Abstract

We propose a method for designing a correlator for achieving rotation-invariant and controllable space-variant optical correlation. The design concept is based on a combination of fractional correlation and circular-harmonic decomposition of the reference object. The suggested method is described and analyzed in detail. Numerical simulations show that this new correlator might provide potential applications in practice.

© 1998 Optical Society of America

PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–140 (1964).
  2. C. S. Weaver, J. W. Goodman, “A technique for optically convolving two functions,” Appl. Opt. 5, 1248–1249 (1966).
    [CrossRef] [PubMed]
  3. D. Mendlovic, H. M. Ozaktas, A. W. Lohmann, “Fractional correlation,” Appl. Opt. 34, 303–309 (1995).
    [CrossRef] [PubMed]
  4. A. W. Lohmann, Z. Zalevsky, D. Mendlovic, “Synthesis of pattern recognition filters for fractional Fourier processing,” Opt. Commun. 128, 199–204 (1996).
    [CrossRef]
  5. S. Granieri, R. Arizaga, E. E. Sicre, “Optical correlation based on the fractional Fourier transform,” Appl. Opt. 36, 6636–6645 (1997).
    [CrossRef]
  6. Y. N. Hsu, H. H. Arsenault, “Optical pattern recognition using the circular harmonic expansion,” Appl. Opt. 21, 4016–4019 (1982).
    [CrossRef] [PubMed]
  7. Y. Sheng, H. H. Arsenault, “Method for determining expansion centers and predicting sidelobe levels for circular harmonic filters,” J. Opt. Soc. Am. A 4, 1793–1799 (1987).
    [CrossRef]
  8. Z. Zalevsky, I. Ouzieli, D. Mendlovic, “Wavelet-transform-based composite filters for invariant pattern recognition,” Appl. Opt. 35, 3141–3147 (1996).
    [CrossRef] [PubMed]
  9. V. Namias, “The fractional order Fourier transform and its application to quantum mechanics,” J. Inst. Math. Appl. 25, 241–265 (1980).
    [CrossRef]
  10. D. Mendlovic, H. M. Ozaktas, “Fractional Fourier transforms and their implementations: I,” J. Opt. Soc. Am. A 10, 1875–1881 (1993).
    [CrossRef]
  11. H. M. Ozaktas, D. Mendlovic, “Fractional Fourier transforms and their implementations: II,” J. Opt. Soc. Am. A 10, 2522–2531 (1993).
    [CrossRef]
  12. A. W. Lohmann, “Image rotation, Wigner rotation, and the fractional Fourier transform,” J. Opt. Soc. Am. A 10, 2181–2186 (1993).
    [CrossRef]
  13. H. M. Ozaktas, D. Mendlovic, “Fourier transforms of fractional orders and their optical interpretation,” Opt. Commun. 101, 163–169 (1993).
    [CrossRef]
  14. S. Liu, J. Xu, Y. Zhang, L. Chen, C. Li, “General optical implementations of the fractional Fourier transform,” Opt. Lett. 20, 1053–1055 (1995).
    [CrossRef] [PubMed]
  15. H. M. Ozaktas, O. Arikan, M. A. Kutay, G. Bozdag, “Digital computation of the fractional Fourier transform,” IEEE Trans. Signal Process. 44, 2141–2150 (1996).
    [CrossRef]
  16. H. M. Ozaktas, B. Barshan, D. Mendlovic, L. Onural, “Convolution, filtering, and multiplexing in the fractional Fourier domain and their relation to chirp and wavelet transforms,” J. Opt. Soc. Am. A 11, 547–559 (1994).
    [CrossRef]
  17. B.-Z. Dong, Y. Zhang, B.-Y. Gu, G.-Z. Yang, “Numerical investigation of phase retrieval in a fractional Fourier transform,” J. Opt. Soc. Am. A 14, 2709–2714 (1997).
    [CrossRef]
  18. Y. Zhang, B.-Z. Dong, B.-Y. Gu, G.-Z. Yang, “Beam shaping in the fractional Fourier transform domain,” J. Opt. Soc. Am. A 15, 1114–1120 (1998).
    [CrossRef]
  19. Z. Zalevsky, D. Mendlovic, J. Garcia, “Invariant pattern recognition by use of wavelength multiplexing,” Appl. Opt. 36, 1059–1063 (1997).
    [CrossRef] [PubMed]

