Abstract

By tilting both the input and the image planes of a holographic system and adopting a diverging reference wave for hologram recording, a special type of multiplex hologram can be produced in one-step. Due to symmetry of reconstruction geometry, the reconstructed 3D image from this type of rainbow hologram can be viewed by the surrounding observers simultaneously. Theoretical formulation for the holographic process is presented. Some numerical simulation and experimental result demonstrating the characteristics of the reconstructed image are included.

©2010 Optical Society of America

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References

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  1. R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography, (Academic Press, New York, 1971).
  2. G. Saxby, Practical Holography, 2nd ed. (Prentice-Hall, Englewood Cliffs, N.J., 1994).
  3. D. J. DeBitetto, “Holographic panoramic stereograms synthesized from white light recordings,” Appl. Opt. 8(8), 1740–1741 (1969).
    [Crossref] [PubMed]
  4. L. Huff and R. L. Fusek, “Color holographic stereograms,” Opt. Eng. 19, 691–695 (1980).
  5. E. N. Leith and P. Voulgaris, “Multiplex holography: some new methods,” Opt. Eng. 24, 171–175 (1985).
  6. K. Okada, S. Yoshii, Y. Yamaji, J. Tsujiuchi, and T. Ose, “Conical holographic stereograms,” Opt. Commun. 73(5), 347–350 (1989).
    [Crossref]
  7. L. M. Murillo-Mora, K. Okada, T. Honda, and J. Tsujiuchi, “Color conical holographic stereogram,” Opt. Eng. 34(3), 814–817 (1995).
    [Crossref]
  8. Y. S. Cheng, W. H. Su, and R. C. Chang, “Disk-type multiplex holography,” Appl. Opt. 38(14), 3093–3100 (1999).
    [Crossref]
  9. J. Kim, “etc, “360° viewable flat hologram,” Proc. SPIE 2333, 418–423 (1995).
    [Crossref]
  10. M. C. King, A. M. Noll, and D. H. Berry, “A new approach to computer-generated holography,” Appl. Opt. 9(2), 471–475 (1970).
    [Crossref] [PubMed]
  11. Y. S. Cheng and C. M. Lai, “Image-plane conical multiplex holography by one-step recording,” Opt. Eng. 42(6), 1631–1639 (2003).
    [Crossref]
  12. Y. S. Cheng and R. C. Chang, “Image-plane cylindrical holographic stereogram,” Appl. Opt. 39(23), 4058–4069 (2000).
    [Crossref]
  13. Y. S. Cheng and C. H. Chen, “Image-plane disk-type multiplex hologram,” Appl. Opt. 42(35), 7013–7022 (2003).
    [Crossref] [PubMed]
  14. C. H. Chen, Y. S. Cheng, and Z. Y. Lei, “Single-beam copying system of 360-degree viewable image-plane disk-type multiplex hologram and polarization effects on diffraction efficiency,” Opt. Express 15(17), 10804–10813 (2007).
    [Crossref] [PubMed]
  15. Y. S. Cheng, C. H. Chen, and Y. C. Hsieh, “Reflection disk-type multiplex holography using two-step recording,” Jpn. J. Appl. Phys. 47(9), 7173–7181 (2008).
    [Crossref]

2008 (1)

Y. S. Cheng, C. H. Chen, and Y. C. Hsieh, “Reflection disk-type multiplex holography using two-step recording,” Jpn. J. Appl. Phys. 47(9), 7173–7181 (2008).
[Crossref]

2007 (1)

2003 (2)

Y. S. Cheng and C. H. Chen, “Image-plane disk-type multiplex hologram,” Appl. Opt. 42(35), 7013–7022 (2003).
[Crossref] [PubMed]

Y. S. Cheng and C. M. Lai, “Image-plane conical multiplex holography by one-step recording,” Opt. Eng. 42(6), 1631–1639 (2003).
[Crossref]

2000 (1)

1999 (1)

1995 (2)

J. Kim, “etc, “360° viewable flat hologram,” Proc. SPIE 2333, 418–423 (1995).
[Crossref]

L. M. Murillo-Mora, K. Okada, T. Honda, and J. Tsujiuchi, “Color conical holographic stereogram,” Opt. Eng. 34(3), 814–817 (1995).
[Crossref]

1989 (1)

K. Okada, S. Yoshii, Y. Yamaji, J. Tsujiuchi, and T. Ose, “Conical holographic stereograms,” Opt. Commun. 73(5), 347–350 (1989).
[Crossref]

1985 (1)

E. N. Leith and P. Voulgaris, “Multiplex holography: some new methods,” Opt. Eng. 24, 171–175 (1985).

1980 (1)

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

1970 (1)

1969 (1)

Berry, D. H.

