1751:
Furthermore, it has been demonstrated experimentally that reciprocity does apply in a TEM under the right conditions, but the underlying physics of the principle dictates that reciprocity can only be truly exact if ray transmission occurs through only scalar fields, i.e. no magnetic fields. We can therefore conclude that the distortions to reciprocity due to magnetic fields of the electromagnetic lenses in TEM may be ignored under typical operating conditions. However, users should be careful not to apply reciprocity to magnetic imaging techniques, TEM of ferromagnetic materials, or extraneous TEM situations without careful consideration. Generally, polepieces for TEM are designed using finite element analysis of generated magnetic fields to ensure symmetry.
1755:
enhancement effects that one might expect. This system works by placing the sample in between the front and back objective lens polepieces, as in an ordinary TEM, but the two polepieces are kept in exact mirror symmetry with respect to the sample plane between them. Meanwhile, their excitation polarities are exactly opposite, generating magnetic fields that cancel almost perfectly at the plane of the sample. However, since they do not cancel elsewhere, the electron trajectory must still pass through magnetic fields.
1530:
1762:, which is characterized in principle by switching the position of the electron source and observation point. This is effectively the same as reversing time on a TEM so that electrons travel in the opposite direction. Therefore, under appropriate conditions (in which reciprocity does apply), knowledge of TEM imaging can be useful in taking and interpreting images with STEM.
204:, which is described by distinct accounts of the interacting electric and magnetic fields. The Helmholtz principle rests mainly on the linearity and superposability of the light field, and it has close analogues in non-electromagnetic linear propagating fields, such as sound. It was discovered before the electromagnetic nature of light became known.
1225:
1233:
993:
633:
1750:
with small energy loss, it can be shown that reciprocity may be used to approximate intensity (rather than wave amplitude). So in very thick samples or samples in which inelastic scattering dominates, the benefits of using reciprocity for the previously mentioned TEM applications are no longer valid.
180:
Simply put, in suitable conditions, the principle states that the source and observation point may be switched without changing the measured intensity. Intuitively, "If I can see you, you can see me." Like the principles of thermodynamics, in suitable conditions, this principle is reliable enough to
1721:
One simple yet important implication of this reciprocity principle is that any light directed through a lens in one direction (from object to image plane) is optically equal to its conjugate, i.e. light being directed through the same set-up but in the opposite direction. An electron being focused
447:
199:
Helmholtz reciprocity referred originally to light. This is a particular form of electromagnetism that may be called far-field radiation. For this, the electric and magnetic fields do not need distinct descriptions, because they propagate feeding each other evenly. So the
Helmholtz principle is a
1754:
Magnetic objective lens systems have been used in TEM to achieve atomic-scale resolution while maintaining a magnetic field free environment at the plane of the sample, but the method of doing so still requires a large magnetic field above (and below) the sample, thus negating any reciprocity
1001:
1722:
through any series of optical components does not âcareâ from which direction it comes; as long as the same optical events happen to it, the resulting wave function will be the same. For that reason, this principle has important applications in the field of
1525:{\displaystyle +(-4\pi ^{2})^{3}\int d\mathbf {r_{1}} \int d\mathbf {r_{2}} \int G(\mathbf {r_{O},r_{1}} )G(\mathbf {r_{1},r_{2}} )G(\mathbf {r_{2},r_{3}} )V(\mathbf {r_{1}} )V(\mathbf {r_{2}} )V(\mathbf {r_{3}} )G(\mathbf {r_{3},r_{A}} )d\mathbf {r_{3}} }
771:
195:
When there are magnetic fields in the path of the ray, the principle does not apply. Departure of the optical medium from linearity also causes departure from
Helmholtz reciprocity, as well as the presence of moving objects in the path of the ray.
787:
1741:
An important caveat to note is that in a situation where electrons lose energy after interacting with the scattering medium of the sample, there is not time-reversal symmetry. Therefore, reciprocity only truly applies in situations of
37:(BRDF) outcome. If light was measured with a sensor and that light reflected on a material with a BRDF that obeys the Helmholtz reciprocity principle one would be able to swap the sensor and light source and the measurement of
280:
462:
1711:
29:
of light and its reverse ray encounter matched optical adventures, such as reflections, refractions, and absorptions in a passive medium, or at an interface. It does not apply to moving, non-linear, or magnetic media.
