340:
776:
294:
1512:
767:
pole of the lens on a cross-section of the eye can approximately scale the retina over more than an entire hemisphere. It is only in the 2000s that the limitations of this approximation have become apparent, with an exploration into why some intraocular lens (IOL) patients see dark shadows in the far periphery (negative dysphotopsia, which is probably due to the IOL being much smaller than the natural lens.)
642:
89:
275:
671:
356:
1229:
754:
1018:
1314:
are the points where each optical surface crosses the optical axis. They are important primarily because they are physically measurable parameters for the optical element positions, and so the positions of the cardinal points of the optical system must be known with respect to the surface vertices to
761:
The eye itself has a second special use of the nodal point that tends to be obscured by paraxial discussions. The cornea and retina are highly curved, unlike most imaging systems, and the optical design of the eye has the property that a "direction line" that is parallel to the input rays can be used
393:
to have crossed the front principal plane, as viewed from the front of the lens. This means that the lens can be treated as if all of the refraction happened at the principal planes, and rays travel parallel to the optical axis between the planes. (Linear magnification between the principal planes is
70:
systems, the basic imaging properties such as image size, location, and orientation are completely determined by the locations of the cardinal points; in fact, only four points are necessary: the two focal points and either the principal points or the nodal points. The only ideal system that has been
1472:
elsewhere. For example, object rays are real on the object side of the optical system, while image rays are real on the image side of the system. In stigmatic imaging, an object ray intersecting any specific point in object space must be conjugate to an image ray intersecting the conjugate point in
698:
since the nodal points and principal points coincide in this case. This is a valuable addition in its own right to what has come to be called "Gaussian optics", and if the image was in fluid instead, then that same ray would refract into the new medium, as it does in the diagram to the right. A ray
305:
or "stop" at the rear focal plane of a lens can be used to filter rays by angle, since an aperture centred on the optical axis there will only pass rays that were emitted from the object at a sufficiently small angle from the optical axis. Using a sufficiently small aperture in the rear focal plane
1297:
error. These claims generally arise from confusion about the optics of camera lenses, as well as confusion between the nodal points and the other cardinal points of the system. A better choice of the point about which to pivot a camera for panoramic photography can be shown to be the centre of the
766:
in 1836, but most discussions incorrectly imply that paraxial properties of rays extend to very large angles, rather than recognizing this as a unique property of the eye's design. This scaling property is well-known, very useful, and very simple: angles drawn with a ruler centred on the posterior
659:
The front and rear nodal points of a lens have the property that a ray aimed at one of them will be refracted by the lens such that it appears to have come from the other with the same angle to the optical axis. (Angular magnification between nodal points is +1.) The nodal points therefore do for
1398:
Rotational symmetry greatly simplifies the analysis of optical systems, which otherwise must be analyzed in three dimensions. Rotational symmetry allows the system to be analyzed by considering only rays confined to a single transverse plane containing the optical axis. Such a plane is called a
841:
762:
to find the magnification or to scale retinal locations. This line passes approximately through the 2nd nodal point, but rather than being an actual paraxial ray, it identifies the image formed by ray bundles that pass through the centre of the pupil. The terminology comes from
587:
667:, was the first to describe the nodal points in 1845 to evaluate the human eye, where the image is in fluid. The cardinal points were all included in a single diagram as early as 1864 (Donders), with the object in air and the image in a different medium.
660:
angles what the principal planes do for transverse distance. If the medium on both sides of an optical system is the same (e.g., air or vacuum), then the front and rear nodal points coincide with the front and rear principal points, respectively.
313:
Similarly, the allowed range of angles on the output side of the lens can be filtered by putting an aperture at the front focal plane of the lens (or a lens group within the overall lens), and a sufficiently small aperture will make the lens
79:
the behavior of real optical systems. Cardinal points provide a way to analytically simplify an optical system with many components, allowing the imaging characteristics of the system to be approximately determined with simple calculations.
