  In the two space dimensions of screens in optical sy stems, rotations,
gyrations, and fractional Fourier transformations form the Fourier subgroup of
the symplectic group of linear canonical transformations: U(2) F $\subset$
Sp(4,R). Here we study the action of this Fourier group on pixellated images
within generic rectangular $N_x$ $\times$ $N_y$ screens; its elements here
compose properly and act unitarily, i.e., without loss of information.
