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====Diffraction and optical resolution==== {{Main|Diffraction|Optical resolution}} [[File:Double slit diffraction.svg|class=skin-invert-image|upright=1.35|right|thumb|Diffraction on two slits separated by distance {{mvar|d}}. The bright fringes occur along lines where black lines intersect with black lines and white lines intersect with white lines. These fringes are separated by angle {{mvar|θ}} and are numbered as order {{mvar|n}}.]] Diffraction is the process by which light interference is most commonly observed. The effect was first described in 1665 by [[Francesco Maria Grimaldi]], who also coined the term from the Latin {{lang|la|diffringere}} {{gloss|to break into pieces}}.<ref>{{cite book |last= Aubert |first= J. L. |date= 1760 |title= Memoires pour l'histoire des sciences et des beaux arts |trans-title= Memoirs for the history of science and fine arts |language= fr |publisher= Impr. de S.A.S.; Chez E. Ganeau |place= Paris |page= [https://archive.org/details/memoirespourlhi146aubegoog/page/n151 149] |url= https://archive.org/details/memoirespourlhi146aubegoog}}</ref><ref>{{cite book |last= Brewster |first= D. |date= 1831 |title= A Treatise on Optics |publisher= Longman, Rees, Orme, Brown & Green and John Taylor |place= London |page= [https://archive.org/details/atreatiseonopti00brewgoog/page/n113 95] |url= https://archive.org/details/atreatiseonopti00brewgoog}}</ref> Later that century, Robert Hooke and Isaac Newton also described phenomena now known to be diffraction in [[Newton's rings]]<ref>{{cite book |last= Hooke |first= R. |date= 1665 |title= Micrographia: or, Some physiological descriptions of minute bodies made by magnifying glasses |url= https://archive.org/details/micrographiaorso00hook |place= London |publisher= J. Martyn and J. Allestry |isbn= 978-0-486-49564-4}}</ref> while [[James Gregory (astronomer and mathematician)|James Gregory]] recorded his observations of diffraction patterns from bird feathers.<ref>{{cite journal |last= Turnbull |first= H. W. |date= 1940–1941 |title= Early Scottish Relations with the Royal Society: I. James Gregory, F.R.S. (1638–1675) |journal= Notes and Records of the Royal Society of London |volume= 3 |pages= 22–38 |doi= 10.1098/rsnr.1940.0003|doi-access= free }}</ref> The first physical optics model of diffraction that relied on the Huygens–Fresnel principle was developed in 1803 by Thomas Young in his interference experiments with the interference patterns of two closely spaced slits. Young showed that his results could only be explained if the two slits acted as two unique sources of waves rather than corpuscles.<ref>{{cite book |last= Rothman |first= T. |date= 2003 |author-link= Tony Rothman |title= Everything's Relative and Other Fables in Science and Technology |publisher= Wiley |place= New Jersey |isbn= 978-0-471-20257-8 |url-access= registration |url= https://archive.org/details/everythingsrelat0000roth}}</ref> In 1815 and 1818, Augustin-Jean Fresnel firmly established the mathematics of how wave interference can account for diffraction.{{sfnp|Hecht|2017|p=5}} The simplest physical models of diffraction use equations that describe the angular separation of light and dark fringes due to light of a particular wavelength ({{mvar|λ}}). In general, the equation takes the form <math display="block">m \lambda = d \sin \theta</math> where {{mvar|d}} is the separation between two wavefront sources (in the case of Young's experiments, it was [[Double-slit experiment|two slits]]), {{mvar|θ}} is the angular separation between the central fringe and the {{nowrap|{{mvar|m}}-th}} order fringe, where the central maximum is {{math|1= ''m'' = 0}}.{{sfnmp |1a1=Hecht|1y=2017|1pp=398–399 |2a1=Young|2a2=Freedman|2y=2020|2p=1192}} This equation is modified slightly to take into account a variety of situations such as diffraction through a single gap, diffraction through multiple slits, or diffraction through a [[diffraction grating]] that contains a large number of slits at equal spacing.