Abstract

The aperture of refractive X-ray lenses is limited by absorption and geometry. We introduce a specific simulation method to develop an aperture-optimized lens design for hard X-ray full field microscopy. The aperture-optimized lens, referred to as Taille-lens, allows for high spatial resolution as well as homogeneous image quality. This is achieved by the individual adaptation of the apertures of hundreds of lens elements of an X-ray imaging lens to the respective microscopy setup. For full field microscopy, the simulations result in lenses with both a large entrance and exit aperture and lens elements with smaller apertures in the middle of the lens.

© 2016 Optical Society of America

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References

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  1. T. Tomie, “X-ray lens,” Japanese patent 6-045288 (February 18, 1994); U.S. patents 5,594, 773 (January 14, 1997) and 5,684, 852 (November 4, 1997).
  2. A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, “A compound refractive lens for focusing high-energy x-rays,” Nature 384, 49–51 (1996).
    [Crossref]
  3. B. Lengeler, C. G. Schroer, M. Kuhlmann, B. Benner, T. F. Gunzler, O. Kurapova, A. Somogyi, A. Snigirev, and I. Snigireva, “Beryllium parabolic refractive x-ray lenses,” AIP Conf Proc 705, 748–751 (2004).
    [Crossref]
  4. B. Lengeler, C. G. Schroer, B. Benner, A. Gerhardus, T. F. Gunzler, M. Kuhlmann, J. Meyer, and C. Zimprich, “Parabolic refractive x-ray lenses,” J. Synchrotron Rad. 9, 119–124 (2002).
    [Crossref]
  5. A. Stein, K. Evans-Lutterodt, N. Bozovic, and A. Taylor, “Fabrication of silicon kinoform lenses for hard x-ray focusing by electron beam lithography and deep reactive ion etching,” J. Vac. Sci. Technol. B 26 (1), 122–127 (2008).
    [Crossref]
  6. B. Nhammer, C. David, H. Rothuizen, J. Hoszowska, and A. Simionovici, “Deep reactive ion etching of silicon and diamond for the fabrication of planar refractive hard x-ray lenses,” Microelectron Eng. 67–68, 453–460 (2003).
    [Crossref]
  7. Y. Ohishi, A. Q. R. Baron, M. Ishii, T. Ishikawa, and O. Shimomura, “Refractive x-ray lens for high pressure experiments at SPring-8,” Nucl. Instr. Meth. Phys. Res. A 467–468, 962–965 (2001).
    [Crossref]
  8. F. Marschall, A. Last, M. Simon, M. Kluge, V. Nazmov, H. Vogt, M. Ogurreck, I. Greving, and J. Mohr, “X-ray full field microscopy at 30 keV,” J. Phys.: Conf. Ser. 499, 012007 (2014).
  9. E. Reznikova, T. Weitkamp, V. Nazmov, M. Simon, A. Last, and V. Saile, “Transmission hard x-ray microscope with increased view field using planar refractive objectives and condensers made of SU-8 polymer,” J. Phys.: Conf. Ser. 186, 012070 (2009).
  10. V. Nazmov, E. Reznikova, A. Last, J. Mohr, V. Saile, M. DiMichiel, and J. Gttert, “Crossed planar x-ray lenses made from nickel for x-ray micro focusing and imaging applications”, Nucl. Instr. Meth. Phys. Res. A,  582, 120–122 (2007).
    [Crossref]
  11. A. Snigirev, I. Snigireva, G. Vaughan, J. Wright, M. Rossat, A. Bytchkov, and C. Curfs, “High energy x-ray transfocator based on Al parabolic refractive lenses for focusing and collimation,” J. Phys.: Conf. Ser. 186, 012073 (2009).
  12. C. G. Schroer and B. Lengeler, “Focusing hard x-rays to nanometer dimensions by adiabatically focusing lenses,” Phys. Rev. Lett. 94, 054802 (2005).
    [Crossref]
  13. C. G. Schroer, T. F. Gnzler, B. Benner, M. Kuhlmann, J. Tmmler, B. Lengeler, C. Rau, T. Weitkamp, A. Snigirev, and I. Snigireva, “Hard x-ray full field microscopy and magnifying microtomography using compound refractive lenses,” Nucl. Instr. Meth. Phys. Res. A 467–468, 966–969 (2001).
    [Crossref]
  14. V. G. Kohn, “An exact theory of imaging with a parabolic continuously refractive x-ray lens,” J. Exp. Theor. Phys. 97, 204–215 (2003).
    [Crossref]
  15. V. Saile, LIGA and Its Applications (Wiley-VCH Verlag GmbH & Co. KGaA, 2008).
    [Crossref]
  16. A. Thompson, I. Lindau, D. Attwood, Y. Liu, and H. Winick, “X-ray data booklet,” Lawrence Berkeley National Lab, http://xdb.lbl.gov (2009).
  17. R. Simon, V. Nazmov, E. Reznikova, J. Mohr, and V. Saile, “Hard x-ray imaging and microscopy with lithographic CRL developed at ANKA synchrotron radiation facility,” IPAP Conf. Series 7, 115–116 (2005).

