Abstract

We present a simple and fast calculation algorithm for a computer-generated hologram (CGH) by use of wavefront recording plane. The wavefront recording plane is placed between the object data and a CGH. When the wavefront recording plane is placed close to the object, the object light passes through a small region on the wave recording plane. The computational complexity for the object light is very small. We can obtain a CGH to execute diffraction calculation from the wavefront recording plane to the CGH. The computational complexity is constant. The total computational complexity is dramatically reduced in comparison with conventional CGH calculations.

© 2009 Optical Society of America

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References

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  1. S. A. Benton, in SPIE Institute on Holography, P.Greguss and T.Jeong, eds. (SPIE, 1990), Vol. IS8, pp. 247-267.
  2. M. Lucente, in Computer Graphics: Proceedings: SIGGRAPH 97 Conference Proceedings (Addison Wesley, 1997), p. 63.
    [CrossRef]
  3. C. Slinger, C. Cameron, and M. Stanley, Computer 38, 46 (2005).
    [CrossRef]
  4. D. Leseberg and C. Frére, Appl. Opt. 27, 3020 (1988).
    [CrossRef] [PubMed]
  5. K. Matsushima, Appl. Opt. 44, 4607 (2005).
    [CrossRef] [PubMed]
  6. H. Yoshikawa, T. Yamaguchi, and R. Kitayama, in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2009), paper DWC4.
  7. M. Lucente, J. Electron. Imaging 2, 28 (1993).
    [CrossRef]
  8. T. Shimobaba, S. Hishinuma, and T. Ito, Comput. Phys. Commun. 148, 160 (2002).
    [CrossRef]
  9. M. Lucente and T. A. Galyean, SIGGRAPH 95 Conference Proceedings (Addison Wesley, 1995), p. 387.
    [CrossRef]
  10. N. Masuda, T. Ito, T. Tanaka, A. Shiraki, and T. Sugie, Opt. Express 14, 587 (2006).
    [CrossRef] [PubMed]
  11. L. Ahrenberg, P. Benzie, M. Magnor, and J. Watson, Opt. Express 14, 7636 (2006).
    [CrossRef] [PubMed]
  12. M. Frigo and S. G. Johnson, Proc. IEEE 93, 216 (2005).
    [CrossRef]
  13. T. Shimobaba, T. Ito, N. Masuda, Y. Abe, Y. Ichihashi, H. Nakayama, N. Takada, A. Shiraki, and T. Sugie, J. Opt. A 10, 075308 (2008).
    [CrossRef]

2008 (1)

T. Shimobaba, T. Ito, N. Masuda, Y. Abe, Y. Ichihashi, H. Nakayama, N. Takada, A. Shiraki, and T. Sugie, J. Opt. A 10, 075308 (2008).
[CrossRef]

2006 (2)

2005 (3)

C. Slinger, C. Cameron, and M. Stanley, Computer 38, 46 (2005).
[CrossRef]

M. Frigo and S. G. Johnson, Proc. IEEE 93, 216 (2005).
[CrossRef]

K. Matsushima, Appl. Opt. 44, 4607 (2005).
[CrossRef] [PubMed]

2002 (1)

T. Shimobaba, S. Hishinuma, and T. Ito, Comput. Phys. Commun. 148, 160 (2002).
[CrossRef]

1993 (1)

M. Lucente, J. Electron. Imaging 2, 28 (1993).
[CrossRef]

1988 (1)

Abe, Y.

T. Shimobaba, T. Ito, N. Masuda, Y. Abe, Y. Ichihashi, H. Nakayama, N. Takada, A. Shiraki, and T. Sugie, J. Opt. A 10, 075308 (2008).
[CrossRef]

Ahrenberg, L.

Benton, S. A.

S. A. Benton, in SPIE Institute on Holography, P.Greguss and T.Jeong, eds. (SPIE, 1990), Vol. IS8, pp. 247-267.

Benzie, P.

