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

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1998

1997

1996

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

1994

1993

1987

1982

1980

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

1966

1964

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.

IEEE Trans. Inf. Theory

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

IEEE Trans. Signal Process.

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.

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

Opt. Commun.

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.

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