Abstract

In the paper Wigner Distribution (WD) representation analysis of holographic display is presented. The display reconstructs holographic image by means of Spatial Light Modulator. Two major aspects are covered: imaging and viewing. Optically reconstructed images are characterized by low and spatially variant resolution. Utilizing WD representation we present a simple formula for resolution as a function of both coordinates: transverse and longitudinal. The analysis of an aliasing effect allows for meaningful extension of the field of view. All theoretical results are proven experimentally. The WD representation of angularly and spatially limited holographic image is extended to cover its visual perception as well. Angular resolution and field of view are theoretically examined. Both monocular and binocular perception are studied and illustrated experimentally.

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References

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2009 (1)

2008 (3)

2007 (1)

T. Latychevskaia and H.-W. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett. 98(23), 233901 (2007).
[Crossref] [PubMed]

2004 (4)

1997 (1)

1996 (3)

1995 (1)

1982 (1)

1980 (1)

1948 (1)

D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
[Crossref] [PubMed]

Ambs, P.

Arsenault, H. H.

Bastiaans, M. J.

Bergeron, A.

Bos, P. J.

A. Michałkiewicz, M. Kujawińska, T. Kozacki, X. Wang, and P. J. Bos, “Holographic three-dimensional displays with liquid crystal on silicon spatial light modulator,” Proc. SPIE 5531, 85–94 (2004).
[Crossref]

Choi, K.

Cohn, R. W.

Dorsch, R. G.

Doucet, M.

Ferreira, C.

Fienup, J. R.

Fink, H.-W.

T. Latychevskaia and H.-W. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett. 98(23), 233901 (2007).
[Crossref] [PubMed]

Fukaya, N.

K. Maeno, N. Fukaya, O. Nishikawa, K. Sato, and T. Honda, “Electro-holographic display using 15 mega pixels LCD,” Proc. SPIE 2652, 15–23 (1996).
[Crossref]

Gabor, D.

D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
[Crossref] [PubMed]

Gagnon, F.

Gauvin, J.

Gingras, D.

Hahn, J.

Honda, T.

K. Maeno, N. Fukaya, O. Nishikawa, K. Sato, and T. Honda, “Electro-holographic display using 15 mega pixels LCD,” Proc. SPIE 2652, 15–23 (1996).
[Crossref]

Javidi, B.

Kim, D.-W.

Kim, H.

Kim, S.-K.

Kozacki, T.

T. Kozacki, “Numerical errors of diffraction computing using plane wave spectrum decomposition,” Opt. Commun. 281, 4219–4223 (2008).
[Crossref]

A. Michałkiewicz, M. Kujawińska, T. Kozacki, X. Wang, and P. J. Bos, “Holographic three-dimensional displays with liquid crystal on silicon spatial light modulator,” Proc. SPIE 5531, 85–94 (2004).
[Crossref]

Kujawinska, M.

A. Michałkiewicz, M. Kujawińska, T. Kozacki, X. Wang, and P. J. Bos, “Holographic three-dimensional displays with liquid crystal on silicon spatial light modulator,” Proc. SPIE 5531, 85–94 (2004).
[Crossref]

Kwon, Y. M.

Latychevskaia, T.

T. Latychevskaia and H.-W. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett. 98(23), 233901 (2007).
[Crossref] [PubMed]

Lee, B.

Lim, Y.

Lohmann, A. W.

Maeno, K.

K. Maeno, N. Fukaya, O. Nishikawa, K. Sato, and T. Honda, “Electro-holographic display using 15 mega pixels LCD,” Proc. SPIE 2652, 15–23 (1996).
[Crossref]

Mendlovic, D.

Michalkiewicz, A.

A. Michałkiewicz, M. Kujawińska, T. Kozacki, X. Wang, and P. J. Bos, “Holographic three-dimensional displays with liquid crystal on silicon spatial light modulator,” Proc. SPIE 5531, 85–94 (2004).
[Crossref]

Millán, M. S.

Nishikawa, O.

K. Maeno, N. Fukaya, O. Nishikawa, K. Sato, and T. Honda, “Electro-holographic display using 15 mega pixels LCD,” Proc. SPIE 2652, 15–23 (1996).
[Crossref]

Otón, J.

Park, G.

Pérez-Cabré, E.

Sato, K.

K. Maeno, N. Fukaya, O. Nishikawa, K. Sato, and T. Honda, “Electro-holographic display using 15 mega pixels LCD,” Proc. SPIE 2652, 15–23 (1996).
[Crossref]

Son, J.-Y.

Stern, A.

van de Mortel, P. G. J.

Wang, X.

A. Michałkiewicz, M. Kujawińska, T. Kozacki, X. Wang, and P. J. Bos, “Holographic three-dimensional displays with liquid crystal on silicon spatial light modulator,” Proc. SPIE 5531, 85–94 (2004).
[Crossref]

Xun, X.

Yamaguchi, I.

Zalevsky, Z.

Zhang, T.