2014 (1)

F. Marschall, A. Last, M. Simon, M. Kluge, V. Nazmov, H. Vogt, M. Ogurreck, I. Greving, and J. Mohr, “X-ray full field microscopy at 30 keV,” J. Phys.: Conf. Ser. 499, 012007 (2014).

2009 (2)

E. Reznikova, T. Weitkamp, V. Nazmov, M. Simon, A. Last, and V. Saile, “Transmission hard x-ray microscope with increased view field using planar refractive objectives and condensers made of SU-8 polymer,” J. Phys.: Conf. Ser. 186, 012070 (2009).

A. Snigirev, I. Snigireva, G. Vaughan, J. Wright, M. Rossat, A. Bytchkov, and C. Curfs, “High energy x-ray transfocator based on Al parabolic refractive lenses for focusing and collimation,” J. Phys.: Conf. Ser. 186, 012073 (2009).

2008 (1)

A. Stein, K. Evans-Lutterodt, N. Bozovic, and A. Taylor, “Fabrication of silicon kinoform lenses for hard x-ray focusing by electron beam lithography and deep reactive ion etching,” J. Vac. Sci. Technol. B 26 (1), 122–127 (2008).
[Crossref]

2007 (1)

V. Nazmov, E. Reznikova, A. Last, J. Mohr, V. Saile, M. DiMichiel, and J. Gttert, “Crossed planar x-ray lenses made from nickel for x-ray micro focusing and imaging applications”, Nucl. Instr. Meth. Phys. Res. A,  582, 120–122 (2007).
[Crossref]

2005 (2)

C. G. Schroer and B. Lengeler, “Focusing hard x-rays to nanometer dimensions by adiabatically focusing lenses,” Phys. Rev. Lett. 94, 054802 (2005).
[Crossref]

R. Simon, V. Nazmov, E. Reznikova, J. Mohr, and V. Saile, “Hard x-ray imaging and microscopy with lithographic CRL developed at ANKA synchrotron radiation facility,” IPAP Conf. Series 7, 115–116 (2005).

2004 (1)

B. Lengeler, C. G. Schroer, M. Kuhlmann, B. Benner, T. F. Gunzler, O. Kurapova, A. Somogyi, A. Snigirev, and I. Snigireva, “Beryllium parabolic refractive x-ray lenses,” AIP Conf Proc 705, 748–751 (2004).
[Crossref]

2003 (2)

B. Nhammer, C. David, H. Rothuizen, J. Hoszowska, and A. Simionovici, “Deep reactive ion etching of silicon and diamond for the fabrication of planar refractive hard x-ray lenses,” Microelectron Eng. 67–68, 453–460 (2003).
[Crossref]

V. G. Kohn, “An exact theory of imaging with a parabolic continuously refractive x-ray lens,” J. Exp. Theor. Phys. 97, 204–215 (2003).
[Crossref]

2002 (1)

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

2001 (2)

Y. Ohishi, A. Q. R. Baron, M. Ishii, T. Ishikawa, and O. Shimomura, “Refractive x-ray lens for high pressure experiments at SPring-8,” Nucl. Instr. Meth. Phys. Res. A 467–468, 962–965 (2001).
[Crossref]

C. G. Schroer, T. F. Gnzler, B. Benner, M. Kuhlmann, J. Tmmler, B. Lengeler, C. Rau, T. Weitkamp, A. Snigirev, and I. Snigireva, “Hard x-ray full field microscopy and magnifying microtomography using compound refractive lenses,” Nucl. Instr. Meth. Phys. Res. A 467–468, 966–969 (2001).
[Crossref]

1996 (1)

A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, “A compound refractive lens for focusing high-energy x-rays,” Nature 384, 49–51 (1996).
[Crossref]

Attwood, D.

A. Thompson, I. Lindau, D. Attwood, Y. Liu, and H. Winick, “X-ray data booklet,” Lawrence Berkeley National Lab, http://xdb.lbl.gov (2009).

Baron, A. Q. R.

Y. Ohishi, A. Q. R. Baron, M. Ishii, T. Ishikawa, and O. Shimomura, “Refractive x-ray lens for high pressure experiments at SPring-8,” Nucl. Instr. Meth. Phys. Res. A 467–468, 962–965 (2001).
[Crossref]

Benner, B.

B. Lengeler, C. G. Schroer, M. Kuhlmann, B. Benner, T. F. Gunzler, O. Kurapova, A. Somogyi, A. Snigirev, and I. Snigireva, “Beryllium parabolic refractive x-ray lenses,” AIP Conf Proc 705, 748–751 (2004).
[Crossref]

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

C. G. Schroer, T. F. Gnzler, B. Benner, M. Kuhlmann, J. Tmmler, B. Lengeler, C. Rau, T. Weitkamp, A. Snigirev, and I. Snigireva, “Hard x-ray full field microscopy and magnifying microtomography using compound refractive lenses,” Nucl. Instr. Meth. Phys. Res. A 467–468, 966–969 (2001).
[Crossref]

Bozovic, N.

