Abstract

On the basis of a lensless shadow-casting technique, a new, simple method of optically implementing digital logic gates has been developed. These gates are capable of performing a complete set of logical operations on a large array of binary variables in parallel, i.e., the pattern logics. A light-emitting diode (LED) array is used as an incoherent light source in the lensless shadow-casting system. Sixteen possible functions of two binary variables are simply realizable with these gates in parallel by controlling the switching modes of the LED’s. Experimental results demonstrate the feasibility of various gate arrays, such as AND, OR, NOR, XOR, and NAND. As an example of application of the proposed method, we construct an optical logic array processor that can implement parallel operations of addition or subtraction for two binary variables without considering the carry mechanism. Use of the light-modulated LED array means that the proposed method can be applied to combinational circuits.

© 1983 Optical Society of America

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References

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  1. D. R. Maure, “Optical logic function generator,” U.S. Patent3,680,080 (July25, 1972).
  2. D. H. Schaefer and J. P. Strong, “Tse computers,” Proc. IEEE 65, 129–138 (1977).
    [Crossref]
  3. R. A. Athale and S. H. Lee, “Development of an optical parallel logic device and a half-adder circuit for digital optical processing,” Opt. Eng. 18, 513–517 (1979).
    [Crossref]
  4. B. H. Soffer, D. Boswell, A. M. Lackner, P. Chavel, A. A. Sawchuk, T. C. Strand, and A. R. Tanguay, “Optical computing with variable grating mode liquid crystal devices,” Proc. Soc. Photo-Opt. Instrum. Eng. 232, 128–136 (1980).
  5. S. H. Lee, “Nonlinear optical processing,” in Optical Information Processing Fundamentals, S. H. Lee, ed. (Springer-Verlag, Berlin, 1981), pp. 261–303.
    [Crossref]
  6. M. T. Feteri, K. C. Wasmundt, and S. A. Collins, “Optical logic gates using liquid crystal light valve: implementation and application example,” Appl. Opt. 20, 2250–2256 (1981).
    [Crossref]
  7. A. W. Lohmann, Optical Information Processing (Lohmann, Erlangen, Federal Republic of Germany, 1979).

1981 (1)

1980 (1)

B. H. Soffer, D. Boswell, A. M. Lackner, P. Chavel, A. A. Sawchuk, T. C. Strand, and A. R. Tanguay, “Optical computing with variable grating mode liquid crystal devices,” Proc. Soc. Photo-Opt. Instrum. Eng. 232, 128–136 (1980).

1979 (1)

R. A. Athale and S. H. Lee, “Development of an optical parallel logic device and a half-adder circuit for digital optical processing,” Opt. Eng. 18, 513–517 (1979).
[Crossref]

1977 (1)

D. H. Schaefer and J. P. Strong, “Tse computers,” Proc. IEEE 65, 129–138 (1977).
[Crossref]

Athale, R. A.

R. A. Athale and S. H. Lee, “Development of an optical parallel logic device and a half-adder circuit for digital optical processing,” Opt. Eng. 18, 513–517 (1979).
[Crossref]

Boswell, D.

B. H. Soffer, D. Boswell, A. M. Lackner, P. Chavel, A. A. Sawchuk, T. C. Strand, and A. R. Tanguay, “Optical computing with variable grating mode liquid crystal devices,” Proc. Soc. Photo-Opt. Instrum. Eng. 232, 128–136 (1980).

Chavel, P.

B. H. Soffer, D. Boswell, A. M. Lackner, P. Chavel, A. A. Sawchuk, T. C. Strand, and A. R. Tanguay, “Optical computing with variable grating mode liquid crystal devices,” Proc. Soc. Photo-Opt. Instrum. Eng. 232, 128–136 (1980).

Collins, S. A.

Feteri, M. T.

Lackner, A. M.

B. H. Soffer, D. Boswell, A. M. Lackner, P. Chavel, A. A. Sawchuk, T. C. Strand, and A. R. Tanguay, “Optical computing with variable grating mode liquid crystal devices,” Proc. Soc. Photo-Opt. Instrum. Eng. 232, 128–136 (1980).

Lee, S. H.

R. A. Athale and S. H. Lee, “Development of an optical parallel logic device and a half-adder circuit for digital optical processing,” Opt. Eng. 18, 513–517 (1979).
[Crossref]

S. H. Lee, “Nonlinear optical processing,” in Optical Information Processing Fundamentals, S. H. Lee, ed. (Springer-Verlag, Berlin, 1981), pp. 261–303.
[Crossref]

Lohmann, A. W.

A. W. Lohmann, Optical Information Processing (Lohmann, Erlangen, Federal Republic of Germany, 1979).

Maure, D. R.

D. R. Maure, “Optical logic function generator,” U.S. Patent3,680,080 (July25, 1972).

Sawchuk, A. A.

B. H. Soffer, D. Boswell, A. M. Lackner, P. Chavel, A. A. Sawchuk, T. C. Strand, and A. R. Tanguay, “Optical computing with variable grating mode liquid crystal devices,” Proc. Soc. Photo-Opt. Instrum. Eng. 232, 128–136 (1980).

Schaefer, D. H.

D. H. Schaefer and J. P. Strong, “Tse computers,” Proc. IEEE 65, 129–138 (1977).
[Crossref]

Soffer, B. H.

B. H. Soffer, D. Boswell, A. M. Lackner, P. Chavel, A. A. Sawchuk, T. C. Strand, and A. R. Tanguay, “Optical computing with variable grating mode liquid crystal devices,” Proc. Soc. Photo-Opt. Instrum. Eng. 232, 128–136 (1980).

