Abstract

An efficient storage format was developed for computer-generated holograms for use in electron-beam lithography. This method employs run-length encoding and Lempel–Ziv–Welch compression and succeeds in exposing holograms that were previously infeasible owing to the hologram’s tremendous pattern-data file size. These holograms also require significant computation; thus the algorithm was implemented on a parallel computer, which improved performance by 2 orders of magnitude. The decompression algorithm was integrated into the Cambridge electron-beam machine’s front-end processor.

Although this provides much-needed ability, some hardware enhancements will be required in the future to overcome inadequacies in the current front-end processor that result in a lengthy exposure time.

© 1993 Optical Society of America

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References

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  1. S. M. Arnold, “Electron beam fabrication of computer generated holograms,” Opt. Eng. 24, 803 (1985).
  2. R. W. Hawley, N. C. Gallagher, “Efficient electron beam pattern data format for the production of binary computer generated holograms,” Appl. Opt. 29, 216–224 (1990).
    [CrossRef] [PubMed]
  3. T. A. Welch, “A technique for high-performance data compression,” Computer 17(6), 8–19 (1984).
    [CrossRef]
  4. D. M. Newman, R. W. Hawley, N. C. Gallagher, “Implementation of a packed data format for production of computer generated holograms by e-beam lithography,” in Diffractive Optics: Design, Fabrication, and Applications, Vol. 9 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), paper WA2-1.
  5. W. H. Lee, “Binary synthetic holograms,” Appl. Opt. 13, 1677–1682 (1974).
    [CrossRef] [PubMed]
  6. D. E. Knuth, The Art of Computer Programming: Sorting and Searching (Addison-Wesley, Reading, Mass., 1975), Vol. 3.
  7. D. M. Newman, D. L. Goeckel, R. D. Crawford, S. Abraham, “Parallel holographic image calculation and compression,” in Frontiers 1992: Frontiers of Massively Parallel Computation, H. J. Siegel, ed. (Institute of Electrical and Electronics Engineers, New York, 1992).
  8. T. Blank, “The MasPar MP-1 architecture,” in Compcon 90 (Institute of Electrical and Electronics Engineers, New York, 1990), pp. 20–24.
  9. J. R. Nickolls, “The design of the MasPar MP-1: a cost effective massively parallel computer,” in Compcon 90 (Institute of Electrical and Electronics Engineers, New York, 1990), pp. 25–28.

1990 (1)

1985 (1)

S. M. Arnold, “Electron beam fabrication of computer generated holograms,” Opt. Eng. 24, 803 (1985).

1984 (1)

T. A. Welch, “A technique for high-performance data compression,” Computer 17(6), 8–19 (1984).
[CrossRef]

1974 (1)

Abraham, S.

D. M. Newman, D. L. Goeckel, R. D. Crawford, S. Abraham, “Parallel holographic image calculation and compression,” in Frontiers 1992: Frontiers of Massively Parallel Computation, H. J. Siegel, ed. (Institute of Electrical and Electronics Engineers, New York, 1992).

Arnold, S. M.

S. M. Arnold, “Electron beam fabrication of computer generated holograms,” Opt. Eng. 24, 803 (1985).

Blank, T.

T. Blank, “The MasPar MP-1 architecture,” in Compcon 90 (Institute of Electrical and Electronics Engineers, New York, 1990), pp. 20–24.

Crawford, R. D.

D. M. Newman, D. L. Goeckel, R. D. Crawford, S. Abraham, “Parallel holographic image calculation and compression,” in Frontiers 1992: Frontiers of Massively Parallel Computation, H. J. Siegel, ed. (Institute of Electrical and Electronics Engineers, New York, 1992).

Gallagher, N. C.

R. W. Hawley, N. C. Gallagher, “Efficient electron beam pattern data format for the production of binary computer generated holograms,” Appl. Opt. 29, 216–224 (1990).
[CrossRef] [PubMed]

D. M. Newman, R. W. Hawley, N. C. Gallagher, “Implementation of a packed data format for production of computer generated holograms by e-beam lithography,” in Diffractive Optics: Design, Fabrication, and Applications, Vol. 9 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), paper WA2-1.

Goeckel, D. L.

D. M. Newman, D. L. Goeckel, R. D. Crawford, S. Abraham, “Parallel holographic image calculation and compression,” in Frontiers 1992: Frontiers of Massively Parallel Computation, H. J. Siegel, ed. (Institute of Electrical and Electronics Engineers, New York, 1992).

Hawley, R. W.