72:
1726:. The notion that conjugate optical processes produce equivalent results allows the microscope user to grasp a deeper understanding of, and have considerable flexibility in, techniques involving
1220:{\displaystyle +(-4\pi ^{2})^{2}\int d\mathbf {r_{1}} \int G(\mathbf {r_{O},r_{1}} )G(\mathbf {r_{1},r_{2}} )V(\mathbf {r_{1}} )V(\mathbf {r_{2}} )G(\mathbf {r_{2},r_{A}} )d\mathbf {r_{2}} }
1623:
1594:
268:
988:{\displaystyle \Psi (\mathbf {r_{O},r_{A}} )=G(\mathbf {r_{O},r_{A}} )-4\pi ^{2}\int G(\mathbf {r_{O},r_{1}} )V(\mathbf {r_{1}} )G(\mathbf {r_{1},r_{A}} )d\mathbf {r_{1}} }
192:
stated the basic idea of reciprocity as a consequence of the linearity of propagation of small vibrations, light consisting of sinusoidal vibrations in a linear medium.
211:. As these more mathematically complicated proofs may detract from the simplicity of the theorem, A.P Pogany and P. S. Turner have proven it in only a few steps using a
104:
A ray of light proceeding from point 1 arrives at point 2 after suffering any number of refractions, reflections, &c. At point 1 let any two perpendicular planes
644:
1846:"On the perfect blackness of the central spot in Newton's rings, and on the verification of Fresnel's formulae for the intensities of reflected and refracted rays"
1562:
1713:, which is the mathematical statement of the reciprocity theorem: switching the light source A and observation point O does not alter the observed wave function.
442:{\displaystyle (\bigtriangledown ^{2}+4\pi K^{2})\Psi (\mathbf {r,r_{A}} )=-4\pi K^{2}V(\mathbf {r} )\Psi (\mathbf {r,r_{A}} )+\delta (\mathbf {r-r_{A}} )}
628:{\displaystyle \Psi (\mathbf {r,r_{A}} )=G(\mathbf {r,r_{A}} )-4\pi ^{2}\int G(\mathbf {r,r'} V(\mathbf {r'} \Psi (\mathbf {r',r_{A}} )d\mathbf {r'} }
181:
use as a check on the correct performance of experiments, in contrast with the usual situation in which the experiments are tests of a proposed law.
2527:
Shibata, N.; Kohno, Y.; Nakamura, A.; Morishita, S.; Seki, T.; Kumamoto, A.; Sawada, H.; Matsumoto, T.; Findlay, S. D.; Ikuhara, Y. (May 24, 2019).
118:
be taken in the direction of the ray; and let the vibrations of the ray be divided into two parts, one in each of these planes. Take similar planes
2384:
1628:
34:
2323:
Wells, Oliver C. (July 23, 2008). "Reciprocity between the reflection electron microscope and the lowâloss scanning electron microscope".
777:
Next, it is valid to assume the solution inside the scattering medium at point O may be approximated by a Born series, making use of the
2358:
Spindler, Paul (de
Chemnitz) Auteur du texte; Meyer, Georg (1857-1950) Auteur du texte; Meerburg, Jacob Hendrik Auteur du texte (1860).
1915:
Stewart, B. (1858). An account of some experiments on radiant heat, involving an extension of
Professor Prevost's theory of exchanges,
1759:
781:
in scattering theory. In doing so, the series may be iterated through in the usual way to generate the following integral solution:
189:
185:
2511:
207:
The
Helmholtz reciprocity theorem has been rigorously proven in a number of ways, generally making use of quantum mechanical
48:, the Helmholtz reciprocity principle is important if the global illumination algorithm reverses light paths (for example
2277:
Kirchhoff, G. (1860). On the
Relation between the Radiating and Absorbing Powers of different Bodies for Light and Heat,
1936:
Kirchhoff, G. (1860). On the
Relation between the Radiating and Absorbing Powers of different Bodies for Light and Heat,
67:
2201:
2175:
2149:
1825:
1804:
1876:
1723:
1841:
1771:
201:
78:
2179:
33:
For example, incoming and outgoing light can be considered as reversals of each other, without affecting the
2147:
Clarke, F.J.J., Parry, D.J. (1985). Helmholtz reciprocity: its validity and application to reflectometry,
1845:
132:
in the ray at point 2; then the following proposition may be demonstrated. If when the quantity of light
2405:
Pogany, A. P.; Turner, P. S. (January 23, 1968). "Reciprocity in electron diffraction and microscopy".
