Abstract

A large-scale full-parallax computer-generated hologram (CGH) with four billion (216×216) pixels is created to reconstruct a fine true 3D image of a scene, with occlusions. The polygon-based method numerically generates the object field of a surface object, whose shape is provided by a set of vertex data of polygonal facets, while the silhouette method makes it possible to reconstruct the occluded scene. A novel technique using the segmented frame buffer is presented for handling and propagating large wave fields even in the case where the whole wave field cannot be stored in memory. We demonstrate that the full-parallax CGH, calculated by the proposed method and fabricated by a laser lithography system, reconstructs a fine 3D image accompanied by a strong sensation of depth.

© 2009 Optical Society of America

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References

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  1. M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2, 28-34 (1993).
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  3. K. Matsushima and M. Takai, “Recurrence formulas for fast creation of synthetic three-dimensional holograms,” Appl. Opt. 39, 6587-6594 (2000).
    [CrossRef]
  4. H. Yoshikawa, S. Iwase, and T. Oneda, “Fast computation of Fresnel holograms employing difference,” Proc. SPIE 3956, 48-55 (2000).
  5. T. Ito, N. Masuda, K. Yoshimura, A. Shiraki, T. Shimobaba, and T. Sugie, “Special-purpose computer HORN-5 for a real-time electroholography,” Opt. Express 13, 1923-1932(2005).
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  7. T. Shimobaba, A. Shiraki, Y. Ichihashi, N. Masuda, and T. Ito, “Interactive color electroholography using the FPGA technology and time division switching method,” IEICE Electron. Express 5, 271-277 (2008).
    [CrossRef]
  8. K. Matsushima, “Computer-generated holograms for three-dimensional surface objects with shade and texture,” Appl. Opt. 44, 4607-4614 (2005).
    [CrossRef]
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  11. K. Matsushima and A. Kondoh, “A wave optical algorithm for hidden-surface removal in digitally synthetic full-parallax holograms for three-dimensional objects,” Proc. SPIE Proc. 5290, 90-97 (2004).
  12. A. Kondoh and K. Matsushima, “Hidden surface removal in full-parallax CGHs by silhouette approximation,” Syst. Comput. Jpn. 38(6), 53-61 (2007).
    [CrossRef]
  13. K. Matsushima, “Exact hidden-surface removal in digitally synthetic full-parallax holograms,” Proc. SPIE 5742, 25-32(2005).
  14. R. P. Muffoletto, J. M. Tyler, and J. E. Tohline, “Shifted Fresnel diffraction for computational holography,” Opt. Express 15, 5631-5640 (2007).
    [CrossRef]
  15. K. Matsushima, H. Schimmel, and F. Wyrowski, “Fast calculation method for optical diffraction on tilted planes by use of the angular spectrum of plane waves,” J. Opt. Soc. Am. A 20, 1755-1762 (2003).
    [CrossRef]
  16. K. Matsushima, “Formulation of the rotational transformation of wave fields and their application to digital holography,” Appl. Opt. 47, D110-D116 (2008).
    [CrossRef]
  17. R. Bräuer, F. Wyrowski, and O. Bryngdahl, “Diffusers in digital holography,” J. Opt. Soc. Am. A 8, 572-578 (1991).
    [CrossRef]
  18. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996), chap. 3.10.
  19. D. H. Bailey and P. N. Swarztrauber, “The fractional Fourier transform and applications,” SIAM Rev. 33, 389-404(1991).
    [CrossRef]

2008 (4)

2007 (2)

R. P. Muffoletto, J. M. Tyler, and J. E. Tohline, “Shifted Fresnel diffraction for computational holography,” Opt. Express 15, 5631-5640 (2007).
[CrossRef]

A. Kondoh and K. Matsushima, “Hidden surface removal in full-parallax CGHs by silhouette approximation,” Syst. Comput. Jpn. 38(6), 53-61 (2007).
[CrossRef]

2006 (1)

2005 (3)

2004 (1)

K. Matsushima and A. Kondoh, “A wave optical algorithm for hidden-surface removal in digitally synthetic full-parallax holograms for three-dimensional objects,” Proc. SPIE Proc. 5290, 90-97 (2004).

