Abstract

An analytical approach has been developed to derive aberration effects in parabolic and elliptic multilayer optics with weak interaction between photons and matter. The method is based on geometrical ray tracing including refraction effects up to the first order of the refractive index decrement δ. In the parabolic case, the derivation leads to simple parametric equations for the caustic shape. In the elliptic case, the analytical results more involved, but can be well approximated by the parabolic solution. Both geometries are compared with regard to the fundamental impact on their focusing properties.

© 2008 Optical Society of America

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  1. W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, "Soft X-ray microscopy at a spatial resolution better than 15 nm," Nature 435, 1210-1213 (2005).
    [CrossRef] [PubMed]
  2. C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Küchler, "Hard X-ray nanoprobe based on refractive X-ray lenses," Appl. Phys. Lett. 87, 124103 (2005).
    [CrossRef]
  3. A. Jarre, C. Fuhse, C. Ollinger, J. Seeger, R. Tucoulou, and T. Salditt, "Two-dimensional hard X-ray beam compression by combined focusing and waveguide optics," Phys. Rev. Lett. 94, 074801 (2005).
    [CrossRef] [PubMed]
  4. D. H. Bilderback, S. A. Hoffman, and D. J. Thiel, "Nanometer spatial resolution achieved in hard X-ray imaging and Laue diffraction experiments," Science 263, 201-203 (1994).
    [CrossRef] [PubMed]
  5. H. Mimura, S. Matsuyama, H. Yumoto, H. Hara, K. Yamamura, Y. Sano, M. Shibahara, K. Endo, Y. Mori, Y. Nishino, K. Tamasaku, M. Yabashi, T. Ishikawa, and K. Yamauchi, "Hard X-ray diffraction-limited nanofocusing with Kirkpatrick-Baez mirrors," J. J. Appl. Phys. 44, L539 - L542 (2005).
  6. W. Liu, G. E. Ice, J. Z. Tischler, A. Khounsary, C. Liu, L. Assoufid, and A.T. Macrander, "Short focal length Kirkpatrick-Baez mirrors for a hard X-ray nanoprobe," Rev. Sci. Instr. 76, 113701 (2005).
    [CrossRef]
  7. Ch. Morawe, O. Hignette, P. Cloetens, W. Ludwig, Ch. Borel, P. Bernard, and A. Rommeveaux, "Graded multilayers for focusing hard X rays below 50 nm," Proc. SPIE 6317, 63170F (2006).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  10. K. Yamauchi, K. Yamamura, H. Mimura, Y. Sano, A. Saito, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, Y. Mori, "Nearly diffraction-limited line focusing of hard X-ray beam with an elliptically figured mirror," J. Synchrotron Rad. 9, 313 - 316 (2002).
    [CrossRef]
  11. C. M. Kewish, L. Assoufid, A. T. Macrander, and J. Qian, "Wave-optical simulation of hard X-ray nanofocusing by precisely figured elliptical mirrors," Appl. Opt. 46, 2010 - 2021 (2007).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  14. H. Mimura, S. Matsuyama, H. Yumoto, S. Handa, T. Kimura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, K. Yamauchi, "Reflective optics for sub-10nm hard X-ray focusing," Proc. SPIE 6705, 67050L (2007).
    [CrossRef]
  15. A. Authier, Dynamical Theory of X-ray Diffraction, IUCr monographs, (Oxford, University Press. 2001)

2007

C. M. Kewish, L. Assoufid, A. T. Macrander, and J. Qian, "Wave-optical simulation of hard X-ray nanofocusing by precisely figured elliptical mirrors," Appl. Opt. 46, 2010 - 2021 (2007).
[CrossRef] [PubMed]

H. Yan, J. Maser, A.T. Macrander, Q. Shen, S. Vogt, G.B. Stephenson, H.C. Kang, "Takagi-Taupin description of X-ray dynamical diffraction from diffractive optics with large numerical aperture," Phys. Rev. B 76, 115438 (2007).
[CrossRef]

H. Mimura, S. Matsuyama, H. Yumoto, S. Handa, T. Kimura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, K. Yamauchi, "Reflective optics for sub-10nm hard X-ray focusing," Proc. SPIE 6705, 67050L (2007).
[CrossRef]

2006

C. G. Schroer, "Focusing hard X rays to nanometer dimensions using Fresnel zone plates," Phys. Rev. B 74, 033405 (2006).
[CrossRef]

Ch. Morawe, O. Hignette, P. Cloetens, W. Ludwig, Ch. Borel, P. Bernard, and A. Rommeveaux, "Graded multilayers for focusing hard X rays below 50 nm," Proc. SPIE 6317, 63170F (2006).
[CrossRef]

F. Pfeiffer, C. David, J. F. van der Veen, and C. Bergemann, "Nanometer focusing properties of Fresnel zone plates described by dynamical diffraction theory," Phys. Rev. B 73, 245331 (2006).
[CrossRef]

2005

C. G. Schroer and B. Lengeler, "Focusing hard X rays to nanometer dimensions by adiabatically focusing lenses," Phys. Rev. Lett. 94, 054802 (2005).
[CrossRef] [PubMed]

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, "Soft X-ray microscopy at a spatial resolution better than 15 nm," Nature 435, 1210-1213 (2005).
[CrossRef] [PubMed]

