Abstract

We propose a novel approach to massively reduce the memory of the novel look-up table (N-LUT) for computer-generated holograms by employing one-dimensional (1-D) sub-principle fringe patterns (sub-PFPs). Two-dimensional (2-D) PFPs used in the conventional N-LUT method are decomposed into a pair of 1-D sub-PFPs through a trigonometric relation. Then, these 1-D sub-PFPs are pre-calculated and stored in the proposed method, which results in a remarkable reduction of the memory of the N-LUT. Experimental results reveal that the memory capacity of the LUT, N-LUT and proposed methods have been calculated to be 149.01 TB, 2.29 GB and 1.51 MB, respectively for the 3-D object having image points of 500 × 500 × 256, which means the memory of the proposed method could be reduced by 103 × 106 fold and 1.55 × 103 fold compared to those of the conventional LUT and N-LUT methods, respectively.

© 2012 OSA

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References

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  1. C. J. Kuo and M. H. Tsai, “Three-Dimensional Holographic Imaging,” (John Wiley & Sons, 2002).
  2. U. Schnars and W. Jueptner, “Digital Holography -Digital Hologram Recording, Numerical Reconstruction, and Related Techniques,” (Springer Verlag, 2004).
  3. T.-C. Poon, “Digital Holography and Three-dimensional Display,” (Springer Verlag, 2007).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  7. T. Ito and T. Shimobaba, “One-unit system for electroholography by use of a special-purpose computational chip with a high-resolution liquid-crystal display toward a three-dimensional television,” Opt. Express 12(9), 1788–1793 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-9-1788 .
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    [CrossRef] [PubMed]
  10. M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2(1), 28–34 (1993).
    [CrossRef]
  11. 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, D55–D62 (2008).
    [CrossRef] [PubMed]
  12. S.-C. Kim and E.-S. Kim, “Fast computation of hologram patterns of a 3-D object using run-length encoding and novel look-up table methods,” Appl. Opt. 48(6), 1030–1041 (2009).
    [CrossRef]
  13. S.-C. Kim, J.-H. Yoon, and E.-S. Kim, “Fast generation of three-dimensional video holograms by combined use of data compression and lookup table techniques,” Appl. Opt. 47, 5986–5995 (2008).
    [CrossRef] [PubMed]
  14. S.-C. Kim, W.-Y. Choe, and E.-S. Kim, “Accelerated computation of hologram patterns by use of interline redundancy of 3-D object images,” Opt. Eng. 50(9), 091305 (2011).
    [CrossRef]
  15. P. Hariharan, “Optical Holography; Principles, techniques, and applications,” (Cambridge Studies in Modern Optics, 1996).
  16. S.-C. Kim, J.-H. Kim, and E.-S. Kim, “Effective reduction of the novel look-up table memory size based on a relationship between the pixel pitch and reconstruction distance of a computer-generated hologram,” Appl. Opt. 50(19), 3375–3382 (2011).
    [CrossRef] [PubMed]

2012

2011

2010

2009

2008

2004

1993

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

1950

G. L. Rogers, “Gabor diffraction microscopy: the hologram as a generalized zone-plate,” Nature 166(4214), 237 (1950).
[CrossRef] [PubMed]

Cheung, K. W. K.

P. W. M. Tsang, J. P. Liu, K. W. K. Cheung, and T.-C. Poon, “Modern Methods for fast generation of digital holograms,” 3D Research 1(2), 11–18 (2010).
[CrossRef]

Choe, W.-Y.

S.-C. Kim, W.-Y. Choe, and E.-S. Kim, “Accelerated computation of hologram patterns by use of interline redundancy of 3-D object images,” Opt. Eng. 50(9), 091305 (2011).
[CrossRef]

Chong, T.-C.

Ichihashi, Y.

Ito, T.

Kim, E.-S.

Kim, J.-H.

Kim, S.-C.

Kurihara, T.

Liang, X.

Liu, J. P.

P. W. M. Tsang, J. P. Liu, K. W. K. Cheung, and T.-C. Poon, “Modern Methods for fast generation of digital holograms,” 3D Research 1(2), 11–18 (2010).
[CrossRef]

Lucente, M.

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

Masuda, N.

Pan, Y.

Poon, T.-C.

P. W. M. Tsang, J. P. Liu, K. W. K. Cheung, and T.-C. Poon, “Modern Methods for fast generation of digital holograms,” 3D Research 1(2), 11–18 (2010).
[CrossRef]

Rogers, G. L.

G. L. Rogers, “Gabor diffraction microscopy: the hologram as a generalized zone-plate,” Nature 166(4214), 237 (1950).
[CrossRef] [PubMed]

Shimobaba, T.

Solanki, S.

Takada, N.

Takaki, Y.

Tan, C.

Tanjung, R. B. A.

Tsang, P. W. M.

P. W. M. Tsang, J. P. Liu, K. W. K. Cheung, and T.-C. Poon, “Modern Methods for fast generation of digital holograms,” 3D Research 1(2), 11–18 (2010).
[CrossRef]

Xu, X.

Yoon, J.-H.

3D Research

P. W. M. Tsang, J. P. Liu, K. W. K. Cheung, and T.-C. Poon, “Modern Methods for fast generation of digital holograms,” 3D Research 1(2), 11–18 (2010).
[CrossRef]

Appl. Opt.

