Abstract

The single-sideband method of holography, as is well known, cuts off beams that come from conjugate images for holograms produced in the Fraunhofer region and from objects with no phase components. The single-sideband method with half-zone-plate processing is also effective in the Fresnel region for beams from an object that has phase components. However, this method restricts the viewing zone to a narrow range. We propose a method to improve this restriction by time-alternating switching of hologram patterns and a spatial filter set on the focal plane of a reconstruction lens.

© 1999 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 wave front 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. E. N. Leith, J. Upatnieks, “Reconstructed wavefront and communication theory,” J. Opt. Soc. Am. 52, 1123–1130 (1962).
    [CrossRef]
  4. O. Bryngdahl, A. Lohmann, “Single-sideband holography,” J. Opt. Soc. Am. 58, 620–624 (1968).
    [CrossRef]
  5. T. Takemori, “3-dimensional display using liquid crystal devices—fast computation of hologram—,” 21, No. 46 (Institute of Image Information and Television Engineers, Tokyo, 1997), pp. 13–19.
  6. C. B. Burckhardt, “Use of a random phase mask for the recording of Fourier transform holograms of data masks,” Appl. Opt. 9, 695–700 (1970).
    [CrossRef] [PubMed]

1970

1968

1962

Amako, J.

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

Bryngdahl, O.

Burckhardt, C. B.

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).

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).

Leith, E. N.

Lohmann, A.

Miura, H.

T. Sonehara, H. Miura, J. Amako, “Moving 3D-CGH reconstruction using a liquid crystal spatial wave front 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).

Sonehara, T.

T. Sonehara, H. Miura, J. Amako, “Moving 3D-CGH reconstruction using a liquid crystal spatial wave front 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—,” 21, No. 46 (Institute of Image Information and Television Engineers, Tokyo, 1997), pp. 13–19.

Upatnieks, J.

Appl. Opt.

J. Opt. Soc. Am.

Other

T. Takemori, “3-dimensional display using liquid crystal devices—fast computation of hologram—,” 21, No. 46 (Institute of Image Information and Television Engineers, Tokyo, 1997), pp. 13–19.

T. Sonehara, H. Miura, J. Amako, “Moving 3D-CGH reconstruction using a liquid crystal spatial wave front 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).

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Figures (9)

Fig. 1
Fig. 1

Schematic of the holographic process by use of the single-sideband method with half-zone-plate processing: (a) recording and (b) reconstruction.

Fig. 2
Fig. 2

Configuration used for calculating the field distribution of the conjugate beams on the focal plane.

Fig. 3
Fig. 3

Principle of half-zone-plate processing: (a) The object as an aggregate of light sources. (b) A light source on the object. (c) The Fresnel diffraction pattern of a light source on the hologram. One half of this pattern is removed.

Fig. 4
Fig. 4

Amplitude distributions of conjugate beams on the focal plane: (a) When the angle between the directions of the reference beams and the lens’s optical axis is 0°, most of the conjugate beams are eliminated by a half-plane mask that cuts off the hatched area. (b) When this angle is θ, this distribution is shifted by -2f sin θ.

Fig. 5
Fig. 5

Regions of the beams regenerated from the hologram: (a) With half-zone-plate processing, the conjugate beams separate from the reconstructed beams on the focal plane. (b) Without half-zone-plate processing, the conjugate beams overlap the reconstructed beams.

Fig. 6
Fig. 6

Regions of the reconstructed beam regenerated from the hologram by use of half-zone-plate processing: (a) Recording: the shaded area represents the object beams recorded on the hologram. (b) Reconstruction: only the area more darkly shaded is reconstructed; thus the viewing zone is restricted to within the more darkly shaded area.

Fig. 7
Fig. 7

Principle of the time-alternating method: (a) First time that the reconstructed beams are generated. (b) Second time that the reconstructed beams are generated. (c) Time-alternating switching of the first and the second times of generation. This method reciprocally compensates beams, and the viewing zone is enlarged.

Fig. 8
Fig. 8

Shape of the spatial filter on the focal plane: (a) Pixel arrangement of the LCD panel and (b) shape of the spatial filter. The shape of the spatial filter depends on the pixel arrangement of the LCD, the pixel pitch, and the focal length of the reconstruction lens.

Fig. 9
Fig. 9

Experimental results: (a) Object. (b) Reconstructed image obtained with the single-sideband method with half-zone-plate processing, as observed from a position 0.5° clockwise from the optical axis. The right-hand side of this image is erased because this viewpoint is out of the viewing zone of this method. (c) Reconstructed image obtained with the time-alternating method, as observed from the same place as for (b). This image is reconstructed entirely, and the viewing zone can be enlarged.

