Abstract

An X-ray parabolic refractive axicon, as novel type of beam-shaping optical element, consisting of a refractive lens with a form of the surface represented as a parabolic cone, is proposed and demonstrated. Under coherent X-ray illumination, the axicon generates Bessel-like beam along the optical axis and ring-shaped beam at the imaging distance. A theoretical analysis of the beams formation by the axicons was carried out and corresponding computer simulations were performed. The proposed parabolic axicon was experimentally tested at ID06 ESRF beamline in the X-ray energy range from 10 to 15 keV. Experimentally recorded images of shaped beams are in a good agreement with computer calculations. Future possible applications of the axicon are discussed.

© 2017 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
X-ray multilens interferometer based on Si refractive lenses

A. Snigirev, I. Snigireva, M. Lyubomirskiy, V. Kohn, V. Yunkin, and S. Kuznetsov
Opt. Express 22(21) 25842-25852 (2014)

Miniaturized compound refractive X-ray zoom lens

E. Kornemann, O. Márkus, A. Opolka, T. Zhou, I. Greving, M. Storm, C. Krywka, A. Last, and J. Mohr
Opt. Express 25(19) 22455-22466 (2017)

Diamond refractive micro-lenses for full-field X-ray imaging and microscopy produced with ion beam lithography

Polina Medvedskaya, Ivan Lyatun, Sergey Shevyrtalov, Maxim Polikarpov, Irina Snigireva, Vyacheslav Yunkin, and Anatoly Snigirev
Opt. Express 28(4) 4773-4785 (2020)

