Abstract

We develop a novel method to generate hologram of three-dimensional (3D) textured triangle-mesh-model that is reconstructed from ordinary digital photos. This method allows analytically encoding the 3D model consisting of triangles. In contrast to other polygon based holographic computations, our full analytical method will free oneself from the numerical error that is in the angular spectrum due to the Whittaker-Shannon sampling. In order to saving the computation time, we employ the GPU platform that is remarkably superior to the CPU’s. We have rendered a true-life scene with colored textures as the first demo by our homemade software. The holographic reconstructed scene possesses high performances in many aspects such as depth cues, surface textures, shadings, and occlusions, etc. The GPU’s algorithm performs hundreds of times faster than those of CPU.

© 2010 OSA

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  25. “Autodesk® ImageModeler™,” URL http://usa.autodesk.com/adsk/servlet/index?siteID=123112&id=11390028
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2009 (2)

2008 (4)

2006 (2)

2005 (1)

C. Slinger, C. Cameron, and M. Stanley, “Computer-generated holography as a generic display technology,” Computer 38(8), 46–53 (2005).
[CrossRef]

2003 (2)

1999 (1)

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164(4-6), 233–245 (1999).
[CrossRef]

1998 (1)

1997 (1)

D. Mendlovic, Z. Zalevsky, and N. Konforti, “Computation considerations and fast algorithms for calculation the diffraction integral,” J. Mod. Opt. 44, 407–414 (1997).
[CrossRef]

1996 (1)

1995 (1)

J. Watlington, M. Lucente, C. Sparrell, V. M. Bove, and J. Tamitani, “A Hardware Architecture for Rapid Generation of Electro-Holographic Fringe Patterns,” Proc. SPIE 2406, 172–183 (1995).

1993 (2)

R. N. Bracewell, K.-Y. Chang, A. K. Jha, and Y.-H. Wang, “Affine theorem for two-dimensional Fourier transform,” Electron. Lett. 29(3), 304–306 (1993).
[CrossRef]

M. Lucente, “Interactive Computation of Holograms Using a Look-Up Table,” J. Electron. Imaging 2(1), 28–34 (1993).
[CrossRef]

1988 (1)

1968 (1)

E. Lalor, “Conditions for the Validity of the Angular Spectrun of Plane Waves,” J. Opt. Soc. Am. A 58(9), 1235–1237 (1968).
[CrossRef]

Ahrenberg, L.

Benzie, P.

Bernardo, L. M.

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164(4-6), 233–245 (1999).
[CrossRef]

Bove, V. M.

J. Watlington, M. Lucente, C. Sparrell, V. M. Bove, and J. Tamitani, “A Hardware Architecture for Rapid Generation of Electro-Holographic Fringe Patterns,” Proc. SPIE 2406, 172–183 (1995).

Bracewell, R. N.

R. N. Bracewell, K.-Y. Chang, A. K. Jha, and Y.-H. Wang, “Affine theorem for two-dimensional Fourier transform,” Electron. Lett. 29(3), 304–306 (1993).
[CrossRef]

Cameron, C.

C. Slinger, C. Cameron, and M. Stanley, “Computer-generated holography as a generic display technology,” Computer 38(8), 46–53 (2005).
[CrossRef]

Chang, K.-Y.

R. N. Bracewell, K.-Y. Chang, A. K. Jha, and Y.-H. Wang, “Affine theorem for two-dimensional Fourier transform,” Electron. Lett. 29(3), 304–306 (1993).
[CrossRef]

Delen, N.

Di, J. L.

Dorsch, R. G.

Ferreira, C.

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164(4-6), 233–245 (1999).
[CrossRef]

Frère, C.

Garcia, J.

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164(4-6), 233–245 (1999).
[CrossRef]

García, J.

Hahn, J.

Hooker, B.

Iizuka, K.

K. Iizuka, “Welcome to the wonderful world of 3D: introduction, principles and history,” Opt. Photon. News 17(7), 42–51 (2006).
[CrossRef]

Jha, A. K.

R. N. Bracewell, K.-Y. Chang, A. K. Jha, and Y.-H. Wang, “Affine theorem for two-dimensional Fourier transform,” Electron. Lett. 29(3), 304–306 (1993).
[CrossRef]

Jiang, H. Z.

Kim, E. S.

Kim, H.

Kim, S. C.

Konforti, N.

