116:
832:. This is similar to the pixel size for the majority of commercially available 'full frame' (43mm sensor diagonal) cameras and so these will operate in regime 3 for f-numbers around 8 (few lenses are close to diffraction limited at f-numbers smaller than 8). Cameras with smaller sensors will tend to have smaller pixels, but their lenses will be designed for use at smaller f-numbers and it is likely that they will also operate in regime 3 for those f-numbers for which their lenses are diffraction limited.
553:. The point spread function of the camera, otherwise called the instrument response function (IRF) can be approximated by a rectangle function, with a width equivalent to the pixel pitch. A more complete derivation of the modulation transfer function (derived from the PSF) of image sensors is given by Fliegel. Whatever the exact instrument response function, it is largely independent of the f-number of the lens. Thus at different f-numbers a camera may operate in three different regimes, as follows:
1503:
1604:
533:(0.25 μm), which is small compared to most biological cells (1 μm to 100 μm), but large compared to viruses (100 nm), proteins (10 nm) and less complex molecules (1 nm). To increase the resolution, shorter wavelengths can be used such as UV and X-ray microscopes. These techniques offer better resolution but are expensive, suffer from lack of contrast in biological samples and may damage the sample.
31:
877:, uses two opposing objectives to double the effective numerical aperture, effectively halving the diffraction limit, by collecting the forward and backward scattered light. When imaging a transparent sample, with a combination of incoherent or structured illumination, as well as collecting both forward, and backward scattered light it is possible to image the complete
1616:
862:, this is achieved by using a condenser. Under spatially incoherent conditions, the image is understood as a composite of images illuminated from each point on the condenser, each of which covers a different portion of the object's spatial frequencies. This effectively improves the resolution by, at most, a factor of two.
1017:) to achieve high resolution images. Other massive particles such as helium, neon, and gallium ions have been used to produce images at resolutions beyond what can be attained with visible light. Such instruments provide nanometer scale imaging, analysis and fabrication capabilities at the expense of system complexity.
870:) synthesize the condenser illumination by acquiring a sequence of images with known illumination parameters. Typically, these images are composited to form a single image with data covering a larger portion of the object's spatial frequencies when compared to using a fully closed condenser (which is also rarely used).
119:
Log-log plot of aperture diameter vs angular resolution at the diffraction limit for various light wavelengths compared with various astronomical instruments. For example, the blue star shows that the Hubble Space
Telescope is almost diffraction-limited in the visible spectrum at 0.1 arcsecs, whereas
975:
The limits on focusing or collimating a laser beam are very similar to the limits on imaging with a microscope or telescope. The only difference is that laser beams are typically soft-edged beams. This non-uniformity in light distribution leads to a coefficient slightly different from the 1.22 value
865:
Simultaneously illuminating from all angles (fully open condenser) drives down interferometric contrast. In conventional microscopes, the maximum resolution (fully open condenser, at N = 1) is rarely used. Further, under partially coherent conditions, the recorded image is often non-linear
904:
techniques that operate less than ≈1 wavelength of light away from the image plane can obtain substantially higher resolution. These techniques exploit the fact that the evanescent field contains information beyond the diffraction limit which can be used to construct very high resolution images, in
262:
with near-ideal beam propagation properties may be described as being diffraction-limited. A diffraction-limited laser beam, passed through diffraction-limited optics, will remain diffraction-limited, and will have a spatial or angular extent essentially equal to the resolution of the optics at the
950:
Far-field imaging techniques are most desirable for imaging objects that are large compared to the illumination wavelength but that contain fine structure. This includes nearly all biological applications in which cells span multiple wavelengths but contain structure down to molecular scales. In
846:
There are techniques for producing images that appear to have higher resolution than allowed by simple use of diffraction-limited optics. Although these techniques improve some aspect of resolution, they generally come at an enormous increase in cost and complexity. Usually the technique is only
966:
dyes. The nonlinear response to illumination caused by the quenching process in which adding more light causes the image to become less bright generates sub-diffraction limited information about the location of dye molecules, allowing resolution far beyond the diffraction limit provided high
888:, such systems are still limited by the diffraction limit of the illumination (condenser) and collection optics (objective), although in practice they can provide substantial resolution improvements compared to conventional methods.