C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Küchler, "Hard X-ray nanoprobe based on refractive X-ray lenses," Appl. Phys. Lett. 87, 124103 (2005).
[CrossRef]

A. Jarre, C. Fuhse, C. Ollinger, J. Seeger, R. Tucoulou, and T. Salditt, "Two-dimensional hard X-ray beam compression by combined focusing and waveguide optics," Phys. Rev. Lett. 94, 074801 (2005).
[CrossRef] [PubMed]

H. Mimura, S. Matsuyama, H. Yumoto, H. Hara, K. Yamamura, Y. Sano, M. Shibahara, K. Endo, Y. Mori, Y. Nishino, K. Tamasaku, M. Yabashi, T. Ishikawa, and K. Yamauchi, "Hard X-ray diffraction-limited nanofocusing with Kirkpatrick-Baez mirrors," J. J. Appl. Phys. 44, L539 - L542 (2005).

W. Liu, G. E. Ice, J. Z. Tischler, A. Khounsary, C. Liu, L. Assoufid, and A.T. Macrander, "Short focal length Kirkpatrick-Baez mirrors for a hard X-ray nanoprobe," Rev. Sci. Instr. 76, 113701 (2005).
[CrossRef]

2002

K. Yamauchi, K. Yamamura, H. Mimura, Y. Sano, A. Saito, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, Y. Mori, "Nearly diffraction-limited line focusing of hard X-ray beam with an elliptically figured mirror," J. Synchrotron Rad. 9, 313 - 316 (2002).
[CrossRef]

1994

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

Anderson, E. H.

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, "Soft X-ray microscopy at a spatial resolution better than 15 nm," Nature 435, 1210-1213 (2005).
[CrossRef] [PubMed]

Assoufid, L.

C. M. Kewish, L. Assoufid, A. T. Macrander, and J. Qian, "Wave-optical simulation of hard X-ray nanofocusing by precisely figured elliptical mirrors," Appl. Opt. 46, 2010 - 2021 (2007).
[CrossRef] [PubMed]

W. Liu, G. E. Ice, J. Z. Tischler, A. Khounsary, C. Liu, L. Assoufid, and A.T. Macrander, "Short focal length Kirkpatrick-Baez mirrors for a hard X-ray nanoprobe," Rev. Sci. Instr. 76, 113701 (2005).
[CrossRef]

Attwood, D. T.

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, "Soft X-ray microscopy at a spatial resolution better than 15 nm," Nature 435, 1210-1213 (2005).
[CrossRef] [PubMed]

Bergemann, C.

F. Pfeiffer, C. David, J. F. van der Veen, and C. Bergemann, "Nanometer focusing properties of Fresnel zone plates described by dynamical diffraction theory," Phys. Rev. B 73, 245331 (2006).
[CrossRef]

Bernard, P.

Ch. Morawe, O. Hignette, P. Cloetens, W. Ludwig, Ch. Borel, P. Bernard, and A. Rommeveaux, "Graded multilayers for focusing hard X rays below 50 nm," Proc. SPIE 6317, 63170F (2006).
[CrossRef]

Bilderback, D. H.

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

Borel, Ch.

Ch. Morawe, O. Hignette, P. Cloetens, W. Ludwig, Ch. Borel, P. Bernard, and A. Rommeveaux, "Graded multilayers for focusing hard X rays below 50 nm," Proc. SPIE 6317, 63170F (2006).
[CrossRef]

Boye, P.

C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Küchler, "Hard X-ray nanoprobe based on refractive X-ray lenses," Appl. Phys. Lett. 87, 124103 (2005).
[CrossRef]

Burghammer, M.

C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Küchler, "Hard X-ray nanoprobe based on refractive X-ray lenses," Appl. Phys. Lett. 87, 124103 (2005).
[CrossRef]

Chao, W.

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, "Soft X-ray microscopy at a spatial resolution better than 15 nm," Nature 435, 1210-1213 (2005).
[CrossRef] [PubMed]

Cloetens, P.

Ch. Morawe, O. Hignette, P. Cloetens, W. Ludwig, Ch. Borel, P. Bernard, and A. Rommeveaux, "Graded multilayers for focusing hard X rays below 50 nm," Proc. SPIE 6317, 63170F (2006).
[CrossRef]

David, C.

F. Pfeiffer, C. David, J. F. van der Veen, and C. Bergemann, "Nanometer focusing properties of Fresnel zone plates described by dynamical diffraction theory," Phys. Rev. B 73, 245331 (2006).
[CrossRef]

Endo, K.

H. Mimura, S. Matsuyama, H. Yumoto, H. Hara, K. Yamamura, Y. Sano, M. Shibahara, K. Endo, Y. Mori, Y. Nishino, K. Tamasaku, M. Yabashi, T. Ishikawa, and K. Yamauchi, "Hard X-ray diffraction-limited nanofocusing with Kirkpatrick-Baez mirrors," J. J. Appl. Phys. 44, L539 - L542 (2005).

Feldkamp, J.

C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Küchler, "Hard X-ray nanoprobe based on refractive X-ray lenses," Appl. Phys. Lett. 87, 124103 (2005).
[CrossRef]

Fuhse, C.

A. Jarre, C. Fuhse, C. Ollinger, J. Seeger, R. Tucoulou, and T. Salditt, "Two-dimensional hard X-ray beam compression by combined focusing and waveguide optics," Phys. Rev. Lett. 94, 074801 (2005).
[CrossRef] [PubMed]

Handa, S.

