Abstract

One of the major problems in computer-generated holography is the high computation cost involved for the calculation of fringe patterns. Recently, the problem has been addressed by imposing a horizontal parallax only constraint whereby the process can be simplified to the computation of one-dimensional sublines, each representing a scan plane of the object scene. Subsequently the sublines can be expanded to a two-dimensional hologram through multiplication with a reference signal. Furthermore, economical hardware is available with which sublines can be generated in a computationally free manner with high throughput of approximately 100M pixels/second. Apart from decreasing the computation loading, the sublines can be treated as intermediate data that can be compressed by simply downsampling the number of sublines. Despite these favorable features, the method is suitable only for the generation of white light (rainbow) holograms, and the resolution of the reconstructed image is inferior to the classical Fresnel hologram. We propose to generate holograms from one-dimensional sublines so that the above- mentioned problems can be alleviated. However, such an approach also leads to a substantial increase in computation loading. To overcome this problem we encapsulated the conversion of sublines to holograms as a multirate filtering process and implemented the latter by use of a fast Fourier transform. Evaluation reveals that, for holograms of moderate size, our method is capable of operating 40,000 times faster than the calculation of Fresnel holograms based on the precomputed table lookup method. Although there is no relative vertical parallax between object points at different distance planes, a global vertical parallax is preserved for the object scene as a whole and the reconstructed image can be observed easily.

© 2009 Optical Society of America

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References

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  1. T.-C.Poon, ed., Digital Holography and Three-Dimensional Display (Springer-Verlag, 2006).
    [CrossRef]
  2. H. Yoshikawa and K. Takei, “Development of a compact direct fringe printer for computer-generated holograms,” Proc. SPIE 5290, 114-121 (2004).
    [CrossRef]
  3. H. Yoshikawa and M. Tachinami, “Development of direct fringe printer for computer-generated holograms,” Proc. SPIE 5742, 259-266 (2005).
    [CrossRef]
  4. T.-C. Poon, “Three-dimensional television using optical scanning holography,” Inf. Disp. 3, 12-16 (2002).
    [CrossRef]
  5. T. Shimobaba, Y. Sato, J. Miura, M. Takenouchi, and T. Ito, “Real-time digital holographic microscopy using the graphic processing unit,” Opt. Express 16, 11776-11781 (2008).
    [CrossRef] [PubMed]
  6. L. Ahrenberg, “Computer generated holography using parallel commodity graphics hardware,” Opt. Express 14, 7636-7641(2006).
    [CrossRef] [PubMed]
  7. Y. Seo, H. Cho, and D. Kim, “High-performance CGH processor for real-time digital holography,” in Laser Applications to Chemical, Security, and Environmental Analysis, OSA Technical Digest (CD) (Optical Society, 2008), paper JMA9.
  8. 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]
  9. M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron Imaging 2, 28-34 (1993).
    [CrossRef]
  10. S. C. Kim and E. S. Kim, “Effective generation of digital holograms of three-dimensional objects using a novel lookup table method,” Appl. Opt. 47, D55-D62 (2008).
    [CrossRef] [PubMed]
  11. S. C. Kim and E. S. Kim, “Fast computation of hologram patterns of a 3D object using run-length encoding and novel lookup table methods,” Appl. Opt. 48, 1030-1041(2009).
    [CrossRef]
  12. T. Yamaguchi, G. Okabe, and H. Yoshikawa, “Real-time image plane full-color and full-parallax holographic video display system,” Opt. Eng. 46, 125801 (2007).
    [CrossRef]
  13. H. Yoshikawa and H. Taniguchi, “Computer henerated rainbow hologram,” Opt. Rev. 6, 118-123 (1999).
    [CrossRef]
  14. H. Yoshikawa and A. Kagotani, “Full color computer-generated rainbow hologram with enlarged viewing angle,” Opt. Rev. 9, 251-254 (2002).
    [CrossRef]
  15. H. Yoshikawa, “Computer-generated holograms for white light reconstruction,” in Digital Holography and Three-Dimensional Display: Principles and Applications, T. -C. Poon, ed. (Springer-Verlag, 2006).
    [CrossRef]
  16. H. Yoshikawa, “Fast computation of Fresnel holograms employing difference,” Opt. Rev. 8, 331-335 (2001).
    [CrossRef]
  17. P. Tsang, J. Liu, T.-C. Poon, and W. K. Cheung, “Fast generation of hologram sublines based on field programmable gate array,” in Holography and Three-Dimensional Imaging, OSA Technical Digest Series (Optical Society of America, 2009), paper Dwc2.
  18. V. L. Tuft and S. Øystein , “Holovision 2.2 user's manual,” http://www2.edge.no/projects/holovision/doc/holovision_221_manual.pdf, 2001.
  19. P. P. Vaidyanathan, “Multirate Systems and Filter Banks" (Prentice-Hall, 1993).

