Abstract

Since Gabor's first hologram, the meanings of that term have grown with increased use of the invention. Computers expanded applications further, and this paper surveys the methods and techniques of computer generated holograms.

© 1987 Optical Society of America

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References

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  1. D. Gabor, “A New Microscopic Principle,” Nature London 161, 777 (1948).
    [CrossRef] [PubMed]
  2. E. N. Leith, J. Upatnieks, “Wavefront Reconstruction with Continuous Tone Objects,” J. Opt. Soc. Am. 53, 1377 (1963).
    [CrossRef]
  3. L. J. Cutrona et al., “A High Resolution Radar Combat Surveillance System,” IEEE Trans. Military Electron. MIL-5, 127 (1961).
    [CrossRef]
  4. M. Francon, Holography (Academic, New York, 1974).
  5. G. W. Stroke, An Introduction to Coherent Optics and Holography (Academic, New York, 1966).
  6. J. B. DeVelis, G. O. Reynolds, Theory and Application of Holography (Addison-Wesley, Reading, MA, 1967).
  7. H. J. Caufield, S. Lu, The Applications of Holography (Wiley-Interscience, New York, 1970).
  8. B. P. Hildebrand, B. B. Brenden, An Introduction to Acoustical Holography (Plenum, New York, 1972).
  9. G. Tricoles, N. Farhat, “Microwave Holography: Techniques and Applications,” Proc. IEEE 65, 108 (1977).
    [CrossRef]
  10. A. Kozma, D. L. Kelly, “Spatial Filtering for Detection of Signals Submerged in Noise,” Appl. Opt. 4, 387 (1965).
    [CrossRef]
  11. B. R. Brown, A. W. Lohmann, “Complex Spatial Filtering with Binary Masks,” Appl. Opt. 5, 967 (1966).
    [CrossRef] [PubMed]
  12. A. W. Lohmann, D. P. Paris, “Binary Fraunhofer Holograms, Generated by Computer,” Appl. Opt. 6, 1739 (1967).
    [CrossRef] [PubMed]
  13. J. Bucklew, N. C. Gallagher, “Detour Phase Error in the Lohmann Hologram,” Appl. Opt. 18, 575 (1979).
    [CrossRef] [PubMed]
  14. J. Bucklew, N. C. Gallagher, “Comprehensive Error Models and a Comparative Study of Some Detour Phase Holograms,” Appl. Opt. 18, 2861 (1979).
    [CrossRef] [PubMed]
  15. W. T. Cathey, “The Effect Of Finite Sampling in Holography,” Optik 27, 317 (1968).
  16. J. Bucklew, N. C. Gallagher, “Aliasing Error in Digital Holography,” Appl. Opt. 15, 2183 (1976).
    [CrossRef]
  17. J. W. Goodman, A. M. Silvestri, “Some Effects of Fourier Domain Phase Quantization,” IBM J. Res. Dev. 14, 478 (1970).
    [CrossRef]
  18. P. S. Naidu, “Quantization Noise in Binary Hologram,” Opt. Commun. 15, 361 (1975).
    [CrossRef]
  19. B. R. Brown, A. W. Lohmann, “Computer Generated Binary Holograms,” IBM J. Res. Dev. 13, 168 (1969).
    [CrossRef]
  20. W.-H. Lee, “Sampled Fourier Transform Holograms Generated by Computer,” Appl. Opt. 9, 639 (1970).
    [CrossRef] [PubMed]
  21. C. K. Hsueh, A. A. Sawchuck, “Computer Generated Double Phase Holograms,” Appl. Opt. 17, 3874 (1978).
    [CrossRef] [PubMed]
  22. C. B. Burckhardt, “A Simplification of Lee's Method of Generating Holograms by Computer,” Appl. Opt. 9, 1949 (1970).
    [PubMed]
  23. W.-H. Lee, “Binary Synthetic Holograms,” Appl. Opt. 13, 1677 (1974).
    [CrossRef] [PubMed]
  24. W.-H. Lee, “Binary Computer Generated Holograms,” Appl. Opt. 18, 3661 (1979).
    [CrossRef] [PubMed]
  25. N. C. Gallagher, J. A. Bucklew, “Nondetour Phase Digital Holograms: An Analysis: Errata,” Appl. Opt. 19, 4266 (1980).
    [CrossRef] [PubMed]
  26. J. J. Burch, “A Computer Algorithm for Synthesis of Spatial Frequency Filters,” Proc. IEEE 55, 599 (1967).
    [CrossRef]
  27. L. B. Lesem, P. M. Hirsch, J. Jordan, “Kinoforms,” IBM J. Res. Dev. 13, 150 (1969).
    [CrossRef]
  28. J. C. Patau et al., “Incoherent Filtering Using Kinoforms,” IBM J. Res. Dev. 14, 485 (1970).
    [CrossRef]
  29. W. J. Dallas, “Computer Generated Holograms,” in The Computer in Optical Research, B. R. Frieden, Ed. (Springer-Verlag, Berlin, 1980), p. 291.
  30. D. Schreier, Ed., Synthetische Holografie (Physik-Verlag, Location, 1984).
  31. W.-H. Lee, “Computer Generated Holograms,” Prog. Opt. 16, 121 (1978).