A. Stein, K. Evans-Lutterodt, N. Bozovic, and A. Taylor, “Fabrication of silicon kinoform lenses for hard x-ray focusing by electron beam lithography and deep reactive ion etching,” J. Vac. Sci. Technol. B 26 (1), 122–127 (2008).
[Crossref]

Bytchkov, A.

A. Snigirev, I. Snigireva, G. Vaughan, J. Wright, M. Rossat, A. Bytchkov, and C. Curfs, “High energy x-ray transfocator based on Al parabolic refractive lenses for focusing and collimation,” J. Phys.: Conf. Ser. 186, 012073 (2009).

Curfs, C.

A. Snigirev, I. Snigireva, G. Vaughan, J. Wright, M. Rossat, A. Bytchkov, and C. Curfs, “High energy x-ray transfocator based on Al parabolic refractive lenses for focusing and collimation,” J. Phys.: Conf. Ser. 186, 012073 (2009).

David, C.

B. Nhammer, C. David, H. Rothuizen, J. Hoszowska, and A. Simionovici, “Deep reactive ion etching of silicon and diamond for the fabrication of planar refractive hard x-ray lenses,” Microelectron Eng. 67–68, 453–460 (2003).
[Crossref]

DiMichiel, M.

V. Nazmov, E. Reznikova, A. Last, J. Mohr, V. Saile, M. DiMichiel, and J. Gttert, “Crossed planar x-ray lenses made from nickel for x-ray micro focusing and imaging applications”, Nucl. Instr. Meth. Phys. Res. A,  582, 120–122 (2007).
[Crossref]

Evans-Lutterodt, K.

A. Stein, K. Evans-Lutterodt, N. Bozovic, and A. Taylor, “Fabrication of silicon kinoform lenses for hard x-ray focusing by electron beam lithography and deep reactive ion etching,” J. Vac. Sci. Technol. B 26 (1), 122–127 (2008).
[Crossref]

Gerhardus, A.

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

Gnzler, T. F.

C. G. Schroer, T. F. Gnzler, B. Benner, M. Kuhlmann, J. Tmmler, B. Lengeler, C. Rau, T. Weitkamp, A. Snigirev, and I. Snigireva, “Hard x-ray full field microscopy and magnifying microtomography using compound refractive lenses,” Nucl. Instr. Meth. Phys. Res. A 467–468, 966–969 (2001).
[Crossref]

Greving, I.

F. Marschall, A. Last, M. Simon, M. Kluge, V. Nazmov, H. Vogt, M. Ogurreck, I. Greving, and J. Mohr, “X-ray full field microscopy at 30 keV,” J. Phys.: Conf. Ser. 499, 012007 (2014).

Gttert, J.

V. Nazmov, E. Reznikova, A. Last, J. Mohr, V. Saile, M. DiMichiel, and J. Gttert, “Crossed planar x-ray lenses made from nickel for x-ray micro focusing and imaging applications”, Nucl. Instr. Meth. Phys. Res. A,  582, 120–122 (2007).
[Crossref]

Gunzler, T. F.

B. Lengeler, C. G. Schroer, M. Kuhlmann, B. Benner, T. F. Gunzler, O. Kurapova, A. Somogyi, A. Snigirev, and I. Snigireva, “Beryllium parabolic refractive x-ray lenses,” AIP Conf Proc 705, 748–751 (2004).
[Crossref]

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

Hoszowska, J.

B. Nhammer, C. David, H. Rothuizen, J. Hoszowska, and A. Simionovici, “Deep reactive ion etching of silicon and diamond for the fabrication of planar refractive hard x-ray lenses,” Microelectron Eng. 67–68, 453–460 (2003).
[Crossref]

Ishii, M.

Y. Ohishi, A. Q. R. Baron, M. Ishii, T. Ishikawa, and O. Shimomura, “Refractive x-ray lens for high pressure experiments at SPring-8,” Nucl. Instr. Meth. Phys. Res. A 467–468, 962–965 (2001).
[Crossref]

Ishikawa, T.

Y. Ohishi, A. Q. R. Baron, M. Ishii, T. Ishikawa, and O. Shimomura, “Refractive x-ray lens for high pressure experiments at SPring-8,” Nucl. Instr. Meth. Phys. Res. A 467–468, 962–965 (2001).
[Crossref]

Kluge, M.

F. Marschall, A. Last, M. Simon, M. Kluge, V. Nazmov, H. Vogt, M. Ogurreck, I. Greving, and J. Mohr, “X-ray full field microscopy at 30 keV,” J. Phys.: Conf. Ser. 499, 012007 (2014).

Kohn, V.

A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, “A compound refractive lens for focusing high-energy x-rays,” Nature 384, 49–51 (1996).
[Crossref]

Kohn, V. G.

V. G. Kohn, “An exact theory of imaging with a parabolic continuously refractive x-ray lens,” J. Exp. Theor. Phys. 97, 204–215 (2003).
[Crossref]

Kuhlmann, M.

