Abstract

A fast algorithm is proposed for the reconstruction of digital holograms that are recorded at high numerical aperture. The method directly evaluates the Rayleigh–Sommerfeld diffraction integral by use of a fast convolution algorithm. A shift parameter that accounts for the coordinate system’s transverse displacement of the object plane and the hologram plane is introduced in a discrete representation of the diffraction kernel. Combination of the samplings reconstructed with different shift values yields diffraction-limited resolution over the full field of view. The algorithm is suitable for various applications such as holographic microscopy and metrology. Simulation and experimental results are presented.

© 2006 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

2005 (1)

2004 (1)

2001 (1)

G. Pedrini, S. Schedin, and H. J. Tiziani, J. Mod. Opt. 48, 1035 (2001).

1999 (1)

1997 (2)

I. Yamaguchi and T. Zhang, Opt. Lett. 22, 1268 (1997).
[CrossRef] [PubMed]

T. M. Kreis, M. Adams, and W. P. O. Jüptner, in Proc. SPIE 3098, 224 (1997).
[CrossRef]

1994 (1)

1992 (1)

Adams, M.

T. M. Kreis, M. Adams, and W. P. O. Jüptner, in Proc. SPIE 3098, 224 (1997).
[CrossRef]

Asundi, A.

Boyer, K.

Cullen, D.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996), pp. 59-60.

Guo, Z.

Haddad, W. S.

Jüptner, W. P. O.

T. M. Kreis, M. Adams, and W. P. O. Jüptner, in Proc. SPIE 3098, 224 (1997).
[CrossRef]

U. Schnars and W. P. O. Jüptner, Appl. Opt. 33, 179 (1994).
[CrossRef] [PubMed]

Kreis, T. M.

T. M. Kreis, M. Adams, and W. P. O. Jüptner, in Proc. SPIE 3098, 224 (1997).
[CrossRef]

Longworth, J. W.

McPherson, A.

Miao, J.

Ohzu, H.

Pedrini, G.

G. Pedrini, S. Schedin, and H. J. Tiziani, J. Mod. Opt. 48, 1035 (2001).

Peng, X.

Rhodes, C. K.

Schedin, S.

G. Pedrini, S. Schedin, and H. J. Tiziani, J. Mod. Opt. 48, 1035 (2001).

Schnars, U.

Solem, J. C.

Takaki, Y.

Tiziani, H. J.

G. Pedrini, S. Schedin, and H. J. Tiziani, J. Mod. Opt. 48, 1035 (2001).

Xu, L.

Yamaguchi, I.

Yaroslavsky, L. P.

F. Zhang, I. Yamaguchi, and L. P. Yaroslavsky, Opt. Lett. 29, 1668 (2004).
[CrossRef] [PubMed]

L. P. Yaroslavsky, Digital Holography and Digital Image Processing (Kluwer Academic, 2004).

Zhang, F.

Zhang, T.

Appl. Opt. (3)

J. Mod. Opt. (1)

G. Pedrini, S. Schedin, and H. J. Tiziani, J. Mod. Opt. 48, 1035 (2001).

Opt. Express (1)

Opt. Lett. (2)

Proc. SPIE (1)

T. M. Kreis, M. Adams, and W. P. O. Jüptner, in Proc. SPIE 3098, 224 (1997).
[CrossRef]

Other (2)

L. P. Yaroslavsky, Digital Holography and Digital Image Processing (Kluwer Academic, 2004).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996), pp. 59-60.

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Figures (5)

Fig. 1
Fig. 1

Reconstruction geometry for the modified convolution algorithm.

Fig. 2
Fig. 2

Reconstruction of point object by CV algorithm; the subpeaks are due to Eq. (3b).

Fig. 3
Fig. 3

Simulation of the reconstruction of a four-point object by (a) a Fresnel algorithm and (b) a modified CV algorithm.

Fig. 4
Fig. 4

Comparison of the reconstruction with (a) the Fresnel algorithm and (b) a modified CV algorithm.

Fig. 5
Fig. 5

Comparison of the normalized amplitude of the dark spots in two reconstructions.

Equations (6)

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U ( f x , f y ; s , t ; d ) = U ( f x , f y ; 0 ) H ( f x , f y ; s , t ; d ) ,
H ( f x , f y ; s , t ; d ) = exp [ i 2 π ( f x s + f y t ) ] exp [ i 2 π d λ 1 ( 1 λ 2 f x 2 λ 2 f y 2 ) 1 2 ] ,
U R ( f x , f y ; s , t ; d ) = m , n = U ( f x m Δ x , f y n Δ y ; 0 ) p , q = H ( f x p Δ x , f y q Δ y ; s , t ; d )
= m , n = U ( f x m Δ x , f y n Δ y ; 0 ) H ( f x m Δ x , f y n Δ y ; s , t ; d )
+ m , n = U ( f x m Δ x , f y n Δ y ; 0 ) p , q = p m ; q n H ( f x p Δ x , f y q Δ y ; s , t ; d ) ,
S obj λ d Δ x .

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