References

  • View by:
  • |
  • |
  • |

  1. A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).
  2. M. Sutton, S. G. J. Mochrie, T. Greytak, S. E. Nagler, L. E. Berman, G. A. Held, and G. B. Stephenson, “Observation of speckle by diffraction with coherent X-rays,” Nature 352(6336), 608–610 (1991).
  3. J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400(6742), 342–344 (1999).
  4. A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, “A compound refractive lens for focusing high-energy X-rays,” Nature 384(6604), 49–51 (1996).
  5. A. Snigirev and I. Snigireva, “High energy X-ray micro-optics,” C. R. Phys. 9(5–6), 507–516 (2008).
  6. V. Kohn, I. Snigireva, and A. Snigirev, “Diffraction theory of imaging with X-ray compound refractive lens,” Opt. Commun. 216(4–6), 247–260 (2003).
  7. M. Drakopoulos, J. Zegenhagen, A. Snigirev, I. Snigireva, M. Hauser, K. Eberl, V. Aristov, L. Shabelnikov, and V. Yunkin, “X-ray standing wave microscopy: Chemical microanalysis with atomic resolution,” Appl. Phys. Lett. 81(12), 2279–2281 (2002).
  8. M. Drakopoulos, A. Snigirev, I. Snigireva, and J. Schilling, “X-ray high-resolution diffraction using refractive lenses,” Appl. Phys. Lett. 86(1), 014102 (2005).
  9. A. Bosak, I. Snigireva, K. S. Napolskii, and A. Snigirev, “High-resolution transmission X-ray microscopy: a new tool for mesoscopic materials,” Adv. Mater. 22(30), 3256–3259 (2010).
    [PubMed]
  10. P. Ershov, S. Kuznetsov, I. Snigireva, V. Yunkin, A. Goikhman, and A. Snigirev, “Fourier crystal diffractometry based on refractive optics,” J. Appl. Cryst. 46(5), 1475–1480 (2013).
  11. D. Byelov, J.-M. Meijer, I. Snigireva, A. Snigirev, L. Rossi, E. van den Pol, A. Kuijk, A. Phillipse, A. Imhof, A. van Blaaderen, G. J. Vroege, and A. Petukhov, “In-situ hard X-ray microscopy of self-assembly in colloidal suspentions,” RSC Advances 3(36), 15670–15677 (2013).
  12. H. Simons, A. King, W. Ludwig, C. Detlefs, W. Pantleon, S. Schmidt, I. Snigireva, A. Snigirev, and H. F. Poulsen, “Dark-field X-ray microscopy for multiscale structural characterization,” Nat. Commun. 6, 6098 (2015).
    [PubMed]
  13. K. V. Falch, D. Casari, M. Di Michiel, C. Detlefs, A. Snigirev, I. Snigireva, V. Honkimaki, and R. H. Mathiesen, “In situ hard X-ray transmission microscopy in material science,” J. Mater. Sci. 52(6), 3497–3507 (2017).
  14. A. Snigirev, I. Snigireva, V. Kohn, V. Yunkin, S. Kuznetsov, M. B. Grigoriev, T. Roth, G. Vaughan, and C. Detlefs, “X-ray nanointerferometer based on Si refractive bilenses,” Phys. Rev. Lett. 103(6), 064801 (2009).
    [PubMed]
  15. A. Snigirev, I. Snigireva, M. Lyubomirskiy, V. Kohn, V. Yunkin, and S. Kuznetsov, “X-ray multilens interferometer based on Si refractive lenses,” Opt. Express 22(21), 25842–25852 (2014).
    [PubMed]
  16. M. Lyubomirskiy, I. Snigireva, V. Kohn, S. Kuznetsov, V. Yunkin, G. Vaughan, and A. Snigirev, “30-Lens interferometer for high-energy X-rays,” J. Synchrotron Radiat. 23(Pt 5), 1104–1109 (2016).
    [PubMed]
  17. E. Di Fabrizio, D. Cojoc, S. Cabrini, B. Kaulich, J. Susini, P. Facci, and T. Wilhein, “Diffractive optical elements for differential interference contrast x-ray microscopy,” Opt. Express 11(19), 2278–2288 (2003).
    [PubMed]
  18. G. K. Skinner and J. F. Krizmanic, “X-ray interferometry with transmissive beam combiners for ultra-high angular resolution astronomy,” Exp. Astron. 27(1–2), 61–76 (2009).
  19. K. Jefimovs, J. Vila-Comamala, M. Stampanoni, B. Kaulich, and C. David, “Beam-shaping condenser lenses for full-field transmission X-ray microscopy,” J. Synchrotron Radiat. 15(Pt 1), 106–108 (2008).
    [PubMed]
  20. U. Vogt, M. Lindblom, P. Charalambous, B. Kaulich, and T. Wilhein, “Condenser for Koehler-like illumination in transmission x-ray microscopes at undulator sources,” Opt. Lett. 31(10), 1465–1467 (2006).
    [PubMed]
  21. J. H. McLeod, “The Axicon: A New Type of Optical Element,” J. Opt. Soc. Am. 44(8), 592–597 (1954).
  22. J. H. McLeod, “Axicons and their uses,” J. Opt. Soc. Am. 50(2), 166–169 (1960).
  23. G. S. Bakken, “The parabolic axicon,” Appl. Opt. 13(6), 1291–1292 (1974).
    [PubMed]
  24. D. McGloin and K. Dholakia, “Bessel beams: diffraction in s new light,” Contemp. Phys. 46(1), 15–28 (2005).
  25. O. Ren and R. Birngruber, “Axicon: a new laser beam delivery system for corneal surgery,” IEEE J. Quantum Electron. 26(12), 2305–2308 (1990).
  26. M. Duocastella and C. B. Arnold, “Bessel and annular beams for materials processing,” Laser Photonics Rev. 6(5), 607–621 (2012).
  27. F. Courvoisier, J. Zhang, M. K. Bhuyan, M. Jacquot, and J. M. Dudley, “Applications of femtosecond Bessel beams to laser ablation,” Appl. Phys., A Mater. Sci. Process. 112(1), 29–34 (2013).
  28. S. Akturk, B. Zhou, M. Franco, A. Couairon, and A. Mysyrowicz, “Generation of long plasma channels in air by focusing ulrashort laser pulses with an axicon,” Opt. Commun. 282(1), 129–134 (2009).
  29. B. Lengeler, C. Schroer, J. Tummler, B. Benner, M. Richwin, A. Snigirev, I. Snigireva, and M. Drakopoulos, “Imaging by parabolic refractive lenses in the hard x-ray range,” J. Synchrotron Radiat. 6(6), 1153–1167 (1999).
  30. C. Holzner, M. Feser, S. Vogt, B. Hornberger, S. B. Baines, and C. Jacobsen, “Zernike phase contrast in scanning microscopy with X-rays,” Nat. Phys. 6(11), 883–887 (2010).
    [PubMed]
  31. A. Snigirev, A. Bjeoumikhov, A. Erko, I. Snigireva, M. Grigoriev, V. Yunkin, M. Erko, and S. Bjeoumikhova, “Two-step hard X-ray focusing combining Fresnel zone plate and single-bounce ellipsoidal capillary,” J. Synchrotron Radiat. 14(Pt 4), 326–330 (2007).
    [PubMed]
  32. M. Polikarpov, I. Snigireva, and A. Snigirev, “X-ray harmonics rejection on third-generation synchrotron sources using compound refractive lenses,” J. Synchrotron Radiat. 21(Pt 3), 484–487 (2014).
    [PubMed]

