Abstract

Curved reflecting mirrors are widely used as x-ray optical elements for both laboratory and synchrotron radiation sources. In general, the mirror parameters are optimized by numerical simulation. We discuss an analytical approach that is useful for deriving the mirror parameters, including eccentricity, length, angular acceptance, and magnification. We have examined in particular an elliptical surface from which we learned that, given the distance between the foci of the ellipse, the magnification, and the critical angle of total external reflection, it is possible to find analytically the optimal eccentricity that maximizes the angular acceptance and the optimal mirror length. We found that the last-named parameter, in a first approximation, depends only on the distance between the foci of the ellipse and on the magnification factor. We present as well a comparison of optimal parameters obtained with analytical calculation and with ray-tracing simulation that yielded good agreement.

© 2004 Optical Society of America

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  1. S. Lagomarsino, A. Cedola, “X-ray microscopy and nanodiffraction,” in Encyclopedia of Nanoscience and Nanotechnology, H. S. Nalwa, ed. (American Scientific, Stevenson Ranch, Calif., 2004), Vol. 10, pp. 681–710.
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    [CrossRef]
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    [CrossRef]
  5. B. Lengeler, C. G. Schroer, B. Benner, A. Gerhardus, T. F. Gunzler, M. Kuhlmann, J. Meyer, C. Zimprich, “Parabolic refractive x-ray lenses,” J. Synchrotron Radiat. 9, 119–124 (2002).
    [CrossRef] [PubMed]
  6. G. Schmahl, P. Cheng, “X-ray microscopy,” in Handbook on Synchrotron Radiation, S. Ebashi, M. Koch, E. Rubenstein, eds. (Elsevier, Amsterdam, 1991), Vol. 4.
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    [CrossRef]
  8. C. David, B. Kaulich, R. Barret, M. Salomè, J. Susini, “High-resolution lenses for sub-100 nm x-ray fluorescence microscopy,” Appl. Phys. Lett. 77, 3851–3853 (2000).
    [CrossRef]
  9. V. Aristov, Yu. A. Basov, S. V. Redkin, A. Snigirev, V. A. Yunkin, “Bragg zone plates for hard x-ray focusing,” Nucl. Instrum. Methods Phys. Res. A 261, 72–74 (1987).
    [CrossRef]
  10. S. M. Kuznetsov, I. I. Snigireva, A. A. Snigirev, P. Engström, C. Riekel, “Submicrometer fluorescence microprobe based on Bragg–Fresnel optics,” Appl. Phys. Lett. 65, 827–829 (1994).
    [CrossRef]
  11. P. Cloetens, O. Hignette, S. Bohic, E. Pereiro, C. Morawe, W. Ludwig, “Hard x-ray phase contrast microscopy and fluorescence mapping with KB optics,” presented at the Eighth International Conference on Synchrotron Radiation Instrumentation, San Francisco, Calif., 24–29 August 2003.
  12. O. Hignette, G. Rostaing, P. Cloetens, A. Rommeveaux, W. Ludwig, A. K. Freund, “Submicron focusing of hard x-rays with reflecting surfaces at the ESRF,” in X-Ray Micro- and Nano-Focusing: Applications and Techniques II, I. McNulty, ed., Proc. SPIE4499, 105–116 (2001).
    [CrossRef]
  13. A. Iida, K. Girano, “Kirkpatrick–Baez optics for a sub-μm synchrotron x-ray microbeam and its applications to x-ray analysis,” Nucl. Instrum. Methods Phys. Res. B 114, 149–153 (1996).
    [CrossRef]
  14. H. A. Padmore, G. Ackerman, R. Celestre, C. H. Chang, K. Franck, M. Howells, Z. Hussain, S. Irick, S. Locklin, A. A. MacDowell, J. R. Patel, S. Y. Rah, T. R. Renner, R. Sandler, “Submicron white beam focusing using elliptically bent mirrors,” Synchrotron Radiat. News 10(6), 18–26 (1997).
    [CrossRef]
  15. P. Engström, S. Lasson, A. Rindby, A. Buttkewitz, S. Garbe, G. Gaul, A. Knöchel, F. Lechtenberg, “A submicron synchrotron x-ray beam generated by capillary optics,” Nucl. Instrum. Methods Phys. Res. A 302, 547–550 (1991).
    [CrossRef]
  16. D. H. Bilderback, S. A. Hoffman, D. J. Thiel, “Nanometer spatial resolution achieved in hard x-ray imaging and Laue diffraction applications,” Science 263, 201–203 (1994).
    [CrossRef] [PubMed]
  17. W. Jark, A. Cedola, S. Di Fonzo, M. Fiordelisi, S. Lagomarsino, N. V. Kovalenko, V. A. Chernov, “High gain beam compression in new-generation thin-film x-ray waveguides,” Appl. Phys. Lett. 78, 1192–1194 (2001).
    [CrossRef]
  18. E. Pfeiffer, C. David, M. Burghammer, C. Riekel, T. Salditt, “Two-dimensional x-ray waveguides and point sources,” Science 12, 230–234 (2002).
    [CrossRef]
  19. Y. P. Feng, S. K. Sinha, H. W. Deckman, J. B. Hastings, D. P. Siddons, “X-ray Fraunhofer diffraction patterns from a thin-film waveguide,” Appl. Phys. Lett. 67, 3647–3649 (1995).
    [CrossRef]
  20. S. Lagomarsino, W. Jark, S. Di Fonzo, A. Cedola, B. Muller, P. Engstrom, C. Riekel, “Submicrometer x-ray beam production by a thin film waveguide,” J. Appl. Phys. 79, 4471–4473 (1996).
    [CrossRef]
  21. A. V. Vinogradov, N. N. Zorev, I. V. Kozhenikov, “On limiting abilities of optics for soft x-ray region,” Proc. P. N. Lebedev Phys. Inst. 176, 195–210 (1986).
  22. A. V. Vinogradov, O. I. Tolstihin, “Concentrators for soft x-ray radiation,” Proc. P. N. Lebedev Phys. Inst. 196, 168–181 (1989).
  23. A. V. Vinogradov, I. A. Brytov, A. Ya. Grudski, M. N. Kogan, I. V. Kozhevnikov, V. A. Slemzin, Reflective X-Ray Optics (Mashinostroenie, Leningrad, 1989).
  24. I. A. Atryukov, A. V. Vinogradov, I. V. Kozhevnikov, “Efficiency of grazing incidence optics: the spiral collimator,” Appl. Opt. 30, 4154–4157 (1991).
    [CrossRef]
  25. I. A. Atrukov, I. V. Kozhevnikov, N. I. Kozhevnikova, “Optimum collimator for proximity x-ray lithography—theoretical analysis,” J. X-Ray Sci. Technol. 8, 199–220 (1998).

