833:
1020:
816:
has a chapter on sources which quotes a line width of around 0.052 angstroms for each of the Sodium D lines in an uncooled low-pressure sodium lamp, corresponding to a coherence length of around 67 mm for each line by itself. Cooling the low pressure sodium discharge to
165:
428:
730:
43:
is strong when the paths taken by all of the interfering waves differ by less than the coherence length. A wave with a longer coherence length is closer to a perfect sinusoidal wave. Coherence length is important in
583:
to 50%. It is important to note that this is a roundtrip coherence length — this definition is applied in applications like OCT where the light traverses the measured displacement twice (as in a
1024:
85:
642:
519:
552:
804:
due to the narrow linewidth of each tooth. Non-zero visibility is present only for short intervals of pulses repeated after cavity length distances up to this long coherence length.
247:
343:
298:
821:
temperatures increases the individual D line coherence length by a factor of 6. A very narrow-band interference filter would be required to isolate an individual D line.
453:
273:
577:
755:
484:
335:
212:
190:
788:
have a typical coherence length on the order of centimeters, while the coherence length of longitudinally single-mode lasers can exceed 1 km.
650:
792:
can reach some 100 m, but small, inexpensive semiconductor lasers have shorter lengths, with one source claiming 20 cm. Singlemode
1029:
955:
930:
160:{\displaystyle L={\frac {c}{\,n\,\mathrm {\Delta } f\,}}\approx {\frac {\lambda ^{2}}{\,n\,\mathrm {\Delta } \lambda \,}}~,}
605:
1062:
1004:
800:
of a few kHz can have coherence lengths exceeding 100 km. Similar coherence lengths can be reached with optical
761:
875:
Akcay, C.; Parrein, P.; Rolland, J.P. (2002). "Estimation of longitudinal resolution in optical coherence imaging".
497:
851:
832:
1035:
588:
40:
532:
49:
423:{\displaystyle L={\frac {\,2\ln 2\,}{\pi }}\,{\frac {\lambda ^{2}}{\,n_{g}\,\mathrm {\Delta } \lambda \,}}~,}
250:
225:
308:
64:
1077:
278:
526:
921:
Izatt; Choma; Dhalla (2014). "Theory of
Optical Coherence Tomography". In Drexler; Fujimoto (eds.).
1067:
591:, the light traverses the displacement only once, and the coherence length is effectively doubled.
584:
436:
256:
557:
785:
884:
738:
462:
318:
304:
195:
173:
32:
8:
789:
765:
595:
36:
28:
888:
594:
The coherence length can also be measured using a
Michelson interferometer and is the
1000:
971:
951:
926:
900:
856:
580:
60:
56:
1039:
892:
487:
215:
818:
797:
491:
219:
1072:
846:
838:
801:
522:
16:
Distance over which a propagating wave maintains a certain degree of coherence
1056:
68:
764:
systems, the coherence length may be reduced by propagation factors such as
904:
725:{\displaystyle V={\frac {\;I_{\max }-I_{\min }\;}{I_{\max }+I_{\min }}}~,}
1045:
896:
793:
773:
769:
599:
456:
45:
312:
874:
20:
79:
In radio-band systems, the coherence length is approximated by
644:
fringe visibility, where the fringe visibility is defined as
525:
of the source. If the source has a
Gaussian spectrum with
300:
is the width of the range of wavelengths in the signal.
741:
653:
608:
560:
535:
500:
465:
439:
346:
321:
281:
259:
228:
198:
176:
88:
63:, there is a mathematically analogous concept of the
828:
749:
724:
637:{\displaystyle \,{\frac {1}{\,e\,}}\approx 37\%\,}
636:
571:
546:
513:
478:
447:
422:
329:
315:emission spectrum, the roundtrip coherence length
292:
267:
241:
206:
184:
159:
587:). In transmissive applications, such as with a
1054:
920:
708:
695:
682:
669:
514:{\displaystyle \,\mathrm {\Delta } \lambda \,}
687:
663:
547:{\displaystyle \mathrm {\Delta } \lambda }
945:
746:
742:
633:
620:
616:
609:
568:
561:
510:
501:
444:
440:
410:
401:
390:
376:
369:
356:
326:
322:
289:
282:
264:
260:
238:
229:
203:
199:
181:
177:
147:
138:
134:
114:
105:
101:
55:This article focuses on the coherence of
27:is the propagation distance over which a
994:
242:{\displaystyle \,\mathrm {\Delta } f\,}
1055:
914:
807:
311:(OCT), assuming that the source has a
868:
293:{\displaystyle \,\Delta \lambda \,}
13:
630:
537:
503:
403:
283:
231:
140:
107:
14:
1089:
997:An Introduction to Interferometry
814:An introduction to Interferometry
598:difference of a self-interfering
192:is the speed of light in vacuum,
1023: This article incorporates
1018:
972:"Sam's Laser FAQ - Diode Lasers"
948:Holography: A Practical Approach
852:Superconducting coherence length
831:
1036:General Services Administration
988:
964:
946:Ackermann, Gerhard K. (2007).
