Abstract

Digitally synthetic holograms of surface model objects are investigated for reconstructing three-dimensional objects with shade and texture. The objects in the proposed techniques are composed of planar surfaces, and a property function defined for each surface provides shape and texture. The field emitted from each surface is independently calculated by a method based on rotational transformation of the property function by use of a fast Fourier transform (FFT) and totaled on the hologram. This technique has led to a reduction in computational cost: FFT operation is required only once for calculating a surface. In addition, another technique based on a theoretical model of the brightness of the reconstructed surfaces enables us to shade the surface of a reconstructed object as designed. Optical reconstructions of holograms synthesized by the proposed techniques are demonstrated.

© 2005 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2003 (1)

2002 (1)

K. Matsushima, A. Joko, “A high-resolution printer for fabricating computer-generated display holograms (in Japanese),” J. Inst. Image Inf. Television Eng. 56, 1989–1994 (2002).
[CrossRef]

2000 (1)

1999 (1)

1998 (1)

1997 (1)

1996 (1)

T. Ito, H. Eldeib, K. Yoshida, S. Takahashi, T. Yabe, T. Kunugi, “Special purpose computer for holography HORN-2,” Comput. Phys. Commun. 93, 13–20 (1996).
[CrossRef]

1993 (2)

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

T. Tommasi, B. Bianco, “Computer-generated holograms of tilted planes by a spatial frequency approach,” J. Opt. Soc. Am. A 10, 299–305 (1993).
[CrossRef]

1992 (2)

D. Leseberg, “Computer-generated three-dimensional image holograms,” Appl. Opt. 31, 223–229 (1992).
[CrossRef] [PubMed]

A. D. Stein, Z. Wang, J. J. S. Leigh, “Computer-generated holograms: a simplified ray-tracing approach,” Comput. Phys. 6, 389–392 (1992).
[CrossRef]

1991 (1)

1988 (1)

1966 (1)

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

Berriel-Valdos, R.

Bianco, B.

Böttger, J.

Bräuer, R.

Bryngdahl, O.

Delen, N.

Deussen, O.

Eldeib, H.

T. Ito, H. Eldeib, K. Yoshida, S. Takahashi, T. Yabe, T. Kunugi, “Special purpose computer for holography HORN-2,” Comput. Phys. Commun. 93, 13–20 (1996).
[CrossRef]

Frère, C.

Goodman, J. W.

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

Hooker, B.

Ito, T.

T. Ito, H. Eldeib, K. Yoshida, S. Takahashi, T. Yabe, T. Kunugi, “Special purpose computer for holography HORN-2,” Comput. Phys. Commun. 93, 13–20 (1996).
[CrossRef]

Iwase, S.

H. Yoshikawa, S. Iwase, T. Oneda, “Fast computation of Fresnel holograms employing difference,” in Practical Holography XIV and Holographic Materials VI, S. A. Benton, S. H. Stevenson, J. T. Trout, eds., Proc. SPIE3956, 48–55 (2000).
[CrossRef]

Joko, A.

K. Matsushima, A. Joko, “A high-resolution printer for fabricating computer-generated display holograms (in Japanese),” J. Inst. Image Inf. Television Eng. 56, 1989–1994 (2002).
[CrossRef]

Juárez-Pérez, J. L.

Kondoh, A.

K. Matsushima, A. Kondoh, “Wave optical algorithm for creating digitally synthetic holograms of three-dimensional surface objects,” in Practical Holography XVII and Holographic Materials IX, T. H. Jeong, S. H. Stevenson, eds., Proc. SPIE5005, 190–197 (2003).
[CrossRef]

König, M.

Kunugi, T.

T. Ito, H. Eldeib, K. Yoshida, S. Takahashi, T. Yabe, T. Kunugi, “Special purpose computer for holography HORN-2,” Comput. Phys. Commun. 93, 13–20 (1996).
[CrossRef]

Leigh, J. J. S.

A. D. Stein, Z. Wang, J. J. S. Leigh, “Computer-generated holograms: a simplified ray-tracing approach,” Comput. Phys. 6, 389–392 (1992).
[CrossRef]

Leseberg, D.

Lucente, M.

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

Matsushima, K.

K. Matsushima, H. Schimmel, 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, A. Joko, “A high-resolution printer for fabricating computer-generated display holograms (in Japanese),” J. Inst. Image Inf. Television Eng. 56, 1989–1994 (2002).
[CrossRef]

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

K. Matsushima, A. Kondoh, “Wave optical algorithm for creating digitally synthetic holograms of three-dimensional surface objects,” in Practical Holography XVII and Holographic Materials IX, T. H. Jeong, S. H. Stevenson, eds., Proc. SPIE5005, 190–197 (2003).
[CrossRef]

Olivares-Pérez, A.