2002 (2)

B. Lengeler, C. G. Schroer, B. Benner, A. Gerhardus, T. F. Gunzler, M. Kuhlmann, J. Meyer, C. Zimprich, “Parabolic refractive x-ray lenses,” J. Synchrotron Radiat. 9, 119–124 (2002).
[CrossRef] [PubMed]

E. Pfeiffer, C. David, M. Burghammer, C. Riekel, T. Salditt, “Two-dimensional x-ray waveguides and point sources,” Science 12, 230–234 (2002).
[CrossRef]

2001 (1)

W. Jark, A. Cedola, S. Di Fonzo, M. Fiordelisi, S. Lagomarsino, N. V. Kovalenko, V. A. Chernov, “High gain beam compression in new-generation thin-film x-ray waveguides,” Appl. Phys. Lett. 78, 1192–1194 (2001).
[CrossRef]

2000 (1)

C. David, B. Kaulich, R. Barret, M. Salomè, J. Susini, “High-resolution lenses for sub-100 nm x-ray fluorescence microscopy,” Appl. Phys. Lett. 77, 3851–3853 (2000).
[CrossRef]

1999 (1)

E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, R. Barret, “High-efficiency multilevel zone plates for keV x-rays,” Nature 401, 895–298 (1999).
[CrossRef]

1998 (1)

I. A. Atrukov, I. V. Kozhevnikov, N. I. Kozhevnikova, “Optimum collimator for proximity x-ray lithography—theoretical analysis,” J. X-Ray Sci. Technol. 8, 199–220 (1998).

1997 (1)

H. A. Padmore, G. Ackerman, R. Celestre, C. H. Chang, K. Franck, M. Howells, Z. Hussain, S. Irick, S. Locklin, A. A. MacDowell, J. R. Patel, S. Y. Rah, T. R. Renner, R. Sandler, “Submicron white beam focusing using elliptically bent mirrors,” Synchrotron Radiat. News 10(6), 18–26 (1997).
[CrossRef]

1996 (3)

A. Snigirev, V. Kohn, I. Snigireva, B. Lengeler, “A compound refractive lens for focusing high-energy x-rays,” Nature 387, 49–51 (1996).
[CrossRef]

S. Lagomarsino, W. Jark, S. Di Fonzo, A. Cedola, B. Muller, P. Engstrom, C. Riekel, “Submicrometer x-ray beam production by a thin film waveguide,” J. Appl. Phys. 79, 4471–4473 (1996).
[CrossRef]

A. Iida, K. Girano, “Kirkpatrick–Baez optics for a sub-μm synchrotron x-ray microbeam and its applications to x-ray analysis,” Nucl. Instrum. Methods Phys. Res. B 114, 149–153 (1996).
[CrossRef]

1995 (1)

Y. P. Feng, S. K. Sinha, H. W. Deckman, J. B. Hastings, D. P. Siddons, “X-ray Fraunhofer diffraction patterns from a thin-film waveguide,” Appl. Phys. Lett. 67, 3647–3649 (1995).
[CrossRef]

1994 (2)

D. H. Bilderback, S. A. Hoffman, D. J. Thiel, “Nanometer spatial resolution achieved in hard x-ray imaging and Laue diffraction applications,” Science 263, 201–203 (1994).
[CrossRef] [PubMed]

S. M. Kuznetsov, I. I. Snigireva, A. A. Snigirev, P. Engström, C. Riekel, “Submicrometer fluorescence microprobe based on Bragg–Fresnel optics,” Appl. Phys. Lett. 65, 827–829 (1994).
[CrossRef]

1991 (2)

P. Engström, S. Lasson, A. Rindby, A. Buttkewitz, S. Garbe, G. Gaul, A. Knöchel, F. Lechtenberg, “A submicron synchrotron x-ray beam generated by capillary optics,” Nucl. Instrum. Methods Phys. Res. A 302, 547–550 (1991).
[CrossRef]

I. A. Atryukov, A. V. Vinogradov, I. V. Kozhevnikov, “Efficiency of grazing incidence optics: the spiral collimator,” Appl. Opt. 30, 4154–4157 (1991).
[CrossRef]

1989 (1)

A. V. Vinogradov, O. I. Tolstihin, “Concentrators for soft x-ray radiation,” Proc. P. N. Lebedev Phys. Inst. 196, 168–181 (1989).

1987 (1)

V. Aristov, Yu. A. Basov, S. V. Redkin, A. Snigirev, V. A. Yunkin, “Bragg zone plates for hard x-ray focusing,” Nucl. Instrum. Methods Phys. Res. A 261, 72–74 (1987).
[CrossRef]

1986 (1)

A. V. Vinogradov, N. N. Zorev, I. V. Kozhenikov, “On limiting abilities of optics for soft x-ray region,” Proc. P. N. Lebedev Phys. Inst. 176, 195–210 (1986).

Ackerman, G.

H. A. Padmore, G. Ackerman, R. Celestre, C. H. Chang, K. Franck, M. Howells, Z. Hussain, S. Irick, S. Locklin, A. A. MacDowell, J. R. Patel, S. Y. Rah, T. R. Renner, R. Sandler, “Submicron white beam focusing using elliptically bent mirrors,” Synchrotron Radiat. News 10(6), 18–26 (1997).
[CrossRef]

Aristov, V.

V. Aristov, Yu. A. Basov, S. V. Redkin, A. Snigirev, V. A. Yunkin, “Bragg zone plates for hard x-ray focusing,” Nucl. Instrum. Methods Phys. Res. A 261, 72–74 (1987).
[CrossRef]

Atrukov, I. A.

I. A. Atrukov, I. V. Kozhevnikov, N. I. Kozhevnikova, “Optimum collimator for proximity x-ray lithography—theoretical analysis,” J. X-Ray Sci. Technol. 8, 199–220 (1998).

Atryukov, I. A.

Barret, R.

C. David, B. Kaulich, R. Barret, M. Salomè, J. Susini, “High-resolution lenses for sub-100 nm x-ray fluorescence microscopy,” Appl. Phys. Lett. 77, 3851–3853 (2000).
[CrossRef]

E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, R. Barret, “High-efficiency multilevel zone plates for keV x-rays,” Nature 401, 895–298 (1999).
[CrossRef]

Basov, Yu. A.

V. Aristov, Yu. A. Basov, S. V. Redkin, A. Snigirev, V. A. Yunkin, “Bragg zone plates for hard x-ray focusing,” Nucl. Instrum. Methods Phys. Res. A 261, 72–74 (1987).
[CrossRef]

Benner, B.

B. Lengeler, C. G. Schroer, B. Benner, A. Gerhardus, T. F. Gunzler, M. Kuhlmann, J. Meyer, C. Zimprich, “Parabolic refractive x-ray lenses,” J. Synchrotron Radiat. 9, 119–124 (2002).
[CrossRef] [PubMed]

Bilderback, D. H.

D. H. Bilderback, S. A. Hoffman, D. J. Thiel, “Nanometer spatial resolution achieved in hard x-ray imaging and Laue diffraction applications,” Science 263, 201–203 (1994).
[CrossRef] [PubMed]

Bohic, S.

P. Cloetens, O. Hignette, S. Bohic, E. Pereiro, C. Morawe, W. Ludwig, “Hard x-ray phase contrast microscopy and fluorescence mapping with KB optics,” presented at the Eighth International Conference on Synchrotron Radiation Instrumentation, San Francisco, Calif., 24–29 August 2003.

Brytov, I. A.

A. V. Vinogradov, I. A. Brytov, A. Ya. Grudski, M. N. Kogan, I. V. Kozhevnikov, V. A. Slemzin, Reflective X-Ray Optics (Mashinostroenie, Leningrad, 1989).

Burghammer, M.

E. Pfeiffer, C. David, M. Burghammer, C. Riekel, T. Salditt, “Two-dimensional x-ray waveguides and point sources,” Science 12, 230–234 (2002).
[CrossRef]

Buttkewitz, A.

