Abstract

The feasibility of on-axis synthetic near-field amplitude holograms for three-dimensional display applications is demonstrated. An iterative optimization algorithm is used that generates an object-dependent diffuser that utilizes the phase and, to some extent, amplitude freedoms in the reconstruction plane. The discrimination between twin images and undiffracted terms is thus improved. The on-axis approach presents important advantages: a low coherence requirement for the illuminating source, a lower space–bandwidth and higher viewing angle than with the off-axis alternatives. Defocusing and parallax are experimentally attained with an extended white-light source and a lensless setup.

© 1997 Optical Society of America

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References

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  1. D. Leseberg, Appl. Opt. 31, 223 (1992).
    [Crossref] [PubMed]
  2. A. Jendral, R. Braüer, and O. Bryngdahl, Opt. Commun. 109, 47 (1994).
    [Crossref]
  3. A. Jendral and O. Bryngdahl, Opt. Lett. 20, 1204 (1995).
    [Crossref] [PubMed]
  4. R. Piestun, B. Spektor, and J. Shamir, Opt. Commun. 136, 85 (1997).
    [Crossref]
  5. R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, New York, 1971).
  6. O. Bryngdahl and F. Wyrowski, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1990), Vol.  28, p. 1.
    [Crossref]
  7. R. Piestun and J. Shamir, Opt. Lett. 19, 771 (1994).
    [Crossref] [PubMed]
  8. R. Aharoni and Y. Censor, Linear Algebra Appl. 120, 165 (1989).
    [Crossref]
  9. R. Piestun, B. Spektor, and J. Shamir, J. Opt. Soc. Am. A 13, 1837 (1996).
    [Crossref]

1997 (1)

R. Piestun, B. Spektor, and J. Shamir, Opt. Commun. 136, 85 (1997).
[Crossref]

1996 (1)

1995 (1)

1994 (2)

R. Piestun and J. Shamir, Opt. Lett. 19, 771 (1994).
[Crossref] [PubMed]

A. Jendral, R. Braüer, and O. Bryngdahl, Opt. Commun. 109, 47 (1994).
[Crossref]

1992 (1)

1989 (1)

R. Aharoni and Y. Censor, Linear Algebra Appl. 120, 165 (1989).
[Crossref]

Aharoni, R.

R. Aharoni and Y. Censor, Linear Algebra Appl. 120, 165 (1989).
[Crossref]

Braüer, R.

A. Jendral, R. Braüer, and O. Bryngdahl, Opt. Commun. 109, 47 (1994).
[Crossref]

Bryngdahl, O.

A. Jendral and O. Bryngdahl, Opt. Lett. 20, 1204 (1995).
[Crossref] [PubMed]

A. Jendral, R. Braüer, and O. Bryngdahl, Opt. Commun. 109, 47 (1994).
[Crossref]

O. Bryngdahl and F. Wyrowski, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1990), Vol.  28, p. 1.
[Crossref]

Burckhardt, C. B.

R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, New York, 1971).

Censor, Y.

R. Aharoni and Y. Censor, Linear Algebra Appl. 120, 165 (1989).
[Crossref]

Collier, R. J.

R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, New York, 1971).

Jendral, A.

A. Jendral and O. Bryngdahl, Opt. Lett. 20, 1204 (1995).
[Crossref] [PubMed]

A. Jendral, R. Braüer, and O. Bryngdahl, Opt. Commun. 109, 47 (1994).
[Crossref]

Leseberg, D.

Lin, L. H.

R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, New York, 1971).

Piestun, R.

Shamir, J.

Spektor, B.

R. Piestun, B. Spektor, and J. Shamir, Opt. Commun. 136, 85 (1997).
[Crossref]

R. Piestun, B. Spektor, and J. Shamir, J. Opt. Soc. Am. A 13, 1837 (1996).
[Crossref]

Wyrowski, F.

O. Bryngdahl and F. Wyrowski, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1990), Vol.  28, p. 1.
[Crossref]

Appl. Opt. (1)

J. Opt. Soc. Am. A (1)

Linear Algebra Appl. (1)

R. Aharoni and Y. Censor, Linear Algebra Appl. 120, 165 (1989).
[Crossref]

Opt. Commun. (2)

A. Jendral, R. Braüer, and O. Bryngdahl, Opt. Commun. 109, 47 (1994).
[Crossref]

R. Piestun, B. Spektor, and J. Shamir, Opt. Commun. 136, 85 (1997).
[Crossref]

Opt. Lett. (2)

Other (2)

R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, New York, 1971).

O. Bryngdahl and F. Wyrowski, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1990), Vol.  28, p. 1.
[Crossref]

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Figures (2)

Fig. 1
Fig. 1

Experimental reconstruction with collimated laser light and a reduced input pupil: (a), (b) Different lateral views when the observer is focusing on the triangle plane placed at z0=3 cm from the hologram. (c), (d) The same lateral views when the observer is focusing on the circle plane at z0=5 cm. In (a)–(d) the border of the diffraction image of the iris is visible at the very edges of the recordings. (e) On-axis observation focusing on the image plane of the ring. The background occupies the central portion of the iris. Note the parallax and defocusing, which give three-dimensional clues.

Fig. 2
Fig. 2

Observation setup: The observation is performed off axis despite the object’s being around the optical axis. 1, hologram frame; 2, eye lens; 3, eye pupil; 4, fovea (detection plane). The shadowed area corresponds to the region of observation. This area is located inside the conical field of view (angle α), allowing one to separate the true and the conjugate images (angle β) and to screen out the undiffracted light (angle γ).

Equations (5)

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ux, y, z0=F-1exp2πiz0λ-2-μ2-ν21/2×FWx, yHx, y,
Hr+1=CHr=P-1CˆPHr,
CˆPHr=Cˆhrx, y, z0=K expiϕhrx, y, z0if fx, y=1minK/100, hrx, y, z0expiϕhrx, y, z0if fx, y=0.
Cˆ1PHr=K expiϕhrx, y, z0if fx, y=1hrx, y, z0if fx, y=0, 
Hr+1=0.01P-1Cˆhrx, y, z0+0.99P-1Cˆ1hrx, y, z0.

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