Abstract

When one illuminates a computer-generated hologram by a plane wave, the obtained two-dimensional image is usually displayed on a planar plane. Other possibilities for reconstructing images on arbitrary curved surfaces are discussed herein. As an example, the reconstruction of an image on a virtual spherical surface is demonstrated.

© 1999 Optical Society of America

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References

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  1. O. Bryngdahl, F. Wyrowski, “Digital holography/computer-generated holograms,” in Progress In Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1990), Vol. 28, pp. 1–86.
    [CrossRef]
  2. J. P. Waters, “holographic image synthesis utilizing theoretical methods,” Appl. Phys. Lett. 9, 405–407 (1966).
    [CrossRef]
  3. D. Leseberg, C. Frère, “Computer-generated holograms of 3-D objects composed of tilted planar segments,” Appl. Opt. 27, 3020–3024 (1988).
    [CrossRef] [PubMed]
  4. C. Frère, D. Leseberg, “Large objects reconstructed from computer-generated holograms,” Appl. Opt. 28, 2422–2425 (1989).
    [CrossRef] [PubMed]
  5. T. Tommasi, B. Bianco, “Computer-generated holograms of tilted planes by a spatial-frequency approach,” J. Opt. Soc. Am. A 10, 299–305 (1993).
    [CrossRef]
  6. J. S. Loomis, “Computer-generated holography and optical testing,” Opt. Eng. 19, 679–685 (1980).
    [CrossRef]
  7. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), Chap. 5, p. 104.

1993

1989

1988

1980

J. S. Loomis, “Computer-generated holography and optical testing,” Opt. Eng. 19, 679–685 (1980).
[CrossRef]

1966

J. P. Waters, “holographic image synthesis utilizing theoretical methods,” Appl. Phys. Lett. 9, 405–407 (1966).
[CrossRef]

Bianco, B.

Bryngdahl, O.

O. Bryngdahl, F. Wyrowski, “Digital holography/computer-generated holograms,” in Progress In Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1990), Vol. 28, pp. 1–86.
[CrossRef]

Frère, C.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), Chap. 5, p. 104.

Leseberg, D.

Loomis, J. S.

J. S. Loomis, “Computer-generated holography and optical testing,” Opt. Eng. 19, 679–685 (1980).
[CrossRef]

Tommasi, T.

Waters, J. P.

J. P. Waters, “holographic image synthesis utilizing theoretical methods,” Appl. Phys. Lett. 9, 405–407 (1966).
[CrossRef]

Wyrowski, F.

O. Bryngdahl, F. Wyrowski, “Digital holography/computer-generated holograms,” in Progress In Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1990), Vol. 28, pp. 1–86.
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

J. P. Waters, “holographic image synthesis utilizing theoretical methods,” Appl. Phys. Lett. 9, 405–407 (1966).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Eng.

J. S. Loomis, “Computer-generated holography and optical testing,” Opt. Eng. 19, 679–685 (1980).
[CrossRef]

Other

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), Chap. 5, p. 104.

O. Bryngdahl, F. Wyrowski, “Digital holography/computer-generated holograms,” in Progress In Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1990), Vol. 28, pp. 1–86.
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Optical setup used to obtain an image reconstruction from the CGH on a virtual spherical surface.

Fig. 2
Fig. 2

Binary image used for the CGH design and aimed to be displayed on the spherical surface.

Fig. 3
Fig. 3

Upper left-hand corner of the synthesized gray-scale CGH (128 × 128 pixels out of 512 × 512 pixels).

Fig. 4
Fig. 4

Reconstruction results from the gray-scale CGH on the plane z = 20 mm behind the rear focal plane.

Fig. 5
Fig. 5

Reconstruction results from the gray-scale CGH, in the first diffraction order, behind the rear focus, on the transverse planes: (a) z = 4 mm, (b) z = 6 mm, (c) z = 8 mm, (d) z = 10 mm, (e) z = 12 mm, (f) z = 14 mm, (g) z = 16 mm, (h) z = 18 mm, (d) z = 20 mm.

Fig. 6
Fig. 6

Upper left-hand corner of the synthesized binary CGH (128 × 128 pixels out of 512 × 512 pixels).

Fig. 7
Fig. 7

Reconstruction results from the binary CGH on the plane z = 20 mm behind the rear focal plane.

Equations (9)

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A expj πzu2+v2λf2-j 2πλfxu+yv
hu, v=nNmM Anm expj πznmu2+v2λf2-j 2πλfxnmu+ynmv.
hu, v=  Ax, yexpj πzx, yu2+v2λf2-j 2πλfxx, yu+yx, yvdxdy,
zx, y=axx, y+byx, y+c,x, y  Pc,
x=rπ/2-ϕ, y=rπ/2-θ,
x=r cosϕ=r sinx/r,y=r cosθsinϕ=r siny/rcosx/r,z=r sinθsinϕ=r cosy/rcosx/r.
hu, v=  Ax, yexpj cosyr×cosxrπru2+v2λf2-j 2πrλfsinxru+sinyr×cosxrvdxdy.
hru, v=1+Rehu, vexpj2πλfdxu+dyv,
hbu, v=1Rehu, vexpj2πλfdxu+dyv0otherwise>0.

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