Abstract

A general design algorithm is presented for the multioutput polarization-encoded optical shadow-casting scheme. A set of POSC equations is obtained from the truth table of the desired logic unit and is solved in terms of four possible pixel characteristics (transparent, opaque, vertically polarized, and horizontally polarized) and four possible source characteristics (off, unpolarized, vertically polarized, and horizontally polarized). To demonstrate its feasibility, the algorithm is used to determine the input pixel characteristics of a full adder and a full subtracter.

© 1987 Optical Society of America

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References

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  1. R. Normandin, “All-optical, Fiber-Optic Modulator and Logic Gate Using Nonlinear Refraction and Absorption,” Opt. Lett. 11, 751 (1986).
    [CrossRef] [PubMed]
  2. H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, “Differential Gain and Bistability Using a Sodium Filled Fabry-Perot Interferometer,” Phys. Rev. Lett. 37, 1135 (1976).
    [CrossRef]
  3. G. R. Olbright, N. Peyghambarian, H. M. Gibbs, H. A. Macleod, F. V. Milligen, “Microsecond Room Temperature Optical Bistability and Crosstalk Studies in ZnS and ZnSe Interference Filters with Visible Light and Milliwatt Powers,” Appl. Phys. Lett. 45, 1031 (1984).
    [CrossRef]
  4. J. Tanida, Y. Ichioka, “Optical Logic Array Processor Using Shadowgrams,” J. Opt. Soc. Am. 73, 800 (1983).
    [CrossRef]
  5. Y. Ichioka, J. Tanida, “Optical Parallel Logic Gates Using a Shadow-Casting System for Optical Digital Computing,” Proc. IEEE. 72, 787 (1984).
    [CrossRef]
  6. J. Tanida, Y. Ichioka, “Optical-Logic-Array Processor Using Shadowgrams. II. Optical Parallel Digital Image Processing,” J. Opt. Soc. Am. A. 2, 1237 (1985).
    [CrossRef]
  7. J. Tanida, Y. Ichioka, “Optical-Logic-Array Processor Using Shadowgrams. III. Parallel Neighborhood Operations and An Architecture of An Optical Digital-Computing System,” J. Opt. Soc. Am. A 2, 1245 (1985).
    [CrossRef]
  8. T. Yatagai, “Optical Space-Variant Logic Gate Array Based on Spatial Encoding Technique,” Opt. Lett. 11, 260 (1986).
    [CrossRef] [PubMed]
  9. J. Tanida, Y. Ichioka, “OPALS: Optical Parallel Array Logic System,” Appl. Opt. 25, 1565 (1986).
    [CrossRef] [PubMed]
  10. Y. Li, G. Eichmann, R. R. Alfano, “Optical Computing Using Hybrid Encoding Shadow Casting,” Appl. Opt. 25, 2636 (1986).
    [CrossRef] [PubMed]
  11. J.D. Gaskill, “Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978).
  12. E. L. Johnson, M. A. Karim, Digital Design: A Pragmatic Approach (PWS, Boston, 1987).
  13. R. Arrathoon, S. Kozaitis, “Shadow Casting for Multiple-valued Associative Logic,” Optic. Eng. 25, 29 (1986).
    [CrossRef]
  14. W. E. Ross, D. Psaltis, R. H. Anderson, “Two-Dimensional Magneto-Optic Spatial Light Modulator for Signal Processing,” Proc. Soc. Photo-Opt. Instrum. Eng. 341, 191 (1982).

1986 (5)

1985 (2)

J. Tanida, Y. Ichioka, “Optical-Logic-Array Processor Using Shadowgrams. III. Parallel Neighborhood Operations and An Architecture of An Optical Digital-Computing System,” J. Opt. Soc. Am. A 2, 1245 (1985).
[CrossRef]

J. Tanida, Y. Ichioka, “Optical-Logic-Array Processor Using Shadowgrams. II. Optical Parallel Digital Image Processing,” J. Opt. Soc. Am. A. 2, 1237 (1985).
[CrossRef]

1984 (2)

Y. Ichioka, J. Tanida, “Optical Parallel Logic Gates Using a Shadow-Casting System for Optical Digital Computing,” Proc. IEEE. 72, 787 (1984).
[CrossRef]

G. R. Olbright, N. Peyghambarian, H. M. Gibbs, H. A. Macleod, F. V. Milligen, “Microsecond Room Temperature Optical Bistability and Crosstalk Studies in ZnS and ZnSe Interference Filters with Visible Light and Milliwatt Powers,” Appl. Phys. Lett. 45, 1031 (1984).
[CrossRef]

1983 (1)

1982 (1)

W. E. Ross, D. Psaltis, R. H. Anderson, “Two-Dimensional Magneto-Optic Spatial Light Modulator for Signal Processing,” Proc. Soc. Photo-Opt. Instrum. Eng. 341, 191 (1982).

