Abstract

Double-step Fresnel diffraction (DSF) is an efficient diffraction calculation in terms of the amount of usage memory and calculation time. This paper describes band-limited DSF, which will be useful for large computer-generated holograms (CGHs) and gigapixel digital holography, mitigating the aliasing noise of the DSF. As the application, we demonstrate a CGH generation with nearly 8K × 4K pixels from texture and depth maps of a three-dimensional scene captured by a depth camera.

© 2013 OSA

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
  4. F. Yaras, H. Kang, and L. Onural, “Circular holographic video display system,” Opt. Express 19, 9147–9156 (2011).
    [Crossref] [PubMed]
  5. M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging,  2, 28–34 (1993).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  10. J. R. Fienup and A. E. Tippie, “Gigapixel synthetic-aperture digital holography,” Proc. SPIE 8122, 812203 (2011).
    [Crossref]
  11. S. O. Isikman, A. Greenbaum, W. Luo, A.F. Coskun, and A. Ozcan, “Giga-pixel lensfree holographic microscopy and tomography using color image sensors,” PLoS ONE 7, e45044 (2012).
    [Crossref]
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2012 (2)

S. O. Isikman, A. Greenbaum, W. Luo, A.F. Coskun, and A. Ozcan, “Giga-pixel lensfree holographic microscopy and tomography using color image sensors,” PLoS ONE 7, e45044 (2012).
[Crossref]

Y. Ichihashi, R. Oi, T. Senoh, K. Yamamoto, and T. Kurita, “Real-time capture and reconstruction system with multiple GPUs for a 3D live scene by a generation from 4K IP images to 8K holograms,” Opt. Express 20, 21645–21655 (2012).
[Crossref] [PubMed]

2011 (2)

F. Yaras, H. Kang, and L. Onural, “Circular holographic video display system,” Opt. Express 19, 9147–9156 (2011).
[Crossref] [PubMed]

J. R. Fienup and A. E. Tippie, “Gigapixel synthetic-aperture digital holography,” Proc. SPIE 8122, 812203 (2011).
[Crossref]

2009 (1)

2005 (1)

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

2004 (1)

2000 (1)

1999 (1)

1994 (1)

U. Schnars and W. Juptner, “Direct recording of holograms by a CCD target and numerical Reconstruction,” Appl.Opt.,  33, 179–181 (1994).
[Crossref]

1993 (1)

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

Aida, T.

Benton, S. A.

S. A. Benton and V. M. Bove, Holographic Imaging (Wiley-Interscience, 2008).
[Crossref]

Bove, V. M.

S. A. Benton and V. M. Bove, Holographic Imaging (Wiley-Interscience, 2008).
[Crossref]

Brady, D. J.

D. J. Brady and S. Lim, “Gigapixel holography,” 2011 ICO International Conference on Information Photonics (IP), 1–2, (2011).
[Crossref]

Cameron, C.

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

Coskun, A.F.

S. O. Isikman, A. Greenbaum, W. Luo, A.F. Coskun, and A. Ozcan, “Giga-pixel lensfree holographic microscopy and tomography using color image sensors,” PLoS ONE 7, e45044 (2012).
[Crossref]

Fienup, J. R.

J. R. Fienup and A. E. Tippie, “Gigapixel synthetic-aperture digital holography,” Proc. SPIE 8122, 812203 (2011).
[Crossref]

Fujikake, H.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (3rd ed.), (Robert & Company, 2005).

Greenbaum, A.

S. O. Isikman, A. Greenbaum, W. Luo, A.F. Coskun, and A. Ozcan, “Giga-pixel lensfree holographic microscopy and tomography using color image sensors,” PLoS ONE 7, e45044 (2012).
[Crossref]

Ichihashi, Y.

Iizuka, K.

Isikman, S. O.

S. O. Isikman, A. Greenbaum, W. Luo, A.F. Coskun, and A. Ozcan, “Giga-pixel lensfree holographic microscopy and tomography using color image sensors,” PLoS ONE 7, e45044 (2012).
[Crossref]

Ito, T.

Juptner, W.

U. Schnars and W. Juptner, “Direct recording of holograms by a CCD target and numerical Reconstruction,” Appl.Opt.,  33, 179–181 (1994).
[Crossref]

Kang, H.

Kawakita, M.

Kikuchi, H.

Kitayama, R.

H. Yoshikawa, T. Yamaguchi, and R. Kitayama, “Real-time generation of full color image hologram with compact distance look-up table,” OSA Topical Meeting on Digital Holography and Three-Dimensional Imaging 2009, DWC4 (2009).

Kurita, T.

Lim, S.

D. J. Brady and S. Lim, “Gigapixel holography,” 2011 ICO International Conference on Information Photonics (IP), 1–2, (2011).
[Crossref]

Lucente, M.

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

Luo, W.

S. O. Isikman, A. Greenbaum, W. Luo, A.F. Coskun, and A. Ozcan, “Giga-pixel lensfree holographic microscopy and tomography using color image sensors,” PLoS ONE 7, e45044 (2012).
[Crossref]

Masuda, N.

Mishina, T.

Oi, R.

Okano, F.

Onural, L.

Ozcan, A.

S. O. Isikman, A. Greenbaum, W. Luo, A.F. Coskun, and A. Ozcan, “Giga-pixel lensfree holographic microscopy and tomography using color image sensors,” PLoS ONE 7, e45044 (2012).
[Crossref]

Schnars, U.