2017 (1)

K. V. Falch, D. Casari, M. Di Michiel, C. Detlefs, A. Snigirev, I. Snigireva, V. Honkimaki, and R. H. Mathiesen, “In situ hard X-ray transmission microscopy in material science,” J. Mater. Sci. 52(6), 3497–3507 (2017).

2016 (1)

M. Lyubomirskiy, I. Snigireva, V. Kohn, S. Kuznetsov, V. Yunkin, G. Vaughan, and A. Snigirev, “30-Lens interferometer for high-energy X-rays,” J. Synchrotron Radiat. 23(Pt 5), 1104–1109 (2016).
[PubMed]

2015 (1)

H. Simons, A. King, W. Ludwig, C. Detlefs, W. Pantleon, S. Schmidt, I. Snigireva, A. Snigirev, and H. F. Poulsen, “Dark-field X-ray microscopy for multiscale structural characterization,” Nat. Commun. 6, 6098 (2015).
[PubMed]

2014 (2)

A. Snigirev, I. Snigireva, M. Lyubomirskiy, V. Kohn, V. Yunkin, and S. Kuznetsov, “X-ray multilens interferometer based on Si refractive lenses,” Opt. Express 22(21), 25842–25852 (2014).
[PubMed]

M. Polikarpov, I. Snigireva, and A. Snigirev, “X-ray harmonics rejection on third-generation synchrotron sources using compound refractive lenses,” J. Synchrotron Radiat. 21(Pt 3), 484–487 (2014).
[PubMed]

2013 (3)

F. Courvoisier, J. Zhang, M. K. Bhuyan, M. Jacquot, and J. M. Dudley, “Applications of femtosecond Bessel beams to laser ablation,” Appl. Phys., A Mater. Sci. Process. 112(1), 29–34 (2013).

P. Ershov, S. Kuznetsov, I. Snigireva, V. Yunkin, A. Goikhman, and A. Snigirev, “Fourier crystal diffractometry based on refractive optics,” J. Appl. Cryst. 46(5), 1475–1480 (2013).

D. Byelov, J.-M. Meijer, I. Snigireva, A. Snigirev, L. Rossi, E. van den Pol, A. Kuijk, A. Phillipse, A. Imhof, A. van Blaaderen, G. J. Vroege, and A. Petukhov, “In-situ hard X-ray microscopy of self-assembly in colloidal suspentions,” RSC Advances 3(36), 15670–15677 (2013).

2012 (1)

M. Duocastella and C. B. Arnold, “Bessel and annular beams for materials processing,” Laser Photonics Rev. 6(5), 607–621 (2012).

2010 (2)

C. Holzner, M. Feser, S. Vogt, B. Hornberger, S. B. Baines, and C. Jacobsen, “Zernike phase contrast in scanning microscopy with X-rays,” Nat. Phys. 6(11), 883–887 (2010).
[PubMed]

A. Bosak, I. Snigireva, K. S. Napolskii, and A. Snigirev, “High-resolution transmission X-ray microscopy: a new tool for mesoscopic materials,” Adv. Mater. 22(30), 3256–3259 (2010).
[PubMed]

2009 (3)

A. Snigirev, I. Snigireva, V. Kohn, V. Yunkin, S. Kuznetsov, M. B. Grigoriev, T. Roth, G. Vaughan, and C. Detlefs, “X-ray nanointerferometer based on Si refractive bilenses,” Phys. Rev. Lett. 103(6), 064801 (2009).
[PubMed]

S. Akturk, B. Zhou, M. Franco, A. Couairon, and A. Mysyrowicz, “Generation of long plasma channels in air by focusing ulrashort laser pulses with an axicon,” Opt. Commun. 282(1), 129–134 (2009).

