Fractionalization of the linear cyclic transforms
| dc.contributor.author | Alieva Krasheninnikova, Tatiana | |
| dc.contributor.author | Calvo Padilla, María Luisa | |
| dc.date.accessioned | 2023-06-20T18:59:36Z | |
| dc.date.available | 2023-06-20T18:59:36Z | |
| dc.date.issued | 2000-12 | |
| dc.description | © 2000 Optical Society of America. International Conference on Optical Science and Applications for Sustainable Development (2000. Dakar, Senegal). This research was financially supported by the Rectorate of the Complutense University of Madrid (UCM), under Multidisciplinary Project PR486/97-7477/97. T. Alieva is grateful for a grant from UCM. Partial results of this study were presented at the International Conference on Optical Science and Applications for Sustainable Development, Dakar (Senegal), April 10–14, 2000. | |
| dc.description.abstract | In this study the general algorithm for the fractionalization of the linear cyclic integral transforms is established. It is shown that there are an infinite number of continuous fractional transforms related to a given cyclic integral transform. The main properties of the fractional transforms used in optics are considered. As an example, two different types of fractional Hartley transform are introduced, and the experimental setups for their optical implementation are proposed. | |
| dc.description.department | Depto. de Óptica | |
| dc.description.faculty | Fac. de Ciencias Físicas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Universidad Complutense de Madrid (UCM) | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/25632 | |
| dc.identifier.doi | 10.1364/JOSAA.17.002330 | |
| dc.identifier.issn | 0740-3232 | |
| dc.identifier.officialurl | http://dx.doi.org/10.1364/JOSAA.17.002330 | |
| dc.identifier.relatedurl | http://www.opticsinfobase.org | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/59065 | |
| dc.issue.number | 12 | |
| dc.journal.title | Journal of the Optical Society of America A-Optics Image Science And Vision | |
| dc.language.iso | eng | |
| dc.page.final | 2338 | |
| dc.page.initial | 2330 | |
| dc.publisher | Optical Society of America | |
| dc.relation.projectID | PR486/97-7477/97 | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 535 | |
| dc.subject.keyword | Optical Implementation | |
| dc.subject.keyword | Fourier-Transforms | |
| dc.subject.keyword | Hilbert Transform | |
| dc.subject.ucm | Óptica (Física) | |
| dc.subject.unesco | 2209.19 Óptica Física | |
| dc.title | Fractionalization of the linear cyclic transforms | |
| dc.type | journal article | |
| dc.volume.number | 17 | |
| dcterms.references | 1. D. Mendlovic and H. M. Ozaktas, “Fractional Fourier transforms and their optical implementation”, J. Opt. Soc. Am. A 10, 1875–1881 (1993). 2. A. W. Lohmann, D. Mendlovic, and Z. Zalevsky, “Fractional transformation in optics”, in Progress in Optics, XXXVIII, E. Wolf, ed. (Elsevier, Amsterdam, 1998), pp. 263–342. 3. H. M. Ozaktas, M. A. Kutay, and D. Mendlovic, “Introduction to the fractional Fourier transform and its applications”, Adv. Imaging Electron Phys. 106, 239–291 (1999). 4. A. W. Lohmann, D. Mendlovic, and Z. Zalevsky, “Fractional Hilbert transform”, Opt. Lett. 21, 281–283 (1996). 5. A. W. Lohmann, E. Tepichin, and J. G. Ramirez, “Optical implementation of the fractional Hilbert transform for two-dimensional objects”, Appl. Opt. 36, 6620–6626 (1997). 6. L. Yu, Y. Lu, X. Zeng, M. Huang, M. Chen, W. Huang, and Z. Zhu, “Deriving the integral representation of a fractional Hankel transform from a fractional Fourier transform”, Opt. Lett. 23, 1158–1160 (1998). 7. B. W. Dickinson and K. Steiglitz, “Eigenvectors and functions of the discrete Fourier transform”, IEEE Trans. Acoust. Speech Signal Process. 30, 25–31 (1982). 8. C. C. Shih, “Fractionalization of Fourier transform”, Opt. Commun. 118, 495–498 (1995). 9. S. Liu, J. Jiang, Y. Zhang, and J. Zhang, “Generalized fractional Fourier transforms”, J. Phys. A 30, 973–981 (1997). 10. T. Alieva and M. J. Bastiaans, “Powers of transfer matrices determined by means of eigenfunctions”, J. Opt. Soc. Am. A 16, 2413–2418 (1999). 11. D. A. Linden, “A discussion of sampling theorems”, Proc. IRE 47, 1219–1226 (1959). 12. R. P. Kanwal, Linear Integral Equations: Theory and Techniques (Academic, New York, 1971), Chaps. 8 and 9. 13. T. Alieva and A. Barbe, “Self-fractional Fourier functions and selection of modes”, J. Phys. A 30, L211–L215 (1997). 14. R. N. Bracewell, H. Bartelt, A. W. Lohmann, and N. Streibl, “Optical synthesis of the Hartley transform”, Appl. Opt. 24, 1401–1402 (1985). | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | f1512137-328a-4bb6-9714-45de778c1be4 | |
| relation.isAuthorOfPublication | e2846481-608d-43dd-a835-d70f73a4dd48 | |
| relation.isAuthorOfPublication.latestForDiscovery | e2846481-608d-43dd-a835-d70f73a4dd48 |
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