B. Lengeler, C. G. Schroer, M. Kuhlmann, B. Benner, T. F. Gunzler, O. Kurapova, A. Somogyi, A. Snigirev, and I. Snigireva, “Beryllium parabolic refractive x-ray lenses,” AIP Conf Proc 705, 748–751 (2004).
[Crossref]

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

C. G. Schroer, T. F. Gnzler, B. Benner, M. Kuhlmann, J. Tmmler, B. Lengeler, C. Rau, T. Weitkamp, A. Snigirev, and I. Snigireva, “Hard x-ray full field microscopy and magnifying microtomography using compound refractive lenses,” Nucl. Instr. Meth. Phys. Res. A 467–468, 966–969 (2001).
[Crossref]

Kurapova, O.

B. Lengeler, C. G. Schroer, M. Kuhlmann, B. Benner, T. F. Gunzler, O. Kurapova, A. Somogyi, A. Snigirev, and I. Snigireva, “Beryllium parabolic refractive x-ray lenses,” AIP Conf Proc 705, 748–751 (2004).
[Crossref]

Last, A.

F. Marschall, A. Last, M. Simon, M. Kluge, V. Nazmov, H. Vogt, M. Ogurreck, I. Greving, and J. Mohr, “X-ray full field microscopy at 30 keV,” J. Phys.: Conf. Ser. 499, 012007 (2014).

E. Reznikova, T. Weitkamp, V. Nazmov, M. Simon, A. Last, and V. Saile, “Transmission hard x-ray microscope with increased view field using planar refractive objectives and condensers made of SU-8 polymer,” J. Phys.: Conf. Ser. 186, 012070 (2009).

V. Nazmov, E. Reznikova, A. Last, J. Mohr, V. Saile, M. DiMichiel, and J. Gttert, “Crossed planar x-ray lenses made from nickel for x-ray micro focusing and imaging applications”, Nucl. Instr. Meth. Phys. Res. A,  582, 120–122 (2007).
[Crossref]

Lengeler, B.

C. G. Schroer and B. Lengeler, “Focusing hard x-rays to nanometer dimensions by adiabatically focusing lenses,” Phys. Rev. Lett. 94, 054802 (2005).
[Crossref]

B. Lengeler, C. G. Schroer, M. Kuhlmann, B. Benner, T. F. Gunzler, O. Kurapova, A. Somogyi, A. Snigirev, and I. Snigireva, “Beryllium parabolic refractive x-ray lenses,” AIP Conf Proc 705, 748–751 (2004).
[Crossref]

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

C. G. Schroer, T. F. Gnzler, B. Benner, M. Kuhlmann, J. Tmmler, B. Lengeler, C. Rau, T. Weitkamp, A. Snigirev, and I. Snigireva, “Hard x-ray full field microscopy and magnifying microtomography using compound refractive lenses,” Nucl. Instr. Meth. Phys. Res. A 467–468, 966–969 (2001).
[Crossref]

A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, “A compound refractive lens for focusing high-energy x-rays,” Nature 384, 49–51 (1996).
[Crossref]

Lindau, I.

A. Thompson, I. Lindau, D. Attwood, Y. Liu, and H. Winick, “X-ray data booklet,” Lawrence Berkeley National Lab, http://xdb.lbl.gov (2009).

Liu, Y.

A. Thompson, I. Lindau, D. Attwood, Y. Liu, and H. Winick, “X-ray data booklet,” Lawrence Berkeley National Lab, http://xdb.lbl.gov (2009).

Marschall, F.

F. Marschall, A. Last, M. Simon, M. Kluge, V. Nazmov, H. Vogt, M. Ogurreck, I. Greving, and J. Mohr, “X-ray full field microscopy at 30 keV,” J. Phys.: Conf. Ser. 499, 012007 (2014).

Meyer, J.

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

Mohr, J.

F. Marschall, A. Last, M. Simon, M. Kluge, V. Nazmov, H. Vogt, M. Ogurreck, I. Greving, and J. Mohr, “X-ray full field microscopy at 30 keV,” J. Phys.: Conf. Ser. 499, 012007 (2014).

V. Nazmov, E. Reznikova, A. Last, J. Mohr, V. Saile, M. DiMichiel, and J. Gttert, “Crossed planar x-ray lenses made from nickel for x-ray micro focusing and imaging applications”, Nucl. Instr. Meth. Phys. Res. A,  582, 120–122 (2007).
[Crossref]

R. Simon, V. Nazmov, E. Reznikova, J. Mohr, and V. Saile, “Hard x-ray imaging and microscopy with lithographic CRL developed at ANKA synchrotron radiation facility,” IPAP Conf. Series 7, 115–116 (2005).

Nazmov, V.

F. Marschall, A. Last, M. Simon, M. Kluge, V. Nazmov, H. Vogt, M. Ogurreck, I. Greving, and J. Mohr, “X-ray full field microscopy at 30 keV,” J. Phys.: Conf. Ser. 499, 012007 (2014).

