Abstract

An efficient technique to achieve isotropic edge enhancement in optics involves applying a radial Hilbert transform on the object spectrum. Here we demonstrate a simple setup for isotropic edge-enhancement in soft-x-ray microscopy, using a single diffractive Laguerre-Gaussian zone plate (LGZP) for radial Hilbert transform. Since the LGZP acts as a beam-splitter, diffraction efficiency problems usually associated with x-ray microscopy optics are not present in this system. As numerically demonstrated, the setup can detect optical path differences as small as λ/50 with high contrast.

© 2009 Optical Society of America

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  1. A. Sakdinawat and Y. Liu, “Soft-x-ray microscopy using spiral zone plates,” Opt. Lett. 32, 2635–2637 (2007).
    [Crossref] [PubMed]
  2. G. Schmal, D. Rudolph, P. Guttmann, G. Schneider, J. Thieme, and B. Niemann, “Phase contrast studies of biological specimens with the x-ray microscope at BESSY,” Rev. Sci. Instrum. 66, 1282–1286 (1995).
    [Crossref]
  3. C. David, B. Nöhammer, H.H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81, 3287–3289 (2002).
    [Crossref]
  4. B. Kaulich, T. Wilhein, E. Di Fabrizio, F. Romanato, M. Altissimo, S. Cabrini, B. Fayard, and J. Susini, “Differential interference contrast x-ray microscopy with twin zone plates,” J. Opt. Soc. Am. A 19, 797–806 (2002).
    [Crossref]
  5. J. A. Davis, D. E. McNamara, D. M. Cottrell, and J. Campos, “Image processing with the radial Hilbert transform: theory and experiments,” Opt. Lett. 25, 99–101 (2000).
    [Crossref]
  6. S. Fürhaupter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “Spiral phase contrast imaging in microscopy,” Opt. Express 13, 689–694 (2005).
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  11. http://www.ntt-at.com/products_e/x-ray_FZP/index.html
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    [Crossref] [PubMed]
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    [Crossref]
  14. http://www.princetoninstruments.com/products/xraycam/

2007 (2)

K. Nagai, Y. Iketaki, A. Domondon, Y. Sato, and T. Watanabe, “A graphite-based multiplayer mirror for microscopy in the XANES region of biomolecules,” IEEJ Trans. EIS 127, 1304–1307 (2007).
[Crossref]

A. Sakdinawat and Y. Liu, “Soft-x-ray microscopy using spiral zone plates,” Opt. Lett. 32, 2635–2637 (2007).
[Crossref] [PubMed]

2006 (1)

2005 (2)

2003 (1)

A. Stein, C. Jacobsen, K. Evans-Lutterodt, D. M. Tennant, G. Bogart, F. Klemens, L. E. Ocola, B. J. Choi, and S. V. Sreenivasan, “Diffractive x-ray optics using production fabrication methods,” J. Vac. Sci. Technol. B 21, 214–219 (2003).
[Crossref]

2002 (2)

B. Kaulich, T. Wilhein, E. Di Fabrizio, F. Romanato, M. Altissimo, S. Cabrini, B. Fayard, and J. Susini, “Differential interference contrast x-ray microscopy with twin zone plates,” J. Opt. Soc. Am. A 19, 797–806 (2002).
[Crossref]

C. David, B. Nöhammer, H.H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81, 3287–3289 (2002).
[Crossref]

2001 (1)

W. Leitenberger and A. Snigirev, “Microscopic imaging with high energy x-rays by Fourier transform holography,” J. Appl. Phys. 90, 538–544 (2001).
[Crossref]

2000 (1)

1995 (1)

G. Schmal, D. Rudolph, P. Guttmann, G. Schneider, J. Thieme, and B. Niemann, “Phase contrast studies of biological specimens with the x-ray microscope at BESSY,” Rev. Sci. Instrum. 66, 1282–1286 (1995).
[Crossref]

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]

Altissimo, M.

Anderson, E. H.

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]

Bernet, S.

Bogart, G.

A. Stein, C. Jacobsen, K. Evans-Lutterodt, D. M. Tennant, G. Bogart, F. Klemens, L. E. Ocola, B. J. Choi, and S. V. Sreenivasan, “Diffractive x-ray optics using production fabrication methods,” J. Vac. Sci. Technol. B 21, 214–219 (2003).
[Crossref]

Bokor, N.

Cabrini, S.

Campos, J.

Choi, B. J.

A. Stein, C. Jacobsen, K. Evans-Lutterodt, D. M. Tennant, G. Bogart, F. Klemens, L. E. Ocola, B. J. Choi, and S. V. Sreenivasan, “Diffractive x-ray optics using production fabrication methods,” J. Vac. Sci. Technol. B 21, 214–219 (2003).
[Crossref]

Cottrell, D. M.

