Abstract

We describe a point-focusing x-ray lens made of a rolled polyimide film with etched prisms. The resulting lens is a cylinder with a large number of prisms forming an internal conic structure. The method allows for the manufacturing of lenses with large apertures and short focal lengths, for energies up to at least 100keV. In order to evaluate the concept, we have hand-rolled a few lenses and evaluated them at a synchrotron source. The measured performance of the prototype is promising, and deviations from the theoretical limits are quantitatively explained.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. N. Kamijo, Y. Suzuki, H. Takano, S. Tamura, M. Yasumoto, A. Takeuchi, and M. Awaji, Rev. Sci. Instrum. 74, 5101(2003).
  2. Y. Suzuki, A. Takeuchi, and Y. Terada, Rev. Sci. Instrum. 78, 053713 (2007).
    [PubMed]
  3. A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, Nature 384, 49 (1996).
  4. B. Cederström, R. Cahn, M. Danielsson, M. Lundqvist, and D. Nygren, Nature 404, 951 (2000).
    [PubMed]
  5. B. Lengeler, C. G. Schroer, B. Benner, A. Gerhardus, T. F. Günzler, M. Kuhlmann, J. Meyer, and C. Zimprich, J. Synchrotron Radiat. 9, 119 (2002).
    [PubMed]
  6. V. V. Aristov, M. Grigoriev, S. Kuznetsov, L. Shabelnikov, V. Yunkin, T. Weitkamp, C. Rau, I. Snigireva, A. Snigirev, M. Hoffmann, and E. Voges, Appl. Phys. Lett. 77, 4058 (2000).
  7. B. Nöhammer, J. Hoszowska, A. Freund, and C. David, J. Synchrotron Radiat. 10, 168 (2003).
    [PubMed]
  8. B. Cederström, C. Ribbing, and M. Lundqvist, J. Synchrotron Radiat. 12, 340 (2005).
    [PubMed]
  9. W. Jark, F. Pérennès, M. Matteucci, L. Mancini, F. Montanari, L. Rigon, G. Tromba, A. Somogyi, R. Tucoulou, and S. Bohic, J. Synchrotron Radiat. 11, 248 (2004).
    [PubMed]
  10. S. Karlsson, “Approach and device for focusing x-rays,” U.S. Patent 7,742,574 (June 22, 2010).
  11. M. Simon, E. Reznikova, V. Nazmov, T. Grund, and A. Last, AIP Conf. Proc. 1221, 85–90 (2010).
  12. F. van der Have, B. Vastenhouw, R. M. Ramakers, W. Branderhorst, J. O. Krah, C. Ji, S. G. Staelens, and F. J. Beekman, J. Nucl. Med. 50, 599 (2009).
    [PubMed]
  13. P. Nillius and M. Danielsson, IEEE Trans. Med. Imaging 29, 1390 (2010).
    [PubMed]

2010 (2)

M. Simon, E. Reznikova, V. Nazmov, T. Grund, and A. Last, AIP Conf. Proc. 1221, 85–90 (2010).

P. Nillius and M. Danielsson, IEEE Trans. Med. Imaging 29, 1390 (2010).
[PubMed]

2009 (1)

F. van der Have, B. Vastenhouw, R. M. Ramakers, W. Branderhorst, J. O. Krah, C. Ji, S. G. Staelens, and F. J. Beekman, J. Nucl. Med. 50, 599 (2009).
[PubMed]

2007 (1)

Y. Suzuki, A. Takeuchi, and Y. Terada, Rev. Sci. Instrum. 78, 053713 (2007).
[PubMed]

2005 (1)

B. Cederström, C. Ribbing, and M. Lundqvist, J. Synchrotron Radiat. 12, 340 (2005).
[PubMed]

2004 (1)

W. Jark, F. Pérennès, M. Matteucci, L. Mancini, F. Montanari, L. Rigon, G. Tromba, A. Somogyi, R. Tucoulou, and S. Bohic, J. Synchrotron Radiat. 11, 248 (2004).
[PubMed]

2003 (2)

N. Kamijo, Y. Suzuki, H. Takano, S. Tamura, M. Yasumoto, A. Takeuchi, and M. Awaji, Rev. Sci. Instrum. 74, 5101(2003).

B. Nöhammer, J. Hoszowska, A. Freund, and C. David, J. Synchrotron Radiat. 10, 168 (2003).
[PubMed]

2002 (1)

