Abstract

We report the tabletop acquisition of soft x-ray holographic images of nanostructures with a spatial resolution of 46±2nm, nearly equal to the wavelength of the illumination. Holograms of carbon nanotubes were recorded using a compact, tabletop capillary-discharge soft x-ray laser emitting at 46.9nm in a high-numerical-aperture Gabor configuration.

© 2008 Optical Society of America

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    [CrossRef] [PubMed]
  2. A. V. Baez, “A study in diffraction microscopy with special reference to X-Rays,” J. Opt. Soc. Am. 42, 756-762 (1952).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  5. S. Lindaas, H. Howells, C. Jacobsen, and A. Kalinovsky, “X-ray holographic microscopy by means of photoresist recording and atomic-force microscope readout,” J. Opt. Soc. Am. A 13, 1788-1800 (1996).
    [CrossRef]
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    [CrossRef] [PubMed]
  7. A. Rosenhahn, R. Barth, X. Cao, M. Schurmann, M. Grunze, and S. Eisebitt, “Vacuum-ultraviolet Gabor holography with synchrotron radiation,” Ultramicroscopy 107, 1171-1177 (2007).
    [CrossRef] [PubMed]
  8. R. I. Tobey, M. E. Siemens, O. Cohen, M. M. Murnane, H. C. Kapteyn, and K. A. Nelson, “Ultrafast extreme ultraviolet holography: dynamic monitoring of surface deformation,” Opt. Lett. 32, 286-288 (2007).
    [CrossRef] [PubMed]
  9. P. Wachulak, R. Bartels, M. C. Marconi, C. S. Menoni, J. J. Rocca, Y. Lu, and B. Parkinson, “Sub 400 nm spatial resolution extreme ultraviolet holography with a table top laser,” Opt. Express 14, 9636-9642 (2006).
    [CrossRef] [PubMed]
  10. P. Wachulak, M. C. Marconi, R. Bartels, C. S. Menoni, and J. J. Rocca, “Volume extreme ultraviolet holographic imaging with numerical optical sectioning,” Opt. Express 15, 10622-10628 (2007).
    [CrossRef] [PubMed]
  11. CXRO, “http://www-cxro.lbl.gov/.”
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    [CrossRef]
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    [CrossRef]
  14. U. Schnars and W. P. O. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85-R101 (2002).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]

2008 (1)

2007 (3)

2006 (2)

P. Wachulak, R. Bartels, M. C. Marconi, C. S. Menoni, J. J. Rocca, Y. Lu, and B. Parkinson, “Sub 400 nm spatial resolution extreme ultraviolet holography with a table top laser,” Opt. Express 14, 9636-9642 (2006).
[CrossRef] [PubMed]

Y. Wang, E. Granados, M. A. Larotonda, M. Berrill, B. M. Luther, D. Patel, C. S. Menoni, and J. J. Rocca, “High-brightness injection-seeded soft-x-ray-laser amplifier using a solid target,” Phys. Rev. Lett. 97, 123901 (2006).
[CrossRef] [PubMed]

2002 (1)

U. Schnars and W. P. O. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85-R101 (2002).
[CrossRef]

2001 (1)

Y. Liu, M. Seminario, F. G. Tomasel, C. Chang, J. J. Rocca, and D. T. Attwood, “Achievement of essentially full spatial coherence in a high-average-power soft-x-ray laser,” Phys. Rev. A 63, 033802 (2001).
[CrossRef]

1999 (2)

H. H. Solak, D. He, W. Li, S. Singh-Gasson, F. Cerrina, B. H. Sohn, X. M. Yang, and P. Nealey, “Exposure of 38 nm period grating patterns with extreme ultraviolet interferometric lithography,” Appl. Phys. Lett. 75, 2328-2330 (1999).
[CrossRef]

C. D. Macchietto, B. R. Benware, and J. J. Rocca, “Generation of millijoule-level soft-x-ray laser pulses at a 4-Hz repetition rate in a highly saturated tabletop capillary discharge amplifier,” Opt. Lett. 24, 1115-1117 (1999).
[CrossRef]

1998 (1)