H. Mimura, S. Matsuyama, H. Yumoto, S. Handa, T. Kimura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, K. Yamauchi, "Reflective optics for sub-10nm hard X-ray focusing," Proc. SPIE 6705, 67050L (2007).
[CrossRef]

Hara, H.

H. Mimura, S. Matsuyama, H. Yumoto, H. Hara, K. Yamamura, Y. Sano, M. Shibahara, K. Endo, Y. Mori, Y. Nishino, K. Tamasaku, M. Yabashi, T. Ishikawa, and K. Yamauchi, "Hard X-ray diffraction-limited nanofocusing with Kirkpatrick-Baez mirrors," J. J. Appl. Phys. 44, L539 - L542 (2005).

Harteneck, B. D.

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, "Soft X-ray microscopy at a spatial resolution better than 15 nm," Nature 435, 1210-1213 (2005).
[CrossRef] [PubMed]

Hignette, O.

Ch. Morawe, O. Hignette, P. Cloetens, W. Ludwig, Ch. Borel, P. Bernard, and A. Rommeveaux, "Graded multilayers for focusing hard X rays below 50 nm," Proc. SPIE 6317, 63170F (2006).
[CrossRef]

Hoffman, S. A.

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

Ice, G. E.

W. Liu, G. E. Ice, J. Z. Tischler, A. Khounsary, C. Liu, L. Assoufid, and A.T. Macrander, "Short focal length Kirkpatrick-Baez mirrors for a hard X-ray nanoprobe," Rev. Sci. Instr. 76, 113701 (2005).
[CrossRef]

Ishikawa, T.

H. Mimura, S. Matsuyama, H. Yumoto, S. Handa, T. Kimura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, K. Yamauchi, "Reflective optics for sub-10nm hard X-ray focusing," Proc. SPIE 6705, 67050L (2007).
[CrossRef]

H. Mimura, S. Matsuyama, H. Yumoto, H. Hara, K. Yamamura, Y. Sano, M. Shibahara, K. Endo, Y. Mori, Y. Nishino, K. Tamasaku, M. Yabashi, T. Ishikawa, and K. Yamauchi, "Hard X-ray diffraction-limited nanofocusing with Kirkpatrick-Baez mirrors," J. J. Appl. Phys. 44, L539 - L542 (2005).

K. Yamauchi, K. Yamamura, H. Mimura, Y. Sano, A. Saito, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, Y. Mori, "Nearly diffraction-limited line focusing of hard X-ray beam with an elliptically figured mirror," J. Synchrotron Rad. 9, 313 - 316 (2002).
[CrossRef]

Jarre, A.

A. Jarre, C. Fuhse, C. Ollinger, J. Seeger, R. Tucoulou, and T. Salditt, "Two-dimensional hard X-ray beam compression by combined focusing and waveguide optics," Phys. Rev. Lett. 94, 074801 (2005).
[CrossRef] [PubMed]

Kang, H.C.

H. Yan, J. Maser, A.T. Macrander, Q. Shen, S. Vogt, G.B. Stephenson, H.C. Kang, "Takagi-Taupin description of X-ray dynamical diffraction from diffractive optics with large numerical aperture," Phys. Rev. B 76, 115438 (2007).
[CrossRef]

Kewish, C. M.

Khounsary, A.

W. Liu, G. E. Ice, J. Z. Tischler, A. Khounsary, C. Liu, L. Assoufid, and A.T. Macrander, "Short focal length Kirkpatrick-Baez mirrors for a hard X-ray nanoprobe," Rev. Sci. Instr. 76, 113701 (2005).
[CrossRef]

Kimura, T.

H. Mimura, S. Matsuyama, H. Yumoto, S. Handa, T. Kimura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, K. Yamauchi, "Reflective optics for sub-10nm hard X-ray focusing," Proc. SPIE 6705, 67050L (2007).
[CrossRef]

Küchler, M.

C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Küchler, "Hard X-ray nanoprobe based on refractive X-ray lenses," Appl. Phys. Lett. 87, 124103 (2005).
[CrossRef]

Kurapova, O.

C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Küchler, "Hard X-ray nanoprobe based on refractive X-ray lenses," Appl. Phys. Lett. 87, 124103 (2005).
[CrossRef]

Lengeler, B.

C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Küchler, "Hard X-ray nanoprobe based on refractive X-ray lenses," Appl. Phys. Lett. 87, 124103 (2005).
[CrossRef]

C. G. Schroer and B. Lengeler, "Focusing hard X rays to nanometer dimensions by adiabatically focusing lenses," Phys. Rev. Lett. 94, 054802 (2005).
[CrossRef] [PubMed]

Liddle, J. A.

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, "Soft X-ray microscopy at a spatial resolution better than 15 nm," Nature 435, 1210-1213 (2005).
[CrossRef] [PubMed]

Liu, C.

W. Liu, G. E. Ice, J. Z. Tischler, A. Khounsary, C. Liu, L. Assoufid, and A.T. Macrander, "Short focal length Kirkpatrick-Baez mirrors for a hard X-ray nanoprobe," Rev. Sci. Instr. 76, 113701 (2005).
[CrossRef]

Liu, W.