1976 (1)

H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, “Differential Gain and Bistability Using a Sodium Filled Fabry-Perot Interferometer,” Phys. Rev. Lett. 37, 1135 (1976).
[CrossRef]

Alfano, R. R.

Anderson, R. H.

W. E. Ross, D. Psaltis, R. H. Anderson, “Two-Dimensional Magneto-Optic Spatial Light Modulator for Signal Processing,” Proc. Soc. Photo-Opt. Instrum. Eng. 341, 191 (1982).

Arrathoon, R.

R. Arrathoon, S. Kozaitis, “Shadow Casting for Multiple-valued Associative Logic,” Optic. Eng. 25, 29 (1986).
[CrossRef]

Eichmann, G.

Gaskill, J.D.

J.D. Gaskill, “Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978).

Gibbs, H. M.

G. R. Olbright, N. Peyghambarian, H. M. Gibbs, H. A. Macleod, F. V. Milligen, “Microsecond Room Temperature Optical Bistability and Crosstalk Studies in ZnS and ZnSe Interference Filters with Visible Light and Milliwatt Powers,” Appl. Phys. Lett. 45, 1031 (1984).
[CrossRef]

H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, “Differential Gain and Bistability Using a Sodium Filled Fabry-Perot Interferometer,” Phys. Rev. Lett. 37, 1135 (1976).
[CrossRef]

Ichioka, Y.

Johnson, E. L.

E. L. Johnson, M. A. Karim, Digital Design: A Pragmatic Approach (PWS, Boston, 1987).

Karim, M. A.

E. L. Johnson, M. A. Karim, Digital Design: A Pragmatic Approach (PWS, Boston, 1987).

Kozaitis, S.

R. Arrathoon, S. Kozaitis, “Shadow Casting for Multiple-valued Associative Logic,” Optic. Eng. 25, 29 (1986).
[CrossRef]

Li, Y.

Macleod, H. A.

G. R. Olbright, N. Peyghambarian, H. M. Gibbs, H. A. Macleod, F. V. Milligen, “Microsecond Room Temperature Optical Bistability and Crosstalk Studies in ZnS and ZnSe Interference Filters with Visible Light and Milliwatt Powers,” Appl. Phys. Lett. 45, 1031 (1984).
[CrossRef]

McCall, S. L.

H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, “Differential Gain and Bistability Using a Sodium Filled Fabry-Perot Interferometer,” Phys. Rev. Lett. 37, 1135 (1976).
[CrossRef]

Milligen, F. V.

G. R. Olbright, N. Peyghambarian, H. M. Gibbs, H. A. Macleod, F. V. Milligen, “Microsecond Room Temperature Optical Bistability and Crosstalk Studies in ZnS and ZnSe Interference Filters with Visible Light and Milliwatt Powers,” Appl. Phys. Lett. 45, 1031 (1984).
[CrossRef]

Normandin, R.

Olbright, G. R.

G. R. Olbright, N. Peyghambarian, H. M. Gibbs, H. A. Macleod, F. V. Milligen, “Microsecond Room Temperature Optical Bistability and Crosstalk Studies in ZnS and ZnSe Interference Filters with Visible Light and Milliwatt Powers,” Appl. Phys. Lett. 45, 1031 (1984).
[CrossRef]

Peyghambarian, N.

G. R. Olbright, N. Peyghambarian, H. M. Gibbs, H. A. Macleod, F. V. Milligen, “Microsecond Room Temperature Optical Bistability and Crosstalk Studies in ZnS and ZnSe Interference Filters with Visible Light and Milliwatt Powers,” Appl. Phys. Lett. 45, 1031 (1984).
[CrossRef]

Psaltis, D.

W. E. Ross, D. Psaltis, R. H. Anderson, “Two-Dimensional Magneto-Optic Spatial Light Modulator for Signal Processing,” Proc. Soc. Photo-Opt. Instrum. Eng. 341, 191 (1982).

Ross, W. E.

W. E. Ross, D. Psaltis, R. H. Anderson, “Two-Dimensional Magneto-Optic Spatial Light Modulator for Signal Processing,” Proc. Soc. Photo-Opt. Instrum. Eng. 341, 191 (1982).

Tanida, J.

