Editing Stereographic projection (section)

===Crystallography===
[[Image:DiamondPoleFigure111.png|right|thumb|A crystallographic pole figure for the [[Diamond cubic|diamond lattice]] in [[Miller index|[111] direction]]]]
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In [[crystallography]], the orientations of [[crystal]] axes and faces in three-dimensional space are a central geometric concern, for example in the interpretation of [[X-ray diffraction|X-ray]] and [[electron diffraction]] patterns. These orientations can be visualized as in the section [[Stereographic projection#Visualization of lines and planes|Visualization of lines and planes]] above. That is, crystal axes and poles to crystal planes are intersected with the northern hemisphere and then plotted using stereographic projection. A plot of poles is called a '''pole figure'''.

In [[electron diffraction]], [[Kikuchi line (solid state physics)|Kikuchi line]] pairs appear as bands decorating the intersection between lattice plane traces and the [[Ewald sphere]] thus providing ''experimental access'' to a crystal's stereographic projection.  Model Kikuchi maps in reciprocal space,<ref>M. von Heimendahl, W. Bell and G. Thomas (1964) Applications of Kikuchi line analyses in electron microscopy, ''J. Appl. Phys.'' '''35''':12, 3614&ndash;3616.</ref> and fringe visibility maps for use with bend contours in direct space,<ref>P. Fraundorf, Wentao Qin, P. Moeck and Eric Mandell (2005) Making sense of nanocrystal lattice fringes, ''J. Appl. Phys.'' '''98''':114308.</ref> thus act as road maps for exploring orientation space with crystals in the [[transmission electron microscope]].
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