W. Liu, G. E. Ice, J. Z. Tischler, A. Khounsary, C. Liu, L. Assoufid, and A.T. Macrander, "Short focal length Kirkpatrick-Baez mirrors for a hard X-ray nanoprobe," Rev. Sci. Instr. 76, 113701 (2005).
[CrossRef]

Ludwig, W.

Ch. Morawe, O. Hignette, P. Cloetens, W. Ludwig, Ch. Borel, P. Bernard, and A. Rommeveaux, "Graded multilayers for focusing hard X rays below 50 nm," Proc. SPIE 6317, 63170F (2006).
[CrossRef]

Macrander, A. T.

Macrander, A.T.

H. Yan, J. Maser, A.T. Macrander, Q. Shen, S. Vogt, G.B. Stephenson, H.C. Kang, "Takagi-Taupin description of X-ray dynamical diffraction from diffractive optics with large numerical aperture," Phys. Rev. B 76, 115438 (2007).
[CrossRef]

W. Liu, G. E. Ice, J. Z. Tischler, A. Khounsary, C. Liu, L. Assoufid, and A.T. Macrander, "Short focal length Kirkpatrick-Baez mirrors for a hard X-ray nanoprobe," Rev. Sci. Instr. 76, 113701 (2005).
[CrossRef]

Maser, J.

H. Yan, J. Maser, A.T. Macrander, Q. Shen, S. Vogt, G.B. Stephenson, H.C. Kang, "Takagi-Taupin description of X-ray dynamical diffraction from diffractive optics with large numerical aperture," Phys. Rev. B 76, 115438 (2007).
[CrossRef]

Matsuyama, S.

H. Mimura, S. Matsuyama, H. Yumoto, S. Handa, T. Kimura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, K. Yamauchi, "Reflective optics for sub-10nm hard X-ray focusing," Proc. SPIE 6705, 67050L (2007).
[CrossRef]

H. Mimura, S. Matsuyama, H. Yumoto, H. Hara, K. Yamamura, Y. Sano, M. Shibahara, K. Endo, Y. Mori, Y. Nishino, K. Tamasaku, M. Yabashi, T. Ishikawa, and K. Yamauchi, "Hard X-ray diffraction-limited nanofocusing with Kirkpatrick-Baez mirrors," J. J. Appl. Phys. 44, L539 - L542 (2005).

Mimura, H.

H. Mimura, S. Matsuyama, H. Yumoto, S. Handa, T. Kimura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, K. Yamauchi, "Reflective optics for sub-10nm hard X-ray focusing," Proc. SPIE 6705, 67050L (2007).
[CrossRef]

H. Mimura, S. Matsuyama, H. Yumoto, H. Hara, K. Yamamura, Y. Sano, M. Shibahara, K. Endo, Y. Mori, Y. Nishino, K. Tamasaku, M. Yabashi, T. Ishikawa, and K. Yamauchi, "Hard X-ray diffraction-limited nanofocusing with Kirkpatrick-Baez mirrors," J. J. Appl. Phys. 44, L539 - L542 (2005).

K. Yamauchi, K. Yamamura, H. Mimura, Y. Sano, A. Saito, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, Y. Mori, "Nearly diffraction-limited line focusing of hard X-ray beam with an elliptically figured mirror," J. Synchrotron Rad. 9, 313 - 316 (2002).
[CrossRef]

Morawe, Ch.

Ch. Morawe, O. Hignette, P. Cloetens, W. Ludwig, Ch. Borel, P. Bernard, and A. Rommeveaux, "Graded multilayers for focusing hard X rays below 50 nm," Proc. SPIE 6317, 63170F (2006).
[CrossRef]

Mori, Y.

H. Mimura, S. Matsuyama, H. Yumoto, H. Hara, K. Yamamura, Y. Sano, M. Shibahara, K. Endo, Y. Mori, Y. Nishino, K. Tamasaku, M. Yabashi, T. Ishikawa, and K. Yamauchi, "Hard X-ray diffraction-limited nanofocusing with Kirkpatrick-Baez mirrors," J. J. Appl. Phys. 44, L539 - L542 (2005).

K. Yamauchi, K. Yamamura, H. Mimura, Y. Sano, A. Saito, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, Y. Mori, "Nearly diffraction-limited line focusing of hard X-ray beam with an elliptically figured mirror," J. Synchrotron Rad. 9, 313 - 316 (2002).
[CrossRef]

Nishino, Y.

H. Mimura, S. Matsuyama, H. Yumoto, S. Handa, T. Kimura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, K. Yamauchi, "Reflective optics for sub-10nm hard X-ray focusing," Proc. SPIE 6705, 67050L (2007).
[CrossRef]

H. Mimura, S. Matsuyama, H. Yumoto, H. Hara, K. Yamamura, Y. Sano, M. Shibahara, K. Endo, Y. Mori, Y. Nishino, K. Tamasaku, M. Yabashi, T. Ishikawa, and K. Yamauchi, "Hard X-ray diffraction-limited nanofocusing with Kirkpatrick-Baez mirrors," J. J. Appl. Phys. 44, L539 - L542 (2005).

Ollinger, C.

A. Jarre, C. Fuhse, C. Ollinger, J. Seeger, R. Tucoulou, and T. Salditt, "Two-dimensional hard X-ray beam compression by combined focusing and waveguide optics," Phys. Rev. Lett. 94, 074801 (2005).
[CrossRef] [PubMed]

Patommel, J.

