Abstract

A new architecture of an optical wavelet transform system with a lenslet array is proposed, and its optical performance and optical limits are analyzed.

© 1994 Optical Society of America

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References

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  1. H. Szu, Y. Sheng, J. Chen, “Wavelet transform as a bank of the matched filters,” Appl. Opt. 31, 3267–3277 (1992).
    [CrossRef] [PubMed]
  2. Y. Sheng, T. Lu, D. Roberge, H. J. Caulfield, “Optical N4 implementation of a 2-D wavelet transform,” Opt. Eng. 31, 1859–1864 (1992).
    [CrossRef]
  3. Y. Zhang, Y. Li, “Optical realization of wavelet transform for 1-D signal,” Opt. Lett. 17, 210–212 (1992).
    [CrossRef] [PubMed]
  4. E. Freszy, B. Pouligny, S. Argoul, A. Arneodo, “Optical wavelet transform of fractal aggregates,” Phys. Rev. Lett. 64, 745–748(1990).
    [CrossRef]
  5. T. J. Burns, K. H. Fielding, S. K. Rogers, S. D. Pinski, D. W. Ruck, “Optical Haar wavelet transform,” Opt. Eng. 31, 1852–1857(1992).
    [CrossRef]
  6. X. Yang, H. Szu, Y. Sheng, H. J. Caufield, “Optical Haar wavelet transform of binary images,” Opt. Eng 31, 1846–1851 (1992).
    [CrossRef]
  7. D.-X. Wang, J.-W. Tai, Y.-X. Zhang, Y. Ma, “Programmable 2-D optical wavelet transform,” presented at the International Conference on Optical Computing, Edinburgh, UK, August 1994.
  8. D.-X. Wang, “Research on neural network theory and optical implementation of tensor interconnections for 2-D programmable neural network,” M.S. thesis (Institute of Modern Optics, Nankai University, Tianjin, China, 1991).
    [PubMed]
  9. Y.-X. Zhang, D.-X. Wang, G.-G. Mu, “The optical implementation of tensor interconnection for 2-D programmable neural networks,” in Annals of Optoelectronics in High Technology (Qinghua U. Press, Beijing, China, 1991), pp. 632–636.
  10. T. Sakano, K. Noguchi, T. Matsumoto, “Optical limits for spatial interconnection networks using 2-D optical devices,” Appl. Opt. 29, 1094–1100 (1990).
    [CrossRef] [PubMed]

1992 (5)

T. J. Burns, K. H. Fielding, S. K. Rogers, S. D. Pinski, D. W. Ruck, “Optical Haar wavelet transform,” Opt. Eng. 31, 1852–1857(1992).
[CrossRef]

X. Yang, H. Szu, Y. Sheng, H. J. Caufield, “Optical Haar wavelet transform of binary images,” Opt. Eng 31, 1846–1851 (1992).
[CrossRef]

Y. Sheng, T. Lu, D. Roberge, H. J. Caulfield, “Optical N4 implementation of a 2-D wavelet transform,” Opt. Eng. 31, 1859–1864 (1992).
[CrossRef]

Y. Zhang, Y. Li, “Optical realization of wavelet transform for 1-D signal,” Opt. Lett. 17, 210–212 (1992).
[CrossRef] [PubMed]

H. Szu, Y. Sheng, J. Chen, “Wavelet transform as a bank of the matched filters,” Appl. Opt. 31, 3267–3277 (1992).
[CrossRef] [PubMed]

1990 (2)

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

T. Sakano, K. Noguchi, T. Matsumoto, “Optical limits for spatial interconnection networks using 2-D optical devices,” Appl. Opt. 29, 1094–1100 (1990).
[CrossRef] [PubMed]

Argoul, S.

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

Arneodo, A.

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

Burns, T. J.

T. J. Burns, K. H. Fielding, S. K. Rogers, S. D. Pinski, D. W. Ruck, “Optical Haar wavelet transform,” Opt. Eng. 31, 1852–1857(1992).
[CrossRef]

Caufield, H. J.

