Abstract

We demonstrate, both theoretically and experimentally, that a disk-type multiplex hologram can be fabricated as an image-plane hologram that is suitable for white-light line-source reconstruction. By adopting the method of direct object-image relationship, we build the theory based on the imaging property of lenses and on coordinate transformation. Numerical simulation shows the characteristics of this type of hologram. Experimental results reveal that the picket-fence effect that is encountered in the traditional multiplex hologram for images viewed at various distances has been eliminated. Using a reconstruction white-light line source of sufficient length, we observed an achromatic three-dimensional image.

© 2003 Optical Society of America

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References

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  1. D. J. Debitetto, “Holographic panoramic stereograms synthesized from white light recordings,” Appl. Opt. 8, 1740–1741 (1969).
    [CrossRef] [PubMed]
  2. M. C. King, A. M. Noll, D. H. Berry, “A new approach to computer-generated holography,” Appl. Opt. 9, 471–475 (1970).
    [CrossRef] [PubMed]
  3. G. Saxby, Practical Holography, 2nd ed. (Prentice-Hall, Englewood Cliffs, N.J., 1994), pp. 308–311.
  4. K. Okada, S. Yoshii, Y. Yamaji, J. Tsujiuchi, “Conical holographic stereograms,” Opt. Commun. 73, 347–350 (1989).
    [CrossRef]
  5. L. M. Murillo-Mora, K. Okada, T. Honda, J. Tsujiuchi, “Color conical holographic stereogram,” Opt. Eng. 34, 814–817 (1995).
    [CrossRef]
  6. Y. S. Cheng, W. H. Su, R. C. Chang, “Disk-type multiplex holography,” Appl. Opt. 38, 3093–3100 (1999).
    [CrossRef]
  7. M. E. Hansen, “Method and apparatus of producing an arcuate rainbow hologram,” U.S. patent4,988,154 (29January1991).
  8. S. A. Benton, “Achromatic images from white-light transmission holograms,” J. Opt. Soc. Am. 68, 1441(1978).
  9. Y. S. Cheng, R. C. Chang, “Image-plane cylindrical holographic stereogram,” Appl. Opt. 39, 4058–4069 (2000).
    [CrossRef]
  10. Y. S. Cheng, C.-M. Lai, “Image-plane conical multiplex holography by one-step recording,” Opt. Eng. 42, 1631–1639 (2003).
    [CrossRef]

2003 (1)

Y. S. Cheng, C.-M. Lai, “Image-plane conical multiplex holography by one-step recording,” Opt. Eng. 42, 1631–1639 (2003).
[CrossRef]

2000 (1)

1999 (1)

1995 (1)

L. M. Murillo-Mora, K. Okada, T. Honda, J. Tsujiuchi, “Color conical holographic stereogram,” Opt. Eng. 34, 814–817 (1995).
[CrossRef]

1989 (1)

K. Okada, S. Yoshii, Y. Yamaji, J. Tsujiuchi, “Conical holographic stereograms,” Opt. Commun. 73, 347–350 (1989).
[CrossRef]

1978 (1)

S. A. Benton, “Achromatic images from white-light transmission holograms,” J. Opt. Soc. Am. 68, 1441(1978).

1970 (1)

1969 (1)

Benton, S. A.

S. A. Benton, “Achromatic images from white-light transmission holograms,” J. Opt. Soc. Am. 68, 1441(1978).

Berry, D. H.

Chang, R. C.

Cheng, Y. S.

Debitetto, D. J.

Hansen, M. E.

M. E. Hansen, “Method and apparatus of producing an arcuate rainbow hologram,” U.S. patent4,988,154 (29January1991).

Honda, T.

L. M. Murillo-Mora, K. Okada, T. Honda, J. Tsujiuchi, “Color conical holographic stereogram,” Opt. Eng. 34, 814–817 (1995).
[CrossRef]

King, M. C.

Lai, C.-M.

Y. S. Cheng, C.-M. Lai, “Image-plane conical multiplex holography by one-step recording,” Opt. Eng. 42, 1631–1639 (2003).
[CrossRef]

Murillo-Mora, L. M.

L. M. Murillo-Mora, K. Okada, T. Honda, J. Tsujiuchi, “Color conical holographic stereogram,” Opt. Eng. 34, 814–817 (1995).
[CrossRef]

Noll, A. M.

Okada, K.

L. M. Murillo-Mora, K. Okada, T. Honda, J. Tsujiuchi, “Color conical holographic stereogram,” Opt. Eng. 34, 814–817 (1995).
[CrossRef]

K. Okada, S. Yoshii, Y. Yamaji, J. Tsujiuchi, “Conical holographic stereograms,” Opt. Commun. 73, 347–350 (1989).
[CrossRef]

Saxby, G.

G. Saxby, Practical Holography, 2nd ed. (Prentice-Hall, Englewood Cliffs, N.J., 1994), pp. 308–311.

Su, W. H.

Tsujiuchi, J.

L. M. Murillo-Mora, K. Okada, T. Honda, J. Tsujiuchi, “Color conical holographic stereogram,” Opt. Eng. 34, 814–817 (1995).
[CrossRef]

K. Okada, S. Yoshii, Y. Yamaji, J. Tsujiuchi, “Conical holographic stereograms,” Opt. Commun. 73, 347–350 (1989).
[CrossRef]

Yamaji, Y.

K. Okada, S. Yoshii, Y. Yamaji, J. Tsujiuchi, “Conical holographic stereograms,” Opt. Commun. 73, 347–350 (1989).
[CrossRef]

Yoshii, S.