E. Reznikova, T. Weitkamp, V. Nazmov, M. Simon, A. Last, and V. Saile, “Transmission hard x-ray microscope with increased view field using planar refractive objectives and condensers made of SU-8 polymer,” J. Phys.: Conf. Ser. 186, 012070 (2009).

V. Nazmov, E. Reznikova, A. Last, J. Mohr, V. Saile, M. DiMichiel, and J. Gttert, “Crossed planar x-ray lenses made from nickel for x-ray micro focusing and imaging applications”, Nucl. Instr. Meth. Phys. Res. A,  582, 120–122 (2007).
[Crossref]

R. Simon, V. Nazmov, E. Reznikova, J. Mohr, and V. Saile, “Hard x-ray imaging and microscopy with lithographic CRL developed at ANKA synchrotron radiation facility,” IPAP Conf. Series 7, 115–116 (2005).

Nhammer, B.

B. Nhammer, C. David, H. Rothuizen, J. Hoszowska, and A. Simionovici, “Deep reactive ion etching of silicon and diamond for the fabrication of planar refractive hard x-ray lenses,” Microelectron Eng. 67–68, 453–460 (2003).
[Crossref]

Ogurreck, M.

F. Marschall, A. Last, M. Simon, M. Kluge, V. Nazmov, H. Vogt, M. Ogurreck, I. Greving, and J. Mohr, “X-ray full field microscopy at 30 keV,” J. Phys.: Conf. Ser. 499, 012007 (2014).

Ohishi, Y.

Y. Ohishi, A. Q. R. Baron, M. Ishii, T. Ishikawa, and O. Shimomura, “Refractive x-ray lens for high pressure experiments at SPring-8,” Nucl. Instr. Meth. Phys. Res. A 467–468, 962–965 (2001).
[Crossref]

Rau, C.

C. G. Schroer, T. F. Gnzler, B. Benner, M. Kuhlmann, J. Tmmler, B. Lengeler, C. Rau, T. Weitkamp, A. Snigirev, and I. Snigireva, “Hard x-ray full field microscopy and magnifying microtomography using compound refractive lenses,” Nucl. Instr. Meth. Phys. Res. A 467–468, 966–969 (2001).
[Crossref]

Reznikova, E.

E. Reznikova, T. Weitkamp, V. Nazmov, M. Simon, A. Last, and V. Saile, “Transmission hard x-ray microscope with increased view field using planar refractive objectives and condensers made of SU-8 polymer,” J. Phys.: Conf. Ser. 186, 012070 (2009).

V. Nazmov, E. Reznikova, A. Last, J. Mohr, V. Saile, M. DiMichiel, and J. Gttert, “Crossed planar x-ray lenses made from nickel for x-ray micro focusing and imaging applications”, Nucl. Instr. Meth. Phys. Res. A,  582, 120–122 (2007).
[Crossref]

R. Simon, V. Nazmov, E. Reznikova, J. Mohr, and V. Saile, “Hard x-ray imaging and microscopy with lithographic CRL developed at ANKA synchrotron radiation facility,” IPAP Conf. Series 7, 115–116 (2005).

Rossat, M.

A. Snigirev, I. Snigireva, G. Vaughan, J. Wright, M. Rossat, A. Bytchkov, and C. Curfs, “High energy x-ray transfocator based on Al parabolic refractive lenses for focusing and collimation,” J. Phys.: Conf. Ser. 186, 012073 (2009).

Rothuizen, H.

B. Nhammer, C. David, H. Rothuizen, J. Hoszowska, and A. Simionovici, “Deep reactive ion etching of silicon and diamond for the fabrication of planar refractive hard x-ray lenses,” Microelectron Eng. 67–68, 453–460 (2003).
[Crossref]

Saile, V.

E. Reznikova, T. Weitkamp, V. Nazmov, M. Simon, A. Last, and V. Saile, “Transmission hard x-ray microscope with increased view field using planar refractive objectives and condensers made of SU-8 polymer,” J. Phys.: Conf. Ser. 186, 012070 (2009).

V. Nazmov, E. Reznikova, A. Last, J. Mohr, V. Saile, M. DiMichiel, and J. Gttert, “Crossed planar x-ray lenses made from nickel for x-ray micro focusing and imaging applications”, Nucl. Instr. Meth. Phys. Res. A,  582, 120–122 (2007).
[Crossref]

R. Simon, V. Nazmov, E. Reznikova, J. Mohr, and V. Saile, “Hard x-ray imaging and microscopy with lithographic CRL developed at ANKA synchrotron radiation facility,” IPAP Conf. Series 7, 115–116 (2005).

V. Saile, LIGA and Its Applications (Wiley-VCH Verlag GmbH & Co. KGaA, 2008).
[Crossref]

Schroer, C. G.

