Abstract

One problem in electronic holography, which is caused by the display performance of spatial light modulators (SLM), is that the size of reconstructed 3D objects is small. Although methods for increasing the size using multiple SLMs have been considered, they typically had the problem that some parts of 3D objects were missing as a result of the gap between adjacent SLMs or 3D objects lost the vertical parallax. This paper proposes a method of resolving this problem by locating an optical system containing a lens array and other components in front of multiple SLMs. We used an optical system and 9 SLMs to construct a device equivalent to an SLM with approximately 74,600,000 pixels and used this to reconstruct 3D objects in both the horizontal and vertical parallax with an image size of 63 mm without losing any part of 3D objects.

© 2012 OSA

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    [CrossRef]
  2. K. Yamamoto, T. Mishina, R. Oi, T. Senoh, and T. Kurita, “Real-time color holography system for live scene using 4K2K video system,” Proc. SPIE7619, 761906, 761906-10 (2010).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2011

T. Senoh, T. Mishina, K. Yamamoto, R. Oi, and T. Kurita, “Wide viewing-zone-angle full-color electronic holography system using very high resolution liquid crystal display panels,” Proc. SPIE7957, 795709, 795709-12 (2011).
[CrossRef]

T. Senoh, T. Mishina, K. Yamamoto, R. Oi, and T. Kurita, “Viewing-zone-angle-expanded color electronic holography system using ultra-high-definition liquid crystal displays with undesirable light elimination,” J. Disp. Technol.7(7), 382–390 (2011).
[CrossRef]

F. Yaraş, H. Kang, and L. Onural, “Circular holographic video display system,” Opt. Express19(10), 9147–9156 (2011).
[CrossRef] [PubMed]

2010

K. Yamamoto, T. Mishina, R. Oi, T. Senoh, and T. Kurita, “Real-time color holography system for live scene using 4K2K video system,” Proc. SPIE7619, 761906, 761906-10 (2010).
[CrossRef]

2009

2008

J. Hahn, H. Kim, Y. Lim, G. Park, and B. Lee, “Wide viewing angle dynamic holographic stereogram with a curved array of spatial light modulators,” Opt. Express16(16), 12372–12386 (2008).
[CrossRef] [PubMed]

N. Peyghambarian, S. Tay, P.-A. Blanche, R. Norwood, and M. Yamamoto, “Rewritable holographic 3D displays,” Opt. Photon. News19(7), 22–27 (2008).
[CrossRef]

K. Yamamoto, R. Oi, T. Mishina, and M. Okui, “Half-zone-plate processing for objects on both sides of hologram display,” Proc. SPIE6912, 69120Q, 69120Q-10 (2008).
[CrossRef]

2003

T. Mishina, M. Okui, K. Doi, and F. Okano, “Holographic display with enlarged viewing-zone using high-resolution LC panel,” Proc. SPIE5005, 137–144 (2003).
[CrossRef]

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. G. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, “100 Mega-pixel computer generated holographic images from Active TilingTM – a dynamic and scalable electro-optic modulator system,” Proc. SPIE5005, 247–258 (2003).
[CrossRef]

1999

1995

N. Fukaya, K. Maeno, O. Nishikawa, K. Matsumoto, K. Sato, and T. Honda, “Expansion of the image size and viewing zone in holographic display using liquid crystal devices,” Proc. SPIE2406, 283–289 (1995).

Bannister, R. W.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. G. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, “100 Mega-pixel computer generated holographic images from Active TilingTM – a dynamic and scalable electro-optic modulator system,” Proc. SPIE5005, 247–258 (2003).
[CrossRef]

Blanche, P.-A.

N. Peyghambarian, S. Tay, P.-A. Blanche, R. Norwood, and M. Yamamoto, “Rewritable holographic 3D displays,” Opt. Photon. News19(7), 22–27 (2008).
[CrossRef]

Cameron, C. D.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. G. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, “100 Mega-pixel computer generated holographic images from Active TilingTM – a dynamic and scalable electro-optic modulator system,” Proc. SPIE5005, 247–258 (2003).
[CrossRef]

Coomber, S. D.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. G. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, “100 Mega-pixel computer generated holographic images from Active TilingTM – a dynamic and scalable electro-optic modulator system,” Proc. SPIE5005, 247–258 (2003).
[CrossRef]

Cresswell, I. G.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. G. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, “100 Mega-pixel computer generated holographic images from Active TilingTM – a dynamic and scalable electro-optic modulator system,” Proc. SPIE5005, 247–258 (2003).
[CrossRef]

Doi, K.

