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Optics Express

Optics Express

  • Vol. 17, Iss. 7 — Mar. 30, 2009
  • pp: 4976–4983

Programmable two-dimensional optical fractional Fourier processor

José A. Rodrigo, Tatiana Alieva, and María L. Calvo  »View Author Affiliations


Optics Express, Vol. 17, Issue 7, pp. 4976-4983 (2009)
http://dx.doi.org/10.1364/OE.17.004976


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Abstract

A flexible optical system able to perform the fractional Fourier transform (FRFT) almost in real time is presented. In contrast to other FRFT setups the resulting transformation has no additional scaling and phase factors depending on the fractional orders. The feasibility of the proposed setup is demonstrated experimentally for a wide range of fractional orders. The fast modification of the fractional orders, offered by this optical system, allows to implement various proposed algorithms for beam characterization, phase retrieval, information processing, etc.

© 2009 Optical Society of America

OCIS Codes
(070.2590) Fourier optics and signal processing : ABCD transforms
(120.4820) Instrumentation, measurement, and metrology : Optical systems
(140.3300) Lasers and laser optics : Laser beam shaping
(200.4740) Optics in computing : Optical processing

ToC Category:
Fourier Optics and Signal Processing

History
Original Manuscript: December 18, 2008
Revised Manuscript: January 27, 2009
Manuscript Accepted: February 13, 2009
Published: March 16, 2009

Citation
Jose Augusto Rodrigo, Tatiana Alieva, and Maria L. Calvo, "Programmable two-dimensional optical fractional Fourier processor," Opt. Express 17, 4976-4983 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-7-4976


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References

  1. H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (John Wiley&Sons, NY, USA, 2001).
  2. D. F. McAlister, M. Beck, L. Clarke, A. Mayer, and M. G. Raymer, "Optical phase retrieval by phase-space tomography and fractional-order Fourier transforms," Opt. Lett. 20, 1181-1183 (1995). URL http://ol.osa.org/abstract.cfm?URI=ol-20-10-1181. [CrossRef] [PubMed]
  3. J. A. Rodrigo, T. Alieva, and M. L. Calvo, "Optical system design for orthosymplectic transformations in phase space," J. Opt. Soc. Am. A 23, 2494-2500 (2006), http://josaa.osa.org/abstract.cfm?URI=josaa-23-10-2494. [CrossRef]
  4. D. Mendlovic and H. M. Ozaktas, "Fractional Fourier transform and their optical implementation," J. Opt. Soc. Am. A 10, 1875-1881 (1993). [CrossRef]
  5. A. W. Lohmann, "Image rotation, Wigner rotation, and the fractional order Fourier transform," J. Opt. Soc. Am. A 10, 2181-2186 (1993). [CrossRef]
  6. A. Sahin, H. M. Ozaktas, and D. Mendlovic, "Optical Implementations of Two-Dimensional Fractional Fourier Transforms and Linear Canonical Transforms with Arbitrary Parameters," Appl. Opt. 37, 2130-2141 (1998), http://ao.osa.org/abstract.cfm?URI=ao-37-11-2130. [CrossRef]
  7. I. Moreno, J. A. Davis, and K. Crabtree, "Fractional Fourier transform optical system with programmable diffractive lenses," Appl. Opt. 42, 6544-6548 (2003). [CrossRef] [PubMed]
  8. A. A. Malyutin, "Tunable Fourier transformer of the fractional order," Quantum Electron. 36, 79-83 (2006). [CrossRef]
  9. I. Moreno, C. Ferreira, and M. M. Sánchez-López, "Ray matrix analysis of anamorphic fractional Fourier systems," J. Opt. A: Pure and Applied Optics 8, 427-435 (2006), http://stacks.iop.org/1464-4258/8/427. [CrossRef]
  10. J. A. Rodrigo, T. Alieva, and M. L. Calvo, "Gyrator transform: properties and applications," Opt. Express 15, 2190-2203 (2007), http://www.opticsexpress.org/abstract.cfm?URI=oe-15-5-2190. [CrossRef] [PubMed]
  11. J. A. Rodrigo, T. Alieva, and M. L. Calvo, "Experimental implementation of the gyrator transform," J. Opt. Soc. Am. A 24, 3135-3139 (2007), http://josaa.osa.org/abstract.cfm?URI=josaa-24-10-3135. [CrossRef]
  12. G. Nemes and A. E. Seigman, "Measurement of all ten second-order moments of an astigmatic beam by use of rotating simple astigmatic (anamorphic) optics," J. Opt. Soc. Am. A 11, 2257-2264 (1994). [CrossRef]
  13. J. A. Rodrigo, "First-order optical systems in information processing and optronic devices," Ph.D. thesis, Universidad Complutense de Madrid (2008).
  14. T. Alieva and M. J. Bastiaans, "Orthonormal mode sets for the two-dimensional fractional Fourier transformation," Opt. Lett. 32, 1226-1228 (2007), http://ol.osa.org/abstract.cfm?URI=ol-32-10-1226. [CrossRef] [PubMed]
  15. A. Jesacher, A. Schwaighofer, S. Fürhapter, C. Maurer, S. Bernet, and M. Ritsch-Marte, "Wavefront correction of spatial light modulators using an optical vortex image," Opt. Express 15, 5801-5808 (2007), http://www.opticsexpress.org/abstract.cfm?URI=oe-15-9-5801. [CrossRef] [PubMed]
  16. D. Mendlovic, R. G. Dorsch, A. W. Lohmann, Z. Zalevsky, and C. Ferreira, "Optical illustration of a varied fractional Fourier-transform order and the Radon—Wigner display," Appl. Opt. 35, 3925-3929 (1996), http://ao.osa.org/abstract.cfm?URI=ao-35-20-3925. [CrossRef] [PubMed]

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