Abstract

We have been investigating disk holograms made from a computer-generated hologram (CGH). Since a general flat format hologram has a limited viewable area, we usually cannot see the other side of the reconstructed object. Therefore, we propose a computer-generated cylindrical hologram (CGCH) to obtain a hologram with a 360 deg viewable area. The CGCH has a special shape that is difficult to construct and calculation of such a hologram takes too much time. In contrast, a disk-type hologram is well known as a 360 deg viewable hologram. Since a regular disk hologram is a flat reflective type, the reconstruction setup is easy. However, there are just a few reports about creating a disk hologram by use of a CGH. Because the output device lacks spatial resolution, the hologram cannot provide a large diffraction angle. In addition, the viewing zone depends on the hologram size; the maximum size of the fringe pattern is decided on the basis of the special frequency of the output device. The calculation amount of the proposed hologram is approximately a quarter of that of a CGCH. In a previous study, a disk hologram made from a CGH was achieved. However, since the relation between the vertical viewing zone and reconstructed image size is a trade-off, the size of the reconstructed image and view zone is not enough for practical use. To improve both parameters, we modified a fringe printer to issue a high-resolution fringe pattern for a disk hologram. In addition, we propose a new calculation method for fast calculation.

© 2009 Optical Society of America

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References

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  1. T. Yamaguchi, T. Fujii, and H. Yoshikawa, “Fast calculation method for computer-generated cylindrical holograms,” Appl. Opt. 47, D63-D70 (2008).
    [CrossRef] [PubMed]
  2. T. H. Jeong, “Cylindrical holography and some proposed applications,” J. Opt. Soc. Am. 57, 1396-1398 (1967).
    [CrossRef]
  3. T. Yamaguchi, T. Fujii, and H. Yoshikawa, “Computer-generated disk hologram,” in Digital Holography and Three-Dimensional Imaging on CD-ROM, JMA12 (Optical Society of America, 2008).
  4. J. Kim, J. Hill, J. Honack, W. Roth, R. Roberts, E. Villasenor, O. Gonzales, and E. Baker, “360 Viewable flat hologram,” Proc. SPIE 2333, 418-423 (1994).
    [CrossRef]
  5. H. Yoshikawa and K. Mitsui, “Improvement of direct fringe printer for computer-generated holograms,” in Proceedings of the Seventh International Symposium on Display Holography (2006), pp. 102-106.
  6. J. P. Waters, “Holographic image synthesis utilizing theoretical method,” Appl. Phys. Lett. 9, 405-407 (1966).
    [CrossRef]
  7. M. Lucente, “Interactive computation of hologram using a look-up table,” J. Electron. Imaging 2, 28-34 (1993).
    [CrossRef]
  8. H. Yoshikawa, “Fast computation of Fresnel holograms employing difference,” Opt. Rev. 8, 331-335 (2001).
    [CrossRef]
  9. T. Fujii and H. Yoshikawa, “Improvement of hidden-surface removal for computer-generated holograms from CG,” in Digital Holography and Three-Dimensional Imaging on CD-ROM (Optical Society of America, 2007), paper DWB3.

2008 (1)

2001 (1)

H. Yoshikawa, “Fast computation of Fresnel holograms employing difference,” Opt. Rev. 8, 331-335 (2001).
[CrossRef]

1994 (1)

J. Kim, J. Hill, J. Honack, W. Roth, R. Roberts, E. Villasenor, O. Gonzales, and E. Baker, “360 Viewable flat hologram,” Proc. SPIE 2333, 418-423 (1994).
[CrossRef]

1993 (1)

M. Lucente, “Interactive computation of hologram using a look-up table,” J. Electron. Imaging 2, 28-34 (1993).
[CrossRef]

1967 (1)

1966 (1)

J. P. Waters, “Holographic image synthesis utilizing theoretical method,” Appl. Phys. Lett. 9, 405-407 (1966).
[CrossRef]

Baker, E.

J. Kim, J. Hill, J. Honack, W. Roth, R. Roberts, E. Villasenor, O. Gonzales, and E. Baker, “360 Viewable flat hologram,” Proc. SPIE 2333, 418-423 (1994).
[CrossRef]

Fujii, T.

T. Yamaguchi, T. Fujii, and H. Yoshikawa, “Fast calculation method for computer-generated cylindrical holograms,” Appl. Opt. 47, D63-D70 (2008).
[CrossRef] [PubMed]

T. Yamaguchi, T. Fujii, and H. Yoshikawa, “Computer-generated disk hologram,” in Digital Holography and Three-Dimensional Imaging on CD-ROM, JMA12 (Optical Society of America, 2008).