737:. For collimated light, a lens could be placed in air at the second nodal point of an optical system to give the same paraxial properties as an original lens system with an image in fluid. The power of the entire eye is about 60
1388:
of the system. Optical systems can be folded using plane mirrors; the system is still considered to be rotationally symmetric if it possesses rotational symmetry when unfolded. Any point on the optical axis (in any space) is an
1013:{\textstyle {\frac {\overline {R_{2}}}{\overline {OC_{2}}}}={\frac {\overline {R_{1}}}{\overline {OC_{1}}}}\rightarrow {\frac {\overline {R_{2}}}{\overline {R_{1}}}}={\frac {\overline {OC_{2}}}{\overline {OC_{1}}}}}
326:
sensors. The pixels in these sensors are more sensitive to rays that hit them straight on than to those that strike at an angle. A lens that does not control the angle of incidence at the detector will produce
1542:
The transformation between object space and image space is completely defined by the cardinal points of the system, and these points can be used to map any point on the object to its conjugate image point.
699:
through the nodal points has parallel input and output portions (blue). A simple method to find the rear nodal point for a lens with air on one side and fluid on the other is to take the rear focal length
1213:
445:
1499:
in image space. Focal systems also have an axial object point F such that any ray through F is conjugate to an image ray parallel to the optical axis. F is the object space focal point of the system.
1476:
Geometrical similarity implies the image is a scale model of the object. There is no restriction on the image's orientation; the image may be inverted or otherwise rotated with respect to the object.
1489:
systems have no focal points, principal points, or nodal points. In such systems an object ray parallel to the optical axis is conjugate to an image ray parallel to the optical axis. A system is
791:
The optical center of a spherical lens is a point such that If a ray passes through it, then its lens-exiting angle with respect to the optical axis is not deviated from the lens-entering angle.
450:
290:
at the rear focal plane. For an object at a finite distance, the image is formed at a different location, but rays that leave the object parallel to one another cross at the rear focal plane.
271:. The rear (or back) focal point of the system has the reverse property: rays that enter the system parallel to the optical axis are focused such that they pass through the rear focal point.
694:
The nodal points characterize a ray that goes through the centre of a lens without any angular deviation. For a lens in air with the aperture stop at the principal planes, this would be a
206:
172:
1356:
each other. This term also applies to corresponding pairs of object and image points and planes. The object and image rays, points, and planes are considered to be in two distinct
1094:
1495:
if an object ray parallel to the axis is conjugate to an image ray that intersects the optical axis. The intersection of the image ray with the optical axis is the focal point F
241:
1060:
286:
are defined as the planes, perpendicular to the optic axis, which pass through the front and rear focal points. An object infinitely far from the optical system forms an
398:
of the system is determined by the distance from an object to the front principal plane and the distance from the rear principal plane to the object's image. The
1148:
1121:
622:
in air, the principal planes both lie at the location of the lens. The point where they cross the optical axis is sometimes misleadingly called the
615:
are the radii of curvature of its surfaces. Positive signs indicate distances to the right of the corresponding vertex, and negative to the left.
1302:. On the other hand, swing-lens cameras with fixed film position rotate the lens about the rear nodal point to stabilize the image on the film.
1820:
1677:
1449:
In some optical systems imaging is stigmatic for one or perhaps a few object points, but to be an ideal system imaging must be stigmatic for
626:
of the lens. For a real lens the principal planes do not necessarily pass through the centre of the lens and can even be outside the lens.
421:
of the system. In the more general case, the distance to the foci is the focal length multiplied by the index of refraction of the medium.
245:
Aperture effects are ignored: rays that do not pass through the aperture stop of the system are not considered in the discussion below.
1840:
1346:
entering an optical system, a single and unique image ray exits from the system. In mathematical terms, the optical system performs a
267:
of an optical system, by definition, has the property that any ray that passes through it will emerge from the system parallel to the
1880:
1652:
1627:
1602:
1268:
1157:
1992:
1250:
1562:
1347:
360:
1473:
image space. A consequence is that every point on an object ray is conjugate to some point on the conjugate image ray.