939:
925:. Springer Berlin Heidelberg.
50:telecommunications engineering
1:
862:
275:is the signal wavelength and
923:Optical Coherence Tomography
448:{\displaystyle \,\lambda \,}
309:optical coherence tomography
268:{\displaystyle \,\lambda \,}
59:electromagnetic fields. In
7:
824:
589:Mach–Zehnder interferometer
74:
10:
1094:
1063:Electromagnetic radiation
995:Tolansky, Samuel (1973).
779:
757:is the fringe intensity.
572:{\displaystyle \,\pm L\,}
585:Michelson interferometer
554:, then a path offset of
35:) maintains a specified
1031:Federal Standard 1037C
1025:public domain material
751:
726:
638:
573:
548:
515:
480:
449:
424:
331:
294:
269:
243:
208:
186:
161:
1044: (in support of
752:
750:{\displaystyle \,I\,}
727:
639:
602:which corresponds to
574:
549:
516:
481:
479:{\displaystyle n_{g}}
450:
425:
332:
330:{\displaystyle \,L\,}
295:
270:
244:
209:
207:{\displaystyle \,n\,}
187:
185:{\displaystyle \,c\,}
162:
897:10.1364/ao.41.005256
790:Semiconductor lasers
739:
651:
606:
558:
533:
498:
463:
437:
344:
319:
279:
257:
226:
196:
174:
86:
33:electromagnetic wave
889:2002ApOpt..41.5256A
808:Other light sources
596:optical path length
37:degree of coherence
1078:Optical quantities
786:helium–neon lasers
747:
722:
634:
569:
544:
511:
476:
445:
420:
327:
290:
265:
239:
204:
182:
157:
976:www.repairfaq.org
957:978-3-527-40663-0
932:978-3-319-06419-2
883:(25): 5256–5262.
857:Spatial coherence
760:In long-distance
718:
714:
622:
581:fringe visibility
416:
412:
374:
253:of the source or
153:
149:
116:
65:quantum coherence
61:quantum mechanics
41:Wave interference
1085:
1049:
1043:
1038:. Archived from
1022:
1021:
1011:
1010:
992:
986:
985:
983:
982:
968:
962:
961:
943:
937:
936:
918:
912:
911:
872:
841:
836:
835:
756:
754:
753:
748:
731:
729:
728:
723:
716:
715:
713:
712:
711:
699:
698:
688:
686:
685:
673:
672:
661:
643:
641:
640:
635:
623:
621:
611:
579:will reduce the
578:
576:
575:
570:
553:
551:
550:
545:
540:
520:
518:
517:
512:
506:
488:refractive index
485:
483:
482:
477:
475:
474:
454:
452:
451:
446:
429:
427:
426:
421:
414:
413:
411:
406:
400:
399:
388:
387:
378:
375:
370:
354:
336:
334:
333:
328:
299:
297:
296:
291:
274:
272:
271:
266:
248:
246:
245:
240:
234:
216:refractive index
213:
211:
210:
205:
191:
189:
188:
183:
166:
164:
163:
158:
151:
150:
148:
143:
132:
131:
122:
117:
115:
110:
96:
25:coherence length
1093:
1092:
1088:
1087:
1086:
1084:
1083:
1082:
1068:Physical optics
1053:
1052:
1028:
1019:
1017:
1014:
1007:
993:
989:
980:
978:
970:
969:
965:
958:
944:
940:
933:
919:
915:
873:
869:
865:
837:
830:
827:
819:liquid nitrogen
810:
802:frequency combs
782:
740:
737:
736:
707:
703:
694:
690:
689:
681:
677:
668:
664:
662:
660:
652:
649:
648:
615:
610:
607:
604:
603:
559:
556:
555:
536:
534:
531:
530:
529:spectral width
502:
499:
496:
495:
470:
466:
464:
461:
460:
459:of the source,
455:is the central
438:
435:
434:
402:
395:
391:
389:
383:
379:
377:
355:
353:
345:
342:
341:
320:
317:
316:
280:
277:
276:
258:
255:
254:
230:
227:
224:
223:
197:
194:
193:
175:
172:
171:
139:
133:
127:
123:
121:
106:
100:
95:
87:
84:
83:
77:
17:
12:
11:
5:
1091:
1081:
1080:
1075:
1070:
1065:
1051:
1050:
1042:on 2022-01-22.
