Abstract

We describe an electro-optic apparatus capable of displaying a computer-generated hologram in real time. The computer-generated hologram is calculated by a supercomputer, read from a fast frame buffer, and transmitted to a wide-bandwidth acousto-optic modulator. Coherent light is modulated by the acousto-optic modulator and optically processed to produce a three-dimensional image with horizontal parallax. We evaluate different display geometries and their effect on the optical parameters of the system. We then show how the display resolution can be increased by simultaneously writing three acoustic columns on a single crystal and optically multiplexing the resulting holograms. We finally describe some improvements that follow from the analysis.

© 1992 Optical Society of America

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References

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  1. W. J. Dallas, “Computer generated holograms,” in The Computer in Optical Research, B. R. Frieden, ed., Vol. 41 of Springer Series in Applied Physics (Springer-Verlag, Berlin, 1980), pp. 291–366.
    [CrossRef]
  2. G. Tricoles, “Computer generated holograms: a historical review,” Appl. Opt. 26, 4351–4360 (1987).
    [CrossRef] [PubMed]
  3. E. Leith, J. Utpatnieks, K. Hildebrand, K. Haines, “Requirements for a wavefront reconstruction television facsimile system,” J. SMPTE 74, 893–896 (1965).
    [CrossRef]
  4. L. H. Enloe, J. A. Murphy, C. B. Rubinstein, “Hologram transmission via television,” Bell Syst. Tech. J. 1, 335–339 (1966).
  5. C. B. Burckhardt, L. H. Enloe, “Television transmission of holograms with reduced resolution requirements on the camera tube,” Bell Syst. Tech. J. 4, 1529–1535 (1969).
  6. S. A. Benton, “The mathematical optics of white light transmission holograms,” presented at the First International Symposium on Display Holography, Lake Forest College, Lake Forest, Ill. (1982).
  7. P. St. Hilaire, S. A. Benton, M. Lucente, M. L. Jepsen, J. Kollin, H. Yoshikawa, “Electronic display system for computational holography,” in “Practical Holography IV,” S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1212, 174–182 (1990).
    [CrossRef]
  8. S. A. Benton, “Experiments in holographic video,” in Holography, P. Greguss, T. H. Jeong, eds., Proc. Soc. Photo-Opt. Instrum. Eng.IS08, 247–267 (1991).
  9. L. M. Myers, “The Scophony system: an analysis of its possibilities,” TV Shortwave World (1936), pp. 201–294.
  10. A. Korpel, R. Adler, P. Desmares, W. Watson, “A television display using acoustic deflection and modulation of coherent light,” Appl. Opt. 5, 1667–1682 (1966).
    [CrossRef] [PubMed]
  11. M. Lucente, “Optimization of hologram computation for real time display” in Practical Holography VI, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1667(to be published).
  12. A. Goutzoulis, I. Abramovitz, “Digital electronics meets its match,” IEEE Spectrum 25(8), 21–25 (1988).
    [CrossRef]
  13. N. J. Berg, J. N. Lee, eds., Acousto-Optic Signal Processing Theory and Implementation, Vol. 2 of Optical Engineering Series (Dekker, New York, 1983).
  14. L. Beiser, “Laser scanning systems,” in Laser Applications (Academic, San Diego, Calif., 1974), Vol. 2, pp. 53–155.
  15. I. C. Chang, “Acoustooptic devices and applications,”IEEE Trans. Sonics Ultrason. SU-23, 2–22 (1976).
    [CrossRef]
  16. A. Korpel, “Acousto-optics—a review of fundamentals,” Proc. IEEE 69, 48–53 (1981).
    [CrossRef]
  17. R. E. Hopkins, M. J. Buzawa, “Optics for laser scanning,” Opt. Eng. 15, 90–94 (1976).
    [CrossRef]
  18. P. St. Hilaire, S. A. Benton, M. Lucente, J. Underkoffler, H. Yoshikawa, “Real-time holographic display: improvements using a multichannel acousto-optic modulator and holographic optical elements,” in Practical Holography V, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1461, 254–261 (1991).
  19. L. Bademian, “Parallel-channel acousto-optic modulation,” Opt. Eng. 25, 303–308 (1986).
    [CrossRef]
  20. A. VanderLugt, G. S. Moore, S. S. Mathe, “Multichannel Bragg cells: compensation for acoustic spreading,” Appl. Opt. 22, 3906–3912 (1983).
    [CrossRef] [PubMed]

