Abstract

In this paper we propose a new approach for fast generation of computer-generated holograms (CGHs) of a 3D object by using the run-length encoding (RLE) and the novel look-up table (N-LUT) methods. With the RLE method, spatially redundant data of a 3D object are extracted and regrouped into the N-point redundancy map according to the number of the adjacent object points having the same 3D value. Based on this redundancy map, N-point principle fringe patterns (PFPs) are newly calculated by using the 1-point PFP of the N-LUT, and the CGH pattern for the 3D object is generated with these N-point PFPs. In this approach, object points to be involved in calculation of the CGH pattern can be dramatically reduced and, as a result, an increase of computational speed can be obtained. Some experiments with a test 3D object are carried out and the results are compared to those of the conventional methods.

© 2009 Optical Society of America

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References

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  1. K. Iizuka, “Welcome to the wonderful world of 3D: introduction, principles and history,” Opt. Photonics News 17, 42-51(2006).
    [CrossRef]
  2. 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]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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  7. T.-C. Poon, Digital Holography and Three-Dimensional Display (Springer Verlag, 2007).
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    [CrossRef] [PubMed]
  9. S.-C. Kim, D.-C. Hwang, D.-H. Lee, and E.-S. Kim, “Computer-generated holograms of a real 3-D object basing on stereoscopic video images,” Appl. Opt. 45, 5669-5676 (2006).
    [CrossRef] [PubMed]
  10. M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2, 28-34 (1993).
    [CrossRef]
  11. 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]
  12. R. C. Dorf, Electrical Engineering Handbook, 2nd ed. (CRC, 1997).
  13. J. Higgins, Introduction to SNG and ENG Microwave (Butterworth-Heinemann, 2004).
  14. K. N. Ngan, C. W. Yap, and K. T. Tan, Video Coding for Wireless Communication Systems (Marcel Dekker, 2001).
  15. P. Hariharan, Optical Holography; Principles, Techniques, and Applications, Cambridge Studies in Modern Optics (Cambridge University Press, 1996).
    [PubMed]

2008

2006

S.-C. Kim, D.-C. Hwang, D.-H. Lee, and E.-S. Kim, “Computer-generated holograms of a real 3-D object basing on stereoscopic video images,” Appl. Opt. 45, 5669-5676 (2006).
[CrossRef] [PubMed]

K. Iizuka, “Welcome to the wonderful world of 3D: introduction, principles and history,” Opt. Photonics News 17, 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]

1948

D. Gabor, “A new microscopic principle,” Nature 161, 777-778(1948).
[CrossRef] [PubMed]

Dorf, R. C.

R. C. Dorf, Electrical Engineering Handbook, 2nd ed. (CRC, 1997).

Gabor, D.

D. Gabor, “A new microscopic principle,” Nature 161, 777-778(1948).
[CrossRef] [PubMed]

Hariharan, P.

P. Hariharan, Optical Holography; Principles, Techniques, and Applications, Cambridge Studies in Modern Optics (Cambridge University Press, 1996).
[PubMed]

Higgins, J.

J. Higgins, Introduction to SNG and ENG Microwave (Butterworth-Heinemann, 2004).

Hwang, D.-C.

Iizuka, K.

K. Iizuka, “Welcome to the wonderful world of 3D: introduction, principles and history,” Opt. Photonics News 17, 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.

Kuo, C. J.

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

Lee, D.-H.

Lucente, M.

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

Ngan, K. N.

K. N. Ngan, C. W. Yap, and K. T. Tan, Video Coding for Wireless Communication Systems (Marcel Dekker, 2001).

Poon, T.-C.

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

Schnars, U.

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

Sukhbat, P.

Tan, K. T.

K. N. Ngan, C. W. Yap, and K. T. Tan, Video Coding for Wireless Communication Systems (Marcel Dekker, 2001).

Tsai, M. H.

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

Yap, C. W.

K. N. Ngan, C. W. Yap, and K. T. Tan, Video Coding for Wireless Communication Systems (Marcel Dekker, 2001).

Appl. Opt.

J. Electron. Imaging

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

Nature

D. Gabor, “A new microscopic principle,” Nature 161, 777-778(1948).
[CrossRef] [PubMed]

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. Photonics News

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

Other

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).

R. C. Dorf, Electrical Engineering Handbook, 2nd ed. (CRC, 1997).

J. Higgins, Introduction to SNG and ENG Microwave (Butterworth-Heinemann, 2004).

K. N. Ngan, C. W. Yap, and K. T. Tan, Video Coding for Wireless Communication Systems (Marcel Dekker, 2001).

P. Hariharan, Optical Holography; Principles, Techniques, and Applications, Cambridge Studies in Modern Optics (Cambridge University Press, 1996).
[PubMed]

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Figures (13)

Fig. 1
Fig. 1

Geometry for generation of Fresnel holograms.

Fig. 2
Fig. 2

Intensity and depth values in a 3D image: (a) intensity image, (b) depth image, (c) pixel intensity and depth values.

Fig. 3
Fig. 3

Block diagram of the proposed method for generation of CGHs for 3D images.

Fig. 4
Fig. 4

Spatial redundancy of the 3D input image: (a) gray scales of the test image, (b) spatial redundancy map.

Fig. 5
Fig. 5

Generation process of a 3-point PFP.

Fig. 6
Fig. 6

Three examples of N-point PFPs: (a) 1-point PFP, (b) 2-point PFP; (c) 3-point PFP.

Fig. 7
Fig. 7

Generation process of a CGH pattern with the proposed method.

Fig. 8
Fig. 8

Separated spatial redundancy maps of Fig. 4b: (a) 1-point redundancy map, (b) 2-point redundancy map, (c) 3-point redundancy map.

Fig. 9
Fig. 9

Calculated CGH patterns for each redundancy map: (a) CGH for 1-point map, (b) CGH for 2-point map, (c) CGH for 3-point map, (d) CGH for all points.

Fig. 10
Fig. 10

Reconstructed object images from the CGH patterns of Fig. 9: (a) 1-point image, (b) 2-point image, (c) 3-point image, (d) all point image.

Fig. 11
Fig. 11

3D test object of two dice: (a) intensity image, (b) depth image.

Fig. 12
Fig. 12

Spatial redundancy maps extracted from horizontal scanning of the test 3D object: (a) 2-point redundancy map, (b) 3-point redundancy map, (c) 4-point redundancy map.

Fig. 13
Fig. 13

Object images reconstructed from the CGH patterns generated with the conventional LUT/N-LUT and proposed methods at the distance of 650 and 850 mm : (a) conventional LUT method, (b) conventional N-LUT method, (c) proposed method (2-point map), (d) proposed method (3-point map), (e) proposed method (4-point map).

Tables (3)

Tables Icon

Table 1 Calculation Time Needed in the N-LUT and Proposed Methods

Tables Icon

Table 2 Calculated Object Points for Regrouping

Tables Icon

Table 3 Computation Time and Total Memory Space

Equations (5)

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

T ( x , y ; z p ) 1 r p cos [ k r p + k x sin θ R + ϕ p ] .
r 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 2 ( x , y , z p ) T ( x , y ; z p ) + T ( x d , y ; z p ) ,
T n ( x , y ; z p ) k = 1 n T ( x ( k 1 ) d , y ; z p ) .

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