Space-bandwidth product of conventional Fourier transforming systems

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