1988 (1)

A. Goutzoulis, I. Abramovitz, “Digital electronics meets its match,” IEEE Spectrum 25(8), 21–25 (1988).
[CrossRef]

1987 (1)

1986 (1)

L. Bademian, “Parallel-channel acousto-optic modulation,” Opt. Eng. 25, 303–308 (1986).
[CrossRef]

1983 (1)

1981 (1)

A. Korpel, “Acousto-optics—a review of fundamentals,” Proc. IEEE 69, 48–53 (1981).
[CrossRef]

1976 (2)

R. E. Hopkins, M. J. Buzawa, “Optics for laser scanning,” Opt. Eng. 15, 90–94 (1976).
[CrossRef]

I. C. Chang, “Acoustooptic devices and applications,”IEEE Trans. Sonics Ultrason. SU-23, 2–22 (1976).
[CrossRef]

1969 (1)

C. B. Burckhardt, L. H. Enloe, “Television transmission of holograms with reduced resolution requirements on the camera tube,” Bell Syst. Tech. J. 4, 1529–1535 (1969).

1966 (2)

L. H. Enloe, J. A. Murphy, C. B. Rubinstein, “Hologram transmission via television,” Bell Syst. Tech. J. 1, 335–339 (1966).

A. Korpel, R. Adler, P. Desmares, W. Watson, “A television display using acoustic deflection and modulation of coherent light,” Appl. Opt. 5, 1667–1682 (1966).
[CrossRef] [PubMed]

1965 (1)

E. Leith, J. Utpatnieks, K. Hildebrand, K. Haines, “Requirements for a wavefront reconstruction television facsimile system,” J. SMPTE 74, 893–896 (1965).
[CrossRef]

1936 (1)

L. M. Myers, “The Scophony system: an analysis of its possibilities,” TV Shortwave World (1936), pp. 201–294.

Abramovitz, I.

A. Goutzoulis, I. Abramovitz, “Digital electronics meets its match,” IEEE Spectrum 25(8), 21–25 (1988).
[CrossRef]

Adler, R.

Bademian, L.

L. Bademian, “Parallel-channel acousto-optic modulation,” Opt. Eng. 25, 303–308 (1986).
[CrossRef]

Beiser, L.

L. Beiser, “Laser scanning systems,” in Laser Applications (Academic, San Diego, Calif., 1974), Vol. 2, pp. 53–155.

Benton, S. A.

S. A. Benton, “Experiments in holographic video,” in Holography, P. Greguss, T. H. Jeong, eds., Proc. Soc. Photo-Opt. Instrum. Eng.IS08, 247–267 (1991).

P. St. Hilaire, S. A. Benton, M. Lucente, J. Underkoffler, H. Yoshikawa, “Real-time holographic display: improvements using a multichannel acousto-optic modulator and holographic optical elements,” in Practical Holography V, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1461, 254–261 (1991).

S. A. Benton, “The mathematical optics of white light transmission holograms,” presented at the First International Symposium on Display Holography, Lake Forest College, Lake Forest, Ill. (1982).

P. St. Hilaire, S. A. Benton, M. Lucente, M. L. Jepsen, J. Kollin, H. Yoshikawa, “Electronic display system for computational holography,” in “Practical Holography IV,” S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1212, 174–182 (1990).
[CrossRef]

Burckhardt, C. B.

C. B. Burckhardt, L. H. Enloe, “Television transmission of holograms with reduced resolution requirements on the camera tube,” Bell Syst. Tech. J. 4, 1529–1535 (1969).

Buzawa, M. J.

R. E. Hopkins, M. J. Buzawa, “Optics for laser scanning,” Opt. Eng. 15, 90–94 (1976).
[CrossRef]

Chang, I. C.

