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Interferometric visibility

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907: 919: 895: 160:. Under these circumstances, the interferometric visibility is also known as the "Michelson visibility" or the "fringe visibility." For this type of interference, the sum of the intensities (powers) of the two interfering waves equals the average intensity over a given time or space domain. The visibility is written as: 798: 436: 687: 570: 877:
indicates the phase relationship of the original electric field. Any dissimilarity between the optical fields will decrease the visibility from the ideal. In this sense, the visibility is a measure of the
350: 1079: 280: 207: 875: 855: 828: 1063: 1032: 706: 361: 578: 461: 923: 983: 899: 136: 52: 988: 948: 286: 926:. At large delays the photons do not interfere. At zero delays, the detection of coincident photon pairs is suppressed. 76:
to the sum of the powers of the individual waves. The interferometric visibility gives a practical way to measure the
956: 151: 222: 911: 140: 886:. This definition of interference directly applies to the interference of water waves and electric signals. 1094: 936: 115:. Alternately, the phase difference may be manually controlled by the operator, for example by adjusting a 978: 952: 166: 144: 1039: 697: 73: 968: 883: 879: 156: 148: 112: 96: 81: 77: 80:
of two waves (or one wave with itself). A theoretical definition of the coherence is given by the
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varying over time or space. For example, the phase difference varies as a function of space in a
88: 57: 1007: 1057: 944: 100: 65: 860: 68:, water waves, sound waves, or electrical signals. Visibility is defined as the ratio of the 47: 833: 806: 92: 973: 906: 213: 132: 120: 17: 1088: 955:. Photons, atoms, electrons, neutrons, and molecules have exhibited interference in 940: 693: 116: 882:
between two optical fields. A theoretical definition for this is given by the
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can exhibit interference fringes. Atomic populations show interference in a
918: 104: 69: 793:{\displaystyle \nu ={\frac {2{\sqrt {I_{1}I_{2}}}|\gamma |}{I_{1}+I_{2}}},} 103:) of the resulting wave oscillates, forming an interference pattern. The 431:{\displaystyle \nu ={\frac {I_{\max }-I_{\min }}{I_{\max }+I_{\min }}},} 894: 682:{\displaystyle I_{min}=I_{1}+I_{2}-2*{\sqrt {I_{1}*I_{2}}}*|\gamma |,} 565:{\displaystyle I_{max}=I_{1}+I_{2}+2*{\sqrt {I_{1}*I_{2}}}*|\gamma |,} 61: 1020: 917: 905: 893: 696:(consist of only single wavelength) point sources of the same 1008:"Fringe Visibility -- from Eric Weisstein's World of Physics" 216:
of the oscillating intensity and the average intensity:
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and as the phase difference between them varies, the
345:{\displaystyle {\bar {I}}=(I_{\max }+I_{\min })/2.} 869: 849: 822: 792: 681: 564: 430: 344: 274: 201: 448:is the maximum intensity of the oscillations and 417: 404: 392: 379: 326: 313: 253: 240: 857:indicate the intensity of the respective wave. 947:, interference is ubiquitous. Some examples: 8: 943:and all objects can be considered waves in 455:the minimum intensity of the oscillations. 