Abstract

In this paper, we propose an approach, new to our knowledge, to effectively generate and reconstruct the resolution-enhanced computer-generated hologram (CGH) of three-dimensional (3-D) objects with a significantly reduced in memory size novel look-up table (N-LUT) by taking into account a relationship between the pixel pitch and reconstruction distance of the hologram pattern. In the proposed method, a CGH pattern composed of shifted versions of the principal fringe patterns (PFPs) with a short pixel pitch can be reconstructed just by using the CGH generated with a much longer pixel pitch by controll ing the hologram reconstruction distance. Accordingly, the corresponding N-LUT memory size required for resolution-enhanced hologram patterns can be significantly reduced in the proposed method. To confirm the feasibility of the proposed method, experiments are carried out and the results are discussed.

© 2011 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
  4. S.-C. Kim and E.-S. Kim, “A novel configuration of LCD projectors for efficient orthogonal polarization of two projected views,” Opt. Commun. 266, 55–66 (2006).
    [CrossRef]
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    [CrossRef] [PubMed]
  6. Y. Kim, K. Hong, and B. Lee, “Recent researches based on integral imaging display method,” 3D Res. 1, 17–27 (2010).
    [CrossRef]
  7. C. J. Kuo and M. H. Tsai, Three-Dimensional Holographic Imaging (Wiley, 2002).
    [CrossRef]
  8. U. Schnars and W. Jueptner, Digital Holography-Digital Hologram Recording, Numerical Reconstruction, and Related Techniques (Springer-Verlag, 2004).
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  10. P. W. M. Tsang, J. P. Liu, K. W. K. Cheung, and T.-C. Poon, “Modern methods for fast generation of digital holograms,” 3D Res. 1, 11–18 (2010).
    [CrossRef]
  11. S.-C. Kim and E.-S. Kim, “Computational approaches for fast generation of digital 3D video holograms,” Chin. Opt. Lett. 7, 1083–1091 (2009).
    [CrossRef]
  12. M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2, 28–34(1993).
    [CrossRef]
  13. S.-C. Kim and E.-S. Kim, “Effective generation of digital holograms of 3-D objects using a novel look-up table method,” Appl. Opt. 47, D55–D62 (2008).
    [CrossRef] [PubMed]
  14. 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, 1030–1041 (2009).
    [CrossRef]
  15. S.-C. Kim, J.-H. Yoon, and E.-S. Kim, “Fast generation of 3-D video holograms by combined use of data compression and look-up table techniques,” Appl. Opt. 47, 5986–5995(2008).
    [CrossRef] [PubMed]
  16. T.-C. Poon, Optical Scanning Holography with MATLAB (Springer-Verlag, 2007).
    [CrossRef]

2010

S.-C. Kim and E.-S. Kim, “Performance analysis of stereoscopic three-dimensional projection display systems,” 3D Res. 1, 1–16 (2010).
[CrossRef]

Y. Kim, K. Hong, and B. Lee, “Recent researches based on integral imaging display method,” 3D Res. 1, 17–27 (2010).
[CrossRef]

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

2009

2008

2006

K. Iizuka, “Welcome to the wonderful world of 3D: introduction, principles and history,” Opt. Photon. News 17 (7), 42–51 (2006).
[CrossRef]

S.-C. Kim and E.-S. Kim, “A novel configuration of LCD projectors for efficient orthogonal polarization of two projected views,” Opt. Commun. 266, 55–66 (2006).
[CrossRef]

2005

S.-C. Kim and E.-S. Kim, “A new liquid crystal display-based polarized stereoscopic projection method with improved light efficiency,” Opt. Commun. 249, 51–63 (2005).
[CrossRef]

1993

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

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 Res. 1, 11–18 (2010).
[CrossRef]

Hong, K.

Y. Kim, K. Hong, and B. Lee, “Recent researches based on integral imaging display method,” 3D Res. 1, 17–27 (2010).
[CrossRef]

Iizuka, K.

K. Iizuka, “Welcome to the wonderful world of 3D: introduction, principles and history,” Opt. Photon. News 17 (7), 42–51 (2006).
[CrossRef]

Jueptner, W.

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

Kim, E.-S.

Kim, S.-C.

Kim, Y.

Y. Kim, K. Hong, and B. Lee, “Recent researches based on integral imaging display method,” 3D Res. 1, 17–27 (2010).
[CrossRef]

Kuo, C. J.

C. J. Kuo and M. H. Tsai, Three-Dimensional Holographic Imaging (Wiley, 2002).
[CrossRef]

Lee, B.

Y. Kim, K. Hong, and B. Lee, “Recent researches based on integral imaging display method,” 3D Res. 1, 17–27 (2010).
[CrossRef]

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 Res. 1, 11–18 (2010).
[CrossRef]

Lucente, M.

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

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 Res. 1, 11–18 (2010).
[CrossRef]

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

T.-C. Poon, Optical Scanning Holography with MATLAB (Springer-Verlag, 2007).
[CrossRef]

Schnars, U.

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

Sukhbat, P.

Tsai, M. H.