Appl. Opt. (4)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

Nature (1)

D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
[Crossref] [PubMed]

Opt. Commun. (1)

T. Kozacki, “Numerical errors of diffraction computing using plane wave spectrum decomposition,” Opt. Commun. 281, 4219–4223 (2008).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

T. Latychevskaia and H.-W. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett. 98(23), 233901 (2007).
[Crossref] [PubMed]

Proc. SPIE (2)

A. Michałkiewicz, M. Kujawińska, T. Kozacki, X. Wang, and P. J. Bos, “Holographic three-dimensional displays with liquid crystal on silicon spatial light modulator,” Proc. SPIE 5531, 85–94 (2004).
[Crossref]

K. Maeno, N. Fukaya, O. Nishikawa, K. Sato, and T. Honda, “Electro-holographic display using 15 mega pixels LCD,” Proc. SPIE 2652, 15–23 (1996).
[Crossref]

Other (6)

J. W. Goodman, Introduction to Fourier Optics 2nd ed., (McGraw-Hill, New York, 1996).

J. J. Stamnes, Waves in Focal Regions, (Hilger, Bristol, 1986).

C. E. Shanon, “Communication in presence of noise”, Proc. IRE 37, 447–457 (1949).

H. M. Ozaktas, and L. Onural, Three-Dimensional Television (Springer, Berlin, 2008).

D.P. Kelly, D.S. Monaghan, N. Pandey, T. Kozacki, A. Michałkiewicz, B. M. Hennelly, M. Kujawinska, “Digital Holographic Capture and Optoelectronic Reconstruction for 3D Displays,” International Journal of Digital Multimedia Broadcasting, Article ID 759323 (2010).

Y. Le Grand, Physiological Optics (Springer, New York, 1980).

Supplementary Material (1)

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Figures (12)

Fig. 1
Fig. 1

The experimental setup for observation of holographic image generated by SLM based holographic display.

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Fig. 2
Fig. 2

The evolution of WD of holographic signal during propagation.

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Fig. 3
Fig. 3

Generation of holographic point images: (a) for distance z > d min, (b) for distance z < d min, (c) for highly off-axis points.

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Fig. 4
Fig. 4

Transverse resolution and field of view of holographic image.

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Fig. 5
Fig. 5

The experimental setup for capturing a real holographic image.

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Fig. 6
Fig. 6

The resolution of a real holographic image (position of the first zero of point image as a function of reconstruction distance).

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Fig. 7
Fig. 7

The image of a generated target (a) and its image reconstruction (b) from computer generated hologram.

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Fig. 8
Fig. 8

The WD representation of monocular visual perception of holographic image.

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Fig. 9
Fig. 9

The WD representation of binocular visual perception of holographic image.

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Fig. 10
Fig. 10

Binocular observation limitation: zob and zobs as a function of observation distance.

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Fig. 11
Fig. 11

The views of holographic image captured with asymmetric diffuser and digital camera (entrance pupil diameter 8.2 [mm]): (a) left perspective, (b) central perspective, (c) right perspective (Media 1).

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Fig. 12
Fig. 12

Real image captured with CCD.

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Equations (17)

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u ( x , z ) = exp ( i k z ) i λ z ∫ u ( x s , 0 ) exp ( i k ( x − x s ) 2 2 z ) d x s ,
W u ( z = d ) ( x , f ) = W u ( z = 0 ) ( x − λ z f , f ) .
d min ( axial ) = B x Δ λ − 1 .
d min ( offaxis ) = ( B x + 2 x 0 ) Δ λ − 1 .
I ( x , z ) = { sin c 2 ( B f ( x - x 0 )) for | x 0 | ≤ ( B x − B f λ z ) / 2 sin c 2 ( B x x λ z ( x − x 0 )) for |x 0 | < ( B f λ z − B x ) / 2 sin c 2 ( B x + B f λ z − 2 x 0 2 λ z ( x - x 0 )) for | B f λ z − B x 2 | > | x 0 | > B x + B f λ z 2 . 0 otherwise
z o > φ o B x z .
F O V = B x z o + φ o z z + z o .
z o b = ( d o + ϕ o ) B f − 1 λ − 1 − z .
z o b s = z d o B x − 1 where z > ( B x + 2 x o ) Δ λ − 1 ,
g ( ξ ) = exp { − i π ( ξ − ξ 0 ) 2 z λ } comb ( ξ B x ) Π ( ξ B x ) ,
W g ( x , f ) = ∫ g ( x − λ z f + x ' 2 , f ) g * ( x − λ z f − x ' 2 , f ) exp { − 2 π i f x ' } d x ' ,
W g ( x , f ' ) = ∫ comb ( λ z f ' Δ ) Π ( λ z f ' B x ) comb ( λ z Δ ( f ' + x ' λ z )) ⋅ Π ( λ z Δ ( f ' + x ' λ z ))exp{- 2 π i x ' ( x − x 0 ) λ z }dx' .
| g ( x ) | 2 = comb ( Δ λ z (x-x 0 )) ⊗ sin c 2 ( B x λ z (x-x 0 )),
G ( f ) = exp { i π λ z f 2 } ⊗ comb ( Δ − 1 f ) Π ( B f − 1 f ) .
G ( f ) = exp { i π λ z f 2 } Π ( B f − 1 f ) .
W G ( x , f ) = ∫ Π ( B f − 1 ( f + f ' 2 ) ) Π ( B f − 1 ( f − f ' 2 ) ) exp ( 2 π i x f ' ) d f ' .
| g ( x ) | 2 = sin c 2 ( B f x) .

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