Open Access

Fractional Transforms in Optical Information Processing

  • Tatiana Alieva1Email author,
  • Martin J. Bastiaans2 and
  • Maria Luisa Calvo1
EURASIP Journal on Advances in Signal Processing20052005:920687

Received: 31 March 2004

Published: 30 June 2005


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.

Keywords and phrases

fractional Fourier transformfractional convolutionfractional cyclic transformsfractional optics

Authors’ Affiliations

Facultad de Ciencias Físicas, Universidad Complutense de Madrid, Ciudad Universitaria, Madrid, Spain
Faculteit Elektrotechniek, Technische Universiteit Eindhoven, Eindhoven, The Netherlands


© Tatiana Alieva et al. 2005

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.