2009 (1)

2008 (3)

2007 (1)

T. Yamaguchi, G. Okabe, and H. Yoshikawa, “Real-time image plane full-color and full-parallax holographic video display system,” Opt. Eng. 46, 125801 (2007).
[CrossRef]

2006 (1)

2005 (1)

H. Yoshikawa and M. Tachinami, “Development of direct fringe printer for computer-generated holograms,” Proc. SPIE 5742, 259-266 (2005).
[CrossRef]

2004 (1)

H. Yoshikawa and K. Takei, “Development of a compact direct fringe printer for computer-generated holograms,” Proc. SPIE 5290, 114-121 (2004).
[CrossRef]

2002 (2)

T.-C. Poon, “Three-dimensional television using optical scanning holography,” Inf. Disp. 3, 12-16 (2002).
[CrossRef]

H. Yoshikawa and A. Kagotani, “Full color computer-generated rainbow hologram with enlarged viewing angle,” Opt. Rev. 9, 251-254 (2002).
[CrossRef]

2001 (1)

H. Yoshikawa, “Fast computation of Fresnel holograms employing difference,” Opt. Rev. 8, 331-335 (2001).
[CrossRef]

1999 (1)

H. Yoshikawa and H. Taniguchi, “Computer henerated rainbow hologram,” Opt. Rev. 6, 118-123 (1999).
[CrossRef]

1993 (1)

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

Ahrenberg, L.

Cheung, W. K.

P. Tsang, J. Liu, T.-C. Poon, and W. K. Cheung, “Fast generation of hologram sublines based on field programmable gate array,” in Holography and Three-Dimensional Imaging, OSA Technical Digest Series (Optical Society of America, 2009), paper Dwc2.

Cho, H.

Y. Seo, H. Cho, and D. Kim, “High-performance CGH processor for real-time digital holography,” in Laser Applications to Chemical, Security, and Environmental Analysis, OSA Technical Digest (CD) (Optical Society, 2008), paper JMA9.

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.

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. Shimobaba, Y. Sato, J. Miura, M. Takenouchi, and T. Ito, “Real-time digital holographic microscopy using the graphic processing unit,” Opt. Express 16, 11776-11781 (2008).
[CrossRef] [PubMed]

Kagotani, A.

H. Yoshikawa and A. Kagotani, “Full color computer-generated rainbow hologram with enlarged viewing angle,” Opt. Rev. 9, 251-254 (2002).
[CrossRef]

Kim, D.

Y. Seo, H. Cho, and D. Kim, “High-performance CGH processor for real-time digital holography,” in Laser Applications to Chemical, Security, and Environmental Analysis, OSA Technical Digest (CD) (Optical Society, 2008), paper JMA9.

Kim, E. S.

Kim, S. C.

Liu, J.

P. Tsang, J. Liu, T.-C. Poon, and W. K. Cheung, “Fast generation of hologram sublines based on field programmable gate array,” in Holography and Three-Dimensional Imaging, OSA Technical Digest Series (Optical Society of America, 2009), paper Dwc2.

Lucente, M.

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

Masuda, N.

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]

Miura, J.

Okabe, G.

T. Yamaguchi, G. Okabe, and H. Yoshikawa, “Real-time image plane full-color and full-parallax holographic video display system,” Opt. Eng. 46, 125801 (2007).
[CrossRef]

Øystein, S.

V. L. Tuft and S. Øystein , “Holovision 2.2 user's manual,” http://www2.edge.no/projects/holovision/doc/holovision_221_manual.pdf, 2001.

Poon, T.-C.

T.-C. Poon, “Three-dimensional television using optical scanning holography,” Inf. Disp. 3, 12-16 (2002).
[CrossRef]

P. Tsang, J. Liu, T.-C. Poon, and W. K. Cheung, “Fast generation of hologram sublines based on field programmable gate array,” in Holography and Three-Dimensional Imaging, OSA Technical Digest Series (Optical Society of America, 2009), paper Dwc2.

Sato, Y.

Seo, Y.

Y. Seo, H. Cho, and D. Kim, “High-performance CGH processor for real-time digital holography,” in Laser Applications to Chemical, Security, and Environmental Analysis, OSA Technical Digest (CD) (Optical Society, 2008), paper JMA9.

Shimobaba, T.

T. Shimobaba, Y. Sato, J. Miura, M. Takenouchi, and T. Ito, “Real-time digital holographic microscopy using the graphic processing unit,” Opt. Express 16, 11776-11781 (2008).
[CrossRef] [PubMed]

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]

Shiraki, A.

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]

Tachinami, M.

H. Yoshikawa and M. Tachinami, “Development of direct fringe printer for computer-generated holograms,” Proc. SPIE 5742, 259-266 (2005).
[CrossRef]

Takei, K.