I. C. Chang, “Acoustooptic devices and applications,”IEEE Trans. Sonics Ultrason. SU-23, 2–22 (1976).
[CrossRef]

Dallas, W. J.

W. J. Dallas, “Computer generated holograms,” in The Computer in Optical Research, B. R. Frieden, ed., Vol. 41 of Springer Series in Applied Physics (Springer-Verlag, Berlin, 1980), pp. 291–366.
[CrossRef]

Desmares, P.

Enloe, L. H.

C. B. Burckhardt, L. H. Enloe, “Television transmission of holograms with reduced resolution requirements on the camera tube,” Bell Syst. Tech. J. 4, 1529–1535 (1969).

L. H. Enloe, J. A. Murphy, C. B. Rubinstein, “Hologram transmission via television,” Bell Syst. Tech. J. 1, 335–339 (1966).

Goutzoulis, A.

A. Goutzoulis, I. Abramovitz, “Digital electronics meets its match,” IEEE Spectrum 25(8), 21–25 (1988).
[CrossRef]

Haines, K.

E. Leith, J. Utpatnieks, K. Hildebrand, K. Haines, “Requirements for a wavefront reconstruction television facsimile system,” J. SMPTE 74, 893–896 (1965).
[CrossRef]

Hilaire, P. St.

P. St. Hilaire, S. A. Benton, M. Lucente, M. L. Jepsen, J. Kollin, H. Yoshikawa, “Electronic display system for computational holography,” in “Practical Holography IV,” S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1212, 174–182 (1990).
[CrossRef]

P. St. Hilaire, S. A. Benton, M. Lucente, J. Underkoffler, H. Yoshikawa, “Real-time holographic display: improvements using a multichannel acousto-optic modulator and holographic optical elements,” in Practical Holography V, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1461, 254–261 (1991).

Hildebrand, K.

E. Leith, J. Utpatnieks, K. Hildebrand, K. Haines, “Requirements for a wavefront reconstruction television facsimile system,” J. SMPTE 74, 893–896 (1965).
[CrossRef]

Hopkins, R. E.

R. E. Hopkins, M. J. Buzawa, “Optics for laser scanning,” Opt. Eng. 15, 90–94 (1976).
[CrossRef]

Jepsen, M. L.

P. St. Hilaire, S. A. Benton, M. Lucente, M. L. Jepsen, J. Kollin, H. Yoshikawa, “Electronic display system for computational holography,” in “Practical Holography IV,” S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1212, 174–182 (1990).
[CrossRef]

Kollin, J.

P. St. Hilaire, S. A. Benton, M. Lucente, M. L. Jepsen, J. Kollin, H. Yoshikawa, “Electronic display system for computational holography,” in “Practical Holography IV,” S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1212, 174–182 (1990).
[CrossRef]

Korpel, A.

Leith, E.

E. Leith, J. Utpatnieks, K. Hildebrand, K. Haines, “Requirements for a wavefront reconstruction television facsimile system,” J. SMPTE 74, 893–896 (1965).
[CrossRef]

Lucente, M.

P. St. Hilaire, S. A. Benton, M. Lucente, M. L. Jepsen, J. Kollin, H. Yoshikawa, “Electronic display system for computational holography,” in “Practical Holography IV,” S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1212, 174–182 (1990).
[CrossRef]

M. Lucente, “Optimization of hologram computation for real time display” in Practical Holography VI, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1667(to be published).

P. St. Hilaire, S. A. Benton, M. Lucente, J. Underkoffler, H. Yoshikawa, “Real-time holographic display: improvements using a multichannel acousto-optic modulator and holographic optical elements,” in Practical Holography V, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1461, 254–261 (1991).

Mathe, S. S.

Moore, G. S.

Murphy, J. A.

L. H. Enloe, J. A. Murphy, C. B. Rubinstein, “Hologram transmission via television,” Bell Syst. Tech. J. 1, 335–339 (1966).

Myers, L. M.

