224:
52:
537:) in an optical system is the meridional ray that starts at an edge of an object and passes through the center of the aperture stop. The distance between the chief ray (or an extension of it for a virtual image) and the optical axis at an image location defines the size of the image. This ray (or forward and backward extensions of it for virtual image pupils) crosses the optical axis at the locations of the entrance and exit pupils. The marginal and chief rays together define the
451:
199:
describes how rays propagate through an optical system. Objects to be imaged are treated as collections of independent point sources, each producing spherical wavefronts and corresponding outward rays. Rays from each object point can be mathematically propagated to locate the corresponding point on
521:
of the aperture stop, for real image pupils, the distance of the marginal ray from the optical axis at the pupil locations defines the sizes of each pupil. For virtual image pupils, an extended line, forward along the marginal ray before the first optical element or backward along the marginal ray
564:
from an off-axis object point is a ray that propagates in the plane that is perpendicular to the meridional plane and contains the principal ray. Sagittal rays intersect the pupil along a line that is perpendicular to the meridional plane for the ray's object point and passes through the optical
613:
is a ray that propagates close to some defined "base ray" rather than the optical axis. This is more appropriate than the paraxial model in systems that lack symmetry about the optical axis. In computer modeling, parabasal rays are "real rays", that is rays that are treated without making the
799:. This simplification is useful in practice; it is an excellent approximation when the wavelength is small compared to the size of structures with which the light interacts. The techniques are particularly useful in describing geometrical aspects of
595:. When discussing ray tracing this definition is often reversed: a "paraxial ray" is then a ray that is modeled using the paraxial approximation, not necessarily a ray that remains close to the axis.
861:
by discrete amounts. Simple problems can be analyzed by propagating a few rays using simple mathematics. More detailed analysis can be performed by using a computer to propagate many rays.
215:
There are many special rays that are used in optical modelling to analyze an optical system. These are defined and described below, grouped by the type of system they are used to model.
320:
287:
254:
482:
is a ray that does not propagate in a plane that contains both the object point and the optical axis. Such rays do not cross the optical axis anywhere and are not parallel to it.
361:
corresponding to a given incident ray, is the ray that represents the light reflected by the surface. The angle between the surface normal and the reflected ray is known as the
497:) in an optical system is the meridional ray that starts at the point where an object to be imaged crosses the optical axis (the axial object point) and touches an edge of the
849:
off surfaces, complicating analysis. Strictly speaking Ray tracing is when analytic solutions to the ray's trajectories are solved; however Ray tracing is often confused with
591:
is a ray that makes a small angle to the optical axis of the system, and lies close to the axis throughout the system. Such rays can be modeled reasonably well by using the
396:
requires that the power in the incident ray must equal the sum of the power in the refracted ray, the power in the reflected ray, and any power absorbed at the surface.
458:
is an image of the aperture stop formed by the optics in the front of it, and the location and size of the pupil are determined by chief rays and marginal rays.
384:
corresponding to a given incident ray represents the light that is transmitted through the surface. The angle between this ray and the normal is known as the
103:. This allows even very complex optical systems to be analyzed mathematically or simulated by computer. Ray tracing uses approximate solutions to
1279:
1254:
1229:
1151:
1124:
1096:
1032:
1141:
614:
paraxial approximation. Parabasal rays about the optical axis are sometimes used to calculate first-order properties of optical systems.
1064:
871:
that are valid as long as the light waves propagate through and around objects whose dimensions are much greater than the light's
223:
876:
792:
136:
980:
207:, which states that the path taken between two points by a ray of light is the path that can be traversed in the least time.
31:
1179:
1167:
1072:
926:
1327:
1296:
1192:
347:
257:
864:
696:
680:, light entering the fiber will be guided if it makes an angle with the fiber axis that is less than the fiber's
549:
object point, and in this case, the principal ray starting at an edge point of the object may then be called the
72:
669:
704:
296:
263:
230:
51:
916:
868:
592:
393:
104:
1332:
826:
818:
761:
99:
45:
204:
946:
501:
of the system. This ray is useful, because it crosses the optical axis again at the locations where a
846:
420:
97:
up into discrete rays that can be computationally propagated through the system by the techniques of
90:
38:
911:
436:
428:
412:
385:
366:
362:
323:
290:
450:
1003:
834:
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768:
731:
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677:
538:
522:
before the last optical element, determines the size of the entrance or exit pupil, respectively.
