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Fractional transforms in optical information processing. Bastiaans, Martin J. Alieva Krasheninnikova, Tatiana Calvo Padilla, María Luisa 535 Wigner Distribution Function Order Fourier-Transform Orbital Angular-Momentum Schell Model Beams Linear-Fm Signals Image Encryption Partially Coherent Phase Retrieval Hilbert Transform Radon-Wigner Óptica (Física) 2209.19 Óptica Física © 2005 Tatiana Alieva et al. This work has been financially supported partially by the project TIC 2002-01846 from the Spanish Ministry of Education and Science and by the project IST-2001-34168 “Two dimensional optical storage for high density and high data rate” from the European Commission. T. Alieva thanks the Spanish Ministry of Science and Technology (“Ramon y Cajal”grant). 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. Ministerio de Educación y Ciencia (MEC), España Comisión Europea Ministerio de Ciencia y Tecnología, España Depto. de Óptica Fac. de Ciencias Físicas TRUE pub 2023-06-20T10:42:39Z 2023-06-20T10:42:39Z 2005-07-01 journal article https://hdl.handle.net/20.500.14352/51050 1110-8657 10.1155/ASP.2005.1498 eng TIC 2002-01846 IST-2001-34168 Programa Nacional de Contratación e incorporación de RRHH. Subprograma Ramón y Cajal (RYC) Atribución 3.0 España https://creativecommons.org/licenses/by/3.0/es/ open access application/pdf Hindawi Publishing Corporation