B. R. Benware, C. D. Macchietto, C. H. Moreno, and J. J. Rocca, “Demonstration of a high average power tabletop soft X-ray laser,” Phys. Rev. Lett. 81, 5804-5807 (1998).
[CrossRef]

1996 (1)

1992 (1)

I. McNulty, J. Kirz, C. Jacobsen, E. H. Anderson, M. R. Howells, and D. P. Kern, “High resolution imaging by Fourier transform X-ray holography,” Science 256, 1009-1012 (1992).
[CrossRef] [PubMed]

1990 (1)

1987 (1)

J. E. Trebes, S. B. Brown, E. M. Campbell, D. L. Matthews, D. G. Nilson, G. F. Stone, and D. A. Whelan, “Demonstration of X-ray holography with an X-ray laser,” Science 238, 517-519 (1987).
[CrossRef] [PubMed]

1952 (1)

1948 (1)

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

Anderson, E. H.

Attwood, D. T.

Y. Liu, M. Seminario, F. G. Tomasel, C. Chang, J. J. Rocca, and D. T. Attwood, “Achievement of essentially full spatial coherence in a high-average-power soft-x-ray laser,” Phys. Rev. A 63, 033802 (2001).
[CrossRef]

Baez, A. V.

Bartels, R.

Bartels, R. A.

Barth, R.

A. Rosenhahn, R. Barth, X. Cao, M. Schurmann, M. Grunze, and S. Eisebitt, “Vacuum-ultraviolet Gabor holography with synchrotron radiation,” Ultramicroscopy 107, 1171-1177 (2007).
[CrossRef] [PubMed]

Benware, B. R.

C. D. Macchietto, B. R. Benware, and J. J. Rocca, “Generation of millijoule-level soft-x-ray laser pulses at a 4-Hz repetition rate in a highly saturated tabletop capillary discharge amplifier,” Opt. Lett. 24, 1115-1117 (1999).
[CrossRef]

B. R. Benware, C. D. Macchietto, C. H. Moreno, and J. J. Rocca, “Demonstration of a high average power tabletop soft X-ray laser,” Phys. Rev. Lett. 81, 5804-5807 (1998).
[CrossRef]

Berrill, M.

Y. Wang, E. Granados, M. A. Larotonda, M. Berrill, B. M. Luther, D. Patel, C. S. Menoni, and J. J. Rocca, “High-brightness injection-seeded soft-x-ray-laser amplifier using a solid target,” Phys. Rev. Lett. 97, 123901 (2006).
[CrossRef] [PubMed]

Brewer, C. A.

Brizuela, F.

Brown, S. B.

J. E. Trebes, S. B. Brown, E. M. Campbell, D. L. Matthews, D. G. Nilson, G. F. Stone, and D. A. Whelan, “Demonstration of X-ray holography with an X-ray laser,” Science 238, 517-519 (1987).
[CrossRef] [PubMed]

Campbell, E. M.

J. E. Trebes, S. B. Brown, E. M. Campbell, D. L. Matthews, D. G. Nilson, G. F. Stone, and D. A. Whelan, “Demonstration of X-ray holography with an X-ray laser,” Science 238, 517-519 (1987).
[CrossRef] [PubMed]

Cao, X.

A. Rosenhahn, R. Barth, X. Cao, M. Schurmann, M. Grunze, and S. Eisebitt, “Vacuum-ultraviolet Gabor holography with synchrotron radiation,” Ultramicroscopy 107, 1171-1177 (2007).
[CrossRef] [PubMed]

Cerrina, F.

H. H. Solak, D. He, W. Li, S. Singh-Gasson, F. Cerrina, B. H. Sohn, X. M. Yang, and P. Nealey, “Exposure of 38 nm period grating patterns with extreme ultraviolet interferometric lithography,” Appl. Phys. Lett. 75, 2328-2330 (1999).
[CrossRef]

Chang, C.

Y. Liu, M. Seminario, F. G. Tomasel, C. Chang, J. J. Rocca, and D. T. Attwood, “Achievement of essentially full spatial coherence in a high-average-power soft-x-ray laser,” Phys. Rev. A 63, 033802 (2001).
[CrossRef]

Chao, W.

Cohen, O.

Eisebitt, S.