1982:
1913:
582:{\displaystyle {\begin{aligned}H&=-{\frac {f(n-1)d}{r_{2}n}}\\H'&=-{\frac {f(n-1)d}{r_{1}n}},\end{aligned}}}
339:
1987:
1239:
141:. The paraxial approximation assumes that rays travel at shallow angles with respect to the optical axis, so that
775:
1406:
179:
145:
763:
664:
707:
635:
138:
1065:
1439:
1290:
323:
1350:
that maps every object ray to an image ray. The object ray and its associated image ray are said to be
214:
1760:
1705:
1557:
1445:
The image of an object confined to a plane normal to the axis is geometrically similar to the object.
1031:
49:
1938:
1729:
1339:
394:+1.) The principal planes are crucial in defining the properties of an optical system, since the
389:
to have crossed the rear principal plane at the same distance from the optical axis that the ray
302:
663:
Gauss's original 1841 paper only discussed the main rays through the focal points. A colleague,
1285:, where it is commonly asserted that the light rays "intersect" at "the nodal point", that the
1816:
1721:
1673:
1648:
1623:
1598:
1567:
1457:
710:(EFL) of the lens. The EFL is the distance from the rear nodal point to the rear focal point.
1793:
1768:
1713:
742:
417:), then the distance from each principal plane to the corresponding focal point is just the
406:
328:
315:
307:
41:
33:
1376:
Rotationally symmetric optical systems; optical axis, axial points, and meridional planes
1764:
1709:
293:
1884:
1851:
1380:
An optical system is rotationally symmetric if its imaging properties are unchanged by
1323:
1299:
1286:
1126:
1099:
385:
The two principal planes of a lens have the property that a ray emerging from the lens
254:
54:
1511:
1453:
object point. In an ideal system, every object point maps to a different image point.
1976:
1733:
1357:
714:
395:
133:
of an optical system. Each point is defined by the effect the optical system has on
1385:
1343:
418:
268:
258:
134:
130:
72:
45:
1955:
745:, has the same definition for power, with an average value of about 21 dioptres.
1282:
674:
Cardinal point diagram for an optical system with different media on each side.
641:
319:
88:
1552:
1431:
670:
17:
1773:
1748:
1466:
when they are in the part of the optical system to which they apply, and are
816:
meet the lens surfaces. As a result, dashed lines tangent to the surfaces at
278:
Rays that leave the object with the same angle cross at the back focal plane.
1797:
753:
695:
619:
359:
Various lens shapes, and the location of the principal planes for each. The
274:
1725:
1421:, rotationally symmetric, optical imaging system must meet three criteria:
1384:
rotation about some axis. This (unique) axis of rotational symmetry is the
1289:
of the lens is located there, and that this is the correct pivot point for
355:
1294:
1749:"Scaling the retinal image of the wide-angle eye using the nodal point"
1319:
738:
442:
with respect to the respective lens vertices are given by the formulas
1717:
1429:
object point converge to a single and unique image point; imaging is
414:
1940:
Revolving Table Method of
Measuring Focal Lengths of Optical Systems
1668:
Hecht, Eugene (2017). "Chapter 6.1 Thick Lenses and Lens
Systems".
774:
752:
640:
402:
are the points where the principal planes cross the optical axis.
354:
338:
292:
287:
273:
87:
27:
Six points which determine imaging properties of an optical system
741:, for example. Similarly, a lens used totally in fluid, like an
1460:, optical rays extend to infinity in both directions. Rays are
1506:
1372:; additional intermediate optical spaces may be used as well.
1222:
410:
343:
Principal planes of a thick lens. The principal points H and H
1208:{\textstyle {\frac {\overline {OC_{2}}}{\overline {OC_{1}}}}}
424:
For a single lens surrounded by a medium of refractive index
690:
for effective focal length. The chief ray is shown in purple
1914:"Theory of the "No-Parallax" Point in Panorama Photography"
779:
A diagram showing the optical center of a spherical lens.
706:
and divide it by the image medium index, which gives the
297:
Angle filtering with an aperture at the rear focal plane.
1334:
Modeling optical systems as mathematical transformations
1150:
are also same. As a result, the optical center location
1523:
1246:
1160:
1129:
1102:
1034:
844:
634:"Nodal point" redirects here. Not to be confused with
217:
182:
148:
1413:
Ideal, rotationally symmetric, optical imaging system
1238:
may contain excessive or inappropriate references to
1068:
448:
1792:. European Conference on Visual Perception. Cyprus.
