Abstract

A 4f optical system with a single-sideband filter has been used for electronic holographic displays in order to obtain a reconstructed image without a conjugate image and zero-order diffraction light. However, the viewing region is inclined, and the viewing region in which an entire reconstructed image can be viewed is limited. In the present study, one of the Fourier transform lenses constituting the 4f optical system is shifted to correct the viewing region inclination. Moreover, a screen lens is added in the image plane of the 4f optical system to maximize the viewing region. The inclination of the viewing region can also be corrected by shifting the screen lens instead of shifting the Fourier transform lens. Experimental verifications of these corrections are described.

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References

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    [CrossRef] [PubMed]
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2010 (1)

2009 (1)

2008 (3)

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,” Proc. SPIE 5005, 247–258 (2003).
[CrossRef]

1999 (1)

1996 (2)

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]

N. Fukaya, K. Maeno, K. Sato, and T. Honda, “Improved eletroholographic display using liquid crystal device to shorten the viewing distance with both-eye observation,” Opt. Eng. 35(6), 1545–1549 (1996).
[CrossRef]

1968 (2)

1966 (1)

J. P. Waters, “Holographic image synthesis utilizing theoretical methods,” Appl. Phys. Lett. 9(11), 405–407 (1966).
[CrossRef]

1962 (1)

1950 (1)

G. L. Rogers, “Gabor diffraction microscopy: the hologram as a generalized zone-plate,” Nature 166(4214), 237 (1950).
[CrossRef] [PubMed]

1948 (1)

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

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,” Proc. SPIE 5005, 247–258 (2003).
[CrossRef]

Bryngdahl, O.

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-megapixel computer-generated holographic images from Active Tiling: a dynamic and scalable electro-optic modulator system,” Proc. SPIE 5005, 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-megapixel computer-generated holographic images from Active Tiling: a dynamic and scalable electro-optic modulator system,” Proc. SPIE 5005, 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-megapixel computer-generated holographic images from Active Tiling: a dynamic and scalable electro-optic modulator system,” Proc. SPIE 5005, 247–258 (2003).
[CrossRef]

Fukaya, N.

N. Fukaya, K. Maeno, K. Sato, and T. Honda, “Improved eletroholographic display using liquid crystal device to shorten the viewing distance with both-eye observation,” Opt. Eng. 35(6), 1545–1549 (1996).
[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]

Gabor, D.

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

Givens, M. P.

Hahn, J.

Hayashi, Y.

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]

N. Fukaya, K. Maeno, K. Sato, and T. Honda, “Improved eletroholographic display using liquid crystal device to shorten the viewing distance with both-eye observation,” Opt. Eng. 35(6), 1545–1549 (1996).
[CrossRef]

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,” Proc. SPIE 5005, 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-megapixel computer-generated holographic images from Active Tiling: a dynamic and scalable electro-optic modulator system,” Proc. SPIE 5005, 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-megapixel computer-generated holographic images from Active Tiling: a dynamic and scalable electro-optic modulator system,” Proc. SPIE 5005, 247–258 (2003).
[CrossRef]

Kim, H.

Lee, B.

Leith, E. N.

Lim, Y.

Lohmann, A.

Maeno, K.

N. Fukaya, K. Maeno, K. Sato, and T. Honda, “Improved eletroholographic display using liquid crystal device to shorten the viewing distance with both-eye observation,” Opt. Eng. 35(6), 1545–1549 (1996).
[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]

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,” Proc. SPIE 5005, 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-megapixel computer-generated holographic images from Active Tiling: a dynamic and scalable electro-optic modulator system,” Proc. SPIE 5005, 247–258 (2003).
[CrossRef]

Mishina, T.

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]

Okano, F.

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-megapixel computer-generated holographic images from Active Tiling: a dynamic and scalable electro-optic modulator system,” Proc. SPIE 5005, 247–258 (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,” Proc. SPIE 5005, 247–258 (2003).
[CrossRef]

Rogers, G. L.

G. L. Rogers, “Gabor diffraction microscopy: the hologram as a generalized zone-plate,” Nature 166(4214), 237 (1950).
[CrossRef] [PubMed]

Sakamoto, Y.

Y. Yabe and Y. Sakamoto, “Enlargement of visual field with an LCD in computer generated holograms,” Proc. SPIE 6912, 69121A (2008).
[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, 15–23 (1996).
[CrossRef]

N. Fukaya, K. Maeno, K. Sato, and T. Honda, “Improved eletroholographic display using liquid crystal device to shorten the viewing distance with both-eye observation,” Opt. Eng. 35(6), 1545–1549 (1996).
[CrossRef]

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,” Proc. SPIE 5005, 247–258 (2003).
[CrossRef]

Siemens-Wapniarski, W. J.

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-megapixel computer-generated holographic images from Active Tiling: a dynamic and scalable electro-optic modulator system,” Proc. SPIE 5005, 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-megapixel computer-generated holographic images from Active Tiling: a dynamic and scalable electro-optic modulator system,” Proc. SPIE 5005, 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-megapixel computer-generated holographic images from Active Tiling: a dynamic and scalable electro-optic modulator system,” Proc. SPIE 5005, 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-megapixel computer-generated holographic images from Active Tiling: a dynamic and scalable electro-optic modulator system,” Proc. SPIE 5005, 247–258 (2003).
[CrossRef]

Takaki, Y.

