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| [[Image:Optical Talbot Carpet.png|thumb|right|325px|The optical Talbot Effect for monochromatic light, shown as a "Talbot Carpet". At the bottom of the figure the light can be seen diffracting through a grating, and this exact pattern is reproduced at the top of the picture (one Talbot Length away from the grating). Halfway down you see the image shifted to the side, and at regular fractions of the Talbot Length the sub-images are clearly seen.]]
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| The '''Talbot effect''' is a near-field diffraction effect first observed in 1836 by [[Henry Fox Talbot]].<ref>H. F. Talbot 1836 "Facts relating to optical science" ''No. IV, Philos. Mag. 9''</ref> When a plane wave is incident upon a periodic [[diffraction grating]],
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| the image of the grating is repeated at regular distances away from the grating plane. The regular distance is called the Talbot length, and the repeated images are called self images or Talbot images. Furthermore, at half the Talbot length, a self-image also occurs, but phase-shifted by half a period (the physical meaning of this is that it is laterally shifted by half the width of the grating period). At smaller regular fractions of the Talbot length, sub-images can also be observed. At one quarter of the Talbot length, the self-image is halved in size, and appears with half the period of the grating (thus twice as many images are seen). At one eighth of the Talbot length, the period and size of the images is halved again, and so forth creating a fractal pattern of sub images with ever decreasing size, often referred to as a Talbot carpet.<ref>{{cite journal |first=William B. |last=Case |first2=Mathias |last2=Tomandl |first3=Sarayut |last3=Deachapunya |first4=Markus |last4=Arndt |year=2009 |title=Realization of optical carpets in the Talbot and Talbot-Lau configurations |journal=Opt. Exp. |volume=17 |issue=23 |pages=20966–20974 |doi=10.1364/OE.17.020966 }}</ref>
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| [[Lord Rayleigh]] showed that the Talbot effect was a natural consequence of [[Fresnel diffraction]] and that the Talbot length can be found by the following formula:<ref>Lord Rayleigh 1881 "On copying diffraction gratings and on some phenomenon connected therewith" ''Philos. Mag. 11''</ref>
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| :<math>z_T=\frac{2a^2}{\lambda},</math> | |
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| where <math>a</math> is the period of the diffraction grating and <math>\lambda</math> is the [[wavelength]] of the light incident on the grating. However, if wavelength <math>\lambda</math> is comparable to grating period <math>a</math> this expression may lead to errors in <math>z_T</math> up to 100%.<ref>{{cite journal |first=Myun-Sik |last=Kim |first2=Toralf |last2=Scharf |first3=Christoph |last3=Menzel |first4=Carsten |last4=Rockstuhl |first5=Hans Peter |last5=Herzig |year=2013 |title=Phase anomalies in Talbot light carpets of selfimages |journal=Opt. Exp. |volume=21 |issue=1 |pages=1287–1300 |doi=10.1364/OE.21.001287 |bibcode = 2013OExpr..21.1287K }}</ref> In this case exact expression derived by Lord Rayleigh should be used
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| :<math>z_T=\frac{\lambda}{1 - \sqrt{ 1 - \frac{\lambda^2}{a^2} }},</math>
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| ==The atomic Talbot effect==
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| Due to the [[quantum mechanical]] wave nature of [[Elementary particle|particles]], diffraction effects have also
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| been observed with [[atoms]]—effects which are similar to those in the case of light.
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| Chapman ''et al.'' carried out an experiment in which a collimated beam of [[sodium]] atoms was passed through two diffraction gratings (the second used as a mask) to observe the Talbot effect and measure the Talbot length.<ref>{{cite journal |first=Michael S. |last=Chapman |first2=Christopher R. |last2=Ekstrom |first3=Troy D. |last3=Hammond |first4=Jörg |last4=Schmiedmayer |first5=Bridget E. |last5=Tannian |first6=Stefan |last6=Wehinger |first7=David E. |last7=Pritchard |year=1995 |title=Near-field imaging of atom diffraction gratings: The atomic Talbot effect |journal=Physical {{nowrap|Review A}} |volume=51 |issue=1 |pages=R14–R17 |doi=10.1103/PhysRevA.51.R14 |bibcode = 1995PhRvA..51...14C }}</ref> The beam had a mean velocity of {{nowrap|1000 m/s}} corresponding to a [[de Broglie wavelength]] of <math>\lambda_{dB}</math> = {{nowrap|0.017 [[Nanometre|nm]]}}. Their experiment was performed with 200 and {{nowrap|300 nm}} gratings which yielded Talbot lengths of 4.7 and {{nowrap|10.6 mm}} respectively. This showed that for an atomic beam of constant velocity, by using <math>\lambda_{dB}</math>, the atomic Talbot length can be found in the same manner.
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| ==Trivia==
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| The ''[[Nature Physics]]'' website has a Talbot carpet in its header.<ref>http://www.nature.com/nphys/index.html</ref>
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| ==See also==
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| * [[Angle-sensitive pixel]]
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| ==References==
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| <references/>
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| ==External links==
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| *[http://books.google.com/books?id=ewBbAAAAQAAJ&dq=1836%20philosophical%20magazine&pg=PA401#v=onepage&q=&f=false Talbot's 1836 paper via Google Books]
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| *[http://books.google.com/books?id=O5EOAAAAIAAJ&dq=philosophical%20magazine%20rayleigh%201881%20diffraction%20gratings&pg=PA196#v=onepage&q&f=false Raleigh's 1881 paper via Google Books]
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| *[http://www.physics.arizona.edu/~cronin/Research/Lab/wildthesis2.pdf Undergraduate thesis by Rob Wild (PDF)]
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| [[Category:Diffraction]]
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Частное предприятие «Илигран»
220073, г. Минск, ул. Кальварийская, дом 25, офис 424
Телефоны:
+375 44 545-67-00
+375 29 379-91-88
+375 17 204 42 28 (факс)
+375 17 204 42 26 (факс)
+375 17 204 01 72
Email: 2044228@mail.ru
Review my web-site; Разработка отдельных видов работ