G. K. Skinner and J. F. Krizmanic, “X-ray interferometry with transmissive beam combiners for ultra-high angular resolution astronomy,” Exp. Astron. 27(1–2), 61–76 (2009).

2008 (2)

K. Jefimovs, J. Vila-Comamala, M. Stampanoni, B. Kaulich, and C. David, “Beam-shaping condenser lenses for full-field transmission X-ray microscopy,” J. Synchrotron Radiat. 15(Pt 1), 106–108 (2008).
[PubMed]

A. Snigirev and I. Snigireva, “High energy X-ray micro-optics,” C. R. Phys. 9(5–6), 507–516 (2008).

2007 (1)

A. Snigirev, A. Bjeoumikhov, A. Erko, I. Snigireva, M. Grigoriev, V. Yunkin, M. Erko, and S. Bjeoumikhova, “Two-step hard X-ray focusing combining Fresnel zone plate and single-bounce ellipsoidal capillary,” J. Synchrotron Radiat. 14(Pt 4), 326–330 (2007).
[PubMed]

2006 (1)

2005 (2)

D. McGloin and K. Dholakia, “Bessel beams: diffraction in s new light,” Contemp. Phys. 46(1), 15–28 (2005).

M. Drakopoulos, A. Snigirev, I. Snigireva, and J. Schilling, “X-ray high-resolution diffraction using refractive lenses,” Appl. Phys. Lett. 86(1), 014102 (2005).

2003 (2)

V. Kohn, I. Snigireva, and A. Snigirev, “Diffraction theory of imaging with X-ray compound refractive lens,” Opt. Commun. 216(4–6), 247–260 (2003).

E. Di Fabrizio, D. Cojoc, S. Cabrini, B. Kaulich, J. Susini, P. Facci, and T. Wilhein, “Diffractive optical elements for differential interference contrast x-ray microscopy,” Opt. Express 11(19), 2278–2288 (2003).
[PubMed]

2002 (1)

M. Drakopoulos, J. Zegenhagen, A. Snigirev, I. Snigireva, M. Hauser, K. Eberl, V. Aristov, L. Shabelnikov, and V. Yunkin, “X-ray standing wave microscopy: Chemical microanalysis with atomic resolution,” Appl. Phys. Lett. 81(12), 2279–2281 (2002).

1999 (2)

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400(6742), 342–344 (1999).

B. Lengeler, C. Schroer, J. Tummler, B. Benner, M. Richwin, A. Snigirev, I. Snigireva, and M. Drakopoulos, “Imaging by parabolic refractive lenses in the hard x-ray range,” J. Synchrotron Radiat. 6(6), 1153–1167 (1999).

1996 (1)

A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, “A compound refractive lens for focusing high-energy X-rays,” Nature 384(6604), 49–51 (1996).

1995 (1)

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).

1991 (1)

M. Sutton, S. G. J. Mochrie, T. Greytak, S. E. Nagler, L. E. Berman, G. A. Held, and G. B. Stephenson, “Observation of speckle by diffraction with coherent X-rays,” Nature 352(6336), 608–610 (1991).

1990 (1)

O. Ren and R. Birngruber, “Axicon: a new laser beam delivery system for corneal surgery,” IEEE J. Quantum Electron. 26(12), 2305–2308 (1990).

1974 (1)

1960 (1)

1954 (1)

Akturk, S.

S. Akturk, B. Zhou, M. Franco, A. Couairon, and A. Mysyrowicz, “Generation of long plasma channels in air by focusing ulrashort laser pulses with an axicon,” Opt. Commun. 282(1), 129–134 (2009).

Aristov, V.