C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Küchler, "Hard X-ray nanoprobe based on refractive X-ray lenses," Appl. Phys. Lett. 87, 124103 (2005).
[CrossRef]

Pfeiffer, F.

F. Pfeiffer, C. David, J. F. van der Veen, and C. Bergemann, "Nanometer focusing properties of Fresnel zone plates described by dynamical diffraction theory," Phys. Rev. B 73, 245331 (2006).
[CrossRef]

Qian, J.

Riekel, C.

C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Küchler, "Hard X-ray nanoprobe based on refractive X-ray lenses," Appl. Phys. Lett. 87, 124103 (2005).
[CrossRef]

Rommeveaux, A.

Ch. Morawe, O. Hignette, P. Cloetens, W. Ludwig, Ch. Borel, P. Bernard, and A. Rommeveaux, "Graded multilayers for focusing hard X rays below 50 nm," Proc. SPIE 6317, 63170F (2006).
[CrossRef]

Saito, A.

K. Yamauchi, K. Yamamura, H. Mimura, Y. Sano, A. Saito, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, Y. Mori, "Nearly diffraction-limited line focusing of hard X-ray beam with an elliptically figured mirror," J. Synchrotron Rad. 9, 313 - 316 (2002).
[CrossRef]

Salditt, T.

A. Jarre, C. Fuhse, C. Ollinger, J. Seeger, R. Tucoulou, and T. Salditt, "Two-dimensional hard X-ray beam compression by combined focusing and waveguide optics," Phys. Rev. Lett. 94, 074801 (2005).
[CrossRef] [PubMed]

Sano, Y.

H. Mimura, S. Matsuyama, H. Yumoto, S. Handa, T. Kimura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, K. Yamauchi, "Reflective optics for sub-10nm hard X-ray focusing," Proc. SPIE 6705, 67050L (2007).
[CrossRef]

H. Mimura, S. Matsuyama, H. Yumoto, H. Hara, K. Yamamura, Y. Sano, M. Shibahara, K. Endo, Y. Mori, Y. Nishino, K. Tamasaku, M. Yabashi, T. Ishikawa, and K. Yamauchi, "Hard X-ray diffraction-limited nanofocusing with Kirkpatrick-Baez mirrors," J. J. Appl. Phys. 44, L539 - L542 (2005).

K. Yamauchi, K. Yamamura, H. Mimura, Y. Sano, A. Saito, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, Y. Mori, "Nearly diffraction-limited line focusing of hard X-ray beam with an elliptically figured mirror," J. Synchrotron Rad. 9, 313 - 316 (2002).
[CrossRef]

Schroer, C. G.

C. G. Schroer, "Focusing hard X rays to nanometer dimensions using Fresnel zone plates," Phys. Rev. B 74, 033405 (2006).
[CrossRef]

C. G. Schroer and B. Lengeler, "Focusing hard X rays to nanometer dimensions by adiabatically focusing lenses," Phys. Rev. Lett. 94, 054802 (2005).
[CrossRef] [PubMed]

C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Küchler, "Hard X-ray nanoprobe based on refractive X-ray lenses," Appl. Phys. Lett. 87, 124103 (2005).
[CrossRef]

Seeger, J.

A. Jarre, C. Fuhse, C. Ollinger, J. Seeger, R. Tucoulou, and T. Salditt, "Two-dimensional hard X-ray beam compression by combined focusing and waveguide optics," Phys. Rev. Lett. 94, 074801 (2005).
[CrossRef] [PubMed]

Shen, Q.

H. Yan, J. Maser, A.T. Macrander, Q. Shen, S. Vogt, G.B. Stephenson, H.C. Kang, "Takagi-Taupin description of X-ray dynamical diffraction from diffractive optics with large numerical aperture," Phys. Rev. B 76, 115438 (2007).
[CrossRef]

Shibahara, M.

H. Mimura, S. Matsuyama, H. Yumoto, H. Hara, K. Yamamura, Y. Sano, M. Shibahara, K. Endo, Y. Mori, Y. Nishino, K. Tamasaku, M. Yabashi, T. Ishikawa, and K. Yamauchi, "Hard X-ray diffraction-limited nanofocusing with Kirkpatrick-Baez mirrors," J. J. Appl. Phys. 44, L539 - L542 (2005).

Souvorov, A.

K. Yamauchi, K. Yamamura, H. Mimura, Y. Sano, A. Saito, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, Y. Mori, "Nearly diffraction-limited line focusing of hard X-ray beam with an elliptically figured mirror," J. Synchrotron Rad. 9, 313 - 316 (2002).
[CrossRef]

Stephenson, G.B.

H. Yan, J. Maser, A.T. Macrander, Q. Shen, S. Vogt, G.B. Stephenson, H.C. Kang, "Takagi-Taupin description of X-ray dynamical diffraction from diffractive optics with large numerical aperture," Phys. Rev. B 76, 115438 (2007).
[CrossRef]

Tamasaku, K.