{{sfnmp |1a1=Hecht|1y=2017|1pp=488–491 |2a1=Young|2a2=Freedman|2y=2020|2pp=1224–1225}} More complicated models of diffraction require working with the mathematics of [[Fresnel diffraction|Fresnel]] or [[Fraunhofer diffraction]].<ref name=phyoptics>{{cite book |last= Longhurst |first= R. S. |date= 1968 |title= Geometrical and Physical Optics |edition= 2nd |publisher= Longmans |location= London |bibcode= 1967gpo..book.....L}}</ref> [[X-ray diffraction]] makes use of the fact that atoms in a crystal have regular spacing at distances that are on the order of one [[angstrom]]. To see diffraction patterns, x-rays with similar wavelengths to that spacing are passed through the crystal. Since crystals are three-dimensional objects rather than two-dimensional gratings, the associated diffraction pattern varies in two directions according to [[Bragg reflection]], with the associated bright spots occurring in [[Diffraction topography|unique patterns]] and {{mvar|d}} being twice the spacing between atoms.{{sfnmp |1a1=Hecht|1y=2017|1p=497 |2a1=Young|2a2=Freedman|2y=2020|2pp=1228–1230}} Diffraction effects limit the ability of an optical detector to [[optical resolution|optically resolve]] separate light sources. In general, light that is passing through an [[aperture]] will experience diffraction and the best images that can be created (as described in [[Diffraction-limited system|diffraction-limited optics]]) appear as a central spot with surrounding bright rings, separated by dark nulls; this pattern is known as an [[Airy pattern]], and the central bright lobe as an [[Airy disk]].{{sfnp|Hecht|2017|p=482}} The size of such a disk is given by <math display="block"> \sin \theta = 1.22 \frac{\lambda}{D}</math> where {{mvar|θ}} is the angular resolution, {{mvar|λ}} is the wavelength of the light, and {{mvar|D}} is the [[diameter]] of the lens aperture. If the angular separation of the two points is significantly less than the Airy disk angular radius, then the two points cannot be resolved in the image, but if their angular separation is much greater than this, distinct images of the two points are formed and they can therefore be resolved. [[John Strutt, 3rd Baron Rayleigh|Rayleigh]] defined the somewhat arbitrary "[[Angular resolution#The Rayleigh criterion|Rayleigh criterion]]" that two points whose angular separation is equal to the Airy disk radius (measured to first null, that is, to the first place where no light is seen) can be considered to be resolved. It can be seen that the greater the diameter of the lens or its aperture, the finer the resolution.{{sfnmp |1a1=Hecht|1y=2017|1p=485 |2a1=Young|2a2=Freedman|2y=2020|2p=1232}} [[Astronomical interferometer|Interferometry]], with its ability to mimic extremely large baseline apertures, allows for the greatest angular resolution possible.<ref name=interferometry /> For astronomical imaging, the atmosphere prevents optimal resolution from being achieved in the visible spectrum due to the atmospheric [[scattering]] and dispersion which cause stars to [[Scintillation (astronomy)|twinkle]]. Astronomers refer to this effect as the quality of [[astronomical seeing]]. Techniques known as [[adaptive optics]] have been used to eliminate the atmospheric disruption of images and achieve results that approach the diffraction limit.<ref>{{cite thesis |last= Tubbs |first= Robert Nigel |date= September 2003 |type= PhD thesis |title= Lucky Exposures: Diffraction limited astronomical imaging through the atmosphere |url= http://www.mrao.cam.ac.uk/telescopes/coast/theses/rnt/ |publisher=Cambridge University |archive-url= https://web.archive.org/web/20081005013157/http://www.mrao.cam.ac.uk/telescopes/coast/theses/rnt/ |archive-date= 2008-10-05}}</ref>
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