P. Engström, S. Lasson, A. Rindby, A. Buttkewitz, S. Garbe, G. Gaul, A. Knöchel, F. Lechtenberg, “A submicron synchrotron x-ray beam generated by capillary optics,” Nucl. Instrum. Methods Phys. Res. A 302, 547–550 (1991).
[CrossRef]

Cabrini, S.

E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, R. Barret, “High-efficiency multilevel zone plates for keV x-rays,” Nature 401, 895–298 (1999).
[CrossRef]

Cedola, A.

W. Jark, A. Cedola, S. Di Fonzo, M. Fiordelisi, S. Lagomarsino, N. V. Kovalenko, V. A. Chernov, “High gain beam compression in new-generation thin-film x-ray waveguides,” Appl. Phys. Lett. 78, 1192–1194 (2001).
[CrossRef]

S. Lagomarsino, W. Jark, S. Di Fonzo, A. Cedola, B. Muller, P. Engstrom, C. Riekel, “Submicrometer x-ray beam production by a thin film waveguide,” J. Appl. Phys. 79, 4471–4473 (1996).
[CrossRef]

S. Lagomarsino, A. Cedola, “X-ray microscopy and nanodiffraction,” in Encyclopedia of Nanoscience and Nanotechnology, H. S. Nalwa, ed. (American Scientific, Stevenson Ranch, Calif., 2004), Vol. 10, pp. 681–710.

Celestre, R.

H. A. Padmore, G. Ackerman, R. Celestre, C. H. Chang, K. Franck, M. Howells, Z. Hussain, S. Irick, S. Locklin, A. A. MacDowell, J. R. Patel, S. Y. Rah, T. R. Renner, R. Sandler, “Submicron white beam focusing using elliptically bent mirrors,” Synchrotron Radiat. News 10(6), 18–26 (1997).
[CrossRef]

Chang, C. H.

H. A. Padmore, G. Ackerman, R. Celestre, C. H. Chang, K. Franck, M. Howells, Z. Hussain, S. Irick, S. Locklin, A. A. MacDowell, J. R. Patel, S. Y. Rah, T. R. Renner, R. Sandler, “Submicron white beam focusing using elliptically bent mirrors,” Synchrotron Radiat. News 10(6), 18–26 (1997).
[CrossRef]

Cheng, P.

G. Schmahl, P. Cheng, “X-ray microscopy,” in Handbook on Synchrotron Radiation, S. Ebashi, M. Koch, E. Rubenstein, eds. (Elsevier, Amsterdam, 1991), Vol. 4.

Chernov, V. A.

W. Jark, A. Cedola, S. Di Fonzo, M. Fiordelisi, S. Lagomarsino, N. V. Kovalenko, V. A. Chernov, “High gain beam compression in new-generation thin-film x-ray waveguides,” Appl. Phys. Lett. 78, 1192–1194 (2001).
[CrossRef]

Cloetens, P.

P. Cloetens, O. Hignette, S. Bohic, E. Pereiro, C. Morawe, W. Ludwig, “Hard x-ray phase contrast microscopy and fluorescence mapping with KB optics,” presented at the Eighth International Conference on Synchrotron Radiation Instrumentation, San Francisco, Calif., 24–29 August 2003.

O. Hignette, G. Rostaing, P. Cloetens, A. Rommeveaux, W. Ludwig, A. K. Freund, “Submicron focusing of hard x-rays with reflecting surfaces at the ESRF,” in X-Ray Micro- and Nano-Focusing: Applications and Techniques II, I. McNulty, ed., Proc. SPIE4499, 105–116 (2001).
[CrossRef]

David, C.

E. Pfeiffer, C. David, M. Burghammer, C. Riekel, T. Salditt, “Two-dimensional x-ray waveguides and point sources,” Science 12, 230–234 (2002).
[CrossRef]

C. David, B. Kaulich, R. Barret, M. Salomè, J. Susini, “High-resolution lenses for sub-100 nm x-ray fluorescence microscopy,” Appl. Phys. Lett. 77, 3851–3853 (2000).
[CrossRef]

Deckman, H. W.

Y. P. Feng, S. K. Sinha, H. W. Deckman, J. B. Hastings, D. P. Siddons, “X-ray Fraunhofer diffraction patterns from a thin-film waveguide,” Appl. Phys. Lett. 67, 3647–3649 (1995).
[CrossRef]

Di Fabrizio, E.

E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, R. Barret, “High-efficiency multilevel zone plates for keV x-rays,” Nature 401, 895–298 (1999).
[CrossRef]

Di Fonzo, S.

W. Jark, A. Cedola, S. Di Fonzo, M. Fiordelisi, S. Lagomarsino, N. V. Kovalenko, V. A. Chernov, “High gain beam compression in new-generation thin-film x-ray waveguides,” Appl. Phys. Lett. 78, 1192–1194 (2001).
[CrossRef]

S. Lagomarsino, W. Jark, S. Di Fonzo, A. Cedola, B. Muller, P. Engstrom, C. Riekel, “Submicrometer x-ray beam production by a thin film waveguide,” J. Appl. Phys. 79, 4471–4473 (1996).
[CrossRef]

Engstrom, P.

S. Lagomarsino, W. Jark, S. Di Fonzo, A. Cedola, B. Muller, P. Engstrom, C. Riekel, “Submicrometer x-ray beam production by a thin film waveguide,” J. Appl. Phys. 79, 4471–4473 (1996).
[CrossRef]

Engström, P.

S. M. Kuznetsov, I. I. Snigireva, A. A. Snigirev, P. Engström, C. Riekel, “Submicrometer fluorescence microprobe based on Bragg–Fresnel optics,” Appl. Phys. Lett. 65, 827–829 (1994).
[CrossRef]

P. Engström, S. Lasson, A. Rindby, A. Buttkewitz, S. Garbe, G. Gaul, A. Knöchel, F. Lechtenberg, “A submicron synchrotron x-ray beam generated by capillary optics,” Nucl. Instrum. Methods Phys. Res. A 302, 547–550 (1991).
[CrossRef]

Feng, Y. P.

Y. P. Feng, S. K. Sinha, H. W. Deckman, J. B. Hastings, D. P. Siddons, “X-ray Fraunhofer diffraction patterns from a thin-film waveguide,” Appl. Phys. Lett. 67, 3647–3649 (1995).
[CrossRef]

Fiordelisi, M.

W. Jark, A. Cedola, S. Di Fonzo, M. Fiordelisi, S. Lagomarsino, N. V. Kovalenko, V. A. Chernov, “High gain beam compression in new-generation thin-film x-ray waveguides,” Appl. Phys. Lett. 78, 1192–1194 (2001).
[CrossRef]

Franck, K.

H. A. Padmore, G. Ackerman, R. Celestre, C. H. Chang, K. Franck, M. Howells, Z. Hussain, S. Irick, S. Locklin, A. A. MacDowell, J. R. Patel, S. Y. Rah, T. R. Renner, R. Sandler, “Submicron white beam focusing using elliptically bent mirrors,” Synchrotron Radiat. News 10(6), 18–26 (1997).
[CrossRef]

Freund, A. K.