Venkatesan, T. N. C.

H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, “Differential Gain and Bistability Using a Sodium Filled Fabry-Perot Interferometer,” Phys. Rev. Lett. 37, 1135 (1976).
[CrossRef]

Yatagai, T.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

G. R. Olbright, N. Peyghambarian, H. M. Gibbs, H. A. Macleod, F. V. Milligen, “Microsecond Room Temperature Optical Bistability and Crosstalk Studies in ZnS and ZnSe Interference Filters with Visible Light and Milliwatt Powers,” Appl. Phys. Lett. 45, 1031 (1984).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. A. (1)

J. Tanida, Y. Ichioka, “Optical-Logic-Array Processor Using Shadowgrams. II. Optical Parallel Digital Image Processing,” J. Opt. Soc. Am. A. 2, 1237 (1985).
[CrossRef]

Opt. Lett. (2)

Optic. Eng. (1)

R. Arrathoon, S. Kozaitis, “Shadow Casting for Multiple-valued Associative Logic,” Optic. Eng. 25, 29 (1986).
[CrossRef]

Phys. Rev. Lett. (1)

H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, “Differential Gain and Bistability Using a Sodium Filled Fabry-Perot Interferometer,” Phys. Rev. Lett. 37, 1135 (1976).
[CrossRef]

Proc. IEEE (1)

Y. Ichioka, J. Tanida, “Optical Parallel Logic Gates Using a Shadow-Casting System for Optical Digital Computing,” Proc. IEEE. 72, 787 (1984).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

W. E. Ross, D. Psaltis, R. H. Anderson, “Two-Dimensional Magneto-Optic Spatial Light Modulator for Signal Processing,” Proc. Soc. Photo-Opt. Instrum. Eng. 341, 191 (1982).

Other (2)

J.D. Gaskill, “Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978).

E. L. Johnson, M. A. Karim, Digital Design: A Pragmatic Approach (PWS, Boston, 1987).

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Figures (1)

Fig. 1
Fig. 1

A polarization-encoded optical shadow-casting (POSC) system.

Tables (3)

Tables Icon

Table I A POSC example.

Tables Icon

Table II Full adder truth table.

Tables Icon

Table III Full subtracter design.

Equations (44)

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

f H = A B ¯ ,
f v = B ¯ ,
f V H = f H V = A + B ¯ ,
f T = A + B ¯ .
x T = x
x F = F
x x = x
H V = V H = F
A = [ a 11 a 12 a 21 a 22 ]
Set 1 : a ¯ 11 b ¯ 11 c ¯ 11 = F ,
a ¯ 12 b ¯ 12 c ¯ 12 = F ,
a ¯ 21 b ¯ 21 c ¯ 21 = F ,
a ¯ 22 b ¯ 22 c ¯ 22 = F .
Set 2 : a 11 b 11 c 11 = V ,
a 12 b 12 c 12 = d ,
a 21 b 21 c 21 = H ,
a 22 b 22 c 22 = d ,
a ¯ 12 b 12 c ¯ 12 = V ,
a ¯ 12 b 12 c 12 = H .
a 22 b ¯ 22 c ¯ 22 = V ,
a 22 b ¯ 22 c 22 = H .
a ¯ 12 b ¯ 12 c 12 = V ,
a 12 b 12 c ¯ 12 = H .
a ¯ 21 b ¯ 21 c 21 = V ,
a 11 b 11 c ¯ 11 = H .
A = [ T F H T ]             B = [ T T H F ]             C = [ V H T H ] ,
A = [ H H T V ]             B = [ H V T H ]             C = [ T H V H ]
a ¯ 12 b 12 c ¯ 12 = V ,
a 12 b ¯ 12 c 12 = H
a 22 b ¯ 22 c ¯ 22 = V ,
a ¯ 22 b 22 c 22 = H .
a 11 b 11 c 11 = H ,
a ¯ 11 b ¯ 11 c 11 = V ,
a 21 b 21 c 21 = V ,
a 21 b 21 c ¯ 21 = H .
a 11 b 11 c 11 = V ,
a ¯ 11 b 11 c ¯ 11 = H .
a 21 b 21 c 21 = H ,
a ¯ 21 b ¯ 21 c 21 = V
a ¯ 12 b ¯ 12 c 12 = H ,
a ¯ 12 b 12 c ¯ 12 = V
a ¯ 22 b 22 c 22 = H ,
a 22 b ¯ 22 c ¯ 22 = V ,
A = [ V F H V ]             B = [ T V H H ]             C = [ V H T H ] .

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