Abstract

The use of computer-generated holograms to display three-dimensional images is suggested. To simplify the calculation of the hologram, the parallax in the vertical direction is eliminated where a projection of the object onto the hologram plane is performed. The synthesis of the horizontal parallax involves one-dimensional transforms. This procedure reduces computer-memory requirements and permits a high-speed generation.

© 1986 Optical Society of America

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References

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  1. T. Okoshi, “Three-dimensional displays,” Proc. IEEE 68, 548–564 (1980).
    [CrossRef]
  2. T. Okoshi, Three-Dimensional Imaging Techniques (Academic, New York, 1976).
  3. O. Bryngdahl, A. Lohmann, “One-dimensional holography with spatially incoherent light,” J. Opt. Soc. Am. 58, 625–628 (1968).
    [CrossRef]
  4. L. H. Lin, “A method of hologram information reduction by spatial frequency sampling,” Appl. Opt. 7, 545–548 (1968).
    [CrossRef] [PubMed]
  5. D. J. de Bitetto, “Bandwidth reduction of hologram transmission systems by elimination of vertical parallax,” Appl. Phys. Lett. 12, 176–178 (1968).
    [CrossRef]
  6. N. George, J. T. McCrickered, “Holography and stereoscopy: the holographic stereogram,” Photogr. Sci. Eng. 13, 342–350 (1969).
  7. D. J. de Bitetto, “Transmission bandwidth reduction of holographic stereograms recorded in white light,” Appi. Phys. Lett. 12, 343–344 (1968).
    [CrossRef]
  8. S. A. Benton, “Survey of holographic stereograms,” Proc. Soc. Photo-Opt. Instrum. Eng. 367, 15–19 (1982).
  9. M. C. King, A. M. Noll, D. H. Berry, “A new approach to computer-generated holography,” Appl. Opt. 9, 471–475 (1970).
    [CrossRef] [PubMed]
  10. L. P. Yaroslavskii, N. S. Mearzlyakov, Methods of Digital Holography (Plenum, New York, 1980).
  11. T. Yatagai, “Stereoscopic approach to 3-D display using computer-generated holograms,” Appl. Opt. 15, 2722–2729 (1976).
    [CrossRef] [PubMed]
  12. S. A. Benton, “Hologram reconstruction with extended incoherent sources,” J. Opt. Soc. Am. 59, 1545 (A) (1969).
  13. D. Leseberg, O. Bryngdahl, “Computer-generated rainbow holograms,” Appl. Opt. 23, 2441–2447 (1984).
    [CrossRef] [PubMed]
  14. J. W. Goodman, An Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  15. A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968).
  16. J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978).
  17. D. Schreier, Synthetische Holografie (Physik-Verlag, Weinheim, 1984).
  18. W.-H. Lee, “Computer-generated holograms: techniques and applications,” in Progress in Optics 16, E. Wolf, ed. (North-Holland, Amsterdam, 1978), pp. 119–232.
    [CrossRef]
  19. W. J. Dallas, “Computer-generated holograms,” in The Computer in Optical Research, B. R. Frieden, ed., (Springer-Verlag, New York, 1980), pp. 291–366.

1984 (1)

1982 (1)

S. A. Benton, “Survey of holographic stereograms,” Proc. Soc. Photo-Opt. Instrum. Eng. 367, 15–19 (1982).

1980 (1)

T. Okoshi, “Three-dimensional displays,” Proc. IEEE 68, 548–564 (1980).
[CrossRef]

1976 (1)

1970 (1)

1969 (2)

N. George, J. T. McCrickered, “Holography and stereoscopy: the holographic stereogram,” Photogr. Sci. Eng. 13, 342–350 (1969).

S. A. Benton, “Hologram reconstruction with extended incoherent sources,” J. Opt. Soc. Am. 59, 1545 (A) (1969).

1968 (4)

D. J. de Bitetto, “Transmission bandwidth reduction of holographic stereograms recorded in white light,” Appi. Phys. Lett. 12, 343–344 (1968).
[CrossRef]

O. Bryngdahl, A. Lohmann, “One-dimensional holography with spatially incoherent light,” J. Opt. Soc. Am. 58, 625–628 (1968).
[CrossRef]

L. H. Lin, “A method of hologram information reduction by spatial frequency sampling,” Appl. Opt. 7, 545–548 (1968).
[CrossRef] [PubMed]

D. J. de Bitetto, “Bandwidth reduction of hologram transmission systems by elimination of vertical parallax,” Appl. Phys. Lett. 12, 176–178 (1968).
[CrossRef]

Benton, S. A.

S. A. Benton, “Survey of holographic stereograms,” Proc. Soc. Photo-Opt. Instrum. Eng. 367, 15–19 (1982).

S. A. Benton, “Hologram reconstruction with extended incoherent sources,” J. Opt. Soc. Am. 59, 1545 (A) (1969).

Berry, D. H.

Bryngdahl, O.

Dallas, W. J.

W. J. Dallas, “Computer-generated holograms,” in The Computer in Optical Research, B. R. Frieden, ed., (Springer-Verlag, New York, 1980), pp. 291–366.

de Bitetto, D. J.