Oneda, T.

H. Yoshikawa, S. Iwase, T. Oneda, “Fast computation of Fresnel holograms employing difference,” in Practical Holography XIV and Holographic Materials VI, S. A. Benton, S. H. Stevenson, J. T. Trout, eds., Proc. SPIE3956, 48–55 (2000).
[CrossRef]

Ritter, A.

Schimmel, H.

Stein, A. D.

A. D. Stein, Z. Wang, J. J. S. Leigh, “Computer-generated holograms: a simplified ray-tracing approach,” Comput. Phys. 6, 389–392 (1992).
[CrossRef]

Strothotte, T.

Takahashi, S.

T. Ito, H. Eldeib, K. Yoshida, S. Takahashi, T. Yabe, T. Kunugi, “Special purpose computer for holography HORN-2,” Comput. Phys. Commun. 93, 13–20 (1996).
[CrossRef]

Takai, M.

Tommasi, T.

Wang, Z.

A. D. Stein, Z. Wang, J. J. S. Leigh, “Computer-generated holograms: a simplified ray-tracing approach,” Comput. Phys. 6, 389–392 (1992).
[CrossRef]

Waters, J. P.

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

Wyrowski, F.

Yabe, T.

T. Ito, H. Eldeib, K. Yoshida, S. Takahashi, T. Yabe, T. Kunugi, “Special purpose computer for holography HORN-2,” Comput. Phys. Commun. 93, 13–20 (1996).
[CrossRef]

Yoshida, K.

T. Ito, H. Eldeib, K. Yoshida, S. Takahashi, T. Yabe, T. Kunugi, “Special purpose computer for holography HORN-2,” Comput. Phys. Commun. 93, 13–20 (1996).
[CrossRef]

Yoshikawa, H.

H. Yoshikawa, S. Iwase, T. Oneda, “Fast computation of Fresnel holograms employing difference,” in Practical Holography XIV and Holographic Materials VI, S. A. Benton, S. H. Stevenson, J. T. Trout, eds., Proc. SPIE3956, 48–55 (2000).
[CrossRef]

Appl. Opt. (5)

Appl. Phys. Lett. (1)

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

Comput. Phys. (1)

A. D. Stein, Z. Wang, J. J. S. Leigh, “Computer-generated holograms: a simplified ray-tracing approach,” Comput. Phys. 6, 389–392 (1992).
[CrossRef]

Comput. Phys. Commun. (1)

T. Ito, H. Eldeib, K. Yoshida, S. Takahashi, T. Yabe, T. Kunugi, “Special purpose computer for holography HORN-2,” Comput. Phys. Commun. 93, 13–20 (1996).
[CrossRef]

J. Electron. Imag. (1)

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

J. Inst. Image Inf. Television Eng. (1)

K. Matsushima, A. Joko, “A high-resolution printer for fabricating computer-generated display holograms (in Japanese),” J. Inst. Image Inf. Television Eng. 56, 1989–1994 (2002).
[CrossRef]

J. Opt. Soc. Am. A (4)

Other (3)

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

K. Matsushima, A. Kondoh, “Wave optical algorithm for creating digitally synthetic holograms of three-dimensional surface objects,” in Practical Holography XVII and Holographic Materials IX, T. H. Jeong, S. H. Stevenson, eds., Proc. SPIE5005, 190–197 (2003).
[CrossRef]

H. Yoshikawa, S. Iwase, T. Oneda, “Fast computation of Fresnel holograms employing difference,” in Practical Holography XIV and Holographic Materials VI, S. A. Benton, S. H. Stevenson, J. T. Trout, eds., Proc. SPIE3956, 48–55 (2000).
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Geometry and definitions of global coordinates and tilted local coordinates defined for a planar surface.

Fig. 2
Fig. 2

Fields emitted from surfaces with (a) a constant phase, (b) a diffusive phase, and (c) a diffusive phase multiplied by the phase of a plane wave propagating to a hologram.

Fig. 3
Fig. 3

Schematic of rotation upon two axes: (a) a plane rotated upon the z ^ axis before the x axis and (b) resampling areas of the Fourier spectrum at several rotation angles in the rotation scheme.

Fig. 4
Fig. 4

(a) Planar object used for fabricating the hologram of a plane rotated upon a single axis. (b) Geometry for capturing the reconstruction. The dimensions of texture of a checker embedded in the property function are 16.4 mm × 8.2 mm.

Fig. 5
Fig. 5

Optically reconstructed images of a hologram captured by moving a camera (a)–(c) from left to right and (d)–(f) back and forth.

Fig. 6
Fig. 6

Planar object used for fabricating a hologram in two-axis rotation.

Fig. 7
Fig. 7

Optical reconstructions of holograms of planar surfaces rotated at several angles.