D. Mendlovic, Z. Zalevsky, and N. Konforti, “Computation considerations and fast algorithms for calculation the diffraction integral,” J. Mod. Opt. 44, 407–414 (1997).
[CrossRef]

Lalor, E.

E. Lalor, “Conditions for the Validity of the Angular Spectrun of Plane Waves,” J. Opt. Soc. Am. A 58(9), 1235–1237 (1968).
[CrossRef]

Lee, B.

Leseberg, D.

Lim, Y.

Lucente, M.

J. Watlington, M. Lucente, C. Sparrell, V. M. Bove, and J. Tamitani, “A Hardware Architecture for Rapid Generation of Electro-Holographic Fringe Patterns,” Proc. SPIE 2406, 172–183 (1995).

M. Lucente, “Interactive Computation of Holograms Using a Look-Up Table,” J. Electron. Imaging 2(1), 28–34 (1993).
[CrossRef]

Magnor, M.

Marinho, F.

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164(4-6), 233–245 (1999).
[CrossRef]

Mas, D.

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164(4-6), 233–245 (1999).
[CrossRef]

J. García, D. Mas, and R. G. Dorsch, “Fractional-Fourier-transform calculation through the fast-Fourier-transform algorithm,” Appl. Opt. 35(35), 7013–7018 (1996).
[CrossRef] [PubMed]

Matsushima, K.

Mendlovic, D.

D. Mendlovic, Z. Zalevsky, and N. Konforti, “Computation considerations and fast algorithms for calculation the diffraction integral,” J. Mod. Opt. 44, 407–414 (1997).
[CrossRef]

Park, G.

Petz, C.

C. Petz and M. Magnor, “Fast Hologram Synthesis for 3D Geometry Models using Graphics Hardware,” Proc. SPIE 5005, 266–275 (2003).
[CrossRef]

Schimmel, H.

Shimobaba, T.

Slinger, C.

C. Slinger, C. Cameron, and M. Stanley, “Computer-generated holography as a generic display technology,” Computer 38(8), 46–53 (2005).
[CrossRef]

Sparrell, C.

J. Watlington, M. Lucente, C. Sparrell, V. M. Bove, and J. Tamitani, “A Hardware Architecture for Rapid Generation of Electro-Holographic Fringe Patterns,” Proc. SPIE 2406, 172–183 (1995).

Stanley, M.

C. Slinger, C. Cameron, and M. Stanley, “Computer-generated holography as a generic display technology,” Computer 38(8), 46–53 (2005).
[CrossRef]

Tamitani, J.

J. Watlington, M. Lucente, C. Sparrell, V. M. Bove, and J. Tamitani, “A Hardware Architecture for Rapid Generation of Electro-Holographic Fringe Patterns,” Proc. SPIE 2406, 172–183 (1995).

Wang, Y.-H.

R. N. Bracewell, K.-Y. Chang, A. K. Jha, and Y.-H. Wang, “Affine theorem for two-dimensional Fourier transform,” Electron. Lett. 29(3), 304–306 (1993).
[CrossRef]

Watlington, J.

J. Watlington, M. Lucente, C. Sparrell, V. M. Bove, and J. Tamitani, “A Hardware Architecture for Rapid Generation of Electro-Holographic Fringe Patterns,” Proc. SPIE 2406, 172–183 (1995).

Watson, J.

Wyrowski, F.

Zalevsky, Z.

D. Mendlovic, Z. Zalevsky, and N. Konforti, “Computation considerations and fast algorithms for calculation the diffraction integral,” J. Mod. Opt. 44, 407–414 (1997).
[CrossRef]

Zhao, J. L.

Appl. Opt. (5)

Computer (1)

C. Slinger, C. Cameron, and M. Stanley, “Computer-generated holography as a generic display technology,” Computer 38(8), 46–53 (2005).
[CrossRef]

Electron. Lett. (1)

R. N. Bracewell, K.-Y. Chang, A. K. Jha, and Y.-H. Wang, “Affine theorem for two-dimensional Fourier transform,” Electron. Lett. 29(3), 304–306 (1993).
[CrossRef]

J. Electron. Imaging (1)

M. Lucente, “Interactive Computation of Holograms Using a Look-Up Table,” J. Electron. Imaging 2(1), 28–34 (1993).
[CrossRef]

J. Mod. Opt. (1)

D. Mendlovic, Z. Zalevsky, and N. Konforti, “Computation considerations and fast algorithms for calculation the diffraction integral,” J. Mod. Opt. 44, 407–414 (1997).
[CrossRef]