2490:
1599:
1570:
218:
2268:, second edition translated by M. Masius, P. Blakiston's Son and Co., Philadelphia, pages 35, 38,39.
456:, the above equation can be solved for the wave function in an integral (and thus iterative) form:
215:. Assuming a light source at a point A and an observation point O, with various scattering points
2084:
271:
766:{\displaystyle G(\mathbf {r,r'} )=-{\frac {\exp(2\pi iK|\mathbf {r-r'} |)}{|\mathbf {r-r'} |}}}
49:
1735:
2056:, second edition translated by M. Masius, P. Blakiston's Son and Co., Philadelphia, page 35.
1899:
Helmholtz, H. (1859/60). Theorie der
Luftschwingungen in Röhren mit offenen Enden, Crelle's
2540:
2414:
2223:
2191:
1747:
1727:
1538:
8:
453:
188:, Planck makes repeated and essential use of the StokesâHelmholtz reciprocity principle.
45:
2544:
2418:
2307:
2227:
1990:
Rayleigh, Lord (1876). On the application of the
Principle of Reciprocity to acoustics,
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1743:
778:
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82:
2286:
2073:
1945:
2564:
2548:
2499:
2461:
2422:
2332:
2231:
1969:
Strutt, J.W. (Lord
Rayleigh) (1873). Some general theorems relating to vibrations,
90:
2598:
2117:
Tingwaldt, C.P. (1952). Ăber das Helmholtzsche ReziprozitĂ€tsgesetz in der Optik,
1731:
2359:
2552:
1758:
Reciprocity can also be used to understand the main difference between TEM and
2503:
2466:
2449:
2426:
2194:: Electromagnetic theory of propagation, interference and diffraction of light
2592:
2560:
2475:
2434:
2344:
2243:
1567:
Noting again the form of the Green's function, it is apparent that switching
63:
2529:"Atomic resolution electron microscopy in a magnetic field free environment"
2578:
1875:, first edition cited by Planck, Leopold Voss, Leipzig, volume 1, page 169.
1706:{\displaystyle \Psi (\mathbf {r_{A},r_{O}} )=\Psi (\mathbf {r_{O},r_{A}} )}
26:
212:
2032:
Rayleigh, Lord (1900). On the law of reciprocity in diffuse reflection,
2016:, second revised edition, Dover, New York, volume 1, sections 107-111a.
1890:, edited by F. Richarz, Johann Ambrosius Barth, Leipzig, pages 158-162.
208:
94:
100:
As cited by Kirchhoff in 1860, the principle is translated as follows:
2336:
2065:
Minnaert, M. (1941). The reciprocity principle in lunar photometry,
186:
Kirchhoff's law of equality of radiative emissivity and absorptivity
2306:
Helmholtz, Hermann von (1867). a, Hermann von Helmholtz u (ed.).
274:
may be used to represent the resulting wave function in space:
2489:
Hren, John J; Goldstein, Joseph I; Joy, David C, eds. (1979).
1625:
in the above form will not change the result; that is to say,
18:
Principle in optics relating light rays and their reverse rays
2526:
2492:
Introduction to Analytical Electron Microscopy | SpringerLink
2108:, Oxford University Press, Oxford, pages 20-21, 171-177, 182.
143:
proceeds from 1 in the direction of the given ray, that part
2028:
2026:
2024:
2022:
38:
81:(1849) and with reference to polarization on page 169 of
2019:
154:
arrives at 2, then, conversely, if the quantity of light
2214:
Potton, R J (April 27, 2004). "Reciprocity in optics".
2085:
A mathematical proof of Stokes' reversibility principle
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1631:
1602:
1573:
1541:
1236:
1004:
790:
647:
465:
283:
221:
60:
The StokesâHelmholtz reversionâreciprocity principle
2048:
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1556:
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1219:
987:
765:
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441:
262:
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2138:, 2 volumes, Wiley, New York, volume 1, page 84.