H. Mimura, S. Matsuyama, H. Yumoto, S. Handa, T. Kimura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, K. Yamauchi, "Reflective optics for sub-10nm hard X-ray focusing," Proc. SPIE 6705, 67050L (2007).
[CrossRef]

H. Mimura, S. Matsuyama, H. Yumoto, H. Hara, K. Yamamura, Y. Sano, M. Shibahara, K. Endo, Y. Mori, Y. Nishino, K. Tamasaku, M. Yabashi, T. Ishikawa, and K. Yamauchi, "Hard X-ray diffraction-limited nanofocusing with Kirkpatrick-Baez mirrors," J. J. Appl. Phys. 44, L539 - L542 (2005).

K. Yamauchi, K. Yamamura, H. Mimura, Y. Sano, A. Saito, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, Y. Mori, "Nearly diffraction-limited line focusing of hard X-ray beam with an elliptically figured mirror," J. Synchrotron Rad. 9, 313 - 316 (2002).
[CrossRef]

Thiel, D. J.

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

Tischler, J. Z.

W. Liu, G. E. Ice, J. Z. Tischler, A. Khounsary, C. Liu, L. Assoufid, and A.T. Macrander, "Short focal length Kirkpatrick-Baez mirrors for a hard X-ray nanoprobe," Rev. Sci. Instr. 76, 113701 (2005).
[CrossRef]

Tucoulou, R.

A. Jarre, C. Fuhse, C. Ollinger, J. Seeger, R. Tucoulou, and T. Salditt, "Two-dimensional hard X-ray beam compression by combined focusing and waveguide optics," Phys. Rev. Lett. 94, 074801 (2005).
[CrossRef] [PubMed]

van der Hart, A.

C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Küchler, "Hard X-ray nanoprobe based on refractive X-ray lenses," Appl. Phys. Lett. 87, 124103 (2005).
[CrossRef]

van der Veen, J. F.

F. Pfeiffer, C. David, J. F. van der Veen, and C. Bergemann, "Nanometer focusing properties of Fresnel zone plates described by dynamical diffraction theory," Phys. Rev. B 73, 245331 (2006).
[CrossRef]

Vincze, L.

C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Küchler, "Hard X-ray nanoprobe based on refractive X-ray lenses," Appl. Phys. Lett. 87, 124103 (2005).
[CrossRef]

Vogt, S.

H. Yan, J. Maser, A.T. Macrander, Q. Shen, S. Vogt, G.B. Stephenson, H.C. Kang, "Takagi-Taupin description of X-ray dynamical diffraction from diffractive optics with large numerical aperture," Phys. Rev. B 76, 115438 (2007).
[CrossRef]

Yabashi, M.

H. Mimura, S. Matsuyama, H. Yumoto, S. Handa, T. Kimura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, K. Yamauchi, "Reflective optics for sub-10nm hard X-ray focusing," Proc. SPIE 6705, 67050L (2007).
[CrossRef]

H. Mimura, S. Matsuyama, H. Yumoto, H. Hara, K. Yamamura, Y. Sano, M. Shibahara, K. Endo, Y. Mori, Y. Nishino, K. Tamasaku, M. Yabashi, T. Ishikawa, and K. Yamauchi, "Hard X-ray diffraction-limited nanofocusing with Kirkpatrick-Baez mirrors," J. J. Appl. Phys. 44, L539 - L542 (2005).

K. Yamauchi, K. Yamamura, H. Mimura, Y. Sano, A. Saito, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, Y. Mori, "Nearly diffraction-limited line focusing of hard X-ray beam with an elliptically figured mirror," J. Synchrotron Rad. 9, 313 - 316 (2002).
[CrossRef]

Yamamura, K.

H. Mimura, S. Matsuyama, H. Yumoto, H. Hara, K. Yamamura, Y. Sano, M. Shibahara, K. Endo, Y. Mori, Y. Nishino, K. Tamasaku, M. Yabashi, T. Ishikawa, and K. Yamauchi, "Hard X-ray diffraction-limited nanofocusing with Kirkpatrick-Baez mirrors," J. J. Appl. Phys. 44, L539 - L542 (2005).

K. Yamauchi, K. Yamamura, H. Mimura, Y. Sano, A. Saito, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, Y. Mori, "Nearly diffraction-limited line focusing of hard X-ray beam with an elliptically figured mirror," J. Synchrotron Rad. 9, 313 - 316 (2002).
[CrossRef]

Yamauchi, K.

H. Mimura, S. Matsuyama, H. Yumoto, S. Handa, T. Kimura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, K. Yamauchi, "Reflective optics for sub-10nm hard X-ray focusing," Proc. SPIE 6705, 67050L (2007).
[CrossRef]

H. Mimura, S. Matsuyama, H. Yumoto, H. Hara, K. Yamamura, Y. Sano, M. Shibahara, K. Endo, Y. Mori, Y. Nishino, K. Tamasaku, M. Yabashi, T. Ishikawa, and K. Yamauchi, "Hard X-ray diffraction-limited nanofocusing with Kirkpatrick-Baez mirrors," J. J. Appl. Phys. 44, L539 - L542 (2005).

K. Yamauchi, K. Yamamura, H. Mimura, Y. Sano, A. Saito, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, Y. Mori, "Nearly diffraction-limited line focusing of hard X-ray beam with an elliptically figured mirror," J. Synchrotron Rad. 9, 313 - 316 (2002).
[CrossRef]

Yan, H.