O. Hignette, G. Rostaing, P. Cloetens, A. Rommeveaux, W. Ludwig, A. K. Freund, “Submicron focusing of hard x-rays with reflecting surfaces at the ESRF,” in X-Ray Micro- and Nano-Focusing: Applications and Techniques II, I. McNulty, ed., Proc. SPIE4499, 105–116 (2001).
[CrossRef]

Garbe, S.

P. Engström, S. Lasson, A. Rindby, A. Buttkewitz, S. Garbe, G. Gaul, A. Knöchel, F. Lechtenberg, “A submicron synchrotron x-ray beam generated by capillary optics,” Nucl. Instrum. Methods Phys. Res. A 302, 547–550 (1991).
[CrossRef]

Gaul, G.

P. Engström, S. Lasson, A. Rindby, A. Buttkewitz, S. Garbe, G. Gaul, A. Knöchel, F. Lechtenberg, “A submicron synchrotron x-ray beam generated by capillary optics,” Nucl. Instrum. Methods Phys. Res. A 302, 547–550 (1991).
[CrossRef]

Gentili, M.

E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, R. Barret, “High-efficiency multilevel zone plates for keV x-rays,” Nature 401, 895–298 (1999).
[CrossRef]

Gerhardus, A.

B. Lengeler, C. G. Schroer, B. Benner, A. Gerhardus, T. F. Gunzler, M. Kuhlmann, J. Meyer, C. Zimprich, “Parabolic refractive x-ray lenses,” J. Synchrotron Radiat. 9, 119–124 (2002).
[CrossRef] [PubMed]

Girano, K.

A. Iida, K. Girano, “Kirkpatrick–Baez optics for a sub-μm synchrotron x-ray microbeam and its applications to x-ray analysis,” Nucl. Instrum. Methods Phys. Res. B 114, 149–153 (1996).
[CrossRef]

Grudski, A. Ya.

A. V. Vinogradov, I. A. Brytov, A. Ya. Grudski, M. N. Kogan, I. V. Kozhevnikov, V. A. Slemzin, Reflective X-Ray Optics (Mashinostroenie, Leningrad, 1989).

Gunzler, T. F.

B. Lengeler, C. G. Schroer, B. Benner, A. Gerhardus, T. F. Gunzler, M. Kuhlmann, J. Meyer, C. Zimprich, “Parabolic refractive x-ray lenses,” J. Synchrotron Radiat. 9, 119–124 (2002).
[CrossRef] [PubMed]

Hastings, J. B.

Y. P. Feng, S. K. Sinha, H. W. Deckman, J. B. Hastings, D. P. Siddons, “X-ray Fraunhofer diffraction patterns from a thin-film waveguide,” Appl. Phys. Lett. 67, 3647–3649 (1995).
[CrossRef]

Hignette, O.

P. Cloetens, O. Hignette, S. Bohic, E. Pereiro, C. Morawe, W. Ludwig, “Hard x-ray phase contrast microscopy and fluorescence mapping with KB optics,” presented at the Eighth International Conference on Synchrotron Radiation Instrumentation, San Francisco, Calif., 24–29 August 2003.

O. Hignette, G. Rostaing, P. Cloetens, A. Rommeveaux, W. Ludwig, A. K. Freund, “Submicron focusing of hard x-rays with reflecting surfaces at the ESRF,” in X-Ray Micro- and Nano-Focusing: Applications and Techniques II, I. McNulty, ed., Proc. SPIE4499, 105–116 (2001).
[CrossRef]

Hoffman, S. A.

D. H. Bilderback, S. A. Hoffman, D. J. Thiel, “Nanometer spatial resolution achieved in hard x-ray imaging and Laue diffraction applications,” Science 263, 201–203 (1994).
[CrossRef] [PubMed]

Howells, M.

H. A. Padmore, G. Ackerman, R. Celestre, C. H. Chang, K. Franck, M. Howells, Z. Hussain, S. Irick, S. Locklin, A. A. MacDowell, J. R. Patel, S. Y. Rah, T. R. Renner, R. Sandler, “Submicron white beam focusing using elliptically bent mirrors,” Synchrotron Radiat. News 10(6), 18–26 (1997).
[CrossRef]

Hussain, Z.

H. A. Padmore, G. Ackerman, R. Celestre, C. H. Chang, K. Franck, M. Howells, Z. Hussain, S. Irick, S. Locklin, A. A. MacDowell, J. R. Patel, S. Y. Rah, T. R. Renner, R. Sandler, “Submicron white beam focusing using elliptically bent mirrors,” Synchrotron Radiat. News 10(6), 18–26 (1997).
[CrossRef]

Iida, A.

A. Iida, K. Girano, “Kirkpatrick–Baez optics for a sub-μm synchrotron x-ray microbeam and its applications to x-ray analysis,” Nucl. Instrum. Methods Phys. Res. B 114, 149–153 (1996).
[CrossRef]

Irick, S.

H. A. Padmore, G. Ackerman, R. Celestre, C. H. Chang, K. Franck, M. Howells, Z. Hussain, S. Irick, S. Locklin, A. A. MacDowell, J. R. Patel, S. Y. Rah, T. R. Renner, R. Sandler, “Submicron white beam focusing using elliptically bent mirrors,” Synchrotron Radiat. News 10(6), 18–26 (1997).
[CrossRef]

Jark, W.

W. Jark, A. Cedola, S. Di Fonzo, M. Fiordelisi, S. Lagomarsino, N. V. Kovalenko, V. A. Chernov, “High gain beam compression in new-generation thin-film x-ray waveguides,” Appl. Phys. Lett. 78, 1192–1194 (2001).
[CrossRef]

S. Lagomarsino, W. Jark, S. Di Fonzo, A. Cedola, B. Muller, P. Engstrom, C. Riekel, “Submicrometer x-ray beam production by a thin film waveguide,” J. Appl. Phys. 79, 4471–4473 (1996).
[CrossRef]

Kaulich, B.

C. David, B. Kaulich, R. Barret, M. Salomè, J. Susini, “High-resolution lenses for sub-100 nm x-ray fluorescence microscopy,” Appl. Phys. Lett. 77, 3851–3853 (2000).
[CrossRef]

E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, R. Barret, “High-efficiency multilevel zone plates for keV x-rays,” Nature 401, 895–298 (1999).
[CrossRef]

Knöchel, A.

P. Engström, S. Lasson, A. Rindby, A. Buttkewitz, S. Garbe, G. Gaul, A. Knöchel, F. Lechtenberg, “A submicron synchrotron x-ray beam generated by capillary optics,” Nucl. Instrum. Methods Phys. Res. A 302, 547–550 (1991).
[CrossRef]

Kogan, M. N.

A. V. Vinogradov, I. A. Brytov, A. Ya. Grudski, M. N. Kogan, I. V. Kozhevnikov, V. A. Slemzin, Reflective X-Ray Optics (Mashinostroenie, Leningrad, 1989).

Kohn, V.

A. Snigirev, V. Kohn, I. Snigireva, B. Lengeler, “A compound refractive lens for focusing high-energy x-rays,” Nature 387, 49–51 (1996).
[CrossRef]

Kovalenko, N. V.

W. Jark, A. Cedola, S. Di Fonzo, M. Fiordelisi, S. Lagomarsino, N. V. Kovalenko, V. A. Chernov, “High gain beam compression in new-generation thin-film x-ray waveguides,” Appl. Phys. Lett. 78, 1192–1194 (2001).
[CrossRef]

Kozhenikov, I. V.