B. Lengeler, C. G. Schroer, B. Benner, A. Gerhardus, T. F. Günzler, M. Kuhlmann, J. Meyer, and C. Zimprich, J. Synchrotron Radiat. 9, 119 (2002).
[PubMed]

2000 (2)

V. V. Aristov, M. Grigoriev, S. Kuznetsov, L. Shabelnikov, V. Yunkin, T. Weitkamp, C. Rau, I. Snigireva, A. Snigirev, M. Hoffmann, and E. Voges, Appl. Phys. Lett. 77, 4058 (2000).

B. Cederström, R. Cahn, M. Danielsson, M. Lundqvist, and D. Nygren, Nature 404, 951 (2000).
[PubMed]

1996 (1)

A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, Nature 384, 49 (1996).

Aristov, V. V.

V. V. Aristov, M. Grigoriev, S. Kuznetsov, L. Shabelnikov, V. Yunkin, T. Weitkamp, C. Rau, I. Snigireva, A. Snigirev, M. Hoffmann, and E. Voges, Appl. Phys. Lett. 77, 4058 (2000).

Awaji, M.

N. Kamijo, Y. Suzuki, H. Takano, S. Tamura, M. Yasumoto, A. Takeuchi, and M. Awaji, Rev. Sci. Instrum. 74, 5101(2003).

Beekman, F. J.

F. van der Have, B. Vastenhouw, R. M. Ramakers, W. Branderhorst, J. O. Krah, C. Ji, S. G. Staelens, and F. J. Beekman, J. Nucl. Med. 50, 599 (2009).
[PubMed]

Benner, B.

B. Lengeler, C. G. Schroer, B. Benner, A. Gerhardus, T. F. Günzler, M. Kuhlmann, J. Meyer, and C. Zimprich, J. Synchrotron Radiat. 9, 119 (2002).
[PubMed]

Bohic, S.

W. Jark, F. Pérennès, M. Matteucci, L. Mancini, F. Montanari, L. Rigon, G. Tromba, A. Somogyi, R. Tucoulou, and S. Bohic, J. Synchrotron Radiat. 11, 248 (2004).
[PubMed]

Branderhorst, W.

F. van der Have, B. Vastenhouw, R. M. Ramakers, W. Branderhorst, J. O. Krah, C. Ji, S. G. Staelens, and F. J. Beekman, J. Nucl. Med. 50, 599 (2009).
[PubMed]

Cahn, R.

B. Cederström, R. Cahn, M. Danielsson, M. Lundqvist, and D. Nygren, Nature 404, 951 (2000).
[PubMed]

Cederström, B.

B. Cederström, C. Ribbing, and M. Lundqvist, J. Synchrotron Radiat. 12, 340 (2005).
[PubMed]

B. Cederström, R. Cahn, M. Danielsson, M. Lundqvist, and D. Nygren, Nature 404, 951 (2000).
[PubMed]

Danielsson, M.

P. Nillius and M. Danielsson, IEEE Trans. Med. Imaging 29, 1390 (2010).
[PubMed]

B. Cederström, R. Cahn, M. Danielsson, M. Lundqvist, and D. Nygren, Nature 404, 951 (2000).
[PubMed]

David, C.

B. Nöhammer, J. Hoszowska, A. Freund, and C. David, J. Synchrotron Radiat. 10, 168 (2003).
[PubMed]

Freund, A.

B. Nöhammer, J. Hoszowska, A. Freund, and C. David, J. Synchrotron Radiat. 10, 168 (2003).
[PubMed]

Gerhardus, A.

B. Lengeler, C. G. Schroer, B. Benner, A. Gerhardus, T. F. Günzler, M. Kuhlmann, J. Meyer, and C. Zimprich, J. Synchrotron Radiat. 9, 119 (2002).
[PubMed]

Grigoriev, M.

V. V. Aristov, M. Grigoriev, S. Kuznetsov, L. Shabelnikov, V. Yunkin, T. Weitkamp, C. Rau, I. Snigireva, A. Snigirev, M. Hoffmann, and E. Voges, Appl. Phys. Lett. 77, 4058 (2000).

Grund, T.