Cameron, C.

C. Slinger, C. Cameron, and M. Stanley, Computer 38, 46 (2005).
[CrossRef]

Frére, C.

Frigo, M.

M. Frigo and S. G. Johnson, Proc. IEEE 93, 216 (2005).
[CrossRef]

Galyean, T. A.

M. Lucente and T. A. Galyean, SIGGRAPH 95 Conference Proceedings (Addison Wesley, 1995), p. 387.
[CrossRef]

Hishinuma, S.

T. Shimobaba, S. Hishinuma, and T. Ito, Comput. Phys. Commun. 148, 160 (2002).
[CrossRef]

Ichihashi, Y.

T. Shimobaba, T. Ito, N. Masuda, Y. Abe, Y. Ichihashi, H. Nakayama, N. Takada, A. Shiraki, and T. Sugie, J. Opt. A 10, 075308 (2008).
[CrossRef]

Ito, T.

T. Shimobaba, T. Ito, N. Masuda, Y. Abe, Y. Ichihashi, H. Nakayama, N. Takada, A. Shiraki, and T. Sugie, J. Opt. A 10, 075308 (2008).
[CrossRef]

N. Masuda, T. Ito, T. Tanaka, A. Shiraki, and T. Sugie, Opt. Express 14, 587 (2006).
[CrossRef] [PubMed]

T. Shimobaba, S. Hishinuma, and T. Ito, Comput. Phys. Commun. 148, 160 (2002).
[CrossRef]

Johnson, S. G.

M. Frigo and S. G. Johnson, Proc. IEEE 93, 216 (2005).
[CrossRef]

Kitayama, R.

H. Yoshikawa, T. Yamaguchi, and R. Kitayama, in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2009), paper DWC4.

Leseberg, D.

Lucente, M.

M. Lucente, J. Electron. Imaging 2, 28 (1993).
[CrossRef]

M. Lucente and T. A. Galyean, SIGGRAPH 95 Conference Proceedings (Addison Wesley, 1995), p. 387.
[CrossRef]

M. Lucente, in Computer Graphics: Proceedings: SIGGRAPH 97 Conference Proceedings (Addison Wesley, 1997), p. 63.
[CrossRef]

Magnor, M.

Masuda, N.

T. Shimobaba, T. Ito, N. Masuda, Y. Abe, Y. Ichihashi, H. Nakayama, N. Takada, A. Shiraki, and T. Sugie, J. Opt. A 10, 075308 (2008).
[CrossRef]

N. Masuda, T. Ito, T. Tanaka, A. Shiraki, and T. Sugie, Opt. Express 14, 587 (2006).
[CrossRef] [PubMed]

Matsushima, K.

Nakayama, H.

T. Shimobaba, T. Ito, N. Masuda, Y. Abe, Y. Ichihashi, H. Nakayama, N. Takada, A. Shiraki, and T. Sugie, J. Opt. A 10, 075308 (2008).
[CrossRef]

Shimobaba, T.

T. Shimobaba, T. Ito, N. Masuda, Y. Abe, Y. Ichihashi, H. Nakayama, N. Takada, A. Shiraki, and T. Sugie, J. Opt. A 10, 075308 (2008).
[CrossRef]

T. Shimobaba, S. Hishinuma, and T. Ito, Comput. Phys. Commun. 148, 160 (2002).
[CrossRef]

Shiraki, A.

T. Shimobaba, T. Ito, N. Masuda, Y. Abe, Y. Ichihashi, H. Nakayama, N. Takada, A. Shiraki, and T. Sugie, J. Opt. A 10, 075308 (2008).
[CrossRef]

N. Masuda, T. Ito, T. Tanaka, A. Shiraki, and T. Sugie, Opt. Express 14, 587 (2006).
[CrossRef] [PubMed]

Slinger, C.