R. W. Hawley, N. C. Gallagher, “Efficient electron beam pattern data format for the production of binary computer generated holograms,” Appl. Opt. 29, 216–224 (1990).
[CrossRef] [PubMed]

D. M. Newman, R. W. Hawley, N. C. Gallagher, “Implementation of a packed data format for production of computer generated holograms by e-beam lithography,” in Diffractive Optics: Design, Fabrication, and Applications, Vol. 9 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), paper WA2-1.

Knuth, D. E.

D. E. Knuth, The Art of Computer Programming: Sorting and Searching (Addison-Wesley, Reading, Mass., 1975), Vol. 3.

Lee, W. H.

Newman, D. M.

D. M. Newman, R. W. Hawley, N. C. Gallagher, “Implementation of a packed data format for production of computer generated holograms by e-beam lithography,” in Diffractive Optics: Design, Fabrication, and Applications, Vol. 9 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), paper WA2-1.

D. M. Newman, D. L. Goeckel, R. D. Crawford, S. Abraham, “Parallel holographic image calculation and compression,” in Frontiers 1992: Frontiers of Massively Parallel Computation, H. J. Siegel, ed. (Institute of Electrical and Electronics Engineers, New York, 1992).

Nickolls, J. R.

J. R. Nickolls, “The design of the MasPar MP-1: a cost effective massively parallel computer,” in Compcon 90 (Institute of Electrical and Electronics Engineers, New York, 1990), pp. 25–28.

Welch, T. A.

T. A. Welch, “A technique for high-performance data compression,” Computer 17(6), 8–19 (1984).
[CrossRef]

Appl. Opt. (2)

Computer (1)

T. A. Welch, “A technique for high-performance data compression,” Computer 17(6), 8–19 (1984).
[CrossRef]

Opt. Eng. (1)

S. M. Arnold, “Electron beam fabrication of computer generated holograms,” Opt. Eng. 24, 803 (1985).

Other (5)

D. M. Newman, R. W. Hawley, N. C. Gallagher, “Implementation of a packed data format for production of computer generated holograms by e-beam lithography,” in Diffractive Optics: Design, Fabrication, and Applications, Vol. 9 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), paper WA2-1.

D. E. Knuth, The Art of Computer Programming: Sorting and Searching (Addison-Wesley, Reading, Mass., 1975), Vol. 3.

D. M. Newman, D. L. Goeckel, R. D. Crawford, S. Abraham, “Parallel holographic image calculation and compression,” in Frontiers 1992: Frontiers of Massively Parallel Computation, H. J. Siegel, ed. (Institute of Electrical and Electronics Engineers, New York, 1992).

T. Blank, “The MasPar MP-1 architecture,” in Compcon 90 (Institute of Electrical and Electronics Engineers, New York, 1990), pp. 20–24.

J. R. Nickolls, “The design of the MasPar MP-1: a cost effective massively parallel computer,” in Compcon 90 (Institute of Electrical and Electronics Engineers, New York, 1990), pp. 25–28.

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Figures (14)

Fig. 1
Fig. 1

Comparison of encoding methods.

Fig. 2
Fig. 2

Typical fringe pattern (produces conical wave front).

Fig. 3
Fig. 3

15-bit exposure field organization.

Fig. 4
Fig. 4

Sample fringe.

Fig. 5
Fig. 5

Pseudocode for compression.

Fig. 6
Fig. 6

LZW compression example.

Fig. 7
Fig. 7

16-bit-word mapping for LZW and RLE codes.

Fig. 8
Fig. 8

Simplified MasPar architecture.

Fig. 9
Fig. 9

Parallel run-length encoding.

Fig. 10
Fig. 10

Decompression pseudocode.

Fig. 11
Fig. 11

LZW decompression example.

Fig. 12
Fig. 12

Decompression block diagram.

Fig. 13
Fig. 13

Front-end processor independence.

Fig. 14
Fig. 14

Enhancement of existing hardware.

Tables (4)

Tables Icon

Table 1 File-Size Comparison of Lempel–Ziv–Welch Encoding versus DIP Encoding

Tables Icon

Table 2 Overall Performance of Parallel Implementation

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Table 3 Performance by Function of Parallel Implementation

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Table 4 Exposure Timings

Equations (3)

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

hash ( ω , K ) = [ LZW ( ω ) + σ K + 1 ] modulo table size .
rehash ( J , K ) = [ J 10 + K ] modulo table size .
ϕ ( x , y ) = 2 π ( x 2 + y 2 ) 1 / 2 R 0 + 2 π x T .

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