Abstract

A method to numerically remove the twin image for inline digital holography, using multiple digital holograms, is discussed. Each individual hologram is recorded by using a statistically independent speckle field to illuminate the object. If the holograms are recorded in this manner and then numerically reconstructed, the twin image appears as a different speckle pattern in each of the reconstructions. By performing speckle-reduction techniques the presence of the twin image can be greatly reduced. A theoretical model is developed, and experimental results are presented that validate this approach. We show experimentally that the dc object intensity term can also be removed by using this technique.

© 2009 Optical Society of America

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2009 (1)

D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, W. T. Rhodes, Opt. Eng. 48, 095801 (2009).
[CrossRef]

2008 (1)

2004 (1)

2002 (1)

T. M. Kreis, Opt. Eng. 41, 1829 (2002).
[CrossRef]

1997 (2)

1996 (1)

1994 (2)

1981 (1)

F. Gori, Opt. Commun. 39, 293 (1981).
[CrossRef]

1976 (1)

1967 (1)

J. W. Goodman and R. W. Lawrence, Appl. Phys. Lett. 11, 77 (1967).
[CrossRef]

1962 (1)

1949 (1)

D. Gabor, Proc. R. Soc. London, Ser. A 197, 454 (1949).
[CrossRef]

1948 (1)

D. Gabor, Nature 161, 777 (1948).
[CrossRef] [PubMed]

Dorsch, R. G.

Ferreira, C.

Gabor, D.

D. Gabor, Proc. R. Soc. London, Ser. A 197, 454 (1949).
[CrossRef]

D. Gabor, Nature 161, 777 (1948).
[CrossRef] [PubMed]

Goodman, J. W.

J. W. Goodman, J. Opt. Soc. Am. 66, 1145 (1976).
[CrossRef]

J. W. Goodman and R. W. Lawrence, Appl. Phys. Lett. 11, 77 (1967).
[CrossRef]

J. W. Goodman, Speckle Phenomena in Optics (Roberts, 2007).

Gori, F.

F. Gori, Opt. Commun. 39, 293 (1981).
[CrossRef]

Han, B.

Han, G. S.

Hennelly, B. M.

D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, W. T. Rhodes, Opt. Eng. 48, 095801 (2009).
[CrossRef]

D. S. Monaghan, D. P. Kelly, N. Pandey, and B. M. Hennelly, Presented at China-Ireland International Conference on Information and Communications Technologies (Maynooth, Ireland, August 19-21, 2009).

Juptner, W.

T. Kreis and W. Juptner, Opt. Eng. 36, 2357 (1997).
[CrossRef]

Jüptner, W.

Kelly, D. P.

D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, W. T. Rhodes, Opt. Eng. 48, 095801 (2009).
[CrossRef]

D. S. Monaghan, D. P. Kelly, N. Pandey, and B. M. Hennelly, Presented at China-Ireland International Conference on Information and Communications Technologies (Maynooth, Ireland, August 19-21, 2009).

Kim, S. W.

Kreis, T.

T. Kreis and W. Juptner, Opt. Eng. 36, 2357 (1997).
[CrossRef]

Kreis, T. M.

T. M. Kreis, Opt. Eng. 41, 1829 (2002).
[CrossRef]

Lawrence, R. W.

J. W. Goodman and R. W. Lawrence, Appl. Phys. Lett. 11, 77 (1967).
[CrossRef]

Leith, E. N.

Lohmann, A. W.

Mendlovic, D.

Monaghan, D. S.

D. S. Monaghan, D. P. Kelly, N. Pandey, and B. M. Hennelly, Presented at China-Ireland International Conference on Information and Communications Technologies (Maynooth, Ireland, August 19-21, 2009).

Naughton, T. J.

D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, W. T. Rhodes, Opt. Eng. 48, 095801 (2009).
[CrossRef]

Pandey, N.

D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, W. T. Rhodes, Opt. Eng. 48, 095801 (2009).
[CrossRef]

D. S. Monaghan, D. P. Kelly, N. Pandey, and B. M. Hennelly, Presented at China-Ireland International Conference on Information and Communications Technologies (Maynooth, Ireland, August 19-21, 2009).