A. V. Vinogradov, N. N. Zorev, I. V. Kozhenikov, “On limiting abilities of optics for soft x-ray region,” Proc. P. N. Lebedev Phys. Inst. 176, 195–210 (1986).

Kozhevnikov, I. V.

I. A. Atrukov, I. V. Kozhevnikov, N. I. Kozhevnikova, “Optimum collimator for proximity x-ray lithography—theoretical analysis,” J. X-Ray Sci. Technol. 8, 199–220 (1998).

I. A. Atryukov, A. V. Vinogradov, I. V. Kozhevnikov, “Efficiency of grazing incidence optics: the spiral collimator,” Appl. Opt. 30, 4154–4157 (1991).
[CrossRef]

A. V. Vinogradov, I. A. Brytov, A. Ya. Grudski, M. N. Kogan, I. V. Kozhevnikov, V. A. Slemzin, Reflective X-Ray Optics (Mashinostroenie, Leningrad, 1989).

Kozhevnikova, N. I.

I. A. Atrukov, I. V. Kozhevnikov, N. I. Kozhevnikova, “Optimum collimator for proximity x-ray lithography—theoretical analysis,” J. X-Ray Sci. Technol. 8, 199–220 (1998).

Kuhlmann, M.

B. Lengeler, C. G. Schroer, B. Benner, A. Gerhardus, T. F. Gunzler, M. Kuhlmann, J. Meyer, C. Zimprich, “Parabolic refractive x-ray lenses,” J. Synchrotron Radiat. 9, 119–124 (2002).
[CrossRef] [PubMed]

Kuznetsov, S. M.

S. M. Kuznetsov, I. I. Snigireva, A. A. Snigirev, P. Engström, C. Riekel, “Submicrometer fluorescence microprobe based on Bragg–Fresnel optics,” Appl. Phys. Lett. 65, 827–829 (1994).
[CrossRef]

Lagomarsino, S.

W. Jark, A. Cedola, S. Di Fonzo, M. Fiordelisi, S. Lagomarsino, N. V. Kovalenko, V. A. Chernov, “High gain beam compression in new-generation thin-film x-ray waveguides,” Appl. Phys. Lett. 78, 1192–1194 (2001).
[CrossRef]

S. Lagomarsino, W. Jark, S. Di Fonzo, A. Cedola, B. Muller, P. Engstrom, C. Riekel, “Submicrometer x-ray beam production by a thin film waveguide,” J. Appl. Phys. 79, 4471–4473 (1996).
[CrossRef]

S. Lagomarsino, A. Cedola, “X-ray microscopy and nanodiffraction,” in Encyclopedia of Nanoscience and Nanotechnology, H. S. Nalwa, ed. (American Scientific, Stevenson Ranch, Calif., 2004), Vol. 10, pp. 681–710.

Lasson, S.

P. Engström, S. Lasson, A. Rindby, A. Buttkewitz, S. Garbe, G. Gaul, A. Knöchel, F. Lechtenberg, “A submicron synchrotron x-ray beam generated by capillary optics,” Nucl. Instrum. Methods Phys. Res. A 302, 547–550 (1991).
[CrossRef]

Lechtenberg, F.

P. Engström, S. Lasson, A. Rindby, A. Buttkewitz, S. Garbe, G. Gaul, A. Knöchel, F. Lechtenberg, “A submicron synchrotron x-ray beam generated by capillary optics,” Nucl. Instrum. Methods Phys. Res. A 302, 547–550 (1991).
[CrossRef]

Lengeler, B.

B. Lengeler, C. G. Schroer, B. Benner, A. Gerhardus, T. F. Gunzler, M. Kuhlmann, J. Meyer, C. Zimprich, “Parabolic refractive x-ray lenses,” J. Synchrotron Radiat. 9, 119–124 (2002).
[CrossRef] [PubMed]

A. Snigirev, V. Kohn, I. Snigireva, B. Lengeler, “A compound refractive lens for focusing high-energy x-rays,” Nature 387, 49–51 (1996).
[CrossRef]

Locklin, S.

H. A. Padmore, G. Ackerman, R. Celestre, C. H. Chang, K. Franck, M. Howells, Z. Hussain, S. Irick, S. Locklin, A. A. MacDowell, J. R. Patel, S. Y. Rah, T. R. Renner, R. Sandler, “Submicron white beam focusing using elliptically bent mirrors,” Synchrotron Radiat. News 10(6), 18–26 (1997).
[CrossRef]

Ludwig, W.

P. Cloetens, O. Hignette, S. Bohic, E. Pereiro, C. Morawe, W. Ludwig, “Hard x-ray phase contrast microscopy and fluorescence mapping with KB optics,” presented at the Eighth International Conference on Synchrotron Radiation Instrumentation, San Francisco, Calif., 24–29 August 2003.

O. Hignette, G. Rostaing, P. Cloetens, A. Rommeveaux, W. Ludwig, A. K. Freund, “Submicron focusing of hard x-rays with reflecting surfaces at the ESRF,” in X-Ray Micro- and Nano-Focusing: Applications and Techniques II, I. McNulty, ed., Proc. SPIE4499, 105–116 (2001).
[CrossRef]

MacDowell, A. A.

H. A. Padmore, G. Ackerman, R. Celestre, C. H. Chang, K. Franck, M. Howells, Z. Hussain, S. Irick, S. Locklin, A. A. MacDowell, J. R. Patel, S. Y. Rah, T. R. Renner, R. Sandler, “Submicron white beam focusing using elliptically bent mirrors,” Synchrotron Radiat. News 10(6), 18–26 (1997).
[CrossRef]

Meyer, J.

B. Lengeler, C. G. Schroer, B. Benner, A. Gerhardus, T. F. Gunzler, M. Kuhlmann, J. Meyer, C. Zimprich, “Parabolic refractive x-ray lenses,” J. Synchrotron Radiat. 9, 119–124 (2002).
[CrossRef] [PubMed]

Morawe, C.

P. Cloetens, O. Hignette, S. Bohic, E. Pereiro, C. Morawe, W. Ludwig, “Hard x-ray phase contrast microscopy and fluorescence mapping with KB optics,” presented at the Eighth International Conference on Synchrotron Radiation Instrumentation, San Francisco, Calif., 24–29 August 2003.

Muller, B.

S. Lagomarsino, W. Jark, S. Di Fonzo, A. Cedola, B. Muller, P. Engstrom, C. Riekel, “Submicrometer x-ray beam production by a thin film waveguide,” J. Appl. Phys. 79, 4471–4473 (1996).
[CrossRef]

Padmore, H. A.

H. A. Padmore, G. Ackerman, R. Celestre, C. H. Chang, K. Franck, M. Howells, Z. Hussain, S. Irick, S. Locklin, A. A. MacDowell, J. R. Patel, S. Y. Rah, T. R. Renner, R. Sandler, “Submicron white beam focusing using elliptically bent mirrors,” Synchrotron Radiat. News 10(6), 18–26 (1997).
[CrossRef]

Patel, J. R.

H. A. Padmore, G. Ackerman, R. Celestre, C. H. Chang, K. Franck, M. Howells, Z. Hussain, S. Irick, S. Locklin, A. A. MacDowell, J. R. Patel, S. Y. Rah, T. R. Renner, R. Sandler, “Submicron white beam focusing using elliptically bent mirrors,” Synchrotron Radiat. News 10(6), 18–26 (1997).
[CrossRef]

Pereiro, E.

