Abstract

A nonconventional joint-transform correlator (NJTC) is discussed. We show that the shift-invariant property of the usual joint-transform arrangement can be preserved. The advantages of the NJTC are the efficient use of the light source, the use of smaller transform lenses, higher correlation peaks, and a higher carrier fringe frequency.

© 1989 Optical Society of America

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References

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  1. C. S. Weaver, J. W. Goodman, Appl. Opt. 5, 1248 (1966).
    [CrossRef] [PubMed]
  2. F. T. S. Yu, X. J. Lu, Opt. Commun. 52, 10 (1984).
    [CrossRef]
  3. D. A. Gregory, J. A. Loudin, F. T. S. Yu, “Illumination dependence of the joint-transform correlation,” Appl. Opt. (to be published).
  4. M. Born, E. Wolf, Principle of Optics, 2nd ed. (Pergamon, New York, 1964), p. 441.
  5. F. T. S. Yu, J. E. Ludman, “Joint Fourier transform processor,” Microwave Opt. Technol. Lett. 1, 374 (1988).
    [CrossRef]

1988 (1)

F. T. S. Yu, J. E. Ludman, “Joint Fourier transform processor,” Microwave Opt. Technol. Lett. 1, 374 (1988).
[CrossRef]

1984 (1)

F. T. S. Yu, X. J. Lu, Opt. Commun. 52, 10 (1984).
[CrossRef]

1966 (1)

Born, M.

M. Born, E. Wolf, Principle of Optics, 2nd ed. (Pergamon, New York, 1964), p. 441.

Goodman, J. W.

Gregory, D. A.

D. A. Gregory, J. A. Loudin, F. T. S. Yu, “Illumination dependence of the joint-transform correlation,” Appl. Opt. (to be published).

Loudin, J. A.

D. A. Gregory, J. A. Loudin, F. T. S. Yu, “Illumination dependence of the joint-transform correlation,” Appl. Opt. (to be published).

Lu, X. J.

F. T. S. Yu, X. J. Lu, Opt. Commun. 52, 10 (1984).
[CrossRef]

Ludman, J. E.

F. T. S. Yu, J. E. Ludman, “Joint Fourier transform processor,” Microwave Opt. Technol. Lett. 1, 374 (1988).
[CrossRef]

Weaver, C. S.

Wolf, E.

M. Born, E. Wolf, Principle of Optics, 2nd ed. (Pergamon, New York, 1964), p. 441.

Yu, F. T. S.

F. T. S. Yu, J. E. Ludman, “Joint Fourier transform processor,” Microwave Opt. Technol. Lett. 1, 374 (1988).
[CrossRef]

F. T. S. Yu, X. J. Lu, Opt. Commun. 52, 10 (1984).
[CrossRef]

D. A. Gregory, J. A. Loudin, F. T. S. Yu, “Illumination dependence of the joint-transform correlation,” Appl. Opt. (to be published).

Appl. Opt. (1)

Microwave Opt. Technol. Lett. (1)

F. T. S. Yu, J. E. Ludman, “Joint Fourier transform processor,” Microwave Opt. Technol. Lett. 1, 374 (1988).
[CrossRef]

Opt. Commun. (1)

F. T. S. Yu, X. J. Lu, Opt. Commun. 52, 10 (1984).
[CrossRef]

Other (2)

D. A. Gregory, J. A. Loudin, F. T. S. Yu, “Illumination dependence of the joint-transform correlation,” Appl. Opt. (to be published).

M. Born, E. Wolf, Principle of Optics, 2nd ed. (Pergamon, New York, 1964), p. 441.

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Figures (8)

Fig. 1
Fig. 1

Quasi-Fourier transformation. P 2 is the image of P2.

Fig. 2
Fig. 2

Fourier diffraction condition.

Fig. 3
Fig. 3

Quasi-joint-Fourier transformation.

Fig. 4
Fig. 4

Nonconventional joint Fourier transformation.

Fig. 5
Fig. 5

Nonconventional quasi-joint-Fourier transformation.

Fig. 6
Fig. 6

(a) Input object and reference function. (b) Output correlation spots.

Fig. 7
Fig. 7

(a) Input and reference objects. (b) Joint-transform holograms.

Fig. 8
Fig. 8

(a) Output correlation spots. (b) Photometer traces of the output correlation peaks.

Equations (12)

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

L = f 2 / δ
Δ L λ / 4 .
L ( b / 2 ) 2 2 Δ L ,
L b 2 / 2 λ .
L L .
δ 2 λ ( f / b ) 2 .
a = δ f d ,
a λf / 2 b .
d f 2 λ 2 .
α m = f max = W / b ,
θ arctan ( δ / α m ) ,
θ arctan ( 2 f / bW ) ,

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