1438:
Object planes perpendicular to the optical axis are
1696:Simpson, M. J. (2022). "Nodal points and the eye".
1841:"The Proper Pivot Point for Panoramic Photography"
1207:
1142:
1115:
1088:
1054:
1012:
581:
405:If the medium surrounding an optical system has a
235:
200:
166:
1811:Hecht, Eugene (2017). "Focal Points and Planes".
75:, however the cardinal points are widely used to
1215:on the optical axis, is fixed for a given lens.
655:The front and rear nodal points of a thick lens.
1943:. Optical Convention. London. pp. 168–171.
802:are where parallel lines of radii of curvature
1907:
1905:
1903:
1874:
1872:
1647:(4th ed.). Addison Wesley. p. 155.
1584:
1582:
1281:The nodal points are widely misunderstood in
757:Use of the nodal point in analysis of the eye
8:
1096:are same and the curvature center locations
92:The cardinal points of a thick lens in air.
838:are similar (i.e., their angles are same),
1442:to image planes perpendicular to the axis.
1772:
1691:
1689:
1269:Learn how and when to remove this message
1192:
1172:
1161:
1159:
1134:
1128:
1107:
1101:
1075:
1069:
1067:
1041:
1035:
1033:
997:
977:
966:
951:
936:
929:
913:
894:
887:
871:
852:
845:
843:
824:are also parallel. Because two triangles
560:
530:
496:
466:
449:
447:
216:
181:
147:
1788:Strasburger, H.; Simpson, M. J. (2023).
669:
431:, the locations of the principal points
201:{\textstyle \tan \theta \approx \theta }
167:{\textstyle \sin \theta \approx \theta }
1881:"Misconceptions in photographic optics"
1790:Is visual angle equal to retinal angle?
1578:
347:and front and rear focal points F and F
52:, focal, optical system. These are the
1834:
1832:
1815:(5th ed.). Pearson. p. 169.
1672:(5th ed.). Pearson. p. 257.
1480:Focal and afocal systems, focal points
1326:are called the anterior and posterior
363:of the lens surfaces are indicated as
1249:by removing references to unreliable
137:that pass through that point, in the
7:
1912:Littlefield, Rik (6 February 2006).
1322:, the surface vertices of the eye's
1253:where they are used inappropriately.
1089:{\displaystyle {\overline {R_{2}}}}
236:{\textstyle \cos \theta \approx 1}
25:
1839:Kerr, Douglas A. (4 April 2019).
1591:Field Guide to Geometrical Optics
593:is the focal length of the lens,
114:front and rear principal points;
1510:
1227:
1055:{\textstyle {\overline {R_{1}}}}
794:In the right figure, the points
125:front and rear surface vertices.
129:The cardinal points lie on the
1620:Aberrations of Optical Systems
926:
548:
536:
484:
472:
1:
1589:Greivenkamp, John E. (2004).
282:The front and rear (or back)
103:front and rear focal points;
66:; there are two of each. For
1563:Radius of curvature (optics)
1425:All rays "originating" from
1199:
1179:
1081:
1047:
1004:
984:
957:
942:
920:
900:
878:
858:
1956:"Anatomy of the Human Body"
335:Principal planes and points
2009:
1028:, the radii of curvatures
787:are the lens nodal points.
633:
252:
71:achieved in practice is a
40:consist of three pairs of
1937:Searle, G. F. C. (1912).
1593:. SPIE Field Guides vol.
1774:10.3390/photonics8070284
1020:. In whatever choice of
749:Nodal points and the eye
318:. This is important for
308:object-space telecentric
1747:Simpson, M. J. (2021).
1618:Welford, W. T. (1986).
1597:. SPIE. pp. 5–20.
1154:, defined by the ratio
316:image-space telecentric
249:Focal points and planes
1993:Science of photography
1643:Hecht, Eugene (2002).
1240:self-published sources
1209:
1144:
1117:
1090:
1056:
1014:
788:
758:
717:of a lens is equal to
708:effective focal length
691:
656:
636:Nodal admissions point
597:is its thickness, and
583:
382:
352:
298:
279:
237:
202:
168:
139:paraxial approximation
126:
50:rotationally symmetric
1798:10.31219/osf.io/tuy68
1315:describe the system.