M. Simon, E. Reznikova, V. Nazmov, T. Grund, and A. Last, AIP Conf. Proc. 1221, 85–90 (2010).

Günzler, T. F.

B. Lengeler, C. G. Schroer, B. Benner, A. Gerhardus, T. F. Günzler, M. Kuhlmann, J. Meyer, and C. Zimprich, J. Synchrotron Radiat. 9, 119 (2002).
[PubMed]

Hoffmann, M.

V. V. Aristov, M. Grigoriev, S. Kuznetsov, L. Shabelnikov, V. Yunkin, T. Weitkamp, C. Rau, I. Snigireva, A. Snigirev, M. Hoffmann, and E. Voges, Appl. Phys. Lett. 77, 4058 (2000).

Hoszowska, J.

B. Nöhammer, J. Hoszowska, A. Freund, and C. David, J. Synchrotron Radiat. 10, 168 (2003).
[PubMed]

Jark, W.

W. Jark, F. Pérennès, M. Matteucci, L. Mancini, F. Montanari, L. Rigon, G. Tromba, A. Somogyi, R. Tucoulou, and S. Bohic, J. Synchrotron Radiat. 11, 248 (2004).
[PubMed]

Ji, C.

F. van der Have, B. Vastenhouw, R. M. Ramakers, W. Branderhorst, J. O. Krah, C. Ji, S. G. Staelens, and F. J. Beekman, J. Nucl. Med. 50, 599 (2009).
[PubMed]

Kamijo, N.

N. Kamijo, Y. Suzuki, H. Takano, S. Tamura, M. Yasumoto, A. Takeuchi, and M. Awaji, Rev. Sci. Instrum. 74, 5101(2003).

Karlsson, S.

S. Karlsson, “Approach and device for focusing x-rays,” U.S. Patent 7,742,574 (June 22, 2010).

Kohn, V.

A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, Nature 384, 49 (1996).

Krah, J. O.

F. van der Have, B. Vastenhouw, R. M. Ramakers, W. Branderhorst, J. O. Krah, C. Ji, S. G. Staelens, and F. J. Beekman, J. Nucl. Med. 50, 599 (2009).
[PubMed]

Kuhlmann, M.

B. Lengeler, C. G. Schroer, B. Benner, A. Gerhardus, T. F. Günzler, M. Kuhlmann, J. Meyer, and C. Zimprich, J. Synchrotron Radiat. 9, 119 (2002).
[PubMed]

Kuznetsov, S.

V. V. Aristov, M. Grigoriev, S. Kuznetsov, L. Shabelnikov, V. Yunkin, T. Weitkamp, C. Rau, I. Snigireva, A. Snigirev, M. Hoffmann, and E. Voges, Appl. Phys. Lett. 77, 4058 (2000).

Last, A.

M. Simon, E. Reznikova, V. Nazmov, T. Grund, and A. Last, AIP Conf. Proc. 1221, 85–90 (2010).

Lengeler, B.

B. Lengeler, C. G. Schroer, B. Benner, A. Gerhardus, T. F. Günzler, M. Kuhlmann, J. Meyer, and C. Zimprich, J. Synchrotron Radiat. 9, 119 (2002).
[PubMed]

A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, Nature 384, 49 (1996).

Lundqvist, M.

B. Cederström, C. Ribbing, and M. Lundqvist, J. Synchrotron Radiat. 12, 340 (2005).
[PubMed]

B. Cederström, R. Cahn, M. Danielsson, M. Lundqvist, and D. Nygren, Nature 404, 951 (2000).
[PubMed]

Mancini, L.

W. Jark, F. Pérennès, M. Matteucci, L. Mancini, F. Montanari, L. Rigon, G. Tromba, A. Somogyi, R. Tucoulou, and S. Bohic, J. Synchrotron Radiat. 11, 248 (2004).
[PubMed]

Matteucci, M.

W. Jark, F. Pérennès, M. Matteucci, L. Mancini, F. Montanari, L. Rigon, G. Tromba, A. Somogyi, R. Tucoulou, and S. Bohic, J. Synchrotron Radiat. 11, 248 (2004).
[PubMed]

Meyer, J.

B. Lengeler, C. G. Schroer, B. Benner, A. Gerhardus, T. F. Günzler, M. Kuhlmann, J. Meyer, and C. Zimprich, J. Synchrotron Radiat. 9, 119 (2002).
[PubMed]

Montanari, F.

