Abstract

The modulation transfer function characteristics of image-plane holographic stereograms are calculated, and the behavior of the modulation transfer function with respect to factors such as image depth, resolution, and perspective window size is described. The expression for the modulation transfer function is then used to determine the optimum stereogram parameters, and it is shown how this approach can lead to significant computational economies in the display of three-dimensional data.

© 1994 Optical Society of America

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  1. E. Leith, J. Utpatnieks, K. Hildebrand, K. Haines, “Requirements for a wave-front reconstruction television facsimile system,” J. SMPTE 74, 893–896 (1965).
    [Crossref]
  2. C. B. Burckhardt, L. H. Enloe, “Television transmission of holograms with reduced resolution requirements on the camera tube,” Bell Sys. Tech. J. 3, 1529–1535 (1969).
  3. L. H. Enloe, J. A. Murphy, C. B. Rubinstein, “Hologram transmission via television,” Bell Sys. Tech. J. 1, 335–339 (1966).
  4. 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]
  5. G. Tricoles, “Computer-generated holograms: a historical review,” Appl. Opt. 26, 4351–4360 (1987).
    [Crossref] [PubMed]
  6. W. H. Lee, “Computer-generated holograms: techniques and applications,” Prog. Opt. 16, 119–232 (1978).
    [Crossref]
  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).
  8. S. A. Benton, “Experiments in holographic video,” in Holography, P. Greguss, ed., Proc. Soc. Photo-Opt. Instrum. Eng.IS08, 247–267 (1991).
  9. P. St Hilaire, S. A. Benton, M. Lucente, J. S. 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).
  10. J. D. Redman, “Three-dimensional reconstruction of people and outdoor scenes using holographic multiplexing,” J. Sci. Instrum. 8, 1740–1746 (1969).
  11. M. C. King, A. M. Noll, D. H. Berry, “A new approach to computer-generated holography,” Appl. Opt. 9, 471–475 (1970).
    [Crossref] [PubMed]
  12. D. J. De Bitetto, “Holographic panoramic stereograms synthesized from white light recordings,” Appl. Opt. 8, 1740–1741 (1969).
    [Crossref]
  13. S. A. Benton, “Achromatic holographic stereograms,” J. Opt. Soc. Am. 71, 1568 (1981).
  14. L. Huff, R. L. Fusek, “Color holographic stereograms,” Opt. Eng. 19, 691–695 (1980).
  15. J. L. Walker, S. A. Benton, “In situ swelling for holographic color control,” in Practical Holography III, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1051, 192–199 (1989).
  16. S. A. Benton, “Survey of holographic stereograms,” in Processing and Display of Three-Dimensional Data, J. J. Pearson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.367, 254–261 (1982).
  17. I. Glaser, A. A. Friesem, “Imaging properties of holographic stereograms,” Three-Dimensional Imaging, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.120, 150–162 (1977).
  18. M. W. Halle, S. A. Benton, M. A. Klug, J. S. Underkoffler, “The ultragram: a generalized holographic stereogram,” in Practical Holography V, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1461, 142–155 (1991).
  19. M. W. Hale, “The generalized holographic stereogram,” M.S. thesis (Massachusetts Institute of Technology, Cambridge, Mass., 1991).
  20. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 101–133.

1987 (1)

1981 (1)

S. A. Benton, “Achromatic holographic stereograms,” J. Opt. Soc. Am. 71, 1568 (1981).

1980 (1)

L. Huff, R. L. Fusek, “Color holographic stereograms,” Opt. Eng. 19, 691–695 (1980).

1978 (1)

W. H. Lee, “Computer-generated holograms: techniques and applications,” Prog. Opt. 16, 119–232 (1978).
[Crossref]

1970 (1)

1969 (3)

D. J. De Bitetto, “Holographic panoramic stereograms synthesized from white light recordings,” Appl. Opt. 8, 1740–1741 (1969).
[Crossref]

J. D. Redman, “Three-dimensional reconstruction of people and outdoor scenes using holographic multiplexing,” J. Sci. Instrum. 8, 1740–1746 (1969).

C. B. Burckhardt, L. H. Enloe, “Television transmission of holograms with reduced resolution requirements on the camera tube,” Bell Sys. Tech. J. 3, 1529–1535 (1969).

1966 (1)

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

1965 (1)

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

Benton, S. A.

S. A. Benton, “Achromatic holographic stereograms,” J. Opt. Soc. Am. 71, 1568 (1981).

J. L. Walker, S. A. Benton, “In situ swelling for holographic color control,” in Practical Holography III, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1051, 192–199 (1989).

