Fractional transforms in optical information processing

We review the progress achieved in optical information processing during the last decade by applying fractional linear integral transforms. The fractional Fourier transform and its applications for phase retrieval, beam characterization, space-variant pattern recognition, adaptive filter design, encryption, watermarking, and so forth is discussed in detail. A general algorithm for the fractionalization of linear cyclic integral transforms is introduced and it is shown that they can be fractionalized in an infinite number of ways. Basic properties of fractional cyclic transforms are considered. The implementation of some fractional transforms in optics, such as fractional Hankel, sine, cosine, Hartley, and Hilbert transforms, is discussed. New horizons of the application of fractional transforms for optical information processing are underlined.