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27:
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35:
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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
1739:
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.
773:
620:
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
1471:
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,
1756:
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:
171:, 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.
1358:
1243:
74:. 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.
108:
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.
989:{\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}}}
1448:
704:
1802:); 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
778:
190:
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
160:. 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
609:, 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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1139:
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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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Early Clark lenses follow the
Fraunhofer design. After the late 1860s, they changed to the Littrow design, approximately equiconvex crown,
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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.
137:
1918:
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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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270:
for the most part has eliminated the issue of ghost images, and modern optical designs are preferred for other merits.
2007:
1955:
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of the doublet and the two glasses to use. The choice of glass gives the mean refractive index, often written as
2124:
1930:– A review of the events of the invention of the achromatic doublet with emphasis on the roles of Hall, Bass,
1006:
30:
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 (
148:. Hall wished to keep his work on the achromatic lenses a secret and contracted the manufacture of the
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226:
denotes the first lens surface counted from the object. A doublet lens has four surfaces with radii
101:
93:
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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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1997:
1945:
1910:
1353:{\displaystyle \ {\frac {f_{2}}{\ f_{\mathsf {dblt}}\ }}={\frac {-V_{1}+V_{2}\;}{V_{2}}}~.}
767:). To make the linear dispersion of the system zero, the system must satisfy the equations
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161:
149:
105:
71:
67:
50:
In an achromatic lens, two wavelengths are brought into the same focus, here red and blue.
8:
1803:
1748:
1238:{\displaystyle {\frac {f_{1}}{\ f_{\mathsf {dblt}}\ }}={\frac {+V_{1}-V_{2}\;}{V_{1}}}\ }
764:
140:). Credit for the invention of the first achromatic doublet is often given to an English
89:
1971:
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124:. 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
26:
1835:
Scientific
Instruments of the Seventeenth and Eighteenth Centuries and Their Makers
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267:
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Focus error for four types of lens, over the visible and near infrared spectrum.
16:
Lens that is designed to limit the effects of chromatic and spherical aberration
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121:
100:
such as F2, which has relatively high dispersion, and the other is a positive (
80:
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positive is a convex first surface); negative radii curve toward the object (
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20:
2002:. Press monograph. Vol. 163 (illustrated ed.). SPIE. p. 38.
1931:
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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
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552:, thereby avoiding ghosting caused by reflections within the airspace.
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117:
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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.
19:"Achromat" redirects here. For the form of color blindness, see
2098:
1795:
210:
206:
1465:
other than just color are present in all lenses. For example,
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wavelengths into a common focus and requires costly materials
1443:{\displaystyle \ f_{1}=-f_{2}\ {\frac {\ V_{2}\ }{V_{1}}}\ ,}
164:, but his invention did not become widely known at the time.
85:
364:
34:
1890:
Astronomy; A history of man's investigation of the universe
244:. Surfaces with positive radii curve away from the object (
310:
and a complementary-curved second flint glass lens (with
1999:
Optics Made Clear: The nature of light and how We Use it
429:. In a Fraunhofer doublet, the dissimilar curvatures of
136:'s statement that such a correction was impossible (see
699:{\displaystyle \ {\frac {1}{\ f_{\mathsf {dblt}}\ }}\ }
84:, which is composed of two individual lenses made from
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1947:
Techniques in microscopy for biomedical applications
343:
A Littrow doublet can produce a ghost image between
167:In the late 1750s, Bass mentioned Hall's lenses to
2042:. Bellingham, WA: SPIE Press. p. 174 ff.
1790:In theory, the process can continue indefinitely:
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2023:Warner, Deborah Jean; Ariail, Robert B. (1995).
1673:for lens 2) that will all produce the same
1798:typically have six or more simple lenses (e.g.
1862:Stargazer: the life and times of the telescope
112:In the most common type (shown), the positive
1457:
2022:
2027:(2nd ed.). Willmann-Bell. p. 174.
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1852:
1850:
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182:, an improvement on the achromat, in 1763.
2059:. Cambridge University Press. p. 55.
1330:
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278:Uses an equiconvex crown glass lens (i.e.
2025:Alvan Clark & Sons, Artists In Optics
1944:Dokland, Terje; Ng, Mary Mah-Lee (2006).
1943:
400:is set close to, but not quite equal to,
365:Fraunhofer doublet (Fraunhofer objective)
329:The back of the flint glass lens is flat
66:that is designed to limit the effects of
1919:Museum of the History of Science, Oxford
1847:
1747:
92:. Typically, one element is a negative (
77:The most common type of achromat is the
45:
33:
25:
2112:
2037:
1902:
1865:. Allen & Unwin. pp. 140–55.
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1786:and to considerably tighter tolerances
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1037:{\displaystyle \ {\frac {1}{\ f\ }}\ }
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262:negative is a concave first surface).