H. Yan, J. Maser, A.T. Macrander, Q. Shen, S. Vogt, G.B. Stephenson, H.C. Kang, "Takagi-Taupin description of X-ray dynamical diffraction from diffractive optics with large numerical aperture," Phys. Rev. B 76, 115438 (2007).
[CrossRef]

Yumoto, H.

H. Mimura, S. Matsuyama, H. Yumoto, S. Handa, T. Kimura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, K. Yamauchi, "Reflective optics for sub-10nm hard X-ray focusing," Proc. SPIE 6705, 67050L (2007).
[CrossRef]

H. Mimura, S. Matsuyama, H. Yumoto, H. Hara, K. Yamamura, Y. Sano, M. Shibahara, K. Endo, Y. Mori, Y. Nishino, K. Tamasaku, M. Yabashi, T. Ishikawa, and K. Yamauchi, "Hard X-ray diffraction-limited nanofocusing with Kirkpatrick-Baez mirrors," J. J. Appl. Phys. 44, L539 - L542 (2005).

Appl. Opt.

Appl. Phys. Lett.

C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Küchler, "Hard X-ray nanoprobe based on refractive X-ray lenses," Appl. Phys. Lett. 87, 124103 (2005).
[CrossRef]

J. J. Appl. Phys.

H. Mimura, S. Matsuyama, H. Yumoto, H. Hara, K. Yamamura, Y. Sano, M. Shibahara, K. Endo, Y. Mori, Y. Nishino, K. Tamasaku, M. Yabashi, T. Ishikawa, and K. Yamauchi, "Hard X-ray diffraction-limited nanofocusing with Kirkpatrick-Baez mirrors," J. J. Appl. Phys. 44, L539 - L542 (2005).

J. Synchrotron Rad.

K. Yamauchi, K. Yamamura, H. Mimura, Y. Sano, A. Saito, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, Y. Mori, "Nearly diffraction-limited line focusing of hard X-ray beam with an elliptically figured mirror," J. Synchrotron Rad. 9, 313 - 316 (2002).
[CrossRef]

Nature

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, "Soft X-ray microscopy at a spatial resolution better than 15 nm," Nature 435, 1210-1213 (2005).
[CrossRef] [PubMed]

Phys. Rev. B

F. Pfeiffer, C. David, J. F. van der Veen, and C. Bergemann, "Nanometer focusing properties of Fresnel zone plates described by dynamical diffraction theory," Phys. Rev. B 73, 245331 (2006).
[CrossRef]

C. G. Schroer, "Focusing hard X rays to nanometer dimensions using Fresnel zone plates," Phys. Rev. B 74, 033405 (2006).
[CrossRef]

H. Yan, J. Maser, A.T. Macrander, Q. Shen, S. Vogt, G.B. Stephenson, H.C. Kang, "Takagi-Taupin description of X-ray dynamical diffraction from diffractive optics with large numerical aperture," Phys. Rev. B 76, 115438 (2007).
[CrossRef]

Phys. Rev. Lett.

C. G. Schroer and B. Lengeler, "Focusing hard X rays to nanometer dimensions by adiabatically focusing lenses," Phys. Rev. Lett. 94, 054802 (2005).
[CrossRef] [PubMed]

A. Jarre, C. Fuhse, C. Ollinger, J. Seeger, R. Tucoulou, and T. Salditt, "Two-dimensional hard X-ray beam compression by combined focusing and waveguide optics," Phys. Rev. Lett. 94, 074801 (2005).
[CrossRef] [PubMed]

Proc. SPIE

Ch. Morawe, O. Hignette, P. Cloetens, W. Ludwig, Ch. Borel, P. Bernard, and A. Rommeveaux, "Graded multilayers for focusing hard X rays below 50 nm," Proc. SPIE 6317, 63170F (2006).
[CrossRef]

H. Mimura, S. Matsuyama, H. Yumoto, S. Handa, T. Kimura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, K. Yamauchi, "Reflective optics for sub-10nm hard X-ray focusing," Proc. SPIE 6705, 67050L (2007).
[CrossRef]

Rev. Sci. Instr.

W. Liu, G. E. Ice, J. Z. Tischler, A. Khounsary, C. Liu, L. Assoufid, and A.T. Macrander, "Short focal length Kirkpatrick-Baez mirrors for a hard X-ray nanoprobe," Rev. Sci. Instr. 76, 113701 (2005).
[CrossRef]

Science

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

Other

A. Authier, Dynamical Theory of X-ray Diffraction, IUCr monographs, (Oxford, University Press. 2001)

Cited By

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Figures (4)

Fig. 1.
Fig. 1.

Focusing geometry of a parabolic RML. The red solid line shows a ray reflected from the entrance RML surface reaching the ideal focus F. The blue solid line indicates a ray that is first refracted when crossing (P) in point C, then reflected at point N on (P’), and again refracted when crossing (P) in point D. The green solid line illustrates the resulting envelope of all rays reflected from (P’). The polar angle φ is defined by the virtual ray reflected in point N without refraction in the RML medium (broken line). The dimensions are not in scale.

Fig. 2.
Fig. 2.

Focusing geometry of an elliptic RML using a notation similar to that used in Fig. 1.

Fig. 3.
Fig. 3.

Positive branch of the caustic curve y (x) (red) and corresponding grazing incidence angle θ (x) (blue) for a given set of parameters. The insert is a zoom into the zone around the ideal focus and the corresponding angles of incidence. Arrows indicate the evolution of the curves starting at normal incidence. The curves clearly indicate the “left turn” of the caustic when starting from normal incidence.

