Abstract

Holographic optical elements (HOEs) of space-variant impulse response have been designed and generated using a computerized optical system. HOEs made of dichromated gelatin have been produced and used for spatial light modulator defect removal and optical interconnects. Experimental performance and characteristics are presented.

© 1988 Optical Society of America

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References

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  1. J. W. Goodman, “Linear Space-Variant Optical Data Processing,” in Optical Data Processing Fundamentals, S. H. Lee, Ed. (Springer-Verlag, New York, 1981), pp. 235–259.
  2. P. Ambs, Y. Fainman, S. H. Lee, J. Gresser, “Computerized Design and Generation of Space-Variant Holographic Filter,” Proc. Soc. Photo-Opt. Instrum. Eng. 884, 62 (Jan.1988); see also P. Ambs, Y. Fainman, S. H. Lee, J. Gresser, “Computerized Design and Generation of Space-Variant Filters. 1: System Design Consideration and Applications of Space-Variant Filters to Image Processing,” Appl. Opt. 27, 4753 (15Nov.1988).
    [CrossRef] [PubMed]
  3. H. J. Caulfield, “Parallel N4 Weighted Optical Interconnections,” Appl. Opt. 26, 4039 (1987).
    [CrossRef] [PubMed]
  4. S. H. Lee, S. C. Esener, M. A. Title, T. J. Drabik “Two-Dimensional Silicon/PLZT Spatial Light Modulators: Design Consideration and Technology,” Opt. Eng. 25, 250 (1986).
    [CrossRef]
  5. S. C. Esener, J. H. Wang, T. J. Drabik, M. A. Title, S. H. Lee “One-dimensional Silicon/PLZT Spatial Light Modulators,” Opt. Eng. 26, 406 (1987).
    [CrossRef]
  6. T. Georgekutty, H. K. Liu, “A Simplified Dichromated Gelatin Hologram Recording Process,” Appl. Opt. 26, 372 (1987).
    [CrossRef] [PubMed]
  7. J. Goodman, F. Leonbergger, S. Kung, R. Athale “Optical Interconnections for VLSI Systems,” Proc. IEEE 72, 850 (1984).
    [CrossRef]
  8. R. Kostuk, J. Goodman, L. Hesselink “Optical Imaging Applied to Microelectronic Chip to Chip Interconnections,” Appl. Opt. 24, 2851 (1985).
    [CrossRef] [PubMed]
  9. L. Bergman et al., “Holographic Optical Interconnects for VLSI,” Opt. Eng. 10, 1109 (1986).
  10. M. Feldman, C. C. Guest “Computer Generated Holographic Optical Elements for Optical Interconnection of Very Large Scale Integrated Circuit,” Appl. Opt. 26, 4377 (1987).
    [CrossRef] [PubMed]
  11. A. A. Sawchuk, B. K. Jenkins, C. S. Raghavendra, “Optical Crossbar Networks,” IEEE Computer50 (June1987).
    [CrossRef]
  12. C. Seitz, “System Timing,” in Introduction to VLSI Systems, C. Mead, L. Conway, Eds. (Addison-Wesley, Reading, MA, 1980).
  13. D. Hillis, The Connection Machine (MIT Press, Cambridge, 1985).
  14. C. W. Stirk, R. A. Athale, M. W. Haney, “Folded Perfect Shuffle Optical Processor,” Appl. Opt. 27, 202 (1988).
    [CrossRef] [PubMed]

1988 (2)

P. Ambs, Y. Fainman, S. H. Lee, J. Gresser, “Computerized Design and Generation of Space-Variant Holographic Filter,” Proc. Soc. Photo-Opt. Instrum. Eng. 884, 62 (Jan.1988); see also P. Ambs, Y. Fainman, S. H. Lee, J. Gresser, “Computerized Design and Generation of Space-Variant Filters. 1: System Design Consideration and Applications of Space-Variant Filters to Image Processing,” Appl. Opt. 27, 4753 (15Nov.1988).
[CrossRef] [PubMed]