Fig. 8
Fig. 8

Model of brightness of a planar surface expressed by a property function sampled at an equidistant grid.

Fig. 9
Fig. 9

Curves of the angle factor for several values of γ.

Fig. 10
Fig. 10

Optical reconstructions of unshaded hexagonal prisms (a) without brightness compensation and (b), (c) with compensation in γ = 0, 0.5, respectively.

Fig. 11
Fig. 11

Optical reconstructions of 3-D objects shaded with illumination light. Cubes are illuminated from the upper right in (a) le = 0 and from the upper left in (b) le = 0.7; a hexagonal prism (le = 0.5) is shown in (c). Brightnesses of objects are all compensated for at γ = 0.5. Arrows and numbers in parentheses define the illumination vector in global coordinates.

Equations (31)

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h n ( x n , y n ) = a n ( x n , y n ) Ψ ( x n , y n ) p n ( x n , y n ) ,
Ψ ( x n , y n ) = exp [ i k ϕ d ( x n , y n ) ] ,
p n ( x n , y n ) = exp [ i ( k x , n x n + k y , n y n ) ] ,
h ^ n ( x ^ n , y ^ n ) = R θ x θ y θ z { h n ( x n , y n ) } ,
h ^ ( x ^ , y ^ ) = n P d n { h ^ n ( x ^ n , y ^ n ) } ,
H ( u ,     v ) = { h ( x , y ) } = - h ( x , y ) exp [ - i 2 π ( u x + v y ) ] d x d y ,
u = α ( u ^ , v ^ ) = a 1 u ^ + a 2 v ^ + a 3 w ^ ( u ^ , v ^ ) , v = β ( u ^ , v ^ ) = a 4 u ^ + a 5 v ^ + a 6 w ^ ( u ^ , v ^ ) ,
T - 1 = [ a 1 a 2 a 3 a 4 a 5 a 6 a 7 a 8 a 9 ] .
H ^ ( u ^ , v ^ ) = H [ α ( u ^ , v ^ ) ,     β ( u ^ , v ^ ) ] .
h ^ ( x ^ , y ^ ) = F - 1 { H ^ ( u ^ , v ^ ) } = - H ^ ( u ^ , v ^ ) exp [ i 2 π ( x ^ u ^ + y ^ v ^ ) ] d u ^ d v ^ .
T - 1 = [ cos θ y cos θ z cos θ y cos θ z - sin θ y - sin θ z cos θ z 0 sin θ y cos θ z sin θ y sin θ z cos θ y ] .
u 0 = α ( 0 , 0 ) = a 3 / λ ,             v 0 = β ( 0 , 0 ) = a 6 / λ .
u = u - u 0 ,             v = v - v 0 .
H ( u , v ) = H ( u + u 0 , v + v 0 ) .
H ^ ( u ^ , v ^ ) H ( u - u 0 , v - v 0 ) = H ( α ( u ^ , v ^ ) - u 0 ,     β ( u ^ , v ^ ) - v 0 ) ,
H ( u , v ) = F { h ( x , y ) exp [ - i 2 π ( u 0 x + v 0 y ) ] } .
H ( u , v ) = F { a ( x , y ) Ψ ( x , y ) exp { i [ ( k x - 2 π u 0 ) x + ( k y - 2 π v 0 ) y ] } } ,
k x = 2 π a 3 / λ ,             k y = 2 π a 6 / λ .
H ( u , v ) = F { a ( x , y ) Ψ ( x , y ) } .
h ( x , y ) a ( x , y ) Ψ ( x , y ) ,
H ( u , v ) F { h ( x , y ) } .
H ^ ( u ^ , v ^ ) H ( α ( u ^ , v ^ ) - α ( 0 , 0 ) ,     β ( u ^ , v ^ ) - β ( 0 , 0 ) ) .
Φ = δ A h ( x , y ) 2 d x d y δ A σ a 2 ,
L = d Φ / d Ω cos θ v δ A .
L σ a 2 π tan 2 ψ d cos θ v .
L = σ a 2 π tan 2 φ d ( 1 + γ ) ( cos θ v + γ ) ,
a = [ L π tan 2 φ d σ ( cos θ v + γ ) ( 1 + γ ) ] 1 / 2 .
L n = L 0 ( cos θ ^ n + l e ) ,
a n = a 0 [ ( cos θ ^ n + l e ) ( cos θ n + γ ) 1 + γ ] 1 / 2 ,
a 0 [ L 0 π tan 2 φ d σ ] 1 / 2 .
h ^ ( x ^ , y ^ ) = F - 1 { n H ^ n ( u ^ n , v ^ n ) exp [ i 2 π w ^ ( u ^ n , v ^ n ) d n ] } ,

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