Abstract

We demonstrate a method of enlarging the viewing zone for holography that has holograms with a pixel structure. First, aliasing generated by the sampling of a hologram by pixel is described. Next the high-order diffracted beams reproduced from the hologram that contains aliasing are explained. Finally, we show that the viewing zone can be enlarged by combining these high-order reconstructed beams from the hologram with aliasing.

© 2002 Optical Society of America

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References

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  1. T. Sonehara, H. Miura, J. Amako, “Moving 3D-CGH reconstruction using a liquid crystal spatial wavefront modulator,” in Proceedings of the Twelfth International Display Research Conference, S. Kobayashi, ed. (Society for Information Display, San Jose, Calif., 1992), pp. 315–318.
  2. N. Hashimoto, S. Morokawa, K. Kitamura, “Real-time holography using the high-resolution LCTV-SLM,” in Practical Holography V, S. A. Benton, ed., Proc. SPIE1461, 291–302 (1991).
  3. T. Mishina, F. Okano, I. Yuyama, “Time-alternating method based on single-sideband holography with half-zone-plate processing for the enlargement of viewing zones,” Appl. Opt. 38, 3703–3713 (1999).
    [CrossRef]
  4. K. Maeno, N. Fukaya, O. Nishikawa, “Electro-holographic display using 15mega pixels LCD,” in Practical Holography X, S. A. Benton, ed., Proc. SPIE2652, 15–23 (1996).
    [CrossRef]
  5. T. Okoshi, Three-Dimensional Imaging Techniques (Academic, New York, 1976).
  6. K. Iizuka, Engineering Optics (Springer-Verlag, New York, 1985).
    [CrossRef]
  7. M. Onoe, M. Kaneko, “Characteristics of three-dimensional reconstructed images from a computer generated hologram,” Trans. Inst. Electron. Commun. Eng. J. J62-C, 771–776 (1979).
  8. T. Takemori, “3-dimensional display using liquid crystal devices—fast computation of hologram,” ITE Tech. Report21, No. 46 (Institute of Image Information and Television Engineers, Tokyo, 1997), 13–19.

1999 (1)

1979 (1)

M. Onoe, M. Kaneko, “Characteristics of three-dimensional reconstructed images from a computer generated hologram,” Trans. Inst. Electron. Commun. Eng. J. J62-C, 771–776 (1979).

Amako, J.

T. Sonehara, H. Miura, J. Amako, “Moving 3D-CGH reconstruction using a liquid crystal spatial wavefront modulator,” in Proceedings of the Twelfth International Display Research Conference, S. Kobayashi, ed. (Society for Information Display, San Jose, Calif., 1992), pp. 315–318.

Fukaya, N.

K. Maeno, N. Fukaya, O. Nishikawa, “Electro-holographic display using 15mega pixels LCD,” in Practical Holography X, S. A. Benton, ed., Proc. SPIE2652, 15–23 (1996).
[CrossRef]

Hashimoto, N.

N. Hashimoto, S. Morokawa, K. Kitamura, “Real-time holography using the high-resolution LCTV-SLM,” in Practical Holography V, S. A. Benton, ed., Proc. SPIE1461, 291–302 (1991).

Iizuka, K.

K. Iizuka, Engineering Optics (Springer-Verlag, New York, 1985).
[CrossRef]

Kaneko, M.

M. Onoe, M. Kaneko, “Characteristics of three-dimensional reconstructed images from a computer generated hologram,” Trans. Inst. Electron. Commun. Eng. J. J62-C, 771–776 (1979).

Kitamura, K.

N. Hashimoto, S. Morokawa, K. Kitamura, “Real-time holography using the high-resolution LCTV-SLM,” in Practical Holography V, S. A. Benton, ed., Proc. SPIE1461, 291–302 (1991).

Maeno, K.

K. Maeno, N. Fukaya, O. Nishikawa, “Electro-holographic display using 15mega pixels LCD,” in Practical Holography X, S. A. Benton, ed., Proc. SPIE2652, 15–23 (1996).
[CrossRef]

Mishina, T.