H. Yoshikawa and K. Takei, “Development of a compact direct fringe printer for computer-generated holograms,” Proc. SPIE 5290, 114-121 (2004).
[CrossRef]

Takenouchi, M.

Taniguchi, H.

H. Yoshikawa and H. Taniguchi, “Computer henerated rainbow hologram,” Opt. Rev. 6, 118-123 (1999).
[CrossRef]

Tsang, P.

P. Tsang, J. Liu, T.-C. Poon, and W. K. Cheung, “Fast generation of hologram sublines based on field programmable gate array,” in Holography and Three-Dimensional Imaging, OSA Technical Digest Series (Optical Society of America, 2009), paper Dwc2.

Tuft, V. L.

V. L. Tuft and S. Øystein , “Holovision 2.2 user's manual,” http://www2.edge.no/projects/holovision/doc/holovision_221_manual.pdf, 2001.

Vaidyanathan, P. P.

P. P. Vaidyanathan, “Multirate Systems and Filter Banks" (Prentice-Hall, 1993).

Yamaguchi, T.

T. Yamaguchi, G. Okabe, and H. Yoshikawa, “Real-time image plane full-color and full-parallax holographic video display system,” Opt. Eng. 46, 125801 (2007).
[CrossRef]

Yoshikawa, H.

T. Yamaguchi, G. Okabe, and H. Yoshikawa, “Real-time image plane full-color and full-parallax holographic video display system,” Opt. Eng. 46, 125801 (2007).
[CrossRef]

H. Yoshikawa and M. Tachinami, “Development of direct fringe printer for computer-generated holograms,” Proc. SPIE 5742, 259-266 (2005).
[CrossRef]

H. Yoshikawa and K. Takei, “Development of a compact direct fringe printer for computer-generated holograms,” Proc. SPIE 5290, 114-121 (2004).
[CrossRef]

H. Yoshikawa and A. Kagotani, “Full color computer-generated rainbow hologram with enlarged viewing angle,” Opt. Rev. 9, 251-254 (2002).
[CrossRef]

H. Yoshikawa, “Fast computation of Fresnel holograms employing difference,” Opt. Rev. 8, 331-335 (2001).
[CrossRef]

H. Yoshikawa and H. Taniguchi, “Computer henerated rainbow hologram,” Opt. Rev. 6, 118-123 (1999).
[CrossRef]

H. Yoshikawa, “Computer-generated holograms for white light reconstruction,” in Digital Holography and Three-Dimensional Display: Principles and Applications, T. -C. Poon, ed. (Springer-Verlag, 2006).
[CrossRef]

Appl. Opt. (2)

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]

Inf. Disp. (1)

T.-C. Poon, “Three-dimensional television using optical scanning holography,” Inf. Disp. 3, 12-16 (2002).
[CrossRef]

J. Electron Imaging (1)

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

Opt. Eng. (1)

T. Yamaguchi, G. Okabe, and H. Yoshikawa, “Real-time image plane full-color and full-parallax holographic video display system,” Opt. Eng. 46, 125801 (2007).
[CrossRef]

Opt. Express (2)

Opt. Rev. (3)

H. Yoshikawa, “Fast computation of Fresnel holograms employing difference,” Opt. Rev. 8, 331-335 (2001).
[CrossRef]

H. Yoshikawa and H. Taniguchi, “Computer henerated rainbow hologram,” Opt. Rev. 6, 118-123 (1999).
[CrossRef]

H. Yoshikawa and A. Kagotani, “Full color computer-generated rainbow hologram with enlarged viewing angle,” Opt. Rev. 9, 251-254 (2002).
[CrossRef]

Proc. SPIE (1)

H. Yoshikawa and K. Takei, “Development of a compact direct fringe printer for computer-generated holograms,” Proc. SPIE 5290, 114-121 (2004).
[CrossRef]

Proc. SPIE (1)

H. Yoshikawa and M. Tachinami, “Development of direct fringe printer for computer-generated holograms,” Proc. SPIE 5742, 259-266 (2005).
[CrossRef]

Other (6)

Y. Seo, H. Cho, and D. Kim, “High-performance CGH processor for real-time digital holography,” in Laser Applications to Chemical, Security, and Environmental Analysis, OSA Technical Digest (CD) (Optical Society, 2008), paper JMA9.

H. Yoshikawa, “Computer-generated holograms for white light reconstruction,” in Digital Holography and Three-Dimensional Display: Principles and Applications, T. -C. Poon, ed. (Springer-Verlag, 2006).
[CrossRef]

P. Tsang, J. Liu, T.-C. Poon, and W. K. Cheung, “Fast generation of hologram sublines based on field programmable gate array,” in Holography and Three-Dimensional Imaging, OSA Technical Digest Series (Optical Society of America, 2009), paper Dwc2.

