Space-bandwidth product of conventional Fourier transforming systems

It is shown that the space-bandwidth product of conventional “2 f ” Fourier transforming configurations can be increased without bound by increasing the diameter D and focal length f of the lens simultaneously to D∝f 3 4 . This results in space-bandwidth product growth ∝f 1 2 and accompanying system linear extent growth ∝f 3 4 . These are derived by considering the validity of the Fresnel approximation, the thin lens approximation, and the effects of aberrations.