1291:panoramic photography
1210:
1145:
1118:
1091:
1057:
1015:
778:
756:
686:for Nodal Point, and
682:for Principal point,
673:
644:
584:
358:
342:
296:
277:
238:
203:
169:
91:
1954:Gray, Henry (1918).
1574:Notes and references
1558:Pinhole camera model
1409:through the system.
1158:
1127:
1100:
1066:
1032:
842:
446:
215:
180:
146:
1765:2021Photo...8..284S
1710:2022ApOpt..61.2797S
1458:rays in mathematics
306:will make the lens
1983:Geometrical optics
1879:van Walree, Paul.
1522:. You can help by
1340:geometrical optics
1205:
1143:{\textstyle C_{2}}
1140:
1116:{\textstyle C_{1}}
1113:
1086:
1052:
1010:
789:
759:
692:
657:
579:
577:
383:
361:radii of curvature
353:
299:
280:
233:
198:
164:
127:
1988:Geometric centers
1822:978-1-292-09693-3
1718:10.1364/AO.455464
1704:(10): 2797–2804.
1679:978-1-292-09693-3
1568:Vergence (optics)
1540:
1539:
1293:, so as to avoid
1279:
1278:
1271:
1203:
1202:
1182:
1084:
1050:
1008:
1007:
987:
961:
960:
945:
924:
923:
903:
882:
881:
861:
678:for Focal point,
570:
506:
16:(Redirected from
2000:
1968:
1967:
1965:
1963:
1951:
1945:
1944:
1934:
1928:
1927:
1925:
1923:
1918:
1909:
1898:
1896:
1894:
1892:
1887:on 19 April 2015
1883:. Archived from
1876:
1867:
1866:
1864:
1862:
1856:
1850:. Archived from
1845:
1836:
1827:
1826:
1808:
1802:
1801:
1785:
1779:
1778:
1776:
1744:
1738:
1737:
1693:
1684:
1683:
1665:
1659:
1658:
1640:
1634:
1633:
1615:
1609:
1608:
1586:
1535:
1532:
1514:
1507:
1498:
1402:meridional plane
1312:surface vertices
1306:Surface vertices
1274:
1267:
1263:
1260:
1254:
1231:
1230:
1223:
1214:
1212:
1211:
1206:
1204:
1198:
1197:
1196:
1183:
1178:
1177:
1176:
1163:
1162:
1149:
1147:
1146:
1141:
1139:
1138:
1122:
1120:
1119:
1114:
1112:
1111:
1095:
1093:
1092:
1087:
1085:
1080:
1079:
1070:
1061:
1059:
1058:
1053:
1051:
1046:
1045:
1036:
1019:
1017:
1016:
1011:
1009:
1003:
1002:
1001:
988:
983:
982:
981:
968:
967:
962:
956:
955:
946:
941:
940:
931:
930:
925:
919:
918:
917:
904:
899:
898:
889:
888:
883:
877:
876:
875:
862:
857:
856:
847:
846:
743:intraocular lens
736:
734:
727:
720:
705:
704:
653:
614:
605:
596:
592:
588:
586:
585:
580:
578:
571:
569:
565:
564:
554:
531:
519:
507:
505:
501:
500:
490:
467:
441:
440:
434:
430:
407:refractive index
400:principal points
380:
371:
350:
346:
329:pixel vignetting
244:
242:
240:
239:
234:
209:
207:
205:
204:
199:
175:
173:
171:
170:
165:
123:
112:
101:
60:principal points
21:
2008:
2007:
2003:
2002:
2001:
1999:
1998:
1997:
1973:
1972:
1971:
1961:
1959:
1953:
1952:
1948:
1936:
1935:
1931:
1921:
1919:
1916:
1911:
1910:
1901:
1890:
1888:
1878:
1877:
1870:
1860:
1858:
1854:
1843:
1838:
1837:
1830:
1823:
1810:
1809:
1805:
1787:
1786:
1782:
1746:
1745:
1741:
1695:
1694:
1687:
1680:
1667:
1666:
1662:
1655:
1642:
1641:
1637:
1630:
1617:
1616:
1612:
1605:
1588:
1587:
1580:
1576:
1549:
1536:
1530:
1527:
1520:needs expansion
1505:
1496:
1493:
1487:
1482:
1470:
1464:
1415:
1403:
1393:
1378:
1370:
1364:
1354:
1336:
1308:
1275:
1264:
1258:
1255:
1244:
1232:
1228:
1221:
1188:
1184:
1168:
1164:
1156:
1155:
1130:
1125:
1124:
1103:
1098:
1097:
1071:
1064:
1063:
1037:
1030:
1029:
993:
989:
973:
969:
947:
932:
909:
905:
890:
867:
863:
848:
840:
839:
837:
830:
815:
808:
773:
751:
732:
725:
722:
718:
702:
700:
651:
639:
632:
613:
607:
604:
598:
594:
590:
576:
575:
556:
555:
532:
520:
512:
509:
508:
492:
491:
468:
456:
444:
443:
438:
436:
432:
425:
379:
373:
370:
364:
348:
344:
337:
331:in the images.
