A lens performs an optical Fourier transform: the far-field diffraction pattern of an aperture IS its 2D Fourier transform. Draw an aperture, see the diffraction pattern in real time.
Aperture (draw here)
Fourier Magnitude (far-field intensity)
Phase
The Abbe theory of imaging: a lens takes the Fourier transform, and the image is the inverse FT. Spatial frequency filtering happens in the focal plane.