Projection-slice theorem: Difference between revisions

Revision as of 19:48, 26 July 2015

Revision as of 19:49, 26 July 2015

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The projection-slice theorem is easily proven for the case of two dimensions.

Without loss of generality, we can take the projection line to be the ''x''-axis.

There is no loss of generality because using a shifted and rotated line the law still applies. Using a shifted line (in y) gives the same projection and therefore the same 1D Fourier transform. RotatedThe rotated function is the Fourier pair of the rotated Fourier transform, this completes the explanation.

If ''f''(''x'', ''y'') is a two-dimensional function, then the projection of ''f''(''x'', ''y'') onto the ''x'' axis is ''p''(''x'') where