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[[Image: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]] modify the image of a sample.<ref name=":0">{{Cite journal|url = http://www.sciencedirect.com/science/article/pii/0304399192900118|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 = |access-date =|volume=46|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>
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 [[cryo-electron microscopy]]. Its equivalent in light-based optics, is the [[optical transfer function]].
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