L. M. Myers, “The Scophony system: an analysis of its possibilities,” TV Shortwave World (1936), pp. 201–294.

Rubinstein, C. B.

L. H. Enloe, J. A. Murphy, C. B. Rubinstein, “Hologram transmission via television,” Bell Syst. Tech. J. 1, 335–339 (1966).

Tricoles, G.

Underkoffler, J.

P. St. Hilaire, S. A. Benton, M. Lucente, J. Underkoffler, H. Yoshikawa, “Real-time holographic display: improvements using a multichannel acousto-optic modulator and holographic optical elements,” in Practical Holography V, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1461, 254–261 (1991).

Utpatnieks, J.

E. Leith, J. Utpatnieks, K. Hildebrand, K. Haines, “Requirements for a wavefront reconstruction television facsimile system,” J. SMPTE 74, 893–896 (1965).
[CrossRef]

VanderLugt, A.

Watson, W.

Yoshikawa, H.

P. St. Hilaire, S. A. Benton, M. Lucente, J. Underkoffler, H. Yoshikawa, “Real-time holographic display: improvements using a multichannel acousto-optic modulator and holographic optical elements,” in Practical Holography V, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1461, 254–261 (1991).

P. St. Hilaire, S. A. Benton, M. Lucente, M. L. Jepsen, J. Kollin, H. Yoshikawa, “Electronic display system for computational holography,” in “Practical Holography IV,” S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1212, 174–182 (1990).
[CrossRef]

Appl. Opt. (3)

Bell Syst. Tech. J. (2)

L. H. Enloe, J. A. Murphy, C. B. Rubinstein, “Hologram transmission via television,” Bell Syst. Tech. J. 1, 335–339 (1966).

C. B. Burckhardt, L. H. Enloe, “Television transmission of holograms with reduced resolution requirements on the camera tube,” Bell Syst. Tech. J. 4, 1529–1535 (1969).

IEEE Spectrum (1)

A. Goutzoulis, I. Abramovitz, “Digital electronics meets its match,” IEEE Spectrum 25(8), 21–25 (1988).
[CrossRef]

IEEE Trans. Sonics Ultrason. (1)

I. C. Chang, “Acoustooptic devices and applications,”IEEE Trans. Sonics Ultrason. SU-23, 2–22 (1976).
[CrossRef]

J. SMPTE (1)

E. Leith, J. Utpatnieks, K. Hildebrand, K. Haines, “Requirements for a wavefront reconstruction television facsimile system,” J. SMPTE 74, 893–896 (1965).
[CrossRef]

Opt. Eng. (2)

R. E. Hopkins, M. J. Buzawa, “Optics for laser scanning,” Opt. Eng. 15, 90–94 (1976).
[CrossRef]

L. Bademian, “Parallel-channel acousto-optic modulation,” Opt. Eng. 25, 303–308 (1986).
[CrossRef]

Proc. IEEE (1)

A. Korpel, “Acousto-optics—a review of fundamentals,” Proc. IEEE 69, 48–53 (1981).
[CrossRef]

TV Shortwave World (1)

L. M. Myers, “The Scophony system: an analysis of its possibilities,” TV Shortwave World (1936), pp. 201–294.

Other (8)

W. J. Dallas, “Computer generated holograms,” in The Computer in Optical Research, B. R. Frieden, ed., Vol. 41 of Springer Series in Applied Physics (Springer-Verlag, Berlin, 1980), pp. 291–366.
[CrossRef]

S. A. Benton, “The mathematical optics of white light transmission holograms,” presented at the First International Symposium on Display Holography, Lake Forest College, Lake Forest, Ill. (1982).

P. St. Hilaire, S. A. Benton, M. Lucente, M. L. Jepsen, J. Kollin, H. Yoshikawa, “Electronic display system for computational holography,” in “Practical Holography IV,” S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1212, 174–182 (1990).
[CrossRef]

S. A. Benton, “Experiments in holographic video,” in Holography, P. Greguss, T. H. Jeong, eds., Proc. Soc. Photo-Opt. Instrum. Eng.IS08, 247–267 (1991).