261:
251:
213:
212:
211:
178:
177:
176:
144:
143:
142:
121:
110:
99:
86:
44:located on the
38:cardinal points
34:Gaussian optics
28:
23:
22:
15:
12:
11:
5:
2006:
2004:
1996:
1995:
1990:
1985:
1975:
1974:
1970:
1969:
1958:. p. 1019
1946:
1929:
1899:
1868:
1857:on 2 July 2024
1828:
1821:
1803:
1780:
1739:
1698:Applied Optics
1685:
1678:
1660:
1653:
1635:
1628:
1610:
1603:
1577:
1575:
1572:
1571:
1570:
1565:
1560:
1555:
1548:
1545:
1538:
1537:
1531:September 2013
1517:
1515:
1504:
1503:Transformation
1501:
1491:
1485:
1481:
1478:
1468:
1462:
1452:
1447:
1446:
1443:
1436:
1428:
1420:
1414:
1411:
1401:
1391:
1383:
1377:
1374:
1368:
1362:
1358:optical spaces
1352:
1348:transformation
1335:
1332:
1307:
1304:
1300:entrance pupil
1287:iris diaphragm
1277:
1276:
1235:
1233:
1226:
1220:
1217:
1201:
1195:
1191:
1187:
1181:
1175:
1171:
1167:
1137:
1133:
1110:
1106:
1083:
1078:
1074:
1049:
1044:
1040:
1006:
1000:
996:
992:
986:
980:
976:
972:
965:
959:
954:
950:
944:
939:
935:
928:
922:
916:
912:
908:
902:
897:
893:
886:
880:
874:
870:
866:
860:
855:
851:
835:
828:
813:
806:
772:
771:Optical center
769:
750:
747:
665:Johann Listing
631:
628:
624:optical centre
611:
602:
574:
568:
563:
559:
553:
550:
547:
544:
541:
538:
535:
529:
526:
523:
521:
518:
515:
511:
510:
504:
499:
495:
489:
486:
483:
480:
477:
474:
471:
465:
462:
459:
457:
455:
452:
451:
392:
388:
377:
368:
336:
333:
255:Focus (optics)
250:
247:
232:
229:
226:
223:
220:
197:
194:
191:
188:
185:
163:
160:
157:
154:
151:
85:
82:
78:
26:
24:
18:Optical centre
14:
13:
10:
9:
6:
4:
3:
2:
2005:
1994:
1991:
1989:
1986:
1984:
1981:
1980:
1978:
1957:
1950:
1947:
1942:
1941:
1933:
1930:
1915:
1908:
1906:
1904:
1900:
1886:
1882:
1875:
1873:
1869:
1853:
1849:
1842:
1835:
1833:
1829:
1824:
1818:
1814:
1807:
1804:
1799:
1795:
1791:
1784:
1781:
1775:
1770:
1766:
1762:
1758:
1754:
1750:
1743:
1740:
1735:
1731:
1727:
1723:
1719:
1715:
1711:
1707:
1703:
1699:
1692:
1690:
1686:
1681:
1675:
1671:
1664:
1661:
1656:
1654:0-321-18878-0
1650:
1646:
1639:
1636:
1631:
1629:0-85274-564-8
1625:
1621:
1614:
1611:
1606:
1604:0-8194-5294-7
1600:
1596:
1592:
1585:
1583:
1579:
1573:
1569:
1566:
1564:
1561:
1559:
1556:
1554:
1551:
1550:
1546:
1544:
1534:
1525:
1521:
1518:This section
1516:
1513:
1509:
1508:
1502:
1500:
1494:
1488:
1479:
1477:
1474:
1471:
1465:
1459:
1454:
1450:
1444:
1441:
1437:
1434:
1433:
1426:
1424:
1423:
1422:
1418:
1412:
1410:
1408:
1407:cross-section
1404:
1396:
1394:
1387:
1381:
1375:
1373:
1371:
1365:
1359:
1355:
1349:
1345:
1341:
1333:
1331:
1330:of the lens.