C. J. Kuo and M. H. Tsai, Three-Dimensional Holographic Imaging (Wiley, 2002).
[CrossRef]

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 Res. 1, 11–18 (2010).
[CrossRef]

Yoon, J.-H.

3D Res.

Y. Kim, K. Hong, and B. Lee, “Recent researches based on integral imaging display method,” 3D Res. 1, 17–27 (2010).
[CrossRef]

S.-C. Kim and E.-S. Kim, “Performance analysis of stereoscopic three-dimensional projection display systems,” 3D Res. 1, 1–16 (2010).
[CrossRef]

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

Appl. Opt.

Chin. Opt. Lett.

J. Electron. Imaging

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

Opt. Commun.

S.-C. Kim and E.-S. Kim, “A new liquid crystal display-based polarized stereoscopic projection method with improved light efficiency,” Opt. Commun. 249, 51–63 (2005).
[CrossRef]

S.-C. Kim and E.-S. Kim, “A novel configuration of LCD projectors for efficient orthogonal polarization of two projected views,” Opt. Commun. 266, 55–66 (2006).
[CrossRef]

Opt. Photon. News

K. Iizuka, “Welcome to the wonderful world of 3D: introduction, principles and history,” Opt. Photon. News 17 (7), 42–51 (2006).
[CrossRef]

Other

T.-C. Poon, Optical Scanning Holography with MATLAB (Springer-Verlag, 2007).
[CrossRef]

C. J. Kuo and M. H. Tsai, Three-Dimensional Holographic Imaging (Wiley, 2002).
[CrossRef]

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).

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Figures (6)

Fig. 1
Fig. 1

Computational model for generation of a Fresnel hologram.

Fig. 2
Fig. 2

Reconstruction of two neighboring image points and human visual system.

Fig. 3
Fig. 3

Relationship between the hologram pixel pitch and the PFP resolution.

Fig. 4
Fig. 4

Three kinds of PFPs and their reconstructed point images. (a)–(c) PFPs of ( 5 μm , 150 mm ), ( 10 μm , 600 mm ), ( 20 μm , 2 , 400 mm ) and their reconstructed point images; (d)–(e) PFPs of ( 10 μm , 600 mm ), ( 20 μm , 20,400 mm) and their point images reconstructed with 5 μm pixel pitch at 150 mm .

Fig. 5
Fig. 5

3-D test object (a) intensity image, (b) depth image.

Fig. 6
Fig. 6

Reconstructed object images from CGH patterns with different pixel pitches of (a)–(b)  5 μm at 150.975 and 155.775 mm , (c)–(d)  10 μm at 150.975 and 155.775 mm , (e)–(f)  20 μm at 150.975 and 155.775 mm .

Tables (1)

Tables Icon

Table 1 Comparisons of Resolution of PFP, Total Memory Size of N-LUT, Total Calculation Time for CGH, and Calculation Time for One Point Depending on Three Kinds of Pixel Pitch

Equations (10)

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ψ o = δ ( x x p , y y p ) * h ( x , y ; z p ) = exp ( j k 0 z p ) j k 0 2 π z p exp { j k 0 [ ( x x p ) 2 + ( y y p ) 2 ] / 2 z p } ,
t ( x , y ) | ψ r + ψ o | 2 = | a r + j k 0 2 π z p exp ( j k 0 z p ) j k 0 2 π z p exp { j k 0 [ ( x x p ) 2 + ( y y p ) 2 ] / 2 z p } | 2 = A + B sin { k 0 2 z p [ ( x x p ) 2 + ( y y p ) 2 ] } ,
T ( x , y ; z p ) = 1 + sin { k 0 2 z p [ ( x x p ) 2 + ( y y p ) 2 ] } .
I ( x , y ) = p = 1 N a p T ( x x p , y y p ; z p ) ,
horizontal resolution of the PFP,   [ h x + ( p x _ shift × O x ) ] ; vertical resolution of the PFP,   [ h y + ( p x _ shift × O y ) ] ;
T 1 ( x , y ; z 1 ) = 1 + sin { k 0 2 z 1 [ ( x 1 x 01 ) 2 + ( y 1 y 01 ) 2 ] } , T 2 ( x , y ; z 2 ) = 1 + sin { k 0 2 z 2 [ ( x 2 x 02 ) 2 + ( y 2 y 02 ) 2 ] } .
k 0 2 z 1 [ ( x 1 x 01 ) 2 + ( y 1 y 01 ) 2 ] = 2 n π + k 0 2 z 2 [ ( x 2 x 02 ) 2 + ( y 2 y 02 ) 2 ] , ( n = 0 , ± 1 , ± 2 , ) .
z 2 z 1 = ( x 2 x 02 ) 2 + ( y 2 y 02 ) 2 ( x 1 x 01 ) 2 + ( y 1 y 01 ) 2 .
z 2 z 1 = ( k x 1 k x 01 ) 2 + ( l y 1 l y 01 ) 2 ( x 1 x 01 ) 2 + ( y 1 y 01 ) 2 = k 2 ( x 1 x 01 ) 2 + l 2 ( y 1 y 01 ) 2 ( x 1 x 01 ) 2 + ( y 1 y 01 ) 2 .
z 2 z 1 = k 2 .

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