2003 (1)

2000 (2)

K. Matsushima and M. Takai, “Recurrence formulas for fast creation of synthetic three-dimensional holograms,” Appl. Opt. 39, 6587-6594 (2000).
[CrossRef]

H. Yoshikawa, S. Iwase, and T. Oneda, “Fast computation of Fresnel holograms employing difference,” Proc. SPIE 3956, 48-55 (2000).

1999 (1)

1993 (1)

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

1991 (2)

R. Bräuer, F. Wyrowski, and O. Bryngdahl, “Diffusers in digital holography,” J. Opt. Soc. Am. A 8, 572-578 (1991).
[CrossRef]

D. H. Bailey and P. N. Swarztrauber, “The fractional Fourier transform and applications,” SIAM Rev. 33, 389-404(1991).
[CrossRef]

Ahrenberg, L.

Bailey, D. H.

D. H. Bailey and P. N. Swarztrauber, “The fractional Fourier transform and applications,” SIAM Rev. 33, 389-404(1991).
[CrossRef]

Benzie, P.

Böttger, J.

Bräuer, R.

Bryngdahl, O.

Deussen, O.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996), chap. 3.10.

Hahn, J.

Ichihashi, Y.

T. Shimobaba, A. Shiraki, Y. Ichihashi, N. Masuda, and T. Ito, “Interactive color electroholography using the FPGA technology and time division switching method,” IEICE Electron. Express 5, 271-277 (2008).
[CrossRef]

Ito, T.

Iwase, S.

H. Yoshikawa, S. Iwase, and T. Oneda, “Fast computation of Fresnel holograms employing difference,” Proc. SPIE 3956, 48-55 (2000).

Kim, H.

Kondoh, A.

A. Kondoh and K. Matsushima, “Hidden surface removal in full-parallax CGHs by silhouette approximation,” Syst. Comput. Jpn. 38(6), 53-61 (2007).
[CrossRef]

K. Matsushima and A. Kondoh, “A wave optical algorithm for hidden-surface removal in digitally synthetic full-parallax holograms for three-dimensional objects,” Proc. SPIE Proc. 5290, 90-97 (2004).

König, M.

Lee, B.

Lucente, M.

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

Magnor, M.

Masuda, N.

Matsushima, K.

K. Matsushima, “Formulation of the rotational transformation of wave fields and their application to digital holography,” Appl. Opt. 47, D110-D116 (2008).
[CrossRef]

A. Kondoh and K. Matsushima, “Hidden surface removal in full-parallax CGHs by silhouette approximation,” Syst. Comput. Jpn. 38(6), 53-61 (2007).
[CrossRef]

K. Matsushima, “Exact hidden-surface removal in digitally synthetic full-parallax holograms,” Proc. SPIE 5742, 25-32(2005).

K. Matsushima, “Computer-generated holograms for three-dimensional surface objects with shade and texture,” Appl. Opt. 44, 4607-4614 (2005).
[CrossRef]

K. Matsushima and A. Kondoh, “A wave optical algorithm for hidden-surface removal in digitally synthetic full-parallax holograms for three-dimensional objects,” Proc. SPIE Proc. 5290, 90-97 (2004).

K. Matsushima, H. Schimmel, and F. Wyrowski, “Fast calculation method for optical diffraction on tilted planes by use of the angular spectrum of plane waves,” J. Opt. Soc. Am. A 20, 1755-1762 (2003).
[CrossRef]

K. Matsushima and M. Takai, “Recurrence formulas for fast creation of synthetic three-dimensional holograms,” Appl. Opt. 39, 6587-6594 (2000).
[CrossRef]

Muffoletto, R. P.

Oneda, T.

H. Yoshikawa, S. Iwase, and T. Oneda, “Fast computation of Fresnel holograms employing difference,” Proc. SPIE 3956, 48-55 (2000).

Ritter, A.

Schimmel, H.

Shimobaba, T.