P. St. Hilaire, S. A. Benton, M. Lucente, J. Underkoffler, H. Yoshikawa, “Real-time holographic display: improvements using a multichannel acousto-optic modulator and holographic optical elements,” in Practical Holography V, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1461, 254–261 (1991).

N. J. Berg, J. N. Lee, eds., Acousto-Optic Signal Processing Theory and Implementation, Vol. 2 of Optical Engineering Series (Dekker, New York, 1983).

L. Beiser, “Laser scanning systems,” in Laser Applications (Academic, San Diego, Calif., 1974), Vol. 2, pp. 53–155.

M. Lucente, “Optimization of hologram computation for real time display” in Practical Holography VI, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1667(to be published).

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Figures (11)

Fig. 1
Fig. 1

Schematic view of the MIT electronic holography display.

Fig. 2
Fig. 2

Holographic display signal processing: D/A, digital-to-analog.

Fig. 3
Fig. 3

Hologram geometry for the computation of a single point. θ is the simulated reference beam angle. The fringe pattern is sampled at the hologram plane.

Fig. 4
Fig. 4

Horizontal scanning geometry for the focal scanning case. The vertical scanning optics are not shown for clarity. L1 is a cylindrical lens.

Fig. 5
Fig. 5

Horizontal scanning geometry for the nonfocal scanning case. P0 is the virtual image created by the fringe pattern on the AOM.

Fig. 6
Fig. 6

Apertured modulator.

Fig. 7
Fig. 7

Display resolution time dependence for a stationary observer. The diffracted rays are vignetted by the observer’s pupil during intervals t1t2 and t3t4.

Fig. 8
Fig. 8

Vertical scanning geometry for a single-channel AOM. The output lens L2 is the same as in Figs. 4 and 5. L3 and L4 are cylindrical.

Fig. 9
Fig. 9

Three-channel AOM and holographic beam multiplexer.

Fig. 10
Fig. 10

Vertical scanning geometry for a three-channel AOM.

Fig. 11
Fig. 11

Shaded image displayed by the MIT system.

Equations (35)

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

f h λ = sin θ ,
f s = 2 f h ,
N = d f s = 2 d sin θ λ .
N t = l N s = 2 d l sin θ λ .
N t = 4 d w sin 2 θ λ 2 .
λ sound = v s / F .
ω = - 1 2 d θ d t = - v s 2 f 1 ,
ω = 2 π N τ ,
f 1 = v s N τ 4 π .
K = 1 / M = f 1 / f 2 ,
M l = M t 2 = ( f 2 / f 1 ) 2 .
f 1 / f 2 = λ sound / λ fringe ,
1 / f 1 = 1 / d 0 + 1 / d i .
v i = M t l v s = - v s ( d i - f 1 ) f 1 ,
v i 2 ω = D - d i ,
f 1 v s 2 ω + D ( d 0 - f 1 ) - f 1 d 0 = 0.
Δ f s = Δ ν v s ,
Δ x = λ D Δ f s = λ D Δ ν v s ,
Δ x = N τ λ Δ ν 4 π .
N res = W θ a λ ,
W θ λ τ Δ ν ,
Δ x θ λ τ a Δ ν ,
τ a = τ - τ r
θ eff = 4 π N - 4 tan - 1 ( Δ x 2 R ) ,
4 π N - 4 tan - 1 ( Δ x 2 R ) - λ τ a Δ ν Δ x 0.
4 π N - 2 Δ x R - λ τ a Δ ν Δ x 0.
τ r - ( τ a + τ r ) 2 λ N 2 Δ ν 8 π 2 R 0.
k τ r 2 + ( 2 k τ a - 1 ) τ r + k τ a 2 0 ,
k = λ N 2 Δ ν 8 π 2 R .
1 - 4 k τ a 0 ,
R λ N 2 τ a Δ ν 2 π 2 .
τ r = τ a .
P = 2 f 2 tan ( θ eff 2 ) + Δ x .
z 1 S < z 2 s ,
S > Δ z s M ( z obs - Δ z ) ,

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