Abstract

Multifractional correlation is proposed that is based on a new generalized fractional Fourier transform to which we refer as a multifractional Fourier transform. The multifractional correlation yields remarkable improvements in the correlation output peak intensity, peak sharpness, and light efficiency compared with convention correlation, which uses matched and phase-only filters, and still maintains better target discrimination capability and a reasonable robustness to noise. An optoelectronic hybrid system that can implement the multifractional correlation is also suggested.

© 2001 Optical Society of America

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References

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2000

B. Zhu, S. Liu, and Q. Ran, Opt. Lett. 25, 1159 (2000).
[CrossRef]

S. Lai, B. King, and M. Neifeld, Opt. Commun. 173, 155 (2000).
[CrossRef]

1997

1996

1995

C. C. Shih, Opt. Commun. 118, 495 (1995).
[CrossRef]

1993

1990

Hassebroo, L.

Javidi, B.

King, B.

S. Lai, B. King, and M. Neifeld, Opt. Commun. 173, 155 (2000).
[CrossRef]

Kumar, B. V. K.

Kutay, M. A.

H. M. Ozaktas, M. A. Kutay, and D. Mendlovic, Introduction to the Fractional Fourier Transform and Its Applications, Vol. 106 of Advances in Imaging and Electron Physics (Academic, San Diego, Calif., 1999), pp. 239–291 and references therein.

Lai, S.

S. Lai, B. King, and M. Neifeld, Opt. Commun. 173, 155 (2000).
[CrossRef]

Liu, S.

Lohmann, A. W.

Mendlovic, D.

A. W. Lohmann and D. Mendlovic, Appl. Opt. 36, 7402 (1997).
[CrossRef]

D. Mendlovic and H. M. Ozaktas, J. Opt. Soc. Am. A 10, 1875 (1993).
[CrossRef]

H. M. Ozaktas, M. A. Kutay, and D. Mendlovic, Introduction to the Fractional Fourier Transform and Its Applications, Vol. 106 of Advances in Imaging and Electron Physics (Academic, San Diego, Calif., 1999), pp. 239–291 and references therein.

Neifeld, M.

S. Lai, B. King, and M. Neifeld, Opt. Commun. 173, 155 (2000).
[CrossRef]

Ozaktas, H. M.

D. Mendlovic and H. M. Ozaktas, J. Opt. Soc. Am. A 10, 1875 (1993).
[CrossRef]

H. M. Ozaktas, M. A. Kutay, and D. Mendlovic, Introduction to the Fractional Fourier Transform and Its Applications, Vol. 106 of Advances in Imaging and Electron Physics (Academic, San Diego, Calif., 1999), pp. 239–291 and references therein.

Painchaud, D.

Ran, Q.

Shih, C. C.

C. C. Shih, Opt. Commun. 118, 495 (1995).
[CrossRef]

Zhu, B.

Appl. Opt.

J. Opt. Soc. Am. A

Opt. Commun.

S. Lai, B. King, and M. Neifeld, Opt. Commun. 173, 155 (2000).
[CrossRef]

C. C. Shih, Opt. Commun. 118, 495 (1995).
[CrossRef]

Opt. Lett.

Other

H. M. Ozaktas, M. A. Kutay, and D. Mendlovic, Introduction to the Fractional Fourier Transform and Its Applications, Vol. 106 of Advances in Imaging and Electron Physics (Academic, San Diego, Calif., 1999), pp. 239–291 and references therein.

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Figures (3)

Fig. 1
Fig. 1

Input images of (a) the target (Lena) and (b) the nontarget (Barbara).

Fig. 2
Fig. 2

Autocorrelation peaks of (a) the conventional MF correlator, (b) the POF correlator, (c) MFC with periodicty K and fractional order α, i.e., K,α8,1.2, and (d) MFC with {32, 2.2}.

Fig. 3
Fig. 3

Optoelectronic hybrid setup for the implementation of multifractional correlation: RB, reference beam; P’s, planes; BS’s, beam splitters; other abbreviations defined in text.

Tables (1)

Tables Icon

Table 1 Comparison of Performance of Various Correlators

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

Fαfx,yu,v=-+Kαx,y;u,vfx,ydxdy,
Kαx,u=Aϕexpiπx2cotϕ-2xucscϕ+u2cotϕ,
PKαfx,yx,y=l=0K-1Alαflx,y.
PKαfx,yx,y=1K×l=0K-1n=0K-1exp-2πα-lniKflx,y.
Gu,v=Fu,vH*u,v,
gK,αx,y=F-1PKαfx1,y1u,v×PKα*hx2,y2u,vx,y.

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