P. Cloetens, O. Hignette, S. Bohic, E. Pereiro, C. Morawe, W. Ludwig, “Hard x-ray phase contrast microscopy and fluorescence mapping with KB optics,” presented at the Eighth International Conference on Synchrotron Radiation Instrumentation, San Francisco, Calif., 24–29 August 2003.

Pfeiffer, E.

E. Pfeiffer, C. David, M. Burghammer, C. Riekel, T. Salditt, “Two-dimensional x-ray waveguides and point sources,” Science 12, 230–234 (2002).
[CrossRef]

Rah, S. Y.

H. A. Padmore, G. Ackerman, R. Celestre, C. H. Chang, K. Franck, M. Howells, Z. Hussain, S. Irick, S. Locklin, A. A. MacDowell, J. R. Patel, S. Y. Rah, T. R. Renner, R. Sandler, “Submicron white beam focusing using elliptically bent mirrors,” Synchrotron Radiat. News 10(6), 18–26 (1997).
[CrossRef]

Redkin, S. V.

V. Aristov, Yu. A. Basov, S. V. Redkin, A. Snigirev, V. A. Yunkin, “Bragg zone plates for hard x-ray focusing,” Nucl. Instrum. Methods Phys. Res. A 261, 72–74 (1987).
[CrossRef]

Renner, T. R.

H. A. Padmore, G. Ackerman, R. Celestre, C. H. Chang, K. Franck, M. Howells, Z. Hussain, S. Irick, S. Locklin, A. A. MacDowell, J. R. Patel, S. Y. Rah, T. R. Renner, R. Sandler, “Submicron white beam focusing using elliptically bent mirrors,” Synchrotron Radiat. News 10(6), 18–26 (1997).
[CrossRef]

Riekel, C.

E. Pfeiffer, C. David, M. Burghammer, C. Riekel, T. Salditt, “Two-dimensional x-ray waveguides and point sources,” Science 12, 230–234 (2002).
[CrossRef]

S. Lagomarsino, W. Jark, S. Di Fonzo, A. Cedola, B. Muller, P. Engstrom, C. Riekel, “Submicrometer x-ray beam production by a thin film waveguide,” J. Appl. Phys. 79, 4471–4473 (1996).
[CrossRef]

S. M. Kuznetsov, I. I. Snigireva, A. A. Snigirev, P. Engström, C. Riekel, “Submicrometer fluorescence microprobe based on Bragg–Fresnel optics,” Appl. Phys. Lett. 65, 827–829 (1994).
[CrossRef]

Rindby, A.

P. Engström, S. Lasson, A. Rindby, A. Buttkewitz, S. Garbe, G. Gaul, A. Knöchel, F. Lechtenberg, “A submicron synchrotron x-ray beam generated by capillary optics,” Nucl. Instrum. Methods Phys. Res. A 302, 547–550 (1991).
[CrossRef]

Romanato, F.

E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, R. Barret, “High-efficiency multilevel zone plates for keV x-rays,” Nature 401, 895–298 (1999).
[CrossRef]

Rommeveaux, A.

O. Hignette, G. Rostaing, P. Cloetens, A. Rommeveaux, W. Ludwig, A. K. Freund, “Submicron focusing of hard x-rays with reflecting surfaces at the ESRF,” in X-Ray Micro- and Nano-Focusing: Applications and Techniques II, I. McNulty, ed., Proc. SPIE4499, 105–116 (2001).
[CrossRef]

Rostaing, G.

O. Hignette, G. Rostaing, P. Cloetens, A. Rommeveaux, W. Ludwig, A. K. Freund, “Submicron focusing of hard x-rays with reflecting surfaces at the ESRF,” in X-Ray Micro- and Nano-Focusing: Applications and Techniques II, I. McNulty, ed., Proc. SPIE4499, 105–116 (2001).
[CrossRef]

Salditt, T.

E. Pfeiffer, C. David, M. Burghammer, C. Riekel, T. Salditt, “Two-dimensional x-ray waveguides and point sources,” Science 12, 230–234 (2002).
[CrossRef]

Salomè, M.

C. David, B. Kaulich, R. Barret, M. Salomè, J. Susini, “High-resolution lenses for sub-100 nm x-ray fluorescence microscopy,” Appl. Phys. Lett. 77, 3851–3853 (2000).
[CrossRef]

Sandler, R.

H. A. Padmore, G. Ackerman, R. Celestre, C. H. Chang, K. Franck, M. Howells, Z. Hussain, S. Irick, S. Locklin, A. A. MacDowell, J. R. Patel, S. Y. Rah, T. R. Renner, R. Sandler, “Submicron white beam focusing using elliptically bent mirrors,” Synchrotron Radiat. News 10(6), 18–26 (1997).
[CrossRef]

Schmahl, G.

G. Schmahl, P. Cheng, “X-ray microscopy,” in Handbook on Synchrotron Radiation, S. Ebashi, M. Koch, E. Rubenstein, eds. (Elsevier, Amsterdam, 1991), Vol. 4.

Schroer, C. G.

B. Lengeler, C. G. Schroer, B. Benner, A. Gerhardus, T. F. Gunzler, M. Kuhlmann, J. Meyer, C. Zimprich, “Parabolic refractive x-ray lenses,” J. Synchrotron Radiat. 9, 119–124 (2002).
[CrossRef] [PubMed]

Siddons, D. P.

Y. P. Feng, S. K. Sinha, H. W. Deckman, J. B. Hastings, D. P. Siddons, “X-ray Fraunhofer diffraction patterns from a thin-film waveguide,” Appl. Phys. Lett. 67, 3647–3649 (1995).
[CrossRef]

Sinha, S. K.

Y. P. Feng, S. K. Sinha, H. W. Deckman, J. B. Hastings, D. P. Siddons, “X-ray Fraunhofer diffraction patterns from a thin-film waveguide,” Appl. Phys. Lett. 67, 3647–3649 (1995).
[CrossRef]

Slemzin, V. A.

A. V. Vinogradov, I. A. Brytov, A. Ya. Grudski, M. N. Kogan, I. V. Kozhevnikov, V. A. Slemzin, Reflective X-Ray Optics (Mashinostroenie, Leningrad, 1989).

Snigirev, A.

A. Snigirev, V. Kohn, I. Snigireva, B. Lengeler, “A compound refractive lens for focusing high-energy x-rays,” Nature 387, 49–51 (1996).
[CrossRef]

V. Aristov, Yu. A. Basov, S. V. Redkin, A. Snigirev, V. A. Yunkin, “Bragg zone plates for hard x-ray focusing,” Nucl. Instrum. Methods Phys. Res. A 261, 72–74 (1987).
[CrossRef]

Snigirev, A. A.

S. M. Kuznetsov, I. I. Snigireva, A. A. Snigirev, P. Engström, C. Riekel, “Submicrometer fluorescence microprobe based on Bragg–Fresnel optics,” Appl. Phys. Lett. 65, 827–829 (1994).
[CrossRef]

Snigireva, I.

A. Snigirev, V. Kohn, I. Snigireva, B. Lengeler, “A compound refractive lens for focusing high-energy x-rays,” Nature 387, 49–51 (1996).
[CrossRef]

Snigireva, I. I.

