Abstract

The Hadamard transform is an example of a matrix transform that allows images to be represented in terms of orthogonal basis functions with binary-valued matrix elements. Such basis functions can be displayed on binary amplitude modulating ferroelectric-liquid-crystal-over-silicon spatial light modulators, permitting novel, real-time, and high-speed implementation of the transform on incoherently illuminated input scenes. An example of an optical Hadamard transform performed in real time by using a spatial light modulator is described. To show the validity of this optical decomposition, we electronically reconstruct the transformation data for comparison with the original input scene.

© 1993 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. T. S. Huang, ed., Picture Processing and Digital Filtering (Springer-Verlag, Berlin, 1979), Chap. 2, pp. 21–67.
  2. J. Gourlay, P. McOwan, D. G. Vass, I. Underwood, M. Worboys, in Spatial Light Modulators and Applications, Vol. 6 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 100–103.
  3. M. Harwit, N. J. Sloane, Hadamard Transform Optics (Academic, New York, 1979), Chap. 2, pp. 20–61.
  4. I. Underwood, D. G. Vass, R. M. Sillitto, Proc. Inst. Electr. Eng. Part J 133, 77 (1986).
  5. K. M. Johnson, D. J. McKnight, I. Underwood, IEEE J. Quantum Electron. 29, 699 (1993).
    [Crossref]
  6. N. Collings, W. A. Crossland, P. J. Ayliff, D. G. Vass, I. Underwood, Appl. Opt. 28, 4740 (1989).
    [Crossref] [PubMed]
  7. J. Gourlay, P. McOwan, D. G. Vass, I. Underwood, M. Worboys, in Proceedings of the Conference on Applied Optics and Opto-electronics (Institute of Physics, Bristol, UK, 1992), pp. 211–213.

1993 (1)

K. M. Johnson, D. J. McKnight, I. Underwood, IEEE J. Quantum Electron. 29, 699 (1993).
[Crossref]

1989 (1)

1986 (1)

I. Underwood, D. G. Vass, R. M. Sillitto, Proc. Inst. Electr. Eng. Part J 133, 77 (1986).

Ayliff, P. J.

Collings, N.

Crossland, W. A.

Gourlay, J.

J. Gourlay, P. McOwan, D. G. Vass, I. Underwood, M. Worboys, in Proceedings of the Conference on Applied Optics and Opto-electronics (Institute of Physics, Bristol, UK, 1992), pp. 211–213.

J. Gourlay, P. McOwan, D. G. Vass, I. Underwood, M. Worboys, in Spatial Light Modulators and Applications, Vol. 6 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 100–103.

Harwit, M.

M. Harwit, N. J. Sloane, Hadamard Transform Optics (Academic, New York, 1979), Chap. 2, pp. 20–61.

Johnson, K. M.

K. M. Johnson, D. J. McKnight, I. Underwood, IEEE J. Quantum Electron. 29, 699 (1993).
[Crossref]

McKnight, D. J.

K. M. Johnson, D. J. McKnight, I. Underwood, IEEE J. Quantum Electron. 29, 699 (1993).
[Crossref]

McOwan, P.

J. Gourlay, P. McOwan, D. G. Vass, I. Underwood, M. Worboys, in Proceedings of the Conference on Applied Optics and Opto-electronics (Institute of Physics, Bristol, UK, 1992), pp. 211–213.

J. Gourlay, P. McOwan, D. G. Vass, I. Underwood, M. Worboys, in Spatial Light Modulators and Applications, Vol. 6 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 100–103.

Sillitto, R. M.

I. Underwood, D. G. Vass, R. M. Sillitto, Proc. Inst. Electr. Eng. Part J 133, 77 (1986).

Sloane, N. J.

M. Harwit, N. J. Sloane, Hadamard Transform Optics (Academic, New York, 1979), Chap. 2, pp. 20–61.

Underwood, I.

K. M. Johnson, D. J. McKnight, I. Underwood, IEEE J. Quantum Electron. 29, 699 (1993).
[Crossref]

N. Collings, W. A. Crossland, P. J. Ayliff, D. G. Vass, I. Underwood, Appl. Opt. 28, 4740 (1989).
[Crossref] [PubMed]

I. Underwood, D. G. Vass, R. M. Sillitto, Proc. Inst. Electr. Eng. Part J 133, 77 (1986).

J. Gourlay, P. McOwan, D. G. Vass, I. Underwood, M. Worboys, in Spatial Light Modulators and Applications, Vol. 6 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 100–103.

J. Gourlay, P. McOwan, D. G. Vass, I. Underwood, M. Worboys, in Proceedings of the Conference on Applied Optics and Opto-electronics (Institute of Physics, Bristol, UK, 1992), pp. 211–213.

Vass, D. G.

N. Collings, W. A. Crossland, P. J. Ayliff, D. G. Vass, I. Underwood, Appl. Opt. 28, 4740 (1989).
[Crossref] [PubMed]

I. Underwood, D. G. Vass, R. M. Sillitto, Proc. Inst. Electr. Eng. Part J 133, 77 (1986).

J. Gourlay, P. McOwan, D. G. Vass, I. Underwood, M. Worboys, in Spatial Light Modulators and Applications, Vol. 6 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 100–103.

J. Gourlay, P. McOwan, D. G. Vass, I. Underwood, M. Worboys, in Proceedings of the Conference on Applied Optics and Opto-electronics (Institute of Physics, Bristol, UK, 1992), pp. 211–213.

Worboys, M.

J. Gourlay, P. McOwan, D. G. Vass, I. Underwood, M. Worboys, in Proceedings of the Conference on Applied Optics and Opto-electronics (Institute of Physics, Bristol, UK, 1992), pp. 211–213.

J. Gourlay, P. McOwan, D. G. Vass, I. Underwood, M. Worboys, in Spatial Light Modulators and Applications, Vol. 6 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 100–103.

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

K. M. Johnson, D. J. McKnight, I. Underwood, IEEE J. Quantum Electron. 29, 699 (1993).
[Crossref]

Proc. Inst. Electr. Eng. Part J (1)

I. Underwood, D. G. Vass, R. M. Sillitto, Proc. Inst. Electr. Eng. Part J 133, 77 (1986).

Other (4)

T. S. Huang, ed., Picture Processing and Digital Filtering (Springer-Verlag, Berlin, 1979), Chap. 2, pp. 21–67.

J. Gourlay, P. McOwan, D. G. Vass, I. Underwood, M. Worboys, in Spatial Light Modulators and Applications, Vol. 6 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 100–103.

M. Harwit, N. J. Sloane, Hadamard Transform Optics (Academic, New York, 1979), Chap. 2, pp. 20–61.

J. Gourlay, P. McOwan, D. G. Vass, I. Underwood, M. Worboys, in Proceedings of the Conference on Applied Optics and Opto-electronics (Institute of Physics, Bristol, UK, 1992), pp. 211–213.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

Hadamard transform basis functions for individual display on the SLM.

Fig. 2
Fig. 2

Typical Hadamard transform basis function displayed on a FLCOS SLM.

Fig. 3
Fig. 3

Optical system used in the Hadamard transform experiments. PC, personal computer.

Fig. 4
Fig. 4

(a) 8 × 8 input test pattern, (b) the 8 × 8 test pattern on reflection from the SLM device.

Fig. 5
Fig. 5

Optically measured Hadamard transform coefficients (aij) of the test pattern.

Fig. 6
Fig. 6

Electronic reconstruction of the input pattern from the optical Hadamard transform coefficients.

Metrics