M. Drakopoulos, J. Zegenhagen, A. Snigirev, I. Snigireva, M. Hauser, K. Eberl, V. Aristov, L. Shabelnikov, and V. Yunkin, “X-ray standing wave microscopy: Chemical microanalysis with atomic resolution,” Appl. Phys. Lett. 81(12), 2279–2281 (2002).

Arnold, C. B.

M. Duocastella and C. B. Arnold, “Bessel and annular beams for materials processing,” Laser Photonics Rev. 6(5), 607–621 (2012).

Baines, S. B.

C. Holzner, M. Feser, S. Vogt, B. Hornberger, S. B. Baines, and C. Jacobsen, “Zernike phase contrast in scanning microscopy with X-rays,” Nat. Phys. 6(11), 883–887 (2010).
[PubMed]

Bakken, G. S.

Benner, B.

B. Lengeler, C. Schroer, J. Tummler, B. Benner, M. Richwin, A. Snigirev, I. Snigireva, and M. Drakopoulos, “Imaging by parabolic refractive lenses in the hard x-ray range,” J. Synchrotron Radiat. 6(6), 1153–1167 (1999).

Berman, L. E.

M. Sutton, S. G. J. Mochrie, T. Greytak, S. E. Nagler, L. E. Berman, G. A. Held, and G. B. Stephenson, “Observation of speckle by diffraction with coherent X-rays,” Nature 352(6336), 608–610 (1991).

Bhuyan, M. K.

F. Courvoisier, J. Zhang, M. K. Bhuyan, M. Jacquot, and J. M. Dudley, “Applications of femtosecond Bessel beams to laser ablation,” Appl. Phys., A Mater. Sci. Process. 112(1), 29–34 (2013).

Birngruber, R.

O. Ren and R. Birngruber, “Axicon: a new laser beam delivery system for corneal surgery,” IEEE J. Quantum Electron. 26(12), 2305–2308 (1990).

Bjeoumikhov, A.

A. Snigirev, A. Bjeoumikhov, A. Erko, I. Snigireva, M. Grigoriev, V. Yunkin, M. Erko, and S. Bjeoumikhova, “Two-step hard X-ray focusing combining Fresnel zone plate and single-bounce ellipsoidal capillary,” J. Synchrotron Radiat. 14(Pt 4), 326–330 (2007).
[PubMed]

Bjeoumikhova, S.

A. Snigirev, A. Bjeoumikhov, A. Erko, I. Snigireva, M. Grigoriev, V. Yunkin, M. Erko, and S. Bjeoumikhova, “Two-step hard X-ray focusing combining Fresnel zone plate and single-bounce ellipsoidal capillary,” J. Synchrotron Radiat. 14(Pt 4), 326–330 (2007).
[PubMed]

Bosak, A.

A. Bosak, I. Snigireva, K. S. Napolskii, and A. Snigirev, “High-resolution transmission X-ray microscopy: a new tool for mesoscopic materials,” Adv. Mater. 22(30), 3256–3259 (2010).
[PubMed]

Byelov, D.

D. Byelov, J.-M. Meijer, I. Snigireva, A. Snigirev, L. Rossi, E. van den Pol, A. Kuijk, A. Phillipse, A. Imhof, A. van Blaaderen, G. J. Vroege, and A. Petukhov, “In-situ hard X-ray microscopy of self-assembly in colloidal suspentions,” RSC Advances 3(36), 15670–15677 (2013).

Cabrini, S.

Casari, D.

K. V. Falch, D. Casari, M. Di Michiel, C. Detlefs, A. Snigirev, I. Snigireva, V. Honkimaki, and R. H. Mathiesen, “In situ hard X-ray transmission microscopy in material science,” J. Mater. Sci. 52(6), 3497–3507 (2017).

Charalambous, P.

U. Vogt, M. Lindblom, P. Charalambous, B. Kaulich, and T. Wilhein, “Condenser for Koehler-like illumination in transmission x-ray microscopes at undulator sources,” Opt. Lett. 31(10), 1465–1467 (2006).
[PubMed]

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400(6742), 342–344 (1999).

Cojoc, D.

Couairon, A.

S. Akturk, B. Zhou, M. Franco, A. Couairon, and A. Mysyrowicz, “Generation of long plasma channels in air by focusing ulrashort laser pulses with an axicon,” Opt. Commun. 282(1), 129–134 (2009).