David, C.

C. David, B. Nöhammer, H.H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81, 3287–3289 (2002).
[Crossref]

Davis, J. A.

Ding, J.

Domondon, A.

K. Nagai, Y. Iketaki, A. Domondon, Y. Sato, and T. Watanabe, “A graphite-based multiplayer mirror for microscopy in the XANES region of biomolecules,” IEEJ Trans. EIS 127, 1304–1307 (2007).
[Crossref]

Evans-Lutterodt, K.

A. Stein, C. Jacobsen, K. Evans-Lutterodt, D. M. Tennant, G. Bogart, F. Klemens, L. E. Ocola, B. J. Choi, and S. V. Sreenivasan, “Diffractive x-ray optics using production fabrication methods,” J. Vac. Sci. Technol. B 21, 214–219 (2003).
[Crossref]

Fabrizio, E. Di

Fayard, B.

Fujii, M.

Fürhaupter, S.

Guo, C-S.

Guttmann, P.

G. Schmal, D. Rudolph, P. Guttmann, G. Schneider, J. Thieme, and B. Niemann, “Phase contrast studies of biological specimens with the x-ray microscope at BESSY,” Rev. Sci. Instrum. 66, 1282–1286 (1995).
[Crossref]

Han, Y-J.

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]

Iketaki, Y.

K. Nagai, Y. Iketaki, A. Domondon, Y. Sato, and T. Watanabe, “A graphite-based multiplayer mirror for microscopy in the XANES region of biomolecules,” IEEJ Trans. EIS 127, 1304–1307 (2007).
[Crossref]

N. Bokor, Y. Iketaki, T. Watanabe, and M. Fujii, “Investigation of polarization effects for high-numerical-aperture first-order Laguerre-Gaussian beams by 2D scanning with a single fluorescent microbead,” Opt. Express 13, 10440–10447 (2005).
[Crossref] [PubMed]

Jacobsen, C.

A. Stein, C. Jacobsen, K. Evans-Lutterodt, D. M. Tennant, G. Bogart, F. Klemens, L. E. Ocola, B. J. Choi, and S. V. Sreenivasan, “Diffractive x-ray optics using production fabrication methods,” J. Vac. Sci. Technol. B 21, 214–219 (2003).
[Crossref]

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]

Jesacher, A.

Kaulich, B.

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]

Klemens, F.

A. Stein, C. Jacobsen, K. Evans-Lutterodt, D. M. Tennant, G. Bogart, F. Klemens, L. E. Ocola, B. J. Choi, and S. V. Sreenivasan, “Diffractive x-ray optics using production fabrication methods,” J. Vac. Sci. Technol. B 21, 214–219 (2003).
[Crossref]

Leitenberger, W.

W. Leitenberger and A. Snigirev, “Microscopic imaging with high energy x-rays by Fourier transform holography,” J. Appl. Phys. 90, 538–544 (2001).
[Crossref]

Liu, Y.

McNamara, D. E.

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]

Nagai, K.

K. Nagai, Y. Iketaki, A. Domondon, Y. Sato, and T. Watanabe, “A graphite-based multiplayer mirror for microscopy in the XANES region of biomolecules,” IEEJ Trans. EIS 127, 1304–1307 (2007).
[Crossref]

Niemann, B.

G. Schmal, D. Rudolph, P. Guttmann, G. Schneider, J. Thieme, and B. Niemann, “Phase contrast studies of biological specimens with the x-ray microscope at BESSY,” Rev. Sci. Instrum. 66, 1282–1286 (1995).
[Crossref]

Nöhammer, B.

C. David, B. Nöhammer, H.H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81, 3287–3289 (2002).
[Crossref]

Ocola, L. E.

A. Stein, C. Jacobsen, K. Evans-Lutterodt, D. M. Tennant, G. Bogart, F. Klemens, L. E. Ocola, B. J. Choi, and S. V. Sreenivasan, “Diffractive x-ray optics using production fabrication methods,” J. Vac. Sci. Technol. B 21, 214–219 (2003).
[Crossref]

Ritsch-Marte, M.

Romanato, F.

Rudolph, D.

G. Schmal, D. Rudolph, P. Guttmann, G. Schneider, J. Thieme, and B. Niemann, “Phase contrast studies of biological specimens with the x-ray microscope at BESSY,” Rev. Sci. Instrum. 66, 1282–1286 (1995).
[Crossref]

Sakdinawat, A.

Sato, Y.

K. Nagai, Y. Iketaki, A. Domondon, Y. Sato, and T. Watanabe, “A graphite-based multiplayer mirror for microscopy in the XANES region of biomolecules,” IEEJ Trans. EIS 127, 1304–1307 (2007).
[Crossref]

Schmal, G.

