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[[File:Fourier Slice Theorem.png|thumb|A visual explanation of the Fourier Slice Theorem: The parallel 2-D projection in spatial ___domain and subsequent 1-D Fourier transform is identical to a slice through 2-D Fourier space.<ref name=Maier2018>{{cite book |author = Andreas Maier, Stefan Steidl, Vincent Christlein, Joachim Hornegger |title = Medical Imaging Systems - An Introductory Guide |publisher = Springer, Heidelberg |year = 2018 |isbn = 978-3-319-96520-8 | url = https://link.springer.com/book/10.1007%2F978-3-319-96520-8 }}</ref>]]
In [[mathematics]], the '''projection-slice theorem''', '''central slice theorem''' or '''Fourier slice theorem''' in two dimensions states that the results of the following two calculations are equal:
* Take a two-dimensional function ''f''('''r'''), [[Projection (mathematics)|project]] it onto a (one-dimensional) line, and do a [[Fourier transform]] of that projection.{{Dubious |Talk section Misleading Use of term "Projection"|reason=Inappropriately general definition of projection|date=August 2018}}
* Take that same function, but do a two-dimensional Fourier transform first, and then '''slice''' it through its origin, which is parallel to the projection line.
In operator terms, if
* ''F''<sub>1</sub> and ''F''<sub>2</sub> are the 1- and 2-dimensional Fourier transform operators mentioned above,
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