Courvoisier, F.

F. Courvoisier, J. Zhang, M. K. Bhuyan, M. Jacquot, and J. M. Dudley, “Applications of femtosecond Bessel beams to laser ablation,” Appl. Phys., A Mater. Sci. Process. 112(1), 29–34 (2013).

David, C.

K. Jefimovs, J. Vila-Comamala, M. Stampanoni, B. Kaulich, and C. David, “Beam-shaping condenser lenses for full-field transmission X-ray microscopy,” J. Synchrotron Radiat. 15(Pt 1), 106–108 (2008).
[PubMed]

Detlefs, C.

K. V. Falch, D. Casari, M. Di Michiel, C. Detlefs, A. Snigirev, I. Snigireva, V. Honkimaki, and R. H. Mathiesen, “In situ hard X-ray transmission microscopy in material science,” J. Mater. Sci. 52(6), 3497–3507 (2017).

H. Simons, A. King, W. Ludwig, C. Detlefs, W. Pantleon, S. Schmidt, I. Snigireva, A. Snigirev, and H. F. Poulsen, “Dark-field X-ray microscopy for multiscale structural characterization,” Nat. Commun. 6, 6098 (2015).
[PubMed]

A. Snigirev, I. Snigireva, V. Kohn, V. Yunkin, S. Kuznetsov, M. B. Grigoriev, T. Roth, G. Vaughan, and C. Detlefs, “X-ray nanointerferometer based on Si refractive bilenses,” Phys. Rev. Lett. 103(6), 064801 (2009).
[PubMed]

Dholakia, K.

D. McGloin and K. Dholakia, “Bessel beams: diffraction in s new light,” Contemp. Phys. 46(1), 15–28 (2005).

Di Fabrizio, E.

Di Michiel, M.

K. V. Falch, D. Casari, M. Di Michiel, C. Detlefs, A. Snigirev, I. Snigireva, V. Honkimaki, and R. H. Mathiesen, “In situ hard X-ray transmission microscopy in material science,” J. Mater. Sci. 52(6), 3497–3507 (2017).

Drakopoulos, M.

M. Drakopoulos, A. Snigirev, I. Snigireva, and J. Schilling, “X-ray high-resolution diffraction using refractive lenses,” Appl. Phys. Lett. 86(1), 014102 (2005).

M. Drakopoulos, J. Zegenhagen, A. Snigirev, I. Snigireva, M. Hauser, K. Eberl, V. Aristov, L. Shabelnikov, and V. Yunkin, “X-ray standing wave microscopy: Chemical microanalysis with atomic resolution,” Appl. Phys. Lett. 81(12), 2279–2281 (2002).

B. Lengeler, C. Schroer, J. Tummler, B. Benner, M. Richwin, A. Snigirev, I. Snigireva, and M. Drakopoulos, “Imaging by parabolic refractive lenses in the hard x-ray range,” J. Synchrotron Radiat. 6(6), 1153–1167 (1999).

Dudley, J. M.

F. Courvoisier, J. Zhang, M. K. Bhuyan, M. Jacquot, and J. M. Dudley, “Applications of femtosecond Bessel beams to laser ablation,” Appl. Phys., A Mater. Sci. Process. 112(1), 29–34 (2013).

Duocastella, M.

M. Duocastella and C. B. Arnold, “Bessel and annular beams for materials processing,” Laser Photonics Rev. 6(5), 607–621 (2012).

Eberl, K.

M. Drakopoulos, J. Zegenhagen, A. Snigirev, I. Snigireva, M. Hauser, K. Eberl, V. Aristov, L. Shabelnikov, and V. Yunkin, “X-ray standing wave microscopy: Chemical microanalysis with atomic resolution,” Appl. Phys. Lett. 81(12), 2279–2281 (2002).

Erko, A.

A. Snigirev, A. Bjeoumikhov, A. Erko, I. Snigireva, M. Grigoriev, V. Yunkin, M. Erko, and S. Bjeoumikhova, “Two-step hard X-ray focusing combining Fresnel zone plate and single-bounce ellipsoidal capillary,” J. Synchrotron Radiat. 14(Pt 4), 326–330 (2007).
[PubMed]

Erko, M.