Chang, R. C.

Chen, C. H.

Cheng, Y. S.

DeBitetto, D. J.

Fusek, R. L.

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

Honda, T.

L. M. Murillo-Mora, K. Okada, T. Honda, and J. Tsujiuchi, “Color conical holographic stereogram,” Opt. Eng. 34(3), 814–817 (1995).
[Crossref]

Hsieh, Y. C.

Y. S. Cheng, C. H. Chen, and Y. C. Hsieh, “Reflection disk-type multiplex holography using two-step recording,” Jpn. J. Appl. Phys. 47(9), 7173–7181 (2008).
[Crossref]

Huff, L.

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

Kim, J.

J. Kim, “etc, “360° viewable flat hologram,” Proc. SPIE 2333, 418–423 (1995).
[Crossref]

King, M. C.

Lai, C. M.

Y. S. Cheng and C. M. Lai, “Image-plane conical multiplex holography by one-step recording,” Opt. Eng. 42(6), 1631–1639 (2003).
[Crossref]

Lei, Z. Y.

Leith, E. N.

E. N. Leith and P. Voulgaris, “Multiplex holography: some new methods,” Opt. Eng. 24, 171–175 (1985).

Murillo-Mora, L. M.

L. M. Murillo-Mora, K. Okada, T. Honda, and J. Tsujiuchi, “Color conical holographic stereogram,” Opt. Eng. 34(3), 814–817 (1995).
[Crossref]

Noll, A. M.

Okada, K.

L. M. Murillo-Mora, K. Okada, T. Honda, and J. Tsujiuchi, “Color conical holographic stereogram,” Opt. Eng. 34(3), 814–817 (1995).
[Crossref]

K. Okada, S. Yoshii, Y. Yamaji, J. Tsujiuchi, and T. Ose, “Conical holographic stereograms,” Opt. Commun. 73(5), 347–350 (1989).
[Crossref]

Ose, T.

K. Okada, S. Yoshii, Y. Yamaji, J. Tsujiuchi, and T. Ose, “Conical holographic stereograms,” Opt. Commun. 73(5), 347–350 (1989).
[Crossref]

Su, W. H.

Tsujiuchi, J.

L. M. Murillo-Mora, K. Okada, T. Honda, and J. Tsujiuchi, “Color conical holographic stereogram,” Opt. Eng. 34(3), 814–817 (1995).
[Crossref]

K. Okada, S. Yoshii, Y. Yamaji, J. Tsujiuchi, and T. Ose, “Conical holographic stereograms,” Opt. Commun. 73(5), 347–350 (1989).
[Crossref]

Voulgaris, P.

E. N. Leith and P. Voulgaris, “Multiplex holography: some new methods,” Opt. Eng. 24, 171–175 (1985).

Yamaji, Y.

K. Okada, S. Yoshii, Y. Yamaji, J. Tsujiuchi, and T. Ose, “Conical holographic stereograms,” Opt. Commun. 73(5), 347–350 (1989).
[Crossref]

Yoshii, S.

K. Okada, S. Yoshii, Y. Yamaji, J. Tsujiuchi, and T. Ose, “Conical holographic stereograms,” Opt. Commun. 73(5), 347–350 (1989).
[Crossref]

Appl. Opt. (5)

Jpn. J. Appl. Phys. (1)

Y. S. Cheng, C. H. Chen, and Y. C. Hsieh, “Reflection disk-type multiplex holography using two-step recording,” Jpn. J. Appl. Phys. 47(9), 7173–7181 (2008).
[Crossref]

Opt. Commun. (1)

K. Okada, S. Yoshii, Y. Yamaji, J. Tsujiuchi, and T. Ose, “Conical holographic stereograms,” Opt. Commun. 73(5), 347–350 (1989).
[Crossref]

Opt. Eng. (4)

