Abstract

A Fraunhofer computer-generated hologram (CGH) is proved to be valid in display for three-dimensional (3D) objects from the Fresnel to the far-field region without a Fourier lens for reconstruction. To quickly compute large and complicated 3D objects that consist of slanted diffused surfaces in the Fresnel region, a Fraunhofer-based analytical approach using a basic-triangle tiling diffuser is developed. Both theoretical and experimental results reveal that Fraunhofer CGH can perform the same effects as Fresnel CGH but require less calculation time. Impressive 3D solid effects are achieved in the Fresnel region.

© 2011 Optical Society of America

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P. A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W. Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwooe, M. Yamamoto, and N. Peyghambarian, Nature 468, 80 (2010).
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Dong, J. W.

Flores, D.

P. A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W. Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwooe, M. Yamamoto, and N. Peyghambarian, Nature 468, 80 (2010).
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P. A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W. Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwooe, M. Yamamoto, and N. Peyghambarian, Nature 468, 80 (2010).
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Hahn, J.

He, H. X.

Hsieh, W. Y.

P. A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W. Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwooe, M. Yamamoto, and N. Peyghambarian, Nature 468, 80 (2010).
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Ichihashi, Y.

Ito, T.

Kathaperumal, M.

P. A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W. Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwooe, M. Yamamoto, and N. Peyghambarian, Nature 468, 80 (2010).
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Katz, B.

Kim, H.

Kim, M. K.

Kiwaki, J. T.

Lee, B.

Li, D. H.

Lin, W.

P. A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W. Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwooe, M. Yamamoto, and N. Peyghambarian, Nature 468, 80 (2010).
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Liu, Y. Z.

Magnor, M.

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Matsushima, K.

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P. A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W. Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwooe, M. Yamamoto, and N. Peyghambarian, Nature 468, 80 (2010).
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Peyghambarian, N.

P. A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W. Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwooe, M. Yamamoto, and N. Peyghambarian, Nature 468, 80 (2010).
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P. A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W. Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwooe, M. Yamamoto, and N. Peyghambarian, Nature 468, 80 (2010).
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P. A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W. Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwooe, M. Yamamoto, and N. Peyghambarian, Nature 468, 80 (2010).
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Voorakaranam, R.

P. A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W. Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwooe, M. Yamamoto, and N. Peyghambarian, Nature 468, 80 (2010).
[CrossRef] [PubMed]

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Wang, H. Z.

Wang, P.

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[CrossRef] [PubMed]

Wang, Q. H.

Waters, J. P.

Watson, J.

Wyrowski, F.

Yamamoto, M.

P. A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W. Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwooe, M. Yamamoto, and N. Peyghambarian, Nature 468, 80 (2010).
[CrossRef] [PubMed]

Yu, L.

Zhao, W. X.

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Nature

P. A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W. Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwooe, M. Yamamoto, and N. Peyghambarian, Nature 468, 80 (2010).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Other

J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, 2004).

T.C.Poon, ed., Digital Holography and Three-Dimensional Display (Springer, 2006).
[CrossRef]

S. A. Benton and V. M. Bove, Jr., Holographic Imaging(Wiley, 2008).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

(a) Normalized error power between the intensities of holographic reconstructed image and original input object for different Fresnel numbers. (b) Comparison of computation time between Fh-CGH and Fr-CGH, while Nf = 1.

Fig. 2
Fig. 2

(a) Setup for optical reconstruction. MO, microscope objective; SF, spatial filter; L, lens; HWP, half-wave plates. Reconstruction in 800 mm ( N f 410 ) for (b) Fr-CGH and (c) Fh-CGH and in 1100 mm ( N f 540 ) for (d) Fr-CGH and (e) Fh-CGH.

Fig. 3
Fig. 3

Scheme of the FT calculation of diffusive triangle using basic-triangle tiling method.

Fig. 4
Fig. 4

Optical reconstruction results of two 3D teapots. Reconstruction in (a)  800 mm and (b)  1100 mm .

Equations (4)

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O H Fr ( x H , y H ) = [ exp ( j 2 π z / λ ) / j λ z ] Q ( x H , y H ) O o ( x o , y o ) × P ( x o , y o ) exp [ j 2 π ( x H x o + y H y o ) / λ z ] d x o d y o ,
O H Fh ( x H , y H ) = [ exp ( j 2 π z / λ ) / j λ z ] Q ( x H , y H ) F [ O o ( x o , y o ) ] ,
O H ( x H , y H ) = { exp [ j 2 π ( z c + r 0 ) / λ ] / j λ r 0 } O o ( x l , y l ) × S ( x l , y l ) exp [ j 2 π ( x H x l + y H y l ) / λ r 0 ] d x l d y l ,
O H ( x H , y H ) = exp [ j 2 π ( z c + r 0 ) / λ ] j λ r 0 ( a 22 a 11 a 12 a 21 ) × exp ( j 2 π a 13 x H + a 23 y H λ r 0 ) F Π ( a 11 x H + a 21 y H λ r 0 , a 12 x H + a 22 y H λ r 0 ) ,

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