Editing Diffraction (section)

== Mechanism ==
[[Image:Single-slit-diffraction-ripple-tank.jpg|thumb|left|Single-slit diffraction in a circular [[ripple tank]]]]

In [[classical physics]] diffraction arises because of how [[wave]]s propagate; this is described by the [[Huygens–Fresnel principle]] and the [[superposition principle|principle of superposition of waves]]. The propagation of a wave can be visualized by considering every particle of the transmitted medium on a wavefront as a [[point source]] for a secondary [[wave equation#Spherical waves|spherical wave]]. The wave displacement at any subsequent point is the sum of these secondary waves. When waves are added together, their sum is determined by the relative [[Phase (waves)|phases]] as well as the [[amplitude]]s of the individual waves so that the summed amplitude of the waves can have any value between zero and the sum of the individual amplitudes.  Hence, diffraction patterns usually have a series of maxima and minima.

In the [[Quantum mechanics|modern quantum mechanical]] understanding of light propagation through a slit (or slits) every [[photon]] is described by its [[wavefunction]] that determines the [[Probability amplitude|probability distribution]] for the photon: the light and dark bands are the areas where the photons are more or less likely to be detected. The wavefunction is determined by the physical surroundings such as slit geometry, screen distance, and initial conditions when the photon is created. The wave nature of individual photons (as opposed to wave properties only arising from the interactions between multitudes of photons) was implied by a low-intensity [[double-slit experiment]] first performed by [[G. I. Taylor]] in [[1909 in science|1909]]. The quantum approach has some striking similarities to the [[Huygens-Fresnel principle]]; based on that principle, as light travels through slits and boundaries, secondary point light sources are created near or along these obstacles, and the resulting diffraction pattern is going to be the intensity profile based on the collective interference of all these light sources that have different optical paths. In the quantum formalism, that is similar to considering the limited regions around the slits and boundaries from which photons are more likely to originate, and calculating the probability distribution (that is proportional to the resulting intensity of classical formalism).

