Abstract

Two possible forms of numerical truth-table look-up processors using content-addressable optical holographic memories are presented. Application of these processors to performing numerical calculations in direct binary and in binary-coded residue number systems is discussed. Specific examples of the number of input and output bits required and the number of truth-table combinations holographically recorded for computation in both numerical systems are given. Truth-table look-up processing using binary-coded residue is shown to require the recording of dramatically fewer reference patterns than direct binary.

© 1980 Optical Society of America

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References

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  1. A. L. Robinson, Science 203, 156 (1979).
    [CrossRef] [PubMed]
  2. J. W. Goodman, A. R. Dias, L. M. Woody, Opt. Lett. 2, 1 (1978).
    [CrossRef] [PubMed]
  3. P. N. Tamura, J. C. Wyant, Opt. Eng. 18, 198 (1979).
    [CrossRef]
  4. D. Psaltis, D. Casasent, Appl. Opt. 18, 163 (1979).
    [CrossRef] [PubMed]
  5. S. A. Collins, Proc. Soc. Photo-Opt. Instrum. Eng. 128, 313 (1977).
  6. A. Huang, in Proceedings, International Optical Computing Conference (IEEE, New York, 1975), p. 14.
  7. C. C. Guest, T. K. Gaylord, Proc. Soc. Photo-Opt. Instrum. Eng. 185, 42 (1979).
  8. T. Kohonen, Associative Memory (Springer, New York, 1977).
    [CrossRef]
  9. P. E. Tverdokhleb, in Optical Information Processing, E. S. Barrekette, G. W. Stroke, Y. E. Nesterikhin, W. E. Koch, Eds. (Plenum, New York, 1978), Vol. 2, p. 283.
  10. G. R. Knight, Appl. Opt. 14, 1088 (1975).
    [CrossRef] [PubMed]
  11. The exclusive or-based and nand-based systems are fully explained in Ref. 7. The nand-based processor is referred to as the nand OR or-based processor in that paper because (b1∩b2∩b3∩...)¯∪(c1∪c2∪c3∪...)=(b1∩b2∩b3∩...c̅1∩c̅2∩c̅3∩...)¯, i.e., a nand OR or combination of operations is equivalent to a single nand operation with inputs to the OR complemented. Thus the nand OR or-based processor may be referred to simply as a nand-based processor.
  12. D. W. Vahey, C. M. Verber, R. P. Kenan, Proc. Soc. Photo-Opt. Instrum. Eng. 139, 151 (1978).
  13. K. Preston, Coherent Optical Computers (McGraw-Hill, New York, 1972), Chap. 8.
  14. F. A. Horrigan, W. W. Stoner, Proc. Soc. Photo-Opt. Instrum. Eng. 185, 19 (1979).
  15. A. Tai, I. Cindrich, J. R. Fienup, C. C. Aleksoff, Appl. Opt. 18, 2812 (1979).
    [CrossRef] [PubMed]
  16. A. Huang, Y. Tsunoda, J. W. Goodman, S. Ishihara, Appl. Opt. 18, 149 (1979).
    [CrossRef] [PubMed]
  17. H. L. Garner, IRE Trans. Electron. Comput. 8, 140 (1959).
    [CrossRef]
  18. N. S. Szabo, R. I. Tanaka, Residue Arithmetic and Its Applications to Computer Technology (McGraw Hill, New York, 1967).
  19. D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, Phys. Lett. 18, 116 (1965).
    [CrossRef]
  20. J. P. Huignard, J. P. Herriau, F. Micheron, Appl. Phys. Lett. 26, 256 (1975).
    [CrossRef]

1979 (7)

A. L. Robinson, Science 203, 156 (1979).
[CrossRef] [PubMed]

P. N. Tamura, J. C. Wyant, Opt. Eng. 18, 198 (1979).
[CrossRef]

D. Psaltis, D. Casasent, Appl. Opt. 18, 163 (1979).
[CrossRef] [PubMed]

F. A. Horrigan, W. W. Stoner, Proc. Soc. Photo-Opt. Instrum. Eng. 185, 19 (1979).

A. Tai, I. Cindrich, J. R. Fienup, C. C. Aleksoff, Appl. Opt. 18, 2812 (1979).
[CrossRef] [PubMed]

A. Huang, Y. Tsunoda, J. W. Goodman, S. Ishihara, Appl. Opt. 18, 149 (1979).
[CrossRef] [PubMed]

C. C. Guest, T. K. Gaylord, Proc. Soc. Photo-Opt. Instrum. Eng. 185, 42 (1979).

1978 (2)

