Abstract

A novel technique for the fabrication of binary-phase computer-generated reflection holograms is described. By use of integrated circuit technology, the holographic pattern is etched into a silicon wafer and then aluminum coated to make a reflection hologram. Because these holograms reflect virtually all the incident radiation, they may find application in machining with high-power lasers. A number of possible modifications of the hologram fabrication procedure are discussed.

© 1977 Optical Society of America

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References

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  1. E. N. Leith, J. Upatnieks, J. Opt. Soc. Am. 52, 1295 (1964).
    [Crossref]
  2. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  3. W. T. Cathey, Optical Information Processing and Holography (Wiley, New York, 1974).
  4. G. Stroke, IEEE Spectrum 9, 24 (1972).
    [Crossref]
  5. D. Casasent, Opt. Eng. 13, 228 (1974).
    [Crossref]
  6. B. R. Brown, A. W. Lohmann, Appl. Opt. 5, 967 (1966).
    [Crossref] [PubMed]
  7. A. W. Lohmann, D. P. Paris, H. W. Werlich, Appl. Opt. 6, 1139 (1967).
    [Crossref] [PubMed]
  8. A. W. Lohmann, D. P. Paris, Appl. Opt. 6, 1739 (1967).
    [Crossref] [PubMed]
  9. B. R. Brown, A. W. Lohmann, IBM J. Res. Dev. 13, 160 (1969).
    [Crossref]
  10. Entire issue, Opt. Eng. 13, 175–283 (May/June 1974).
  11. Entire issue, Proc. Soc. Photo-Opt. Instrum. Eng. “Acquisition and Analysis of Pictorial Data,” 48 (19–20 August1974).
  12. W. H. Lee, Appl. Opt. 9, 639 (1970).
    [Crossref] [PubMed]
  13. M. Severcan, “Computer Generation of Coherent Optical Filters with High Light Efficiency and Large Dynamic Range,” Ph.D. Dissertation, Stanford University (December1973).
  14. R. E. Haskell, B. C. Culver, Appl. Opt. 11, 2712 (1972).
    [Crossref] [PubMed]
  15. J. P. Allebach, N. C. Gallagher, B. Liu, “Aliasing Error in Digital Holography,” to appear in Appl. Opt.
  16. R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971).
  17. N. C. Gallagher, B. Liu, Appl. Opt. 12, 2328 (1973).
    [Crossref] [PubMed]
  18. B. Liu, N. C. Gallagher, Appl. Opt. 13, 2470 (1974).
    [Crossref] [PubMed]
  19. B. Liu, N. C. Gallagher, J. Opt. Soc. Am. 64, 1227 (1974).
    [Crossref]
  20. J. P. Allebach, B. Liu, Appl. Opt. 14, 3062 (1975).
    [Crossref] [PubMed]
  21. J. R. Fienup, “Improved Synthesis and Computational Methods for Computer-Generated Holograms,” Ph.D. Dissertation, Stanford University (May1975).
  22. R. A. Gabel, Appl. Opt. 14, 2252 (1975).
    [Crossref] [PubMed]
  23. R. S. Powers, “Quantization Errors in Computer-Generated Holograms,” Ph.D. Dissertation, Stanford University (February1975).
  24. R. S. Powers, J. W. Goodman, Appl. Opt. 14, 1690 (1975).
    [Crossref] [PubMed]
  25. W. A. Pearlman, “Quantization Error Bounds for Computer-Generated Holograms,” Ph.D. Dissertation, Stanford University (August1974).
  26. N. C. Gallagher, “The Optimum Quantization and Relative Information Content of Holographic Magnitude and Phase,” to appear” in Acoustical Imaging and Holography, Crane, Russak & Co., New York.
  27. L. B. Lesem, P. M. Hirsch, J. A. Jordan, IBM J. Res. Dev. 13, 150 (1969).
    [Crossref]

1975 (3)

1974 (5)

B. Liu, N. C. Gallagher, Appl. Opt. 13, 2470 (1974).
[Crossref] [PubMed]

B. Liu, N. C. Gallagher, J. Opt. Soc. Am. 64, 1227 (1974).
[Crossref]

D. Casasent, Opt. Eng. 13, 228 (1974).
[Crossref]

Entire issue, Opt. Eng. 13, 175–283 (May/June 1974).

Entire issue, Proc. Soc. Photo-Opt. Instrum. Eng. “Acquisition and Analysis of Pictorial Data,” 48 (19–20 August1974).

