Abstract

We present a reconstruction technique for simultaneous retrieval of absorption and phase shifting properties of an object recorded by in-line holography. The routine is experimentally tested by applying it to optical holograms of a pure phase respectively a pure amplitude object of micrometer dimensions that has been machined into a glass-plate using a focused ion beam. The method has also been applied to previously published electron holograms of single DNA molecules.

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References

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  1. D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
    [CrossRef] [PubMed]
  2. X. M. H. Huang, J. M. Zuo, and J. C. H. Spence, “Wavefront reconstruction for in-line holograms formed by pure amplitude objects,” Appl. Surf. Sci. 148(3-4), 229–234 (1999).
    [CrossRef]
  3. E. Cuche, F. Bevilacqua, and C. Depeursinge, “Digital holography for quantitative phase-contrast imaging,” Opt. Lett. 24(5), 291–293 (1999).
    [CrossRef]
  4. T. Matsumoto, T. Tanji, and A. Tonomura, “Phase contrast visualization of an undecagold cluster by in-line electron holography,” Ultramicroscopy 54(2-4), 317–334 (1994).
    [CrossRef]
  5. T. Matsumoto, “Visualization of DNA in solution by Fraunhofer in-line electron holography: I. Simulation,” Optik (Stuttg.) 99, 25–28 (1995).
  6. T. Matsumoto, T. Tanji, and A. Tonomura, “Visualization of DNA in solution by Fraunhofer in-line electron holography: II. Experiments,” Optik (Stuttg.) 100, 71–74 (1995).
  7. H.-W. Fink, W. Stocker, and H. Schmid, “Holography with low-energy electrons,” Phys. Rev. Lett. 65(10), 1204–1206 (1990).
    [CrossRef] [PubMed]
  8. J. J. Barton, “Removing multiple scattering and twin images from holographic images,” Phys. Rev. Lett. 67(22), 3106–3109 (1991).
    [CrossRef] [PubMed]
  9. S. Y. Tong, H. Li, and H. Huang, “Energy extension in three-dimensional atomic imaging by electron emission holography,” Phys. Rev. Lett. 67(22), 3102–3105 (1991).
    [CrossRef] [PubMed]
  10. Y. Zhang and X. Zhang, “Reconstruction of a complex object from two in-line holograms,” Opt. Express 11(6), 572–578 (2003).
    [CrossRef] [PubMed]
  11. Y. Zhang, G. Pedrini, W. Osten, and H. J. Tiziani, “Whole optical wave field reconstruction from double or multi in-line holograms by phase retrieval algorithm,” Opt. Express 11(24), 3234–3241 (2003).
    [CrossRef] [PubMed]
  12. Y. Zhang, G. Pedrini, W. Osten, and H. J. Tiziani, “Reconstruction of in-line digital holograms from two intensity measurements,” Opt. Lett. 29(15), 1787–1789 (2004).
    [CrossRef] [PubMed]
  13. G. Pedrini, W. Osten, and Y. Zhang, “Wave-front reconstruction from a sequence of interferograms recorded at different planes,” Opt. Lett. 30(8), 833–835 (2005).
    [CrossRef] [PubMed]
  14. H. Yamazaki, Y. Kohmura, T. Sakurai, and T. Ishikawa, “Reconstruction of complex-valued electron density with x-ray in-line holograms,” J. Opt. Soc. Am. A 23(12), 3171–3176 (2006).
    [CrossRef]
  15. J. J. Barton, “Photoelectron holography,” Phys. Rev. Lett. 61(12), 1356–1359 (1988).
    [CrossRef] [PubMed]
  16. H.-W. Fink, H. Schmidt, E. Ermantraut, and T. Schulz, “Electron holography of individual DNA molecules,” J. Opt. Soc. Am. A 14(9), 2168–2172 (1997).
    [CrossRef]

2006 (1)

2005 (1)

2004 (1)

2003 (2)

1999 (2)

