Fourier lens

A Fourier lens is a rather uncommon term for any converging lens that is used as Fourier optics : The electric field of the diffraction image located in the image-side focal plane corresponds exactly to the spatial Fourier transform of the electric field in the object-side focal plane. This fact can be used for spatial filtering. One possible setup for spatial filtering is two identical converging lenses at a distance of twice the focal length. The first lens generates the spatial Fourier transform of an object located in the object-side focal plane in its focal plane. Certain spatial frequencies can now be masked out using suitable screens. The second lens transforms the field distribution back into the spatial space and thus generates a manipulated image of the object in its focal plane. For example, a pinhole in the Fourier plane fades out high spatial frequencies and thus filters out small image disturbances.