X. Yang, H. Szu, Y. Sheng, H. J. Caufield, “Optical Haar wavelet transform of binary images,” Opt. Eng 31, 1846–1851 (1992).
[CrossRef]

Caulfield, H. J.

Y. Sheng, T. Lu, D. Roberge, H. J. Caulfield, “Optical N4 implementation of a 2-D wavelet transform,” Opt. Eng. 31, 1859–1864 (1992).
[CrossRef]

Chen, J.

Fielding, K. H.

T. J. Burns, K. H. Fielding, S. K. Rogers, S. D. Pinski, D. W. Ruck, “Optical Haar wavelet transform,” Opt. Eng. 31, 1852–1857(1992).
[CrossRef]

Freszy, E.

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

Li, Y.

Lu, T.

Y. Sheng, T. Lu, D. Roberge, H. J. Caulfield, “Optical N4 implementation of a 2-D wavelet transform,” Opt. Eng. 31, 1859–1864 (1992).
[CrossRef]

Ma, Y.

D.-X. Wang, J.-W. Tai, Y.-X. Zhang, Y. Ma, “Programmable 2-D optical wavelet transform,” presented at the International Conference on Optical Computing, Edinburgh, UK, August 1994.

Matsumoto, T.

Mu, G.-G.

Y.-X. Zhang, D.-X. Wang, G.-G. Mu, “The optical implementation of tensor interconnection for 2-D programmable neural networks,” in Annals of Optoelectronics in High Technology (Qinghua U. Press, Beijing, China, 1991), pp. 632–636.

Noguchi, K.

Pinski, S. D.

T. J. Burns, K. H. Fielding, S. K. Rogers, S. D. Pinski, D. W. Ruck, “Optical Haar wavelet transform,” Opt. Eng. 31, 1852–1857(1992).
[CrossRef]

Pouligny, B.

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

Roberge, D.

Y. Sheng, T. Lu, D. Roberge, H. J. Caulfield, “Optical N4 implementation of a 2-D wavelet transform,” Opt. Eng. 31, 1859–1864 (1992).
[CrossRef]

Rogers, S. K.

T. J. Burns, K. H. Fielding, S. K. Rogers, S. D. Pinski, D. W. Ruck, “Optical Haar wavelet transform,” Opt. Eng. 31, 1852–1857(1992).
[CrossRef]

Ruck, D. W.

T. J. Burns, K. H. Fielding, S. K. Rogers, S. D. Pinski, D. W. Ruck, “Optical Haar wavelet transform,” Opt. Eng. 31, 1852–1857(1992).
[CrossRef]

Sakano, T.

Sheng, Y.

H. Szu, Y. Sheng, J. Chen, “Wavelet transform as a bank of the matched filters,” Appl. Opt. 31, 3267–3277 (1992).
[CrossRef] [PubMed]

X. Yang, H. Szu, Y. Sheng, H. J. Caufield, “Optical Haar wavelet transform of binary images,” Opt. Eng 31, 1846–1851 (1992).
[CrossRef]

Y. Sheng, T. Lu, D. Roberge, H. J. Caulfield, “Optical N4 implementation of a 2-D wavelet transform,” Opt. Eng. 31, 1859–1864 (1992).
[CrossRef]

Szu, H.

X. Yang, H. Szu, Y. Sheng, H. J. Caufield, “Optical Haar wavelet transform of binary images,” Opt. Eng 31, 1846–1851 (1992).
[CrossRef]

H. Szu, Y. Sheng, J. Chen, “Wavelet transform as a bank of the matched filters,” Appl. Opt. 31, 3267–3277 (1992).
[CrossRef] [PubMed]

Tai, J.-W.

D.-X. Wang, J.-W. Tai, Y.-X. Zhang, Y. Ma, “Programmable 2-D optical wavelet transform,” presented at the International Conference on Optical Computing, Edinburgh, UK, August 1994.

Wang, D.-X.

D.-X. Wang, “Research on neural network theory and optical implementation of tensor interconnections for 2-D programmable neural network,” M.S. thesis (Institute of Modern Optics, Nankai University, Tianjin, China, 1991).
[PubMed]

D.-X. Wang, J.-W. Tai, Y.-X. Zhang, Y. Ma, “Programmable 2-D optical wavelet transform,” presented at the International Conference on Optical Computing, Edinburgh, UK, August 1994.