J. Electron. Imaging

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

Nature

G. L. Rogers, “Gabor diffraction microscopy: the hologram as a generalized zone-plate,” Nature 166(4214), 237 (1950).
[CrossRef] [PubMed]

Opt. Eng.

S.-C. Kim, W.-Y. Choe, and E.-S. Kim, “Accelerated computation of hologram patterns by use of interline redundancy of 3-D object images,” Opt. Eng. 50(9), 091305 (2011).
[CrossRef]

Opt. Express

Other

C. J. Kuo and M. H. Tsai, “Three-Dimensional Holographic Imaging,” (John Wiley & Sons, 2002).

U. Schnars and W. Jueptner, “Digital Holography -Digital Hologram Recording, Numerical Reconstruction, and Related Techniques,” (Springer Verlag, 2004).

T.-C. Poon, “Digital Holography and Three-dimensional Display,” (Springer Verlag, 2007).

P. Hariharan, “Optical Holography; Principles, techniques, and applications,” (Cambridge Studies in Modern Optics, 1996).

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Figures (13)

Fig. 1
Fig. 1

Geometry for generation of the Fresnel hologram pattern

Fig. 2
Fig. 2

Overall block diagram of the proposed method

Fig. 3
Fig. 3

A pair of 1-D sine and cosine sub-PFPs and the restored 2-D PFP for an object point: (a) 1-D sine sub-PFP, (b) 1-D cosine sub-PFP, (c) Restored 2-D PFP

Fig. 4
Fig. 4

A 3-D car object: (a) Intensity data, (b) Depth data

Fig. 5
Fig. 5

Restoring-time dependence of the 2-D PFP on the resolution of the PFP

Fig. 6
Fig. 6

A minimization process of the file-size of the 2-D PFP: (a) Four object points on the depth plane of z1, (b) Selected regions for 4 object points in the 2-D PFP, (c) Restored 2-D PFP minimized in size, (d) Generated CGH pattern

Fig. 7
Fig. 7

Outline detection of the car object and restoration of the corresponding region of the 2-D PFP: (a) Detected outlines of the car object, (b) Originally restored 2-D PFP, (c) Restored 2-D PFP minimized in size

Fig. 8
Fig. 8

A generation process of the CGH pattern with the proposed method: (a) Object points at each depth plane, (b) Restored 2-D PFPs minimized in size at each depth plane (c) Shifting of the restored 2-D PFPs depending on the object point’s locations at each depth plane, (d) Adding of four shifted-versions of the restored 2-D PFPs, (e) Generated CGH pattern

Fig. 9
Fig. 9

Reconstructed car object images from the CGHs generated by the proposed method: (a) Reconstructed car object focused on the rear wheel, (b) Reconstructed car object focused on the front wheel

Fig. 10
Fig. 10

Comparison of the total memory capacity of the LUT, N-LUT and proposed methods depending on: (a) Resolution of the input image, (b) Resolution of the CGH, (c) Number of depth planes, (d) Pixel-pitch of the CGH

Fig. 11
Fig. 11

Memory capacity dependence of the proposed method on the: (a) Resolution of the input image, (b) Resolution of the CGH, (c) Number of depth planes, (d) Pixel-pitch of the CGH

Fig. 12
Fig. 12

Intensity and depth images of three test 3-D objects

Fig. 13
Fig. 13

Reconstructed test object images from the CGH patterns generated by the conventional N-LUT and the proposed methods

Tables (2)

Tables Icon

Table 1 Comparison of the resolution of the PFPs and the memory capacity depending on the resolution of the object image for three cases of the LUT, N-LUT and proposed methods

Tables Icon

Table 2 Number of calculated points and the calculation time for 1-point in the N-LUT and proposed methods

Equations (8)

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T(x,y; z p )cos[ k z p { ( x x p ) 2 + ( y y p ) 2 + z p 2 } ]
I(x,y)= p=1 N a p T( x x p ,y y p ; z p )
T(x,y; z p )=cos[ k z p ( Δ x 2 +Δ y 2 + z p 2 ) ] = cos[ k( Δ x 2 z p + Δ y 2 z p + z p 2 2 + z p 2 2 ) ]=cos[ k( Δ x 2 z p + z p 2 2 )+k( Δ y 2 z p + z p 2 2 ) ] = cos[ k( Δ x 2 z p + z p 2 2 ) ]cos[ k( Δ y 2 z p + z p 2 2 ) ]sin[ k( Δ x 2 z p + z p 2 2 ) ]sin[ k( Δ y 2 z p + z p 2 2 ) ]
Horizontal resolution of the PFP : [ ( x rightmost x leftmost )×disc+ h x ] Vertical resolution of the PFP : [ ( y top y bottom )×disc+ h y ]
t RT = d=1 d max { t gen_holo × t multi_amp × N D }
t LUT = d=1 d max { ( t load_EFP + t multi_amp )× N D }
t NLUT = d=1 d max { t load_PFP +( t multi_amp × N D ) }
t Proposed = d=1 d max { t load_subPFP + t restore_PFP +( t multi_amp × N D ) }

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