Abstract

Reconstruction of in-line holograms suffers from the superposition of two twin images having different foci but identical information content. A simple iterative method of twin-image elimination is presented here. It is based on the fact that, if the object has a finite support and the recording distance is not too small, the out-of-focus field is known on a large part of the reconstruction plane and is only superposed by the in-focus one inside a restricted support. An iterative procedure is developed to recover the out-of-focus wave inside the in-focus image support. Inverse diffraction then gives the reconstructed image. This procedure can be easily auto-mated and works for finite-support real or complex objects, recorded in geometries with a Fresnel number of ~1.

© 1991 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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1990 (2)

1987 (2)

G. Liu, P. D. Scott, J. Opt. Soc. Am. A 4, 159 (1987).
[CrossRef]

L. Onural, P. D. Scott, Opt. Eng. 26, 1124 (1987).

1986 (1)

1982 (1)

1979 (1)

K. H. S. Marie, J. C. Bennett, A. P. Anderson, Electron. Lett. 15, 241 (1979).
[CrossRef]

1977 (1)

A. Lannes, Opt. Commun. 20, 356 (1977).
[CrossRef]

Anderson, A. P.

K. H. S. Marie, J. C. Bennett, A. P. Anderson, Electron. Lett. 15, 241 (1979).
[CrossRef]

Bennett, J. C.

K. H. S. Marie, J. C. Bennett, A. P. Anderson, Electron. Lett. 15, 241 (1979).
[CrossRef]

Bernstein, A.

D. Joyeux, S. Lowenthal, F. Polack, A. Bernstein, X-Ray Microscopy II (Springer-Verlag, Berlin, 1988), pp. 246–252.

Fienup, J. R.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 48–55.

Howells, M. R.

Iarocci, M. A.

Jacobsen, C.

Joyeux, D.

D. Joyeux, S. Lowenthal, F. Polack, A. Bernstein, X-Ray Microscopy II (Springer-Verlag, Berlin, 1988), pp. 246–252.

Kirz, J.

Lannes, A.

A. Lannes, Opt. Commun. 20, 356 (1977).
[CrossRef]

Liu, G.

Lowenthal, S.

D. Joyeux, S. Lowenthal, F. Polack, A. Bernstein, X-Ray Microscopy II (Springer-Verlag, Berlin, 1988), pp. 246–252.

Marie, K. H. S.

K. H. S. Marie, J. C. Bennett, A. P. Anderson, Electron. Lett. 15, 241 (1979).
[CrossRef]

Nugent, K. A.

K. A. Nugent, Opt. Commun. 78, 293 (1990).
[CrossRef]

Onural, L.

L. Onural, P. D. Scott, Opt. Eng. 26, 1124 (1987).

Polack, F.

D. Joyeux, S. Lowenthal, F. Polack, A. Bernstein, X-Ray Microscopy II (Springer-Verlag, Berlin, 1988), pp. 246–252.

Rothman, S.

Scott, P. D.

G. Liu, P. D. Scott, J. Opt. Soc. Am. A 4, 159 (1987).
[CrossRef]

L. Onural, P. D. Scott, Opt. Eng. 26, 1124 (1987).

Appl. Opt. (1)

Electron. Lett. (1)

K. H. S. Marie, J. C. Bennett, A. P. Anderson, Electron. Lett. 15, 241 (1979).
[CrossRef]

J. Opt. Soc. Am. A (3)

Opt. Commun. (2)

K. A. Nugent, Opt. Commun. 78, 293 (1990).
[CrossRef]

A. Lannes, Opt. Commun. 20, 356 (1977).
[CrossRef]

Opt. Eng. (1)

L. Onural, P. D. Scott, Opt. Eng. 26, 1124 (1987).

Other (2)

D. Joyeux, S. Lowenthal, F. Polack, A. Bernstein, X-Ray Microscopy II (Springer-Verlag, Berlin, 1988), pp. 246–252.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 48–55.

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Figures (3)

Fig. 1
Fig. 1

Original one-dimensional complex object. (a) Object amplitude, (b) object phase.

Fig. 2
Fig. 2

Image directly reconstructed from a hologram. (a) Reconstructed image amplitude, (b) reconstructed image phase.

Fig. 3
Fig. 3

Results of twin-image elimination algorithm after 40 iterations. (a) Reconstructed object amplitude, (b) reconstructed object phase.

Equations (10)

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U h ( X ) = [ 1 - α ( X ) ] * * h z ( X ) .
t h ( X ) = α + β I z ( X ) .
U r ( X ) = t h ( X ) * * h z ( X ) .
U r ( X ) = D - a * ( X ) - a ( X ) * * h 2 z ( X ) + a ( X ) * * h z ( X ) 2 * * h z ( X ) .
G ( X ) = grad U r ( X ) 2 .
U ^ o ( 1 ) ( X ) = { U r ( X ) X Σ U ¯ r X Σ ,
U ^ i ( 1 ) ( X ) = U ^ o ( 1 ) ( X ) * * h - 2 z ( X ) .
U ^ i ( 2 ) ( X ) = { D X Σ and U ^ l ( 1 ) ( X ) > D U ^ i ( 1 ) ( X ) elsewhere .
U ^ o ( 2 ) ( X ) = U ^ i ( 2 ) ( X ) * * h 2 z ( X ) .
U ^ o ( 3 ) ( X ) = { U r ( X ) X Σ U ^ o ( 2 ) ( X ) X Σ .

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