Fig. 4.
Fig. 4.

Overview of a set of caustic curves. y(x(θ)) (red lines) plotted for increasing values of s (red arrow). y(x(s)) (blue lines) is given for increasing θ (blue arrow). Decreasing s and increasing θ clearly reduce the aberrations caused by the optical system.

Equations (40)

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

ρ = p 1 + cos φ and ρ = p + 2 s 1 + cos φ = p 1 + cos φ = kp 1 + cos φ , with k = p p
t = tan ( φ 2 ) ,
ε C = δ tan ( φ C 2 ) δ tan ( φ A 2 ) = δkt and ε D = δt
x D ( t ) = p cos φ D 1 + cos φ D = p [ 1 t 2 + ht 2 ( 1 + t 2 ) ] 2
y D ( t ) = p sin φ D 1 + cos φ D = pt [ 1 h ( 1 + t 2 ) 2 ]
m ( t ) = tan ( φ + ε C ε D ) = 2 t 1 t 2 + ( 1 + t 2 1 t 2 ) 2 δ ( k 1 ) t
Y m ( t ) X = y D ( t ) m ( t ) x D ( t )
m ( t ) X = ( y D mx D )
X ( t ) = ( m 1 x 0 + m 0 x 1 y 1 ) m′ 0 , Y ( t ) = X ( t ) + y 1 m 1 x 0 m 0 x 1
X ( t ) = δ S ( 1 + s p ) ( 1 + 6 t 2 3 t 4 )
Y ( t ) = δ S ( 1 + s p ) 8 t 3
x ( t ) 3 δ s ( 1 + s p ) t 4
y ( t ) = 8 δs ( 1 + s p ) t 3
x ( t ) 3 δs t 4
y ( t ) = 8 δs t 3
y ( x ) 8 3 3/4 ( δ s ) 1/4 x 3/4
x ( t ) δ s ( 1 + s p ) ( 1 + 6 t 2 )
y ( t ) = 8 δ s ( 1 + s p ) t 3
x ( t ) δs ( 1 + 6 t 2 )
y ( t ) = 8 δs t 3
y ( x ) ± 8 6 3/2 ( δ s ) −1/2 x 3/2
ρ S = p 1ecosα ρ F = p 1+ecosϕ ,where c=SF/2=ea,p= a 2 c 2 a =(1 e 2 )a
ε C = δ tan ( ω A 2 ) = sin α 1 e cos α , ε D = δ tan ( ω B 2 ) = sin φ 1 + e cos φ
η = ε C SA SN = ε C p ( 1 e′ cos α ) p ( 1 e cos α ) = k sin α 1 e cos α ( 1 e cos α ) 2
β = η BN BF = η [ p ( 1 + e cos φ ) p ( 1 + e cos φ ) 1 ] = η k 1 + ( ke e ) cos φ 1 + e cos φ
x D = p cos ( φ β ) 1 + e cos ( φ β ) = p cos φ 1 + e cos φ + β p sin φ ( 1 + e cos φ ) 2
y D = p sin ( φ β ) 1 + e cos ( φ β ) = p sin φ 1 + e cos φ β p ( e + cos φ ) ( 1 + e cos φ ) 2
m = tan ( φ + η ε D ) = tan φ F + ( η ε D ) ( 1 + tan 2 φ )
1 e cos α = 1 ( 1 g + g 2 2 ) ( 1 g 2 t 2 2 ) = g ( 1 + g t 2 1 2 )
1 e cos α = 1 ( 1 g + g 2 2 ) ( 1 g 2 t 2 2 ) = g ( 1 + g k 2 t 2 1 2 )
1 e cos α ( 1 e cos α ) 2 = k g [ 1 + k g t 2 1 2 g ( k 2 t 2 1 ) ]
k e e = k ( 1 g ) ( 1 k g ) = k 1 ; 1 + cos φ 1 + e cos φ = 1 + g 1 t 2 2
η = k δ t [ 1 + g ( 1 t 2 k 2 + k t 2 1 2 ) ] ; η ε D = e δ ( k 1 ) t [ 1 + g ( 1 + t 2 ) ( 1 + k ) 2 ]
β = h t ( 1 g k 2 t 2 ) , where h = k ( k 1 ) δ
x D = p 1 t 2 2 [ 1 + g 1 t 2 2 ] + pht 2 1 + t 2 2 [ 1 + g ( 1 t 2 k 2 t 2 ) ]
y D = pt [ 1 + g 1 t 2 2 ] pht [ 1 g k 2 t 2 ] 1 + t 2 2 [ 1 + g 1 3 t 2 2 ]
m = 2 t 1 t 2 + t ( 1 + t 2 1 t 2 ) 2 δ ( k 1 ) { 1 g 2 ( 1 + k ) [ 1 + t 2 ( 1 + k ) ] }
x D = p 1 t 2 2 [ 1 + g 1 t 2 2 ] + p δ k ( k 1 ) t 2 1 + t 2 2
y D = p t [ 1 + g 1 t 2 2 ] p δ k ( k 1 ) t 1 + t 2 2
m = 2 t 1 t 2 + t ( 1 + t 2 1 t 2 ) 2 δ ( k 1 )

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