L. M. Murillo-Mora, K. Okada, T. Honda, and J. Tsujiuchi, “Color conical holographic stereogram,” Opt. Eng. 34(3), 814–817 (1995).
[Crossref]

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

E. N. Leith and P. Voulgaris, “Multiplex holography: some new methods,” Opt. Eng. 24, 171–175 (1985).

Y. S. Cheng and C. M. Lai, “Image-plane conical multiplex holography by one-step recording,” Opt. Eng. 42(6), 1631–1639 (2003).
[Crossref]

Opt. Express (1)

Proc. SPIE (1)

J. Kim, “etc, “360° viewable flat hologram,” Proc. SPIE 2333, 418–423 (1995).
[Crossref]

Other (2)

R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography, (Academic Press, New York, 1971).

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

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Figures (12)

Fig. 1
Fig. 1 Optical system for recording image-plane disk-type multiplex hologram.

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Fig. 2
Fig. 2 The relationship between the laboratory coordinate system X o − Y o − Z o and the object coordinate system X − Y − Z .

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Fig. 3
Fig. 3 Object point in CCD coordinates and its image on the detector plane.

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Fig. 4
Fig. 4 Object point on LCD panel is imaged by the optical system onto the recording film plane.

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Fig. 5
Fig. 5 Schematic for the direction of the object ray in the film coordinate system. PS is the focus point of the illuminating wave. Pf is the object point on the recording film.

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Fig. 6
Fig. 6 Schematic for the direction of the reference ray in the film coordinate system.

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Fig. 7
Fig. 7 Position of image point on film expressed in the observation coordinate system X v − Y v − Z v .

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Fig. 8
Fig. 8 Hologram viewing geometry.

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Fig. 9
Fig. 9 Reconstructed image of a cube from simulation.

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Fig. 10
Fig. 10 Width-to-height ratio as a function of viewing distance.

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Fig. 11
Fig. 11 Images with correct parallax, (a) for right eye (b) for left eye, as observed at best-viewing distance (89cm from the center of individual hologram).

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Fig. 12
Fig. 12 Effect of viewing distance on observed image: (a) 45cm from center of individual hologram, (b) 90cm from center of individual hologram, (c) 180cm from center of individual hologram.

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Tables (1)

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Table 1 The parameters for the simulated reconstructed image of Fig. 9

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Equations (12)

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[ x o y o z o ] = [ cos ( N   θ o )         0     sin ( N   θ o )         0             1           0 − sin ( N   θ o )     0     cos ( N   θ o ) ] [ x y z ] ,
[ x c y c z c ] = [     1       0             0     0       cos θ c     − sin θ c       0       sin θ c     cos θ c ] [ x o y o z o ] .
P d ( x d = − d i d o − z c x c ,   y d = − d i d o − z c y c ) .
[ x f y f z f ] = [ 1       0           0 0     cos θ 1       sin θ 1 0   − sin θ 1   cos θ 1 ] [ M   0     0 0     M   0 0         0     0 ] [ 1       0           0 0       cos θ 2     sin θ 2 0   − sin θ 2   cos θ 2 ] [ x l y l   0 ]
( cos α o ,   cos β o ,   cos γ o ) = ( − x f ,     − d f e sin θ 1 − y f ,     d f e cos θ 1 )   x f 2 + ( d f e sin θ 1 + y f ) 2 + ( d f e cos θ 1 ) 2  
( cos α c ,   cos β c ,   cos γ c ) = ( x f ,   y f + R ,   Z d )   x f 2 + ( y f + R ) 2 + Z d 2  
x v = x f 2 + ( R + y f ) 2 sin [ θ + tan − 1 ( x f R + y f ) ]
y v = x f 2 + ( R + y f ) 2 cos [ θ + tan − 1 ( x f R + y f ) ]
[ cos α v cos β v cos γ v ] = [ cos θ   − sin θ   0 sin θ       cos θ       0     0           0       1 ] [ cos α cos β cos γ ] .
( cos α r ,   cos β r ,   cos γ r ) = ( x f , y f + R ,   Z d )   x f 2 +   ( y f + R ) 2 + Z d 2  
cos α i = cos α r + λ r λ c cos α o − λ r λ c cos α c
cos β i = cos β r + λ r λ c cos β o − λ r λ c cos β c

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