Strand, T. C.

B. H. Soffer, D. Boswell, A. M. Lackner, P. Chavel, A. A. Sawchuk, T. C. Strand, and A. R. Tanguay, “Optical computing with variable grating mode liquid crystal devices,” Proc. Soc. Photo-Opt. Instrum. Eng. 232, 128–136 (1980).

Strong, J. P.

D. H. Schaefer and J. P. Strong, “Tse computers,” Proc. IEEE 65, 129–138 (1977).
[Crossref]

Tanguay, A. R.

B. H. Soffer, D. Boswell, A. M. Lackner, P. Chavel, A. A. Sawchuk, T. C. Strand, and A. R. Tanguay, “Optical computing with variable grating mode liquid crystal devices,” Proc. Soc. Photo-Opt. Instrum. Eng. 232, 128–136 (1980).

Wasmundt, K. C.

Appl. Opt. (1)

Opt. Eng. (1)

R. A. Athale and S. H. Lee, “Development of an optical parallel logic device and a half-adder circuit for digital optical processing,” Opt. Eng. 18, 513–517 (1979).
[Crossref]

Proc. IEEE (1)

D. H. Schaefer and J. P. Strong, “Tse computers,” Proc. IEEE 65, 129–138 (1977).
[Crossref]

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

B. H. Soffer, D. Boswell, A. M. Lackner, P. Chavel, A. A. Sawchuk, T. C. Strand, and A. R. Tanguay, “Optical computing with variable grating mode liquid crystal devices,” Proc. Soc. Photo-Opt. Instrum. Eng. 232, 128–136 (1980).

Other (3)

S. H. Lee, “Nonlinear optical processing,” in Optical Information Processing Fundamentals, S. H. Lee, ed. (Springer-Verlag, Berlin, 1981), pp. 261–303.
[Crossref]

A. W. Lohmann, Optical Information Processing (Lohmann, Erlangen, Federal Republic of Germany, 1979).

D. R. Maure, “Optical logic function generator,” U.S. Patent3,680,080 (July25, 1972).

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Figures (19)

Fig. 1
Fig. 1

Schematic diagrams of the lensless shadow-casting system for implementing optical logic gates.

Fig. 2
Fig. 2

(a) Coding of the two binary variables and (b) overlay of the two coded patterns.

Fig. 3
Fig. 3

(a) Geometrical configuration of the shadow-casting system and superposition of shadowgrams and (b) decoding mask.

Fig. 4
Fig. 4

Overlapping of projections of the ij coded cell illuminated with four LED’s and the boxed area in the central part.

Fig. 5
Fig. 5

Spatial representation of the 16 possible logic functions of two binary variables with bright-true-logic. Columns F0F15 show the projections of the combinatorial variables expressed in column 3 with the LED’s with switching states shown at the top. Bright-true-logic is represented by combination of bright (1) and dark (0) in the boxed areas in the central parts of the projections.

Fig. 6
Fig. 6

Realization of XOR gate in the boxed area in the central part.

Fig. 7
Fig. 7

Two binary images.

Fig. 8
Fig. 8

Two coded images and their overlay.

Fig. 9
Fig. 9

Experimental results of optical logic gates for 16 possible functions.

Fig. 10
Fig. 10

Two binary images with 64 × 64 pixels.

Fig. 11
Fig. 11

Experimental results of pattern logic for AND, NAND, XOR, XOR ¯, A B ¯, and NOR gates. Four thousand ninety-six channels of parallel operations are optically implemented.

Fig. 12
Fig. 12

Projection of the slit by a point source.

Fig. 13
Fig. 13

Radiating configuration of LED’s for addition of two binary images.

Fig. 14
Fig. 14

Experimental result of parallel processing for addition of two binary images.

Fig. 15
Fig. 15

Same as Fig 13 but for subtraction.

Fig. 16
Fig. 16

Coding of the ij cell of a gray-level image designated by four-bit signal. (a) Coding for image A, (b) that for image B, and (c) overlay of the two coded patterns.

Fig. 17
Fig. 17

Overlapping of projections of the ij coded cell illuminated with 4 × 4 LED’s.

Fig. 18
Fig. 18

(a) Geometrical configeration of the optical array processor and superposition of shadowgrams and (b) decoding mask.

Fig. 19
Fig. 19

Radiating configuration of LED’s implementable combined operations of four-bit binary adder and of digital-to-analog conversion.

Tables (4)

Tables Icon

Table 1 Sixteen Possible Functions of Two Binary Variables

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Table 2 Region of Shadow Z, Allowable for Slit of Width d

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Table 3 Truth Table for Addition of Two Binary Variables Designated by Binary and Decimal Arithmetic

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Table 4 Truth Table for Subtraction of Two Binary Variables Designated by Binary and Decimal Arithmetic

Equations (5)

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

d = l d 1 l - d 1 , z + z 1 = l z 1 l - d 1 ,             d 1 < l
g i j = α ( a i j b i j ) + β ( a i j b ¯ i j ) + γ ( a ¯ i j b i j ) + δ ( a ¯ i j b ¯ i j ) ,
u ( x , z ) = - d / 2 d / 2 exp { i π λ [ ( x 1 - x p ) 2 z 1 + ( x 1 - x ) 2 z ] } d x 1 .
4 λ < z d 2 λ ( z + z 1 z 1 ) 3 .
4 λ < z d 2 λ .