Abstract

A new algorithm that allows for reconstruction of digital holograms with adjustable magnification is proposed. The algorithm involves two reconstruction steps implemented by a conventional single Fourier-transform algorithm. The advantages of the algorithm lie in its adaptability to various object sizes and recording distances as well as in its capability to maintain the pitch of a reconstructed image, independent of the reconstruction distance and wavelength for objects larger than a CCD. The feasibility of the algorithm is demonstrated by experiments. The algorithm is especially useful for reconstructing color holograms and for metrological applications.

© 2004 Optical Society of America

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References

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2003 (2)

2002 (1)

2001 (1)

1997 (2)

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

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

1994 (1)

Adams, M.

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

Coppola, G.

Ferraro, P.

Finizio, A.

Jüptner, W.

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

Kato, J.

Kreis, T.

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

Matsumura, T.

Meng, H.

Mizuno, J.

Nicola, S.

Ohta, S.

Pan, G.

Pierattini, G.

Schnars, U.

Yamaguchi, I.

Yaroslavsky, L. P.

L. P. Yaroslavsky, Digital Holography and Digital Image Processing (Kluwer Academic, Boston, Mass., 2004), pp. 199–209.

Zhang, T.

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Figures (3)

Fig. 1
Fig. 1

Schematic illustration of the DBFT algorithm.

Fig. 2
Fig. 2

Experimental setup. Abbreviations defined in text.

Fig. 3
Fig. 3

Images reconstructed by four algorithms at various reconstruction distances.

Equations (11)

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UIX,Z=exp-iπX2/λZUxexp-iπx2/λZ×exp2iπXx/λZdx.
UIξ,Z=UξexpiπλZξ2,
U1ξ,z1=Uξexpiπλz1ξ2,
U1ξ,Z=U1ξexpiπλz2ξ2,
UIX,Z=exp-iπX2λz2exp-iπX12Zλz1z2×exp2iπXX1λz2Uxexp-iπx2λz1×expi2πX1xλz1dxdX1,
UIl=N-1/2exp-iπl-N22/Nμ×m=0N-1Umexp-iπμm-N22/N×exp2iπμ¯m-N2l-N2/N,
μ1=NpH2/λz1,  μ2=NΔX12/λz2,
UIl=N-1expiπμ¯1+μ¯2N2×exp-iπl-N22μ1-μμ1/μN-iπl×n=0N-1exp-iπn-N22/Nμ1-μ×m=0N-1Umexp-iπμ1m-N22/N-iπm×exp2iπμ¯1mn/Nexp2iπμ¯2nl/N.
ΔX2=z2/z1pH=pHμ1-μ/μ.
μ1=1±Sview/SHμ,
UIl=1Nn=0N-1expiπn-N22/Nμ0×m=0N-1Umexp2iπmn-N2/N×exp-2iπln-N2/N,

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