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[[File:Contrast transfer function.jpg|thumb|Power spectrum (Fourier transform) of a typical electron micrograph. The effect of the contrast transfer function can be seen in the alternating light and dark rings (Thon rings), which show the relation between contrast and spatial frequency. ]]
The '''contrast transfer function''' ('''CTF''') mathematically describes how aberrations in a [[transmission electron microscope]] (TEM) modify the image of a sample.<ref name=":0">{{Cite journal|title = A brief look at imaging and contrast transfer|last = Wade|first = R. H.|date = October 1992|journal = Ultramicroscopy|doi = 10.1016/0304-3991(92)90011-8|pmid = |volume=46|issue = 1–4|pages=145–156}}</ref><ref name="Spence1982">Spence, John C. H. (1988 2nd ed) ''Experimental high-resolution electron microscopy'' (Oxford U. Press, NY) {{ISBN|0195054059}}.</ref><ref name="Reimer97">Ludwig Reimer (1997 4th ed) ''Transmission electron microscopy: Physics of image formation and microanalysis'' (Springer, Berlin) [https://books.google.com/books?id=3_84SkJXnYkC preview].</ref><ref name="Kirkland1998">Earl J. Kirkland (1998) ''Advanced computing in electron microscopy'' (Plenum Press, NY).</ref> This contrast transfer function (CTF) sets the resolution of [[high-resolution transmission electron microscopy]] (HRTEM), also known as phase contrast TEM.
By considering the recorded image as a CTF-degraded true object, describing the CTF allows the true object to be [[reverse-engineered]]. This is typically denoted CTF-correction, and is vital to obtain high resolution structures in three-dimensional electron microscopy, especially [[electron cryo-microscopy]]. Its equivalent in light-based optics is the [[optical transfer function]].
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== Examples
The contrast transfer function determines how much phase signal gets transmitted to the real space wavefunction in the image plane. As the modulus squared of the real space wavefunction gives the image signal, the contrast transfer function limits how much information can ultimately be translated into an image. The form of the contrast transfer
function determines the quality of real space image formation in the TEM.
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== See also ==
* [[Airy disk]], different but similar phenomena in light▼
* [[Transmission electron microscopy]]▼
* [[Optical transfer function]]
* [[Point spread function]]
▲* [[Transmission electron microscopy]]
▲* [[Airy disk]], different but similar phenomena in light
== References ==
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