[[Image:ProjectionSlice.png|frame|center|512px|A graphical illustration of the projection slice theorem in two dimensions. ''f''('''r''') and ''F''('''k''') are 2-dimensional Fourier transform pairs. The projection of ''f''('''r''') onto the ''x''-axis is the integral of ''f''('''r''') along lines of sight parallel to the ''y''-axis and is labelled ''p''(''x''). The slice through ''F''('''k''') is on the ''k''<sub>''x''</sub> axis, which is parallel to the ''x'' axis and labelled ''s''(''k''<sub>''x''</sub>). The projection-slice theorem states that ''p''(''x'') and ''s''(''k''<sub>''x''</sub>) are 1-dimensional Fourier transform pairs.]]
The projection-slice theorem is easily proven for the case of two dimensions.