There are various analytical models for photons which allow the diffracted field to be calculated, including the [[Kirchhoff's diffraction formula|Kirchhoff diffraction equation]] (derived from the [[wave equation]]),<ref>Baker, B.B. & Copson, E.T. (1939), ''The Mathematical Theory of Huygens' Principle'', Oxford, pp.{{nnbsp}}36–40.</ref> the [[Fraunhofer diffraction]] approximation of the Kirchhoff equation (applicable to the [[near and far field#Far field|far field]]), the [[Fresnel diffraction]] approximation  (applicable to the [[near and far field#Near field|near field]]) and the Feynman [[path integral formulation]].  Most configurations cannot be solved analytically, but can yield numerical solutions through [[finite element]] and [[boundary element]] methods. In many cases it is assumed that there is only one scattering event, what is called [[kinematical diffraction]], with an [[Ewald's sphere]] construction used to represent that there is no change in energy during the diffraction process. For matter waves a similar but slightly different approach is used based upon a relativistically corrected form of the [[Schrödinger equation]],<ref>{{Cite journal |last=Schrödinger |first=E. |date=1926 |title=An Undulatory Theory of the Mechanics of Atoms and Molecules |url=https://journals.aps.org/pr/abstract/10.1103/PhysRev.28.1049 |journal=Physical Review |volume=28 |issue=6 |pages=1049–1070 |doi=10.1103/PhysRev.28.1049|bibcode=1926PhRv...28.1049S }}</ref> as first detailed by [[Hans Bethe]].<ref>{{Cite journal |last=Bethe |first=H. |date=1928 |title=Theorie der Beugung von Elektronen an Kristallen |url=https://onlinelibrary.wiley.com/doi/10.1002/andp.19283921704 |journal=Annalen der Physik |language=en |volume=392 |issue=17 |pages=55–129 |doi=10.1002/andp.19283921704 |bibcode=1928AnP...392...55B |issn=1521-3889}}</ref> The Fraunhofer and Fresnel limits exist for these as well, although they correspond more to approximations for the matter wave [[Green's function]] ([[propagator]])<ref>{{Cite book |last=Schiff |first=Leonard I. |title=Quantum mechanics |date=1987 |publisher=McGraw-Hill |isbn=978-0-07-085643-1 |edition=3. ed., 24. print |series=International series in pure and applied physics |location=New York}}</ref> for the Schrödinger equation.<ref>{{Cite book |last=Cowley |first=J. M. |title=Diffraction physics |date=1995 |publisher=Elsevier |isbn=978-0-444-82218-5 |edition=3rd |series=North-Holland personal library |location=New York}}</ref><ref>{{Cite book |last1=Peng |first1=L.-M. |title=High energy electron diffraction and microscopy |last2=Dudarev |first2=S. L. |last3=Whelan |first3=M. J. |date=2011 |publisher=Oxford Univ. Press |isbn=978-0-19-960224-7 |edition=1. publ. in paperback |series=Monographs on the physics and chemistry of materials |location=Oxford}}</ref> More common is full multiple scattering models particular in [[electron diffraction]];<ref>{{Cite journal |last1=Colliex |first1=C. |last2=Cowley |first2=J. M. |last3=Dudarev |first3=S. L. |last4=Fink |first4=M. |last5=GjÃ¸nnes |first5=J. |last6=Hilderbrandt |first6=R. |last7=Howie |first7=A. |last8=Lynch |first8=D. F. |last9=Peng |first9=L. M. |last10=Ren |first10=G. |last11=Ross |first11=A. W. |last12=Smith |first12=V. H. Jr |last13=Spence |first13=J. C. H. |last14=Steeds |first14=J. W. |last15=Wang |first15=J. |date=2006 |title=Electron diffraction |url=https://xrpp.iucr.org/cgi-bin/itr?url_ver=Z39.88-2003&rft_dat=what%3Dchapter%26volid%3DCb%26chnumo%3D4o3%26chvers%3Dv0001 |journal=Urn:isbn |series=International Tables for Crystallography |language=en |volume=C |pages=259–429 |doi=10.1107/97809553602060000593|isbn=978-1-4020-1900-5 }}</ref> in some cases similar [[dynamical diffraction]]  models are also used for X-rays.<ref>{{Cite journal |last1=Li |first1=Kenan |last2=Wojcik |first2=Michael |last3=Jacobsen |first3=Chris |date=2017-02-06 |title=Multislice does it all—calculating the performance of nanofocusing X-ray optics |url=https://opg.optica.org/abstract.cfm?URI=oe-25-3-1831 |journal=Optics Express |language=en |volume=25 |issue=3 |pages=1831–1846 |doi=10.1364/OE.25.001831 |pmid=29519036 |bibcode=2017OExpr..25.1831L |issn=1094-4087}}</ref>

It is possible to obtain a qualitative understanding of many diffraction phenomena by considering how the relative phases of the individual secondary wave sources vary, and, in particular, the conditions in which the phase difference equals half a cycle in which case waves will cancel one another out.

The simplest descriptions of diffraction are those in which the situation can be reduced to a two-dimensional problem. For [[Wind wave|water waves]], this is already the case; water waves propagate only on the surface of the water. For light, we can often neglect one direction if the diffracting object extends in that direction over a distance far greater than the wavelength. In the case of light shining through small circular holes, we will have to take into account the full three-dimensional nature of the problem.

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File:Square diffraction.jpg|Computer-generated intensity pattern formed on a screen by diffraction from a square aperture
File:Two-Slit Diffraction.png|Generation of an interference pattern from two-slit diffraction
File:Doubleslit.gif|Computational model of an interference pattern from two-slit diffraction
File:Optical diffraction pattern ( laser), (analogous to X-ray crystallography).JPG|Optical diffraction pattern (laser, analogous to X-ray diffraction)
File:Diffraction pattern in spiderweb.JPG|Colors seen in a [[spider web]] are partially due to diffraction, according to some analyses.<ref>{{cite web|url = http://www.itp.uni-hannover.de/%7Ezawischa/ITP/spiderweb.html|title = Optical effects on spider webs|author = Dietrich Zawischa|access-date = 2007-09-21}}</ref>
</gallery>