Abstract

We compare the resolution of the hologram reconstruction synthesis methods based on integral imaging using rectangular and hexagonal lens arrays. By using a hexagonal lens array instead of conventional rectangular lens array, the three-dimensional objects are sampled with hexagonal grids. Due to more efficient sampling of the hexagonal grid, the resolution of the reconstructed object is higher compared with the case of using rectangular lens array. We analyze the resolution enhancement of the hologram reconstruction quantitatively and verify it experimentally.

© 2011 OSA

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References

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  1. N. T. Shaked, B. Katz, and J. Rosen, “Review of three-dimensional holographic imaging by multiple-viewpoint-projection based methods,” Appl. Opt. 48(34), H120–H136 (2009).
    [CrossRef] [PubMed]
  2. J.-H. Park, M.-S. Kim, G. Baasantseren, and N. Kim, “Fresnel and Fourier hologram generation using orthographic projection images,” Opt. Express 17(8), 6320–6334 (2009).
    [CrossRef] [PubMed]
  3. R. V. Pole, “3-D imagery and holograms of objects illuminated in white light,” Appl. Phys. Lett. 10(1), 20–22 (1967).
    [CrossRef]
  4. J. Hong, Y. Kim, H.-J. Choi, J. Hahn, J.-H. Park, H. Kim, S.-W. Min, N. Chen, and B. Lee, “Three-dimensional display technologies of recent interest: principles, status, and issues,” Appl. Opt. 50(34), H87–H115 (2011).
    [CrossRef]
  5. J. Hong, J.-H. Park, S. Jung, and B. Lee, “Depth-enhanced integral imaging by use of optical path control,” Opt. Lett. 29(15), 1790–1792 (2004).
    [CrossRef] [PubMed]
  6. S. Kishk and B. Javidi, “Improved resolution 3D object sensing and recognition using time multiplexed computational integral imaging,” Opt. Express 11(26), 3528–3541 (2003).
    [CrossRef] [PubMed]
  7. J.-S. Jang and B. Javidi, “Improved viewing resolution of three-dimensional integral imaging by use of nonstationary micro-optics,” Opt. Lett. 27(5), 324–326 (2002).
    [CrossRef] [PubMed]
  8. L. Erdmann and K. J. Gabriel, “High-resolution digital integral photography by use of a scanning microlens array,” Appl. Opt. 40(31), 5592–5599 (2001).
    [CrossRef] [PubMed]
  9. N. Chen, J.-H. Park, and N. Kim, “Parameter analysis of integral Fourier hologram and its resolution enhancement,” Opt. Express 18(3), 2152–2167 (2010).
    [CrossRef] [PubMed]
  10. Y.-T. Lim, J.-H. Park, K.-C. Kwon, and N. Kim, “Resolution-enhanced integral imaging microscopy that uses lens array shifting,” Opt. Express 17(21), 19253–19263 (2009).
    [CrossRef] [PubMed]
  11. B. Lee, S. Jung, S.-W. Min, and J.-H. Park, “Three-dimensional display by use of integral photography with dynamically variable image planes,” Opt. Lett. 26(19), 1481–1482 (2001).
    [CrossRef] [PubMed]
  12. J.-H. Park, K. Hong, and B. Lee, “Recent progress in three-dimensional information processing based on integral imaging,” Appl. Opt. 48(34), H77–H94 (2009).
    [CrossRef] [PubMed]
  13. L. Middleton and J. Sivaswamy, Hexagonal Image Processing (Springer Verlag, 2005).
  14. G. Jurasinski and C. Beierkuhnlein, “Spatial patterns of biodiversity-assessing vegetation using hexagonal grids,” Biol. Environ. Proc. R. Irish Acad. 106(3), 401–411 (2006).
    [CrossRef]
  15. D. P. Petersen and D. Middleton, “Sampling and reconstruction of wave-number-limited functions in N-dimensional Euclidean spaces,” Inf. Control 5(4), 279–323 (1962).
    [CrossRef]
  16. P. K. Murphy and N. C. Gallagher, “Hexagonal sampling techniques applied to Fourier and Fresnel digital holograms,” J. Opt. Soc. Am. 72(7), 929–937 (1982).
    [CrossRef]
  17. S. Baronti, A. Capanni, A. Romoli, L. Santurri, and R. Vitulli, “On detector shape in hexagonal sampling grids,” Proc. SPIE 4540, 354–365 (2001).
    [CrossRef]
  18. J.-H. Park, D. Han, and N. Kim, “Capture of the three-dimensional information based on integral imaging and its sampling analysis,” Proc. SPIE 7848, 1B1–1B9 (2010).
  19. N. Chen and J. Yeom, J.-H, Park, and B. Lee, “High resolution Fourier hologram generation using hexagonal lens array based on integral imaging,” in International Meeting on Information Display (Korean Information Display Society, 2011) pp. 729–730.
  20. T. Mishina, M. Okui, and F. Okano, “Calculation of holograms from elemental images captured by integral photography,” Appl. Opt. 45(17), 4026–4036 (2006).
    [CrossRef] [PubMed]
  21. J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005) chap. 9, pp. 356–359.
  22. L. Zhang, D. Wang, and A. Vincent, “Adaptive reconstruction of intermediate views from stereoscopic images,” IEEE Trans. Circ. Syst. Video Tech. 16(1), 102–113 (2006).
    [CrossRef]
  23. J.-H. Park, G. Baasantseren, N. Kim, G. Park, J.-M. Kang, and B. Lee, “View image generation in perspective and orthographic projection geometry based on integral imaging,” Opt. Express 16(12), 8800–8813 (2008).
    [CrossRef] [PubMed]