S. M. Kuznetsov, I. I. Snigireva, A. A. Snigirev, P. Engström, C. Riekel, “Submicrometer fluorescence microprobe based on Bragg–Fresnel optics,” Appl. Phys. Lett. 65, 827–829 (1994).
[CrossRef]

Susini, J.

C. David, B. Kaulich, R. Barret, M. Salomè, J. Susini, “High-resolution lenses for sub-100 nm x-ray fluorescence microscopy,” Appl. Phys. Lett. 77, 3851–3853 (2000).
[CrossRef]

E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, R. Barret, “High-efficiency multilevel zone plates for keV x-rays,” Nature 401, 895–298 (1999).
[CrossRef]

Thiel, D. J.

D. H. Bilderback, S. A. Hoffman, D. J. Thiel, “Nanometer spatial resolution achieved in hard x-ray imaging and Laue diffraction applications,” Science 263, 201–203 (1994).
[CrossRef] [PubMed]

Tolstihin, O. I.

A. V. Vinogradov, O. I. Tolstihin, “Concentrators for soft x-ray radiation,” Proc. P. N. Lebedev Phys. Inst. 196, 168–181 (1989).

Vinogradov, A. V.

I. A. Atryukov, A. V. Vinogradov, I. V. Kozhevnikov, “Efficiency of grazing incidence optics: the spiral collimator,” Appl. Opt. 30, 4154–4157 (1991).
[CrossRef]

A. V. Vinogradov, O. I. Tolstihin, “Concentrators for soft x-ray radiation,” Proc. P. N. Lebedev Phys. Inst. 196, 168–181 (1989).

A. V. Vinogradov, N. N. Zorev, I. V. Kozhenikov, “On limiting abilities of optics for soft x-ray region,” Proc. P. N. Lebedev Phys. Inst. 176, 195–210 (1986).

A. V. Vinogradov, I. A. Brytov, A. Ya. Grudski, M. N. Kogan, I. V. Kozhevnikov, V. A. Slemzin, Reflective X-Ray Optics (Mashinostroenie, Leningrad, 1989).

Yunkin, V. A.

V. Aristov, Yu. A. Basov, S. V. Redkin, A. Snigirev, V. A. Yunkin, “Bragg zone plates for hard x-ray focusing,” Nucl. Instrum. Methods Phys. Res. A 261, 72–74 (1987).
[CrossRef]

Zimprich, C.

B. Lengeler, C. G. Schroer, B. Benner, A. Gerhardus, T. F. Gunzler, M. Kuhlmann, J. Meyer, C. Zimprich, “Parabolic refractive x-ray lenses,” J. Synchrotron Radiat. 9, 119–124 (2002).
[CrossRef] [PubMed]

Zorev, N. N.

A. V. Vinogradov, N. N. Zorev, I. V. Kozhenikov, “On limiting abilities of optics for soft x-ray region,” Proc. P. N. Lebedev Phys. Inst. 176, 195–210 (1986).

Appl. Opt. (1)

Appl. Phys. Lett. (4)

Y. P. Feng, S. K. Sinha, H. W. Deckman, J. B. Hastings, D. P. Siddons, “X-ray Fraunhofer diffraction patterns from a thin-film waveguide,” Appl. Phys. Lett. 67, 3647–3649 (1995).
[CrossRef]

C. David, B. Kaulich, R. Barret, M. Salomè, J. Susini, “High-resolution lenses for sub-100 nm x-ray fluorescence microscopy,” Appl. Phys. Lett. 77, 3851–3853 (2000).
[CrossRef]

S. M. Kuznetsov, I. I. Snigireva, A. A. Snigirev, P. Engström, C. Riekel, “Submicrometer fluorescence microprobe based on Bragg–Fresnel optics,” Appl. Phys. Lett. 65, 827–829 (1994).
[CrossRef]

W. Jark, A. Cedola, S. Di Fonzo, M. Fiordelisi, S. Lagomarsino, N. V. Kovalenko, V. A. Chernov, “High gain beam compression in new-generation thin-film x-ray waveguides,” Appl. Phys. Lett. 78, 1192–1194 (2001).
[CrossRef]

J. Appl. Phys. (1)

S. Lagomarsino, W. Jark, S. Di Fonzo, A. Cedola, B. Muller, P. Engstrom, C. Riekel, “Submicrometer x-ray beam production by a thin film waveguide,” J. Appl. Phys. 79, 4471–4473 (1996).
[CrossRef]

J. Synchrotron Radiat. (1)

B. Lengeler, C. G. Schroer, B. Benner, A. Gerhardus, T. F. Gunzler, M. Kuhlmann, J. Meyer, C. Zimprich, “Parabolic refractive x-ray lenses,” J. Synchrotron Radiat. 9, 119–124 (2002).
[CrossRef] [PubMed]

J. X-Ray Sci. Technol. (1)

I. A. Atrukov, I. V. Kozhevnikov, N. I. Kozhevnikova, “Optimum collimator for proximity x-ray lithography—theoretical analysis,” J. X-Ray Sci. Technol. 8, 199–220 (1998).

Nature (2)

A. Snigirev, V. Kohn, I. Snigireva, B. Lengeler, “A compound refractive lens for focusing high-energy x-rays,” Nature 387, 49–51 (1996).
[CrossRef]

E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, R. Barret, “High-efficiency multilevel zone plates for keV x-rays,” Nature 401, 895–298 (1999).
[CrossRef]

Nucl. Instrum. Methods Phys. Res. A (2)

V. Aristov, Yu. A. Basov, S. V. Redkin, A. Snigirev, V. A. Yunkin, “Bragg zone plates for hard x-ray focusing,” Nucl. Instrum. Methods Phys. Res. A 261, 72–74 (1987).
[CrossRef]

P. Engström, S. Lasson, A. Rindby, A. Buttkewitz, S. Garbe, G. Gaul, A. Knöchel, F. Lechtenberg, “A submicron synchrotron x-ray beam generated by capillary optics,” Nucl. Instrum. Methods Phys. Res. A 302, 547–550 (1991).
[CrossRef]

Nucl. Instrum. Methods Phys. Res. B (1)

A. Iida, K. Girano, “Kirkpatrick–Baez optics for a sub-μm synchrotron x-ray microbeam and its applications to x-ray analysis,” Nucl. Instrum. Methods Phys. Res. B 114, 149–153 (1996).
[CrossRef]

Proc. P. N. Lebedev Phys. Inst. (2)

A. V. Vinogradov, N. N. Zorev, I. V. Kozhenikov, “On limiting abilities of optics for soft x-ray region,” Proc. P. N. Lebedev Phys. Inst. 176, 195–210 (1986).

A. V. Vinogradov, O. I. Tolstihin, “Concentrators for soft x-ray radiation,” Proc. P. N. Lebedev Phys. Inst. 196, 168–181 (1989).

