Abstract

The horizontally scanning holographic display has increased viewing angle and display screen size as compared to conventional holographic displays. Elementary holograms, which are generated by a high-speed SLM and projected by an anamorphic imaging system, are aligned horizontally by a galvano mirror. When the frame rate of the SLM is high, the width of the elementary holograms becomes several times as large as their horizontal display pitch so that several sets of elementary holograms can be displayed. A laser is modulated to illuminate different elementary hologram sets by different laser powers. The grayscale representation of reconstructed images is improved by properly designing the elementary hologram sets and the illumination laser powers.

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2010 (1)

2009 (1)

2008 (1)

2004 (1)

C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27–41 (2004).
[CrossRef]

2003 (1)

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-megapixel computer-generated holographic images from Active Tiling: a dynamic and scalable electro-optic modulator system,” SPIE 5005, 247 (2003).
[CrossRef]

1999 (1)

1996 (1)

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

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N. Fukaya, K. Maeno, O. Nishikawa, K. Matumoto, K. Sato, and T. Honda, “Expansion of the image size and viewing zone in holographic display using liquid crystal devices,” Proc. SPIE 2406, 283–289 (1995).

1992 (2)

P. St. Hilaire, S. A. Benton, and M. Lucente, “Synthetic aperture hologram: a novel approach to three-dimensional display,” J. Opt. Soc. Am. 9(11), 1969–1977 (1992).
[CrossRef]

M. Lucent, “Optimization of hologram computation for real-time display,” Proc. SPIE 1667, 32–43 (1992).
[CrossRef]

1990 (1)

P. St. Hilaire, S. A. Benton, M. Lucente, M. L. Jepsen, J. Kollin, H. Yoshikawa, and J. Underkoffler, “Electronic display system for computational holography,” Proc. SPIE 1212, 174 (1990).
[CrossRef]

1987 (1)

1984 (1)

1974 (1)

1970 (2)

1967 (1)

Allebach, J. P.

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-megapixel computer-generated holographic images from Active Tiling: a dynamic and scalable electro-optic modulator system,” SPIE 5005, 247 (2003).
[CrossRef]

Benton, S. A.

P. St. Hilaire, S. A. Benton, and M. Lucente, “Synthetic aperture hologram: a novel approach to three-dimensional display,” J. Opt. Soc. Am. 9(11), 1969–1977 (1992).
[CrossRef]

P. St. Hilaire, S. A. Benton, M. Lucente, M. L. Jepsen, J. Kollin, H. Yoshikawa, and J. Underkoffler, “Electronic display system for computational holography,” Proc. SPIE 1212, 174 (1990).
[CrossRef]

Bryngdahl, O.

Burckhardt, C. B.

Cameron, C. D.

C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27–41 (2004).
[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-megapixel computer-generated holographic images from Active Tiling: a dynamic and scalable electro-optic modulator system,” SPIE 5005, 247 (2003).
[CrossRef]

Clark, M.

Coomber, S. D.

C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27–41 (2004).
[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-megapixel computer-generated holographic images from Active Tiling: a dynamic and scalable electro-optic modulator system,” SPIE 5005, 247 (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-megapixel computer-generated holographic images from Active Tiling: a dynamic and scalable electro-optic modulator system,” SPIE 5005, 247 (2003).
[CrossRef]

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 (1996).
[CrossRef]

N. Fukaya, K. Maeno, O. Nishikawa, K. Matumoto, K. Sato, and T. Honda, “Expansion of the image size and viewing zone in holographic display using liquid crystal devices,” Proc. SPIE 2406, 283–289 (1995).

Hahn, J.

Hauck, R.

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 (1996).
[CrossRef]

N. Fukaya, K. Maeno, O. Nishikawa, K. Matumoto, K. Sato, and T. Honda, “Expansion of the image size and viewing zone in holographic display using liquid crystal devices,” Proc. SPIE 2406, 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-megapixel computer-generated holographic images from Active Tiling: a dynamic and scalable electro-optic modulator system,” SPIE 5005, 247 (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-megapixel computer-generated holographic images from Active Tiling: a dynamic and scalable electro-optic modulator system,” SPIE 5005, 247 (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-megapixel computer-generated holographic images from Active Tiling: a dynamic and scalable electro-optic modulator system,” SPIE 5005, 247 (2003).
[CrossRef]

Jepsen, M. L.