U. Schnars and W. Juptner, “Direct recording of holograms by a CCD target and numerical Reconstruction,” Appl.Opt.,  33, 179–181 (1994).
[Crossref]

Senoh, T.

Shimobaba, T.

Slinger, C.

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

Stanley, M.

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

Takizawa, K.

Tippie, A. E.

J. R. Fienup and A. E. Tippie, “Gigapixel synthetic-aperture digital holography,” Proc. SPIE 8122, 812203 (2011).
[Crossref]

Yamaguchi, I.

Yamaguchi, T.

H. Yoshikawa, T. Yamaguchi, and R. Kitayama, “Real-time generation of full color image hologram with compact distance look-up table,” OSA Topical Meeting on Digital Holography and Three-Dimensional Imaging 2009, DWC4 (2009).

Yamamoto, K.

Yaras, F.

Yaroslavsky, L. P.

Yonai, J.

Yoshikawa, H.

H. Yoshikawa, T. Yamaguchi, and R. Kitayama, “Real-time generation of full color image hologram with compact distance look-up table,” OSA Topical Meeting on Digital Holography and Three-Dimensional Imaging 2009, DWC4 (2009).

Yuyama, I.

Zhang, F.

Appl. Opt. (2)

Appl.Opt. (1)

U. Schnars and W. Juptner, “Direct recording of holograms by a CCD target and numerical Reconstruction,” Appl.Opt.,  33, 179–181 (1994).
[Crossref]

Computer (1)

C. Slinger, C. Cameron, and M. Stanley, “Computer-generated holography as a generic display technology,” Computer 38, 46–53 (2005).
[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. Express (2)

Opt. Lett. (2)

PLoS ONE (1)

S. O. Isikman, A. Greenbaum, W. Luo, A.F. Coskun, and A. Ozcan, “Giga-pixel lensfree holographic microscopy and tomography using color image sensors,” PLoS ONE 7, e45044 (2012).
[Crossref]

Proc. SPIE (1)

J. R. Fienup and A. E. Tippie, “Gigapixel synthetic-aperture digital holography,” Proc. SPIE 8122, 812203 (2011).
[Crossref]

Other (4)

J. W. Goodman, Introduction to Fourier Optics (3rd ed.), (Robert & Company, 2005).

S. A. Benton and V. M. Bove, Holographic Imaging (Wiley-Interscience, 2008).
[Crossref]

D. J. Brady and S. Lim, “Gigapixel holography,” 2011 ICO International Conference on Information Photonics (IP), 1–2, (2011).
[Crossref]

H. Yoshikawa, T. Yamaguchi, and R. Kitayama, “Real-time generation of full color image hologram with compact distance look-up table,” OSA Topical Meeting on Digital Holography and Three-Dimensional Imaging 2009, DWC4 (2009).

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Figures (3)

Fig. 1
Fig. 1

Band-limited effects. (a) without band-limitation (b) with band-limitation (c) with band-limitation and half-zone plate processing.

Fig. 2
Fig. 2

Texture and depth maps of the 3D scene captured by the depth camera. (a) Texture map (b) depth map.

Fig. 3
Fig. 3

Reconstructed 3D scene from the 8K × 4K CGHs using BL-DSF.

Tables (2)

Tables Icon

Table 1 Performance of BL-DSF on the CPU and GPU, compared with ASM

Tables Icon

Table 2 Calculation times of Eq.(7) using BL-DSF and ASM on the CPU and GPU

Equations (8)

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

u 2 ( x 2 , y 2 ) = u 1 ( x 1 , y 1 ) * p z ( x 1 , y 1 ) = 1 [ [ u 1 ( x 1 , y 1 ) ] P z ( f x , f y ) ] ,
u 2 ( x 2 , y 2 ) = C z u 1 ( x 1 , y 1 ) exp ( i π ( x 1 2 + y 1 2 ) λ z ) exp ( 2 π i ( x 1 x 2 + y 1 y 2 ) λ z ) d x 1 d y 1 ,
u 2 ( m 2 , n 2 ) = SSF z [ u 1 ( m 1 , n 1 ) ] = C z FFT [ u 1 ( m 1 , n 1 ) exp ( i π ( x 1 2 + y 1 2 ) λ z ) ] ,
u 2 ( m 2 , n 2 ) = DSF z [ u 1 ( m 1 , n 1 ) ] = SSF z 2 [ SSF z 1 [ u 1 ( m 1 , n 1 ) ] ] = C z FFT sgn ( z 2 ) [ exp ( i π z ( x v 2 + y v 2 ) λ z 1 z 2 ) Rect ( x v x v max , y v y v max ) FFT sgn ( z 1 ) [ u 1 ( m 1 , n 1 ) exp ( i π ( x 1 2 + y 1 2 ) λ z 1 ) ] ] .
1 / p x v 2 | f x max | = 2 | ϕ ( x v , y v ) x v | = | 2 z x v max λ z 1 z 2 |
1 / p y v 2 | f y max | = 2 | ϕ ( x v , y v ) y v | = | 2 z y v max λ z 1 z 2 |
u ( m 2 , n 2 ) = i = 0 255 DSF z + i Δ z [ tex ( m 1 , n 1 ) exp ( i 2 π n ( m 1 , n 1 ) ) × mask i ( m 1 , n 1 ) ] ,
mask i ( m 1 , n 1 ) = { 1 ( if dep ( m 1 , n 1 ) = i ) 0 ( otherwise )

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