Tables (1)

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Table 1 Specifications of the LCD Panel Used in the Experiment

Equations (27)

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Ix1, y1=|Ox1, y1|2+|Rx1, y1|2+Ox1, y1R*x1, y1+O*x1, y1Rx1, y1,
Dx1, y1=|Ox1, y1|2+|Rx1, y1|2Rx1, y1+Ox1, y1|Rx1, y1|2+O*x1, y1R2x1, y1,
Ox1, y1=jλdexp-jkdx0,y0=-   gx0, y0×exp-jkx0-x12+y0-y122ddx0dy0,Frdgx0, y0,
gx0, y0=pq1Δx1Δy Cpq expjϕpq  x0-xpΔx, y0-yqΔy,
O*x1, y1=pqOpq*x1, y1,
Opq*x1, y1=1jλd1Δx1Δy Cpq exp-jϕpq×expjkdexpjkx˜12+y˜122d×x˜0,y˜0=- x˜0Δx, y˜0Δyexpjkx˜02+y˜022d×exp-jkx˜0x˜1+y˜0y˜1ddx˜0dy˜0
Spqx1, y1=Sˆx1-xp, y1-yq=Sˆx˜1, y˜1=1x˜1>0 or x1>xp1/2x˜1=0 or x1=xp0x˜1<0 or x1<xp.
gix2, y2=FrfpqOpq*x1, y1Spqx1, y1.
gox2, y2=gix2, y2Px2, y2,
Px2, y2=expjkx22+y222f.
gfx3, y3=Frfgox2, y2=K2x3, y3pqKpqx3, y3×x˜1, y˜1=- Sˆ-x˜1, -y˜1×expjkx˜1-xˆ32+y˜1-yˆ322ddx˜1dy˜1
K2x3, y3x˜1,y˜1=- Sˆ-x˜1, -y˜1×expjkx˜1-xˆ32+y˜1-yˆ322ddx˜1dy˜1×pq Kpqx3, y3,
K2x3, y3=f2πdexp-j2kfexpjkd×exp-jkxˆ32+yˆ322d,
Kpqx3, y3=Cpq exp-jϕpqexpjkxpx3+yqy3f,
xˆ3=d/fx3,
yˆ3=d/fy3.
sin φ=λ/2ph.
Ω=tan-1xp/f+d tan φ/f-tan-1xp/f-d tan φ/f,=tan-1xp/f+dλ/2fph-tan-1xp/f-dλ/2fph,
Ωs=tan-1xp/f+dλ/2fph-tan-1xp/f.
gix2, y2=jλfexp-jkfexp-jkx22+y222f ×x1,y1=-pqOpq*x1, y1Spqx1, y1×exp-jkx12+y122f×expjkx1x2+y1y2fdx1dy1.
gfx3, y3=jλfexp-jkfexp-jkx32+y322f×x2,y2=- gox2, y2exp-jkx22+y222f×expjkx2x3+y2y3fdx2dy2=jλfexp-jkfexp-jkx32+y322f×x2,y2=- gix2, y2×expjkx2x3+y2y3fdx2dy2=j2πλfexp-j2kf×x1,y1=-pqOpq*x1, y1Spqx1, y1×expjkx1x3+y1y3fdx1dy1.
gfx3, y3=j2πλfexp-j2kfpq1jλd Cpq×exp-jϕpqexpjkdx1,y1=- x˜0,y˜0=-×1Δx1Δy× x˜0Δx, y˜0Δyexpjkx˜02+y˜022d×exp-jkx˜0x˜1+y˜0y˜1ddx˜0dy˜0×expjkx˜12+y˜122dSpqx1, y1×expjkx1x3+y1y3fdx1dy1=K1pqKpqx3, y3x˜1,y˜1=-×x˜0,y˜0=-1Δx1Δy x˜0Δx, y˜0Δy×expjkx˜02+y˜022dexp-jkx˜0x˜1+y˜0y˜1d×dx˜0dy˜0expjkx˜12+y˜122dSˆx˜1, y˜1×expjkx˜1x3+y˜1y3fdx˜1dy˜1,
K1=12πλ2fdexp-j2kfexpjkd,
Kpqx3, y3=Cpq exp-jϕpqexpjkxpx3+yqy3f.
x˜1,y˜1=-=x˜1,y˜1=-x˜0,y˜0=-1Δx1Δy  x˜0Δx, y˜0Δy×expjkx˜02+y˜022dexp-jkx˜0x˜1+y˜0y˜1d×dx˜0dy˜0expjkx˜1x3+y˜1y3fdx˜1dy˜1* x˜1,y˜1=- expjkx˜12+y˜122dSˆx˜1, y˜1×expjkx˜1x3+y˜1y3fdx˜1dy˜1=λd2δdf x3, df y3expj kd2f2x32+y32* x˜1,y˜1=- expjkx˜12+y˜122d×Sˆx˜1, y˜1expjkx˜1x3+y˜1y3fdx˜1dy˜1,
x˜1,y˜1=-=λf2δxˆ3, yˆ3expj k2dxˆ32+yˆ32* x˜1,y˜1=- expjkx˜12+y˜122dSˆx˜1, y˜1×expjkx˜1xˆ3+y˜1yˆ3ddx˜1dy˜1=λf2x˜1,y˜1=- expjkx˜12+y˜122dSˆx˜1, y˜1×expjkx˜1xˆ3+y˜1yˆ3ddx˜1dy˜1=λf2x˜1,y˜1=-Sˆx˜1, y˜1expjk-x˜12+-y˜122d×expjkx˜1xˆ3+y˜1yˆ3ddx˜1dy˜1=λf2 exp-jkxˆ32+yˆ322dx˜1,y˜1=- Sˆx˜1, y˜1×expjk-x˜1-xˆ32+-y˜1-yˆ322ddx˜1dy˜1=λf2 exp-jkxˆ32+yˆ322dx˜1,y˜1=- Sˆ-x˜1,-y˜1expjkx˜1-xˆ32+y˜1-yˆ322ddx˜1dy˜1.
gfx3, y3=K2x3, y3pqKpqx3, y3×x˜1,y˜1=- Sˆ-x˜1,-y˜1×expjkx˜1-xˆ32+y˜1-yˆ322ddx˜1dy˜1.

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