1980 (1)

1979 (3)

1978 (2)

1977 (1)

G. Tricoles, N. Farhat, “Microwave Holography: Techniques and Applications,” Proc. IEEE 65, 108 (1977).
[CrossRef]

1976 (1)

1975 (1)

P. S. Naidu, “Quantization Noise in Binary Hologram,” Opt. Commun. 15, 361 (1975).
[CrossRef]

1974 (1)

1970 (4)

J. C. Patau et al., “Incoherent Filtering Using Kinoforms,” IBM J. Res. Dev. 14, 485 (1970).
[CrossRef]

J. W. Goodman, A. M. Silvestri, “Some Effects of Fourier Domain Phase Quantization,” IBM J. Res. Dev. 14, 478 (1970).
[CrossRef]

C. B. Burckhardt, “A Simplification of Lee's Method of Generating Holograms by Computer,” Appl. Opt. 9, 1949 (1970).
[PubMed]

W.-H. Lee, “Sampled Fourier Transform Holograms Generated by Computer,” Appl. Opt. 9, 639 (1970).
[CrossRef] [PubMed]

1969 (2)

L. B. Lesem, P. M. Hirsch, J. Jordan, “Kinoforms,” IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

B. R. Brown, A. W. Lohmann, “Computer Generated Binary Holograms,” IBM J. Res. Dev. 13, 168 (1969).
[CrossRef]

1968 (1)

W. T. Cathey, “The Effect Of Finite Sampling in Holography,” Optik 27, 317 (1968).

1967 (2)

J. J. Burch, “A Computer Algorithm for Synthesis of Spatial Frequency Filters,” Proc. IEEE 55, 599 (1967).
[CrossRef]

A. W. Lohmann, D. P. Paris, “Binary Fraunhofer Holograms, Generated by Computer,” Appl. Opt. 6, 1739 (1967).
[CrossRef] [PubMed]

1966 (1)

1965 (1)

1963 (1)

1961 (1)

L. J. Cutrona et al., “A High Resolution Radar Combat Surveillance System,” IEEE Trans. Military Electron. MIL-5, 127 (1961).
[CrossRef]

1948 (1)

D. Gabor, “A New Microscopic Principle,” Nature London 161, 777 (1948).
[CrossRef] [PubMed]

Brenden, B. B.

B. P. Hildebrand, B. B. Brenden, An Introduction to Acoustical Holography (Plenum, New York, 1972).

Brown, B. R.

B. R. Brown, A. W. Lohmann, “Computer Generated Binary Holograms,” IBM J. Res. Dev. 13, 168 (1969).
[CrossRef]

B. R. Brown, A. W. Lohmann, “Complex Spatial Filtering with Binary Masks,” Appl. Opt. 5, 967 (1966).
[CrossRef] [PubMed]

Bucklew, J.

Bucklew, J. A.

Burch, J. J.

J. J. Burch, “A Computer Algorithm for Synthesis of Spatial Frequency Filters,” Proc. IEEE 55, 599 (1967).
[CrossRef]

Burckhardt, C. B.

Cathey, W. T.

W. T. Cathey, “The Effect Of Finite Sampling in Holography,” Optik 27, 317 (1968).

Caufield, H. J.

H. J. Caufield, S. Lu, The Applications of Holography (Wiley-Interscience, New York, 1970).

Cutrona, L. J.

L. J. Cutrona et al., “A High Resolution Radar Combat Surveillance System,” IEEE Trans. Military Electron. MIL-5, 127 (1961).
[CrossRef]

Dallas, W. J.

W. J. Dallas, “Computer Generated Holograms,” in The Computer in Optical Research, B. R. Frieden, Ed. (Springer-Verlag, Berlin, 1980), p. 291.

DeVelis, J. B.

J. B. DeVelis, G. O. Reynolds, Theory and Application of Holography (Addison-Wesley, Reading, MA, 1967).

Farhat, N.

G. Tricoles, N. Farhat, “Microwave Holography: Techniques and Applications,” Proc. IEEE 65, 108 (1977).
[CrossRef]

Francon, M.

M. Francon, Holography (Academic, New York, 1974).

Gabor, D.

D. Gabor, “A New Microscopic Principle,” Nature London 161, 777 (1948).
[CrossRef] [PubMed]

Gallagher, N. C.