A. Rosenhahn, R. Barth, X. Cao, M. Schurmann, M. Grunze, and S. Eisebitt, “Vacuum-ultraviolet Gabor holography with synchrotron radiation,” Ultramicroscopy 107, 1171-1177 (2007).
[CrossRef] [PubMed]

Gabor, D.

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

Granados, E.

Y. Wang, E. Granados, M. A. Larotonda, M. Berrill, B. M. Luther, D. Patel, C. S. Menoni, and J. J. Rocca, “High-brightness injection-seeded soft-x-ray-laser amplifier using a solid target,” Phys. Rev. Lett. 97, 123901 (2006).
[CrossRef] [PubMed]

Grunze, M.

A. Rosenhahn, R. Barth, X. Cao, M. Schurmann, M. Grunze, and S. Eisebitt, “Vacuum-ultraviolet Gabor holography with synchrotron radiation,” Ultramicroscopy 107, 1171-1177 (2007).
[CrossRef] [PubMed]

He, D.

H. H. Solak, D. He, W. Li, S. Singh-Gasson, F. Cerrina, B. H. Sohn, X. M. Yang, and P. Nealey, “Exposure of 38 nm period grating patterns with extreme ultraviolet interferometric lithography,” Appl. Phys. Lett. 75, 2328-2330 (1999).
[CrossRef]

Howells, H.

Howells, M.

Howells, M. R.

I. McNulty, J. Kirz, C. Jacobsen, E. H. Anderson, M. R. Howells, and D. P. Kern, “High resolution imaging by Fourier transform X-ray holography,” Science 256, 1009-1012 (1992).
[CrossRef] [PubMed]

Jacobsen, C.

Juptner, W. P. O.

U. Schnars and W. P. O. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85-R101 (2002).
[CrossRef]

Kalinovsky, A.

Kapteyn, H. C.

Kern, D. P.

I. McNulty, J. Kirz, C. Jacobsen, E. H. Anderson, M. R. Howells, and D. P. Kern, “High resolution imaging by Fourier transform X-ray holography,” Science 256, 1009-1012 (1992).
[CrossRef] [PubMed]

Kirz, J.

I. McNulty, J. Kirz, C. Jacobsen, E. H. Anderson, M. R. Howells, and D. P. Kern, “High resolution imaging by Fourier transform X-ray holography,” Science 256, 1009-1012 (1992).
[CrossRef] [PubMed]

C. Jacobsen, M. Howells, J. Kirz, and S. Rothman, “X-Ray holographic microscopy using photoresists,” J. Opt. Soc. Am. A 7, 1847-1861 (1990).
[CrossRef]

Larotonda, M. A.

Y. Wang, E. Granados, M. A. Larotonda, M. Berrill, B. M. Luther, D. Patel, C. S. Menoni, and J. J. Rocca, “High-brightness injection-seeded soft-x-ray-laser amplifier using a solid target,” Phys. Rev. Lett. 97, 123901 (2006).
[CrossRef] [PubMed]

Li, W.

H. H. Solak, D. He, W. Li, S. Singh-Gasson, F. Cerrina, B. H. Sohn, X. M. Yang, and P. Nealey, “Exposure of 38 nm period grating patterns with extreme ultraviolet interferometric lithography,” Appl. Phys. Lett. 75, 2328-2330 (1999).
[CrossRef]

Lindaas, S.

Liu, Y.

Y. Liu, M. Seminario, F. G. Tomasel, C. Chang, J. J. Rocca, and D. T. Attwood, “Achievement of essentially full spatial coherence in a high-average-power soft-x-ray laser,” Phys. Rev. A 63, 033802 (2001).
[CrossRef]

Lu, Y.

Luther, B. M.

Y. Wang, E. Granados, M. A. Larotonda, M. Berrill, B. M. Luther, D. Patel, C. S. Menoni, and J. J. Rocca, “High-brightness injection-seeded soft-x-ray-laser amplifier using a solid target,” Phys. Rev. Lett. 97, 123901 (2006).
[CrossRef] [PubMed]

Macchietto, C. D.

