Abstract

We propose a wave-front filtering concept of wavelet optics and present its associated theory of wavelet optics. We analyze the filtering phenomenon of wavelet optics at the spatial-frequency domain—multiscale edge detection and multiscale feature recognition—using the theory, and we also perform the analysis with the Mexican-hat wavelet and the Haar wavelet. By use of our theory, information is obtained from an optical image that is processed multiscalely and delicately by stretching and translation of the factors. With this technique it is possible to perform real-time programming in information processing in a mixed optical system.

© 2001 Optical Society of America

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References

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  1. Y. Li, H. H. Szu, Y. Sheng, H. J. Caufield, “Wavelet and optics,” IEEE Proc. 84, 720–732 (1996).
    [CrossRef]
  2. Y. Sheng, D. Roberge, H. H. Szu, “Optical wavelet transform,” Opt. Eng. 31, 1840–1845 (1992).
    [CrossRef]
  3. J. Ma, L. Tan, Q. Ran, “The elementary theory of optical wavelet filtering,” Chin. J. Lasers A26, 343–346 (1999) (in Chinese).
  4. J. Ma, L. Tan, Q. Ran, “The application of wavelet analysis to optical information processing,” Acta Physica Sin. 48, 1223–1229 (1999) (in Chinese).
  5. S. Mallat, W. L. Hwang, “Singularity detection and processing with wavelets,” IEEE Trans. Inf. Theory 38, 617–643 (1992).
    [CrossRef]

1999 (2)

J. Ma, L. Tan, Q. Ran, “The elementary theory of optical wavelet filtering,” Chin. J. Lasers A26, 343–346 (1999) (in Chinese).

J. Ma, L. Tan, Q. Ran, “The application of wavelet analysis to optical information processing,” Acta Physica Sin. 48, 1223–1229 (1999) (in Chinese).

1996 (1)

Y. Li, H. H. Szu, Y. Sheng, H. J. Caufield, “Wavelet and optics,” IEEE Proc. 84, 720–732 (1996).
[CrossRef]

1992 (2)

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

S. Mallat, W. L. Hwang, “Singularity detection and processing with wavelets,” IEEE Trans. Inf. Theory 38, 617–643 (1992).
[CrossRef]

Caufield, H. J.

Y. Li, H. H. Szu, Y. Sheng, H. J. Caufield, “Wavelet and optics,” IEEE Proc. 84, 720–732 (1996).
[CrossRef]

Hwang, W. L.

S. Mallat, W. L. Hwang, “Singularity detection and processing with wavelets,” IEEE Trans. Inf. Theory 38, 617–643 (1992).
[CrossRef]

Li, Y.

Y. Li, H. H. Szu, Y. Sheng, H. J. Caufield, “Wavelet and optics,” IEEE Proc. 84, 720–732 (1996).
[CrossRef]

Ma, J.

J. Ma, L. Tan, Q. Ran, “The application of wavelet analysis to optical information processing,” Acta Physica Sin. 48, 1223–1229 (1999) (in Chinese).

J. Ma, L. Tan, Q. Ran, “The elementary theory of optical wavelet filtering,” Chin. J. Lasers A26, 343–346 (1999) (in Chinese).

Mallat, S.

S. Mallat, W. L. Hwang, “Singularity detection and processing with wavelets,” IEEE Trans. Inf. Theory 38, 617–643 (1992).
[CrossRef]

Ran, Q.

J. Ma, L. Tan, Q. Ran, “The application of wavelet analysis to optical information processing,” Acta Physica Sin. 48, 1223–1229 (1999) (in Chinese).

J. Ma, L. Tan, Q. Ran, “The elementary theory of optical wavelet filtering,” Chin. J. Lasers A26, 343–346 (1999) (in Chinese).

Roberge, D.

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

Sheng, Y.

Y. Li, H. H. Szu, Y. Sheng, H. J. Caufield, “Wavelet and optics,” IEEE Proc. 84, 720–732 (1996).
[CrossRef]

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

Szu, H. H.

Y. Li, H. H. Szu, Y. Sheng, H. J. Caufield, “Wavelet and optics,” IEEE Proc. 84, 720–732 (1996).
[CrossRef]

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

Tan, L.

J. Ma, L. Tan, Q. Ran, “The application of wavelet analysis to optical information processing,” Acta Physica Sin. 48, 1223–1229 (1999) (in Chinese).

J. Ma, L. Tan, Q. Ran, “The elementary theory of optical wavelet filtering,” Chin. J. Lasers A26, 343–346 (1999) (in Chinese).

Acta Physica Sin. (1)

J. Ma, L. Tan, Q. Ran, “The application of wavelet analysis to optical information processing,” Acta Physica Sin. 48, 1223–1229 (1999) (in Chinese).

Chin. J. Lasers (1)

J. Ma, L. Tan, Q. Ran, “The elementary theory of optical wavelet filtering,” Chin. J. Lasers A26, 343–346 (1999) (in Chinese).

IEEE Proc. (1)

Y. Li, H. H. Szu, Y. Sheng, H. J. Caufield, “Wavelet and optics,” IEEE Proc. 84, 720–732 (1996).
[CrossRef]

IEEE Trans. Inf. Theory (1)

S. Mallat, W. L. Hwang, “Singularity detection and processing with wavelets,” IEEE Trans. Inf. Theory 38, 617–643 (1992).
[CrossRef]

Opt. Eng. (1)

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

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Figures (3)

Fig. 1
Fig. 1

Spatial-filtering system.

Fig. 2
Fig. 2

Filtering system of spatial-frequency domain.

Fig. 3
Fig. 3

Mixed optical information-processing system.

Equations (15)

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ha,b;c,dx1, y1=a-1/2c-1/2hb-x1a, d-y1c,
Ux, y=Σ U1x1, y1ha,b;c,dx1, y1dx1dy1,
Ex, y=k Σ fx, yha,b;c,dx, ydxdy.
gx, y=fx, yha,b;c,dx, y.
α=λf2π px,  β=λf2π qy,
Ep, q=Fp, qha,b;c,db-pa, d-qc,
gα, β=Fp, qha,b;c,db-pa, d-qc.
Ψ1p, q=θp, qp,
Ψ2p, q=θp, qq,
Ψa1x, y=1a2 Ψ1pa, qa,
Ψa2x, y=1a2 Ψ2pa, qa.
Wa1Fp, q=Fp, qΨa1p, q,Wa2Fp, q=Fp, qΨa2p, q.
Wa1Fp, qWa2Fp, q=axFθax, yyFθax, y=aFθsp, q.
Ψap, q=12π2-p2+q2exp- p2+q22.
Wgx, y=-+ Gu, vH*au, av×expi2πux+vydudv,Wfx, y=-+ Fu, vH*au, av×expi2πux+vydudv,

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