2052:
1995:
1911:"Peter Dollond answers Jesse Ramsden"
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2082:Basic Optics and Optical Instruments
1908:
600:
534:to create a focus mismatch between
213:that define the optically relevant
13:
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1806:of improved image for the effort.
1067:. Solving these two equations for
605:The Steinheil doublet, devised by
273:
14:
2136:
2091:
763:(for the reciprocal of the glass
733:(for the refractive index at the
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639:have different absolute values.
516:By about 1880, Clark lenses had
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2031:
2016:
1989:
1964:
1937:
1879:
1837:, Portman Books, London 1989
217:lens surfaces. By convention,
1:
1821:
738:"d" spectral line wavelength
7:
1809:
144:and amateur optician named
10:
2141:
2040:Fundamental Optical Design
1996:Wolfe, William L. (2007).
1458:Removing other aberrations
612:
525:set slightly shorter than
127:
88:with different amounts of
18:
1732:{\displaystyle \ f_{2}\ }
1699:{\displaystyle \ f_{1}\ }
1666:{\displaystyle \ R_{4}\ }
1633:{\displaystyle \ R_{3}\ }
1600:{\displaystyle \ R_{2}\ }
1567:{\displaystyle \ R_{1}\ }
1534:{\displaystyle \ f_{2}~.}
1498:{\displaystyle \ f_{1}\ }
1126:{\displaystyle \ f_{2}\ }
1093:{\displaystyle \ f_{1}\ }
642:
607:Carl August von Steinheil
2053:Manly, Peter L. (1995).
1892:, Rathbone Books, 1962,
1744:Further color correction
419:is usually greater than
185:
138:History of the telescope
1976:Encyclopædia Britannica
1774:superachromatic lenses
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96:) element made out of
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2125:Microscope components
2038:Kidger, M.J. (2002).
1859:Watson, Fred (2007).
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726:{\displaystyle n_{d}}
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120:of light to a common
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2106:at Wikimedia Commons
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381:is set greater than
162:achromatic telescope
72:spherical aberration
1972:"Chester Moor Hall"
1804:diminishing returns
1762:apochromatic lenses
1463:Optical aberrations
450:optical aberrations
2056:Unusual Telescopes
1833:Daumas, Maurice,
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556:Oil-spaced doublet
201:In the following,
192:optical dispersion
146:Chester Moore Hall
104:) element made of
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40:achromatic doublet
32:
2104:Achromatic lenses
2102:Media related to
2066:978-0-521-48393-3
1872:978-1-74175-383-7
1843:978-0-7134-0727-3
1800:double-Gauss lens
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1060:{\displaystyle f}
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756:{\displaystyle V}
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601:Steinheil doublet
479:and a flint with
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2084:. p. AJ-4.
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56:achromatic lens
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2092:External links
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1950:. p. 23.
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1176:
1173:
1170:
1167:
1162:
1152:
1148:
1117:
1113:
1084:
1080:
1056:
1024:
1017:
997:
996:
981:
975:
972:
969:
967:
957:
953:
944:
940:
932:
927:
916:
912:
903:
899:
891:
886:
885:
882:
867:
864:
861:
858:
853:
845:
840:
837:
835:
825:
821:
813:
808:
797:
793:
785:
780:
779:
752:
720:
716:
683:
680:
677:
674:
669:
661:
644:
641:
635:
626:
618:Dialyte lenses
614:
611:
602:
599:
593:
584:
573:
566:
557:
554:
548:
539:
530:
521:
510:
503:
492:
485:
473:
466:
457:
454:
444:
435:
425:
415:
406:
396:
387:
375:
366:
363:
357:
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336:
323:
316:
304:
297:
284:
275:
272:
258:
249:
240:
231:
222:
187:
184:
174:Dollond's son
129:
126:
15:
9:
6:
4:
3:
2:
2137:
2126:
2123:
2121:
2118:
2117:
2115:
2105:
2100:
2096:
2095:
2083:
2076:
2068:
2062:
2058:
2057:
2049:
2041:
2034:
2026:
2019:
2011:
2009:9780819463074
2005:
2001:
2000:
1992:
1977:
1973:
1967:
1959:
1957:981-256-434-9
1953:
1949:
1948:
1940:
1933:
1920:
1916:
1912:
1905:
1899:
1895:
1891:
1887:
1882:
1874:
1868:
1864:
1863:
1855:
1853:
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1830:
1826:
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1807:
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1801:
1797:
1793:
1785:
1781:
1777:
1775:
1772:
1769:
1765:
1763:
1760:
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1750:
1741:
1721:
1717:
1688:
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1655:
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1622:
1618:
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1585:
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1552:
1528:
1520:
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1483:
1470:
1469:
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1427:
1423:
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1409:
1394:
1390:
1386:
1383:
1378:
1374:
1347:
1337:
1333:
1325:
1321:
1317:
1312:
1308:
1304:
1298:
1272:
1262:
1258:
1225:
1221:
1213:
1209:
1205:
1200:
1196:
1192:
1186:
1160:
1150:
1146:
1136:
1135:
1134:
1115:
1111:
1082:
1078:
1054:
