Abstract

In lensless digital in-line holographic microscopy, currently applied fast reconstruction techniques use approximations limiting the usable NA for optical resolution. The computational effort for an exact scalar reconstruction with straightforward algorithms depends on the relation between the desired resolution and the given pixel pitch of the detector. So there is a trade-off between achievable image resolution and required computation time. We present an exact reconstruction algorithm that guaranties optimum resolution with affordable computation time. Experimental results show a realized NA of at least 0.62. A 1 megapixel hologram was reconstructed in about 1.5s.

© 2010 Optical Society of America

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References

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  1. D. Gabor, Nature 161, 777 (1948).
    [CrossRef] [PubMed]
  2. D. Wang, J. Zhao, F. Zhang, G. Pedrini, and W. Osten, Appl. Opt. 47, D12 (2008).
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  3. F. Zhang, G. Pedrini, and W. Osten, Opt. Lett. 31, 1633 (2006).
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  4. L. Ahrenberg, A. J. Page, B. M. Hennelly, J. B. McDonald, and T. J. Naughton, J. Display Technol. 5, 111 (2009).
    [CrossRef]
  5. H. J. Kreuzer, K. Nakamura, A. Wierzbicki, H.-W. Fink, and H. Schmid, Ultramicroscopy 45, 381 (1992).
    [CrossRef]
  6. J. Garcia-Sucerquia, D. Alvarez-Palacio, and J. Kreuzer, in Adaptive Optics: Topical Meetings on CD-ROM (2007), p. DMB4.
  7. M. Kanka, R. Riesenberg, and H. J. Kreuzer, Opt. Lett. 34, 1162 (2009).
    [CrossRef] [PubMed]
  8. J. W. Goodman, Introduction To Fourier Optics, 2nd international ed. (McGraw-Hill, 1996).
  9. P. Gaydecki, Foundations of Digital Signal Processing: Theory, Algorithms and Hardware Design (IEE Circuits, Devices and Systems) (The Institution of Engineering and Technology, 2004).
    [CrossRef]
  10. M. Frigo and S. G. Johnson, Proc. IEEE 93, 216 (2005).
    [CrossRef]

2009 (2)

2008 (1)

2006 (1)

2005 (1)

M. Frigo and S. G. Johnson, Proc. IEEE 93, 216 (2005).
[CrossRef]

1992 (1)

H. J. Kreuzer, K. Nakamura, A. Wierzbicki, H.-W. Fink, and H. Schmid, Ultramicroscopy 45, 381 (1992).
[CrossRef]

1948 (1)

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

Ahrenberg, L.

Alvarez-Palacio, D.

J. Garcia-Sucerquia, D. Alvarez-Palacio, and J. Kreuzer, in Adaptive Optics: Topical Meetings on CD-ROM (2007), p. DMB4.

Fink, H.-W.

H. J. Kreuzer, K. Nakamura, A. Wierzbicki, H.-W. Fink, and H. Schmid, Ultramicroscopy 45, 381 (1992).
[CrossRef]

Frigo, M.

M. Frigo and S. G. Johnson, Proc. IEEE 93, 216 (2005).
[CrossRef]

Gabor, D.

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

Garcia-Sucerquia, J.

J. Garcia-Sucerquia, D. Alvarez-Palacio, and J. Kreuzer, in Adaptive Optics: Topical Meetings on CD-ROM (2007), p. DMB4.

Gaydecki, P.

P. Gaydecki, Foundations of Digital Signal Processing: Theory, Algorithms and Hardware Design (IEE Circuits, Devices and Systems) (The Institution of Engineering and Technology, 2004).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction To Fourier Optics, 2nd international ed. (McGraw-Hill, 1996).

Hennelly, B. M.

Johnson, S. G.

M. Frigo and S. G. Johnson, Proc. IEEE 93, 216 (2005).
[CrossRef]

Kanka, M.

Kreuzer, H. J.

M. Kanka, R. Riesenberg, and H. J. Kreuzer, Opt. Lett. 34, 1162 (2009).
[CrossRef] [PubMed]

H. J. Kreuzer, K. Nakamura, A. Wierzbicki, H.-W. Fink, and H. Schmid, Ultramicroscopy 45, 381 (1992).
[CrossRef]

Kreuzer, J.

J. Garcia-Sucerquia, D. Alvarez-Palacio, and J. Kreuzer, in Adaptive Optics: Topical Meetings on CD-ROM (2007), p. DMB4.

McDonald, J. B.

Nakamura, K.

H. J. Kreuzer, K. Nakamura, A. Wierzbicki, H.-W. Fink, and H. Schmid, Ultramicroscopy 45, 381 (1992).
[CrossRef]

Naughton, T. J.

Osten, W.

Page, A. J.

Pedrini, G.

Riesenberg, R.

Schmid, H.

H. J. Kreuzer, K. Nakamura, A. Wierzbicki, H.-W. Fink, and H. Schmid, Ultramicroscopy 45, 381 (1992).
[CrossRef]

Wang, D.

Wierzbicki, A.

H. J. Kreuzer, K. Nakamura, A. Wierzbicki, H.-W. Fink, and H. Schmid, Ultramicroscopy 45, 381 (1992).
[CrossRef]

Zhang, F.

Zhao, J.

Appl. Opt. (1)

J. Display Technol. (1)

Nature (1)

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

Opt. Lett. (2)

Proc. IEEE (1)

M. Frigo and S. G. Johnson, Proc. IEEE 93, 216 (2005).
[CrossRef]

Ultramicroscopy (1)

H. J. Kreuzer, K. Nakamura, A. Wierzbicki, H.-W. Fink, and H. Schmid, Ultramicroscopy 45, 381 (1992).
[CrossRef]

Other (3)

J. Garcia-Sucerquia, D. Alvarez-Palacio, and J. Kreuzer, in Adaptive Optics: Topical Meetings on CD-ROM (2007), p. DMB4.

J. W. Goodman, Introduction To Fourier Optics, 2nd international ed. (McGraw-Hill, 1996).

P. Gaydecki, Foundations of Digital Signal Processing: Theory, Algorithms and Hardware Design (IEE Circuits, Devices and Systems) (The Institution of Engineering and Technology, 2004).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Scheme of the presented propagation technique.

Fig. 2
Fig. 2

1.06 μ m PMMA beads on a cover glass imaged by a lensless in-line holographic microscope. The shown field of view is 219 μ m × 219 μ m . The presented technique enables an increased optical resolution in the whole focal plane (details 1–3).

Fig. 3
Fig. 3

(a) 1.06 μ m PMMA beads imaged by a lensless holographic microscope using the presented reconstruction technique. (b) For the purpose of comparison the same sample was imaged by a bright field microscope ( NA = 0.7 ) . (c) The separated beads in the 3D perspective imply a realized NA of at least 0.62.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

U = ( I I ( 0 ) ) R .
O = F 1 { F { U } H } ,
H ξ , η = exp [ i 2 π z 1 λ 2 ξ 2 + η 2 ( N Δ x ) 2 ] ,
[ Δ x ( N T ) ] 2 < z 2 ( Δ x λ ) 2 1 4 .
O Σ k , l = 1 T O ( k , l ) = k , l = 1 T F 1 { F { U ( k , l ) } H }
O Σ = F 1 { k , l = 1 T F { U ( k , l ) } H }
O Σ = F 1 { U Σ H } .

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