T. Mishina, M. Okui, K. Doi, and F. Okano, “Holographic display with enlarged viewing-zone using high-resolution LC panel,” Proc. SPIE5005, 137–144 (2003).
[CrossRef]

Fukaya, N.

N. Fukaya, K. Maeno, O. Nishikawa, K. Matsumoto, K. Sato, and T. Honda, “Expansion of the image size and viewing zone in holographic display using liquid crystal devices,” Proc. SPIE2406, 283–289 (1995).

Hahn, J.

Honda, T.

N. Fukaya, K. Maeno, O. Nishikawa, K. Matsumoto, K. Sato, and T. Honda, “Expansion of the image size and viewing zone in holographic display using liquid crystal devices,” Proc. SPIE2406, 283–289 (1995).

Hughes, J. R.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. G. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, “100 Mega-pixel computer generated holographic images from Active TilingTM – a dynamic and scalable electro-optic modulator system,” Proc. SPIE5005, 247–258 (2003).
[CrossRef]

Hui, V.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. G. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, “100 Mega-pixel computer generated holographic images from Active TilingTM – a dynamic and scalable electro-optic modulator system,” Proc. SPIE5005, 247–258 (2003).
[CrossRef]

Jackson, P. O.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. G. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, “100 Mega-pixel computer generated holographic images from Active TilingTM – a dynamic and scalable electro-optic modulator system,” Proc. SPIE5005, 247–258 (2003).
[CrossRef]

Kang, H.

Kim, H.

Kurita, T.

T. Senoh, T. Mishina, K. Yamamoto, R. Oi, and T. Kurita, “Viewing-zone-angle-expanded color electronic holography system using ultra-high-definition liquid crystal displays with undesirable light elimination,” J. Disp. Technol.7(7), 382–390 (2011).
[CrossRef]

T. Senoh, T. Mishina, K. Yamamoto, R. Oi, and T. Kurita, “Wide viewing-zone-angle full-color electronic holography system using very high resolution liquid crystal display panels,” Proc. SPIE7957, 795709, 795709-12 (2011).
[CrossRef]

K. Yamamoto, T. Mishina, R. Oi, T. Senoh, and T. Kurita, “Real-time color holography system for live scene using 4K2K video system,” Proc. SPIE7619, 761906, 761906-10 (2010).
[CrossRef]

Lee, B.

Lim, Y.

Maeno, K.

N. Fukaya, K. Maeno, O. Nishikawa, K. Matsumoto, K. Sato, and T. Honda, “Expansion of the image size and viewing zone in holographic display using liquid crystal devices,” Proc. SPIE2406, 283–289 (1995).

Matsumoto, K.

N. Fukaya, K. Maeno, O. Nishikawa, K. Matsumoto, K. Sato, and T. Honda, “Expansion of the image size and viewing zone in holographic display using liquid crystal devices,” Proc. SPIE2406, 283–289 (1995).

Milham, K. A.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. G. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, “100 Mega-pixel computer generated holographic images from Active TilingTM – a dynamic and scalable electro-optic modulator system,” Proc. SPIE5005, 247–258 (2003).
[CrossRef]

Miller, R. J.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. G. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, “100 Mega-pixel computer generated holographic images from Active TilingTM – a dynamic and scalable electro-optic modulator system,” Proc. SPIE5005, 247–258 (2003).
[CrossRef]

Mishina, T.

T. Senoh, T. Mishina, K. Yamamoto, R. Oi, and T. Kurita, “Wide viewing-zone-angle full-color electronic holography system using very high resolution liquid crystal display panels,” Proc. SPIE7957, 795709, 795709-12 (2011).
[CrossRef]

T. Senoh, T. Mishina, K. Yamamoto, R. Oi, and T. Kurita, “Viewing-zone-angle-expanded color electronic holography system using ultra-high-definition liquid crystal displays with undesirable light elimination,” J. Disp. Technol.7(7), 382–390 (2011).
[CrossRef]

K. Yamamoto, T. Mishina, R. Oi, T. Senoh, and T. Kurita, “Real-time color holography system for live scene using 4K2K video system,” Proc. SPIE7619, 761906, 761906-10 (2010).
[CrossRef]

K. Yamamoto, R. Oi, T. Mishina, and M. Okui, “Half-zone-plate processing for objects on both sides of hologram display,” Proc. SPIE6912, 69120Q, 69120Q-10 (2008).
[CrossRef]

T. Mishina, M. Okui, K. Doi, and F. Okano, “Holographic display with enlarged viewing-zone using high-resolution LC panel,” Proc. SPIE5005, 137–144 (2003).
[CrossRef]

T. Mishina, F. Okano, and I. Yuyama, “Time-alternating method based on single-sideband holography with half-zone-plate processing for the enlargement of viewing zones,” Appl. Opt.38(17), 3703–3713 (1999).
[CrossRef] [PubMed]

Nishikawa, O.