P. St. Hilaire, S. A. Benton, M. Lucente, M. L. Jepsen, J. Kollin, H. Yoshikawa, and J. Underkoffler, “Electronic display system for computational holography,” Proc. SPIE 1212, 174 (1990).
[CrossRef]

Kim, H.

Kollin, J.

P. St. Hilaire, S. A. Benton, M. Lucente, M. L. Jepsen, J. Kollin, H. Yoshikawa, and J. Underkoffler, “Electronic display system for computational holography,” Proc. SPIE 1212, 174 (1990).
[CrossRef]

Lee, B.

Lee, W. H.

Lim, Y.

Lohmann, A. W.

Lucent, M.

M. Lucent, “Optimization of hologram computation for real-time display,” Proc. SPIE 1667, 32–43 (1992).
[CrossRef]

Lucente, M.

P. St. Hilaire, S. A. Benton, and M. Lucente, “Synthetic aperture hologram: a novel approach to three-dimensional display,” J. Opt. Soc. Am. 9(11), 1969–1977 (1992).
[CrossRef]

P. St. Hilaire, S. A. Benton, M. Lucente, M. L. Jepsen, J. Kollin, H. Yoshikawa, and J. Underkoffler, “Electronic display system for computational holography,” Proc. SPIE 1212, 174 (1990).
[CrossRef]

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 (1996).
[CrossRef]

N. Fukaya, K. Maeno, O. Nishikawa, K. Matumoto, K. Sato, and T. Honda, “Expansion of the image size and viewing zone in holographic display using liquid crystal devices,” Proc. SPIE 2406, 283–289 (1995).

Matumoto, K.

N. Fukaya, K. Maeno, O. Nishikawa, K. Matumoto, K. Sato, and T. Honda, “Expansion of the image size and viewing zone in holographic display using liquid crystal devices,” Proc. SPIE 2406, 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-megapixel computer-generated holographic images from Active Tiling: a dynamic and scalable electro-optic modulator system,” SPIE 5005, 247 (2003).
[CrossRef]

Miller, R. J.

C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27–41 (2004).
[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-megapixel computer-generated holographic images from Active Tiling: a dynamic and scalable electro-optic modulator system,” SPIE 5005, 247 (2003).
[CrossRef]

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 (1996).
[CrossRef]

N. Fukaya, K. Maeno, O. Nishikawa, K. Matumoto, K. Sato, and T. Honda, “Expansion of the image size and viewing zone in holographic display using liquid crystal devices,” Proc. SPIE 2406, 283–289 (1995).

Okada, N.

Paris, D. P.

Park, G.

Payne, D. A.

C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27–41 (2004).
[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-megapixel computer-generated holographic images from Active Tiling: a dynamic and scalable electro-optic modulator system,” SPIE 5005, 247 (2003).
[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-megapixel computer-generated holographic images from Active Tiling: a dynamic and scalable electro-optic modulator system,” SPIE 5005, 247 (2003).
[CrossRef]

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 (1996).
[CrossRef]

N. Fukaya, K. Maeno, O. Nishikawa, K. Matumoto, K. Sato, and T. Honda, “Expansion of the image size and viewing zone in holographic display using liquid crystal devices,” Proc. SPIE 2406, 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-megapixel computer-generated holographic images from Active Tiling: a dynamic and scalable electro-optic modulator system,” SPIE 5005, 247 (2003).
[CrossRef]

Seldowitz, M. A.

Slinger, C. W.

C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27–41 (2004).
[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-megapixel computer-generated holographic images from Active Tiling: a dynamic and scalable electro-optic modulator system,” SPIE 5005, 247 (2003).
[CrossRef]

Smith, A. P.