1329:
1325:
1321:
1316:
1313:
1305:
1303:
1301:
1296:
1292:
1288:
1284:
1273:
1270:
1262:
1252:
1248:
1242:
1241:
1236:This section
1234:
1225:
1224:
1218:
1216:
1193:
1189:
1185:
1173:
1169:
1165:
1153:
1135:
1131:
1108:
1104:
1076:
1072:
1042:
1038:
1027:
1023:
998:
994:
990:
978:
974:
970:
963:
952:
948:
937:
933:
914:
910:
906:
895:
891:
884:
872:
868:
864:
853:
849:
834:
827:
823:
819:
812:
805:
801:
797:
792:
786:
782:
777:
770:
768:
765:
755:
748:
746:
744:
740:
735:
728:
716:
711:
709:
697:
689:
685:
681:
677:
672:
668:
666:
661:
654:
647:
643:
637:
629:
627:
625:
621:
616:
610:
601:
572:
566:
561:
557:
551:
545:
542:
539:
533:
527:
524:
522:
516:
513:
502:
497:
493:
487:
481:
478:
475:
469:
463:
460:
458:
453:
428:
422:
420:
416:
412:
408:
403:
401:
397:
396:magnification
390:
386:
376:
367:
362:
357:
341:
334:
332:
330:
325:
321:
317:
311:
309:
304:
295:
291:
289:
285:
276:
272:
270:
266:
260:
256:
248:
246:
230:
227:
224:
221:
218:
195:
192:
189:
186:
183:
161:
158:
155:
152:
149:
140:
136:
132:
124:
117:
113:
106:
102:
95:
90:
83:
81:
76:
74:
69:
65:
61:
57:
56:
51:
47:
43:
39:
35:
30:
19:
1960:. Retrieved
1949:
1939:
1932:
1920:. Retrieved
1889:. Retrieved
1885:the original
1859:. Retrieved
1852:the original
1847:
1812:
1806:
1789:
1783:
1756:
1752:
1742:
1701:
1697:
1669:
1663:
1644:
1638:
1619:
1613:
1594:
1590:
1541:
1528:
1524:adding to it
1519:
1490:
1484:
1483:
1475:
1467:
1461:
1455:
1448:
1430:
1416:
1400:
1397:
1390:
1386:optical axis
1379:
1367:
1363:object space
1361:
1353:conjugate to
1351:
1337:
1327:
1317:
1311:
1309:
1280:
1265:
1256:
1245:Please help
1237:
1151:
1025:
1021:
832:
825:
821:
817:
810:
803:
799:
795:
793:
790:
784:
780:
760:
730:
723:
712:
693:
687:
683:
679:
675:
662:
658:
649:
645:
630:Nodal points
623:
617:
608:
599:
426:
423:
419:focal length
409:of 1 (e.g.,
404:
399:
384:
374:
365:
320:DSLR cameras
312:
300:
284:focal planes
283:
281:
269:optical axis
264:
262:
259:Focal length
131:optical axis
128:
119:
115:
108:
104:
97:
93:
73:plane mirror
67:
64:nodal points
63:
59:
55:focal points
53:
46:optical axis
37:
31:
29:
1962:12 February
1848:The Pumpkin
1392:axial point
1369:image space
1342:, for each
1310:In optics,
1283:photography
1259:August 2024
1219:Photography
351:are marked.