1013:
1012:
1005:
987:
963:
956:
938:
931:
913:
877:Applied Optics
866:
864:
861:
860:
859:
854:
849:
847:Coherence time
843:
842:
839:Physics portal
826:
823:
809:
806:
781:
778:
745:
733:
732:
721:
710:
706:
702:
697:
693:
684:
680:
676:
671:
667:
659:
656:
632:
629:
626:
619:
614:
567:
564:
543:
539:
523:spectral width
521:is the (FWHM)
509:
505:
473:
469:
443:
431:
430:
419:
409:
405:
398:
394:
386:
382:
373:
368:
365:
362:
359:
352:
349:
325:
305:communications
288:
285:
263:
237:
233:
202:
180:
168:
167:
156:
146:
142:
137:
130:
126:
120:
113:
109:
104:
99:
94:
91:
76:
73:
31:wave (e.g. an
15:
9:
6:
4:
3:
2:
1090:
1079:
1076:
1074:
1071:
1069:
1066:
1064:
1061:
1060:
1058:
1047:
1041:
1037:
1033:
1032:
1026:
1016:
1015:
1008:
1006:9780582443334
1002:
998:
991:
977:
973:
967:
959:
953:
950:. Wiley-VCH.
949:
942:
934:
928:
924:
917:
910:
906:
902:
898:
894:
890:
886:
882:
878:
871:
867:
858:
855:
853:
850:
848:
845:
844:
840:
834:
829:
822:
820:
815:
805:
803:
799:
795:
791:
787:
777:
775:
771:
767:
763:
758:
743:
719:
704:
700:
691:
678:
674:
665:
657:
654:
647:
646:
645:
627:
624:
617:
612:
601:
597:
592:
590:
586:
582:
565:
562:
541:
528:
524:
507:
493:
489:
486:is the group
471:
467:
458:
441:
417:
407:
396:
392:
384:
380:
371:
366:
363:
360:
357:
350:
347:
340:
339:
338:
337:is given by
323:
314:
310:
306:
301:
286:
261:
252:
235:
221:
217:
200:
178:
154:
144:
135:
128:
124:
118:
111:
102:
97:
92:
89:
82:
81:
80:
72:
70:
69:wave function
66:
62:
58:
53:
51:
47:
42:
38:
34:
30:
26:
22:
1040:the original
1030:
996:
990:
979:. Retrieved
975:
966:
947:
941:
922:
916:
908:
880:
876:
870:
813:
811:
794:fiber lasers
783:
762:transmission
759:
734:
593:
432:
302:
169:
78:
67:length of a
54:
24:
18:
1046:MIL-STD-188
999:. Longman.
812:Tolansky's
774:diffraction
303:In optical
1057:Categories
981:2017-02-06
909:equation 8
863:References
798:linewidths
784:Multimode
770:scattering
766:dispersion
600:laser beam
457:wavelength
46:holography
675:−
631:%
625:≈
563:±
542:λ
538:Δ
508:λ
504:Δ
442:λ
408:λ
404:Δ
381:λ
372:π
364:
287:λ
284:Δ
262:λ
251:bandwidth
232:Δ
145:λ
141:Δ
125:λ
119:≈
108:Δ
57:classical
905:12211551
825:See also
313:Gaussian
75:Formulas
29:coherent
885:Bibcode
490:of the
249:is the
218:of the
214:is the
21:physics
1003:
954:
929:
903:
780:Lasers
772:, and
735:where
717:
494:, and
492:medium
433:where
415:
222:, and
220:medium
170:where
152:
1073:Waves
1027:from
796:with
1001:ISBN
952:ISBN
927:ISBN
901:PMID
527:FWHM
307:and
48:and
893:doi
709:min
696:max
683:min
670:max
39:.
19:In
1059::
1048:).
1034:.
974:.
907:.
899:.
891:.
881:41
879:.
776:.
768:,
628:37
361:ln
71:.
52:.
23:,
1009:.
984:.
960:.
935:.
895::
887::
744:I
720:,
705:I
701:+
692:I
679:I
666:I
658:=
655:V
618:e
613:1
566:L
472:g
468:n
418:,
397:g
393:n
385:2
367:2
358:2
351:=
348:L
324:L
236:f
201:n
179:c
155:,
136:n
129:2
112:f
103:n
98:c
93:=
90:L
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.