T. Shimobaba, A. Shiraki, Y. Ichihashi, N. Masuda, and T. Ito, “Interactive color electroholography using the FPGA technology and time division switching method,” IEICE Electron. Express 5, 271-277 (2008).
[CrossRef]

T. Ito, N. Masuda, K. Yoshimura, A. Shiraki, T. Shimobaba, and T. Sugie, “Special-purpose computer HORN-5 for a real-time electroholography,” Opt. Express 13, 1923-1932(2005).
[CrossRef]

Shiraki, A.

Strothotte, T.

Sugie, T.

Swarztrauber, P. N.

D. H. Bailey and P. N. Swarztrauber, “The fractional Fourier transform and applications,” SIAM Rev. 33, 389-404(1991).
[CrossRef]

Takai, M.

Tanaka, T.

Tohline, J. E.

Tyler, J. M.

Watson, J.

Wyrowski, F.

Yoshikawa, H.

H. Yoshikawa, S. Iwase, and T. Oneda, “Fast computation of Fresnel holograms employing difference,” Proc. SPIE 3956, 48-55 (2000).

Yoshimura, K.

Appl. Opt. (6)

IEICE Electron. Express (1)

T. Shimobaba, A. Shiraki, Y. Ichihashi, N. Masuda, and T. Ito, “Interactive color electroholography using the FPGA technology and time division switching method,” IEICE Electron. Express 5, 271-277 (2008).
[CrossRef]

J. Electron. Imaging (1)

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

J. Opt. Soc. Am. A (2)

Opt. Express (3)

Proc. SPIE (2)

H. Yoshikawa, S. Iwase, and T. Oneda, “Fast computation of Fresnel holograms employing difference,” Proc. SPIE 3956, 48-55 (2000).

K. Matsushima, “Exact hidden-surface removal in digitally synthetic full-parallax holograms,” Proc. SPIE 5742, 25-32(2005).

Proc. SPIE Proc. (1)

K. Matsushima and A. Kondoh, “A wave optical algorithm for hidden-surface removal in digitally synthetic full-parallax holograms for three-dimensional objects,” Proc. SPIE Proc. 5290, 90-97 (2004).

SIAM Rev. (1)

D. H. Bailey and P. N. Swarztrauber, “The fractional Fourier transform and applications,” SIAM Rev. 33, 389-404(1991).
[CrossRef]

Syst. Comput. Jpn. (1)

A. Kondoh and K. Matsushima, “Hidden surface removal in full-parallax CGHs by silhouette approximation,” Syst. Comput. Jpn. 38(6), 53-61 (2007).
[CrossRef]

Other (1)

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996), chap. 3.10.

Supplementary Material (4)

» Media 1: MOV (3737 KB)     
» Media 2: MOV (14206 KB)     
» Media 3: MOV (3897 KB)     
» Media 4: MOV (14569 KB)     

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Figures (9)

Fig. 1
Fig. 1

3D scene of “The Venus” and the definition of the hologram coordinate system.

Fig. 2
Fig. 2

Procedure for producing the object field of a triangular prism by the polygon-based method. (a) Object model. (b) Surface functions in tilted local coordinates. (c) Amplitude images of polygon fields in parallel local coordinates. (d) Amplitude image of the object field.

Fig. 3
Fig. 3

Segmentation of the frame buffer storing the object field. Note that the object plane is illustrated in this figure as a plane that does not slice the object for easy understanding, but in practical computation, it slices the object.

Fig. 4
Fig. 4

Estimation of the maximum diffraction area of a polygon as a bounding box of diffraction rectangles formed by each vertex of the polygon.

Fig. 5
Fig. 5

Numerical propagation in segmented frame buffers by the shifted Fresnel method.

Fig. 6
Fig. 6

Two-stage propagation for light shielding by the silhouette-masking technique. (a) Silhouette-masked wave field of the wallpaper. (b) Object field. (c) Combined field. All images are of amplitude.

Fig. 7
Fig. 7

Photographs of the optical reconstruction of the fabricated CGH by using transmitted illumination of a He–Ne laser. Photographs (a) – (d) are taken from different viewpoints.