2136:Applied Optics: A Guide to Optical System Design
2043:
2008:
2006:
2004:
1986:
1984:
1982:
1932:
1930:
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1818:Theory of Reflectance and Emittance Spectroscopy
1797:Theory of Reflectance and Emittance Spectroscopy
1791:
1789:
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1760:scanning transmission electron microscopy (STEM)
1901:Journal fĂŒr die reine und angewandte Mathematik
35:bidirectional reflectance distribution function
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1820:, Cambridge University Press, Cambridge UK,
1799:, Cambridge University Press, Cambridge UK,
184:In his magisterial proof of the validity of
165:proceeds from 2, the same quantity of light
2383:: CS1 maint: numeric names: authors list (
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2196:, 7th edition, Cambridge University Press,
2012:Strutt, J.W., Baron Rayleigh (1894/1945).
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1850:Cambridge and Dublin Mathematical Journal
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1724:transmission electron microscopy (TEM)
202:electromagnetic reciprocity in general
200:more simply described special case of
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52:versus classic light path tracing).
44:In the computer graphics scheme of
13:
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2309:Handbuch der physiologischen Optik
2150:Lighting Research & Technology
1888:Vorlesungen ĂŒber Theorie der WĂ€rme
1873:Handbuch der physiologischen Optik
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87:Handbuch der physiologischen Optik
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2450:"The Theory of Kikuchi patterns"
2407:Acta Crystallographica Section A
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2312:(in German). Leipzig: L. Voss.
2222:(5). IOP Publishing: 717â754.
2216:Reports on Progress in Physics
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1828:, Chapters 8-9, pages 181-260.
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1:
1807:, Section 10C, pages 263-264.
1777:
77: was stated in part by
2448:Kainuma, Y. (May 10, 1955).
2288:, translated by F. Guthrie,
2266:The Theory of Heat Radiation
2054:The Theory of Heat Radiation
1947:, translated by F. Guthrie,
7:
2189:Born, M., Wolf, E. (1999).
1765:
10:
2615:
2553:10.1038/s41467-019-10281-2
2236:10.1088/0034-4885/67/5/r03
2104:Chandrasekhar, S. (1950).
1917:Trans. Roy. Soc. Edinburgh
1886:Helmholtz, H. von (1903).
1871:Helmholtz, H. von (1856).
68:Excessive citations inline
55:
25:principle describes how a
2504:10.1007/978-1-4757-5581-7
2467:10.1107/S0365110X55000832
2427:10.1107/S0567739468000136
1976:: 357-368, pages 366-368.
2325:Applied Physics Letters
1944:: 275-301, at page 287
136:polarized in the plane
73:considered for deletion
2454:Acta Crystallographica
1971:Proc. Lond. Math. Soc.
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209:time-reversal symmetry
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2533:Nature Communications
2067:Astrophysical Journal
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41:would remain equal.
23:Helmholtz reciprocity
2360:"Annalen der Physik"
2192:Principles of Optics
2168:Theory of reflection
2083:Mahan, A.I. (1943).
1748:inelastic scattering
1728:electron diffraction
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1557:{\displaystyle +...}
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272:Schrödinger equation
219:
89:of 1856 as cited by
2545:2019NatCo..10.2308S
2419:1968AcCrA..24..103P
2264:Planck, M. (1914).
2228:2004RPPh...67..717P
2166:Lekner, J. (1987).
2052:Planck, M. (1914).
2014:The Theory of Sound
1922:(1): 1-20, page 18.
1906:(1): 1-72, page 29.
46:global illumination
2106:Radiative Transfer
1816:Hapke, B. (1993).
1795:Hapke, B. (1993).
1744:elastic scattering
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779:Born approximation
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270:between them, the
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2513:978-1-4757-5583-1
2134:Levi, L. (1968).
1992:Proc. Roy. Soc. A
1955::2-21, at page 9.
1746:. In the case of
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176:will arrive at 1.
83:Hermann Helmholtz
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2317:
2304:
2300:
2276:
2272:
2263:
2259:
2212:
2208:
2188:
2184:
2165:
2161:
2146:
2142:
2133:
2129:
2116:
2112:
2103:
2099:
2082:
2078:
2064:
2060:
2051:
2044:
2031:
2020:
2011:
2002:
1989:
1980:
1968:
1959:
1935:
1926:
1914:
1910:
1898:
1894:
1885:
1881:
1870:
1861:
1839:
1832:
1815:
1811:
1794:
1785:
1780:
1768:
1738:, and others.