W. Jark, F. Pérennès, M. Matteucci, L. Mancini, F. Montanari, L. Rigon, G. Tromba, A. Somogyi, R. Tucoulou, and S. Bohic, J. Synchrotron Radiat. 11, 248 (2004).
[PubMed]

Nazmov, V.

M. Simon, E. Reznikova, V. Nazmov, T. Grund, and A. Last, AIP Conf. Proc. 1221, 85–90 (2010).

Nillius, P.

P. Nillius and M. Danielsson, IEEE Trans. Med. Imaging 29, 1390 (2010).
[PubMed]

Nöhammer, B.

B. Nöhammer, J. Hoszowska, A. Freund, and C. David, J. Synchrotron Radiat. 10, 168 (2003).
[PubMed]

Nygren, D.

B. Cederström, R. Cahn, M. Danielsson, M. Lundqvist, and D. Nygren, Nature 404, 951 (2000).
[PubMed]

Pérennès, F.

W. Jark, F. Pérennès, M. Matteucci, L. Mancini, F. Montanari, L. Rigon, G. Tromba, A. Somogyi, R. Tucoulou, and S. Bohic, J. Synchrotron Radiat. 11, 248 (2004).
[PubMed]

Ramakers, R. M.

F. van der Have, B. Vastenhouw, R. M. Ramakers, W. Branderhorst, J. O. Krah, C. Ji, S. G. Staelens, and F. J. Beekman, J. Nucl. Med. 50, 599 (2009).
[PubMed]

Rau, C.

V. V. Aristov, M. Grigoriev, S. Kuznetsov, L. Shabelnikov, V. Yunkin, T. Weitkamp, C. Rau, I. Snigireva, A. Snigirev, M. Hoffmann, and E. Voges, Appl. Phys. Lett. 77, 4058 (2000).

Reznikova, E.

M. Simon, E. Reznikova, V. Nazmov, T. Grund, and A. Last, AIP Conf. Proc. 1221, 85–90 (2010).

Ribbing, C.

B. Cederström, C. Ribbing, and M. Lundqvist, J. Synchrotron Radiat. 12, 340 (2005).
[PubMed]

Rigon, L.

W. Jark, F. Pérennès, M. Matteucci, L. Mancini, F. Montanari, L. Rigon, G. Tromba, A. Somogyi, R. Tucoulou, and S. Bohic, J. Synchrotron Radiat. 11, 248 (2004).
[PubMed]

Schroer, C. G.

B. Lengeler, C. G. Schroer, B. Benner, A. Gerhardus, T. F. Günzler, M. Kuhlmann, J. Meyer, and C. Zimprich, J. Synchrotron Radiat. 9, 119 (2002).
[PubMed]

Shabelnikov, L.

V. V. Aristov, M. Grigoriev, S. Kuznetsov, L. Shabelnikov, V. Yunkin, T. Weitkamp, C. Rau, I. Snigireva, A. Snigirev, M. Hoffmann, and E. Voges, Appl. Phys. Lett. 77, 4058 (2000).

Simon, M.

M. Simon, E. Reznikova, V. Nazmov, T. Grund, and A. Last, AIP Conf. Proc. 1221, 85–90 (2010).

Snigirev, A.

V. V. Aristov, M. Grigoriev, S. Kuznetsov, L. Shabelnikov, V. Yunkin, T. Weitkamp, C. Rau, I. Snigireva, A. Snigirev, M. Hoffmann, and E. Voges, Appl. Phys. Lett. 77, 4058 (2000).

A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, Nature 384, 49 (1996).

Snigireva, I.

V. V. Aristov, M. Grigoriev, S. Kuznetsov, L. Shabelnikov, V. Yunkin, T. Weitkamp, C. Rau, I. Snigireva, A. Snigirev, M. Hoffmann, and E. Voges, Appl. Phys. Lett. 77, 4058 (2000).

A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, Nature 384, 49 (1996).

Somogyi, A.

W. Jark, F. Pérennès, M. Matteucci, L. Mancini, F. Montanari, L. Rigon, G. Tromba, A. Somogyi, R. Tucoulou, and S. Bohic, J. Synchrotron Radiat. 11, 248 (2004).
[PubMed]

Staelens, S. G.

