Abstract

Generally, speckles impair the reconstruction of digital and optical holograms of diffusely scattering objects. With the help of an iterative method, it is possible to introduce diffusers in digital holography that do not suffer from this disadvantage. Optically obtained speckle-free reconstructions of digital holograms are presented.

© 1989 Optical Society of America

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References

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  1. E. N. Leith, J. Upatnieks, “Wavefront reconstruction with diffused illumination and three-dimensional objects,”J. Opt. Soc. Am. 54, 1295–1301 (1964).
    [CrossRef]
  2. F. Wyrowski, O. Bryngdahl, “Iterative Fourier-transform algorithm applied to computer holography,” J. Opt. Soc. Am. A 5, 1058–1065 (1988).
    [CrossRef]
  3. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).
    [CrossRef] [PubMed]
  4. R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).
  5. N. G. Gallagher, B. Liu, “Method for computing kinoforms that reduces image reconstruction error,” Appl. Opt. 12, 2328–2335 (1973).
    [CrossRef] [PubMed]
  6. P. M. Hirsch, J. A. Jordan, L. B. Lesem, “Method of making an object-dependent diffuser,” U.S. Patent3,619,022 (November9, 1971).
  7. J. J. Burch, “A computer algorithm for the synthesis of spatial frequency filters,” Proc. IEEE 55, 599–601 (1967).
    [CrossRef]
  8. W. J. Dallas, “Computer-generated holograms,” in The Computer in Optical Research, B. R. Frieden, ed., Vol. 41 of Topics in Applied Physics (Springer-Verlag, Berlin, 1980), pp. 291–366.
    [CrossRef]
  9. L. B. Lesem, P. M. Hirsh, J. A. Jordan, “Computer synthesis of holograms for 3-D display,” Commun. ACM 11, 661–674 (1968).
    [CrossRef]
  10. F. Wyrowski, R. Hauck, O. Bryngdahl, “Computer-generated holography: hologram repetition and phase manipulations,” J. Opt. Soc. Am. A 4, 694–698 (1987).
    [CrossRef]

1988 (1)

1987 (1)

1982 (1)

1973 (1)

1972 (1)

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

1968 (1)

L. B. Lesem, P. M. Hirsh, J. A. Jordan, “Computer synthesis of holograms for 3-D display,” Commun. ACM 11, 661–674 (1968).
[CrossRef]

1967 (1)

J. J. Burch, “A computer algorithm for the synthesis of spatial frequency filters,” Proc. IEEE 55, 599–601 (1967).
[CrossRef]

1964 (1)

Bryngdahl, O.

Burch, J. J.

J. J. Burch, “A computer algorithm for the synthesis of spatial frequency filters,” Proc. IEEE 55, 599–601 (1967).
[CrossRef]

Dallas, W. J.

W. J. Dallas, “Computer-generated holograms,” in The Computer in Optical Research, B. R. Frieden, ed., Vol. 41 of Topics in Applied Physics (Springer-Verlag, Berlin, 1980), pp. 291–366.
[CrossRef]

Fienup, J. R.

Gallagher, N. G.

Gerchberg, R. W.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Hauck, R.

Hirsch, P. M.

P. M. Hirsch, J. A. Jordan, L. B. Lesem, “Method of making an object-dependent diffuser,” U.S. Patent3,619,022 (November9, 1971).

Hirsh, P. M.

L. B. Lesem, P. M. Hirsh, J. A. Jordan, “Computer synthesis of holograms for 3-D display,” Commun. ACM 11, 661–674 (1968).
[CrossRef]

Jordan, J. A.

L. B. Lesem, P. M. Hirsh, J. A. Jordan, “Computer synthesis of holograms for 3-D display,” Commun. ACM 11, 661–674 (1968).
[CrossRef]

P. M. Hirsch, J. A. Jordan, L. B. Lesem, “Method of making an object-dependent diffuser,” U.S. Patent3,619,022 (November9, 1971).

Leith, E. N.

Lesem, L. B.

L. B. Lesem, P. M. Hirsh, J. A. Jordan, “Computer synthesis of holograms for 3-D display,” Commun. ACM 11, 661–674 (1968).
[CrossRef]

P. M. Hirsch, J. A. Jordan, L. B. Lesem, “Method of making an object-dependent diffuser,” U.S. Patent3,619,022 (November9, 1971).

Liu, B.

Saxton, W. O.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Upatnieks, J.

Wyrowski, F.

Appl. Opt. (2)

Commun. ACM (1)

L. B. Lesem, P. M. Hirsh, J. A. Jordan, “Computer synthesis of holograms for 3-D display,” Commun. ACM 11, 661–674 (1968).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Optik (1)

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Proc. IEEE (1)

J. J. Burch, “A computer algorithm for the synthesis of spatial frequency filters,” Proc. IEEE 55, 599–601 (1967).
[CrossRef]

Other (2)

W. J. Dallas, “Computer-generated holograms,” in The Computer in Optical Research, B. R. Frieden, ed., Vol. 41 of Topics in Applied Physics (Springer-Verlag, Berlin, 1980), pp. 291–366.
[CrossRef]

P. M. Hirsch, J. A. Jordan, L. B. Lesem, “Method of making an object-dependent diffuser,” U.S. Patent3,619,022 (November9, 1971).

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Figures (3)

Fig. 1
Fig. 1

Calculated reconstruction of a digital amplitude hologram.

Fig. 2
Fig. 2

Optical reconstructions of digital holograms when (a) a random phase and (b) an iterated phase are used.

Fig. 3
Fig. 3

Optical reconstructions of large digital holograms formed by a repetition procedure. In (a) the primary holograms were repeated, and in (b) and (c) phase manipulations, in addition to a repetition, were incorporated into the hologram plane. Furthermore, in (b) a random and in (c) an iterated phase was superimposed upon the signal before the hologram calculation was made.

Equations (11)

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f ( x ) 2 i ( x )
Δ F = Δ I / 2.
f ( m f ) DFT F ( k f ) ,
δ u = ( 1 M f δ x , 1 N f δ y ) .
H ( k ) = RE [ G ( k ) ] + B = F ( k ) cos [ 2 π k m 0 / M - Φ ( k ) ] + B ,
H ( u ) = H ( k ) * rect ( u , δ u )
rect ( u , a ) ~ rect ( u / a ) rect ( v / b ) ,
rect ( u / a ) = { 1 u a / 2 0 else
h ( x ) = FT [ H ( u ) ] = FT [ H ( k ) ] sinc ( x , δ u - 1 ) = ( { ½ f ( x - x 0 ) + ½ f * [ - ( x + x 0 ) ] + B sinc ( x , δ x ) } * comb ( x , δ u - 1 ) ) sinc ( x , δ u - 1 ) ,
sinc ( x , a ) ~ sin ( π x / a ) π x / a sin ( π y / b ) π y / b
h l ( x ) = [ h ( x ) comb ( x , δ x ) ] * sinc ( x , δ x / l )

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