C. W. Stirk, R. A. Athale, M. W. Haney, “Folded Perfect Shuffle Optical Processor,” Appl. Opt. 27, 202 (1988).
[CrossRef] [PubMed]

1987 (5)

1986 (2)

S. H. Lee, S. C. Esener, M. A. Title, T. J. Drabik “Two-Dimensional Silicon/PLZT Spatial Light Modulators: Design Consideration and Technology,” Opt. Eng. 25, 250 (1986).
[CrossRef]

L. Bergman et al., “Holographic Optical Interconnects for VLSI,” Opt. Eng. 10, 1109 (1986).

1985 (1)

1984 (1)

J. Goodman, F. Leonbergger, S. Kung, R. Athale “Optical Interconnections for VLSI Systems,” Proc. IEEE 72, 850 (1984).
[CrossRef]

Ambs, P.

P. Ambs, Y. Fainman, S. H. Lee, J. Gresser, “Computerized Design and Generation of Space-Variant Holographic Filter,” Proc. Soc. Photo-Opt. Instrum. Eng. 884, 62 (Jan.1988); see also P. Ambs, Y. Fainman, S. H. Lee, J. Gresser, “Computerized Design and Generation of Space-Variant Filters. 1: System Design Consideration and Applications of Space-Variant Filters to Image Processing,” Appl. Opt. 27, 4753 (15Nov.1988).
[CrossRef] [PubMed]

Athale, R.

J. Goodman, F. Leonbergger, S. Kung, R. Athale “Optical Interconnections for VLSI Systems,” Proc. IEEE 72, 850 (1984).
[CrossRef]

Athale, R. A.

Bergman, L.

L. Bergman et al., “Holographic Optical Interconnects for VLSI,” Opt. Eng. 10, 1109 (1986).

Caulfield, H. J.

Drabik, T. J.

S. C. Esener, J. H. Wang, T. J. Drabik, M. A. Title, S. H. Lee “One-dimensional Silicon/PLZT Spatial Light Modulators,” Opt. Eng. 26, 406 (1987).
[CrossRef]

S. H. Lee, S. C. Esener, M. A. Title, T. J. Drabik “Two-Dimensional Silicon/PLZT Spatial Light Modulators: Design Consideration and Technology,” Opt. Eng. 25, 250 (1986).
[CrossRef]

Esener, S. C.

S. C. Esener, J. H. Wang, T. J. Drabik, M. A. Title, S. H. Lee “One-dimensional Silicon/PLZT Spatial Light Modulators,” Opt. Eng. 26, 406 (1987).
[CrossRef]

S. H. Lee, S. C. Esener, M. A. Title, T. J. Drabik “Two-Dimensional Silicon/PLZT Spatial Light Modulators: Design Consideration and Technology,” Opt. Eng. 25, 250 (1986).
[CrossRef]

Fainman, Y.

P. Ambs, Y. Fainman, S. H. Lee, J. Gresser, “Computerized Design and Generation of Space-Variant Holographic Filter,” Proc. Soc. Photo-Opt. Instrum. Eng. 884, 62 (Jan.1988); see also P. Ambs, Y. Fainman, S. H. Lee, J. Gresser, “Computerized Design and Generation of Space-Variant Filters. 1: System Design Consideration and Applications of Space-Variant Filters to Image Processing,” Appl. Opt. 27, 4753 (15Nov.1988).
[CrossRef] [PubMed]

Feldman, M.

Georgekutty, T.

Goodman, J.

R. Kostuk, J. Goodman, L. Hesselink “Optical Imaging Applied to Microelectronic Chip to Chip Interconnections,” Appl. Opt. 24, 2851 (1985).
[CrossRef] [PubMed]

J. Goodman, F. Leonbergger, S. Kung, R. Athale “Optical Interconnections for VLSI Systems,” Proc. IEEE 72, 850 (1984).
[CrossRef]

Goodman, J. W.

J. W. Goodman, “Linear Space-Variant Optical Data Processing,” in Optical Data Processing Fundamentals, S. H. Lee, Ed. (Springer-Verlag, New York, 1981), pp. 235–259.

