Diffraction

Thrm Fraunhofer Diffraction Pattern
The Fraunhofer diffraction pattern or far-field diffraction pattern indicates that

Analogue Fourier Computer

Fact The lens maps all plane waves at angle onto a point distance from the optical axis.

Def Fourier Plane
At the focal plane of the lens with focal length we have the Fourier plane .

Prop
Proof At Fourier plane, the amplitude of the field at some point depends on the amplitude of the plane wave components that are focused to that point. And the amplitude of the plane wave components at any given angle are found via the Fourier spectrum of the input wave. Thus