265:focal point
84:Explanation
77:approximate
1977:Categories
1922:14 January
1759:(7): 284.
1553:Film plane
1405:; it is a
1344:object ray
1247:improve it
263:The front
253:See also:
62:, and the
1891:1 January
1861:25 August
1753:Photonics
1734:247300377
1440:conjugate
1432:stigmatic
1298:system's
1200:¯
1180:¯
1082:¯
1048:¯
1005:¯
985:¯
958:¯
943:¯
927:→
921:¯
901:¯
879:¯
859:¯
696:chief ray
620:thin lens
543:−
528:−
479:−
464:−
303:diaphragm
228:≈
225:θ
222:
196:θ
193:≈
190:θ
187:
162:θ
159:≈
156:θ
153:
1897:Item #6.
1726:35471355
1547:See also
1295:parallax
764:Volkmann
739:dioptres
517:′
391:appeared
1761:Bibcode
1706:Bibcode
1622:. CRC.
1469:virtual
1456:Unlike
1320:anatomy
1251:sources
387:appears
322:having
1819:
1813:Optics
1732:
1724:
1676:
1670:Optics
1651:
1645:Optics
1626:
1601:
1486:Afocal
618:For a
589:where
415:vacuum
58:, the
42:points
36:, the
1917:(PDF)
1855:(PDF)
1844:(PDF)
1730:S2CID
1492:focal
1451:every
1419:ideal
1328:poles
719:1/EFL
715:power
288:image
68:ideal
48:of a
1964:2009
1924:2007
1893:2007
1863:2024
1817:ISBN
1722:PMID
1674:ISBN
1649:ISBN
1624:ISBN
1599:ISBN
1595:FG01
1463:real
1427:each
1366:and
1324:lens
1123:and
1062:and
1024:and
831:and
820:and
809:and
798:and
783:and
713:The
606:and
435:and
372:and
257:and
210:and
135:rays
1794:doi
1769:doi
1714:doi
1526:.
1417:An
1382:any
1338:In
1318:In
833:OAC
826:OBC
721:or
688:efl
429:= 1
413:or
411:air
324:CCD
219:cos
184:tan
150:sin
32:In
1979::
1902:^
1871:^
1846:.
1831:^
1767:.
1755:.
1751:.
1728:.
1720:.
1712:.
1702:61
1700:.
1688:^
1581:^
1395:.
1360:,
785:N'
684:NP
648:,
310:.
301:A
118:,
107:,
96:,
1966:.
1926:.
1895:.
1865:.
1825:.
1800:.
1796::
1777:.
1771::
1763::
1757:8
1736:.
1716::
1708::
1682:.
1657:.
1632:.
1607:.
1533:)
1529:(
1497:′
1435:.
1272:)
1266:(
1261:)
1257:(
1243:.
1194:1
1190:C
1186:O
1174:2
1170:C
1166:O
1152:O
1136:2
1132:C
1109:1
1105:C
1077:2
1073:R
1043:1
1039:R
1026:B
1022:A
999:1
995:C
991:O
979:2
975:C
971:O
964:=
953:1
949:R
938:2
934:R
915:1
911:C
907:O
896:1
892:R
885:=
873:2
869:C
865:O
854:2
850:R
836:1
829:2
822:B
818:A
814:2
811:R
807:1
804:R
800:B
796:A
781:N
733:′
731:f
729:/
726:′
724:n
703:′
701:f
680:P
676:F
652:′
650:N
646:N
638:.
612:2
609:r
603:1
600:r
595:d
591:f
573:,
567:n
562:1
558:r
552:d
549:)
546:1
540:n
537:(
534:f
525:=
514:H
503:n
498:2
494:r
488:d
485:)
482:1
476:n
473:(
470:f
461:=
454:H
439:′
437:H
433:H
427:n
381:.
378:2
375:r
369:1
366:r
349:′
345:′
243:.
231:1
208:,
174:,
122:′
120:V
116:V
111:′
109:P
105:P
100:′
98:F
94:F
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
