Abstract

An efficient procedure for the generation of synthetic near-field hologram structures for display purposes is presented. The formation process requires virtually no computation effort.

© 2001 Optical Society of America

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References

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  1. D. Leseberg, “Computer-generated three-dimensional image holograms,” Appl. Opt. 31, 223–229 (1992).
    [CrossRef] [PubMed]
  2. A. Jendral, R. Bräuer, O. Bryngdahl, “Synthetic image holograms: computation and properties,” Opt. Commun. 109, 47–53 (1994).
    [CrossRef]
  3. T. Yatagai, “Stereoscopic approach to 3-D display using computer-generated holograms,” Appl. Opt. 15, 2722–2729 (1976).
    [CrossRef] [PubMed]
  4. G. P. Nordin, J. H. Kulick, M. Jones, P. Nasiatka, R. G. Lindquist, S. T. Kowel, “Demonstration of a novel three-dimensional autostereoscopic display,” Opt. Lett. 19, 901–903 (1994).
    [CrossRef] [PubMed]
  5. M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2, 28–34 (1993).
    [CrossRef]
  6. A. Jendral, O. Bryngdahl, “Synthetic near-field holograms with localized information,” Opt. Lett. 20, 1204–1206 (1995).
    [CrossRef] [PubMed]
  7. A. Jendral, O. Bryngdahl, “Generalized model of synthetic image hologram structures,” in Practical Holography X, S. A. Benton, ed., Proc. SPIE2652, 10–14 (1996).
    [CrossRef]

1995 (1)

1994 (2)

1993 (1)

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

1992 (1)

1976 (1)

Bräuer, R.

A. Jendral, R. Bräuer, O. Bryngdahl, “Synthetic image holograms: computation and properties,” Opt. Commun. 109, 47–53 (1994).
[CrossRef]

Bryngdahl, O.

A. Jendral, O. Bryngdahl, “Synthetic near-field holograms with localized information,” Opt. Lett. 20, 1204–1206 (1995).
[CrossRef] [PubMed]

A. Jendral, R. Bräuer, O. Bryngdahl, “Synthetic image holograms: computation and properties,” Opt. Commun. 109, 47–53 (1994).
[CrossRef]

A. Jendral, O. Bryngdahl, “Generalized model of synthetic image hologram structures,” in Practical Holography X, S. A. Benton, ed., Proc. SPIE2652, 10–14 (1996).
[CrossRef]

Jendral, A.

A. Jendral, O. Bryngdahl, “Synthetic near-field holograms with localized information,” Opt. Lett. 20, 1204–1206 (1995).
[CrossRef] [PubMed]

A. Jendral, R. Bräuer, O. Bryngdahl, “Synthetic image holograms: computation and properties,” Opt. Commun. 109, 47–53 (1994).
[CrossRef]

A. Jendral, O. Bryngdahl, “Generalized model of synthetic image hologram structures,” in Practical Holography X, S. A. Benton, ed., Proc. SPIE2652, 10–14 (1996).
[CrossRef]

Jones, M.

Kowel, S. T.

Kulick, J. H.

Leseberg, D.

Lindquist, R. G.

Lucente, M.

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

Nasiatka, P.

Nordin, G. P.

Yatagai, T.

Appl. Opt. (2)

J. Electron. Imaging (1)

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

Opt. Commun. (1)

A. Jendral, R. Bräuer, O. Bryngdahl, “Synthetic image holograms: computation and properties,” Opt. Commun. 109, 47–53 (1994).
[CrossRef]

Opt. Lett. (2)

Other (1)

A. Jendral, O. Bryngdahl, “Generalized model of synthetic image hologram structures,” in Practical Holography X, S. A. Benton, ed., Proc. SPIE2652, 10–14 (1996).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Three basic types of elementary holograms. The lines in (a) and (b) denote locations of equal phase. The shaded areas in (c) are partial pixels and contain grating structures with orientations analogous to those in (b) but with higher spatial frequencies. The white areas are unmodulated portions.

Fig. 2
Fig. 2

Near-field hologram structure consists of coherently superposed elementary holograms. It can be locally linearized when the structure in small areas is replaced by grating superpositions representing linear combinations of linear phase variations.

Fig. 3
Fig. 3

Hologram structure is specified by an array of integer numbers. Each integer number consists of several bits (four in our example). (a) The bit representation of two one-dimensional elementary holograms are shown in bold, which have been inserted in the integer array. (b) The elementary holograms are superposed.

Fig. 4
Fig. 4

Optimal cell size dopt versus distance z from the hologram plane (λ = 632.8 nm).

Fig. 5
Fig. 5

(a) Axial cross section through the amplitude field of a nonlinearized elementary hologram (logarithmic representation, height 1280 µm, width 25.6 mm). The focus is located at z = 10 mm. On the left the one-dimensional distribution of the elementary hologram is shown. (b)–(f) The elementary hologram used in (a) was linearized with five different cell sizes. The optimal cell size is dopt = 79.5 µm.

Fig. 6
Fig. 6

Axial cross sections through the amplitude fields of elementary holograms linearized with the cell size dopt = 80 µm that is optimal for z = 10 mm (logarithmic representation).

Fig. 7
Fig. 7

Axial sampling point distributions for different numbers of spatial frequencies P. The sampling distance in the hologram structure is δx = 5 µm and the cell size is d = 160 µm.

Fig. 8
Fig. 8

Largest void and average axial resolution of the sampling grids from Fig. 7.

Equations (8)

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

μp0, 1d, 2d,, 12δx
uhx=rp=1P γpr exp-2πiμpxrectx-rdd,
Lqx=p=1d/2δx εpq cos2πiμpxrectxd; q=0,, 2d/2δx-1.
μx=1λ1+zx21/2
μd-μ01d,
d4-λ2d2-λ2z20.
0dλ|z|.
P=λ|z|2δx.

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