Abstract

Since a general flat hologram has a limited viewable area, we usually cannot see the other side of a reconstructed object. There are some holograms that can solve this problem. A cylindrical hologram is well known to be viewable in 360 deg. Most cylindrical holograms are optical holograms, but there are few reports of computer-generated cylindrical holograms. The lack of computer-generated cylindrical holograms is because the spatial resolution of output devices is not great enough; therefore, we have to make a large hologram or use a small object to fulfill the sampling theorem. In addition, in calculating the large fringe, the calculation amount increases in proportion to the hologram size. Therefore, we propose what we believe to be a new calculation method for fast calculation. Then, we print these fringes with our prototype fringe printer. As a result, we obtain a good reconstructed image from a computer-generated cylindrical hologram.

© 2008 Optical Society of America

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References

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  1. T. H. Jeong, “Cylindrical holography and some proposed applications,” J. Opt. Soc. Am. 57, 1396-1398 (1967).
    [CrossRef]
  2. T. Honda, K. Okada, and J. Tsuhiudchi, “Three-dimensional distortion of observed images reconstructed from a cylindrical hologram stereogram,” Opt. Commun. 36, 11-16 (1981).
    [CrossRef]
  3. A. Kashiwagi and Y. Sakamoto, “A fast calculation method of cylindrical computer-generated holograms which perform image-reconstruction of volume data,” in Digital Holography and Three-Dimensional Imaging on CD-ROM (Optical Society of America, 2007), paper DWB7.
  4. G. W. Stroke, “Lensless Fourier-transform method for optical holography,” Appl. Phys. Lett. 6, 201-203 (1965).
    [CrossRef]
  5. H. Yoshikawa and K. Mitsui, “Improvement of direct fringe printer for computer-generated holograms,” Proceedings of Seventh International Symposium on Display Holography (River Valley Press, 2006); pp. 102-106.
  6. J. P. Waters, “Holographic image synthesis utilizing theoretical method,” Appl. Phys. Lett. 9(11), 405-407 (1996).
    [CrossRef]
  7. M. Lucente, “Interactive computation of hologram using a look-up table,” J. Electron. Imaging 2, 28-34 (1993).
    [CrossRef]
  8. H. Yoshikawa and H. Kameyama, “Integral holography,” Proc. SPIE 2406, 226-234 (1995).
  9. H. Yoshikawa and T. Yamaguchi, “Fast hologram calculation for holographic video display,” 20th Congress of the International Commission for Optics, Challenging Optics in Science and Technology (International Commission for Optics, 2005), paper 0408-087.
  10. 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 DBW3.

1996

J. P. Waters, “Holographic image synthesis utilizing theoretical method,” Appl. Phys. Lett. 9(11), 405-407 (1996).
[CrossRef]

1995

H. Yoshikawa and H. Kameyama, “Integral holography,” Proc. SPIE 2406, 226-234 (1995).

1993

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

1981

T. Honda, K. Okada, and J. Tsuhiudchi, “Three-dimensional distortion of observed images reconstructed from a cylindrical hologram stereogram,” Opt. Commun. 36, 11-16 (1981).
[CrossRef]

1967

T. H. Jeong, “Cylindrical holography and some proposed applications,” J. Opt. Soc. Am. 57, 1396-1398 (1967).
[CrossRef]

1965

G. W. Stroke, “Lensless Fourier-transform method for optical holography,” Appl. Phys. Lett. 6, 201-203 (1965).
[CrossRef]

Fujii, T.

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 DBW3.

Honda, T.

T. Honda, K. Okada, and J. Tsuhiudchi, “Three-dimensional distortion of observed images reconstructed from a cylindrical hologram stereogram,” Opt. Commun. 36, 11-16 (1981).
[CrossRef]

Jeong, T. H.

T. H. Jeong, “Cylindrical holography and some proposed applications,” J. Opt. Soc. Am. 57, 1396-1398 (1967).
[CrossRef]

Kameyama, H.

H. Yoshikawa and H. Kameyama, “Integral holography,” Proc. SPIE 2406, 226-234 (1995).

Kashiwagi, A.

A. Kashiwagi and Y. Sakamoto, “A fast calculation method of cylindrical computer-generated holograms which perform image-reconstruction of volume data,” in Digital Holography and Three-Dimensional Imaging on CD-ROM (Optical Society of America, 2007), paper DWB7.

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,” Proceedings of Seventh International Symposium on Display Holography (River Valley Press, 2006); pp. 102-106.

Okada, K.

T. Honda, K. Okada, and J. Tsuhiudchi, “Three-dimensional distortion of observed images reconstructed from a cylindrical hologram stereogram,” Opt. Commun. 36, 11-16 (1981).
[CrossRef]

Sakamoto, Y.