D. J. de Bitetto, “Bandwidth reduction of hologram transmission systems by elimination of vertical parallax,” Appl. Phys. Lett. 12, 176–178 (1968).
[CrossRef]

D. J. de Bitetto, “Transmission bandwidth reduction of holographic stereograms recorded in white light,” Appi. Phys. Lett. 12, 343–344 (1968).
[CrossRef]

Gaskill, J. D.

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978).

George, N.

N. George, J. T. McCrickered, “Holography and stereoscopy: the holographic stereogram,” Photogr. Sci. Eng. 13, 342–350 (1969).

Goodman, J. W.

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

King, M. C.

Lee, W.-H.

W.-H. Lee, “Computer-generated holograms: techniques and applications,” in Progress in Optics 16, E. Wolf, ed. (North-Holland, Amsterdam, 1978), pp. 119–232.
[CrossRef]

Leseberg, D.

Lin, L. H.

Lohmann, A.

McCrickered, J. T.

N. George, J. T. McCrickered, “Holography and stereoscopy: the holographic stereogram,” Photogr. Sci. Eng. 13, 342–350 (1969).

Mearzlyakov, N. S.

L. P. Yaroslavskii, N. S. Mearzlyakov, Methods of Digital Holography (Plenum, New York, 1980).

Noll, A. M.

Okoshi, T.

T. Okoshi, “Three-dimensional displays,” Proc. IEEE 68, 548–564 (1980).
[CrossRef]

T. Okoshi, Three-Dimensional Imaging Techniques (Academic, New York, 1976).

Papoulis, A.

A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968).

Schreier, D.

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

Yaroslavskii, L. P.

L. P. Yaroslavskii, N. S. Mearzlyakov, Methods of Digital Holography (Plenum, New York, 1980).

Yatagai, T.

Appi. Phys. Lett. (1)

D. J. de Bitetto, “Transmission bandwidth reduction of holographic stereograms recorded in white light,” Appi. Phys. Lett. 12, 343–344 (1968).
[CrossRef]

Appl. Opt. (4)

Appl. Phys. Lett. (1)

D. J. de Bitetto, “Bandwidth reduction of hologram transmission systems by elimination of vertical parallax,” Appl. Phys. Lett. 12, 176–178 (1968).
[CrossRef]

J. Opt. Soc. Am. (2)

O. Bryngdahl, A. Lohmann, “One-dimensional holography with spatially incoherent light,” J. Opt. Soc. Am. 58, 625–628 (1968).
[CrossRef]

S. A. Benton, “Hologram reconstruction with extended incoherent sources,” J. Opt. Soc. Am. 59, 1545 (A) (1969).

Photogr. Sci. Eng. (1)

N. George, J. T. McCrickered, “Holography and stereoscopy: the holographic stereogram,” Photogr. Sci. Eng. 13, 342–350 (1969).

Proc. IEEE (1)

T. Okoshi, “Three-dimensional displays,” Proc. IEEE 68, 548–564 (1980).
[CrossRef]

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

S. A. Benton, “Survey of holographic stereograms,” Proc. Soc. Photo-Opt. Instrum. Eng. 367, 15–19 (1982).

Other (8)

T. Okoshi, Three-Dimensional Imaging Techniques (Academic, New York, 1976).

L. P. Yaroslavskii, N. S. Mearzlyakov, Methods of Digital Holography (Plenum, New York, 1980).

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

A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968).

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978).

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

W.-H. Lee, “Computer-generated holograms: techniques and applications,” in Progress in Optics 16, E. Wolf, ed. (North-Holland, Amsterdam, 1978), pp. 119–232.
[CrossRef]

W. J. Dallas, “Computer-generated holograms,” in The Computer in Optical Research, B. R. Frieden, ed., (Springer-Verlag, New York, 1980), pp. 291–366.

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Figures (7)

Fig. 1
Fig. 1

Anamorphic lens system for generation of 1-D holograms.

Fig. 2
Fig. 2

Display and synthetic recording geometry of 3-D objects.

Fig. 3
Fig. 3

Enlarged portion of the CGH generated by use of 1-D transforms displaying only horizontal parallax.

Fig. 4
Fig. 4

Optical reconstruction of artificial object of 64 × 128 pixels.

Fig. 5
Fig. 5

Optical reconstruction with simplified eye. The principal point of the eye lens can be displaced to (xe, ye, ze).

Fig. 6
Fig. 6

Optical reconstruction of computer-generated rainbow hologram. Two perspective views of a 3-D object are shown; the radii are 5, 11, and 16 pixels.

Fig. 7
Fig. 7

Distortions that are due to eye position at ze instead of at the origin. The object point Pj appears at point Pa.

Equations (6)

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u ( x , y ) = a ( x , y ) exp ( i 2 π x x λ f s ) d x ,
u ( x m , y l ) = j 2 π i λ R j k a j k l exp [ i π λ ( x m x k ) 2 R j ] ,
u ( x m , y l ) = j 2 π i λ R j exp ( i π x m 2 λ R j ) F 1 D d [ a j k l exp ( i π x k 2 λ R j ) ] .
t ( x m , y l ) = B 2 + u m l cos [ ϕ m l + ϕ R ( x m , y l ) ] ,
Δ α α 0 = z e z h z e z j z h z j z e .
Δ α = y e z h z j z h z j .

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