1719:
1693:
1689:
1680:
1676:
1675:
1656:
1652:
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1639:
1638:
1630:
1627:
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1137:
1133:
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1099:
1098:
1082:
1078:
1069:
1065:
1064:
1048:
1044:
1043:
1031:
1027:
1021:
1017:
1003:
1000:
999:
978:
974:
973:
960:
956:
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942:
926:
922:
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901:
892:
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887:
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852:
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802:
798:
797:
789:
786:
785:
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746:
739:
734:
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724:
715:
708:
703:
681:
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661:
654:
646:
643:
642:
616:
615:
602:
598:
587:
586:
571:
570:
555:
548:
533:
529:
513:
509:
502:
483:
479:
472:
464:
461:
460:
429:
425:
418:
399:
395:
388:
374:
362:
358:
336:
332:
325:
310:
306:
291:
287:
282:
279:
278:
239:
235:
226:
222:
220:
217:
216:
175:
164:
153:
142:
131:
124:
117:
110:
61:
58:
19:
12:
11:
5:
2612:
2602:
2601:
2585:
2584:
2519:
2512:
2481:
2460:(5): 247â257.
2440:
2413:(1): 103â109.
2390:
2350:
2331:(6): 507â510.
2315:
2298:
2270:
2257:
2206:
2182:
2178:, pages 33-37.
2159:
2140:
2127:
2110:
2097:
2095:(11): 621-626.
2076:
2058:
2042:
2018:
2000:
1978:
1957:
1924:
1908:
1892:
1879:
1859:
1852:. new series.
1830:
1809:
1782:
1781:
1779:
1776:
1775:
1774:
1767:
1764:
1718:
1715:
1702:
1696:
1692:
1688:
1683:
1679:
1674:
1671:
1668:
1665:
1659:
1655:
1651:
1646:
1642:
1637:
1634:
1611:
1607:
1582:
1578:
1565:
1564:
1553:
1550:
1547:
1544:
1533:
1532:
1518:
1514:
1509:
1506:
1500:
1496:
1492:
1487:
1483:
1478:
1475:
1472:
1466:
1462:
1457:
1454:
1451:
1445:
1441:
1436:
1433:
1430:
1424:
1420:
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1412:
1409:
1403:
1399:
1395:
1390:
1386:
1381:
1378:
1375:
1369:
1365:
1361:
1356:
1352:
1347:
1344:
1341:
1335:
1331:
1327:
1322:
1318:
1313:
1310:
1307:
1301:
1297:
1292:
1289:
1283:
1279:
1274:
1271:
1266:
1262:
1256:
1252:
1248:
1245:
1242:
1239:
1228:
1227:
1213:
1209:
1204:
1201:
1195:
1191:
1187:
1182:
1178:
1173:
1170:
1167:
1161:
1157:
1152:
1149:
1146:
1140:
1136:
1131:
1128:
1125:
1119:
1115:
1111:
1106:
1102:
1097:
1094:
1091:
1085:
1081:
1077:
1072:
1068:
1063:
1060:
1057:
1051:
1047:
1042:
1039:
1034:
1030:
1024:
1020:
1016:
1013:
1010:
1007:
996:
995:
981:
977:
972:
969:
963:
959:
955:
950:
946:
941:
938:
935:
929:
925:
920:
917:
914:
908:
904:
900:
895:
891:
886:
883:
880:
875:
871:
867:
864:
861:
855:
851:
847:
842:
838:
833:
830:
827:
824:
818:
814:
810:
805:
801:
796:
793:
775:
774:
758:
752:
749:
745:
742:
737:
731:
727:
721:
718:
714:
711:
706:
702:
699:
696:
693:
690:
687:
684:
678:
675:
672:
667:
664:
660:
657:
653:
650:
636:
635:
622:
619:
614:
611:
605:
601:
597:
593:
590:
585:
582:
577:
574:
569:
566:
561:
558:
554:
551:
547:
544:
541:
536:
532:
528:
525:
522:
516:
512:
508:
505:
501:
498:
495:
492:
486:
482:
478:
475:
471:
468:
452:By applying a
450:
449:
438:
432:
428:
424:
421:
417:
414:
411:
408:
402:
398:
394:
391:
387:
384:
381:
377:
373:
370:
365:
361:
357:
354:
351:
348:
345:
339:
335:
331:
328:
324:
321:
318:
313:
309:
305:
302:
299:
294:
290:
286:
259:
256:
253:
250:
247:
242:
238:
234:
229:
225:
173:
162:
151:
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122:
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57:
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2249:
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2241:
2237:
2233:
2229:
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2221:
2217:
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2203:
2202:0-521-64222-1
2199:
2195:
2193:
2186:
2180:
2177:
2176:90-247-3418-5
2173:
2169:
2163:
2156:
2152:
2151:
2144:
2137:
2131:
2125:(6): 248-253.