Goodman, J. W.

J. W. Goodman, A. M. Silvestri, “Some Effects of Fourier Domain Phase Quantization,” IBM J. Res. Dev. 14, 478 (1970).
[CrossRef]

Hildebrand, B. P.

B. P. Hildebrand, B. B. Brenden, An Introduction to Acoustical Holography (Plenum, New York, 1972).

Hirsch, P. M.

L. B. Lesem, P. M. Hirsch, J. Jordan, “Kinoforms,” IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

Hsueh, C. K.

Jordan, J.

L. B. Lesem, P. M. Hirsch, J. Jordan, “Kinoforms,” IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

Kelly, D. L.

Kozma, A.

Lee, W.-H.

Leith, E. N.

Lesem, L. B.

L. B. Lesem, P. M. Hirsch, J. Jordan, “Kinoforms,” IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

Lohmann, A. W.

Lu, S.

H. J. Caufield, S. Lu, The Applications of Holography (Wiley-Interscience, New York, 1970).

Naidu, P. S.

P. S. Naidu, “Quantization Noise in Binary Hologram,” Opt. Commun. 15, 361 (1975).
[CrossRef]

Paris, D. P.

Patau, J. C.

J. C. Patau et al., “Incoherent Filtering Using Kinoforms,” IBM J. Res. Dev. 14, 485 (1970).
[CrossRef]

Reynolds, G. O.

J. B. DeVelis, G. O. Reynolds, Theory and Application of Holography (Addison-Wesley, Reading, MA, 1967).

Sawchuck, A. A.

Silvestri, A. M.

J. W. Goodman, A. M. Silvestri, “Some Effects of Fourier Domain Phase Quantization,” IBM J. Res. Dev. 14, 478 (1970).
[CrossRef]

Stroke, G. W.

G. W. Stroke, An Introduction to Coherent Optics and Holography (Academic, New York, 1966).

Tricoles, G.

G. Tricoles, N. Farhat, “Microwave Holography: Techniques and Applications,” Proc. IEEE 65, 108 (1977).
[CrossRef]

Upatnieks, J.

Appl. Opt. (12)

A. Kozma, D. L. Kelly, “Spatial Filtering for Detection of Signals Submerged in Noise,” Appl. Opt. 4, 387 (1965).
[CrossRef]

B. R. Brown, A. W. Lohmann, “Complex Spatial Filtering with Binary Masks,” Appl. Opt. 5, 967 (1966).
[CrossRef] [PubMed]

A. W. Lohmann, D. P. Paris, “Binary Fraunhofer Holograms, Generated by Computer,” Appl. Opt. 6, 1739 (1967).
[CrossRef] [PubMed]

W.-H. Lee, “Binary Synthetic Holograms,” Appl. Opt. 13, 1677 (1974).
[CrossRef] [PubMed]

J. Bucklew, N. C. Gallagher, “Aliasing Error in Digital Holography,” Appl. Opt. 15, 2183 (1976).
[CrossRef]

J. Bucklew, N. C. Gallagher, “Detour Phase Error in the Lohmann Hologram,” Appl. Opt. 18, 575 (1979).
[CrossRef] [PubMed]

J. Bucklew, N. C. Gallagher, “Comprehensive Error Models and a Comparative Study of Some Detour Phase Holograms,” Appl. Opt. 18, 2861 (1979).
[CrossRef] [PubMed]

W.-H. Lee, “Binary Computer Generated Holograms,” Appl. Opt. 18, 3661 (1979).
[CrossRef] [PubMed]

N. C. Gallagher, J. A. Bucklew, “Nondetour Phase Digital Holograms: An Analysis: Errata,” Appl. Opt. 19, 4266 (1980).
[CrossRef] [PubMed]

W.-H. Lee, “Sampled Fourier Transform Holograms Generated by Computer,” Appl. Opt. 9, 639 (1970).
[CrossRef] [PubMed]

C. K. Hsueh, A. A. Sawchuck, “Computer Generated Double Phase Holograms,” Appl. Opt. 17, 3874 (1978).
[CrossRef] [PubMed]

C. B. Burckhardt, “A Simplification of Lee's Method of Generating Holograms by Computer,” Appl. Opt. 9, 1949 (1970).
[PubMed]

IBM J. Res. Dev. (4)

J. W. Goodman, A. M. Silvestri, “Some Effects of Fourier Domain Phase Quantization,” IBM J. Res. Dev. 14, 478 (1970).
[CrossRef]

L. B. Lesem, P. M. Hirsch, J. Jordan, “Kinoforms,” IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

J. C. Patau et al., “Incoherent Filtering Using Kinoforms,” IBM J. Res. Dev. 14, 485 (1970).
[CrossRef]

B. R. Brown, A. W. Lohmann, “Computer Generated Binary Holograms,” IBM J. Res. Dev. 13, 168 (1969).
[CrossRef]

IEEE Trans. Military Electron. (1)