415:
557:
In the case where the spread of the IRF is small with respect to the spread of the diffraction PSF, in which case the system may be said to be essentially diffraction limited (so long as the lens itself is diffraction
991:. The ratio of this measured beam parameter product to that of the ideal is defined as M, so that M=1 describes an ideal beam. The M value of a beam is conserved when it is transformed by diffraction-limited optics.
917:
systems, can be used to achieve up to 10-50 nm resolution. The data recorded by such instruments often requires substantial processing, essentially solving an optical inverse problem for each image.
939:
a thin portion of the sample located immediately on the cover glass is excited with an evanescent field, and recorded with a conventional diffraction-limited objective, improving the axial resolution.
1005:
As opposed to light waves (i.e., photons), massive particles have a different relationship between their quantum mechanical wavelength and their energy. This relationship indicates that the effective
866:
with object's scattering potential—especially when looking at non-self-luminous (non-fluorescent) objects. To boost contrast, and sometimes to linearize the system, unconventional microscopes (with
531:
85:
247:
are frequently diffraction-limited, because the wavelengths they use (from millimeters to meters) are so long that the atmospheric distortion is negligible. Space-based telescopes (such as
905:
principle beating the diffraction limit by a factor proportional to how well a specific imaging system can detect the near-field signal. For scattered light imaging, instruments such as
715:
484:
1009:
is inversely proportional to the momentum of the particle. For example, an electron at an energy of 10 keV has a wavelength of 0.01 nm, allowing the electron microscope (
617:
541:
In a digital camera, diffraction effects interact with the effects of the regular pixel grid. The combined effect of the different parts of an optical system is determined by the
773:
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However, because these techniques cannot image beyond 1 wavelength, they cannot be used to image into objects thicker than 1 wavelength which limits their applicability.
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recent years several techniques have shown that sub-diffraction limited imaging is possible over macroscopic distances. These techniques usually exploit optical
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observation is one that achieves the resolution of a theoretically ideal objective in the size of instrument used. However, most observations from Earth are
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work at a much lower resolution than the diffraction limit because of the distortion introduced by the passage of light through several kilometres of
241:
technology, resulting in greater image resolution for faint targets, but it is still difficult to reach the diffraction limit using adaptive optics.
987:(M) is found by measuring the size of the beam at its waist, and its divergence far from the waist, and taking the product of the two, known as the
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if it has reached this limit of resolution performance. Other factors may affect an optical system's performance, such as lens imperfections or
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187:. For telescopes with circular apertures, the size of the smallest feature in an image that is diffraction limited is the size of the
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In the case where the spread of the diffraction PSF is small with respect to the IRF, in which case the system is instrument limited.
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of a lens, whereas the diffraction limit is the maximum resolution possible for a theoretically perfect, or ideal, optical system.
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1014:
1170:
Annalen der Physik und Chemie: Jubelband dem
Herausgeber Johann Christian Poggendorff zur Feier fünfzigjährigen Wirkens gewidmet
120:
the red circle shows that the human eye should have a resolving power of 20 arcsecs in theory, though normally only 60 arcsecs.
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In the case where the spread of the PSF and IRF are similar, in which case both impact the available resolution of the system.
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The outputs of many low and moderately powered lasers have M values of 1.2 or less, and are essentially diffraction-limited.
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41:
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199:, most modern lenses are limited only by diffraction and not by aberrations or other imperfections in the construction.
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has been one of the most successful. In STED, multiple laser beams are used to first excite, and then quench
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251:, or a number of non-optical telescopes) always work at their diffraction limit, if their design is free of
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1209:
Goodman, Joseph W. (2005). "4.4.2 Example of
Fraunhofer Diffraction Patterns for Circular Aperture".
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appropriate for a small subset of imaging problems, with several general approaches outlined below.
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The spread of the diffraction-limited PSF is approximated by the diameter of the first null of the
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In fluorescence microscopy the excitation and emission are typically on different wavelengths. In
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in the inscription) is the half-angle subtended by the optical objective lens (representing the
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The beam quality of a laser beam is characterized by how well its propagation matches an ideal
549:(PSF). The point spread function of a diffraction limited circular-aperture lens is simply the
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familiar in imaging. However, the scaling with wavelength and aperture is exactly the same.
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0.5 μm wavelength) light, the focusing spot diameter will be d = 9.76 μm or 19.5
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The observation of sub-wavelength structures with microscopes is difficult because of the
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The effective resolution of a microscope can be improved by illuminating from the side.
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The same equations apply to other wave-based sensors, such as radar and the human ear.