Fig. 8
Fig. 8

Photographs of the optical reconstruction of the fabricated CGH by using reflected illumination of an ordinary red LED. (a) Medium shot (Media 1 , Media 2). (b) Close-up (Media 3,Media 4).

Fig. 9
Fig. 9

Itemized computation time for computing the Venus CGH.

Tables (1)

Tables Icon

Table 1 Parameters for Computing and Fabricating “The Venus” CGH

Equations (28)

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r ^ n = T n r n , r n = T n 1 r ^ n .
T n = cos θ n I + ( 1 cos θ n ) s n t · s n + sin θ n [ s n ] × ,
s n = z ^ × n n .
h n ( x n , y n ) = a n ( x n , y n ) exp [ i ϕ ( x n , y n ) ] ,
a n ( x n , y n ) = { A n inside polygon 0 outside polygon .
H n ( u n , v n ) = F { h n ( x n , y n ) } ,
T n 1 = [ t 1 , n t 2 , n t 3 , n t 4 , n t 5 , n t 6 , n t 7 , n t 8 , n t 9 , n ] ,
u n = α n ( u ^ n , v ^ n ) = t 1 , n u ^ n + t 2 , n v ^ n + t 3 , n w ^ ( u ^ n , v ^ n ) , v n = β n ( u ^ n , v ^ n ) = t 4 , n u ^ n + t 5 , n v ^ n + t 6 , n w ^ ( u ^ n , v ^ n ) ,
H ^ n ( u ^ n , v ^ n ) = H n ( α n ( u ^ n , v ^ n ) , β n ( u ^ n , v ^ n ) ) .
H ^ n ( u ^ n , v ^ n ) H n ( α n ( u ^ n , v ^ n ) u n ( 0 ) , β n ( u ^ n , v ^ n ) v n ( 0 ) ) ,
u n ( 0 ) = α n ( 0 , 0 ) = t 3 , n / λ ,
v n ( 0 ) = β n ( 0 , 0 ) = t 6 , n / λ ,
H ^ n ( u ^ n , v ^ n ; z ^ obj ) = H ^ n ( u ^ n , v ^ n ) exp [ i 2 π w ^ ( u ^ , v ^ ) ( z ^ obj z ^ n ( 0 ) ) ] .
h ^ n ( x ^ n , y ^ n ; z ^ obj ) = F 1 { H ^ n ( u ^ n , v ^ n ; z ^ obj ) } .
h ( x ^ , y ^ ; z ^ obj ) = n = 1 N p h ^ n ( x ^ n x ^ n ( 0 ) , y ^ n y ^ n ( 0 ) ; z ^ obj ) ,
θ x = sin 1 λ 2 Δ x , θ y = sin 1 λ 2 Δ y ,
h p , q ( x ^ , y ^ ; z ^ dest ) = s , t P z ^ dest z ^ source { h s , t ( x ^ , y ^ ; z ^ source ) } ,
h wp ( x ^ , y ^ ; z ^ wp ) = a wp ( x ^ , y ^ ) exp [ i ϕ ( x ^ , y ^ ) ] ,
a sil ( x ^ , y ^ ) = { 0 inside any projected polygon 1 outside any projected polygon .
h ( x ^ , y ^ ; z ^ obj ) = a sil ( x ^ , y ^ ) h wp ( x ^ , y ^ ; z ^ obj ) + h ( x ^ , y ^ ; z ^ obj ) ,
I ( x ^ , y ^ ) = | h ( x ^ , y ^ ; 0 ) + r ( x ^ , y ^ ) | 2 h ( x ^ , y ^ ; 0 ) r ( x ^ , y ^ ) * + B ,
T ( N ) 24 N ( 2 + log 2 N ) ,
T ( N M ) M 2 16 N M ( 2 + log 2 N log 2 M ) ,
T polygon = T FFT 1 + T interpol + T prop + T FFT 2 ,
T FFT 1 ( N surf ) 2 N surf log 2 N surf ,
T FFT 2 ( N field ) 2 N field log 2 N field ,
T interpol ( N field ) N field ,
T prop ( N field ) N field .

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