Abstract

The single-sideband technique eliminates a conjugate image and zeroth order diffraction light, producing only a reconstructed image of a hologram. A band-limited cosine zone plate appropriate for use with the single-sideband technique is derived. The width of the zone plate is half that of a conventional zone plate in one direction. The proper selection of a transmitted spatial frequency band leads to an interlaced band-limited zone plate that has complex amplitudes in odd or even rows. The use of such a zone plate reduces calculation time for a hologram to approximately 75%. Experimental verification of this is presented.

© 2009 Optical Society of America

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References

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  1. E. N. Leith and J. Upatnieks, “Reconstructed wavefronts and communication theory,” J. Opt. Soc. Am. 52, 1123-1130(1962).
    [CrossRef]
  2. O. Bryngdahl and A. Lohmann, “Single-sideband holography,” J. Opt. Soc. Am. 58, 620-624 (1968).
    [CrossRef]
  3. 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, 3703-3713 (1999).
    [CrossRef]
  4. T. Mishina, M. Okui, and F. Okano, “Viewing-zone enlargement method for sampled hologram that uses high-order diffraction,” Appl. Opt. 41, 1489-1499 (2002).
    [CrossRef] [PubMed]
  5. M. Lucente, “Optimization of hologram computation for real-time display,” Proc. SPIE 1667, 32-43 (1992).
    [CrossRef]
  6. M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2, 28-34 (1993).
    [CrossRef]

2002 (1)

1999 (1)

1993 (1)

M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2, 28-34 (1993).
[CrossRef]

1992 (1)

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

1968 (1)

1962 (1)

Bryngdahl, O.

Leith, E. N.

Lohmann, A.

Lucente, M.

M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2, 28-34 (1993).
[CrossRef]

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

Mishina, T.

Okano, F.

Okui, M.

Upatnieks, J.

Yuyama, I.

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Figures (10)

Fig. 1
Fig. 1

Single-sideband method for elimination of a conjugate image.

Fig. 2
Fig. 2

Band limitation in the Fourier plane.

Fig. 3
Fig. 3

Generation of band-limited zone plates: (a) real part of spherical wave o ( x , y ) ; (b) Fourier transform O ( ν x , ν y ) of o ( x , y ) ; (c)–(e) band-limited Fourier transforms O ( ν x , ν y ) when (c)  ν c = Δ ν / 4 , (d)  ν c = 0 , and (e)  ν c = Δ ν / 4 ; and (f)–(h) band-limited zone plates when (f)  ν c = Δ ν / 4 , (g)  ν c = 0 , and (h)  ν c = Δ ν / 4 .

Fig. 4
Fig. 4

Calculated reconstructed peak distributions when (a)  ν c = Δ ν / 4 , (b)  ν c = 0 , and (c)  ν c = Δ ν / 4 ; calculated conjugate images when (d)  ν c = Δ ν / 4 , (e)  ν c = 0 , and (f)  ν c = Δ ν / 4 .

Fig. 5
Fig. 5

Modeled band-limited cosine zone plate.

Fig. 6
Fig. 6

Interlaced band-limited zone plate: (a) real part and (b) imaginary part.

Fig. 7
Fig. 7

Interpolated zone plates. The sinc function is approximated by finite sequences with (a) 3, (b) 7, (c) 11, and (d) 15 elements.

Fig. 8
Fig. 8

Intensity distributions of reconstructed peak distributions along the y axis: (a) using zone plates interpolated by sinc function; (b) using zone plates shown in Figs. 3f, 5, and zone plate generated by simple average interpolation.

Fig. 9
Fig. 9

Reconstructed images from holograms generated using band-limited cosine zone plates: (a) apple, (b) teapot, and (c) wine glass.

Fig. 10
Fig. 10

Reconstructed images from holograms generated using interlaced band-limited zone plates: (a) apple, (b) teapot, and (c) wine glass.

Equations (2)

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S ( ν x , ν y ) = O ( ν x , ν y Δ ν / 4 + ν c ) + O * ( ν x , ν y Δ ν / 4 + ν c ) .
s ( x , y ) = 2 Re { o ( x , y ) exp [ i 2 π ( Δ ν / 4 ν c ) y ] } + b ( x , y ) ,

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