440:
180:
168:
123:
1275:
1250:
1225:
1147:
1120:
1092:
1060:
1028:
976:
584:= 0. The principal ray is both sagittal and meridional. All other sagittal rays are skew rays.
753:
useful for approximating the paths along which light propagates under certain circumstances.
778:
742:
369:(non-scattering) surface, the angle of reflection is always equal to the angle of incidence.
196:
192:
995:
901:
858:
796:
750:
86:
853:
which numerically solves problems by repeatedly advancing idealized narrow beams called
111:
propagate through and around objects whose dimensions are much greater than the light's
772:
510:
455:
389:
343:
188:
1321:
888:
648:
633:
506:
498:
432:
400:
160:
152:
140:
184:
172:
906:
850:
700:
673:
644:
629:
472:
841:, absorption characteristics, and reflecting surfaces. Under these circumstances,
505:
will be formed, and backward extensions of the ray's path cross the axis where a
921:
884:
880:
788:
176:
156:
132:
128:
94:
872:
681:
656:
514:
502:
424:
117:
112:
108:
842:
164:
81:
1249:. Adam Hilger series on optics and optoelectronics. CRC Press. p. 50.
756:
The simplifying assumptions of geometrical optics include that light rays:
838:
643:
is a ray that travels in a non-planar zig-zag path and never crosses the
17:
1091:. Tutorial texts in optical engineering. Vol. 48. SPIE. p. 1.
787:
Geometrical optics does not account for certain optical effects such as
542:
339:
735:
60:
800:
739:
695:
is a ray in an optical fiber that geometric optics predicts would
606:
is a ray that is traced without making the paraxial approximation.
518:
449:
76:
68:
50:
1220:
Atchison, David A.; Smith, George (2000). "A1: Paraxial optics".
545:
of the optical system. Some authors define a "principal ray" for
830:
203:
A slightly more rigorous definition of a light ray follows from
767:
bend, and in particular circumstances may split in two, at the
471:
is a ray that is confined to the plane containing the system's
707:, but which suffers loss due to the curved core boundary.
85:
of the actual light, and that points in the direction of
44:"Incident light" redirects here. Not to be confused with
1115:
Hecht, Eugene (2017). "5.3.2 Entrance and Exit Pupils".
867:, ray tracing often relies on approximate solutions to
342:. The angle between this ray and the perpendicular or
837:
through a system with regions of varying propagation
760:
propagate in straight-line paths as they travel in a
299:
266:
233:
475:
and the object point from which the ray originated.
37:"Lightray" redirects here. Not to be confused with
30:"Ray of light" redirects here. For other uses, see
314:
281:
248:
139:can be modeled in limited circumstances by adding
875:. Ray theory does not describe phenomena such as
565:axis. If the axis direction is defined to be the
1089:Optical Design Fundamentals for Infrared Systems
454:Single lens imaging with the aperture stop. The
93:through an optical system, by dividing the real
1245:Welford, W. T. (1986). "4: Finite Raytracing".
1046:
1044:
1025:Optical Principles and Technology for Engineers
415:when passing through the birefringent material.
777:follow curved paths in a medium in which the
8:
577:plane, sagittal rays intersect the pupil at
1215:
1213:
191:and may be curved in a medium in which the
1224:. Elsevier Health Sciences. p. 237.
1018:
1016:
1014:
1012:
305:
304:
298:
272:
271:
265:
239:
238:
232:
829:is a method for calculating the path of
541:, which characterizes the throughput or
365:. The Law of Reflection says that for a
222:
1082:
1080:
1000:An Introduction to the Theory of Optics
937:
1140:Malacara, Daniel and Zacarias (2003).
1119:(5th ed.). Pearson. p. 184.
749:. The ray in geometrical optics is an
569:axis, and the meridional plane is the
315:{\displaystyle \theta _{\mathrm {R} }}
282:{\displaystyle \theta _{\mathrm {r} }}
249:{\displaystyle \theta _{\mathrm {i} }}
1272:An Introduction to Hamiltonian Optics
67:is an idealized geometrical model of
7:
1297:"Understanding Paraxial Ray-Tracing"
1193:"Understanding Paraxial Ray-Tracing"
1110:
1108:
227:Diagram of rays at a surface, where
135:theory. Some wave phenomena such as
127:does not describe phenomena such as
403:, the refracted ray may split into
306:
273:
240:
25:
1146:(2nd ed.). CRC. p. 25.