V. L. Tuft and S. Øystein , “Holovision 2.2 user's manual,” http://www2.edge.no/projects/holovision/doc/holovision_221_manual.pdf, 2001.

P. P. Vaidyanathan, “Multirate Systems and Filter Banks" (Prentice-Hall, 1993).

T.-C.Poon, ed., Digital Holography and Three-Dimensional Display (Springer-Verlag, 2006).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Generation of HPO hologram based on [15].

Fig. 2
Fig. 2

(a) Generation of a 2-D hologram from scan planes and (b) side view of (a) without the scan planes for incident angle at θ ill ; d represents the distance between the hologram and the viewer.

Fig. 3
Fig. 3

Downsampling of scan planes by a factor of 2.

Fig. 4
Fig. 4

(a) Diffraction pattern of a single point at z j = d / 2 = 0.5 m , (b reconstructed image with z j = d / 2 = 0.5 m , (c) reconstructed image with z j = 0.496 m .

Fig. 5
Fig. 5

Diffraction pattern generation encapsulated as a filtering process.

Fig. 6
Fig. 6

Multirate filtering: interpolation of the missing gaps between sublines to eliminate the horizontal blank lines generated after upsampling.

Fig. 7
Fig. 7

Test image of (a)  CityU and (b) Star. Reconstructed image of (c) the CityU hologram and (d)  the Star hologram.

Fig. 8
Fig. 8

(a) Original object image and (b) reconstructed image. Reconstructed image for M = 16 (c) before and (d) after interpolation.

Fig. 9
Fig. 9

Reduction factor.

Tables (3)

Tables Icon

Table 1 Breakdown of Number of Complex Multiplications for Each Step in Eq. (16)

Tables Icon

Table 2 Setting for Generating Sublines and Holograms

Tables Icon

Table 3 Reduction Factors for the Test Images in Figs. 7a, 7b, 8a

Equations (18)

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D ( x , y ) = j = 0 N P 1 a j r j exp ( i k r j ) = j = 0 N P 1 [ a j cos ( k r j ) + i a j sin ( k r j ) ] ,
O ( x ) = j = 0 N 1 a j r j exp ( i k r j ) ,
h ( x , y ) = Re [ O ( x ) R * ( y ) ] for   Δ y / 2 y Δ y / 2 ,
D τ ( x , y ) = j = 0 N ( τ ) a j r j exp ( i k ( x x j ) 2 + ( y τ ) 2 + z j 2 ) ,
D τ ( x , y ) j = 0 N ( τ ) a j r j exp ( i k ( x x j ) 2 + ( y τ ) 2 2 z j ) = j = 0 N ( τ ) a j r j exp ( i k ( x x j ) 2 2 z j ) exp ( i k ( y τ ) 2 2 z j ) .
D τ ( x , y ) j = 0 N ( τ ) a j r j exp ( i k ( x x j ) 2 2 z j ) exp ( i k ( y τ ) 2 2 z o ) = exp ( i k ( y τ ) 2 2 z o ) i = 0 N ( τ ) a j r j exp ( i k ( x x j ) 2 2 z j ) = B ( y τ ) O ( x ) .
O ( x , τ ) = j = 0 N ( τ ) a j r j exp ( i k ( x x j ) 2 2 z j ) | y = τ .
D ( x , y ) = τ [ O ( x , τ ) B ( y τ ) ] .
D ( x , y ) = O ( x , y ) * B ( y ) ,
H ( x , y ) = D ( x , y ) R * ( y ) .
H R ( x , y ) = Re [ D ( x , y ) R * ( y ) ] .
D ( x , y ) = [ O ( x , y / M ) * g ( y ) ] * B ( y ) = O ( x , y ) * B ( y ) ,
D ˜ ( x , z ) = O ˜ ( x , z ) B ˜ ( z ) = O ˜ ( x , z M ) G ( z ) B ˜ ( z ) = O ˜ ( x , z M ) E ( z ) ,
D ˜ ( x , e i ω ) = O ˜ ( x , e i M ω ) G ( e i ω ) R ˜ * ( e i ω ) = O ˜ ( x , e i ω ) E ( e i ω ) .
g ( y ) = 0.54 + 0.46 cos ( 2 π y len ) ,
D ( x , y ) = FT 1 [ D ˜ ( x , e i ω ) ] = FT 1 [ O ˜ ( x , e i M ω ) E ( e i ω ) ] ,
X × Y [ 1 + log 2 Y + 1 M log 2 ( Y / M ) ] + X × Y = X × Y [ 2 + log 2 Y + 1 M log 2 ( Y / M ) ] .
2 × X × Y × N P 4 { X × Y [ 2 + log 2 Y + log 2 ( Y ) ] } = N P 4 [ 1 + log 2 ( Y ) ]

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