Miura, H.

T. Sonehara, H. Miura, J. Amako, “Moving 3D-CGH reconstruction using a liquid crystal spatial wavefront modulator,” in Proceedings of the Twelfth International Display Research Conference, S. Kobayashi, ed. (Society for Information Display, San Jose, Calif., 1992), pp. 315–318.

Morokawa, S.

N. Hashimoto, S. Morokawa, K. Kitamura, “Real-time holography using the high-resolution LCTV-SLM,” in Practical Holography V, S. A. Benton, ed., Proc. SPIE1461, 291–302 (1991).

Nishikawa, O.

K. Maeno, N. Fukaya, O. Nishikawa, “Electro-holographic display using 15mega pixels LCD,” in Practical Holography X, S. A. Benton, ed., Proc. SPIE2652, 15–23 (1996).
[CrossRef]

Okano, F.

Okoshi, T.

T. Okoshi, Three-Dimensional Imaging Techniques (Academic, New York, 1976).

Onoe, M.

M. Onoe, M. Kaneko, “Characteristics of three-dimensional reconstructed images from a computer generated hologram,” Trans. Inst. Electron. Commun. Eng. J. J62-C, 771–776 (1979).

Sonehara, T.

T. Sonehara, H. Miura, J. Amako, “Moving 3D-CGH reconstruction using a liquid crystal spatial wavefront modulator,” in Proceedings of the Twelfth International Display Research Conference, S. Kobayashi, ed. (Society for Information Display, San Jose, Calif., 1992), pp. 315–318.

Takemori, T.

T. Takemori, “3-dimensional display using liquid crystal devices—fast computation of hologram,” ITE Tech. Report21, No. 46 (Institute of Image Information and Television Engineers, Tokyo, 1997), 13–19.

Yuyama, I.

Appl. Opt. (1)

Trans. Inst. Electron. Commun. Eng. J. (1)

M. Onoe, M. Kaneko, “Characteristics of three-dimensional reconstructed images from a computer generated hologram,” Trans. Inst. Electron. Commun. Eng. J. J62-C, 771–776 (1979).

Other (6)

T. Takemori, “3-dimensional display using liquid crystal devices—fast computation of hologram,” ITE Tech. Report21, No. 46 (Institute of Image Information and Television Engineers, Tokyo, 1997), 13–19.

T. Sonehara, H. Miura, J. Amako, “Moving 3D-CGH reconstruction using a liquid crystal spatial wavefront modulator,” in Proceedings of the Twelfth International Display Research Conference, S. Kobayashi, ed. (Society for Information Display, San Jose, Calif., 1992), pp. 315–318.

N. Hashimoto, S. Morokawa, K. Kitamura, “Real-time holography using the high-resolution LCTV-SLM,” in Practical Holography V, S. A. Benton, ed., Proc. SPIE1461, 291–302 (1991).

K. Maeno, N. Fukaya, O. Nishikawa, “Electro-holographic display using 15mega pixels LCD,” in Practical Holography X, S. A. Benton, ed., Proc. SPIE2652, 15–23 (1996).
[CrossRef]

T. Okoshi, Three-Dimensional Imaging Techniques (Academic, New York, 1976).

K. Iizuka, Engineering Optics (Springer-Verlag, New York, 1985).
[CrossRef]

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Figures (15)

Fig. 1
Fig. 1

Schematic of holography that uses a lens in reconstruction. The focal length of the lens is f, and the sampling pitch of a hologram is p. The primary image is reproduced from a virtual image to a real image by a lens. The angle of the viewing zone to observe the reproduced primary image is Ω (= λd/ fp).

Fig. 2
Fig. 2

Area of fringe patterns without aliasing in the hologram. In the case that the angle between the object beam and the reference beam exceeds the maximum angle expressed by Eq. (4), aliasing then occurs in the sampled fringe patterns.

