Abstract

A method for comparing and reconstructing two nearly identical planar objects that are composed of the same number of identical apertures is presented. These structures differ only in the location of one of the apertures. The method is based on a subtraction algorithm, which involves the cross-correlation and autocorrelation functions of the compared structures. Simulated results illustrate the feasibility of the method.

© 2001 Optical Society of America

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References

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  1. B. G. Boone, Signal Processing Using Optics, (Oxford U. Press, New York, 1998).
  2. J. L. Horner, Optical Signal Processing (Academic, San Diego, Calif., 1987).
  3. V. B. Markov, Y. Mejia, R. Castañeda, “Correlation analysis of pseudo-identical structures for pattern recognition,” Optical Security and Counterfeit Deterrence Techniques, R. L. Van Renesse, ed., Proc. SPIE2659, 187–196 (1996).
    [Crossref]
  4. J. R. Fienup, T. R. Crimmins, W. Holsztynski, “Reconstruction of the support of an object from the support of its autocorrelation functions,” J. Opt. Soc. Am. 72, 610–624 (1982).
    [Crossref]
  5. Y. Mejía, V. B. Markov, R. Castañeda, “Analysis of a quasi-periodical structure through its autocorrelation function,” Opt. Eng. 35, 2845–2851 (1996).
    [Crossref]
  6. J. E. Rau, “Detection of differences in real distributions,” J. Opt. Soc. Am. 56, 1490–1494 (1966).
    [Crossref]
  7. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  8. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1993).
  9. A. B. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

1996 (1)

Y. Mejía, V. B. Markov, R. Castañeda, “Analysis of a quasi-periodical structure through its autocorrelation function,” Opt. Eng. 35, 2845–2851 (1996).
[Crossref]

1982 (1)

1966 (1)

1964 (1)

A. B. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

Boone, B. G.

B. G. Boone, Signal Processing Using Optics, (Oxford U. Press, New York, 1998).

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1993).

Castañeda, R.

Y. Mejía, V. B. Markov, R. Castañeda, “Analysis of a quasi-periodical structure through its autocorrelation function,” Opt. Eng. 35, 2845–2851 (1996).
[Crossref]

V. B. Markov, Y. Mejia, R. Castañeda, “Correlation analysis of pseudo-identical structures for pattern recognition,” Optical Security and Counterfeit Deterrence Techniques, R. L. Van Renesse, ed., Proc. SPIE2659, 187–196 (1996).
[Crossref]

Crimmins, T. R.

Fienup, J. R.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Holsztynski, W.

Horner, J. L.

J. L. Horner, Optical Signal Processing (Academic, San Diego, Calif., 1987).

Markov, V. B.

Y. Mejía, V. B. Markov, R. Castañeda, “Analysis of a quasi-periodical structure through its autocorrelation function,” Opt. Eng. 35, 2845–2851 (1996).
[Crossref]

V. B. Markov, Y. Mejia, R. Castañeda, “Correlation analysis of pseudo-identical structures for pattern recognition,” Optical Security and Counterfeit Deterrence Techniques, R. L. Van Renesse, ed., Proc. SPIE2659, 187–196 (1996).
[Crossref]

Mejia, Y.

V. B. Markov, Y. Mejia, R. Castañeda, “Correlation analysis of pseudo-identical structures for pattern recognition,” Optical Security and Counterfeit Deterrence Techniques, R. L. Van Renesse, ed., Proc. SPIE2659, 187–196 (1996).
[Crossref]

Mejía, Y.

Y. Mejía, V. B. Markov, R. Castañeda, “Analysis of a quasi-periodical structure through its autocorrelation function,” Opt. Eng. 35, 2845–2851 (1996).
[Crossref]

Rau, J. E.

VanderLugt, A. B.

A. B. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1993).

IEEE Trans. Inf. Theory (1)

A. B. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

J. Opt. Soc. Am. (2)

Opt. Eng. (1)

Y. Mejía, V. B. Markov, R. Castañeda, “Analysis of a quasi-periodical structure through its autocorrelation function,” Opt. Eng. 35, 2845–2851 (1996).
[Crossref]

Other (5)

B. G. Boone, Signal Processing Using Optics, (Oxford U. Press, New York, 1998).

J. L. Horner, Optical Signal Processing (Academic, San Diego, Calif., 1987).

V. B. Markov, Y. Mejia, R. Castañeda, “Correlation analysis of pseudo-identical structures for pattern recognition,” Optical Security and Counterfeit Deterrence Techniques, R. L. Van Renesse, ed., Proc. SPIE2659, 187–196 (1996).
[Crossref]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1993).

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Figures (5)

Fig. 1
Fig. 1

(a–c) Similar structures of nine elements (identical square apertures of side a and transmission A). In comparison with (a), in (b) one aperture was shifted on the right a distance equal to the side a, and in (c) one aperture was shifted on the diagonal a distance equal to the aperture diagonal. (d–f) Intensity distributions of the corresponding Fraunhofer interferograms.

Fig. 2
Fig. 2

Autocorrelation modules of the corresponding structures in Figs. 1(a)1(c).

Fig. 3
Fig. 3

(a) Cross correlation between the structures in Figs. 1(a) and 1(b). (b) Cross correlation between the structures in Figs. 1(a) and 1(c).

Fig. 4
Fig. 4

Subtraction algorithm for comparing the structures f(x, y) [Fig. 1(a)] and g(x, y) [Fig. 1(b)]. (a) Γ fg (x, y) - Γ ff (x, y), and (b) Γ fg (x, y) - Γ gg (x, y).

Fig. 5
Fig. 5

Subtraction algorithm for comparing the structures f(x, y) [Fig. 1(a)] and g(x, y) [Fig. 1(c)]. (a) Γ fg (x, y) - Γ ff (x, y), and (b) Γ fg (x, y) - Γ gg (x, y).

Equations (8)

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tx, y=A rectx/arecty/a*n=1N δx-xn, y-yn=t0x, y*n=1N δx-xn, y-yn.
Iu, v=I0u, vN+m=1N-1n=m+1N 2 cos2πuxm-xn+vym-yn,
Γttx, y=Γ0x, y*m=1Nn=1N δx-xm-xn, y-ym-yn,
Γfgx, y=Γ0x, y*m=1Nn=1N δx-xmg-xnf, y-ymg-ynf.
Γfgx, y-Γffx, y=Γ0x, y * m=1Nδx-xmg-xkf, y-ymg-ykf-δx-xmf-xkf, y-ymf-ykf,
Γfgx, y-Γggx, y=Γ0x, y * m=1Nδx-xmg-xkf, y-ymg-ykf-δx-xmg-xkg, y-ymg-ykg,
Γfgx, y-Γffx, y=Γ0x, y* δx, y-δx-εk, y-ηk* n=1N δx-Δxnkf, y-Δynkf
Γfgx, y-Γggx, y=Γ0x, y* δx, y-δx-εk, y-ηk* m=1N δx-Δxmkg, y-Δymkg,

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