Gresser, J.

P. Ambs, Y. Fainman, S. H. Lee, J. Gresser, “Computerized Design and Generation of Space-Variant Holographic Filter,” Proc. Soc. Photo-Opt. Instrum. Eng. 884, 62 (Jan.1988); see also P. Ambs, Y. Fainman, S. H. Lee, J. Gresser, “Computerized Design and Generation of Space-Variant Filters. 1: System Design Consideration and Applications of Space-Variant Filters to Image Processing,” Appl. Opt. 27, 4753 (15Nov.1988).
[CrossRef] [PubMed]

Guest, C. C.

Haney, M. W.

Hesselink, L.

Hillis, D.

D. Hillis, The Connection Machine (MIT Press, Cambridge, 1985).

Jenkins, B. K.

A. A. Sawchuk, B. K. Jenkins, C. S. Raghavendra, “Optical Crossbar Networks,” IEEE Computer50 (June1987).
[CrossRef]

Kostuk, R.

Kung, S.

J. Goodman, F. Leonbergger, S. Kung, R. Athale “Optical Interconnections for VLSI Systems,” Proc. IEEE 72, 850 (1984).
[CrossRef]

Lee, S. H.

P. Ambs, Y. Fainman, S. H. Lee, J. Gresser, “Computerized Design and Generation of Space-Variant Holographic Filter,” Proc. Soc. Photo-Opt. Instrum. Eng. 884, 62 (Jan.1988); see also P. Ambs, Y. Fainman, S. H. Lee, J. Gresser, “Computerized Design and Generation of Space-Variant Filters. 1: System Design Consideration and Applications of Space-Variant Filters to Image Processing,” Appl. Opt. 27, 4753 (15Nov.1988).
[CrossRef] [PubMed]

S. C. Esener, J. H. Wang, T. J. Drabik, M. A. Title, S. H. Lee “One-dimensional Silicon/PLZT Spatial Light Modulators,” Opt. Eng. 26, 406 (1987).
[CrossRef]

S. H. Lee, S. C. Esener, M. A. Title, T. J. Drabik “Two-Dimensional Silicon/PLZT Spatial Light Modulators: Design Consideration and Technology,” Opt. Eng. 25, 250 (1986).
[CrossRef]

Leonbergger, F.

J. Goodman, F. Leonbergger, S. Kung, R. Athale “Optical Interconnections for VLSI Systems,” Proc. IEEE 72, 850 (1984).
[CrossRef]

Liu, H. K.

Raghavendra, C. S.

A. A. Sawchuk, B. K. Jenkins, C. S. Raghavendra, “Optical Crossbar Networks,” IEEE Computer50 (June1987).
[CrossRef]

Sawchuk, A. A.

A. A. Sawchuk, B. K. Jenkins, C. S. Raghavendra, “Optical Crossbar Networks,” IEEE Computer50 (June1987).
[CrossRef]

Seitz, C.

C. Seitz, “System Timing,” in Introduction to VLSI Systems, C. Mead, L. Conway, Eds. (Addison-Wesley, Reading, MA, 1980).

Stirk, C. W.

Title, M. A.

S. C. Esener, J. H. Wang, T. J. Drabik, M. A. Title, S. H. Lee “One-dimensional Silicon/PLZT Spatial Light Modulators,” Opt. Eng. 26, 406 (1987).
[CrossRef]

S. H. Lee, S. C. Esener, M. A. Title, T. J. Drabik “Two-Dimensional Silicon/PLZT Spatial Light Modulators: Design Consideration and Technology,” Opt. Eng. 25, 250 (1986).
[CrossRef]

Wang, J. H.