D. W. Vahey, C. M. Verber, R. P. Kenan, Proc. Soc. Photo-Opt. Instrum. Eng. 139, 151 (1978).

J. W. Goodman, A. R. Dias, L. M. Woody, Opt. Lett. 2, 1 (1978).
[CrossRef] [PubMed]

1977 (1)

S. A. Collins, Proc. Soc. Photo-Opt. Instrum. Eng. 128, 313 (1977).

1975 (2)

G. R. Knight, Appl. Opt. 14, 1088 (1975).
[CrossRef] [PubMed]

J. P. Huignard, J. P. Herriau, F. Micheron, Appl. Phys. Lett. 26, 256 (1975).
[CrossRef]

1965 (1)

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, Phys. Lett. 18, 116 (1965).
[CrossRef]

1959 (1)

H. L. Garner, IRE Trans. Electron. Comput. 8, 140 (1959).
[CrossRef]

Aleksoff, C. C.

Brumm, D.

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, Phys. Lett. 18, 116 (1965).
[CrossRef]

Casasent, D.

Cindrich, I.

Collins, S. A.

S. A. Collins, Proc. Soc. Photo-Opt. Instrum. Eng. 128, 313 (1977).

Dias, A. R.

Fienup, J. R.

Funkhouser, A.

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, Phys. Lett. 18, 116 (1965).
[CrossRef]

Gabor, D.

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, Phys. Lett. 18, 116 (1965).
[CrossRef]

Garner, H. L.

H. L. Garner, IRE Trans. Electron. Comput. 8, 140 (1959).
[CrossRef]

Gaylord, T. K.

C. C. Guest, T. K. Gaylord, Proc. Soc. Photo-Opt. Instrum. Eng. 185, 42 (1979).

Goodman, J. W.

Guest, C. C.

C. C. Guest, T. K. Gaylord, Proc. Soc. Photo-Opt. Instrum. Eng. 185, 42 (1979).

Herriau, J. P.

J. P. Huignard, J. P. Herriau, F. Micheron, Appl. Phys. Lett. 26, 256 (1975).
[CrossRef]

Horrigan, F. A.

F. A. Horrigan, W. W. Stoner, Proc. Soc. Photo-Opt. Instrum. Eng. 185, 19 (1979).

Huang, A.

A. Huang, Y. Tsunoda, J. W. Goodman, S. Ishihara, Appl. Opt. 18, 149 (1979).
[CrossRef] [PubMed]

A. Huang, in Proceedings, International Optical Computing Conference (IEEE, New York, 1975), p. 14.

Huignard, J. P.

J. P. Huignard, J. P. Herriau, F. Micheron, Appl. Phys. Lett. 26, 256 (1975).
[CrossRef]

Ishihara, S.

Kenan, R. P.

D. W. Vahey, C. M. Verber, R. P. Kenan, Proc. Soc. Photo-Opt. Instrum. Eng. 139, 151 (1978).

Knight, G. R.

Kohonen, T.

T. Kohonen, Associative Memory (Springer, New York, 1977).
[CrossRef]

Micheron, F.

J. P. Huignard, J. P. Herriau, F. Micheron, Appl. Phys. Lett. 26, 256 (1975).
[CrossRef]

Preston, K.

K. Preston, Coherent Optical Computers (McGraw-Hill, New York, 1972), Chap. 8.

Psaltis, D.

Restrick, R.

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, Phys. Lett. 18, 116 (1965).
[CrossRef]

Robinson, A. L.

A. L. Robinson, Science 203, 156 (1979).
[CrossRef] [PubMed]

Stoner, W. W.

F. A. Horrigan, W. W. Stoner, Proc. Soc. Photo-Opt. Instrum. Eng. 185, 19 (1979).

Stroke, G. W.

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, Phys. Lett. 18, 116 (1965).
[CrossRef]

Szabo, N. S.

N. S. Szabo, R. I. Tanaka, Residue Arithmetic and Its Applications to Computer Technology (McGraw Hill, New York, 1967).

Tai, A.

Tamura, P. N.

P. N. Tamura, J. C. Wyant, Opt. Eng. 18, 198 (1979).
[CrossRef]

Tanaka, R. I.

N. S. Szabo, R. I. Tanaka, Residue Arithmetic and Its Applications to Computer Technology (McGraw Hill, New York, 1967).

Tsunoda, Y.

Tverdokhleb, P. E.

P. E. Tverdokhleb, in Optical Information Processing, E. S. Barrekette, G. W. Stroke, Y. E. Nesterikhin, W. E. Koch, Eds. (Plenum, New York, 1978), Vol. 2, p. 283.

Vahey, D. W.

D. W. Vahey, C. M. Verber, R. P. Kenan, Proc. Soc. Photo-Opt. Instrum. Eng. 139, 151 (1978).

Verber, C. M.