C. G. Schroer and B. Lengeler, “Focusing hard x-rays to nanometer dimensions by adiabatically focusing lenses,” Phys. Rev. Lett. 94, 054802 (2005).
[Crossref]

B. Lengeler, C. G. Schroer, M. Kuhlmann, B. Benner, T. F. Gunzler, O. Kurapova, A. Somogyi, A. Snigirev, and I. Snigireva, “Beryllium parabolic refractive x-ray lenses,” AIP Conf Proc 705, 748–751 (2004).
[Crossref]

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

C. G. Schroer, T. F. Gnzler, B. Benner, M. Kuhlmann, J. Tmmler, B. Lengeler, C. Rau, T. Weitkamp, A. Snigirev, and I. Snigireva, “Hard x-ray full field microscopy and magnifying microtomography using compound refractive lenses,” Nucl. Instr. Meth. Phys. Res. A 467–468, 966–969 (2001).
[Crossref]

Shimomura, O.

Y. Ohishi, A. Q. R. Baron, M. Ishii, T. Ishikawa, and O. Shimomura, “Refractive x-ray lens for high pressure experiments at SPring-8,” Nucl. Instr. Meth. Phys. Res. A 467–468, 962–965 (2001).
[Crossref]

Simionovici, A.

B. Nhammer, C. David, H. Rothuizen, J. Hoszowska, and A. Simionovici, “Deep reactive ion etching of silicon and diamond for the fabrication of planar refractive hard x-ray lenses,” Microelectron Eng. 67–68, 453–460 (2003).
[Crossref]

Simon, M.

F. Marschall, A. Last, M. Simon, M. Kluge, V. Nazmov, H. Vogt, M. Ogurreck, I. Greving, and J. Mohr, “X-ray full field microscopy at 30 keV,” J. Phys.: Conf. Ser. 499, 012007 (2014).

E. Reznikova, T. Weitkamp, V. Nazmov, M. Simon, A. Last, and V. Saile, “Transmission hard x-ray microscope with increased view field using planar refractive objectives and condensers made of SU-8 polymer,” J. Phys.: Conf. Ser. 186, 012070 (2009).

Simon, R.

R. Simon, V. Nazmov, E. Reznikova, J. Mohr, and V. Saile, “Hard x-ray imaging and microscopy with lithographic CRL developed at ANKA synchrotron radiation facility,” IPAP Conf. Series 7, 115–116 (2005).

Snigirev, A.

A. Snigirev, I. Snigireva, G. Vaughan, J. Wright, M. Rossat, A. Bytchkov, and C. Curfs, “High energy x-ray transfocator based on Al parabolic refractive lenses for focusing and collimation,” J. Phys.: Conf. Ser. 186, 012073 (2009).

B. Lengeler, C. G. Schroer, M. Kuhlmann, B. Benner, T. F. Gunzler, O. Kurapova, A. Somogyi, A. Snigirev, and I. Snigireva, “Beryllium parabolic refractive x-ray lenses,” AIP Conf Proc 705, 748–751 (2004).
[Crossref]

C. G. Schroer, T. F. Gnzler, B. Benner, M. Kuhlmann, J. Tmmler, B. Lengeler, C. Rau, T. Weitkamp, A. Snigirev, and I. Snigireva, “Hard x-ray full field microscopy and magnifying microtomography using compound refractive lenses,” Nucl. Instr. Meth. Phys. Res. A 467–468, 966–969 (2001).
[Crossref]

A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, “A compound refractive lens for focusing high-energy x-rays,” Nature 384, 49–51 (1996).
[Crossref]

Snigireva, I.

A. Snigirev, I. Snigireva, G. Vaughan, J. Wright, M. Rossat, A. Bytchkov, and C. Curfs, “High energy x-ray transfocator based on Al parabolic refractive lenses for focusing and collimation,” J. Phys.: Conf. Ser. 186, 012073 (2009).

B. Lengeler, C. G. Schroer, M. Kuhlmann, B. Benner, T. F. Gunzler, O. Kurapova, A. Somogyi, A. Snigirev, and I. Snigireva, “Beryllium parabolic refractive x-ray lenses,” AIP Conf Proc 705, 748–751 (2004).
[Crossref]

C. G. Schroer, T. F. Gnzler, B. Benner, M. Kuhlmann, J. Tmmler, B. Lengeler, C. Rau, T. Weitkamp, A. Snigirev, and I. Snigireva, “Hard x-ray full field microscopy and magnifying microtomography using compound refractive lenses,” Nucl. Instr. Meth. Phys. Res. A 467–468, 966–969 (2001).
[Crossref]

A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, “A compound refractive lens for focusing high-energy x-rays,” Nature 384, 49–51 (1996).
[Crossref]

Somogyi, A.

B. Lengeler, C. G. Schroer, M. Kuhlmann, B. Benner, T. F. Gunzler, O. Kurapova, A. Somogyi, A. Snigirev, and I. Snigireva, “Beryllium parabolic refractive x-ray lenses,” AIP Conf Proc 705, 748–751 (2004).
[Crossref]

Stein, A.

A. Stein, K. Evans-Lutterodt, N. Bozovic, and A. Taylor, “Fabrication of silicon kinoform lenses for hard x-ray focusing by electron beam lithography and deep reactive ion etching,” J. Vac. Sci. Technol. B 26 (1), 122–127 (2008).
[Crossref]

Taylor, A.

