Based on a system theory point of view, Fourier transform properties of multi lenses are discussed. The focal length of an added phase compensating lens in a compact 4 optical system is recalculated according to the specific system. The length of the system is reduced once more to about 1/4 of the original system length by using two Fourier transform telephoto lenses. Finally, a design of the compact optical 4 f system is given.