Abstract

A two-step holographic process is introduced to fabricate a cylindrical multiplex hologram as an image-plane hologram. By adoption of the achromatic angle in the process the hologram is capable of generating an achromatic image. The most important factors, the location as well as the width of the viewing slits, that affect the quality of the observed image are analyzed and discussed. The change of aspect ratio for the observed image as a function of the viewing distance is theoretically and numerically analyzed. This method can not only eliminate the annoying picket-fence effect but can also increase the vertical viewing range for the observer. Computer simulations as well as experimental results are provided.

© 2000 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. G. Saxby, Practical Holography, 2nd ed. (Prentice-Hall, New York, 1994), pp. 308–311.
  3. S. A. Benton, “Alcove holograms for computer-aided design,” in True Three-Dimensional Imaging Techniques and Display Technologies, D. F. McAllister, W. E. Robbins, eds., Proc. SPIE761, 1–9 (1987).
  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. N. Ohyama, Y. Minami, A. Watanabe, J. Tsujiuchi, T. Honda, “Multiplex holograms of a skull made of CT images,” Opt. Commun. 61, 96–99 (1987).
    [CrossRef]
  8. S. A. Benton, “Achromatic images from white-light transmission holograms,” J. Opt. Soc. Am. 68, 1441 (1978).
  9. K. Okada, T. Honda, J. Tsujiuchi, “3-D distortion of observed images reconstructed from a cylindrical holographic stereogram. (2) White light reconstruction type,” Opt. Commun. 36, 17–21 (1981).
    [CrossRef]

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]

1987 (1)

N. Ohyama, Y. Minami, A. Watanabe, J. Tsujiuchi, T. Honda, “Multiplex holograms of a skull made of CT images,” Opt. Commun. 61, 96–99 (1987).
[CrossRef]

1981 (1)

K. Okada, T. Honda, J. Tsujiuchi, “3-D distortion of observed images reconstructed from a cylindrical holographic stereogram. (2) White light reconstruction type,” Opt. Commun. 36, 17–21 (1981).
[CrossRef]

1978 (1)

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

1969 (1)

Benton, S. A.

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

S. A. Benton, “Alcove holograms for computer-aided design,” in True Three-Dimensional Imaging Techniques and Display Technologies, D. F. McAllister, W. E. Robbins, eds., Proc. SPIE761, 1–9 (1987).

Chang, R. C.

Cheng, Y. S.

DeBitetto, D. J.

Honda, T.

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

N. Ohyama, Y. Minami, A. Watanabe, J. Tsujiuchi, T. Honda, “Multiplex holograms of a skull made of CT images,” Opt. Commun. 61, 96–99 (1987).
[CrossRef]

K. Okada, T. Honda, J. Tsujiuchi, “3-D distortion of observed images reconstructed from a cylindrical holographic stereogram. (2) White light reconstruction type,” Opt. Commun. 36, 17–21 (1981).
[CrossRef]

Minami, Y.

N. Ohyama, Y. Minami, A. Watanabe, J. Tsujiuchi, T. Honda, “Multiplex holograms of a skull made of CT images,” Opt. Commun. 61, 96–99 (1987).
[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]

Ohyama, N.

N. Ohyama, Y. Minami, A. Watanabe, J. Tsujiuchi, T. Honda, “Multiplex holograms of a skull made of CT images,” Opt. Commun. 61, 96–99 (1987).
[CrossRef]

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]

K. Okada, T. Honda, J. Tsujiuchi, “3-D distortion of observed images reconstructed from a cylindrical holographic stereogram. (2) White light reconstruction type,” Opt. Commun. 36, 17–21 (1981).
[CrossRef]

Saxby, G.

G. Saxby, Practical Holography, 2nd ed. (Prentice-Hall, New York, 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]

N. Ohyama, Y. Minami, A. Watanabe, J. Tsujiuchi, T. Honda, “Multiplex holograms of a skull made of CT images,” Opt. Commun. 61, 96–99 (1987).
[CrossRef]

K. Okada, T. Honda, J. Tsujiuchi, “3-D distortion of observed images reconstructed from a cylindrical holographic stereogram. (2) White light reconstruction type,” Opt. Commun. 36, 17–21 (1981).
[CrossRef]

Watanabe, A.

N. Ohyama, Y. Minami, A. Watanabe, J. Tsujiuchi, T. Honda, “Multiplex holograms of a skull made of CT images,” Opt. Commun. 61, 96–99 (1987).
[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. (2)

J. Opt. Soc. Am. (1)

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

Opt. Commun. (3)

K. Okada, T. Honda, J. Tsujiuchi, “3-D distortion of observed images reconstructed from a cylindrical holographic stereogram. (2) White light reconstruction type,” Opt. Commun. 36, 17–21 (1981).
[CrossRef]

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

N. Ohyama, Y. Minami, A. Watanabe, J. Tsujiuchi, T. Honda, “Multiplex holograms of a skull made of CT images,” Opt. Commun. 61, 96–99 (1987).
[CrossRef]

Opt. Eng. (1)

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

Other (2)

G. Saxby, Practical Holography, 2nd ed. (Prentice-Hall, New York, 1994), pp. 308–311.

S. A. Benton, “Alcove holograms for computer-aided design,” in True Three-Dimensional Imaging Techniques and Display Technologies, D. F. McAllister, W. E. Robbins, eds., Proc. SPIE761, 1–9 (1987).

