Programmable two-dimensional optical fractional Fourier processor.

A flexible optical system able to perform the fractional Fourier transform (FRFT) almost in real time is presented. In contrast to other FRFT setups the resulting transformation has no additional scaling and phase factors depending on the fractional orders. The feasibility of the proposed setup is demonstrated experimentally for a wide range of fractional orders. The fast modification of the fractional orders, offered by this optical system, allows to implement various proposed algorithms for beam characterization, phase retrieval, information processing, etc.