X. M. H. Huang, J. M. Zuo, and J. C. H. Spence, “Wavefront reconstruction for in-line holograms formed by pure amplitude objects,” Appl. Surf. Sci. 148(3-4), 229–234 (1999).
[CrossRef]

E. Cuche, F. Bevilacqua, and C. Depeursinge, “Digital holography for quantitative phase-contrast imaging,” Opt. Lett. 24(5), 291–293 (1999).
[CrossRef]

1997 (1)

1995 (2)

T. Matsumoto, “Visualization of DNA in solution by Fraunhofer in-line electron holography: I. Simulation,” Optik (Stuttg.) 99, 25–28 (1995).

T. Matsumoto, T. Tanji, and A. Tonomura, “Visualization of DNA in solution by Fraunhofer in-line electron holography: II. Experiments,” Optik (Stuttg.) 100, 71–74 (1995).

1994 (1)

T. Matsumoto, T. Tanji, and A. Tonomura, “Phase contrast visualization of an undecagold cluster by in-line electron holography,” Ultramicroscopy 54(2-4), 317–334 (1994).
[CrossRef]

1991 (2)

J. J. Barton, “Removing multiple scattering and twin images from holographic images,” Phys. Rev. Lett. 67(22), 3106–3109 (1991).
[CrossRef] [PubMed]

S. Y. Tong, H. Li, and H. Huang, “Energy extension in three-dimensional atomic imaging by electron emission holography,” Phys. Rev. Lett. 67(22), 3102–3105 (1991).
[CrossRef] [PubMed]

1990 (1)

H.-W. Fink, W. Stocker, and H. Schmid, “Holography with low-energy electrons,” Phys. Rev. Lett. 65(10), 1204–1206 (1990).
[CrossRef] [PubMed]

1988 (1)

J. J. Barton, “Photoelectron holography,” Phys. Rev. Lett. 61(12), 1356–1359 (1988).
[CrossRef] [PubMed]

1948 (1)

D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
[CrossRef] [PubMed]

Barton, J. J.

J. J. Barton, “Removing multiple scattering and twin images from holographic images,” Phys. Rev. Lett. 67(22), 3106–3109 (1991).
[CrossRef] [PubMed]

J. J. Barton, “Photoelectron holography,” Phys. Rev. Lett. 61(12), 1356–1359 (1988).
[CrossRef] [PubMed]

Bevilacqua, F.

Cuche, E.

Depeursinge, C.

Ermantraut, E.

Fink, H.-W.

H.-W. Fink, H. Schmidt, E. Ermantraut, and T. Schulz, “Electron holography of individual DNA molecules,” J. Opt. Soc. Am. A 14(9), 2168–2172 (1997).
[CrossRef]

H.-W. Fink, W. Stocker, and H. Schmid, “Holography with low-energy electrons,” Phys. Rev. Lett. 65(10), 1204–1206 (1990).
[CrossRef] [PubMed]

Gabor, D.

D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
[CrossRef] [PubMed]

Huang, H.

S. Y. Tong, H. Li, and H. Huang, “Energy extension in three-dimensional atomic imaging by electron emission holography,” Phys. Rev. Lett. 67(22), 3102–3105 (1991).
[CrossRef] [PubMed]

Huang, X. M. H.

X. M. H. Huang, J. M. Zuo, and J. C. H. Spence, “Wavefront reconstruction for in-line holograms formed by pure amplitude objects,” Appl. Surf. Sci. 148(3-4), 229–234 (1999).
[CrossRef]

Ishikawa, T.

Kohmura, Y.

Li, H.

S. Y. Tong, H. Li, and H. Huang, “Energy extension in three-dimensional atomic imaging by electron emission holography,” Phys. Rev. Lett. 67(22), 3102–3105 (1991).
[CrossRef] [PubMed]

Matsumoto, T.

T. Matsumoto, “Visualization of DNA in solution by Fraunhofer in-line electron holography: I. Simulation,” Optik (Stuttg.) 99, 25–28 (1995).