1053:Field Guide to Geometrical Optics
628:is a ray that passes through the
338:is a ray of light that strikes a
1295:Nicholson, Mark (21 July 2005).
1191:Nicholson, Mark (21 July 2005).
975:. SPIE Field Guides. p. 2.
817:This section is an excerpt from
723:This section is an excerpt from
973:Field Guide to Geometric Optics
845:may bend, change direction, or
734:, or ray optics, is a model of
183:are straight. They bend at the
1247:Aberrations of Optical Systems
1178:Greivenkamp (2004), pp. 19–20
1002:, London: Edward Arnold, 1904
107:that are valid as long as the
89:. Rays are used to model the
1:
1051:Greivenkamp, John E. (2004).
971:Greivenkamp, John E. (2004).
784:may be absorbed or reflected.
411:, which experience different
79:that is perpendicular to the
32:Ray of light (disambiguation)
927:Ray transfer matrix analysis
863:When applied to problems of
699:at the boundary between the
1301:ZEMAX Users' Knowledge Base
1197:ZEMAX Users' Knowledge Base
951:ZEMAX Users' Knowledge Base
945:Moore, Ken (25 July 2005).
672:, which is confined by the
1349:
1166:Greivenkamp (2004), p. 28
1143:Handbook of Optical Design
1023:Stewart, James E. (1996).
816:
795:, which are considered in
722:
710:
509:will be formed. Since the
418:
43:
36:
29:
1055:. SPIE Field Guides vol.
865:electromagnetic radiation
219:Interaction with surfaces
75:, obtained by choosing a
73:electromagnetic radiation
1270:Buchdahl, H. A. (1993).
670:multi-mode optical fiber
533:(sometimes known as the
27:Idealized model of light
1222:Optics of the Human Eye
771:between two dissimilar
489:(sometimes known as an
187:between two dissimilar
151:A light ray is a line (
1087:Riedl, Max J. (2001).
917:Paraxial approximation
593:paraxial approximation
551:marginal principal ray
459:
394:Conservation of energy
346:to the surface is the
326:
316:
283:
250:
56:
1274:. Dover. p. 26.
819:Ray tracing (physics)
453:
413:indexes of refraction
388:, and it is given by
317:
284:
251:
226:
54:
46:Incident Light (film)
421:Reflection (physics)
297:
264:
231:
91:propagation of light
39:Lightray (superhero)
1027:. CRC. p. 57.
912:Optical path length
869:Maxwell's equations
805:optical aberrations
437:Specular reflection
429:Absorption (optics)
399:If the material is
386:angle of refraction
363:angle of reflection
324:angle of refraction
291:angle of reflection
105:Maxwell's equations
55:Rays and wavefronts
1328:Geometrical optics
732:Geometrical optics
725:Geometrical optics
718:Geometrical optics
713:Numerical aperture
539:Lagrange invariant
495:marginal axial ray
460:
441:Plane of incidence
409:extraordinary rays
348:angle of incidence
327:
312:
279:
258:angle of incidence
246:
205:Fermat's principle
143:to the ray model.
124:geometrical optics
57:
1281:978-0-486-67597-8
1256:978-0-85274-564-9
1231:978-0-7506-3775-6
1153:978-0-8247-4613-1
1126:978-1-292-09693-3
1098:978-0-8194-4051-8
1034:978-0-8247-9705-8
181:homogeneous media
16:(Redirected from
1340:
1313:
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1038:
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1007:
993:
987:
986:
968:
962:
961:
959:
957:
947:"What is a ray?"
942:
883:, which require
779:refractive index
682:acceptance angle
678:step index fiber
378:
377:
359:
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321:
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197:Geometric optics
193:refractive index
179:. Light rays in
131:, which require
21:
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996:Arthur Schuster
994:
990:
983:
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969:
965:
955:
953:
944:
943:
939:
935:
902:Collimated beam
898:
893:
892:
887:(involving the
822:
814:
809:
808:
797:physical optics
738:that describes
728:
720:
715:
697:totally reflect
621:
582:
448:
446:Optical systems
443:
382:transmitted ray
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356:
355:
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332:
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294:
267:
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163:to the light's
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35:
28:
23:
22:
15:
12:
11:
5:
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813:
810:
786:
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775:
765:
729:
721:
719:
716:
709:
708:
685:
668:is a ray in a
652:
637:
626:meridional ray
620:
617:
616:
615:
607:
596:
585:
580:
562:transverse ray
554:
523:
511:entrance pupil
483:
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469:tangential ray
465:meridional ray
456:entrance pupil
447:
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417:
416:
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1066:0-8194-5294-7
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905:
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899:
895:
891:of the wave).