2124:
2120:
2114:
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2101:
2094:
2090:
2086:
2080:
2074:
2071:
2068:
2062:
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2047:
2039:
2035:
2029:
2027:
2025:
2023:
2015:
2009:
2007:
2005:
1997:
1993:
1987:
1985:
1983:
1975:
1972:
1966:
1964:
1962:
1954:
1950:
1946:
1943:
1939:
1933:
1931:
1929:
1921:
1918:
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1889:
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1877:
1874:
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1866:
1864:
1855:
1851:
1847:
1843:
1837:
1835:
1827:
1826:0-521-30789-9
1823:
1819:
1813:
1806:
1805:0-521-30789-9
1802:
1798:
1792:
1790:
1788:
1783:
1773:
1770:
1769:
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1452:
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1269:
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878:
873:
869:
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784:
783:
782:
780:
750:
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700:
697:
694:
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676:
673:
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564:
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277:
276:
275:
273:
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251:
248:
245:
240:
236:
232:
227:
223:
214:
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205:
203:
197:
193:
191:
187:
182:
177:
172:
169:polarized in
168:
161:
158:polarized in
157:
150:
146:
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101:
98:
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92:
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2457:
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2406:
2369:December 11,
2367:. Retrieved
2363:
2353:
2328:
2324:
2318:
2308:
2301:
2293:
2289:
2282:
2278:
2273:
2265:
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2190:
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2148:
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2100:
2092:
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2066:
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2013:
1995:
1991:
1973:
1970:
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1948:
1941:
1937:
1919:
1916:
1911:
1903:
1900:
1895:
1887:
1882:
1872:
1853:
1849:
1842:Stokes, G.G.
1817:
1812:
1796:
1757:
1753:
1740:
1720:
1717:Applications
1566:
776:
637:
451:
206:
198:
194:
183:
179:
170:
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155:
148:
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59:
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2539:(1): 2308.
2204:, page 423.
213:Born series
2292:Series 4,
2290:Phil. Mag.
2285:: 275-301
2279:Ann. Phys.
2157:(1): 1-11.
2072:: 403-410.
2040:: 324-325.
2036:series 5,
2034:Phil. Mag.
1998:: 118-122.
1951:Series 4,
1949:Phil. Mag.
1938:Ann. Phys.
1778:References
95:Max Planck
50:raytracing
2561:2041-1723
2476:0365-110X
2435:1600-5724
2345:0003-6951
2252:250849465
2244:0034-4885
1670:Ψ
1633:Ψ
1306:∫
1288:∫
1270:∫
1251:π
1244:−
1056:∫
1038:∫
1019:π
1012:−
879:∫
870:π
863:−
792:Ψ
744:−
713:−
695:π
686:
677:−
581:Ψ
540:∫
531:π
524:−
467:Ψ
423:−
413:δ
383:Ψ
356:π
350:−
320:Ψ
304:π
289:▽
71:is being
2593:Category
2579:31127111
2379:cite web
1844:(1849).
1766:See also
751:′
720:′
666:′
621:′
592:′
576:′
560:′
190:Rayleigh
64:template
2570:6534592
2541:Bibcode
2415:Bibcode
2364:Gallica
2224:Bibcode
1856:: 1-14.
93:and by
56:Physics
2599:Optics
2577:
2567:
2559:
2510:
2474:
2433:
2343:
2296::2-21.
2250:
2242:
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1803:
638:where
79:Stokes
2496:(PDF)
2248:S2CID
2119:Optik
62:âčThe
2575:PMID
2557:ISSN
2508:ISBN
2472:ISSN
2431:ISSN
2385:link
2371:2019
2341:ISSN
2240:ISSN
2198:ISBN
2172:ISBN
1822:ISBN
1801:ISBN
1596:and
39:flux
21:The
2565:PMC
2549:doi
2500:doi
2462:doi
2423:doi
2333:doi
2283:119
2232:doi
1942:119
683:exp
85:'s
27:ray
2595::
2573:.
2563:.
2555:.
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2537:10
2535:.
2531:.
2506:.
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2393:^
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