Fig. 3
Fig. 3

Spatial frequency of the sampled fringe patterns.

Fig. 4
Fig. 4

Recording of the fringe patterns with aliasing. Fringe patterns with nth aliasing are obtained, provided that the angle between the object beam and the reference beam satisfies Eq. (11).

Fig. 5
Fig. 5

Reconstruction of the fringe patterns with aliasing. (a) The fringe patterns with nth aliasing are illuminated by a beam, θRC = θ R + 2nϕ M . The primary image is formed at the position of the object. (b) In the case that a beam that is equivalent to the reference beam, θ R , irradiates nth aliasing, the position of the primary image shifts (nλ d/ p) from the object position.

Fig. 6
Fig. 6

Reconstruction from a hologram with pixel structure. High-order carrier images (filled squares), primary images (filled circles), and conjugate images (open circles) are repeatedly reproduced perpendicular to the optical axis.

Fig. 7
Fig. 7

Reconstruction that uses aliasing and high-order reconstructed beam. The beam in the shaded area is the n-order reconstructed beam from the nth aliasing and forms the reproduced n-order primary image at the position where the object is imaged by the lens.

Fig. 8
Fig. 8

Shape of the spatial filter in the focal plane. (a) Pixel arrangement of the display device. (b) Shape of the spatial filter.

Fig. 9
Fig. 9

Flow chart of the calculation of the fringe patterns.

Fig. 10
Fig. 10

Area used to calculate the field in the hologram.

Fig. 11
Fig. 11

Flow chart of the procedures for enlarging the viewing zone.

Fig. 12
Fig. 12

Principle of the method of enlarging the viewing zone. (a) The 0-order reconstructed beam is reproduced. (b) The 1-order reconstructed beam is reproduced. (c) The viewing zone is enlarged by time-alternating switching between (a) and (b).

Fig. 13
Fig. 13

Experimental results. (a) A reproduced image that uses only the 0-order reconstructed beam. The right part of this image is not observed. (b) An image that uses both the 0-order reconstructed beam and the 1-order one by the time-alternating switching method. The whole image is observed from the same viewpoint as in (a), and the viewing zone is enlarged.

Fig. 14
Fig. 14

Configuration of sampled holography.

Fig. 15
Fig. 15

Normalized intensity distribution of reconstructed beams on the back focal plane (y 2 = 0). The distribution of high-order reconstructed beams is arranged at equal intervals. The intensity of high-order reconstructed beams gradually weakens as the number of orders increases in absolute value.

Tables (1)

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Table 1 Specifications of the LCD Used in the Experiment

Equations (53)