1973 (1)

1972 (2)

1970 (1)

1969 (2)

B. R. Brown, A. W. Lohmann, IBM J. Res. Dev. 13, 160 (1969).
[Crossref]

L. B. Lesem, P. M. Hirsch, J. A. Jordan, IBM J. Res. Dev. 13, 150 (1969).
[Crossref]

1967 (2)

1966 (1)

1964 (1)

E. N. Leith, J. Upatnieks, J. Opt. Soc. Am. 52, 1295 (1964).
[Crossref]

Allebach, J. P.

J. P. Allebach, B. Liu, Appl. Opt. 14, 3062 (1975).
[Crossref] [PubMed]

J. P. Allebach, N. C. Gallagher, B. Liu, “Aliasing Error in Digital Holography,” to appear in Appl. Opt.

Brown, B. R.

B. R. Brown, A. W. Lohmann, IBM J. Res. Dev. 13, 160 (1969).
[Crossref]

B. R. Brown, A. W. Lohmann, Appl. Opt. 5, 967 (1966).
[Crossref] [PubMed]

Burckhardt, C. B.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971).

Casasent, D.

D. Casasent, Opt. Eng. 13, 228 (1974).
[Crossref]

Cathey, W. T.

W. T. Cathey, Optical Information Processing and Holography (Wiley, New York, 1974).

Collier, R. J.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971).

Culver, B. C.

Fienup, J. R.

J. R. Fienup, “Improved Synthesis and Computational Methods for Computer-Generated Holograms,” Ph.D. Dissertation, Stanford University (May1975).

Gabel, R. A.

Gallagher, N. C.

B. Liu, N. C. Gallagher, Appl. Opt. 13, 2470 (1974).
[Crossref] [PubMed]

B. Liu, N. C. Gallagher, J. Opt. Soc. Am. 64, 1227 (1974).
[Crossref]

N. C. Gallagher, B. Liu, Appl. Opt. 12, 2328 (1973).
[Crossref] [PubMed]

J. P. Allebach, N. C. Gallagher, B. Liu, “Aliasing Error in Digital Holography,” to appear in Appl. Opt.

N. C. Gallagher, “The Optimum Quantization and Relative Information Content of Holographic Magnitude and Phase,” to appear” in Acoustical Imaging and Holography, Crane, Russak & Co., New York.

Goodman, J. W.

R. S. Powers, J. W. Goodman, Appl. Opt. 14, 1690 (1975).
[Crossref] [PubMed]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Haskell, R. E.

Hirsch, P. M.

L. B. Lesem, P. M. Hirsch, J. A. Jordan, IBM J. Res. Dev. 13, 150 (1969).
[Crossref]

Jordan, J. A.

L. B. Lesem, P. M. Hirsch, J. A. Jordan, IBM J. Res. Dev. 13, 150 (1969).
[Crossref]

Lee, W. H.

Leith, E. N.

E. N. Leith, J. Upatnieks, J. Opt. Soc. Am. 52, 1295 (1964).
[Crossref]

Lesem, L. B.

L. B. Lesem, P. M. Hirsch, J. A. Jordan, IBM J. Res. Dev. 13, 150 (1969).
[Crossref]

Lin, L. H.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971).

Liu, B.

Lohmann, A. W.

Paris, D. P.

Pearlman, W. A.

W. A. Pearlman, “Quantization Error Bounds for Computer-Generated Holograms,” Ph.D. Dissertation, Stanford University (August1974).

Powers, R. S.

R. S. Powers, J. W. Goodman, Appl. Opt. 14, 1690 (1975).
[Crossref] [PubMed]

R. S. Powers, “Quantization Errors in Computer-Generated Holograms,” Ph.D. Dissertation, Stanford University (February1975).

Severcan, M.

M. Severcan, “Computer Generation of Coherent Optical Filters with High Light Efficiency and Large Dynamic Range,” Ph.D. Dissertation, Stanford University (December1973).

Stroke, G.

G. Stroke, IEEE Spectrum 9, 24 (1972).
[Crossref]

Upatnieks, J.

E. N. Leith, J. Upatnieks, J. Opt. Soc. Am. 52, 1295 (1964).
[Crossref]

Werlich, H. W.