2011 (1)

2010 (2)

N. Chen, J.-H. Park, and N. Kim, “Parameter analysis of integral Fourier hologram and its resolution enhancement,” Opt. Express 18(3), 2152–2167 (2010).
[CrossRef] [PubMed]

J.-H. Park, D. Han, and N. Kim, “Capture of the three-dimensional information based on integral imaging and its sampling analysis,” Proc. SPIE 7848, 1B1–1B9 (2010).

2009 (4)

2008 (1)

2006 (3)

T. Mishina, M. Okui, and F. Okano, “Calculation of holograms from elemental images captured by integral photography,” Appl. Opt. 45(17), 4026–4036 (2006).
[CrossRef] [PubMed]

L. Zhang, D. Wang, and A. Vincent, “Adaptive reconstruction of intermediate views from stereoscopic images,” IEEE Trans. Circ. Syst. Video Tech. 16(1), 102–113 (2006).
[CrossRef]

G. Jurasinski and C. Beierkuhnlein, “Spatial patterns of biodiversity-assessing vegetation using hexagonal grids,” Biol. Environ. Proc. R. Irish Acad. 106(3), 401–411 (2006).
[CrossRef]

2004 (1)

2003 (1)

2002 (1)

2001 (3)

1982 (1)

1967 (1)

R. V. Pole, “3-D imagery and holograms of objects illuminated in white light,” Appl. Phys. Lett. 10(1), 20–22 (1967).
[CrossRef]

1962 (1)

D. P. Petersen and D. Middleton, “Sampling and reconstruction of wave-number-limited functions in N-dimensional Euclidean spaces,” Inf. Control 5(4), 279–323 (1962).
[CrossRef]

Baasantseren, G.

Baronti, S.

S. Baronti, A. Capanni, A. Romoli, L. Santurri, and R. Vitulli, “On detector shape in hexagonal sampling grids,” Proc. SPIE 4540, 354–365 (2001).
[CrossRef]

Beierkuhnlein, C.

G. Jurasinski and C. Beierkuhnlein, “Spatial patterns of biodiversity-assessing vegetation using hexagonal grids,” Biol. Environ. Proc. R. Irish Acad. 106(3), 401–411 (2006).
[CrossRef]

Capanni, A.

S. Baronti, A. Capanni, A. Romoli, L. Santurri, and R. Vitulli, “On detector shape in hexagonal sampling grids,” Proc. SPIE 4540, 354–365 (2001).
[CrossRef]

Chen, N.

Choi, H.-J.

Erdmann, L.

Gabriel, K. J.

Gallagher, N. C.

Hahn, J.

Han, D.

J.-H. Park, D. Han, and N. Kim, “Capture of the three-dimensional information based on integral imaging and its sampling analysis,” Proc. SPIE 7848, 1B1–1B9 (2010).

Hong, J.

Hong, K.

Jang, J.-S.

Javidi, B.

Jung, S.

Jurasinski, G.

G. Jurasinski and C. Beierkuhnlein, “Spatial patterns of biodiversity-assessing vegetation using hexagonal grids,” Biol. Environ. Proc. R. Irish Acad. 106(3), 401–411 (2006).
[CrossRef]

Kang, J.-M.

Katz, B.

Kim, H.

Kim, M.-S.

Kim, N.

Kim, Y.

Kishk, S.

Kwon, K.-C.

Lee, B.

Lim, Y.-T.

Middleton, D.

D. P. Petersen and D. Middleton, “Sampling and reconstruction of wave-number-limited functions in N-dimensional Euclidean spaces,” Inf. Control 5(4), 279–323 (1962).
[CrossRef]

Min, S.-W.