T. Matsumoto, T. Tanji, and A. Tonomura, “Visualization of DNA in solution by Fraunhofer in-line electron holography: II. Experiments,” Optik (Stuttg.) 100, 71–74 (1995).

T. Matsumoto, T. Tanji, and A. Tonomura, “Phase contrast visualization of an undecagold cluster by in-line electron holography,” Ultramicroscopy 54(2-4), 317–334 (1994).
[CrossRef]

Osten, W.

Pedrini, G.

Sakurai, T.

Schmid, H.

H.-W. Fink, W. Stocker, and H. Schmid, “Holography with low-energy electrons,” Phys. Rev. Lett. 65(10), 1204–1206 (1990).
[CrossRef] [PubMed]

Schmidt, H.

Schulz, T.

Spence, J. C. H.

X. M. H. Huang, J. M. Zuo, and J. C. H. Spence, “Wavefront reconstruction for in-line holograms formed by pure amplitude objects,” Appl. Surf. Sci. 148(3-4), 229–234 (1999).
[CrossRef]

Stocker, W.

H.-W. Fink, W. Stocker, and H. Schmid, “Holography with low-energy electrons,” Phys. Rev. Lett. 65(10), 1204–1206 (1990).
[CrossRef] [PubMed]

Tanji, T.

T. Matsumoto, T. Tanji, and A. Tonomura, “Visualization of DNA in solution by Fraunhofer in-line electron holography: II. Experiments,” Optik (Stuttg.) 100, 71–74 (1995).

T. Matsumoto, T. Tanji, and A. Tonomura, “Phase contrast visualization of an undecagold cluster by in-line electron holography,” Ultramicroscopy 54(2-4), 317–334 (1994).
[CrossRef]

Tiziani, H. J.

Tong, S. Y.

S. Y. Tong, H. Li, and H. Huang, “Energy extension in three-dimensional atomic imaging by electron emission holography,” Phys. Rev. Lett. 67(22), 3102–3105 (1991).
[CrossRef] [PubMed]

Tonomura, A.

T. Matsumoto, T. Tanji, and A. Tonomura, “Visualization of DNA in solution by Fraunhofer in-line electron holography: II. Experiments,” Optik (Stuttg.) 100, 71–74 (1995).

T. Matsumoto, T. Tanji, and A. Tonomura, “Phase contrast visualization of an undecagold cluster by in-line electron holography,” Ultramicroscopy 54(2-4), 317–334 (1994).
[CrossRef]

Yamazaki, H.

Zhang, X.

Zhang, Y.

Zuo, J. M.

X. M. H. Huang, J. M. Zuo, and J. C. H. Spence, “Wavefront reconstruction for in-line holograms formed by pure amplitude objects,” Appl. Surf. Sci. 148(3-4), 229–234 (1999).
[CrossRef]

Appl. Surf. Sci. (1)

X. M. H. Huang, J. M. Zuo, and J. C. H. Spence, “Wavefront reconstruction for in-line holograms formed by pure amplitude objects,” Appl. Surf. Sci. 148(3-4), 229–234 (1999).
[CrossRef]

J. Opt. Soc. Am. A (2)

Nature (1)

D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (3)

Optik (Stuttg.) (2)

T. Matsumoto, “Visualization of DNA in solution by Fraunhofer in-line electron holography: I. Simulation,” Optik (Stuttg.) 99, 25–28 (1995).

T. Matsumoto, T. Tanji, and A. Tonomura, “Visualization of DNA in solution by Fraunhofer in-line electron holography: II. Experiments,” Optik (Stuttg.) 100, 71–74 (1995).