Appl. Opt. (10)

IBM J. Res. Dev. (2)

L. B. Lesem, P. M. Hirsch, J. A. Jordan, IBM J. Res. Dev. 13, 150 (1969).
[Crossref]

B. R. Brown, A. W. Lohmann, IBM J. Res. Dev. 13, 160 (1969).
[Crossref]

IEEE Spectrum (1)

G. Stroke, IEEE Spectrum 9, 24 (1972).
[Crossref]

J. Opt. Soc. Am. (2)

E. N. Leith, J. Upatnieks, J. Opt. Soc. Am. 52, 1295 (1964).
[Crossref]

B. Liu, N. C. Gallagher, J. Opt. Soc. Am. 64, 1227 (1974).
[Crossref]

Opt. Eng. (2)

D. Casasent, Opt. Eng. 13, 228 (1974).
[Crossref]

Entire issue, Opt. Eng. 13, 175–283 (May/June 1974).

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

Entire issue, Proc. Soc. Photo-Opt. Instrum. Eng. “Acquisition and Analysis of Pictorial Data,” 48 (19–20 August1974).

Other (9)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

W. T. Cathey, Optical Information Processing and Holography (Wiley, New York, 1974).

J. R. Fienup, “Improved Synthesis and Computational Methods for Computer-Generated Holograms,” Ph.D. Dissertation, Stanford University (May1975).

J. P. Allebach, N. C. Gallagher, B. Liu, “Aliasing Error in Digital Holography,” to appear in Appl. Opt.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971).

M. Severcan, “Computer Generation of Coherent Optical Filters with High Light Efficiency and Large Dynamic Range,” Ph.D. Dissertation, Stanford University (December1973).

W. A. Pearlman, “Quantization Error Bounds for Computer-Generated Holograms,” Ph.D. Dissertation, Stanford University (August1974).

N. C. Gallagher, “The Optimum Quantization and Relative Information Content of Holographic Magnitude and Phase,” to appear” in Acoustical Imaging and Holography, Crane, Russak & Co., New York.

R. S. Powers, “Quantization Errors in Computer-Generated Holograms,” Ph.D. Dissertation, Stanford University (February1975).

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Figures (6)

Fig. 1
Fig. 1

Representation of Lohmann’s method for constructing holograms.

Fig. 2
Fig. 2

The (m,n)th resolution cell.

Fig. 3
Fig. 3

Typical Calcomp plot of a hologram.

Fig. 4
Fig. 4

Image reconstructed using the high contrast photomask as a transmission hologram.

Fig. 5
Fig. 5

Scanning electron micrographs of etched silicon wafer. The rectangle pits are approximately 0.007 cm wide.

Fig. 6
Fig. 6

Image reconstructed using the reflection hologram constructed with the same photomask that produced the image in Fig. 4.

Equations (14)

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H ( u , v ) = m n rect [ u X - ( m + P m n ) C ] rect ( u X - n W m n ) ,
rect ( x ) = { 1 x 1 / 2 0 elsewhere .
h ( x , y ) = - - H ( u , v ) exp [ i 2 π ( x u + y v ) ] d u d v .
1 p , q = - sin π ( p - u X ) π ( p - u X ) sin π ( q - v X ) π ( q - v X )
h ( x , y ) = m , n , p , q J m , n , p , q ( x , y ) ,
J m , n , p , q ( x , y ) = sin π ( p - u X ) π ( p - u X ) exp ( i 2 π u x ) d u × sin π ( q - v X ) π ( q - v X ) exp ( i 2 π y v ) d v .
J m , n , p , q ( x , y ) exp { i 2 π X [ ( m + P m n ) x + n y ] } sin ( π C X / X ) π x sin ( π W m n y / X ) π y ,
h ( x , y ) = sin ( π C x / X ) π x p , q sin ( π W p q y / X ) π y × exp ( i 2 π X P p q x ) exp [ i 2 π X ( p x + q y ) ] .
sin ( π W p q y / X ) π y W p q / X .
| sin ( π C x / X ) π x |
h ( x , y ) p , q [ W p q π X 2 exp ( i 2 π P p q ) ] exp [ i 2 π X ( p x + q y ) ] .
R ( u , v ) = H ( u , v ) + [ 1 - H ( u , v ) ] exp ( i ϕ ) = [ 1 - exp ( i ϕ ) ] H ( u , v ) + exp ( i ϕ ) ,
r ( x , y ) = [ 1 - exp ( i ϕ ] h ( x , y ) + central order spot .
r ( x , y ) = 2 h ( x , y ) .

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