2D Fourier Transforms
This Demonstration shows an aperture (top) and its 2D Fourier transform (bottom). These can be pictured as an aperture illuminated by plane waves and the diffraction pattern in an optical system with a small Fresnel number. Note how lines of symmetry are shared in the aperture and its Fourier transform and how these are preserved under rotations. Particularly important is the way that the Fourier transform scales with the aperture—if the aperture widens, then the Fourier transform narrows in the same direction, and vice versa. It is instructive to note how the same processes apply analogously when looking at lattices of apertures.