Mishina, T.

Murphy, P. K.

Okano, F.

Okui, M.

Park, G.

Park, J.-H.

J. Hong, Y. Kim, H.-J. Choi, J. Hahn, J.-H. Park, H. Kim, S.-W. Min, N. Chen, and B. Lee, “Three-dimensional display technologies of recent interest: principles, status, and issues,” Appl. Opt. 50(34), H87–H115 (2011).
[CrossRef]

N. Chen, J.-H. Park, and N. Kim, “Parameter analysis of integral Fourier hologram and its resolution enhancement,” Opt. Express 18(3), 2152–2167 (2010).
[CrossRef] [PubMed]

J.-H. Park, D. Han, and N. Kim, “Capture of the three-dimensional information based on integral imaging and its sampling analysis,” Proc. SPIE 7848, 1B1–1B9 (2010).

J.-H. Park, K. Hong, and B. Lee, “Recent progress in three-dimensional information processing based on integral imaging,” Appl. Opt. 48(34), H77–H94 (2009).
[CrossRef] [PubMed]

J.-H. Park, M.-S. Kim, G. Baasantseren, and N. Kim, “Fresnel and Fourier hologram generation using orthographic projection images,” Opt. Express 17(8), 6320–6334 (2009).
[CrossRef] [PubMed]

Y.-T. Lim, J.-H. Park, K.-C. Kwon, and N. Kim, “Resolution-enhanced integral imaging microscopy that uses lens array shifting,” Opt. Express 17(21), 19253–19263 (2009).
[CrossRef] [PubMed]

J.-H. Park, G. Baasantseren, N. Kim, G. Park, J.-M. Kang, and B. Lee, “View image generation in perspective and orthographic projection geometry based on integral imaging,” Opt. Express 16(12), 8800–8813 (2008).
[CrossRef] [PubMed]

J. Hong, J.-H. Park, S. Jung, and B. Lee, “Depth-enhanced integral imaging by use of optical path control,” Opt. Lett. 29(15), 1790–1792 (2004).
[CrossRef] [PubMed]

B. Lee, S. Jung, S.-W. Min, and J.-H. Park, “Three-dimensional display by use of integral photography with dynamically variable image planes,” Opt. Lett. 26(19), 1481–1482 (2001).
[CrossRef] [PubMed]

Petersen, D. P.

D. P. Petersen and D. Middleton, “Sampling and reconstruction of wave-number-limited functions in N-dimensional Euclidean spaces,” Inf. Control 5(4), 279–323 (1962).
[CrossRef]

Pole, R. V.

R. V. Pole, “3-D imagery and holograms of objects illuminated in white light,” Appl. Phys. Lett. 10(1), 20–22 (1967).
[CrossRef]

Romoli, A.

S. Baronti, A. Capanni, A. Romoli, L. Santurri, and R. Vitulli, “On detector shape in hexagonal sampling grids,” Proc. SPIE 4540, 354–365 (2001).
[CrossRef]

Rosen, J.

Santurri, L.

S. Baronti, A. Capanni, A. Romoli, L. Santurri, and R. Vitulli, “On detector shape in hexagonal sampling grids,” Proc. SPIE 4540, 354–365 (2001).
[CrossRef]

Shaked, N. T.

Vincent, A.

L. Zhang, D. Wang, and A. Vincent, “Adaptive reconstruction of intermediate views from stereoscopic images,” IEEE Trans. Circ. Syst. Video Tech. 16(1), 102–113 (2006).
[CrossRef]

Vitulli, R.

S. Baronti, A. Capanni, A. Romoli, L. Santurri, and R. Vitulli, “On detector shape in hexagonal sampling grids,” Proc. SPIE 4540, 354–365 (2001).
[CrossRef]

Wang, D.

L. Zhang, D. Wang, and A. Vincent, “Adaptive reconstruction of intermediate views from stereoscopic images,” IEEE Trans. Circ. Syst. Video Tech. 16(1), 102–113 (2006).
[CrossRef]

Zhang, L.