275:{\displaystyle A=(I_{\max }-I_{\min })/2,} 862: 841: 835: 814: 808: 778: 765: 754: 746: 738: 728: 722: 716: 708: 671: 663: 652: 639: 633: 618: 605: 586: 580: 554: 546: 535: 522: 516: 501: 488: 469: 463: 416: 403: 391: 378: 371: 363: 334: 325: 312: 291: 290: 288: 261: 252: 239: 224: 185: 184: 179: 168: 700:, then the predicted visibility will be 27:Measure of interference in a wave system 999: 1062:: CS1 maint: archived copy as title ( 1055: 692:If the two optical fields are ideally 46:when in context) is a measure of the 7: 147:), interference manifests itself as 1080:Stedman Review of the Sagnac Effect 84:, using the notion of correlation. 202:{\displaystyle \nu =A/{\bar {I}},} 25: 1021:https://spie.org/samples/FG30.pdf 87:Generally, two or more waves are 984:List of types of interferometers 154:over time or space, also called 107:definition may be expanded to a 931:Visibility in quantum mechanics 914:is maximum (80%) at the center. 755: 747: 672: 664: 555: 547: 331: 305: 296: 258: 232: 190: 99:(probability or population in 1: 957:double-slit interferometers 924:Hong–Ou–Mandel interference 900:Mach–Zehnder interferometer 355:So it can be rewritten as: 137:Mach–Zehnder interferometer 1111: 212:in terms of the amplitude 32:interferometric visibility 949:Bose–Einstein condensates 56:in any system subject to 912:double-slit interference 141:Michelson interferometer 870:{\displaystyle \gamma } 60:. Examples include as 36:interference visibility 18:Interference visibility 979:Optical interferometry 927: 915: 903: 871: 851: 824: 794: 683: 566: 432: 346: 276: 203: 989:Hong–Ou–Mandel effect 953:Ramsey interferometer 921: 909: 897: 872: 852: 850:{\displaystyle I_{2}} 825: 823:{\displaystyle I_{1}} 795: 684: 567: 433: 347: 277: 204: 145:Sagnac interferometer 937:Schrödinger equation 861: 834: 807: 707: 579: 462: 362: 287: 223: 167: 127:Visibility in optics 74:interference pattern 969:Degree of coherence 910:Visibility in this 884:degree of coherence 113:two-slit experiment 109:visibility function 82:degree of coherence 928: 916: 904: 867: 847: 820: 790: 679: 562: 428: 342: 272: 199: 131:In linear optical 58:wave superposition 945:quantum mechanics 785: 744: 658: 541: 423: 299: 193: 101:quantum mechanics 66:quantum mechanics 40:fringe visibility 16:(Redirected from 1102: 1068: 1067: 1061: 1053: 1051: 1050: 1044: 1038:. Archived from 1037: 1029: 1023: 1018: 1012: 1011: 1004: 898:Visibility in a 876: 874: 873: 868: 856: 854: 853: 848: 846: 845: 829: 827: 826: 821: 819: 818: 799: 797: 796: 791: 786: 784: 783: 782: 770: 769: 759: 758: 750: 745: 743: 742: 733: 732: 723: 717: 688: 686: 685: 680: 675: 667: 659: 657: 656: 644: 643: 634: 623: 622: 610: 609: 597: 596: 571: 569: 568: 563: 558: 550: 542: 540: 539: 527: 526: 517: 506: 505: 493: 492: 480: 479: 437: 435: 434: 429: 424: 422: 421: 420: 408: 407: 397: 396: 395: 383: 382: 372: 351: 349: 348: 343: 338: 330: 329: 317: 316: 301: 300: 292: 281: 279: 278: 273: 265: 257: 256: 244: 243: 208: 206: 205: 200: 195: 194: 186: 183: 21: 1110: 1109: 1105: 1104: 1103: 1101: 1100: 1099: 1085: 1084: 1076: 1071: 1054: 1048: 1046: 1042: 1035: 1033:"Archived copy" 1031: 1030: 1026: 1019: 1015: 1006: 1005: 1001: 997: 965: 933: 892: 859: 858: 837: 832: 831: 810: 805: 804: 774: 761: 760: 734: 724: 718: 705: 704: 648: 635: 614: 601: 582: 577: 576: 531: 518: 497: 484: 465: 460: 459: 454: 447: 412: 399: 398: 387: 374: 373: 360: 359: 321: 308: 285: 284: 248: 235: 221: 220: 165: 164: 133:interferometers 129: 34:(also known as 28: 23: 22: 15: 12: 11: 5: 1108: 1106: 1098: 1097: 1095:Interferometry 1087: 1086: 1083: 1082: 1075: 1074:External links 1072: 1070: 1069: 1024: 1013: 998: 996: 993: 992: 991: 986: 981: 976: 974:Interferometry 971: 964: 961: 932: 929: 922:Visibility in 891: 888: 866: 844: 840: 817: 813: 801: 800: 789: 781: 777: 773: 768: 764: 757: 753: 749: 741: 737: 731: 727: 721: 