S. A. Benton, “Survey of holographic stereograms,” in Processing and Display of Three-Dimensional Data, J. J. Pearson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.367, 254–261 (1982).

P. St Hilaire, S. A. Benton, M. Lucente, J. S. 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, “Experiments in holographic video,” in Holography, P. Greguss, ed., Proc. Soc. Photo-Opt. Instrum. Eng.IS08, 247–267 (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).

M. W. Halle, S. A. Benton, M. A. Klug, J. S. Underkoffler, “The ultragram: a generalized holographic stereogram,” in Practical Holography V, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1461, 142–155 (1991).

Berry, D. H.

Burckhardt, C. B.

C. B. Burckhardt, L. H. Enloe, “Television transmission of holograms with reduced resolution requirements on the camera tube,” Bell Sys. Tech. J. 3, 1529–1535 (1969).

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]

De Bitetto, D. J.

Enloe, L. H.

C. B. Burckhardt, L. H. Enloe, “Television transmission of holograms with reduced resolution requirements on the camera tube,” Bell Sys. Tech. J. 3, 1529–1535 (1969).

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

Friesem, A. A.

I. Glaser, A. A. Friesem, “Imaging properties of holographic stereograms,” Three-Dimensional Imaging, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.120, 150–162 (1977).

Fusek, R. L.

L. Huff, R. L. Fusek, “Color holographic stereograms,” Opt. Eng. 19, 691–695 (1980).

Glaser, I.

I. Glaser, A. A. Friesem, “Imaging properties of holographic stereograms,” Three-Dimensional Imaging, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.120, 150–162 (1977).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 101–133.

Haines, K.

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

Hale, M. W.

M. W. Hale, “The generalized holographic stereogram,” M.S. thesis (Massachusetts Institute of Technology, Cambridge, Mass., 1991).

Halle, M. W.

M. W. Halle, S. A. Benton, M. A. Klug, J. S. Underkoffler, “The ultragram: a generalized holographic stereogram,” in Practical Holography V, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1461, 142–155 (1991).

Hildebrand, K.

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

Huff, L.

L. Huff, R. L. Fusek, “Color holographic stereograms,” Opt. Eng. 19, 691–695 (1980).

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).

King, M. C.

Klug, M. A.

M. W. Halle, S. A. Benton, M. A. Klug, J. S. Underkoffler, “The ultragram: a generalized holographic stereogram,” in Practical Holography V, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1461, 142–155 (1991).

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).

Lee, W. H.

W. H. Lee, “Computer-generated holograms: techniques and applications,” Prog. Opt. 16, 119–232 (1978).
[Crossref]

Leith, E.

E. Leith, J. Utpatnieks, K. Hildebrand, K. Haines, “Requirements for a wave-front 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).

P. St Hilaire, S. A. Benton, M. Lucente, J. S. 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).

Murphy, J. A.

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

Noll, A. M.

Redman, J. D.

J. D. Redman, “Three-dimensional reconstruction of people and outdoor scenes using holographic multiplexing,” J. Sci. Instrum. 8, 1740–1746 (1969).

Rubinstein, C. B.

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

St Hilaire, P.

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).

P. St Hilaire, S. A. Benton, M. Lucente, J. S. 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).

Tricoles, G.

Underkoffler, J. S.

P. St Hilaire, S. A. Benton, M. Lucente, J. S. 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).

M. W. Halle, S. A. Benton, M. A. Klug, J. S. Underkoffler, “The ultragram: a generalized holographic stereogram,” in Practical Holography V, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1461, 142–155 (1991).

Utpatnieks, J.

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

Walker, J. L.

J. L. Walker, S. A. Benton, “In situ swelling for holographic color control,” in Practical Holography III, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1051, 192–199 (1989).

Yoshikawa, H.

P. St Hilaire, S. A. Benton, M. Lucente, J. S. 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).

Appl. Opt. (3)

Bell Sys. Tech. J. (2)

C. B. Burckhardt, L. H. Enloe, “Television transmission of holograms with reduced resolution requirements on the camera tube,” Bell Sys. Tech. J. 3, 1529–1535 (1969).

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

J. Opt. Soc. Am. (1)

S. A. Benton, “Achromatic holographic stereograms,” J. Opt. Soc. Am. 71, 1568 (1981).

J. Sci. Instrum. (1)

J. D. Redman, “Three-dimensional reconstruction of people and outdoor scenes using holographic multiplexing,” J. Sci. Instrum. 8, 1740–1746 (1969).