A. Stein, K. Evans-Lutterodt, N. Bozovic, and A. Taylor, “Fabrication of silicon kinoform lenses for hard x-ray focusing by electron beam lithography and deep reactive ion etching,” J. Vac. Sci. Technol. B 26 (1), 122–127 (2008).
[Crossref]

Thompson, A.

A. Thompson, I. Lindau, D. Attwood, Y. Liu, and H. Winick, “X-ray data booklet,” Lawrence Berkeley National Lab, http://xdb.lbl.gov (2009).

Tmmler, J.

C. G. Schroer, T. F. Gnzler, B. Benner, M. Kuhlmann, J. Tmmler, B. Lengeler, C. Rau, T. Weitkamp, A. Snigirev, and I. Snigireva, “Hard x-ray full field microscopy and magnifying microtomography using compound refractive lenses,” Nucl. Instr. Meth. Phys. Res. A 467–468, 966–969 (2001).
[Crossref]

Tomie, T.

T. Tomie, “X-ray lens,” Japanese patent 6-045288 (February 18, 1994); U.S. patents 5,594, 773 (January 14, 1997) and 5,684, 852 (November 4, 1997).

Vaughan, G.

A. Snigirev, I. Snigireva, G. Vaughan, J. Wright, M. Rossat, A. Bytchkov, and C. Curfs, “High energy x-ray transfocator based on Al parabolic refractive lenses for focusing and collimation,” J. Phys.: Conf. Ser. 186, 012073 (2009).

Vogt, H.

F. Marschall, A. Last, M. Simon, M. Kluge, V. Nazmov, H. Vogt, M. Ogurreck, I. Greving, and J. Mohr, “X-ray full field microscopy at 30 keV,” J. Phys.: Conf. Ser. 499, 012007 (2014).

Weitkamp, T.

E. Reznikova, T. Weitkamp, V. Nazmov, M. Simon, A. Last, and V. Saile, “Transmission hard x-ray microscope with increased view field using planar refractive objectives and condensers made of SU-8 polymer,” J. Phys.: Conf. Ser. 186, 012070 (2009).

C. G. Schroer, T. F. Gnzler, B. Benner, M. Kuhlmann, J. Tmmler, B. Lengeler, C. Rau, T. Weitkamp, A. Snigirev, and I. Snigireva, “Hard x-ray full field microscopy and magnifying microtomography using compound refractive lenses,” Nucl. Instr. Meth. Phys. Res. A 467–468, 966–969 (2001).
[Crossref]

Winick, H.

A. Thompson, I. Lindau, D. Attwood, Y. Liu, and H. Winick, “X-ray data booklet,” Lawrence Berkeley National Lab, http://xdb.lbl.gov (2009).

Wright, J.

A. Snigirev, I. Snigireva, G. Vaughan, J. Wright, M. Rossat, A. Bytchkov, and C. Curfs, “High energy x-ray transfocator based on Al parabolic refractive lenses for focusing and collimation,” J. Phys.: Conf. Ser. 186, 012073 (2009).

Zimprich, C.

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

AIP Conf Proc (1)

B. Lengeler, C. G. Schroer, M. Kuhlmann, B. Benner, T. F. Gunzler, O. Kurapova, A. Somogyi, A. Snigirev, and I. Snigireva, “Beryllium parabolic refractive x-ray lenses,” AIP Conf Proc 705, 748–751 (2004).
[Crossref]

IPAP Conf. Series (1)

R. Simon, V. Nazmov, E. Reznikova, J. Mohr, and V. Saile, “Hard x-ray imaging and microscopy with lithographic CRL developed at ANKA synchrotron radiation facility,” IPAP Conf. Series 7, 115–116 (2005).

J. Exp. Theor. Phys. (1)

V. G. Kohn, “An exact theory of imaging with a parabolic continuously refractive x-ray lens,” J. Exp. Theor. Phys. 97, 204–215 (2003).
[Crossref]

J. Phys.: Conf. Ser. (3)

A. Snigirev, I. Snigireva, G. Vaughan, J. Wright, M. Rossat, A. Bytchkov, and C. Curfs, “High energy x-ray transfocator based on Al parabolic refractive lenses for focusing and collimation,” J. Phys.: Conf. Ser. 186, 012073 (2009).

F. Marschall, A. Last, M. Simon, M. Kluge, V. Nazmov, H. Vogt, M. Ogurreck, I. Greving, and J. Mohr, “X-ray full field microscopy at 30 keV,” J. Phys.: Conf. Ser. 499, 012007 (2014).

E. Reznikova, T. Weitkamp, V. Nazmov, M. Simon, A. Last, and V. Saile, “Transmission hard x-ray microscope with increased view field using planar refractive objectives and condensers made of SU-8 polymer,” J. Phys.: Conf. Ser. 186, 012070 (2009).