A. Snigirev, A. Bjeoumikhov, A. Erko, I. Snigireva, M. Grigoriev, V. Yunkin, M. Erko, and S. Bjeoumikhova, “Two-step hard X-ray focusing combining Fresnel zone plate and single-bounce ellipsoidal capillary,” J. Synchrotron Radiat. 14(Pt 4), 326–330 (2007).
[PubMed]

Ershov, P.

P. Ershov, S. Kuznetsov, I. Snigireva, V. Yunkin, A. Goikhman, and A. Snigirev, “Fourier crystal diffractometry based on refractive optics,” J. Appl. Cryst. 46(5), 1475–1480 (2013).

Facci, P.

Falch, K. V.

K. V. Falch, D. Casari, M. Di Michiel, C. Detlefs, A. Snigirev, I. Snigireva, V. Honkimaki, and R. H. Mathiesen, “In situ hard X-ray transmission microscopy in material science,” J. Mater. Sci. 52(6), 3497–3507 (2017).

Feser, M.

C. Holzner, M. Feser, S. Vogt, B. Hornberger, S. B. Baines, and C. Jacobsen, “Zernike phase contrast in scanning microscopy with X-rays,” Nat. Phys. 6(11), 883–887 (2010).
[PubMed]

Franco, M.

S. Akturk, B. Zhou, M. Franco, A. Couairon, and A. Mysyrowicz, “Generation of long plasma channels in air by focusing ulrashort laser pulses with an axicon,” Opt. Commun. 282(1), 129–134 (2009).

Goikhman, A.

P. Ershov, S. Kuznetsov, I. Snigireva, V. Yunkin, A. Goikhman, and A. Snigirev, “Fourier crystal diffractometry based on refractive optics,” J. Appl. Cryst. 46(5), 1475–1480 (2013).

Greytak, T.

M. Sutton, S. G. J. Mochrie, T. Greytak, S. E. Nagler, L. E. Berman, G. A. Held, and G. B. Stephenson, “Observation of speckle by diffraction with coherent X-rays,” Nature 352(6336), 608–610 (1991).

Grigoriev, M.

A. Snigirev, A. Bjeoumikhov, A. Erko, I. Snigireva, M. Grigoriev, V. Yunkin, M. Erko, and S. Bjeoumikhova, “Two-step hard X-ray focusing combining Fresnel zone plate and single-bounce ellipsoidal capillary,” J. Synchrotron Radiat. 14(Pt 4), 326–330 (2007).
[PubMed]

Grigoriev, M. B.

A. Snigirev, I. Snigireva, V. Kohn, V. Yunkin, S. Kuznetsov, M. B. Grigoriev, T. Roth, G. Vaughan, and C. Detlefs, “X-ray nanointerferometer based on Si refractive bilenses,” Phys. Rev. Lett. 103(6), 064801 (2009).
[PubMed]

Hauser, M.

M. Drakopoulos, J. Zegenhagen, A. Snigirev, I. Snigireva, M. Hauser, K. Eberl, V. Aristov, L. Shabelnikov, and V. Yunkin, “X-ray standing wave microscopy: Chemical microanalysis with atomic resolution,” Appl. Phys. Lett. 81(12), 2279–2281 (2002).

Held, G. A.

M. Sutton, S. G. J. Mochrie, T. Greytak, S. E. Nagler, L. E. Berman, G. A. Held, and G. B. Stephenson, “Observation of speckle by diffraction with coherent X-rays,” Nature 352(6336), 608–610 (1991).

Holzner, C.

C. Holzner, M. Feser, S. Vogt, B. Hornberger, S. B. Baines, and C. Jacobsen, “Zernike phase contrast in scanning microscopy with X-rays,” Nat. Phys. 6(11), 883–887 (2010).
[PubMed]

Honkimaki, V.

K. V. Falch, D. Casari, M. Di Michiel, C. Detlefs, A. Snigirev, I. Snigireva, V. Honkimaki, and R. H. Mathiesen, “In situ hard X-ray transmission microscopy in material science,” J. Mater. Sci. 52(6), 3497–3507 (2017).