L. J. Cutrona et al., “A High Resolution Radar Combat Surveillance System,” IEEE Trans. Military Electron. MIL-5, 127 (1961).
[CrossRef]

J. Opt. Soc. Am. (1)

Nature London (1)

D. Gabor, “A New Microscopic Principle,” Nature London 161, 777 (1948).
[CrossRef] [PubMed]

Opt. Commun. (1)

P. S. Naidu, “Quantization Noise in Binary Hologram,” Opt. Commun. 15, 361 (1975).
[CrossRef]

Optik (1)

W. T. Cathey, “The Effect Of Finite Sampling in Holography,” Optik 27, 317 (1968).

Proc. IEEE (2)

J. J. Burch, “A Computer Algorithm for Synthesis of Spatial Frequency Filters,” Proc. IEEE 55, 599 (1967).
[CrossRef]

G. Tricoles, N. Farhat, “Microwave Holography: Techniques and Applications,” Proc. IEEE 65, 108 (1977).
[CrossRef]

Prog. Opt. (1)

W.-H. Lee, “Computer Generated Holograms,” Prog. Opt. 16, 121 (1978).

Other (7)

W. J. Dallas, “Computer Generated Holograms,” in The Computer in Optical Research, B. R. Frieden, Ed. (Springer-Verlag, Berlin, 1980), p. 291.

D. Schreier, Ed., Synthetische Holografie (Physik-Verlag, Location, 1984).

M. Francon, Holography (Academic, New York, 1974).

G. W. Stroke, An Introduction to Coherent Optics and Holography (Academic, New York, 1966).

J. B. DeVelis, G. O. Reynolds, Theory and Application of Holography (Addison-Wesley, Reading, MA, 1967).

H. J. Caufield, S. Lu, The Applications of Holography (Wiley-Interscience, New York, 1970).

B. P. Hildebrand, B. B. Brenden, An Introduction to Acoustical Holography (Plenum, New York, 1972).

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Figures (4)

Fig. 1
Fig. 1

Schema of computer generated holography.

Fig. 2
Fig. 2

Typical cell in a binary hologram. Position indices are n and m. Width is Cδν, height Wnmδν, and lateral displacement from the cell center is Pnmδν.

Fig. 3
Fig. 3

Optical setup for reconstruction with a point source (SOU) at x0. HOLO, IMG, and FREQ are, respectively, the hologram, image, and frequency planes.

Fig. 4
Fig. 4

Number of CGH papers published per year.

Tables (1)

Tables Icon

Table I Number of Papers on Each Application Area per Year

Equations (16)

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

h ( x , y ) = const . u ( x , y ) .
h ( x , y ) = rect ( x / Δ x ) rect ( y / Δ y ) H ( ν x , ν y ) E [ ( x + x 0 ) ν x + y ν y ] d ν x d ν y ,
N 2 = ( Δ x Δ y ) / ( δ x ) 2 = ( Δ x Δ y ) ( Δ ν ) 2 .
( Δ ν / δ ν ) 2 ( Δ x / δ x ) 2 = ( Δ x Δ ν ) 2 .
H ( ν x , ν y ) = n m rect { [ ν x ( n + P n m ) δ ν ] / c δ ν } × rect [ ( ν y m δ ν ) / W n m δ ν ] .
h = H ( ν x , ν y ) E [ ( x + x 0 ) ν x + y ν y ] d ν x d ν y = c ( δ ν ) 2 sinc [ c δ ν ( x + x 0 ) ] W n m
× sinc ( y W n m δ ν ) E { δ ν [ ( x + x 0 ) ( n + P n m ) + y m ] } .
u ( x , y ) = u ( ν x , ν y ) E ( x ν x + y ν y ) d ν x d ν y .
u = n m u ( n / Δ x , m / Δ x ) × sinc ( ν x Δ x n ) sinc ( ν y Δ x m ) .
u ( x , y ) = rect ( x / Δ x ) × rect ( y / Δ x ) n m u ( n δ ν , m δ ) E [ δ ν ( x n + y m ) ] .
( δ ν ) 2 W n m E [ x 0 δ ν ( n + P n m ) ] const . u ( n δ ν , m δ ν ) ,
W n m A n m ; P n m + n ϕ n m / 2 π x 0 δ ν .
P n m ϕ n m / 2 π M .
sinc [ c δ ν ( x + x 0 ) ] constant in | x | x / 2 ;
sinc ( y W n m δ ν ) 1 in y ( Δ x / 2 ) ;
E ( x P n m δ ν ) 1 in | x | Δ x / 2 .

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