Tanemoto, 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,” Proc. SPIE 5005, 247–258 (2003).
[CrossRef]

Upatnieks, J.

Waters, J. P.

J. P. Waters, “Holographic image synthesis utilizing theoretical methods,” Appl. Phys. Lett. 9(11), 405–407 (1966).
[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-megapixel computer-generated holographic images from Active Tiling: a dynamic and scalable electro-optic modulator system,” Proc. SPIE 5005, 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-megapixel computer-generated holographic images from Active Tiling: a dynamic and scalable electro-optic modulator system,” Proc. SPIE 5005, 247–258 (2003).
[CrossRef]

Yabe, Y.

Y. Yabe and Y. Sakamoto, “Enlargement of visual field with an LCD in computer generated holograms,” Proc. SPIE 6912, 69121A (2008).
[CrossRef]

Yuyama, I.

Appl. Opt. (4)

Appl. Phys. Lett. (1)

J. P. Waters, “Holographic image synthesis utilizing theoretical methods,” Appl. Phys. Lett. 9(11), 405–407 (1966).
[CrossRef]

J. Opt. Soc. Am. (2)

Nature (2)

G. L. Rogers, “Gabor diffraction microscopy: the hologram as a generalized zone-plate,” Nature 166(4214), 237 (1950).
[CrossRef] [PubMed]

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

Opt. Eng. (1)

N. Fukaya, K. Maeno, K. Sato, and T. Honda, “Improved eletroholographic display using liquid crystal device to shorten the viewing distance with both-eye observation,” Opt. Eng. 35(6), 1545–1549 (1996).
[CrossRef]

Opt. Express (2)

Proc. SPIE (3)

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,” Proc. SPIE 5005, 247–258 (2003).
[CrossRef]

Y. Yabe and Y. Sakamoto, “Enlargement of visual field with an LCD in computer generated holograms,” Proc. SPIE 6912, 69121A (2008).
[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]

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Figures (13)

Fig. 1
Fig. 1

Correction of viewing region inclination of 4f optical system: (a) original 4f optical system, which generates reconstructed image, conjugate image, and zero-order diffraction light, (b) elimination of conjugate image and zero-order diffraction light by single-sideband filter, and (c) correction of viewing region inclination by shifting screen-side Fourier transform lens.

Fig. 2
Fig. 2

Correction of inclined proceeding direction of spherical wave generated by half-zone plate: (a) inclined spherical wave generation by 4f optical system with single-sideband filter, and (b) correction of inclined proceeding direction of spherical wave by shifting screen-side Fourier transform lens.

Fig. 3
Fig. 3

Restricted viewing region in conventional 4f optical system.

Fig. 4
Fig. 4

Maximization of viewing region by screen lens.

Fig. 5
Fig. 5

Width of viewing region v at observation distance z (a) 2fs tan(φ/2) ≥ w and (b) 2fs tan(φ/2) ≤ w.

Fig. 6
Fig. 6

Correction of viewing region inclination of 4f optical system by shifting screen lens.

Fig. 7
Fig. 7

Correction of inclined proceeding direction of spherical wave generated by half-zone plate by shifting screen lens.

Fig. 8
Fig. 8

Correction of viewing region inclination: reconstructed images produced by (a) conventional 4f optical system, and (b) modified 4f optical system by vertically shifting screen-side Fourier transform lens.

Fig. 9
Fig. 9

Reconstructed images produced by conventional 4f optical system: images captured at (a) 15 mm left of center, (b) center, and (c) 15 mm right of center.

Fig. 10
Fig. 10

Reconstructed images produced by modified 4f optical system with screen lens: images captured at (a) 15 mm left of center, (b) center, and (c) 15 mm right of center.

Fig. 11
Fig. 11

Correction of image distortion caused by screen lens (a) conventional hologram calculation method, and (b) modified hologram calculation method.

Fig. 12
Fig. 12

Correction of vertical viewing region inclination: reconstructed images produced (a) without shift of screen lens and (b) with vertical shift of screen lens.

Fig. 13
Fig. 13

Point spread functions (PSFs) of 4f optical system: (a)–(c) when screen-side Fourier transform lens is not shifted, (d)–(f) when it is vertically shifted. (a) and (d) are at the center of image, (b) and (e) are at the uppermost position, and (c) and (f) are at the rightmost position.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

v = 2 z tan ( φ / 2 ) w ,
v = { [ 2 tan ( φ / 2 ) + w / f s ] z w ( z f s ) , [ 2 tan ( φ / 2 ) w / f s ] z + w ( z f s ) ,
x o ' = x o / ( 1 + z o / f ) ,
y o ' = y o / ( 1 + z o / f ) ,
z o ' = z o / ( 1 + z o / f ) .
x o = x o ' / ( 1 z o ' / f ) ,
y o = y o ' / ( 1 z o ' / f ) ,
z o = z o ' / ( 1 z o ' / f ) .

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