J. Synchrotron Rad. (1)

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

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

A. Stein, K. Evans-Lutterodt, N. Bozovic, and A. Taylor, “Fabrication of silicon kinoform lenses for hard x-ray focusing by electron beam lithography and deep reactive ion etching,” J. Vac. Sci. Technol. B 26 (1), 122–127 (2008).
[Crossref]

Microelectron Eng. (1)

B. Nhammer, C. David, H. Rothuizen, J. Hoszowska, and A. Simionovici, “Deep reactive ion etching of silicon and diamond for the fabrication of planar refractive hard x-ray lenses,” Microelectron Eng. 67–68, 453–460 (2003).
[Crossref]

Nature (1)

A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, “A compound refractive lens for focusing high-energy x-rays,” Nature 384, 49–51 (1996).
[Crossref]

Nucl. Instr. Meth. Phys. Res. A (3)

V. Nazmov, E. Reznikova, A. Last, J. Mohr, V. Saile, M. DiMichiel, and J. Gttert, “Crossed planar x-ray lenses made from nickel for x-ray micro focusing and imaging applications”, Nucl. Instr. Meth. Phys. Res. A,  582, 120–122 (2007).
[Crossref]

Y. Ohishi, A. Q. R. Baron, M. Ishii, T. Ishikawa, and O. Shimomura, “Refractive x-ray lens for high pressure experiments at SPring-8,” Nucl. Instr. Meth. Phys. Res. A 467–468, 962–965 (2001).
[Crossref]

C. G. Schroer, T. F. Gnzler, B. Benner, M. Kuhlmann, J. Tmmler, B. Lengeler, C. Rau, T. Weitkamp, A. Snigirev, and I. Snigireva, “Hard x-ray full field microscopy and magnifying microtomography using compound refractive lenses,” Nucl. Instr. Meth. Phys. Res. A 467–468, 966–969 (2001).
[Crossref]

Phys. Rev. Lett. (1)

C. G. Schroer and B. Lengeler, “Focusing hard x-rays to nanometer dimensions by adiabatically focusing lenses,” Phys. Rev. Lett. 94, 054802 (2005).
[Crossref]

Other (3)

V. Saile, LIGA and Its Applications (Wiley-VCH Verlag GmbH & Co. KGaA, 2008).
[Crossref]

A. Thompson, I. Lindau, D. Attwood, Y. Liu, and H. Winick, “X-ray data booklet,” Lawrence Berkeley National Lab, http://xdb.lbl.gov (2009).

T. Tomie, “X-ray lens,” Japanese patent 6-045288 (February 18, 1994); U.S. patents 5,594, 773 (January 14, 1997) and 5,684, 852 (November 4, 1997).

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Figures (7)

Fig. 1
Fig. 1 Schematic (a) and SEM image (b) of an x-ray imaging lens: L – length of one lens element, A – aperture, r – radius in the apex of the parabola, d – smallest thickness of one lens element, a – distance between two lens elements, b = width of the boundary area (1 % of local aperture)
Fig. 2
Fig. 2 Comparison of absorption and geometry limited aperture of a refractive x-ray lens for different photon energies. For calculation we assume a lens from mr-L negative resist with alternating crossed lens elements, 60mm lens length, 100mm focal length and 6μm radius of the parabola in the apex.
Fig. 3
Fig. 3 Comparison of the acceptance angle (α), as well as angle of the top most (αt) and lowest (αb) ray of an x-ray lens with constant aperture and a Taille-lens dependent on the distance to the optical axis.
Fig. 4
Fig. 4 Photon density distribution: a) of a lens with a constant aperture of 70μm and b) of a Taille-lens with variable aperture (entrance aperture 71.5μm, smallest aperture 66μm, exit aperture 82μm). Both lenses have a focal length of 100mm at 30keV. The source with a size of 100μm×100μm is on the left with a distance of 106, 7mm to the entrance principle plane. This is the sample distance for a magnification of 15. The axes scaling is unequal in this drawing. The horizontal edge length of the images is 60mm, which is the length of the lens. The vertical edge length is 82μm like the exit aperture of the Taille-lens.
Fig. 5
Fig. 5 Ray path through a Taille-lens for different points in the field of view. For each point the top most and the lowest ray is drawn. The angular range between the two rays defines the entrance acceptance angle α of the lens for the current point. The Taille-lens is drawn in red. The axes scaling is unequal, so that the single lens elements are not detectable and only the outer shape of the lens is visible. The yellow area represents all transmitted rays starting at the point x.
Fig. 6
Fig. 6 Simulated brightness of the image of a completely homogeneous illuminated sample at 30keV with (a) a lens with constant aperture and (b) a Taille-lens with varying aperture. Both lenses have a focal length of 100mm, the field of view has a size of 100μm × 100μm and the magnification is 15.
Fig. 7
Fig. 7 Entrance acceptance angles of Taille-lenses with different focal lengths dependent on the distance of the sample point to the optical axis for a field of view of 100μm×100μm

Equations (5)

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D eff = 4 f δ μ ,
D g = 2 ( L N d ( N 1 ) a ) r N ,
L = 2 N 1 2 r ( D g 2 ) 2 + ( N 1 ) a + N d ,
f = r 2 δ N + L 6 .
d min = λ 2 NA = λ 2 sin ( α / 2 ) .

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