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410:{\displaystyle d={\frac {\lambda }{2n\sin \theta }}={\frac {\lambda }{2\mathrm {NA} }}}
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in a material's reflected light to generate resolution beyond the diffraction limit.
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Considering green light around 500 nm and a NA of 1, the Abbe limit is roughly
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Describes the Leica APO-Telyt-R 280mm f/4, a diffraction-limited photographic lens.
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of either the objective or the object illumination source, whichever is smaller.
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Optical system with resolution performance at the instrument's theoretical limit
1259:
Streibl, Norbert (February 1985). "Three-dimensional imaging by a microscope".
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found in 1873, and expressed as a formula in 1882, that light with wavelength
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of the light being observed, and inversely proportional to the diameter of its
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can image with a resolution better than the diffraction limit by locating the
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1297:; Mao, X.Q. (September 1989). "Three-dimensional imaging in a microscope".
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The diffraction limit is only valid in the far field as it assumes that no
453:(NA) and can reach about 1.4–1.6 in modern optics, hence the Abbe limit is
1079:"Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung"
663:
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149:
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in the Abbe diffraction limit formula. For instance, for an f/8 lens (
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1078:
486:. The same formula had been proven by Hermann von Helmholtz in 1874.
196:
195:, diffraction proportionately increases. At small apertures, such as
141:
125:
1168:[The Theoretical Limit of the Efficiency of Microscopes)].
1166:"Die theoretische Grenze für die Leistungsfähigkeit der Mikroskope"
1110:"The Relation of Aperture and Power in the Microscope (continued)"
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extremely close (typically hundreds of nanometers) to the object.
259:
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114:
29:
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is the index of refraction of the medium being imaged in, and
191:. As one decreases the size of the aperture of a telescopic
38:, who approximated the diffraction limit of a microscope as
1185:"Modeling and Measurement of Image Sensor Characteristics"
1547:
Total internal reflection fluorescence microscopy (TIRF)
1213:. Englewood, Colorado: Roberts and Company Publishers.
526:{\displaystyle d={\frac {\lambda }{2}}=250{\text{ nm}}}
164:, but these are caused by errors in the manufacture or
237:
atmosphere. Advanced observatories have started using
175:, in radians, of an instrument is proportional to the
80:{\displaystyle d={\frac {\lambda }{2n\sin {\theta }}}}
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For microscopic instruments, the diffraction-limited
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Photo-activated localization microscopy (PALM/STORM)
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In conventional microscopes such as bright-field or
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is proportional to the light wavelength, and to the
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937:total internal reflection fluorescence microscopy
983:at the same wavelength. The beam quality factor
144: – has a principal limit to its
304:, traveling in a medium with refractive index
1488:Interference reflection microscopy (IRM/RICM)
1379:
8:
1299:Journal of the Optical Society of America A
1261:Journal of the Optical Society of America A
710:{\displaystyle 2NA\rightarrow (2.44N)^{-1}}
344:will have a minimum resolvable distance of
272:The Abbe diffraction limit for a microscope
1386:
1372:
1364:
1236:"Many photons get more out of diffraction"
1143:. United Kingdom: Cambridge. p. 340.
1114:Journal of the Royal Microscopical Society
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479:{\displaystyle d={\frac {\lambda }{2.8}}}
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324:and converging to a spot with half-angle
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1458:Differential interference contrast (DIC)
1038:
907:near-field scanning optical microscopes
1453:Quantitative phase-contrast microscopy
1139:Lipson, Lipson and Tannhauser (1998).
156:. An optical instrument is said to be
1338:"Chapter 3: 180 mm and 280 mm lenses"
7:
1615:
1580:Stimulated emission depletion (STED)
612:{\displaystyle d/2=1.22\lambda N,\,}
967:illumination intensities are used.
642:is the wavelength of the light and
229:effects. Optical telescopes on the
1126:10.1111/j.1365-2818.1882.tb04805.x
1083:Archiv für mikroskopische Anatomie
860:differential interference contrast
762:
400:
397:
25:
1552:Lightsheet microscopy (LSFM/SPIM)
1614:
1603:
1602:
1501:
1183:Fliegel, Karel (December 2004).
267:Calculation of diffraction limit
91:is the resolvable feature size,
1164:von Helmholtz, Hermann (1874).
768:{\displaystyle NA\approx 2.5\%}
420:The portion of the denominator
1557:Lattice light-sheet microscopy
1468:Second harmonic imaging (SHIM)
1336:Puts, Erwin (September 2003).
