:
1417:
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1382:
1374:Since
1356:
1304:
1280:
1264:
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1192:
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1132:
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699:
675:
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654:Design
402:, and
389:> 0
298:> 0
218:radius
145:Newton
113:convex
1779:three
301:with
197:Types
187:Peter
165:flint
161:crown
133:focus
125:power
73:is a
2072:ISBN
2015:ISBN
1994:2019
1963:ISBN
1937:2017
1905:LCCN
1878:ISBN
1850:ISBN
1791:four
1717:and
1651:and
1585:and
1479:coma
1256:and
1111:and
641:and
599:and
554:and
508:and
450:and
363:and
163:and
81:and
75:lens
1014:is
350:= ∞
209:).
205:or
69:or
65:An
49:An
2127::
1985:.
1928:.
1924:.
1899:,
1860:^
608:.
580:≈
517:≫
499:≃
480:=
463:.
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352:).
342:(
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330:=
311:=
2080:.
2023:.
1996:.
1971:.
1939:.
1886:.
1733:2
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1663:R
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1568:1
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1540:.
1532:2
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1439:1
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1402:f
1395:=
1390:1
1386:f
1359:.
1349:2
1345:V
1337:2
1333:V
1329:+
1324:1
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1310:=
1298:t
1295:l
1292:b
1289:d
1284:f
1274:2
1270:f
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1233:V
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1198:=
1186:t
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1180:b
1177:d
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1127:2
1123:f
1094:1
1090:f
1066:f
1034:f
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991:;
985:0
982:=
967:2
963:V
954:2
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937:+
926:1
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913:1
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871:b
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863:f
855:1
850:=
835:2
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823:1
818:+
807:1
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762:V
730:d
726:n
693:t
690:l
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684:d
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671:1
647:3
644:R
638:2
635:R
605:3
602:R
596:2
593:R
588:.
585:3
582:R
578:2
575:R
560:3
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551:2
548:R
542:2
539:R
533:3
530:R
525:.
522:3
519:R
515:4
512:R
504:2
501:R
497:3
494:R
488:,
485:2
482:R
478:1
475:R
456:3
453:R
447:2
444:R
442:−
437:3
434:R
432:−
427:4
424:R
418:2
415:R
413:−
408:3
405:R
399:2
396:R
394:−
387:1
384:R
369:3
366:R
360:2
357:R
348:4
345:R
335:2
332:R
328:3
325:R
319:)
316:2
313:R
309:1
306:R
304:−
296:1
293:R
270:1
267:R
261:1
258:R
252:2
249:R
243:1
240:R
234:1
231:R
214:R
34:.
20:)
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