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Ωλd/fp,
Δx=λ|sin θO-sin θR|  λ|θO-θR|,
Δx2p.
ϕMλ/2p.
ϕM|θO-θR|.
|θO-θR|>ϕM.
fh=|θO-θR|λ.
fc=1/p=2ϕM/λ.
fs=fh±nfc=|θO-θR±2nϕM|λ=|θO-θRC|λ, n=1, 2,,
θRC=θR±2nϕM.
2n-1ϕM<|θO-θR|2n+1ϕM,
d sin 2nϕMd tan 2nϕM2nϕMd=nλd/p;
x˜o=xo+nλd/p,
xrs=-d2d+f xo+mΔxr=-fd xo+mΔxr,
Δxr=fλp,
1d+f+1d2=1f.
x˜rs=-fd x˜o+mΔxr,
=-fdxo+nλdp+m fλp,
=-fd xo+m-nfλp.
x˜rs=-fd xo.
gx0, y0=p=0pmq=0qmgpqx0, y0,
=p=0pmq=0qmCpq expφpq1ΔpxΔpy×x0-xpΔpx, y0-yqΔpy,
=p=0pmq=0qmCpq expφpqδx0-xp, y0-yq, Δpx, Δpy 0,
Opqx1, y1=jλdexp-jkdx0,y0=- gpqx0, y0×exp-jkx0-x12+y0-y122ddx0dy0,
2d tan ϕMx  2ϕMxd=λd/px,
2d tan ϕMy  2ϕMyd=λd/py.
Ox1, y1=p=0pmq=0qm Opqx1, y1,
=jλdexp-jkdp=0pmq=0qm × x1-xp+2nxϕMxd2ϕMxd, y1-yq+2nyϕMyd2ϕMyd×Cpq expφpqexp-jkxp-x12+yq-y122d.
hx1, y1=|Ox1, y1+Rx1, y1|2,
Enxλfpx, nyλfpy=1λf2ΔpxΔpypxpy2×sinπnxΔpx/pxπnxΔpx/pxsinπnyΔpy/pyπnyΔpy/py2,
=1λf2ΔpxΔpypxpy2 Knxny
Knxny=sinπnxΔpx/pxπnxΔpx/pxsinπnyΔpy/pyπnyΔpy/py2.
Ox1, y1=jλdexp-jkdx0,y0=- gx0, y0×exp-jkx0-x12+y0-y122d×dx0dy0,
=gx1, y1fdx1, y1,
fdx1, y1=jλdexp-jkdexp-jkx12+y122d,
gix2, y2=Ox2, y2  fd1x2, y2,
grx3, y3=g0x3, y3  fd2x3, y3,
g0x2, y2=gix2, y2expjkx22+y222f.
grx3, y3=gix3, y3expjkx32+y322ffd2x3, y3,
=Ox3, y3fd1x3, y3×expjkx32+y322ffd2x3, y3,
=jλd2exp-jkd1+d2×exp-jkx32+y322d2 ×expjπλd1x32+y32λ2d22×x2,y2=-Ox2, y2expj2πx2x3πd2+y2y3πd2dx2dy2 x2,y2=- expjkx22+y2221f-1d2×expj2πx2x3λd2+y2y3λd2dx2dy2
Osx1, y1=kx=-ky=-Okxpx, kypy×x1-kxpxΔpx, y1-kypyΔpy,
x2,y2=- Osx2, y2expj2πx2x3λd2+y2y3λd2dx2dy2 =kx=-ky=-Okxpx, kypy×x2,y2=-x2-kxpxΔpx, y2-kypyΔpy×expj2πx2x3+y2y3λd2dx2dy2
=ΔpxΔpysinπx3Δpx/λd2πx3Δpx/λd2sinπy3Δpy/λd2πy3Δpy/λd2×kx=-ky=-Okxpx, kypy×expj2πλd2kxpxx3+kypyy3
=ΔpxΔpypxpysinπx3Δpx/λd2πx3Δpx/λd2sinπy3Δpy/λd2πy3Δpy/λd2 ×kx=-ky=-O1λd2x3-λd2px kx,1λd2y3-λd2pyky.
grx3, y3=jλfexp-j2kf×ΔpxΔpypxpysinπx3Δpy/λfπx3Δpy/λfsinπy3Δpy/λfπy3Δpy/λf×a=-b=-O1λfx3-λfpx a,1λfy3-λfpy b,
x3, y3=nxλfpx, nyλfpynx,ny=,-1,0,1,,
Ex3, y3=1λf2ΔpxΔpypxpy2×sinπx3Δpx/λfπx3Δpx/λfsinπy3Δpy/λfπy3Δpy/λf2.
1d+d1+1d2=1f.
grx3, y3=a=0amb=0bmKabx3, y3×g-d+d1d2x3+dfd+d1-fλpx a,-d+d1d2y3+dfd+d1-fλpy b,
Kabx3,y3=-d+d1d2λ21pxpy×exp-jkd+d1+d2×expjπλd+d1x3λd2 -apx2+y3λd2- bpy2×expjπλd1apx2+bpy2.
Δxr=dfd+d1-fλpx, Δyr=dfd+d1-fλpy.
Δxr=fλpx, Δyr=fλpy.

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