C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27–41 (2004).
[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-megapixel computer-generated holographic images from Active Tiling: a dynamic and scalable electro-optic modulator system,” SPIE 5005, 247 (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-megapixel computer-generated holographic images from Active Tiling: a dynamic and scalable electro-optic modulator system,” SPIE 5005, 247 (2003).
[CrossRef]

Smith, M. G.

C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27–41 (2004).
[CrossRef]

St. Hilaire, P.

P. St. Hilaire, S. A. Benton, and M. Lucente, “Synthetic aperture hologram: a novel approach to three-dimensional display,” J. Opt. Soc. Am. 9(11), 1969–1977 (1992).
[CrossRef]

P. St. Hilaire, S. A. Benton, M. Lucente, M. L. Jepsen, J. Kollin, H. Yoshikawa, and J. Underkoffler, “Electronic display system for computational holography,” Proc. SPIE 1212, 174 (1990).
[CrossRef]

Stanley, M.

C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27–41 (2004).
[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-megapixel computer-generated holographic images from Active Tiling: a dynamic and scalable electro-optic modulator system,” SPIE 5005, 247 (2003).
[CrossRef]

Sweeney, D. W.

Takaki, Y.

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-megapixel computer-generated holographic images from Active Tiling: a dynamic and scalable electro-optic modulator system,” SPIE 5005, 247 (2003).
[CrossRef]

Underkoffler, J.

P. St. Hilaire, S. A. Benton, M. Lucente, M. L. Jepsen, J. Kollin, H. Yoshikawa, and J. Underkoffler, “Electronic display system for computational holography,” Proc. SPIE 1212, 174 (1990).
[CrossRef]

Watson, P. J.

C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27–41 (2004).
[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-megapixel computer-generated holographic images from Active Tiling: a dynamic and scalable electro-optic modulator system,” SPIE 5005, 247 (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-megapixel computer-generated holographic images from Active Tiling: a dynamic and scalable electro-optic modulator system,” SPIE 5005, 247 (2003).
[CrossRef]

Yoshikawa, H.

P. St. Hilaire, S. A. Benton, M. Lucente, M. L. Jepsen, J. Kollin, H. Yoshikawa, and J. Underkoffler, “Electronic display system for computational holography,” Proc. SPIE 1212, 174 (1990).
[CrossRef]

Appl. Opt. (7)

J. Opt. Soc. Am. (1)

P. St. Hilaire, S. A. Benton, and M. Lucente, “Synthetic aperture hologram: a novel approach to three-dimensional display,” J. Opt. Soc. Am. 9(11), 1969–1977 (1992).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Express (2)

Proc. SPIE (5)

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SPIE (1)

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-megapixel computer-generated holographic images from Active Tiling: a dynamic and scalable electro-optic modulator system,” SPIE 5005, 247 (2003).
[CrossRef]

Supplementary Material (1)

» Media 1: MOV (3934 KB)     

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Figures (8)

Fig. 1
Fig. 1

Horizontally scanning holographic display.

Fig. 2
Fig. 2

Sets of elementary holograms displayed by the horizontally scanning holographic display.

Fig. 3
Fig. 3

Calculation of the intensity distribution of elementary holograms: the hologram distribution is represented by (a) a bipolar intensity distribution, (b) a non-negative real value distribution, (c) a rectangular wave, (d) a non-negative rectangular wave, and (e) multiple binary distributions.

Fig. 4
Fig. 4

Decomposition methods: (a) bit-plane method, (b) intensity threshold method, (c) amplitude threshold method, and (d) histogram method.

Fig. 5
Fig. 5

Reconstructed images of a test pattern generated by (a) the bit-plane method, (b) the intensity threshold method, (c) the amplitude threshold method, and (d) the histogram method.

Fig. 6
Fig. 6

Measured average light intensities in eight filled rectangles of the reconstructed images generated by the four decomposition methods.

Fig. 7
Fig. 7

Grayscale 3D image used for the experiment: (a) texture and (b) depth.

Fig. 8
Fig. 8

Reconstructed 3D image captured from (a) the left, (b) the center, and (c) the right. (Media 1)

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