Projection-slice theorem: Difference between revisions

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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