Abstract

A novel optical wavelet processor based on the techniques of the joint-transform correlator and computer-generated holograms is proposed. A coding technique that is a simplified version of Lee’s hologram [Appl. Opt. 9, 639 (1970)] is used to represent positive and negative values for the object signal and wavelet functions. We experimentally demonstrate that wavelet transforms of two different daughter wavelet functions can be simultaneously obtained by the appropriate arrangement of the daughter wavelet functions and the object signal on the input plane.

© 1997 Optical Society of America

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References

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  1. E. Freysz, B. Pouligny, F. Argoul, A. Arneodo, “Optical wavelet transform of fractal aggregates,” Phys. Rev. Lett. 64, 745–748 (1990).
    [CrossRef] [PubMed]
  2. D. Mendlovic, N. Konforti, “Optical realization of the wavelet transform for two-dimensional objects,” Appl. Opt. 32, 6542–6546 (1993).
    [CrossRef] [PubMed]
  3. Y. Sheng, D. Roberge, H. H. Szu, “Optical wavelet transform,” Opt. Eng. 31, 1840–1845 (1992).
    [CrossRef]
  4. A. VanderLugt, “Signal detection by complex filters,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
  5. W. Wang, G. Jin, Y. Yan, M. Wu, “Joint wavelet-transform correlator for image feature extraction,” Appl. Opt. 34, 370–376 (1995).
    [CrossRef] [PubMed]
  6. C. S. Weaver, J. W. Goodman, “A technique for optically convolving two functions,” Appl. Opt. 5, 1248–1249 (1966).
    [CrossRef] [PubMed]
  7. W. H. Lee, “Sampled Fourier-transform hologram generated by computer,” Appl. Opt. 9, 639–643 (1970).
    [CrossRef] [PubMed]
  8. G. W. Stoke, “White-light reconstruction of holographic images using transmission holograms recorded with conventionally focused images and in-line background,” Phys. Lett. 23, 325–327 (1966).
    [CrossRef]
  9. L. Rosen, “Focused-image holography with extended sources,” Appl. Phys. Lett. 9, 337–339 (1966).
    [CrossRef]
  10. F. T. S. Yu, X. J. Lu, “A real-time programmable joint transform correlator,” Opt. Commun. 52, 10–16 (1984).
    [CrossRef]

1995 (1)

1993 (1)

1992 (1)

Y. Sheng, D. Roberge, H. H. Szu, “Optical wavelet transform,” Opt. Eng. 31, 1840–1845 (1992).
[CrossRef]

1990 (1)

E. Freysz, B. Pouligny, F. Argoul, A. Arneodo, “Optical wavelet transform of fractal aggregates,” Phys. Rev. Lett. 64, 745–748 (1990).
[CrossRef] [PubMed]

1984 (1)

F. T. S. Yu, X. J. Lu, “A real-time programmable joint transform correlator,” Opt. Commun. 52, 10–16 (1984).
[CrossRef]

1970 (1)

1966 (3)

G. W. Stoke, “White-light reconstruction of holographic images using transmission holograms recorded with conventionally focused images and in-line background,” Phys. Lett. 23, 325–327 (1966).
[CrossRef]

L. Rosen, “Focused-image holography with extended sources,” Appl. Phys. Lett. 9, 337–339 (1966).
[CrossRef]

C. S. Weaver, J. W. Goodman, “A technique for optically convolving two functions,” Appl. Opt. 5, 1248–1249 (1966).
[CrossRef] [PubMed]

1964 (1)

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

Argoul, F.

E. Freysz, B. Pouligny, F. Argoul, A. Arneodo, “Optical wavelet transform of fractal aggregates,” Phys. Rev. Lett. 64, 745–748 (1990).
[CrossRef] [PubMed]

Arneodo, A.

E. Freysz, B. Pouligny, F. Argoul, A. Arneodo, “Optical wavelet transform of fractal aggregates,” Phys. Rev. Lett. 64, 745–748 (1990).
[CrossRef] [PubMed]

Freysz, E.

