VARIABLE FRACTIONAL FOURIER PROCESSOR - A SIMPLE IMPLEMENTATION

A new set of optical implementations of the fractional Fourier transfo rm (FRT) is developed by use of Wigner matrix algebra. The reinterpret ation of some elementary operations that synthesize a rotation in the phase-space domain allows us to propose a lensless setup for obtaining the FRT. This compact configuration is also very flexible, because th e fractional degree of the transformation can be varied continuously b y shifting the input and the output planes along the optical axis by p roper amounts. The above results permit one to build an optical FRT pr ocessor formed by two FRT systems in cascade, with a spatial filter be tween them. We present the design of such a variable FRT processor, wh ich contains only one lens. (C) 1997 Optical Society of America.