Abstract
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.