E. Freysz, B. Pouligny, F. Argoul, A. Arneodo, “Optical wavelet transform of fractal aggregates,” Phys. Rev. Lett. 64, 745–748 (1990).
[CrossRef] [PubMed]

Goodman, J. W.

Jin, G.

Konforti, N.

Lee, W. H.

Lu, X. J.

F. T. S. Yu, X. J. Lu, “A real-time programmable joint transform correlator,” Opt. Commun. 52, 10–16 (1984).
[CrossRef]

Mendlovic, D.

Pouligny, B.

E. Freysz, B. Pouligny, F. Argoul, A. Arneodo, “Optical wavelet transform of fractal aggregates,” Phys. Rev. Lett. 64, 745–748 (1990).
[CrossRef] [PubMed]

Roberge, D.

Y. Sheng, D. Roberge, H. H. Szu, “Optical wavelet transform,” Opt. Eng. 31, 1840–1845 (1992).
[CrossRef]

Rosen, L.

L. Rosen, “Focused-image holography with extended sources,” Appl. Phys. Lett. 9, 337–339 (1966).
[CrossRef]

Sheng, Y.

Y. Sheng, D. Roberge, H. H. Szu, “Optical wavelet transform,” Opt. Eng. 31, 1840–1845 (1992).
[CrossRef]

Stoke, G. W.

G. W. Stoke, “White-light reconstruction of holographic images using transmission holograms recorded with conventionally focused images and in-line background,” Phys. Lett. 23, 325–327 (1966).
[CrossRef]

Szu, H. H.

Y. Sheng, D. Roberge, H. H. Szu, “Optical wavelet transform,” Opt. Eng. 31, 1840–1845 (1992).
[CrossRef]

VanderLugt, A.

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

Wang, W.

Weaver, C. S.

Wu, M.

Yan, Y.

Yu, F. T. S.

F. T. S. Yu, X. J. Lu, “A real-time programmable joint transform correlator,” Opt. Commun. 52, 10–16 (1984).
[CrossRef]

Appl. Opt. (4)

Appl. Phys. Lett. (1)

L. Rosen, “Focused-image holography with extended sources,” Appl. Phys. Lett. 9, 337–339 (1966).
[CrossRef]

IEEE Trans. Inf. Theory (1)

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

Opt. Commun. (1)

F. T. S. Yu, X. J. Lu, “A real-time programmable joint transform correlator,” Opt. Commun. 52, 10–16 (1984).
[CrossRef]

Opt. Eng. (1)

Y. Sheng, D. Roberge, H. H. Szu, “Optical wavelet transform,” Opt. Eng. 31, 1840–1845 (1992).
[CrossRef]

Phys. Lett. (1)

G. W. Stoke, “White-light reconstruction of holographic images using transmission holograms recorded with conventionally focused images and in-line background,” Phys. Lett. 23, 325–327 (1966).
[CrossRef]

Phys. Rev. Lett. (1)

E. Freysz, B. Pouligny, F. Argoul, A. Arneodo, “Optical wavelet transform of fractal aggregates,” Phys. Rev. Lett. 64, 745–748 (1990).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Setup of the experimental optical wavelet processor.

Fig. 2
Fig. 2

Cell structure: (a) h(x, y) < 0 and (b) h(x, y) > 0.

Fig. 3
Fig. 3

Representation of the object signal and two wavelet functions.

Fig. 4
Fig. 4

Results: (a) experimental and (b) numerical.

Equations (8)

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

ga,bx=1agx-ba,
wa,b= ga,b*x fxdx=1a  g*x-ba fxdx,
hx, y=h+x, y-h-x, y.
hsx, y=n m h+x, yδx-nd, y-md+h-x, yδx-nd+d/2, y-md,
Hsν,μ=k l H+ν, μ+H-ν, μexpπikδν-k/d, μ-l/d,
d+x, y=dh+x, yhx, y00,hx, y<0, d-x, y=0hx, y0dh-x, y,hx, y<0.
gx, y=gxgy,
gτ=10 τ<0.5-10.5τ<10otherwise.

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