715: 712: 690: 689: 678: 674: 670: 666: 662: 655: 651: 647: 642: 638: 632: 629: 626: 621: 617: 613: 608: 604: 600: 595: 592: 589: 585: 573: 572: 561: 557: 553: 549: 545: 538: 534: 530: 525: 521: 515: 512: 509: 504: 500: 496: 491: 487: 483: 478: 475: 472: 468: 452: 445: 439: 438: 427: 419: 415: 411: 406: 402: 394: 390: 386: 381: 377: 370: 367: 353: 352: 341: 337: 333: 328: 324: 320: 315: 311: 307: 304: 298: 295: 282: 271: 268: 264: 260: 255: 251: 247: 242: 238: 234: 231: 228: 210: 209: 198: 192: 189: 182: 178: 175: 172: 128: 125: 121:interferometer 26: 24: 14: 13: 10: 9: 6: 4: 3: 2: 1107: 1096: 1093: 1092: 1090: 1081: 1078: 1077: 1073: 1065: 1059: 1045:on 2017-01-22 1041: 1034: 1028: 1025: 1022: 1017: 1014: 1009: 1003: 1000: 994: 990: 987: 985: 982: 980: 977: 975: 972: 970: 967: 966: 962: 960: 958: 954: 950: 946: 942: 941:wave equation 938: 930: 925: 920: 913: 908: 901: 896: 889: 887: 885: 881: 864: 842: 838: 815: 811: 787: 779: 775: 771: 766: 762: 751: 739: 735: 729: 725: 719: 713: 710: 703: 702: 701: 699: 695: 694:monochromatic 676: 668: 660: 653: 649: 645: 640: 636: 630: 627: 624: 619: 615: 611: 606: 602: 598: 593: 590: 587: 583: 575: 574: 559: 551: 543: 536: 532: 528: 523: 519: 513: 510: 507: 502: 498: 494: 489: 485: 481: 476: 473: 470: 466: 458: 457: 456: 451: 444: 425: 413: 409: 400: 388: 384: 375: 368: 365: 358: 357: 356: 339: 335: 322: 318: 309: 302: 293: 283: 269: 266: 262: 249: 245: 236: 229: 226: 219: 218: 217: 215: 196: 187: 180: 176: 173: 170: 163: 162: 161: 159: 158: 153: 150: 146: 142: 138: 134: 126: 124: 122: 118: 114: 110: 106: 102: 98: 94: 90: 85: 83: 79: 75: 71: 67: 63: 59: 55: 54: 49: 45: 41: 37: 33: 19: 1047:. Retrieved 1040:the original 1027: 1016: 1002: 934: 902:is constant. 802: 698:polarization 691: 449: 442: 440: 354: 211: 155: 152:oscillations 130: 108: 89:superimposed 86: 53:interference 51: 43: 39: 35: 31: 29: 119:knob in an 1049:2016-09-25 995:References 935:Since the 135:(like the 44:visibility 42:, or just 880:coherence 865:γ 752:γ 711:ν 669:γ 661:∗ 646:∗ 631:∗ 625:− 552:γ 544:∗ 529:∗ 514:∗ 385:− 366:ν 297:¯ 246:− 191:¯ 171:ν 149:intensity 105:pointwise 97:intensity 78:coherence 70:amplitude 1089:Category 1058:cite web 963:See also 890:Examples 214:envelope 48:contrast 157:fringes 117:vernier 72:of the 803:where 441:where 143:, and 62:optics 1043:(PDF) 1036:(PDF) 939:is a 93:power 1064:link 830:and 38:and 30:The 453:min 446:max 418:min 405:max 393:min 380:max 327:min 314:max 254:min 241:max 95:or 50:of 1091:: 1060:}} 1056:{{ 959:. 340:2. 139:, 123:. 64:, 1066:) 1052:. 1010:. 843:2 839:I 816:1 812:I 788:, 780:2 776:I 772:+ 767:1 763:I 756:| 748:| 740:2 736:I 730:1 726:I 720:2 714:= 677:, 673:| 665:| 654:2 650:I 641:1 637:I 628:2 620:2 616:I 612:+ 607:1 603:I 599:= 594:n 591:i 588:m 584:I 560:, 556:| 548:| 537:2 533:I 524:1 520:I 511:2 508:+ 503:2 499:I 495:+ 490:1 486:I 482:= 477:x 474:a 471:m 467:I 450:I 443:I 426:, 414:I 410:+ 401:I 389:I 376:I 369:= 336:/ 332:) 323:I 319:+ 310:I 306:( 303:= 294:I 270:, 267:2 263:/ 259:) 250:I 237:I 233:( 230:= 227:A 197:, 188:I 181:/ 177:A 174:= 20:)

Index

Interference visibility
contrast
interference
wave superposition
optics
quantum mechanics
amplitude
interference pattern
coherence
degree of coherence
superimposed
power
intensity
quantum mechanics
pointwise
two-slit experiment
vernier
interferometer
interferometers
Mach–Zehnder interferometer
Michelson interferometer
Sagnac interferometer
intensity
oscillations
fringes
envelope
monochromatic
polarization
coherence
degree of coherence

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