C. D. Macchietto, B. R. Benware, and J. J. Rocca, “Generation of millijoule-level soft-x-ray laser pulses at a 4-Hz repetition rate in a highly saturated tabletop capillary discharge amplifier,” Opt. Lett. 24, 1115-1117 (1999).
[CrossRef]

B. R. Benware, C. D. Macchietto, C. H. Moreno, and J. J. Rocca, “Demonstration of a high average power tabletop soft X-ray laser,” Phys. Rev. Lett. 81, 5804-5807 (1998).
[CrossRef]

Marconi, M. C.

Matthews, D. L.

J. E. Trebes, S. B. Brown, E. M. Campbell, D. L. Matthews, D. G. Nilson, G. F. Stone, and D. A. Whelan, “Demonstration of X-ray holography with an X-ray laser,” Science 238, 517-519 (1987).
[CrossRef] [PubMed]

McNulty, I.

I. McNulty, J. Kirz, C. Jacobsen, E. H. Anderson, M. R. Howells, and D. P. Kern, “High resolution imaging by Fourier transform X-ray holography,” Science 256, 1009-1012 (1992).
[CrossRef] [PubMed]

Menoni, C. S.

Moreno, C. H.

B. R. Benware, C. D. Macchietto, C. H. Moreno, and J. J. Rocca, “Demonstration of a high average power tabletop soft X-ray laser,” Phys. Rev. Lett. 81, 5804-5807 (1998).
[CrossRef]

Murnane, M. M.

Nealey, P.

H. H. Solak, D. He, W. Li, S. Singh-Gasson, F. Cerrina, B. H. Sohn, X. M. Yang, and P. Nealey, “Exposure of 38 nm period grating patterns with extreme ultraviolet interferometric lithography,” Appl. Phys. Lett. 75, 2328-2330 (1999).
[CrossRef]

Nelson, K. A.

Nilson, D. G.

J. E. Trebes, S. B. Brown, E. M. Campbell, D. L. Matthews, D. G. Nilson, G. F. Stone, and D. A. Whelan, “Demonstration of X-ray holography with an X-ray laser,” Science 238, 517-519 (1987).
[CrossRef] [PubMed]

Parkinson, B.

Patel, D.

Y. Wang, E. Granados, M. A. Larotonda, M. Berrill, B. M. Luther, D. Patel, C. S. Menoni, and J. J. Rocca, “High-brightness injection-seeded soft-x-ray-laser amplifier using a solid target,” Phys. Rev. Lett. 97, 123901 (2006).
[CrossRef] [PubMed]

Rocca, J. J.

P. W. Wachulak, C. A. Brewer, F. Brizuela, W. Chao, E. H. Anderson, R. A. Bartels, C. S. Menoni, J. J. Rocca, and M. C. Marconi, “Simultaneous determination of feature size and resolution in soft x-ray microscopy images,” J. Opt. Soc. Am. B 25, B20-B26 (2008).
[CrossRef]

P. Wachulak, M. C. Marconi, R. Bartels, C. S. Menoni, and J. J. Rocca, “Volume extreme ultraviolet holographic imaging with numerical optical sectioning,” Opt. Express 15, 10622-10628 (2007).
[CrossRef] [PubMed]

P. Wachulak, R. Bartels, M. C. Marconi, C. S. Menoni, J. J. Rocca, Y. Lu, and B. Parkinson, “Sub 400 nm spatial resolution extreme ultraviolet holography with a table top laser,” Opt. Express 14, 9636-9642 (2006).
[CrossRef] [PubMed]

Y. Wang, E. Granados, M. A. Larotonda, M. Berrill, B. M. Luther, D. Patel, C. S. Menoni, and J. J. Rocca, “High-brightness injection-seeded soft-x-ray-laser amplifier using a solid target,” Phys. Rev. Lett. 97, 123901 (2006).
[CrossRef] [PubMed]

Y. Liu, M. Seminario, F. G. Tomasel, C. Chang, J. J. Rocca, and D. T. Attwood, “Achievement of essentially full spatial coherence in a high-average-power soft-x-ray laser,” Phys. Rev. A 63, 033802 (2001).
[CrossRef]

C. D. Macchietto, B. R. Benware, and J. J. Rocca, “Generation of millijoule-level soft-x-ray laser pulses at a 4-Hz repetition rate in a highly saturated tabletop capillary discharge amplifier,” Opt. Lett. 24, 1115-1117 (1999).
[CrossRef]

B. R. Benware, C. D. Macchietto, C. H. Moreno, and J. J. Rocca, “Demonstration of a high average power tabletop soft X-ray laser,” Phys. Rev. Lett. 81, 5804-5807 (1998).
[CrossRef]

Rosenhahn, A.