T. Fujii and H. Yoshikawa, “Improvement of hidden-surface removal for computer-generated holograms from CG,” in Digital Holography and Three-Dimensional Imaging on CD-ROM (Optical Society of America, 2007), paper DWB3.

Gonzales, O.

J. Kim, J. Hill, J. Honack, W. Roth, R. Roberts, E. Villasenor, O. Gonzales, and E. Baker, “360 Viewable flat hologram,” Proc. SPIE 2333, 418-423 (1994).
[CrossRef]

Hill, J.

J. Kim, J. Hill, J. Honack, W. Roth, R. Roberts, E. Villasenor, O. Gonzales, and E. Baker, “360 Viewable flat hologram,” Proc. SPIE 2333, 418-423 (1994).
[CrossRef]

Honack, J.

J. Kim, J. Hill, J. Honack, W. Roth, R. Roberts, E. Villasenor, O. Gonzales, and E. Baker, “360 Viewable flat hologram,” Proc. SPIE 2333, 418-423 (1994).
[CrossRef]

Jeong, T. H.

Kim, J.

J. Kim, J. Hill, J. Honack, W. Roth, R. Roberts, E. Villasenor, O. Gonzales, and E. Baker, “360 Viewable flat hologram,” Proc. SPIE 2333, 418-423 (1994).
[CrossRef]

Lucente, M.

M. Lucente, “Interactive computation of hologram using a look-up table,” J. Electron. Imaging 2, 28-34 (1993).
[CrossRef]

Mitsui, K.

H. Yoshikawa and K. Mitsui, “Improvement of direct fringe printer for computer-generated holograms,” in Proceedings of the Seventh International Symposium on Display Holography (2006), pp. 102-106.

Roberts, R.

J. Kim, J. Hill, J. Honack, W. Roth, R. Roberts, E. Villasenor, O. Gonzales, and E. Baker, “360 Viewable flat hologram,” Proc. SPIE 2333, 418-423 (1994).
[CrossRef]

Roth, W.

J. Kim, J. Hill, J. Honack, W. Roth, R. Roberts, E. Villasenor, O. Gonzales, and E. Baker, “360 Viewable flat hologram,” Proc. SPIE 2333, 418-423 (1994).
[CrossRef]

Villasenor, E.

J. Kim, J. Hill, J. Honack, W. Roth, R. Roberts, E. Villasenor, O. Gonzales, and E. Baker, “360 Viewable flat hologram,” Proc. SPIE 2333, 418-423 (1994).
[CrossRef]

Waters, J. P.

J. P. Waters, “Holographic image synthesis utilizing theoretical method,” Appl. Phys. Lett. 9, 405-407 (1966).
[CrossRef]

Yamaguchi, T.

T. Yamaguchi, T. Fujii, and H. Yoshikawa, “Fast calculation method for computer-generated cylindrical holograms,” Appl. Opt. 47, D63-D70 (2008).
[CrossRef] [PubMed]

T. Yamaguchi, T. Fujii, and H. Yoshikawa, “Computer-generated disk hologram,” in Digital Holography and Three-Dimensional Imaging on CD-ROM, JMA12 (Optical Society of America, 2008).

Yoshikawa, H.

T. Yamaguchi, T. Fujii, and H. Yoshikawa, “Fast calculation method for computer-generated cylindrical holograms,” Appl. Opt. 47, D63-D70 (2008).
[CrossRef] [PubMed]

H. Yoshikawa, “Fast computation of Fresnel holograms employing difference,” Opt. Rev. 8, 331-335 (2001).
[CrossRef]

T. Fujii and H. Yoshikawa, “Improvement of hidden-surface removal for computer-generated holograms from CG,” in Digital Holography and Three-Dimensional Imaging on CD-ROM (Optical Society of America, 2007), paper DWB3.

T. Yamaguchi, T. Fujii, and H. Yoshikawa, “Computer-generated disk hologram,” in Digital Holography and Three-Dimensional Imaging on CD-ROM, JMA12 (Optical Society of America, 2008).

