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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2003

2002

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

1999

1998

1997

1996

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

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

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

1988

1966

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.

Appl. Phys. Lett.

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

Comput. Phys.

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.

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.

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.

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

Other

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]

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]

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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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