Abstract

The amount of heavy computation in Computer Generated Hologram (CGH) can be significantly reduced by pre-computing look-up tables. However, the huge memory usage of look-up tables is a major challenge. To address this problem, the Look-up tables can be efficiently compressed by methods such as radial symmetric interpolation. In this paper, we notice that there is still data redundancy in the look-up table of radial symmetric interpolation method and the table size can be further compressed to 5%-10% or even less of original, by our proposed mini look-up table approach based on Principal Component Analysis (PCA). The compressed look-up table in our scheme only occupies a memory size of around 200-300 KB or even less. Moreover, the proposed scheme will introduce almost no extra cost of computation speed slowdown and reconstructed image quality degradation, compared to conventional method.

© 2017 Optical Society of America

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References

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  1. M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2(1), 28–34 (1993).
    [Crossref]
  2. S. C. Kim and E. S. Kim, “Effective generation of digital holograms of three-dimensional objects using a novel look-up table method,” Appl. Opt. 47(19), D55–D62 (2008).
    [Crossref] [PubMed]
  3. Y. Pan, X. Xu, S. Solanki, X. Liang, R. B. Tanjung, C. Tan, and T. C. Chong, “Fast CGH computation using S-LUT on GPU,” Opt. Express 17(21), 18543–18555 (2009).
    [Crossref] [PubMed]
  4. J. Jia, Y. Wang, J. Liu, X. Li, Y. Pan, Z. Sun, B. Zhang, Q. Zhao, and W. Jiang, “Reducing the memory usage for effective computer-generated hologram calculation using compressed look-up table in full-color holographic display,” Appl. Opt. 52(7), 1404–1412 (2013).
    [Crossref] [PubMed]
  5. S. C. Kim, J. M. Kim, and E. S. Kim, “Effective memory reduction of the novel look-up table with one-dimensional sub-principle fringe patterns in computer-generated holograms,” Opt. Express 20(11), 12021–12034 (2012).
    [Crossref] [PubMed]
  6. T. Nishitsuji, T. Shimobaba, T. Kakue, N. Masuda, and T. Ito, “Fast calculation of computer-generated hologram using the circular symmetry of zone plates,” Opt. Express 20(25), 27496–27502 (2012).
    [Crossref] [PubMed]
  7. T. Nishitsuji, T. Shimobaba, T. Kakue, and T. Ito, “Fast calculation of computer-generated hologram using run-length encoding based recurrence relation,” Opt. Express 23(8), 9852–9857 (2015).
    [Crossref] [PubMed]
  8. S. Lee, H. Chang, H. Wey, and D. Nam, “Sampling and error analysis of radial symmetric interpolation for fast hologram generation,” Appl. Opt. 55(3), A104–A110 (2016).
    [Crossref] [PubMed]
  9. I. Jolliffe, Principal Component Analysis (John Wiley and Sons Ltd, 2002).
  10. Z. N. Li, M. S. Drew, and J. Liu, Fundamentals of Multimedia (Springer, 2004).
  11. Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13(4), 600–612 (2004).
    [Crossref] [PubMed]
  12. P. Tsang, J. P. Liu, W. K. Cheung, and T. C. Poon, “Fast generation of Fresnel holograms based on multirate filtering,” Appl. Opt. 48(34), H23–H30 (2009).
    [Crossref] [PubMed]
  13. P. Tsang, J. P. Liu, T. C. Poon, and W. K. Cheung, “Fast generation of hologram sub-lines based on Field Programmable Gate Array,” in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2009), paper DWC2.

2016 (1)

2015 (1)

2013 (1)

2012 (2)

2009 (2)

2008 (1)

2004 (1)

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13(4), 600–612 (2004).
[Crossref] [PubMed]

1993 (1)

M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2(1), 28–34 (1993).
[Crossref]

Bovik, A. C.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13(4), 600–612 (2004).
[Crossref] [PubMed]

Chang, H.

Cheung, W. K.

Chong, T. C.

Ito, T.

Jia, J.

Jiang, W.

Kakue, T.

Kim, E. S.

Kim, J. M.

Kim, S. C.

Lee, S.

Li, X.

Liang, X.

Liu, J.

Liu, J. P.

Lucente, M.

M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2(1), 28–34 (1993).
[Crossref]

Masuda, N.

Nam, D.

Nishitsuji, T.

Pan, Y.

Poon, T. C.

Sheikh, H. R.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13(4), 600–612 (2004).
[Crossref] [PubMed]

Shimobaba, T.