Rhodes, W. T.

D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, W. T. Rhodes, Opt. Eng. 48, 095801 (2009).
[CrossRef]

Schnars, U.

Testorf, M.

Upatnieks, J.

Wang, Z.

Yamaguchi, I.

Zalevsky, Z.

Zhang, T.

Appl. Opt. (3)

Appl. Phys. Lett. (1)

J. W. Goodman and R. W. Lawrence, Appl. Phys. Lett. 11, 77 (1967).
[CrossRef]

J. Opt. Soc. Am. (2)

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

Nature (1)

D. Gabor, Nature 161, 777 (1948).
[CrossRef] [PubMed]

Opt. Commun. (1)

F. Gori, Opt. Commun. 39, 293 (1981).
[CrossRef]

Opt. Eng. (3)

D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, W. T. Rhodes, Opt. Eng. 48, 095801 (2009).
[CrossRef]

T. Kreis and W. Juptner, Opt. Eng. 36, 2357 (1997).
[CrossRef]

T. M. Kreis, Opt. Eng. 41, 1829 (2002).
[CrossRef]

Opt. Lett. (2)

Proc. R. Soc. London, Ser. A (1)

D. Gabor, Proc. R. Soc. London, Ser. A 197, 454 (1949).
[CrossRef]

Other (2)

D. S. Monaghan, D. P. Kelly, N. Pandey, and B. M. Hennelly, Presented at China-Ireland International Conference on Information and Communications Technologies (Maynooth, Ireland, August 19-21, 2009).

J. W. Goodman, Speckle Phenomena in Optics (Roberts, 2007).

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Figures (1)

Fig. 1
Fig. 1

(a) Reconstruction of the unprocessed original hologram, which contains the two dc, object, and twin terms. (b) Same reconstruction where I ref has been removed by using a numerical high-pass filter. The twin image appears as corrupting noise in the reconstruction. In (c) a diffuser has been placed in the object beam prior to illuminating the object. The twin is also present in the resulting reconstruction; however, it now appears as a speckle pattern spread out over the entire reconstruction plane. (d) shows the result of averaging together 35 holographic reconstructions, each with a statistically independent speckle pattern. This averaging process reduces the speckle contrast and also the twin image, changing it into a constant dc value. The background dc has been subtracted numerically in (e) and can be compared with a reconstruction from a PSI hologram in (f).

Equations (13)

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u R ( X ) = a R ( X ) exp [ j ϕ R ( X ) ] ,
u OB ( X ) = a OB ( X ) exp [ j ϕ OB ( X ) ]
u ( X ) = u OB ( X ) u R ( X ) .
H ( x ) = | u z ( x ) + ref ( x ) | 2 = I z + I ref + u z ( x ) ref * ( x ) + u z * ( x ) ref ( x ) ,
u z ( x ) = I z { u ( X ) } ( x ) = 1 j λ z u ( X ) exp [ j π λ z ( x X ) 2 ] d X ,
g ( X ) = u ( X ) + I z { u z * ( x ) } ( X ) = u ( X ) + u ̃ ( X ) ,
I recon = g ( X ) g * ( X ) = u ( X ) u * ( X ) + u ̃ ( X ) u ̃ * ( X ) + | u ( X ) | | u ̃ ( X ) | cos ( ϑ R ) ,
I recon = I real + I twin + CT ,
I AV recon = 1 N ( n = 1 N I n real + n = 1 N I n twin + n = 1 N CT n ) .
I n real = ( | a OB | | a R n | ) 2 .
n = 1 N I n real = | a OB | 2 ( | a R 1 | 2 + + | a R N | 2 N ) = | a OB | 2 ( M ) ,
I n twin = ( a R n a OB exp [ j ( ϕ OB + ϕ R n ) ] exp [ j π 2 λ z ( X X 1 ) 2 ] d X 1 ) × ( ( a R n a OB ) * exp [ j ( ϕ OB + ϕ R n ) ] exp [ j π 2 λ z ( X X 2 ) 2 ] d X 2 ) .
1 N n = 1 N I n twin = M .

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