H. Yoshikawa and K. Mitsui, “Improvement of direct fringe printer for computer-generated holograms,” in Proceedings of the Seventh International Symposium on Display Holography (2006), pp. 102-106.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

J. P. Waters, “Holographic image synthesis utilizing theoretical method,” Appl. Phys. Lett. 9, 405-407 (1966).
[CrossRef]

J. Electron. Imaging (1)

M. Lucente, “Interactive computation of hologram using a look-up table,” J. Electron. Imaging 2, 28-34 (1993).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Rev. (1)

H. Yoshikawa, “Fast computation of Fresnel holograms employing difference,” Opt. Rev. 8, 331-335 (2001).
[CrossRef]

Proc. SPIE (1)

J. Kim, J. Hill, J. Honack, W. Roth, R. Roberts, E. Villasenor, O. Gonzales, and E. Baker, “360 Viewable flat hologram,” Proc. SPIE 2333, 418-423 (1994).
[CrossRef]

Other (3)

H. Yoshikawa and K. Mitsui, “Improvement of direct fringe printer for computer-generated holograms,” in Proceedings of the Seventh International Symposium on Display Holography (2006), pp. 102-106.

T. Fujii and H. Yoshikawa, “Improvement of hidden-surface removal for computer-generated holograms from CG,” in Digital Holography and Three-Dimensional Imaging on CD-ROM (Optical Society of America, 2007), paper DWB3.

T. Yamaguchi, T. Fujii, and H. Yoshikawa, “Computer-generated disk hologram,” in Digital Holography and Three-Dimensional Imaging on CD-ROM, JMA12 (Optical Society of America, 2008).

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Figures (15)

Fig. 1
Fig. 1

Disk hologram reconstructed by white-light illumination.

Fig. 2
Fig. 2

Schematic of the optical setup to record a master hologram [4].

Fig. 3
Fig. 3

Optical setup to record the transfer hologram [4].

Fig. 4
Fig. 4

Schematic of the optical model to calculate the proposed hologram (master hologram).

Fig. 5
Fig. 5

Optical model to calculate the master hologram.

Fig. 6
Fig. 6

Model to calculate the Fresnel hologram.

Fig. 7
Fig. 7

Segmentation of the master hologram.

Fig. 8
Fig. 8

Approximate distance error obtained on the (a) x axis and (b) y axis.

Fig. 9
Fig. 9

Simulation of the reconstructed images approximated in (a), (c) and not approximated in (b), (d).

Fig. 10
Fig. 10

Process to create perspective images from different viewpoints.

Fig. 11
Fig. 11

Schematic of the fringe printing system.

Fig. 12
Fig. 12

Optical setup to record the transfer hologram as a disk hologram.

Fig. 13
Fig. 13

(a) Master hologram and (b) reconstructed images of a master hologram from several viewpoints.

Fig. 14
Fig. 14

(a) Final disk hologram and (b)–(i) reconstructed images from several viewpoints.

Fig. 15
Fig. 15

Vertical viewing angle of the disk hologram.

Tables (2)

Tables Icon

Table 1 Parameters of the Fringe Printer

Tables Icon

Table 2 Parameters of the Disk Hologram made from a Computer-Generated Hologram

Equations (12)

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O ( x , y ) = i = 1 N a i r i exp [ j ( k r i + ϕ i ) ] ,
r i = ( x x i ) 2 + ( y y i ) 2 + z i 2 .
R ( x , y ) = a R exp [ j k y sin θ ref ] ,
I = | O + R | 2 = | O | 2 + | R | 2 + 2 Re { O R * } ,
I ( x , y ) = i = 1 N a i r i cos { k r i + ϕ R ( x , y ) + ϕ i } ,
d ( x , y ) = ( x x i ) 2 + ( y y i ) 2 + z i 2 = x 2 + y 2 + x i 2 + y i 2 + z i 2 2 ( x x i + y y i ) .
d ( x m , y n ) = x m 2 + y n 2 + x i 2 + y i 2 + z i 2 2 ( x m x i + y n y i ) .
d ( x m , y mid ) = x m 2 + y mid 2 + x i 2 + y i 2 + z i 2 2 ( x m x i + y mid y i ) ,
d ( x m , y mid ) d ( x m , y n ) = x m 2 + y mid 2 + x i 2 + y i 2 + z i 2 2 ( x m x i + y mid y i ) x m 2 + y n 2 + x i 2 + y i 2 + z i 2 2 ( x m x i + y n y i ) .
C ( n ) = x mid 2 + y mid 2 + x i 2 + y i 2 + z i 2 2 ( x mid x i + y mid y i ) x mid 2 + y n 2 + x i 2 + y i 2 + z i 2 2 ( x mid x i + y n y i ) ( n = 1 , 2 , 3 , , N ) .
d ( x m , y n ) L T x ( m ) C ( n ) .
2 d ( sin θ out sin θ ill ) = λ ,

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