D. W. Vahey, C. M. Verber, R. P. Kenan, Proc. Soc. Photo-Opt. Instrum. Eng. 139, 151 (1978).

Woody, L. M.

Wyant, J. C.

P. N. Tamura, J. C. Wyant, Opt. Eng. 18, 198 (1979).
[CrossRef]

Appl. Opt. (4)

Appl. Phys. Lett. (1)

J. P. Huignard, J. P. Herriau, F. Micheron, Appl. Phys. Lett. 26, 256 (1975).
[CrossRef]

IRE Trans. Electron. Comput. (1)

H. L. Garner, IRE Trans. Electron. Comput. 8, 140 (1959).
[CrossRef]

Opt. Eng. (1)

P. N. Tamura, J. C. Wyant, Opt. Eng. 18, 198 (1979).
[CrossRef]

Opt. Lett. (1)

Phys. Lett. (1)

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, Phys. Lett. 18, 116 (1965).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (4)

S. A. Collins, Proc. Soc. Photo-Opt. Instrum. Eng. 128, 313 (1977).

C. C. Guest, T. K. Gaylord, Proc. Soc. Photo-Opt. Instrum. Eng. 185, 42 (1979).

F. A. Horrigan, W. W. Stoner, Proc. Soc. Photo-Opt. Instrum. Eng. 185, 19 (1979).

D. W. Vahey, C. M. Verber, R. P. Kenan, Proc. Soc. Photo-Opt. Instrum. Eng. 139, 151 (1978).

Science (1)

A. L. Robinson, Science 203, 156 (1979).
[CrossRef] [PubMed]

Other (6)

A. Huang, in Proceedings, International Optical Computing Conference (IEEE, New York, 1975), p. 14.

T. Kohonen, Associative Memory (Springer, New York, 1977).
[CrossRef]

P. E. Tverdokhleb, in Optical Information Processing, E. S. Barrekette, G. W. Stroke, Y. E. Nesterikhin, W. E. Koch, Eds. (Plenum, New York, 1978), Vol. 2, p. 283.

The exclusive or-based and nand-based systems are fully explained in Ref. 7. The nand-based processor is referred to as the nand OR or-based processor in that paper because (b1∩b2∩b3∩...)¯∪(c1∪c2∪c3∪...)=(b1∩b2∩b3∩...c̅1∩c̅2∩c̅3∩...)¯, i.e., a nand OR or combination of operations is equivalent to a single nand operation with inputs to the OR complemented. Thus the nand OR or-based processor may be referred to simply as a nand-based processor.

K. Preston, Coherent Optical Computers (McGraw-Hill, New York, 1972), Chap. 8.

N. S. Szabo, R. I. Tanaka, Residue Arithmetic and Its Applications to Computer Technology (McGraw Hill, New York, 1967).

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Figures (6)

Fig. 1
Fig. 1

exclusive or-based numerical optical processor. (a) Recording the truth-table hologram. () Example of addition with the processor.

Fig. 2
Fig. 2

nand-based numerical optical processor. (a) Recording the truth-table holograms. (b) Example of multiplication with theprocessor.

Fig. 3
Fig. 3

(a) Example phasor diagram for hologram recording in multiphase nand-based numerical optical processing. (b) Phasor diagram showing possible resultant amplitudes at a particular detector. Numbers indicate degeneracy of phasor.

Fig. 4
Fig. 4

(a) Example phasor diagram for hologram recording in biphase nand-based numerical optical processing. (b) Phasor diagram showing possible resultant amplitudes at a particular detector. Numbers indicate degeneracy of phasor.

Fig. 5
Fig. 5

(a) Recording of truth-table holograms for version 1 of nand-based processor for m pairs of input words. (b) Example of multiplication with the processor. Fourier transform lenses have been omitted from the figure for simplicity.

Fig. 6
Fig. 6

(a) Recording of truth-table holograms for version 2 of nand-based processor for m pairs of input words. (b) Example of multiplication with the processor. Fourier transform lenses have been omitted from the figure for simplicity.

Tables (3)

Tables Icon

Table I Summary of Sizes of Components, Sizes of Arrays, and Number of Recordings in exclusive or-Based and nand-Based Numerical Optical Processors Using Direct Binary Arithmetic

Tables Icon

Table II Total Number of Reference Data Patterns To Be Recorded for Multiplication of Two n-Bit Numbers

Tables Icon

Table III Summary of Sizes of Arrays and Number of Recordings for Residue and Direct Binary Numerical Optical Processors

Equations (10)

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1 2 n A k
2 n 1 2 n A k
1 2 n A k
1 2 n A k × m
1 2 n A k
2 n 1 2 n A k
1 2 n A k
1 2 n A k × m
1 2 n A k × m
1 2 n A k

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