Optical implementation of scale invariant fractional Fourier transform of continuously variable orders with a two-lens system

A simple two ordinary lens system is proposed to realize the fractional Fourier transform (FRT) of continuously variable order while keeping the scaling factors of both the input and output functions as the same constant independent of the geometric parameters of the system and the FRT orders. It can remove the necessity and inconvenience of using input masks of different scales or any other special devices, and then is helpful to those who want to observe the FRT but have no specific facilities.