Theory built around the application of two-dimensional Fourier Transforms
to the diffraction of light in the Fraunhoffer
or far-field limit
(the limit in which the image plane is very far from the object plane. Hence, the familiar intensity distribution produced by a slit (the square of a first order bessel function
) is the square of the Fourier transform
of a top-hat
function (a circular aperture produces the same intensity profile rotated through 180 degrees because of the axial symmetry).
This theory works with lenses as well. The intensity pattern of light at the focal plane on one side of a lens is the square of the modulus of the Fourier transform of the light at the object plane.
In fact, most of one-dimensional signal analysis of electrical engineering theory has its equivalent two-dimenisonal treatment in Fourier optics theory.