N. Fukaya, K. Maeno, O. Nishikawa, K. Matsumoto, K. Sato, and T. Honda, “Expansion of the image size and viewing zone in holographic display using liquid crystal devices,” Proc. SPIE2406, 283–289 (1995).

Norwood, R.

N. Peyghambarian, S. Tay, P.-A. Blanche, R. Norwood, and M. Yamamoto, “Rewritable holographic 3D displays,” Opt. Photon. News19(7), 22–27 (2008).
[CrossRef]

Oi, R.

T. Senoh, T. Mishina, K. Yamamoto, R. Oi, and T. Kurita, “Wide viewing-zone-angle full-color electronic holography system using very high resolution liquid crystal display panels,” Proc. SPIE7957, 795709, 795709-12 (2011).
[CrossRef]

T. Senoh, T. Mishina, K. Yamamoto, R. Oi, and T. Kurita, “Viewing-zone-angle-expanded color electronic holography system using ultra-high-definition liquid crystal displays with undesirable light elimination,” J. Disp. Technol.7(7), 382–390 (2011).
[CrossRef]

K. Yamamoto, T. Mishina, R. Oi, T. Senoh, and T. Kurita, “Real-time color holography system for live scene using 4K2K video system,” Proc. SPIE7619, 761906, 761906-10 (2010).
[CrossRef]

K. Yamamoto, R. Oi, T. Mishina, and M. Okui, “Half-zone-plate processing for objects on both sides of hologram display,” Proc. SPIE6912, 69120Q, 69120Q-10 (2008).
[CrossRef]

Okada, N.

Okano, F.

T. Mishina, M. Okui, K. Doi, and F. Okano, “Holographic display with enlarged viewing-zone using high-resolution LC panel,” Proc. SPIE5005, 137–144 (2003).
[CrossRef]

T. Mishina, F. Okano, and I. Yuyama, “Time-alternating method based on single-sideband holography with half-zone-plate processing for the enlargement of viewing zones,” Appl. Opt.38(17), 3703–3713 (1999).
[CrossRef] [PubMed]

Okui, M.

K. Yamamoto, R. Oi, T. Mishina, and M. Okui, “Half-zone-plate processing for objects on both sides of hologram display,” Proc. SPIE6912, 69120Q, 69120Q-10 (2008).
[CrossRef]

T. Mishina, M. Okui, K. Doi, and F. Okano, “Holographic display with enlarged viewing-zone using high-resolution LC panel,” Proc. SPIE5005, 137–144 (2003).
[CrossRef]

Onural, L.

Park, G.

Payne, D. A.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. G. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, “100 Mega-pixel computer generated holographic images from Active TilingTM – a dynamic and scalable electro-optic modulator system,” Proc. SPIE5005, 247–258 (2003).
[CrossRef]

Peyghambarian, N.

N. Peyghambarian, S. Tay, P.-A. Blanche, R. Norwood, and M. Yamamoto, “Rewritable holographic 3D displays,” Opt. Photon. News19(7), 22–27 (2008).
[CrossRef]

Quarrel, J.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. G. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, “100 Mega-pixel computer generated holographic images from Active TilingTM – a dynamic and scalable electro-optic modulator system,” Proc. SPIE5005, 247–258 (2003).
[CrossRef]

Sato, K.

N. Fukaya, K. Maeno, O. Nishikawa, K. Matsumoto, K. Sato, and T. Honda, “Expansion of the image size and viewing zone in holographic display using liquid crystal devices,” Proc. SPIE2406, 283–289 (1995).

Scattergood, D. C.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. G. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, “100 Mega-pixel computer generated holographic images from Active TilingTM – a dynamic and scalable electro-optic modulator system,” Proc. SPIE5005, 247–258 (2003).
[CrossRef]

Senoh, T.