G. Schmal, D. Rudolph, P. Guttmann, G. Schneider, J. Thieme, and B. Niemann, “Phase contrast studies of biological specimens with the x-ray microscope at BESSY,” Rev. Sci. Instrum. 66, 1282–1286 (1995).
[Crossref]

Schneider, G.

G. Schmal, D. Rudolph, P. Guttmann, G. Schneider, J. Thieme, and B. Niemann, “Phase contrast studies of biological specimens with the x-ray microscope at BESSY,” Rev. Sci. Instrum. 66, 1282–1286 (1995).
[Crossref]

Snigirev, A.

W. Leitenberger and A. Snigirev, “Microscopic imaging with high energy x-rays by Fourier transform holography,” J. Appl. Phys. 90, 538–544 (2001).
[Crossref]

Solak, H.H.

C. David, B. Nöhammer, H.H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81, 3287–3289 (2002).
[Crossref]

Sreenivasan, S. V.

A. Stein, C. Jacobsen, K. Evans-Lutterodt, D. M. Tennant, G. Bogart, F. Klemens, L. E. Ocola, B. J. Choi, and S. V. Sreenivasan, “Diffractive x-ray optics using production fabrication methods,” J. Vac. Sci. Technol. B 21, 214–219 (2003).
[Crossref]

Stein, A.

A. Stein, C. Jacobsen, K. Evans-Lutterodt, D. M. Tennant, G. Bogart, F. Klemens, L. E. Ocola, B. J. Choi, and S. V. Sreenivasan, “Diffractive x-ray optics using production fabrication methods,” J. Vac. Sci. Technol. B 21, 214–219 (2003).
[Crossref]

Susini, J.

Tennant, D. M.

A. Stein, C. Jacobsen, K. Evans-Lutterodt, D. M. Tennant, G. Bogart, F. Klemens, L. E. Ocola, B. J. Choi, and S. V. Sreenivasan, “Diffractive x-ray optics using production fabrication methods,” J. Vac. Sci. Technol. B 21, 214–219 (2003).
[Crossref]

Thieme, J.

G. Schmal, D. Rudolph, P. Guttmann, G. Schneider, J. Thieme, and B. Niemann, “Phase contrast studies of biological specimens with the x-ray microscope at BESSY,” Rev. Sci. Instrum. 66, 1282–1286 (1995).
[Crossref]

Watanabe, T.

K. Nagai, Y. Iketaki, A. Domondon, Y. Sato, and T. Watanabe, “A graphite-based multiplayer mirror for microscopy in the XANES region of biomolecules,” IEEJ Trans. EIS 127, 1304–1307 (2007).
[Crossref]

N. Bokor, Y. Iketaki, T. Watanabe, and M. Fujii, “Investigation of polarization effects for high-numerical-aperture first-order Laguerre-Gaussian beams by 2D scanning with a single fluorescent microbead,” Opt. Express 13, 10440–10447 (2005).
[Crossref] [PubMed]

Wilhein, T.

Xu, J-B.

Ziegler, E.

C. David, B. Nöhammer, H.H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81, 3287–3289 (2002).
[Crossref]

Appl. Phys. Lett. (1)

C. David, B. Nöhammer, H.H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81, 3287–3289 (2002).
[Crossref]

IEEJ Trans. EIS (1)

K. Nagai, Y. Iketaki, A. Domondon, Y. Sato, and T. Watanabe, “A graphite-based multiplayer mirror for microscopy in the XANES region of biomolecules,” IEEJ Trans. EIS 127, 1304–1307 (2007).
[Crossref]

J. Appl. Phys. (1)

W. Leitenberger and A. Snigirev, “Microscopic imaging with high energy x-rays by Fourier transform holography,” J. Appl. Phys. 90, 538–544 (2001).
[Crossref]

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

J. Vac. Sci. Technol. B (1)

A. Stein, C. Jacobsen, K. Evans-Lutterodt, D. M. Tennant, G. Bogart, F. Klemens, L. E. Ocola, B. J. Choi, and S. V. Sreenivasan, “Diffractive x-ray optics using production fabrication methods,” J. Vac. Sci. Technol. B 21, 214–219 (2003).
[Crossref]

Opt. Express (2)

Opt. Lett. (3)

Rev. Sci. Instrum. (1)

G. Schmal, D. Rudolph, P. Guttmann, G. Schneider, J. Thieme, and B. Niemann, “Phase contrast studies of biological specimens with the x-ray microscope at BESSY,” Rev. Sci. Instrum. 66, 1282–1286 (1995).
[Crossref]

Science (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]

Other (2)

http://www.ntt-at.com/products_e/x-ray_FZP/index.html

http://www.princetoninstruments.com/products/xraycam/

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