Abstract

In this paper, a fast method for displaying a digital, real and off-axis Fresnel hologram on a lower resolution device is reported. Preserving the original resolution of the hologram upon display is one of the important attributes of the proposed method. Our method can be divided into 3 stages. First, a digital hologram representing a given three dimensional (3D) object is down-sampled based on a fix, jitter down-sampling lattice. Second, the down-sampled hologram is interpolated, through pixel duplication, into a low resolution hologram that can be displayed with a low-resolution spatial light modulator (SLM). Third, the SLM is overlaid with a grating which is generated based on the same jitter down-sampling lattice that samples the hologram. The integration of the grating and the low-resolution hologram results in, to a good approximation, the resolution of the original hologram. As such, our proposed method enables digital holograms to be displayed with lower resolution SLMs, paving the way for the development of low-cost holographic video display.

© 2013 OSA

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References

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  1. J. Weng, T. Shimobaba, N. Okada, H. Nakayama, M. Oikawa, N. Masuda, and T. Ito, “Generation of real-time large computer generated hologram using wavefront recording method,” Opt. Express20(4), 4018–4023 (2012).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  3. M. Stanley et al., “100-megapixel computer-generated holographic images from Active Tiling: a dynamic and scalable electro-optic modulator system,” SPIE5005, 247–258 (2003).
  4. N. Collings, “Optically Addressed Spatial Light Modulators for 3d Display,” J. Nonlinear Opt. Phys. Mater.20(4), 453–457 (2011).
    [CrossRef]
  5. C. Slinger, C. Cameron, and M. Stanley, “Computer-Generated Holography as a Generic Display Technology,” Computer38(8), 46–53 (2005).
    [CrossRef]
  6. H-S. Lee, H. Song, S. Lee, N. Collings, and D. Chu, “High resolution spatial light modulator for wide viewing angle holographic 3D display”, Coll. Conf. 3D Res., (CC3DR), 71–72, (2012).
  7. P. W. Tsang, T.-C. Poon, C. Zhou, and K. W. Cheung, “Binary Mask Programmable Hologram,” Opt. Express20(24), 26480–26485 (2012).
    [CrossRef] [PubMed]
  8. D. E. Golberg, Genetic Algorithms in Search, Optimization, and Machine Learning, Addison Wesley, (1989).
  9. R. L. Cook, “Stochastic sampling in computer graphics,” ACM Trans. Graph.5(1), 51–72 (1986).
    [CrossRef]
  10. A. V. Balakrishnan, “On the problem of time jitter in sampling,” IRE Trans. Inf. Theory8(3), 226–236 (1962).
    [CrossRef]
  11. M. A. Z. Dippé and E. H. Wold, “Antialiasing Through Stochastic Sampling,” SIGGRAPH19(3), 69–78 (1985).
    [CrossRef]

2012

2011

P. Tsang, W. K. Cheung, T.-C. Poon, and C. Zhou, “Holographic video at 40 frames per second for 4-million object points,” Opt. Express19(16), 15205–15211 (2011).
[CrossRef] [PubMed]

N. Collings, “Optically Addressed Spatial Light Modulators for 3d Display,” J. Nonlinear Opt. Phys. Mater.20(4), 453–457 (2011).
[CrossRef]

2005

C. Slinger, C. Cameron, and M. Stanley, “Computer-Generated Holography as a Generic Display Technology,” Computer38(8), 46–53 (2005).
[CrossRef]

1986

R. L. Cook, “Stochastic sampling in computer graphics,” ACM Trans. Graph.5(1), 51–72 (1986).
[CrossRef]

1985

M. A. Z. Dippé and E. H. Wold, “Antialiasing Through Stochastic Sampling,” SIGGRAPH19(3), 69–78 (1985).
[CrossRef]

1962

A. V. Balakrishnan, “On the problem of time jitter in sampling,” IRE Trans. Inf. Theory8(3), 226–236 (1962).
[CrossRef]

Balakrishnan, A. V.

A. V. Balakrishnan, “On the problem of time jitter in sampling,” IRE Trans. Inf. Theory8(3), 226–236 (1962).
[CrossRef]

Cameron, C.

C. Slinger, C. Cameron, and M. Stanley, “Computer-Generated Holography as a Generic Display Technology,” Computer38(8), 46–53 (2005).
[CrossRef]

Cheung, K. W.

Cheung, W. K.

Collings, N.

N. Collings, “Optically Addressed Spatial Light Modulators for 3d Display,” J. Nonlinear Opt. Phys. Mater.20(4), 453–457 (2011).
[CrossRef]

Cook, R. L.