1211:Introduction to Fourier Optics
695:
685:
682:
1:
1046:Born, Max; Emil Wolf (1997).
798:{\displaystyle \lambda _{g}=}
666:of the imaging optics, i.e.,
442:{\displaystyle n\sin \theta }
34:Memorial in Jena, Germany to
1241:Optics & Photonics Focus
958:Among these techniques, the
900:reach the detector. Various
851:Extending numerical aperture
825:{\displaystyle \lambda _{g}}
130:optical instrument or system
95:is the wavelength of light,
842:Super-resolution microscopy
836:Obtaining higher resolution
1669:
1054:Cambridge University Press
884:Unlike methods relying on
839:
1598:
1499:
1401:
263:wavelength of the laser.
635:{\displaystyle \lambda }
297:{\displaystyle \lambda }
171:The diffraction-limited
1518:Fluorescence microscopy
1478:Structured illumination
1433:Bright-field microscopy
1234:Niek van Hulst (2009).
1007:"de Broglie" wavelength
915:atomic force microscope
913:, which are built atop
868:structured illumination
775:) and for green light (
337:{\displaystyle \theta }
1590:Near-field (NSOM/SNOM)
1528:Multiphoton microscopy
1319:10.1364/JOSAA.6.001260
1281:10.1364/JOSAA.2.000121
989:beam parameter product
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278:Abbe diffraction limit
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18:Abbe diffraction limit
1443:Dark-field microscopy
1358:on December 17, 2008.
892:Near-field techniques
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1511:Fluorescence methods
1108:Abbe, Ernst (1882).
1077:Abbe, Ernst (1873).
1049:Principles of Optics
946:Far-field techniques
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1542:Image deconvolution
1523:Confocal microscopy
1463:Dispersion staining
1438:Köhler illumination
1311:1989JOSAA...6.1260S
1273:1985JOSAA...2..121S
873:Another technique,
736:{\displaystyle N=8}
537:Digital photography
219:diffraction-limited
158:diffraction-limited
1414:Optical microscopy
1395:Optical microscopy
1095:10.1007/BF02956173
1027:Rayleigh criterion
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1575:Diffraction limit
1150:978-0-521-43047-0
898:evanescent fields
879:scattering sphere
655:{\displaystyle N}
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185:entrance aperture
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16:(Redirected from
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1424:Illumination and
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1351:. Archived from
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1305:(9): 1260–1269.
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1581:
1578:
1576:
1573:
1572:
1570:
1564:
1558:
1555:
1553:
1550:
1548:
1545:
1543:
1540:
1537:
1533:
1529:
1526:
1524:
1521:
1519:
1516:
1515:
1513:
1509:
1504:
1494:
1491:
1489:
1486:
1484:
1481:
1479:
1476:
1474:
1471:
1469:
1466:
1464:
1461:
1459:
1456:
1454:
1451:
1449:
1446:
1444:
1441:
1439:
1436:
1434:
1431:
1430:
1428:
1422:
1416:
1415:
1411:
1409:
1408:
1404:
1403:
1400:
1396:
1389:
1384:
1382:
1377:
1375:
1370:
1369:
1366:
1354:
1350:
1346:
1339:
1334:
1333:
1329:
1320:
1316:
1312:
1308:
1304:
1300:
1296:
1290:
1287:
1282:
1278:
1274:
1270:
1266:
1262:
1255:
1252:
1247:
1243:
1242:
1237:
1230:
1227:
1222:
1220:0-9747077-2-4
1216:
1212:
1205:
1202:
1197:
1193:
1186:
1179:
1176:
1171:
1167:
1160:
1157:
1152:
1146:
1142:
1135:
1132:
1127:
1123:
1119:
1115:
1111:
1104:
1101:
1096:
1092:
1088:
1084:
1080:
1073:
1070:
1065:
1063:0-521-63921-2
1059:
1055:
1051:
1050:
1042:
1039:
1032:
1028:
1025:
1024:
1020:
1018:
1016:
1012:
1008:
1003:
997:
995:
992:
990:
986:
982:
