Fractional Fourier Transform Optical System with Programmable Diffractive Lenses

We present experimental results for a fractional Fourier transform (FRFT) system implemented with programmable lenses written onto a liquid-crystal spatial light modulator (LCSLM). Because the focal length can be changed, different orders of the FRFT can be obtained without changing the optical setup. The LCSLM can very easily implement more complicated operations, including the realization of simultaneous orders of the FRFT and anamorphic transforms.