C. Slinger, C. Cameron, and M. Stanley, Computer 38, 46 (2005).
[CrossRef]

Stanley, M.

C. Slinger, C. Cameron, and M. Stanley, Computer 38, 46 (2005).
[CrossRef]

Sugie, T.

T. Shimobaba, T. Ito, N. Masuda, Y. Abe, Y. Ichihashi, H. Nakayama, N. Takada, A. Shiraki, and T. Sugie, J. Opt. A 10, 075308 (2008).
[CrossRef]

N. Masuda, T. Ito, T. Tanaka, A. Shiraki, and T. Sugie, Opt. Express 14, 587 (2006).
[CrossRef] [PubMed]

Takada, N.

T. Shimobaba, T. Ito, N. Masuda, Y. Abe, Y. Ichihashi, H. Nakayama, N. Takada, A. Shiraki, and T. Sugie, J. Opt. A 10, 075308 (2008).
[CrossRef]

Tanaka, T.

Watson, J.

Yamaguchi, T.

H. Yoshikawa, T. Yamaguchi, and R. Kitayama, in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2009), paper DWC4.

Yoshikawa, H.

H. Yoshikawa, T. Yamaguchi, and R. Kitayama, in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2009), paper DWC4.

Appl. Opt. (2)

Comput. Phys. Commun. (1)

T. Shimobaba, S. Hishinuma, and T. Ito, Comput. Phys. Commun. 148, 160 (2002).
[CrossRef]

Computer (1)

C. Slinger, C. Cameron, and M. Stanley, Computer 38, 46 (2005).
[CrossRef]

J. Electron. Imaging (1)

M. Lucente, J. Electron. Imaging 2, 28 (1993).
[CrossRef]

J. Opt. A (1)

T. Shimobaba, T. Ito, N. Masuda, Y. Abe, Y. Ichihashi, H. Nakayama, N. Takada, A. Shiraki, and T. Sugie, J. Opt. A 10, 075308 (2008).
[CrossRef]

Opt. Express (2)

Proc. IEEE (1)

M. Frigo and S. G. Johnson, Proc. IEEE 93, 216 (2005).
[CrossRef]

Other (4)

M. Lucente and T. A. Galyean, SIGGRAPH 95 Conference Proceedings (Addison Wesley, 1995), p. 387.
[CrossRef]

H. Yoshikawa, T. Yamaguchi, and R. Kitayama, in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2009), paper DWC4.

S. A. Benton, in SPIE Institute on Holography, P.Greguss and T.Jeong, eds. (SPIE, 1990), Vol. IS8, pp. 247-267.

M. Lucente, in Computer Graphics: Proceedings: SIGGRAPH 97 Conference Proceedings (Addison Wesley, 1997), p. 63.
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Outline of the calculation with the wavefront recording plane.

Fig. 2
Fig. 2

3D images reconstructed by the proposed method: (a) emerald (407 points), (b) teapot (48,277 points), (c) sofa (52,380 points).

Tables (1)

Tables Icon

Table 1 Calculation Time For Ray-Tracing Algorithm on the CPU and GPU and That of the Proposed Method (ms)

Equations (6)

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

I ( x , y ) = j N A j R cos ( 2 π λ R ) .
u w ( x w , y w ) = j N A j R w exp ( i 2 π λ R w ) ,
u ( x , y ) = exp ( i 2 π λ z 2 ) i λ z 2 u w ( x w , y w ) × exp ( i π λ z 2 ( ( x x w ) 2 + ( y y w ) 2 ) ) d x w d y w = exp ( i 2 π λ z 2 ) i λ z 2 F 1 [ F [ u w ( x , y ) ] F [ h ( x , y ) ] ] ,
I ( x , y ) = c + R [ u ( x , y ) ] ,
sin θ o sin θ r = λ 2 p ,
W 1 = | z 1 | tan ( sin 1 λ 2 p ) | z j z 2 | tan ( λ 2 p ) ,

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