A. Kashiwagi and Y. Sakamoto, “A fast calculation method of cylindrical computer-generated holograms which perform image-reconstruction of volume data,” in Digital Holography and Three-Dimensional Imaging on CD-ROM (Optical Society of America, 2007), paper DWB7.

Stroke, G. W.

G. W. Stroke, “Lensless Fourier-transform method for optical holography,” Appl. Phys. Lett. 6, 201-203 (1965).
[CrossRef]

Tsuhiudchi, J.

T. Honda, K. Okada, and J. Tsuhiudchi, “Three-dimensional distortion of observed images reconstructed from a cylindrical hologram stereogram,” Opt. Commun. 36, 11-16 (1981).
[CrossRef]

Waters, J. P.

J. P. Waters, “Holographic image synthesis utilizing theoretical method,” Appl. Phys. Lett. 9(11), 405-407 (1996).
[CrossRef]

Yamaguchi, T.

H. Yoshikawa and T. Yamaguchi, “Fast hologram calculation for holographic video display,” 20th Congress of the International Commission for Optics, Challenging Optics in Science and Technology (International Commission for Optics, 2005), paper 0408-087.

Yoshikawa, H.

H. Yoshikawa and H. Kameyama, “Integral holography,” Proc. SPIE 2406, 226-234 (1995).

H. Yoshikawa and T. Yamaguchi, “Fast hologram calculation for holographic video display,” 20th Congress of the International Commission for Optics, Challenging Optics in Science and Technology (International Commission for Optics, 2005), paper 0408-087.

H. Yoshikawa and K. Mitsui, “Improvement of direct fringe printer for computer-generated holograms,” Proceedings of Seventh International Symposium on Display Holography (River Valley Press, 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 DBW3.

Appl. Phys. Lett.

G. W. Stroke, “Lensless Fourier-transform method for optical holography,” Appl. Phys. Lett. 6, 201-203 (1965).
[CrossRef]

J. P. Waters, “Holographic image synthesis utilizing theoretical method,” Appl. Phys. Lett. 9(11), 405-407 (1996).
[CrossRef]

J. Electron. Imaging

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

J. Opt. Soc. Am.

T. H. Jeong, “Cylindrical holography and some proposed applications,” J. Opt. Soc. Am. 57, 1396-1398 (1967).
[CrossRef]

Opt. Commun.

T. Honda, K. Okada, and J. Tsuhiudchi, “Three-dimensional distortion of observed images reconstructed from a cylindrical hologram stereogram,” Opt. Commun. 36, 11-16 (1981).
[CrossRef]

Proc. SPIE

H. Yoshikawa and H. Kameyama, “Integral holography,” Proc. SPIE 2406, 226-234 (1995).

Other

H. Yoshikawa and T. Yamaguchi, “Fast hologram calculation for holographic video display,” 20th Congress of the International Commission for Optics, Challenging Optics in Science and Technology (International Commission for Optics, 2005), paper 0408-087.

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 DBW3.

A. Kashiwagi and Y. Sakamoto, “A fast calculation method of cylindrical computer-generated holograms which perform image-reconstruction of volume data,” in Digital Holography and Three-Dimensional Imaging on CD-ROM (Optical Society of America, 2007), paper DWB7.

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

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Figures (14)

Fig. 1
Fig. 1

Optical arrangement for making a cylindrical hologram.

Fig. 2
Fig. 2

Model to calculate the Fresnel hologram.

Fig. 3
Fig. 3

System of cylindrical coordinates.

Fig. 4
Fig. 4

Segmentation for the CGCH.

Fig. 5
Fig. 5

Fast calculation method for the CGCH.

Fig. 6
Fig. 6

Error of the distance by using approximation (on the vertical direction).

Fig. 7
Fig. 7

Error of the distance by using approximation (on the θ direction).

Fig. 8
Fig. 8

Simulation of the reconstructed image with approximation and without approximation.

Fig. 9
Fig. 9

Process to take perspective images from different viewpoints.

Fig. 10
Fig. 10

Optical arrangement for making the lensless Fourier transform hologram.

Fig. 11
Fig. 11

Schematic of the fringe printing system.

Fig. 12
Fig. 12

Perspective images of the object data from several viewpoints.

Fig. 13
Fig. 13

Reconstructed images from different viewpoints.

Fig. 14
Fig. 14

Reconstructed images from different vertical viewpoints.

Tables (2)

Tables Icon

Table 1 Parameters of the Computer-Generated Cylindrical Hologram

Tables Icon

Table 2 Parameters of the Fringe Printer

Equations (57)

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

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