Self-fractional Fourier images (SFFIs), which are invariant under the two-d
imensional fractional Fourier transform, are considered. Necessary and suff
icient conditions for an image to be a SFFI for given angles are formulated
. An optical procedure for synthesizing SFFIs from a generator image is dev
eloped. The physical meaning of SFFI synthesis is discussed. An image decom
position on the set of orthogonal SFFIs, which simplifies image processing
in fractional FT optical systems, is proposed.