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Figures (15)

Fig. 1
Fig. 1

Optical system for recording the master hologram H1, which is tilted at the achromatic angle α. Input perspectives are displayed on a LCD and imaged onto the diffusion screen DS sequentially. A horizontal slit with proper width in contact with the master is used to limit the exposure area of the component hologram. M, mirror; L, lens; VBS, variable beam splitter; SF, spatial filter.

Fig. 2
Fig. 2

Optical system for making the IPCHS. The information stored in the master H1 is retrieved with a reference wave and recorded on the second holographic film H2 with the help of a cylindrical reference wave. M, mirror; L, lens; VBS, variable beam splitter; SF, spatial filter.

Fig. 3
Fig. 3

Schematic figure showing the relationship between the widths of the exposure segments on the master H1 and the transfer H2.

Fig. 4
Fig. 4

Illustration showing that extra component holograms are required at the end of the master hologram.

Fig. 5
Fig. 5

To eliminate the lines between the exposure segments on the transfer, the exposure area on the transfer can be taken to be larger than that on the master. However, this results in double exposure at the sides of each exposure segment on the transfer.

Fig. 6
Fig. 6

Object ray E o and reference ray E c are interfering at point Q, and the interference fringes are recorded. These interference fringes are read by the reconstruction reference ray E r , and the image ray E i is generated.

Fig. 7
Fig. 7

2D perspective (shaded area) on the transfer is illuminated by the conjugate reference wave that would focus to be a line S L1. The real image of the component hologram, or the viewing slit, is generated at the dashed gray line.

Fig. 8
Fig. 8

Diverging cylindrical wave from line S L2 is illuminating the 2D perspective on the transfer. The vertical location for the center of the viewing slit is shifted from P o to P o ′.

Fig. 9
Fig. 9

Owing to the bending effect of the hologram, the horizontal location of the viewing slit is shifted. When the divergence of the illuminating reference source is properly chosen, the location of the viewing slit in the vertical direction can be shifted by the same amount.

Fig. 10
Fig. 10

(a) Computer simulation of the trapezoid distortion on the observed image, which is due to the mismatch of the viewing-slit locations in the orthogonal directions. (b) Trapezoid distortion on the image is corrected if the viewing-slit locations in the orthogonal directions are made equal.

Fig. 11
Fig. 11

Illustration showing the relationship between the diameter of eye pupil p and the centers of two adjacent perspectives P1 and P2 for setting proper width for original component holograms.

Fig. 12
Fig. 12

Eye of the observer is at the position P e , which is off the location of the viewing slit P o . The edge of image Q can be seen by the eye through the nth viewing slit P n . From this geometrical relationship, one can estimate the number of perspectives that contribute partial images to the final observed image.

Fig. 13
Fig. 13

Number of perspectives, n, on the hologram surface and the aspect ratio as a function of the viewing distance d e , which is from the eye to the hologram surface. The parameters used for these plots are radius of hologram cylinder R = 10 cm, width of 2D perspective W = 4 cm, slit width S = 0.5 mm, and distance of viewing slit to hologram surface d′ = 45 cm.

Fig. 14
Fig. 14

Reconstructed achromatic image from IPCHS showing that the annoying vertical line structure overlaying the image in traditional cylindrical multiplex holography is eliminated.

Fig. 15
Fig. 15

Image from traditional cylindrical multiplex hologram showing the picket-fence effect (exaggerated for comparison with the image in Fig. 14).

Equations (17)

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α=arctansin θ,
fxaˆx+fyaˆy=sin θo cos ϕoλ aˆx+sin θo sin ϕoλ+sin θcλaˆy,
sin θi cos ϕiλ aˆx+sin θi cos ϕiλ+sin θrλaˆy=fxaˆx+fyaˆy,
sin θi cos ϕiλ=sin θo cos ϕoλ,
sin θi sin ϕiλ=sin θo sin ϕoλ+sin θcλ-sin θrλ.
θo=arctanxi/d,ϕo=0,
d=Rsinxi/Rtanθo-xi/R+cosxiR-1.
θc=arctantan θc+yi/dc,
θo=arctanyi/d,ϕo=-π2,
θr=arctantan θc-yi/R,
θi=arctanyi/d,ϕi=-π/2,
-sinarctanyid=-sinarctanyid+sinarctantan θc+yidc-sinarctantan θc-yiR.
S=pR/R+de,
P0Pn=nSR+d/R,
nSR+dRde-d=R sin Ψde+R-R cos Ψ,
n=R2de-dsinW/2RSR+dde+R1-cosW/2R.
W=2W/2+nS=W+2nS.

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