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1022:
1015:
1002:
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714:
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625:
619:
610:
608:
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583:
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565:
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547:
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520:
509:
502:
491:
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456:Clark doublet
453:
451:
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414:
405:
395:
386:
374:
362:
356:
347:
335:
322:
315:
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296:
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271:
269:
263:
257:
248:
239:
230:
221:
216:
212:
208:
199:
197:
193:
183:
181:
178:invented the
177:
172:
170:
165:
163:
159:
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151:
147:
143:
139:
135:
125:
123:
119:
115:
110:
107:
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87:
83:
82:
75:
73:
69:
65:
61:
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48:
41:
36:
28:
22:
21:achromatopsia
2081:
2075:
2055:
2048:
2039:
2033:
2024:
2018:
1998:
1991:
1979:. Retrieved
1975:
1966:
1946:
1939:
1932:John Dollond
1924:November 27,
1922:. Retrieved
1914:
1904:
1889:
1881:
1861:
1834:
1829:
1789:
1779:
1767:
1755:
1467:
1461:
1452:Abbe numbers
1362:
1046:focal length
998:
646:
632:
623:
616:
604:
590:
581:
570:
563:
559:
545:
536:
527:
518:
507:
500:
489:
482:
470:
463:
459:
441:
432:
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412:
403:
393:
384:
372:
368:
354:
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320:
313:
301:
294:
281:
277:
266:of advanced
264:
255:
246:
237:
228:
219:
205:denotes the
200:
189:
173:
169:John Dollond
166:
131:
111:
78:
76:
59:
55:
53:
39:
1981:16 February
1934:and others.
1816:Barlow lens
742:Abbe number
740:), and the
196:Abbe number
158:George Bass
118:wavelengths
106:crown glass
98:flint glass
79:achromatic
2114:Categories
1886:Fred Hoyle
1822:References
1001:lens power
999:where the
765:dispersion
735:Fraunhofer
215:refracting
180:apochromat
90:dispersion
1915:Sphaera 8
1909:J. A. B.
1387:−
1305:−
1206:−
142:barrister
68:chromatic
1898:62-14108
1810:See also
1794:used in
1450:and the
235:through
60:achromat
1796:cameras
613:Dialyte
211:spheres
209:of the
128:History
94:concave
86:glasses
81:doublet
2120:Lenses
2063:
2006:
1954:
1896:
1869:
1841:
1778:bring
1766:bring
1727:
1714:
1694:
1681:
1661:
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1406:
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1371:
1363:Since
1345:
1293:
1269:
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1121:
1108:
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664:
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643:Design
391:, and
378:> 0
287:> 0
207:radius
134:Newton
102:convex
1768:three
290:with
186:Types
176:Peter
154:flint
150:crown
122:focus
114:power
62:is a
2061:ISBN
2004:ISBN
1983:2019
1952:ISBN
1926:2017
1894:LCCN
1867:ISBN
1839:ISBN
1780:four
1706:and
1640:and
1574:and
1468:coma
1245:and
1100:and
630:and
588:and
543:and
497:and
439:and
352:and
152:and
70:and
64:lens
1003:is
339:= ∞
198:).
194:or
58:or
54:An
38:An
2116::
1974:.
1917:.
1913:.
1888:,
1849:^
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506:≫
488:≃
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341:).
331:(
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319:=
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2069:.
2012:.
1985:.
1960:.
1928:.
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1722:2
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1379:1
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1348:.
1338:2
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1326:2
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1318:+
1313:1
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1299:=
1287:t
1284:l
1281:b
1278:d
1273:f
1263:2
1259:f
1226:1
1222:V
1214:2
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1187:=
1175:t
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1169:b
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980:;
974:0
971:=
956:2
952:V
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852:f
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820:f
812:1
807:+
796:1
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719:d
715:n
682:t
679:l
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673:d
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660:1
636:3
633:R
627:2
624:R
594:3
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585:2
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577:.
574:3
571:R
567:2
564:R
549:3
546:R
540:2
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531:2
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522:3
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514:.
511:3
508:R
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501:R
493:2
490:R
486:3
483:R
477:,
474:2
471:R
467:1
464:R
445:3
442:R
436:2
433:R
431:−
426:3
423:R
421:−
416:4
413:R
407:2
404:R
402:−
397:3
394:R
388:2
385:R
383:−
376:1
373:R
358:3
355:R
349:2
346:R
337:4
334:R
324:2
321:R
317:3
314:R
308:)
305:2
302:R
298:1
295:R
293:−
285:1
282:R
259:1
256:R
250:1
247:R
241:2
238:R
232:1
229:R
223:1
220:R
203:R
23:.
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