Y.-X. Zhang, D.-X. Wang, G.-G. Mu, “The optical implementation of tensor interconnection for 2-D programmable neural networks,” in Annals of Optoelectronics in High Technology (Qinghua U. Press, Beijing, China, 1991), pp. 632–636.

Yang, X.

X. Yang, H. Szu, Y. Sheng, H. J. Caufield, “Optical Haar wavelet transform of binary images,” Opt. Eng 31, 1846–1851 (1992).
[CrossRef]

Zhang, Y.

Zhang, Y.-X.

D.-X. Wang, J.-W. Tai, Y.-X. Zhang, Y. Ma, “Programmable 2-D optical wavelet transform,” presented at the International Conference on Optical Computing, Edinburgh, UK, August 1994.

Y.-X. Zhang, D.-X. Wang, G.-G. Mu, “The optical implementation of tensor interconnection for 2-D programmable neural networks,” in Annals of Optoelectronics in High Technology (Qinghua U. Press, Beijing, China, 1991), pp. 632–636.

Appl. Opt. (2)

Opt. Eng (1)

X. Yang, H. Szu, Y. Sheng, H. J. Caufield, “Optical Haar wavelet transform of binary images,” Opt. Eng 31, 1846–1851 (1992).
[CrossRef]

Opt. Eng. (2)

T. J. Burns, K. H. Fielding, S. K. Rogers, S. D. Pinski, D. W. Ruck, “Optical Haar wavelet transform,” Opt. Eng. 31, 1852–1857(1992).
[CrossRef]

Y. Sheng, T. Lu, D. Roberge, H. J. Caulfield, “Optical N4 implementation of a 2-D wavelet transform,” Opt. Eng. 31, 1859–1864 (1992).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. Lett. (1)

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

Other (3)

D.-X. Wang, J.-W. Tai, Y.-X. Zhang, Y. Ma, “Programmable 2-D optical wavelet transform,” presented at the International Conference on Optical Computing, Edinburgh, UK, August 1994.

D.-X. Wang, “Research on neural network theory and optical implementation of tensor interconnections for 2-D programmable neural network,” M.S. thesis (Institute of Modern Optics, Nankai University, Tianjin, China, 1991).
[PubMed]

Y.-X. Zhang, D.-X. Wang, G.-G. Mu, “The optical implementation of tensor interconnection for 2-D programmable neural networks,” in Annals of Optoelectronics in High Technology (Qinghua U. Press, Beijing, China, 1991), pp. 632–636.

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Figures (4)

Fig. 1
Fig. 1

Space arrangement of the wavelets.

Fig. 2
Fig. 2

Schematic diagram of the OWT.

Fig. 3
Fig. 3

Optical design of the OWT system.

Fig. 4
Fig. 4

Configuration of the OWT system.

Equations (15)

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

w i j k l = x y s ( x , y ) h [ ( x - x i ) a j , ( y - y k ) a l ] ,
h x y i k = h [ ( x - x i ) a j , ( y - y k ) a l ] ,
X WM = ( 1 + 1 α ) X lens ,
Y WM = ( 1 + 1 α ) Y lens ,
c i = α c w = α C W M N = ( 1 + α ) C a M ,
L = 2 2 C A N + α N α ,
N 2 + [ 2 α - α 2 I ( 1 + α ) 2 β 2 μ ] N + α 2 0 ,
β = C A D ,
I = 3 n + 1 4 n ,
N max = 1 + [ 1 - 4 I ( 1 + α ) 2 β 2 μ / α ] 1 / 2 2 I ( 1 + 1 α ) 2 β 2 - α .
β 2 α 4 I ( 1 + α ) 2 μ .
β 2 2.44 α μ ( 1 + α ) 2 N ef 3 ,
N ef = N max ( λ D ) 1 / 2 ,
N max 0.468 ( D λ μ 2 I ) 1 / 3 ,
N ef 0.468 ( μ 2 I ) - 1 / 3 .

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