Skip to main content
SpringerLink
Log in

Efficient Analytical Approaches to the Optics of Compound Refractive Lenses for Use with Synchrotron X-rays

  • Published:
Metallurgical and Materials Transactions A Aims and scope Submit manuscript

Abstract

The properties of compound refractive lenses (CRLs) of biconcave parabolic lenses for focusing and imaging synchrotron X-rays have been investigated theoretically by ray transfer matrix analysis and Gaussian beam propagation. We present approximate analytical expressions, that allow fast estimation of the CRL characteristics, and build intuition into the design of advanced CRL optics.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Notes

  1. Note that in the following, there will be deviations from expressions found in literature where the sign of the argument of the exponential is chosen negative.

  2. The beam radii are also reduced by focusing while propagating through the CRL, but the effect is found to be small compared to the attenuation for typical materials.

References

  1. G. Möllenstedt, K.H. von Grote, C. Jönsson, X-ray Optics and X-ray Microanalysis (Academic Press, New York, NY, 1963)

    Google Scholar 

  2. E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, R. Barrett, Nature 401, 895–898 (1999)

    Article  Google Scholar 

  3. M. Hart, Rep. Prog. Phys. 34, 435–490 (1971)

    Article  Google Scholar 

  4. P. Kirkpatrick, A.V. Baez, J. Opt. Soc. Am. 28, 766–774 (1948)

    Article  Google Scholar 

  5. H. Wolter, Ann. Phys. 10, 94–114 (1952)

    Article  Google Scholar 

  6. A.V. Inneman, R. Hudec, L. Pina, P. Gorenstein, Proc. SPIE 3766, 72–79 (1999)

    Article  Google Scholar 

  7. M.A. Kumakhov, F.F. Komarov, Phys. Rep. 191, 289–350 (1990)

    Article  Google Scholar 

  8. A. Snigirev, V.G. Kohn, I.I. Snigireva, B. Lengeler, Nature 384, 49–51 (1996)

    Article  Google Scholar 

  9. A. Snigirev, I.I. Snigireva, G.B.M. Vaughan, J.P. Wright, M. Rossat, A. Bytchkov, and C. Curfs: Proc. 9th Int. Conf. on X-ray Microscopy, J. Phys. Conf. Ser., IOP, Bristol, vol. 186, 2009.

  10. G.B.M. Vaughan, J.P. Wright, A. Bytchkov, M. Rossat, H. Gleyzolle, I.I. Snigireva, A. Snigirev, J. Synchrotron Radiat. 18, 125–133 (2011)

    Article  Google Scholar 

  11. V.G. Kohn, JETP Lett. 76, 600–603 (2002)

    Article  Google Scholar 

  12. V.G. Kohn, JETP 97, 204–215 (2003)

    Article  Google Scholar 

  13. V.G. Kohn, J. Surf. Invest. 3, 358–364 (2009)

    Article  Google Scholar 

  14. B. Lengeler, J. Tümmler, A. Snigirev, I.I. Snigireva, C. Raven, J. Appl. Phys. 84, 5855–5861 (1998)

    Article  Google Scholar 

  15. B. Lengeler, C.G. Schroer, J. Tümmler, B. Benner, M. Richwin, A. Snigirev, I.I. Snigireva, M. Drakopoulos, J. Synchrotron Radiat. 6, 1153–1167 (1999)

    Article  Google Scholar 

  16. C.G. Schroer, B. Lengeler, B. Benner, T.F. Günzler, M. Kuhlmann, A.S. Simionovici, S. Bohic, M. Drakapoulos, A. Snigirev, I.I. Snigireva, W. Schröder, Proc. SPIE 4499, 52–63 (2001)

    Article  Google Scholar 

  17. B.E.A. Saleh, M.C. Teich, Fundamentals of Photonics, 2nd edn. (Wiley, Hoboken, NJ, 2007)

    Google Scholar 

  18. M. Born, E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th edn. (Cambridge University Press, Cambridge, 1999)

    Book  Google Scholar 

  19. Y. Takayama, T. Hatano, T. Miyahara, W. Okamoto, J. Synchrotron Radiat. 5, 1187–1194 (1998)

    Article  Google Scholar 

  20. H. Kogelnik, Appl. Optics 4, 1562–1569 (1965)

    Article  Google Scholar 

  21. I.I. Snigireva, V.G. Kohn, A. Snigirev, Proc. SPIE 5539, 218–225 (2004)

    Article  Google Scholar 

  22. C.G. Schroer, F.E. Brack, R. Brendler, S. Honig, R. Hoppe, J. Patommel, S. Ritter, M. Scholz, A. Schropp, F. Seiboth, D. Nilsson, J. Rahomaki, F. Uhlen, U. Vogt, J. Reinhardt, G. Falkenberg, Proc. SPIE 8848, 884807 (2013)

    Article  Google Scholar 

  23. V. Nazmov, L. Shabel’nikov, F.J. Pantenburg, J. Mohr, E. Reznikov, A. Snigirev, I.I. Snigireva, S. Kouznetsov, M. DiMichiel, Nucl. Instrum. Method Phys. Res. B 217, 409–416 (2004)

    Article  Google Scholar 

  24. R. Coïsson, S. Marchesini, J. Synchrotron Radiat. 4, 263–266 (1997)

    Article  Google Scholar 

  25. M.R. Eskildsen, P.L. Gammel, E.D. Isaacs, C. Detlefs, K. Mortensen, D.J. Bishop, Nature 391, 563–566 (1998)

    Article  Google Scholar 

Download references

Acknowledgments

The authors are grateful to Hugh Simons, Carsten Detlefs, Frederik Stöhr, and Anatoly Snigirev for stimulating discussions. HFP acknowledges an ERC advanced Grant “Diffraction based transmission X-ray microscopy”.

Author information

Author notes

  1. Stefan Othmar Poulsen (Post Doctoral Researcher)

    Present address: Department of Materials Science and Engineering, Northwestern University, Evanston, IL, 60208, USA

Authors and Affiliations

  1. NEXMAP, Department of Physics, Technical University of Denmark, Anker Engelunds Vej 1, 2800, Kgs. Lyngby, Denmark

    Henning Friis Poulsen (Professor)

  2. DTU Energy Conversion, Technical University of Denmark, Frederiksborgvej 399, 4000, Roskilde, Denmark

    Stefan Othmar Poulsen (Post Doctoral Researcher)

Authors
  1. Stefan Othmar Poulsen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Henning Friis Poulsen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Stefan Othmar Poulsen.

Additional information

Manuscript submitted January 8, 2014.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Poulsen, S.O., Poulsen, H.F. Efficient Analytical Approaches to the Optics of Compound Refractive Lenses for Use with Synchrotron X-rays. Metall Mater Trans A 45, 4772–4779 (2014). https://doi.org/10.1007/s11661-014-2278-1

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11661-014-2278-1

Keywords

Search

Navigation