F. van der Have, B. Vastenhouw, R. M. Ramakers, W. Branderhorst, J. O. Krah, C. Ji, S. G. Staelens, and F. J. Beekman, J. Nucl. Med. 50, 599 (2009).
[PubMed]

Suzuki, Y.

Y. Suzuki, A. Takeuchi, and Y. Terada, Rev. Sci. Instrum. 78, 053713 (2007).
[PubMed]

N. Kamijo, Y. Suzuki, H. Takano, S. Tamura, M. Yasumoto, A. Takeuchi, and M. Awaji, Rev. Sci. Instrum. 74, 5101(2003).

Takano, H.

N. Kamijo, Y. Suzuki, H. Takano, S. Tamura, M. Yasumoto, A. Takeuchi, and M. Awaji, Rev. Sci. Instrum. 74, 5101(2003).

Takeuchi, A.

Y. Suzuki, A. Takeuchi, and Y. Terada, Rev. Sci. Instrum. 78, 053713 (2007).
[PubMed]

N. Kamijo, Y. Suzuki, H. Takano, S. Tamura, M. Yasumoto, A. Takeuchi, and M. Awaji, Rev. Sci. Instrum. 74, 5101(2003).

Tamura, S.

N. Kamijo, Y. Suzuki, H. Takano, S. Tamura, M. Yasumoto, A. Takeuchi, and M. Awaji, Rev. Sci. Instrum. 74, 5101(2003).

Terada, Y.

Y. Suzuki, A. Takeuchi, and Y. Terada, Rev. Sci. Instrum. 78, 053713 (2007).
[PubMed]

Tromba, G.

W. Jark, F. Pérennès, M. Matteucci, L. Mancini, F. Montanari, L. Rigon, G. Tromba, A. Somogyi, R. Tucoulou, and S. Bohic, J. Synchrotron Radiat. 11, 248 (2004).
[PubMed]

Tucoulou, R.

W. Jark, F. Pérennès, M. Matteucci, L. Mancini, F. Montanari, L. Rigon, G. Tromba, A. Somogyi, R. Tucoulou, and S. Bohic, J. Synchrotron Radiat. 11, 248 (2004).
[PubMed]

van der Have, F.

F. van der Have, B. Vastenhouw, R. M. Ramakers, W. Branderhorst, J. O. Krah, C. Ji, S. G. Staelens, and F. J. Beekman, J. Nucl. Med. 50, 599 (2009).
[PubMed]

Vastenhouw, B.

F. van der Have, B. Vastenhouw, R. M. Ramakers, W. Branderhorst, J. O. Krah, C. Ji, S. G. Staelens, and F. J. Beekman, J. Nucl. Med. 50, 599 (2009).
[PubMed]

Voges, E.

V. V. Aristov, M. Grigoriev, S. Kuznetsov, L. Shabelnikov, V. Yunkin, T. Weitkamp, C. Rau, I. Snigireva, A. Snigirev, M. Hoffmann, and E. Voges, Appl. Phys. Lett. 77, 4058 (2000).

Weitkamp, T.

V. V. Aristov, M. Grigoriev, S. Kuznetsov, L. Shabelnikov, V. Yunkin, T. Weitkamp, C. Rau, I. Snigireva, A. Snigirev, M. Hoffmann, and E. Voges, Appl. Phys. Lett. 77, 4058 (2000).

Yasumoto, M.

N. Kamijo, Y. Suzuki, H. Takano, S. Tamura, M. Yasumoto, A. Takeuchi, and M. Awaji, Rev. Sci. Instrum. 74, 5101(2003).

Yunkin, V.

V. V. Aristov, M. Grigoriev, S. Kuznetsov, L. Shabelnikov, V. Yunkin, T. Weitkamp, C. Rau, I. Snigireva, A. Snigirev, M. Hoffmann, and E. Voges, Appl. Phys. Lett. 77, 4058 (2000).

Zimprich, C.

B. Lengeler, C. G. Schroer, B. Benner, A. Gerhardus, T. F. Günzler, M. Kuhlmann, J. Meyer, and C. Zimprich, J. Synchrotron Radiat. 9, 119 (2002).
[PubMed]

AIP Conf. Proc. (1)

M. Simon, E. Reznikova, V. Nazmov, T. Grund, and A. Last, AIP Conf. Proc. 1221, 85–90 (2010).

Appl. Phys. Lett. (1)

V. V. Aristov, M. Grigoriev, S. Kuznetsov, L. Shabelnikov, V. Yunkin, T. Weitkamp, C. Rau, I. Snigireva, A. Snigirev, M. Hoffmann, and E. Voges, Appl. Phys. Lett. 77, 4058 (2000).