Simoncelli, E. P.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13(4), 600–612 (2004).
[Crossref] [PubMed]

Solanki, S.

Sun, Z.

Tan, C.

Tanjung, R. B.

Tsang, P.

Wang, Y.

Wang, Z.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13(4), 600–612 (2004).
[Crossref] [PubMed]

Wey, H.

Xu, X.

Zhang, B.

Zhao, Q.

Appl. Opt. (4)

IEEE Trans. Image Process. (1)

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13(4), 600–612 (2004).
[Crossref] [PubMed]

J. Electron. Imaging (1)

M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2(1), 28–34 (1993).
[Crossref]

Opt. Express (4)

Other (3)

I. Jolliffe, Principal Component Analysis (John Wiley and Sons Ltd, 2002).

Z. N. Li, M. S. Drew, and J. Liu, Fundamentals of Multimedia (Springer, 2004).

P. Tsang, J. P. Liu, T. C. Poon, and W. K. Cheung, “Fast generation of hologram sub-lines based on Field Programmable Gate Array,” in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2009), paper DWC2.

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Figures (8)

Fig. 1
Fig. 1 One portion of the visualized intensity image representing the real part of a look-up table in radial symmetric interpolation method
Fig. 2
Fig. 2 Flowchart of proposed highly compressed look-up table incorporated with radial symmetric interpolation method for CGH generation
Fig. 3
Fig. 3 Partition of a 2D look-up table (size 6 x 4) into 4 non-overlapping rectangular blocks: (a) before partition; (b) after partition.
Fig. 4
Fig. 4 (a) Original “pepper” image; (b-f) Reconstructed images from CGH calculated by (b) direct analytic method; (c) Radial symmetric interpolation method; (d) Proposed mini look-up table method with W p c a = 22 ; (e) Proposed mini look-up table method with W p c a = 17 ; (f) Proposed mini look-up table method with W p c a = 12 .
Fig. 5
Fig. 5 SSIM value of reconstructed image versus compression ratio curve when the number of depth planes varies.
Fig. 6
Fig. 6 Numerical reconstruction results for a 3D scene containing four characters placed at different distances from a hologram generated by direct analytic method ((a)-(d)) and our proposed method (compression ratio = 19.0413) ((e)-(h)).
Fig. 7
Fig. 7 Numerically reconstructed images from a hologram generated by our proposed method (compression ratio = 19.0413) at different distances, showing the focus change.
Fig. 8
Fig. 8 Numerically reconstructed 3D image: (a) by direct analytic method; (b) by our proposed method (compression ratio = 19.0413); Optically reconstructed 3D image: (c) by direct analytic method; (d) by our proposed method (compression ratio = 19.0413).

Tables (3)

Tables Icon

Table 1 Comparison of SSIM and memory storage size performance of different CGH calculation methods.

Tables Icon

Table 2 Comparison of computation speed performance of different CGH calculation methods.

Tables Icon

Table 3 Comparison of computation speed performance of different CGH calculation methods.

Equations (12)

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H ( x , y ) = j = 0 N 1 D ( x j , y j , z j ) = j = 0 N 1 a j ( x j , y j , z j ) d j ( x , y ) exp ( i 2 π d j ( x , y ) λ )
d j ( x , y ) = ( x x j ) 2 + ( y y j ) 2 + z j 2
F C k ( x , y ) = 1 d k ( x , y ) exp ( i 2 π d k ( x , y ) λ )
d k ( x , y ) = x 2 + y 2 + z k 2
D ( x j , y j , z j ) = a j ( x j , y j , z j ) F C k ( x x j , y y j )
F C k ( r ) = 1 d k ( r ) exp ( i 2 π d k ( r ) λ )
d k ( r ) = r 2 + z k 2
r = x 2 + y 2
F C = [ F C 1 ( r 1 ) F C 2 ( r 1 ) ... F C M 1 ( r 1 ) F C M ( r 1 ) F C 1 ( r 2 ) F C 2 ( r 2 ) ... F C M 1 ( r 2 ) F C M ( r 2 ) ... ... ... ... ... F C 1 ( r Q 1 ) F C 2 ( r Q 1 ) ... F C M 1 ( r Q 1 ) F C M ( r Q 1 ) F C 1 ( r Q ) F C 2 ( r Q ) ... F C M 1 ( r Q ) F C M ( r Q ) ]
F C = F C r e a l + j F C i m a g = Re ( F C ) + j Im ( F C )
f l = 1 W w = 1 W S w l
S w l f l + p = 1 W p c a C p l μ w p

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