S. C. Esener, J. H. Wang, T. J. Drabik, M. A. Title, S. H. Lee “One-dimensional Silicon/PLZT Spatial Light Modulators,” Opt. Eng. 26, 406 (1987).
[CrossRef]

Appl. Opt. (5)

IEEE Computer (1)

A. A. Sawchuk, B. K. Jenkins, C. S. Raghavendra, “Optical Crossbar Networks,” IEEE Computer50 (June1987).
[CrossRef]

Opt. Eng. (3)

L. Bergman et al., “Holographic Optical Interconnects for VLSI,” Opt. Eng. 10, 1109 (1986).

S. H. Lee, S. C. Esener, M. A. Title, T. J. Drabik “Two-Dimensional Silicon/PLZT Spatial Light Modulators: Design Consideration and Technology,” Opt. Eng. 25, 250 (1986).
[CrossRef]

S. C. Esener, J. H. Wang, T. J. Drabik, M. A. Title, S. H. Lee “One-dimensional Silicon/PLZT Spatial Light Modulators,” Opt. Eng. 26, 406 (1987).
[CrossRef]

Proc. IEEE (1)

J. Goodman, F. Leonbergger, S. Kung, R. Athale “Optical Interconnections for VLSI Systems,” Proc. IEEE 72, 850 (1984).
[CrossRef]

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

P. Ambs, Y. Fainman, S. H. Lee, J. Gresser, “Computerized Design and Generation of Space-Variant Holographic Filter,” Proc. Soc. Photo-Opt. Instrum. Eng. 884, 62 (Jan.1988); see also P. Ambs, Y. Fainman, S. H. Lee, J. Gresser, “Computerized Design and Generation of Space-Variant Filters. 1: System Design Consideration and Applications of Space-Variant Filters to Image Processing,” Appl. Opt. 27, 4753 (15Nov.1988).
[CrossRef] [PubMed]

Other (3)

J. W. Goodman, “Linear Space-Variant Optical Data Processing,” in Optical Data Processing Fundamentals, S. H. Lee, Ed. (Springer-Verlag, New York, 1981), pp. 235–259.

C. Seitz, “System Timing,” in Introduction to VLSI Systems, C. Mead, L. Conway, Eds. (Addison-Wesley, Reading, MA, 1980).

D. Hillis, The Connection Machine (MIT Press, Cambridge, 1985).

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Figures (8)

Fig. 1
Fig. 1

Si/PLZT SLM: (a) schematic diagram of one cell; (b) 3-D view of one SLM cell (after Lee et al.4).

Fig. 2
Fig. 2

Diagram showing the principle of the SLM defect removal with a pair of holographic filters HOE1 and HOE2.

Fig. 3
Fig. 3

(a) Hologram array HOE1 is placed at the input plane and matched to the input image size (N × N). (b) PSF of HOE1 maps input pixels (i′,j′) to pixels (p,q) on the SLM, if the PEs at coordinate (i′,j′) are defective. (c) PSF of HOE2 which is placed in the SLM plane recombine the outputs from nondefective cells of the SLM to form an output array of size identical to that of the input image of size N × N.

Fig. 4
Fig. 4

SLM defect removal: (a) input image; (b) transformation of the input image [Fig. 4(a)] by HOE1; (c) optical output of HOE2 when it is illuminated with the pattern of Fig. 4(b).

Fig. 5
Fig. 5

Principle of full interconnection among three processors.

Fig. 6
Fig. 6

Optical reconstruction from one of the 32 × 32 arrays of holograms for full interconnection among the 32 × 32 processing elements.

Fig. 7
Fig. 7

Hypercube interconnect for a 2-D array of PEs: (a) interconnects associated with a single PE in a 2-D 2-cube; F1 and F 1 are the two orthogonal folding axes mapping a 2-D 2-cube into four 2-D 1-cubes; (b) interconnects associated with two PEs in a 2-D 3-cube topology; F2 and F 2 ; are the two orthogonal folding axes mapping a 2-D 3-cube into four 2-D 2-cubes.

Fig. 8
Fig. 8

Reconstruction of the HOE for hypercube interconnect 128 × 128 PEs: (a), (b), and (c) show three examples of the connection pattern for three different nodes of the PE array and are obtained by illuminating the holograms corresponding to these PEs. The log2 128 = 7 visible spots in each direction show the connection from one PE to seven PEs in each direction.

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