Phys. Rev. Lett. (4)

H.-W. Fink, W. Stocker, and H. Schmid, “Holography with low-energy electrons,” Phys. Rev. Lett. 65(10), 1204–1206 (1990).
[CrossRef] [PubMed]

J. J. Barton, “Removing multiple scattering and twin images from holographic images,” Phys. Rev. Lett. 67(22), 3106–3109 (1991).
[CrossRef] [PubMed]

S. Y. Tong, H. Li, and H. Huang, “Energy extension in three-dimensional atomic imaging by electron emission holography,” Phys. Rev. Lett. 67(22), 3102–3105 (1991).
[CrossRef] [PubMed]

J. J. Barton, “Photoelectron holography,” Phys. Rev. Lett. 61(12), 1356–1359 (1988).
[CrossRef] [PubMed]

Ultramicroscopy (1)

T. Matsumoto, T. Tanji, and A. Tonomura, “Phase contrast visualization of an undecagold cluster by in-line electron holography,” Ultramicroscopy 54(2-4), 317–334 (1994).
[CrossRef]

Supplementary Material (1)

» Media 1: MOV (3581 KB)     

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Figures (7)

Fig. 1
Fig. 1

An illustration to the complex transmission function of the glass samples. (a) A pure absorbing object. (b) A pure phase shifting object. The reference wave is formed by the wave passing through the dashed area, where transmission is C0=ea0eiϕ0 . (c) Scanning electron image showing the realization of such structures milled with a focused ion beam.

Fig. 2
Fig. 2

Experimental arrangement for recording optical in-line holograms. For reasons of presentation, sizes and distances are scaled differently.

Fig. 3
Fig. 3

(a) Normalized hologram. The scale bar corresponds to 50 mm on the screen. (b) Reconstructed absorption distribution. (c) Reconstructed phase distribution. The scale bars in (b) and (c) are about 100μm.

Fig. 4
Fig. 4

Normalized hologram of pure amplitude object Ψletter. The scale corresponds to 100 mm on the screen. (b) Reconstructed absorption distribution. (c) Reconstructed phase distribution. The scale bars in (b) and (c) correspond to 100 μm. The intensity profiles along the white lines are shown below the images.

Fig. 5
Fig. 5

(a) Normalized hologram of a pure phase object Ψ letter. The scale bar corresponds to 100 mm on the screen. (b) Reconstructed absorption distribution. (c) Reconstructed phase distribution. The scale bars in (b) and (c) correspond to 100 μm. The intensity profiles along the white lines are shown below the images.

Fig. 6
Fig. 6

(a) Screen capture of a hologram of a DNA molecule. The electron energy amounts to 70 eV. (b) Reconstructed amplitude. The scale bar corresponds to 40nm.

Fig. 7
Fig. 7

(a) Reconstructed absorption. (b) Reconstructed phase (Media 1). The scale corresponds to 40 nm.

Equations (16)

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

ea(r)eiϕ(r).
ea0eiϕ0ea1(r)eiϕ1(r)=C0ea1(r)eiϕ1(r) ,
C0ea1(r)eiϕ1(r)=C0(1+t(r))
AeikrrC0(1+t(r))=AeikrrC0+AeikrrC0t(r) ,
AeikrrC0AC0eikrsrs=AC0R ,
AeikrrC0(1+t(r))AC0(R+O) .
H=|AC0|2|R+O|2 .
B=|AC0|2|R|2 .
HB1=R*O+RO*|R|2 .
U(r)=iλH(rs)exp(ikrrs/rs)rs2dσs
U(x,y,z)=iλH(κ)exp[ikz(1κx2κy2)]exp[ik(xκx+yκy)]1κz2dκxdκy
U(x0,y0,0)=iλH(κ)exp[ik(x0κx+y0κy)]1κz2dκxdκy
U(x,y,z)=iλU(x0,y0,0)exp[ik|rr0|]|rr0|dx0dy0
U(x,y,z)iλzexp(ikr)U(x0,y0,0)exp[i2πλz(x0x+y0y)]exp[iπλz(x02+y02)]dx0dy0.
|1+t(x,y)|=ea(x,y) .
ϕ(x,y)=arg{1+t(x,y)} .

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