IEEE Trans. Med. Imaging (1)

P. Nillius and M. Danielsson, IEEE Trans. Med. Imaging 29, 1390 (2010).
[PubMed]

J. Nucl. Med. (1)

F. van der Have, B. Vastenhouw, R. M. Ramakers, W. Branderhorst, J. O. Krah, C. Ji, S. G. Staelens, and F. J. Beekman, J. Nucl. Med. 50, 599 (2009).
[PubMed]

J. Synchrotron Radiat. (4)

B. Lengeler, C. G. Schroer, B. Benner, A. Gerhardus, T. F. Günzler, M. Kuhlmann, J. Meyer, and C. Zimprich, J. Synchrotron Radiat. 9, 119 (2002).
[PubMed]

B. Nöhammer, J. Hoszowska, A. Freund, and C. David, J. Synchrotron Radiat. 10, 168 (2003).
[PubMed]

B. Cederström, C. Ribbing, and M. Lundqvist, J. Synchrotron Radiat. 12, 340 (2005).
[PubMed]

W. Jark, F. Pérennès, M. Matteucci, L. Mancini, F. Montanari, L. Rigon, G. Tromba, A. Somogyi, R. Tucoulou, and S. Bohic, J. Synchrotron Radiat. 11, 248 (2004).
[PubMed]

Nature (2)

A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, Nature 384, 49 (1996).

B. Cederström, R. Cahn, M. Danielsson, M. Lundqvist, and D. Nygren, Nature 404, 951 (2000).
[PubMed]

Rev. Sci. Instrum. (2)

N. Kamijo, Y. Suzuki, H. Takano, S. Tamura, M. Yasumoto, A. Takeuchi, and M. Awaji, Rev. Sci. Instrum. 74, 5101(2003).

Y. Suzuki, A. Takeuchi, and Y. Terada, Rev. Sci. Instrum. 78, 053713 (2007).
[PubMed]

Other (1)

S. Karlsson, “Approach and device for focusing x-rays,” U.S. Patent 7,742,574 (June 22, 2010).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Lens design and construction. (a) A thin film of thickness h t is indented with parallel ridges of prisms of height h and base b. (b) This sheet is cut out in such a way that, when rolled, (c) it becomes a lens of multiple prisms that approximates a parabolic lens. The number of prisms ranges from n min in the center to n max at the periphery. Prism number n is cut at the distance s n from the bottom of the sheet. (d) The cross section of a rolled lens shows the increasing number of prisms toward the periphery, resulting in the desired focusing effect.

Fig. 2
Fig. 2

Spiral structure of the lens. The film is rolled around a rod of diameter a 0 until the aperture a is reached. The layers of the rolled lens form an Archimedes’ spiral in which the radius r is proportional to the parametrization angle θ. As a result, the normal vectors of the layers point off center with an angle α, which varies with θ such that the lens focuses onto a ring with a diameter that is proportional to the film thickness, h t .

Fig. 3
Fig. 3

(a) Transmission image of the manufactured lens, constructed by stitching together 22 exposures from a CCD camera. (b) Detail [box in (a)] in 1 10 aspect ratio, showing the prism layers, and from which (c) the model used in the simulations is created.

Fig. 4
Fig. 4

Measurements and simulations. (a) Intensity image measured at 22.5 keV photon energy. The double arrows mark the widths of the focal spot at the half-maximum value. (b) Measured and simulated efficiency at different spot sizes.

Tables (1)

Tables Icon

Table 1 Parameters for a Rolled Polyimide Film Lens a

Equations (3)

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

T = 32 δ 2 F 2 a 2 μ 2 h h t ( e a 0 μ h 4 δ F ( 1 + a 0 μ h 4 δ F ) e a μ h 4 δ F ( 1 + a μ h 4 δ F ) ) ,
a max = 2 F 2 δ ,
G = a eff 2 ( 1 + l f l s ) 2 h ( r 0 + w s l f l s ) 2 r 0 2 .

Metrics