981:Gaussian beam
977:
970:
968:
965:
961:
956:
954:
945:
943:
940:
938:
933:
931:
927:
923:
919:
916:
912:
908:
903:
899:
891:
889:
887:
882:
880:
876:
871:
869:
863:
861:
856:
850:
848:
843:
835:
833:
817:
813:
792:
787:
783:
759:
756:
753:
750:
730:
727:
724:
702:
699:
691:
688:
679:
676:
673:
665:
649:
629:
605:
602:
599:
596:
593:
590:
586:
582:
575:
574:
573:
571:
563:
560:
556:
555:
554:
552:
548:
544:
536:
534:
515:
512:
507:
504:
499:
496:
487:
471:
468:
463:
460:
452:
436:
433:
430:
427:
393:
389:
384:
378:
375:
372:
369:
366:
362:
357:
354:
347:
346:
345:
331:
311:
291:
283:
279:
271:
266:
264:
261:
256:
254:
250:
246:
242:
240:
236:
232:
228:
224:
220:
216:
211:
209:
205:
200:
198:
194:
190:
186:
182:
178:
174:
169:
167:
163:
159:
155:
151:
147:
143:
139:
135:
131:
127:
117:
110:
106:
103:(depicted as
102:
98:
94:
90:
70:
66:
63:
60:
57:
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48:
45:
37:
32:
19:
1619:
1607:
1574:
1536:Three-photon
1412:
1405:
1353:the original
1349:Leica Camera
1344:
1302:
1298:
1289:
1264:
1260:
1254:
1245:
1239:
1229:
1210:
1204:
1195:
1191:
1178:
1169:
1159:
1140:
1134:
1117:
1113:
1103:
1086:
1082:
1072:
1047:
1041:
1004:
1001:
993:
978:
974:
957:
953:nonlinearity
949:
941:
934:
922:Metamaterial
920:
895:
886:localization
883:
872:
864:
857:
854:
845:
621:
567:
540:
488:
419:
277:
275:
257:
243:
218:
212:
201:
170:
157:
123:
104:
100:
96:
92:
88:
1653:Microscopes
1643:Diffraction
1089:: 413–468.
998:Other waves
971:Laser beams
964:fluorescent
926:superlenses
543:convolution
227:atmospheric
166:calculation
162:aberrations
154:diffraction
148:due to the
1648:Telescopes
1637:Categories
1532:Two-photon
1407:Microscope
1172:: 557–584.
1033:References
902:near-field
840:See also:
282:Ernst Abbe
177:wavelength
146:resolution
134:microscope
985:M squared
911:nano-FTIR
814:λ
784:λ
763:%
757:≈
700:−
683:→
630:λ
600:λ
570:Airy disk
558:limited).
551:Airy disk
505:λ
469:λ
437:θ
434:
390:λ
379:θ
376:
363:λ
332:θ
292:λ
235:turbulent
215:astronomy
189:Airy disk
181:objective
138:telescope
71:θ
67:
54:λ
1609:Category
1021:See also
664:f-number
520: nm
87:, where
1621:Commons
1307:Bibcode
1269:Bibcode
924:-based
662:is the
545:of the
150:physics
1483:Sarfus
1217:
1147:
1060:
622:where
249:Hubble
223:seeing
142:camera
128:, any
126:optics
1493:Raman
1356:(PDF)
1341:(PDF)
1188:(PDF)
260:laser
231:Earth
140:, or
1248:(1).
1215:ISBN
1198:(4).
1145:ISBN
1058:ISBN
909:and
743:and
689:2.44
597:1.22
217:, a
197:f/22
193:lens
1315:doi
1277:doi
1122:doi
1091:doi
1015:TEM
1013:or
1011:SEM
760:2.5
516:250
472:2.8
431:sin
373:sin
213:In
183:'s
152:of
124:In
64:sin
1639::
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1347:.
1343:.
1313:.
1301:.
1275:.
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1244:.
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1196:13
1194:.
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1112:.
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280:.
255:.
136:,
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1530:(
1387:e
1380:t
1373:v
1321:.
1317::
1309::
1303:6
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1265:2
1246:4
1223:.
1153:.
1128:.
1124::
1118:2
1097:.
1093::
1087:9
1066:.
818:g
793:=
788:g
754:A
751:N
731:8
728:=
725:N
703:1
696:)
692:N
686:(
680:A
677:N
674:2
650:N
606:,
603:N
594:=
591:2
587:/
583:d
513:=
508:2
500:=
497:d
464:=
461:d
428:n
401:A
398:N
394:2
385:=
370:n
367:2
358:=
355:d
312:n
105:α
101:θ
97:n
93:λ
89:d
61:n
58:2
49:=
46:d
20:)
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