J. Opt. Soc. Am. A (3)

Opt. Commun. (1)

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164(4-6), 233–245 (1999).
[CrossRef]

Opt. Express (4)

Opt. Photon. News (1)

K. Iizuka, “Welcome to the wonderful world of 3D: introduction, principles and history,” Opt. Photon. News 17(7), 42–51 (2006).
[CrossRef]

Proc. SPIE (2)

J. Watlington, M. Lucente, C. Sparrell, V. M. Bove, and J. Tamitani, “A Hardware Architecture for Rapid Generation of Electro-Holographic Fringe Patterns,” Proc. SPIE 2406, 172–183 (1995).

C. Petz and M. Magnor, “Fast Hologram Synthesis for 3D Geometry Models using Graphics Hardware,” Proc. SPIE 5005, 266–275 (2003).
[CrossRef]

Other (6)

V. M. Bove, Jr., W. J. Plesniak, T. Quentmeyer, and J. Barabas, “Real-Time Holographic Video Images with Commodity PC Hardware,” Proc. SPIE Stereoscopic Displays and Applications 5664, 255–262 (2005).

NVIDIA, “NVIDIA CUDA Compute Unified Device Architecture Programming Guide Version 2.1,” (2008).

“Autodesk® ImageModeler™,” URL http://usa.autodesk.com/adsk/servlet/index?siteID=123112&id=11390028

See for example, Stanford 3D Scanning Repository, and XYZ RGB Inc.

J. W. Goodman, Introduction to Fourier optics (Roberts & Company Publishers, 2004)

M. Zhang, T. S. Yeo, L. W. Li, and Y. B. Gan, “Parallel FFT Based Fast Algorithms for Solving Large Scale Electromagnetic Problems,” in IEEE Antennas and Propagation Society International Symposium, pp. 3995–3998 (2006).

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Figures (4)

Fig. 1
Fig. 1

(a) Local coordinate system of triangle mesh object and the global coordinate system. (b)Diffraction by one of the triangles

Fig. 2
Fig. 2

(a) A schematic illustration of a slanted triangle reconstruction. (b) and (c) are reconstruction results at the plane I and II where point A and B locate.

Fig. 3
Fig. 3

Images for different aspects of the scene: (a), (c) original photos of the true-life scene taken by digital camera. (b), (d) and (e)-(g) numerical reconstructions of the scene from different aspects.

Fig. 4
Fig. 4

Images of numerical reconstruction: (a) focus on king, (b) focus on pawn

Tables (1)

Tables Icon

Table 1 Holographic computation times for several triangular-mesh models with the resolution of 1024 by 768

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

[ x l y l z l ] = ( r 11 r 12 r 13 r 21 r 22 r 23 r 31 r 32 r 33 ) [ x g x c y g y c z g z c ] ,   and   [ x g y g z g ] = ( r 11 ' r 12 ' r 13 ' r 21 ' r 22 ' r 23 ' r 31 ' r 32 ' r 33 ' ) [ x l y l z l ] + [ x c y c z c ]
O H ( x H , y H ) = ( 1 / i λ ) O O ( x l , y l ) exp [ i 2 π ( r 31 ' x l + r 32 ' y l + z c ) / λ ] [ exp ( i k r ) / r ] d x l d y l
( x H x c ) 2 + ( y H y c ) 2 + z c 2 > > ( x g x c ) 2   and   ( y g y c ) 2
r = r 0 + x l 2 + y l 2 2 r 0 [ r 11 ' ( x H x c ) + r 21 ' ( y H y c ) r 31 ' z c ] x l + [ r 12 ' ( x H x c ) + r 22 ' ( y H y c ) r 32 ' z c ] y l r 0
O H ( x H , y H ) = exp [ i k ( z c + r 0 ) ] i λ r 0 O O ( x l , y l ) Q ( x l , y l ) exp [ i 2 π λ r 0 ( x H ' x l + y H ' y l ) ] d x l d y l
O H ( x H , y H ) = exp [ i k ( z c + r 0 ) ] i λ r 0 F [ O O ( x l , y l ) ]
F [ O O ( x l , y l ) ] = ( a 22 a 11 a 12 a 21 ) exp ( i 2 π a 13 x H ' + a 23 y H ' λ r 0 ) F Δ ( a 11 x H ' + a 21 y H ' λ r 0 , a 12 x H ' + a 22 y H ' λ r 0 )

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