K. Okada, S. Yoshii, Y. Yamaji, J. Tsujiuchi, “Conical holographic stereograms,” Opt. Commun. 73, 347–350 (1989).
[CrossRef]

Appl. Opt. (4)

J. Opt. Soc. Am. (1)

S. A. Benton, “Achromatic images from white-light transmission holograms,” J. Opt. Soc. Am. 68, 1441(1978).

Opt. Commun. (1)

K. Okada, S. Yoshii, Y. Yamaji, J. Tsujiuchi, “Conical holographic stereograms,” Opt. Commun. 73, 347–350 (1989).
[CrossRef]

Opt. Eng. (2)

L. M. Murillo-Mora, K. Okada, T. Honda, J. Tsujiuchi, “Color conical holographic stereogram,” Opt. Eng. 34, 814–817 (1995).
[CrossRef]

Y. S. Cheng, C.-M. Lai, “Image-plane conical multiplex holography by one-step recording,” Opt. Eng. 42, 1631–1639 (2003).
[CrossRef]

Other (2)

M. E. Hansen, “Method and apparatus of producing an arcuate rainbow hologram,” U.S. patent4,988,154 (29January1991).

G. Saxby, Practical Holography, 2nd ed. (Prentice-Hall, Englewood Cliffs, N.J., 1994), pp. 308–311.

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Figures (12)

Fig. 1
Fig. 1

Optical system for recording an image-plane disk-type multiplex hologram.

Fig. 2
Fig. 2

CCD camera taking 2D images of a 3D object at an angle θ a measured from vertical axis z o .

Fig. 3
Fig. 3

An object point at (x r , y r , z r ) imaged by the CCD lens appears at (x c , y c ) on the detector plane.

Fig. 4
Fig. 4

Optical system in the object beam that is designed to image a 2D object on the LCTV onto the recording holographic film and simultaneously to image the illuminating source point to a distance d fe behind the recording film plane.

Fig. 5
Fig. 5

(a) The object point under consideration, at (x f , y f ) in its own FCS, appears at (R, θ) in the observation coordinate system XYZ when the individual hologram is rotated by an angle θ o about the Z axis. (b) Side view of (a), which shows the orientation of the illuminating white-light source point and the eye of the observer in the observation coordinate system XYZ.

Fig. 6
Fig. 6

Schematic diagram showing the formation of the final image point from two lines of sight of the observer.

Fig. 7
Fig. 7

(a) Number of individual holograms N h that will be seen by one eye of an observer as a function of the angle of the reference source point, θ r , for d r = 20 cm and Δθ o = 0.36. (b) Distance of the observed image from hologram plane d if as a function of θ r . (c) Parallax of the observed 3D image θ ν as a function of θ r that is due to the effects of Figs. 7(a) and 7(b). (d) Proper inclined angle of CCD camera θ a as a function of θ r . dfe, designed best viewing distance from hologram surface.

Fig. 8
Fig. 8

Spectral width as well as number of individual holograms with which the eight corners of a cube (Fig. 2) can be seen by the left eye of an observer as a reference source point at several positions [refer to Fig. 5(b)]. (a) at the correct position, (b) shifted 1 cm up, (c) shifted 1 cm down, (d) shifted 1 cm nearer the hologram, and (e) shifted 1 cm away from the hologram.

Fig. 9
Fig. 9

Shortest distance between two lines of sight (Drl) for any corner of the cube as a function of its dimension.

Fig. 10
Fig. 10

Aspect ratio (width to height) of the observed image as a function of observation distance.

Fig. 11
Fig. 11

Experimentally reconstructed images, with white-light line-source (length, ∼2 cm) illumination, observed at various distances from the hologram disk: (a), (b) observed at the proper viewing distance d fe = 47.5 cm; (c), (d) at 95 cm; (e), (f) at 142.5 cm.

Fig. 12
Fig. 12

Achromatic image experimentally reconstructed by use of light from a fluorescent lamp 15 cm long.

Equations (14)

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xc=dixdo-y sin θa-z cos θa, yc=diy cos θa-z sin θado-y sin θa-z cos θa.
M=f2f2-d1f3f2d1/f2-d1+d23-f3,
xf=MclMxc, yf=MclMyc.
cos αo, cos βo, cos γo=-xf, -yf, dfexf2+yf2+dfe21/2.
cos αc, cos βc, cos γc=xf, yf-d sin θc, d cos θcxf2+yf-d sin θc2+d cos θc21/2.
uoxf, yf=expj 2πλxf cos αo+yf cos βo, ucxf, yf=expj 2πλxf cos αc+yf cos βc
R=A+yf2+xf21/2, θ=θo-tan-1xfA+yf.
cos αjcos βjcos γj=cos θo-sin θo0sin θocos θo0001cos αjcos βjcos γj,
cos αr, cos βr, cos γr=-R sin θ, R cos θ-A-dr sin θr, dr cos θrR2 sin2 θ+R cos θ-A-dr sin θr2+dr2 cos2 θr1/2.
cos αi=λλcos αo-cos αc+cos αr, cos βi=λλcos βo-cos βc+cos βr, cos γi=1-cos2 αi-cos2 βi1/2,
xob=-R sin θ+dfe cos αicos γi, yob=R cos θ+dfe cos βicos γi.
dif=2Adfe sinθh/2De-2A sinθh/2,
θν=2 tan-1Adif sinθh2.
θa=sin-12θhtan-1Adif sinθh2,

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