L. Zhang, D. Wang, and A. Vincent, “Adaptive reconstruction of intermediate views from stereoscopic images,” IEEE Trans. Circ. Syst. Video Tech. 16(1), 102–113 (2006).
[CrossRef]

Appl. Opt. (5)

Appl. Phys. Lett. (1)

R. V. Pole, “3-D imagery and holograms of objects illuminated in white light,” Appl. Phys. Lett. 10(1), 20–22 (1967).
[CrossRef]

Biol. Environ. Proc. R. Irish Acad. (1)

G. Jurasinski and C. Beierkuhnlein, “Spatial patterns of biodiversity-assessing vegetation using hexagonal grids,” Biol. Environ. Proc. R. Irish Acad. 106(3), 401–411 (2006).
[CrossRef]

IEEE Trans. Circ. Syst. Video Tech. (1)

L. Zhang, D. Wang, and A. Vincent, “Adaptive reconstruction of intermediate views from stereoscopic images,” IEEE Trans. Circ. Syst. Video Tech. 16(1), 102–113 (2006).
[CrossRef]

Inf. Control (1)

D. P. Petersen and D. Middleton, “Sampling and reconstruction of wave-number-limited functions in N-dimensional Euclidean spaces,” Inf. Control 5(4), 279–323 (1962).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Express (5)

Opt. Lett. (3)

Proc. SPIE (2)

S. Baronti, A. Capanni, A. Romoli, L. Santurri, and R. Vitulli, “On detector shape in hexagonal sampling grids,” Proc. SPIE 4540, 354–365 (2001).
[CrossRef]

J.-H. Park, D. Han, and N. Kim, “Capture of the three-dimensional information based on integral imaging and its sampling analysis,” Proc. SPIE 7848, 1B1–1B9 (2010).

Other (3)

N. Chen and J. Yeom, J.-H, Park, and B. Lee, “High resolution Fourier hologram generation using hexagonal lens array based on integral imaging,” in International Meeting on Information Display (Korean Information Display Society, 2011) pp. 729–730.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005) chap. 9, pp. 356–359.

L. Middleton and J. Sivaswamy, Hexagonal Image Processing (Springer Verlag, 2005).

Supplementary Material (2)

» Media 1: MOV (244 KB)     
» Media 2: MOV (120 KB)     

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Figures (14)

Fig. 1
Fig. 1

Principle of Fourier hologram generation using integral imaging. (a) Hologram generation process. (b) Parameter definition.

Fig. 2
Fig. 2

Sampling in spatial domain. (a) Rectangular sampling grid. (b) Hexagonal sampling grid.

Fig. 3
Fig. 3

Sampling with lens array. (a) Sampling by rectangular lens array. (b) Sampling by hexagonal lens array.

Fig. 4
Fig. 4

Spatial domain representation of the reconstruction.

Fig. 5
Fig. 5

Spatial frequency domain representation of the hologram. (a) Using rectangular lens array. (b)Using hexagonal lens array.

Fig. 6
Fig. 6

Zero padding method. (a) Pixel distribution in an orthographic image. (b) Zero padding of an orthographic image.

Fig. 7
Fig. 7

Plane object used in the simulation.

Fig. 8
Fig. 8

Elemental image generated with hexagonal lens array.

Fig. 9
Fig. 9

Orthographic image generated from the elemental images captured with hexagonal lens array.

Fig. 10
Fig. 10

Generated hologram for red component. (a) Amplitude and (b) phase profile of the generated hologram using hexagonal lens array. (c) Amplitude and (d) phase profile of the generated hologram using rectangular lens array.

Fig. 11
Fig. 11

Comparison of the reconstructed image. (a) Rectangular lens array case. (b) Hexagonal lens array case.

Fig. 12
Fig. 12

Experimental setup for capturing objects.

Fig. 13
Fig. 13

Numerical reconstruction: (a) Rectangular lens array case (Media 1). (b) Hexagonal lens array case (Media 2).

Fig. 14
Fig. 14

PSNR and NCC of the images reconstructed at different distances. (a) NCC, (b) PSNR.

Tables (4)

Tables Icon

Table 1 Parameter definition

Tables Icon

Table 2 Key parameters for the two lens arrays

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Table 3 PSNR and NCC values of the reconstructed images

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Table 4 Average PSNR and NCC values of the reconstructed images

Equations (8)

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

O(u,v)=O(Ms,Mt) = P s,t ( x p , y p )exp(j2πb( x p s+ y p t)) d x p d y p ,
M= 2f l ,b= 2 λl ,
o ˜ rec (x,y)= m,n o(x,y)δ(xmΔx)δ(ynΔy) ,
o ˜ hex (x,y)= m,n o(x,y)δ( x(2m+n)Δx ) δ(ynΔy).
2 L x' = λ 2Δθ ,2 L y' = λ 2Δφ .
FT[ o ˜ rec ( x,y ) ]=FT[o(x,y)] m,n δ( f x m p )δ( f y n p ),
FT[ o ˜ hex ( x,y ) ]=FT[o(x,y)] m,n δ( f x 2m+n p )δ( f y n 3 p ),
f ρ,rec = f x 2 + f y 2 1 2p , f ρ,hex = f x 2 + f y 2 1 3 p ,

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