J. SMPTE (1)

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

Opt. Eng. (1)

L. Huff, R. L. Fusek, “Color holographic stereograms,” Opt. Eng. 19, 691–695 (1980).

Prog. Opt. (1)

W. H. Lee, “Computer-generated holograms: techniques and applications,” Prog. Opt. 16, 119–232 (1978).
[Crossref]

Other (10)

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).

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

P. St Hilaire, S. A. Benton, M. Lucente, J. S. 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).

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]

J. L. Walker, S. A. Benton, “In situ swelling for holographic color control,” in Practical Holography III, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1051, 192–199 (1989).

S. A. Benton, “Survey of holographic stereograms,” in Processing and Display of Three-Dimensional Data, J. J. Pearson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.367, 254–261 (1982).

I. Glaser, A. A. Friesem, “Imaging properties of holographic stereograms,” Three-Dimensional Imaging, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.120, 150–162 (1977).

M. W. Halle, S. A. Benton, M. A. Klug, J. S. Underkoffler, “The ultragram: a generalized holographic stereogram,” in Practical Holography V, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1461, 142–155 (1991).

M. W. Hale, “The generalized holographic stereogram,” M.S. thesis (Massachusetts Institute of Technology, Cambridge, Mass., 1991).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 101–133.

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Figures (4)

Fig. 1
Fig. 1

Wave-front curvature error with respect to the original scene depth. The z-axis origin is at the slit plane: r1, r1, radii of curvature.

Fig. 2
Fig. 2

Apparent motion of a point on the stereogram plane as the observer moves laterally along the slit plane.

Fig. 3
Fig. 3

(a) Plot of the MTF with respect ion spatial frequency with the image parameters given in Subsection 4.B. (b) Contour plot of (a). The contour lines along the [1, 0] interval.

Fig. 4
Fig. 4

MTF versus slit size for a 2 cycles/mm spatial frequency and the parameters given in Subsection 4.B.

Equations (21)

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Δ x image = D viewer - D point D point l ,
H ( f x ) = - H ( ξ - f x 2 ) H * ( ξ + f x 2 ) d ξ - H ( ξ ) 2 d ξ .
P ( λ d i f x ) = P ( λ d i f x ) exp [ j k W ( λ d i f x ) ] ,
H ( f x ) = - P ( ξ - λ d i f x 2 ) P ( ξ + λ d i f x 2 ) exp { j k [ W ( ξ - λ d i f x 2 ) - W ( ξ + λ d i f x 2 ) ] } d ξ - P 2 ( ξ ) d ξ ,
r 1 z 1 + 1 2 z 1 ( x - x 0 ) 2 , r s z s + 1 2 z s ( x - x 0 ) 2 ,
r 1 - r s ( z 1 - z s ) + ( z s - z 1 ) 2 z 1 z s ( x - x 0 ) 2 .
P ( λ d i f x ) = rect ( λ d i f x l ) exp [ j k ( z 1 - z s ) ] × exp [ j k ( z s - z 1 ) 2 z 1 z s ( λ d i f x - λ d i f 0 ) 2 ] ,
P ( λ d i f x ) = rect ( λ d i f x l ) exp [ j k ( z s - z 1 ) 2 z 1 z s ( λ d i f x ) 2 ] .
H ( f x ) = Λ ( λ d i f x l ) sinc [ ( z s - z 1 ) z 1 z s ( l d i f x ) ( 1 - λ d i f x l ) ] ,
Λ ( x ) = { 1 - x x 1 0 otherwise .
H s ( f x s ) = H ( M f x s ) = H ( z s d i f x s ) = Λ ( λ z s f x s l ) × sinc [ ( z s - z 1 ) z 1 z s ( l z s f x s ) ( 1 - λ z s f x s l ) ] .
P ( λ d i f x ) = exp [ - α ( λ d i f x l ) 2 ] exp [ j k ( z s - z 1 ) 2 z 1 z s ( λ d i f x ) 2 ] .
l < 2 ( λ z 1 z s z s - z 1 ) 1 / 2 .
f x s = l λ z s
1 f max 0 f max H s ( f x s ) d f x s
d d l [ 0 f max H s ( f x s ) d f x s ] = 0
N s = 2 f x L s ,
N p = L p l opt ,
N = N s N p = 2 f x L s L p l opt .
N = 2 L s sin θ λ ,
L s = 250 mm , L p = 500 mm , f max = 2 cycles / mm , z s = 600 mm , z max = 100 mm , λ = 520 nm .

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