1998 (1)

1997 (3)

1996 (3)

Z. Zalevsky, I. Ouzieli, D. Mendlovic, “Wavelet-transform-based composite filters for invariant pattern recognition,” Appl. Opt. 35, 3141–3147 (1996).
[CrossRef] [PubMed]

H. M. Ozaktas, O. Arikan, M. A. Kutay, G. Bozdag, “Digital computation of the fractional Fourier transform,” IEEE Trans. Signal Process. 44, 2141–2150 (1996).
[CrossRef]

A. W. Lohmann, Z. Zalevsky, D. Mendlovic, “Synthesis of pattern recognition filters for fractional Fourier processing,” Opt. Commun. 128, 199–204 (1996).
[CrossRef]

1995 (2)

1994 (1)

1993 (4)

1987 (1)

1982 (1)

1980 (1)

V. Namias, “The fractional order Fourier transform and its application to quantum mechanics,” J. Inst. Math. Appl. 25, 241–265 (1980).
[CrossRef]

1966 (1)

1964 (1)

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–140 (1964).

Arikan, O.

H. M. Ozaktas, O. Arikan, M. A. Kutay, G. Bozdag, “Digital computation of the fractional Fourier transform,” IEEE Trans. Signal Process. 44, 2141–2150 (1996).
[CrossRef]

Arizaga, R.

Arsenault, H. H.

Barshan, B.

Bozdag, G.

H. M. Ozaktas, O. Arikan, M. A. Kutay, G. Bozdag, “Digital computation of the fractional Fourier transform,” IEEE Trans. Signal Process. 44, 2141–2150 (1996).
[CrossRef]

Chen, L.

Dong, B.-Z.

Garcia, J.

Goodman, J. W.

Granieri, S.

Gu, B.-Y.

Hsu, Y. N.

Kutay, M. A.

H. M. Ozaktas, O. Arikan, M. A. Kutay, G. Bozdag, “Digital computation of the fractional Fourier transform,” IEEE Trans. Signal Process. 44, 2141–2150 (1996).
[CrossRef]

Li, C.

Liu, S.

Lohmann, A. W.

Mendlovic, D.

Namias, V.

V. Namias, “The fractional order Fourier transform and its application to quantum mechanics,” J. Inst. Math. Appl. 25, 241–265 (1980).
[CrossRef]

Onural, L.

Ouzieli, I.

Ozaktas, H. M.

Sheng, Y.

Sicre, E. E.

VanderLugt, A.

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–140 (1964).

Weaver, C. S.

Xu, J.

Yang, G.-Z.

Zalevsky, Z.

Zhang, Y.

Appl. Opt. (6)

IEEE Trans. Inf. Theory (1)

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–140 (1964).

IEEE Trans. Signal Process. (1)

H. M. Ozaktas, O. Arikan, M. A. Kutay, G. Bozdag, “Digital computation of the fractional Fourier transform,” IEEE Trans. Signal Process. 44, 2141–2150 (1996).
[CrossRef]

J. Inst. Math. Appl. (1)

V. Namias, “The fractional order Fourier transform and its application to quantum mechanics,” J. Inst. Math. Appl. 25, 241–265 (1980).
[CrossRef]

J. Opt. Soc. Am. A (7)

Opt. Commun. (2)

H. M. Ozaktas, D. Mendlovic, “Fourier transforms of fractional orders and their optical interpretation,” Opt. Commun. 101, 163–169 (1993).
[CrossRef]

A. W. Lohmann, Z. Zalevsky, D. Mendlovic, “Synthesis of pattern recognition filters for fractional Fourier processing,” Opt. Commun. 128, 199–204 (1996).
[CrossRef]

Opt. Lett. (1)

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Metrics