T. Senoh, T. Mishina, K. Yamamoto, R. Oi, and T. Kurita, “Wide viewing-zone-angle full-color electronic holography system using very high resolution liquid crystal display panels,” Proc. SPIE7957, 795709, 795709-12 (2011).
[CrossRef]

T. Senoh, T. Mishina, K. Yamamoto, R. Oi, and T. Kurita, “Viewing-zone-angle-expanded color electronic holography system using ultra-high-definition liquid crystal displays with undesirable light elimination,” J. Disp. Technol.7(7), 382–390 (2011).
[CrossRef]

K. Yamamoto, T. Mishina, R. Oi, T. Senoh, and T. Kurita, “Real-time color holography system for live scene using 4K2K video system,” Proc. SPIE7619, 761906, 761906-10 (2010).
[CrossRef]

Slinger, C. W.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. G. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, “100 Mega-pixel computer generated holographic images from Active TilingTM – a dynamic and scalable electro-optic modulator system,” Proc. SPIE5005, 247–258 (2003).
[CrossRef]

Smith, A. P.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. G. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, “100 Mega-pixel computer generated holographic images from Active TilingTM – a dynamic and scalable electro-optic modulator system,” Proc. SPIE5005, 247–258 (2003).
[CrossRef]

Smith, M. A. G.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. G. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, “100 Mega-pixel computer generated holographic images from Active TilingTM – a dynamic and scalable electro-optic modulator system,” Proc. SPIE5005, 247–258 (2003).
[CrossRef]

Stanley, M.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. G. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, “100 Mega-pixel computer generated holographic images from Active TilingTM – a dynamic and scalable electro-optic modulator system,” Proc. SPIE5005, 247–258 (2003).
[CrossRef]

Takaki, Y.

Tay, S.

N. Peyghambarian, S. Tay, P.-A. Blanche, R. Norwood, and M. Yamamoto, “Rewritable holographic 3D displays,” Opt. Photon. News19(7), 22–27 (2008).
[CrossRef]

Tipton, D. L.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. G. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, “100 Mega-pixel computer generated holographic images from Active TilingTM – a dynamic and scalable electro-optic modulator system,” Proc. SPIE5005, 247–258 (2003).
[CrossRef]

Watson, P. J.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. G. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, “100 Mega-pixel computer generated holographic images from Active TilingTM – a dynamic and scalable electro-optic modulator system,” Proc. SPIE5005, 247–258 (2003).
[CrossRef]

Webber, P. J.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. G. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, “100 Mega-pixel computer generated holographic images from Active TilingTM – a dynamic and scalable electro-optic modulator system,” Proc. SPIE5005, 247–258 (2003).
[CrossRef]

Yamamoto, K.

T. Senoh, T. Mishina, K. Yamamoto, R. Oi, and T. Kurita, “Wide viewing-zone-angle full-color electronic holography system using very high resolution liquid crystal display panels,” Proc. SPIE7957, 795709, 795709-12 (2011).
[CrossRef]

T. Senoh, T. Mishina, K. Yamamoto, R. Oi, and T. Kurita, “Viewing-zone-angle-expanded color electronic holography system using ultra-high-definition liquid crystal displays with undesirable light elimination,” J. Disp. Technol.7(7), 382–390 (2011).
[CrossRef]

K. Yamamoto, T. Mishina, R. Oi, T. Senoh, and T. Kurita, “Real-time color holography system for live scene using 4K2K video system,” Proc. SPIE7619, 761906, 761906-10 (2010).
[CrossRef]

K. Yamamoto, R. Oi, T. Mishina, and M. Okui, “Half-zone-plate processing for objects on both sides of hologram display,” Proc. SPIE6912, 69120Q, 69120Q-10 (2008).
[CrossRef]

Yamamoto, M.

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Supplementary Material (1)

» Media 1: MOV (2446 KB)     

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Figures (6)

Fig. 1
Fig. 1

Configuration to eliminate the gaps between SLMs.

Fig. 2
Fig. 2

Exterior view of the constructed device.

Fig. 3
Fig. 3

Display area and gap area.

Fig. 4
Fig. 4

Experimental results of simple graphic on hologram plane.

Fig. 5
Fig. 5

Experimental results of 3D objects located at different depth.

Fig. 6
Fig. 6

Experimental results of video sequence (Media 1).

Tables (2)

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Table 1 Relation among viewing-zone angle, total image size and total gaps

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Table 2 Device parameters

Equations (6)

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S x = N x p x
θ x = 2 sin 1 ( λ / ( 2 p x ) ) λ / p x
S x θ x N x λ
f 1 = ( 1 + T S ) f 0
a = f 0 f 1 ( f 0 + f 1 )
f 3 = ( S ' S ' + T ' ) f 2

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