Science (2)

D. H. Bilderback, S. A. Hoffman, D. J. Thiel, “Nanometer spatial resolution achieved in hard x-ray imaging and Laue diffraction applications,” Science 263, 201–203 (1994).
[CrossRef] [PubMed]

E. Pfeiffer, C. David, M. Burghammer, C. Riekel, T. Salditt, “Two-dimensional x-ray waveguides and point sources,” Science 12, 230–234 (2002).
[CrossRef]

Synchrotron Radiat. News (1)

H. A. Padmore, G. Ackerman, R. Celestre, C. H. Chang, K. Franck, M. Howells, Z. Hussain, S. Irick, S. Locklin, A. A. MacDowell, J. R. Patel, S. Y. Rah, T. R. Renner, R. Sandler, “Submicron white beam focusing using elliptically bent mirrors,” Synchrotron Radiat. News 10(6), 18–26 (1997).
[CrossRef]

Other (7)

P. Cloetens, O. Hignette, S. Bohic, E. Pereiro, C. Morawe, W. Ludwig, “Hard x-ray phase contrast microscopy and fluorescence mapping with KB optics,” presented at the Eighth International Conference on Synchrotron Radiation Instrumentation, San Francisco, Calif., 24–29 August 2003.

O. Hignette, G. Rostaing, P. Cloetens, A. Rommeveaux, W. Ludwig, A. K. Freund, “Submicron focusing of hard x-rays with reflecting surfaces at the ESRF,” in X-Ray Micro- and Nano-Focusing: Applications and Techniques II, I. McNulty, ed., Proc. SPIE4499, 105–116 (2001).
[CrossRef]

G. Schmahl, P. Cheng, “X-ray microscopy,” in Handbook on Synchrotron Radiation, S. Ebashi, M. Koch, E. Rubenstein, eds. (Elsevier, Amsterdam, 1991), Vol. 4.

S. Lagomarsino, A. Cedola, “X-ray microscopy and nanodiffraction,” in Encyclopedia of Nanoscience and Nanotechnology, H. S. Nalwa, ed. (American Scientific, Stevenson Ranch, Calif., 2004), Vol. 10, pp. 681–710.

W. Yun, ed., X-Ray Microbeam Technology and Applications, Proc. SPIE2516, 1–242 (1995).

I. McNulty, ed., X-Ray Microfocusing: Applications and Techniques, Proc. SPIE3449, 1–218 (1998).
[CrossRef]

A. V. Vinogradov, I. A. Brytov, A. Ya. Grudski, M. N. Kogan, I. V. Kozhevnikov, V. A. Slemzin, Reflective X-Ray Optics (Mashinostroenie, Leningrad, 1989).

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Figures (9)

Fig. 1
Fig. 1

Schematic of an elliptical surface. A mirror (bold arc) is part of the ellipse. Polar system coordinates with origin at focal point F1.

Fig. 2
Fig. 2

a, Dependence of grazing angle θ on polar angle φ (along an elliptical surface) for the rays emitted from focus F1 of the ellipse. b, Enlarged view of the curve displaced in part a. The minimum θ0 and φ0 values [relation (5)] are indicated. Calculations were made for a Ni elliptical mirror (θ c = 0.3°, λ = 0.1 nm) with eccentricity e = 1–1.25 × 10-6.

Fig. 3
Fig. 3

The effectively reflecting surface of the mirror limited by angular interval Φ = φmax - φmin is shown by the bold arc on the ellipse.

Fig. 4
Fig. 4

Critical circle given by Eq. (12) (long-dashed curve) and its intersection with the ellipse. The effectively reflecting mirror surface is the portion of ellipse between the two intersection points (shaded arc).

Fig. 5
Fig. 5

Schematic of a focusing mirror. Magnification parameter M is given by Eq. (16).

Fig. 6
Fig. 6

The parts of the magnification circles are shown as bold curves. For illustration purposes we considered θ c = 10°; otherwise, for more-realistic grazing angles, all the circles would appear as straight lines.

Fig. 7
Fig. 7

Shadowed area, location of the effectively reflecting surface of the focusing mirror.

Fig. 8
Fig. 8

a Dependence of angular acceptance Φ on eccentricity e for magnification parameter M = 0.1. b Dependence of maximal angular acceptance Φmax on magnification parameter M with optimal eccentricity e max. Calculations were made for a Ni elliptical mirror (θ c = 0.3°, λ = 0.1 nm).

Fig. 9
Fig. 9

Efficiency and gain of the focusing Ni elliptical mirror relative to the length of the mirror evaluated by ray-tracing simulation. a, Synchrotron radiation source with size S = 100 μm, wavelength λ = 0.1 nm, and mirror with eccentricity 1 - e = 1.16 × 10-7, magnification factor M = 10-2, and distance between focal points 2c = 40 m. Optimal length L opt (dashed line) according to relation (33), L opt ∼ 0.6 m. b, Laboratory source with size S = 15 μm, wavelength λ = 0.154 nm, and mirror with eccentricity 1 - e = 2.18 × 10-6, magnification factor M = 10-1, and distance between focal points 2c = 0.2 m. Optimal length L opt (dashed line) according to relation (33), L opt ∼ 0.027 m.

Tables (1)

Tables Icon

Table 1 Estimation of Normalized Eccentricity, Relation (31), Maximal Acceptance Angle, Relation (30), and Optimal Length, Relation (33), for Several Magnification Valuesa

Equations (36)

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ρφ=P1-e cos φ,P=c 1-e2e,
θ<θc, θc=2δ,
θ=arctanρφρφ, ρφ=dρdφ.
θ=arctan1-e cos φe sin φφ2+1-eφ.
θ0=φ0=arccose=arctan1-e2e21-e.
0<1-e<θc22=δ.
θc=arctan1-e cos φe sin φ.
Φ=φmax-φmin2θc2-21-e1/2,φminmaxθc±θc2-21-e1/2,
L=ρmin cos φmin-ρmax cos φmax2c1-21-eθc21/2.
L=2c sin Φsin 2θcc Φθc.
e=cos θccosφ-θc=1sin φ tan θc+cos φ.
ρ=2 csin 2θccosφ+π2-2θc.
ρcr=csin 2θc, φcr=-π2-2θc.
Rcr=csin 2θc.
y+c cot 2θc2+x2=c2sin2 2θc.
M=ρ1ρ, ρ+ρ1=2a,
Mφ221-ε.
ρ2+4c2-4cρ cos φ=ρ12=M2ρ2.
ρ2-2ρ 2c1-M2cos φ+2c1-M22=4c2M21-M22.
φmag=0,ρmag=2c1-M2.
φmag=π,ρmag=2cM2-1.
Rmag=2cM1-M2.
y2+x±dmag2=Rmag2.
φi2θcM, ei=cos θccosφi-θc φi1-2θc2M.
ρm=ceρ0-R0=2ce1+M, φm=arccos1+e2-M1-e22e2M1-e1/2.
ρex=ce1-e2sin2 θc-sin θce2-cos2 θc1/2, φex=arccoscos2 θc+sin θce2-cos2 θc1/2eθc-θc2-21-e1/2.
ρent cos φent=ρm cos φm-L2=2ρm cos φm-ρex cos φex,
ρent=2ρm-ρex, φent=arccos1e1-P2ρm-ρexφm2+φm2-φex21-α1/2,
Φe=φent-φex,
Φe2φm2-φex21/2-φex2Φ0-Φ02Φ0+φm,
emax1-θc22M1+M.
L=2ρex cos φex-ρm cos φm2c1-1-eθc2/21/2-1-M1+M.
Lopt2c1-2-1+M1+M.
eopt1-12 θc2M,
Φmax56 θcM,
Lopt3cM.

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