A. Rosenhahn, R. Barth, X. Cao, M. Schurmann, M. Grunze, and S. Eisebitt, “Vacuum-ultraviolet Gabor holography with synchrotron radiation,” Ultramicroscopy 107, 1171-1177 (2007).
[CrossRef] [PubMed]

Rothman, S.

Schnars, U.

U. Schnars and W. P. O. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85-R101 (2002).
[CrossRef]

Schurmann, M.

A. Rosenhahn, R. Barth, X. Cao, M. Schurmann, M. Grunze, and S. Eisebitt, “Vacuum-ultraviolet Gabor holography with synchrotron radiation,” Ultramicroscopy 107, 1171-1177 (2007).
[CrossRef] [PubMed]

Seminario, M.

Y. Liu, M. Seminario, F. G. Tomasel, C. Chang, J. J. Rocca, and D. T. Attwood, “Achievement of essentially full spatial coherence in a high-average-power soft-x-ray laser,” Phys. Rev. A 63, 033802 (2001).
[CrossRef]

Siemens, M. E.

Singh-Gasson, S.

H. H. Solak, D. He, W. Li, S. Singh-Gasson, F. Cerrina, B. H. Sohn, X. M. Yang, and P. Nealey, “Exposure of 38 nm period grating patterns with extreme ultraviolet interferometric lithography,” Appl. Phys. Lett. 75, 2328-2330 (1999).
[CrossRef]

Sohn, B. H.

H. H. Solak, D. He, W. Li, S. Singh-Gasson, F. Cerrina, B. H. Sohn, X. M. Yang, and P. Nealey, “Exposure of 38 nm period grating patterns with extreme ultraviolet interferometric lithography,” Appl. Phys. Lett. 75, 2328-2330 (1999).
[CrossRef]

Solak, H. H.

H. H. Solak, D. He, W. Li, S. Singh-Gasson, F. Cerrina, B. H. Sohn, X. M. Yang, and P. Nealey, “Exposure of 38 nm period grating patterns with extreme ultraviolet interferometric lithography,” Appl. Phys. Lett. 75, 2328-2330 (1999).
[CrossRef]

Stone, G. F.

J. E. Trebes, S. B. Brown, E. M. Campbell, D. L. Matthews, D. G. Nilson, G. F. Stone, and D. A. Whelan, “Demonstration of X-ray holography with an X-ray laser,” Science 238, 517-519 (1987).
[CrossRef] [PubMed]

Tobey, R. I.

Tomasel, F. G.

Y. Liu, M. Seminario, F. G. Tomasel, C. Chang, J. J. Rocca, and D. T. Attwood, “Achievement of essentially full spatial coherence in a high-average-power soft-x-ray laser,” Phys. Rev. A 63, 033802 (2001).
[CrossRef]

Trebes, J. E.

J. E. Trebes, S. B. Brown, E. M. Campbell, D. L. Matthews, D. G. Nilson, G. F. Stone, and D. A. Whelan, “Demonstration of X-ray holography with an X-ray laser,” Science 238, 517-519 (1987).
[CrossRef] [PubMed]

Wachulak, P.

Wachulak, P. W.

Wang, Y.

Y. Wang, E. Granados, M. A. Larotonda, M. Berrill, B. M. Luther, D. Patel, C. S. Menoni, and J. J. Rocca, “High-brightness injection-seeded soft-x-ray-laser amplifier using a solid target,” Phys. Rev. Lett. 97, 123901 (2006).
[CrossRef] [PubMed]

Whelan, D. A.

J. E. Trebes, S. B. Brown, E. M. Campbell, D. L. Matthews, D. G. Nilson, G. F. Stone, and D. A. Whelan, “Demonstration of X-ray holography with an X-ray laser,” Science 238, 517-519 (1987).
[CrossRef] [PubMed]

Yang, X. M.