R. L. Cook, “Stochastic sampling in computer graphics,” ACM Trans. Graph.5(1), 51–72 (1986).
[CrossRef]

Dippé, M. A. Z.

M. A. Z. Dippé and E. H. Wold, “Antialiasing Through Stochastic Sampling,” SIGGRAPH19(3), 69–78 (1985).
[CrossRef]

Ito, T.

Masuda, N.

Nakayama, H.

Oikawa, M.

Okada, N.

Poon, T.-C.

Shimobaba, T.

Slinger, C.

C. Slinger, C. Cameron, and M. Stanley, “Computer-Generated Holography as a Generic Display Technology,” Computer38(8), 46–53 (2005).
[CrossRef]

Stanley, M.

C. Slinger, C. Cameron, and M. Stanley, “Computer-Generated Holography as a Generic Display Technology,” Computer38(8), 46–53 (2005).
[CrossRef]

Tsang, P.

Tsang, P. W.

Weng, J.

Wold, E. H.

M. A. Z. Dippé and E. H. Wold, “Antialiasing Through Stochastic Sampling,” SIGGRAPH19(3), 69–78 (1985).
[CrossRef]

Zhou, C.

ACM Trans. Graph.

R. L. Cook, “Stochastic sampling in computer graphics,” ACM Trans. Graph.5(1), 51–72 (1986).
[CrossRef]

Computer

C. Slinger, C. Cameron, and M. Stanley, “Computer-Generated Holography as a Generic Display Technology,” Computer38(8), 46–53 (2005).
[CrossRef]

IRE Trans. Inf. Theory

A. V. Balakrishnan, “On the problem of time jitter in sampling,” IRE Trans. Inf. Theory8(3), 226–236 (1962).
[CrossRef]

J. Nonlinear Opt. Phys. Mater.

N. Collings, “Optically Addressed Spatial Light Modulators for 3d Display,” J. Nonlinear Opt. Phys. Mater.20(4), 453–457 (2011).
[CrossRef]

Opt. Express

SIGGRAPH

M. A. Z. Dippé and E. H. Wold, “Antialiasing Through Stochastic Sampling,” SIGGRAPH19(3), 69–78 (1985).
[CrossRef]

Other

M. Stanley et al., “100-megapixel computer-generated holographic images from Active Tiling: a dynamic and scalable electro-optic modulator system,” SPIE5005, 247–258 (2003).

H-S. Lee, H. Song, S. Lee, N. Collings, and D. Chu, “High resolution spatial light modulator for wide viewing angle holographic 3D display”, Coll. Conf. 3D Res., (CC3DR), 71–72, (2012).

D. E. Golberg, Genetic Algorithms in Search, Optimization, and Machine Learning, Addison Wesley, (1989).

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Figures (4)

Fig. 1
Fig. 1

Proposed method for generating the low-resolution hologram and the high resolution grating.

Fig. 2
Fig. 2

(a) A digital hologram H( x,y ) . (b) The RGJD lattice G( x,y ) , which is also adopted as the grating. In each 2×2 square block, there is only one sampled pixel (the white pixel). (c) The hologram H J ( x,y ) obtained by down-sampling H( x,y ) with G( x,y ) . (d) The low resolution hologram M( x,y ) obtained by filling each k×k square block in H J ( x,y ) with the sampled pixel.

Fig. 3
Fig. 3

Optical setup of the LCoS device, the grating, and the illumination

Fig. 4
Fig. 4

(a) Source image “Lenna eyes”. (b) Numerical reconstruction of original hologram representing the image in Fig. 4(a). (c) Numerical reconstruction of the original hologram after down-sampling by 2 times with a uniform sampling lattice. (d) Numerical reconstruction of the original hologram after down-sampling by 2 times with the RGJD lattice. (e) Numerical reconstruction of the original hologram after down-sampling by 3 times with the RGJD lattice.

Equations (7)

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H C ( x,y )= j=0 P1 a j exp( i2π λ ( x x j ) 2 δ 2 + ( y y j ) 2 δ 2 + z j 2 ),
H( x,y )=Real[ H C ( x,y )R( y ) ].
s d ( x )={ s( x ) (sample point) x=km+ τ 1 0 otherwise ,
S d (ω)=S( ω )ϕ(ω)=S( ω )[ 1 k ( 1sin c 2 ( ω/2k ) ) ]+ 2π k 2 S( ω ) = S( ω ) N j ( ω ) k + 2π k 2 S( ω ),
G( x,y )={ 1 (sample point) x=mk+ τ 1 and y=nk+ τ 2 0 otherwise ,
H J ( x,y )=H( x,y )G( x,y ).
H J ( x,y )=M( x,y )G( x,y ).

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