890:
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748:
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741:
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733:
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694:
693:tunneling ray
690:
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671:
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658:
653:
650:
649:optical fiber
646:
642:
638:
635:
634:optical fiber
631:
627:
623:
622:
618:
612:
611:parabasal ray
608:
605:
601:
597:
594:
590:
586:
583:
576:
572:
568:
563:
559:
555:
552:
548:
544:
540:
536:
532:
528:
527:principal ray
524:
520:
516:
512:
508:
507:virtual image
504:
500:
499:aperture stop
496:
492:
488:
484:
481:
477:
474:
470:
466:
462:
461:
457:
452:
445:
442:
438:
434:
433:Birefringence
430:
426:
422:
414:
410:
406:
402:
398:
395:
391:
387:
383:
379:
376:refracted ray
371:
368:
364:
360:
357:reflected ray
352:
349:
345:
341:
337:
329:
328:
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301:
292:
268:
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210:
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206:
201:
198:
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182:
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174:
170:
166:
162:
161:perpendicular
158:
154:
146:
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138:
134:
130:
126:
125:
120:
119:
114:
110:
106:
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88:
84:
83:
78:
74:
70:
66:
62:
53:
47:
40:
33:
19:
1333:Fiber optics
1305:. Retrieved
1300:
1290:
1271:
1265:
1246:
1240:
1221:
1200:. Retrieved
1196:
1186:
1174:
1162:
1142:
1135:
1116:
1088:
1056:
1052:
1024:
999:
991:
972:
966:
954:. Retrieved
950:
940:
907:Optical path
877:interference
857:through the
854:
851:ray-marching
825:In physics,
824:
803:, including
793:interference
755:
746:
745:in terms of
730:
692:
688:
665:
661:
655:
640:
625:
619:Fiber optics
610:
603:
599:
589:paraxial ray
588:
578:
574:
570:
566:
561:
558:sagittal ray
557:
550:
546:
534:
530:
526:
494:
490:
487:marginal ray
486:
479:
473:optical axis
468:
464:
408:
404:
401:birefringent
381:
373:
354:
334:incident ray
331:
214:
211:Special rays
202:
150:
137:interference
122:
116:
98:
80:
64:
58:
1303:. p. 2
922:Pencil beam
885:wave theory
881:diffraction
827:ray tracing
812:Ray tracing
789:diffraction
762:homogeneous
751:abstraction
743:propagation
666:trapped ray
390:Snell's Law
200:the image.
177:wave vector
133:wave optics
129:diffraction
109:light waves
100:ray tracing
95:light field
87:energy flow
1322:Categories
982:0819452947
933:References
873:wavelength
843:wavefronts
711:See also:
657:guided ray
600:finite ray
515:exit pupil
503:real image
425:Refraction
419:See also:
165:wavefronts
159:) that is
147:Definition
118:Ray optics
113:wavelength
82:wavefronts
1307:17 August
1202:17 August
835:particles
769:interface
689:leaky ray
662:bound ray
531:chief ray
302:θ
269:θ
236:θ
195:changes.
185:interface
175:with the
173:collinear
71:or other
18:Light ray
1071:, p. 25
1059:. SPIE.
896:See also
839:velocity
705:cladding
703:and the
641:skew ray
604:real ray
480:skew ray
405:ordinary
367:specular
153:straight
847:reflect
801:imaging
781:changes
543:etendue
340:surface
322:is the
289:is the
256:is the
169:tangent
1278:
1253:
1228:
1150:
1123:
1117:Optics
1095:
1063:
1031:
1004:online
979:
956:30 May
859:medium
764:medium
736:optics
676:. For
647:of an
632:of an
519:images
439:, and
344:normal
293:, and
167:; its
157:curved
61:optics
889:phase
831:waves
773:media
740:light
664:, or
535:b ray
493:or a
491:a ray
189:media
141:phase
77:curve
69:light
1309:2009
1276:ISBN
1251:ISBN
1226:ISBN
1204:2009
1148:ISBN
1121:ISBN
1093:ISBN
1061:ISBN
1057:FG01
1029:ISBN
977:ISBN
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