H. H. Solak, D. He, W. Li, S. Singh-Gasson, F. Cerrina, B. H. Sohn, X. M. Yang, and P. Nealey, “Exposure of 38 nm period grating patterns with extreme ultraviolet interferometric lithography,” Appl. Phys. Lett. 75, 2328-2330 (1999).
[CrossRef]

Appl. Phys. Lett. (1)

H. H. Solak, D. He, W. Li, S. Singh-Gasson, F. Cerrina, B. H. Sohn, X. M. Yang, and P. Nealey, “Exposure of 38 nm period grating patterns with extreme ultraviolet interferometric lithography,” Appl. Phys. Lett. 75, 2328-2330 (1999).
[CrossRef]

J. Opt. Soc. Am. (1)

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

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

Meas. Sci. Technol. (1)

U. Schnars and W. P. O. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85-R101 (2002).
[CrossRef]

Nature (1)

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

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. A (1)

Y. Liu, M. Seminario, F. G. Tomasel, C. Chang, J. J. Rocca, and D. T. Attwood, “Achievement of essentially full spatial coherence in a high-average-power soft-x-ray laser,” Phys. Rev. A 63, 033802 (2001).
[CrossRef]

Phys. Rev. Lett. (2)

Y. Wang, E. Granados, M. A. Larotonda, M. Berrill, B. M. Luther, D. Patel, C. S. Menoni, and J. J. Rocca, “High-brightness injection-seeded soft-x-ray-laser amplifier using a solid target,” Phys. Rev. Lett. 97, 123901 (2006).
[CrossRef] [PubMed]

B. R. Benware, C. D. Macchietto, C. H. Moreno, and J. J. Rocca, “Demonstration of a high average power tabletop soft X-ray laser,” Phys. Rev. Lett. 81, 5804-5807 (1998).
[CrossRef]

Science (2)

J. E. Trebes, S. B. Brown, E. M. Campbell, D. L. Matthews, D. G. Nilson, G. F. Stone, and D. A. Whelan, “Demonstration of X-ray holography with an X-ray laser,” Science 238, 517-519 (1987).
[CrossRef] [PubMed]

I. McNulty, J. Kirz, C. Jacobsen, E. H. Anderson, M. R. Howells, and D. P. Kern, “High resolution imaging by Fourier transform X-ray holography,” Science 256, 1009-1012 (1992).
[CrossRef] [PubMed]

Ultramicroscopy (1)

A. Rosenhahn, R. Barth, X. Cao, M. Schurmann, M. Grunze, and S. Eisebitt, “Vacuum-ultraviolet Gabor holography with synchrotron radiation,” Ultramicroscopy 107, 1171-1177 (2007).
[CrossRef] [PubMed]

Other (1)

CXRO, “http://www-cxro.lbl.gov/.”

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Figures (4)

Fig. 1
Fig. 1

Experimental setup. (a) Gabor’s hologram configuration. The soft x-ray laser beam illuminates the object composed of carbon nanotubes deposited in a Si membrane. The recording medium is a high-resolution photoresist. (b) Side view of the setup. After developing, the intensity modulation is converted into a height modulation in the photoresist surface.

Fig. 2
Fig. 2

(a) Hologram and (b) reconstructed images of 50 80 nm diameter carbon nanotubes. The holograms were obtained by scanning the photoresist surface with an AFM. The dotted square indicates the zoomed region in Fig. 3a.

Fig. 3
Fig. 3

Knife-edge test applied to estimate the resolution of the image. The intensity lineout through the image from A to B is shown in (b) indicating a 10–90% intensity modulation over approximately 4.5   pixels . An average of multiple cuts obtained at different locations yielded a resolution of 45.8 ± 1.9 nm .

Fig. 4
Fig. 4

Procedure to generate the templates with calibrated resolution. (a) Filtered image to remove the low-frequency background fluctuations. (b) Skeletonizing of the image. (c) Binary template obtained by convolution of skeleton template (b) with a circular template. (d) Template with degraded resolution obtained by convolution of the binary template (c) with a 2D Gaussian filter. (e) Correlation coefficients of the image with the different templates plotted as a function of the nanotube diameter and template resolution. The nanotube diameter and resolution of the image are determined to be 70.6 ± 5 nm and 47.5 ± 5 nm , respectively, by localizing a global maximum in the correlation plot.

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