Hornberger, B.

C. Holzner, M. Feser, S. Vogt, B. Hornberger, S. B. Baines, and C. Jacobsen, “Zernike phase contrast in scanning microscopy with X-rays,” Nat. Phys. 6(11), 883–887 (2010).
[PubMed]

Imhof, A.

D. Byelov, J.-M. Meijer, I. Snigireva, A. Snigirev, L. Rossi, E. van den Pol, A. Kuijk, A. Phillipse, A. Imhof, A. van Blaaderen, G. J. Vroege, and A. Petukhov, “In-situ hard X-ray microscopy of self-assembly in colloidal suspentions,” RSC Advances 3(36), 15670–15677 (2013).

Jacobsen, C.

C. Holzner, M. Feser, S. Vogt, B. Hornberger, S. B. Baines, and C. Jacobsen, “Zernike phase contrast in scanning microscopy with X-rays,” Nat. Phys. 6(11), 883–887 (2010).
[PubMed]

Jacquot, M.

F. Courvoisier, J. Zhang, M. K. Bhuyan, M. Jacquot, and J. M. Dudley, “Applications of femtosecond Bessel beams to laser ablation,” Appl. Phys., A Mater. Sci. Process. 112(1), 29–34 (2013).

Jefimovs, K.

K. Jefimovs, J. Vila-Comamala, M. Stampanoni, B. Kaulich, and C. David, “Beam-shaping condenser lenses for full-field transmission X-ray microscopy,” J. Synchrotron Radiat. 15(Pt 1), 106–108 (2008).
[PubMed]

Kaulich, B.

King, A.

H. Simons, A. King, W. Ludwig, C. Detlefs, W. Pantleon, S. Schmidt, I. Snigireva, A. Snigirev, and H. F. Poulsen, “Dark-field X-ray microscopy for multiscale structural characterization,” Nat. Commun. 6, 6098 (2015).
[PubMed]

Kirz, J.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400(6742), 342–344 (1999).

Kohn, V.

M. Lyubomirskiy, I. Snigireva, V. Kohn, S. Kuznetsov, V. Yunkin, G. Vaughan, and A. Snigirev, “30-Lens interferometer for high-energy X-rays,” J. Synchrotron Radiat. 23(Pt 5), 1104–1109 (2016).
[PubMed]

A. Snigirev, I. Snigireva, M. Lyubomirskiy, V. Kohn, V. Yunkin, and S. Kuznetsov, “X-ray multilens interferometer based on Si refractive lenses,” Opt. Express 22(21), 25842–25852 (2014).
[PubMed]

A. Snigirev, I. Snigireva, V. Kohn, V. Yunkin, S. Kuznetsov, M. B. Grigoriev, T. Roth, G. Vaughan, and C. Detlefs, “X-ray nanointerferometer based on Si refractive bilenses,” Phys. Rev. Lett. 103(6), 064801 (2009).
[PubMed]

V. Kohn, I. Snigireva, and A. Snigirev, “Diffraction theory of imaging with X-ray compound refractive lens,” Opt. Commun. 216(4–6), 247–260 (2003).

A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, “A compound refractive lens for focusing high-energy X-rays,” Nature 384(6604), 49–51 (1996).

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).

Krizmanic, J. F.

G. K. Skinner and J. F. Krizmanic, “X-ray interferometry with transmissive beam combiners for ultra-high angular resolution astronomy,” Exp. Astron. 27(1–2), 61–76 (2009).

Kuijk, A.

D. Byelov, J.-M. Meijer, I. Snigireva, A. Snigirev, L. Rossi, E. van den Pol, A. Kuijk, A. Phillipse, A. Imhof, A. van Blaaderen, G. J. Vroege, and A. Petukhov, “In-situ hard X-ray microscopy of self-assembly in colloidal suspentions,” RSC Advances 3(36), 15670–15677 (2013).

Kuznetsov, S.

M. Lyubomirskiy, I. Snigireva, V. Kohn, S. Kuznetsov, V. Yunkin, G. Vaughan, and A. Snigirev, “30-Lens interferometer for high-energy X-rays,” J. Synchrotron Radiat. 23(Pt 5), 1104–1109 (2016).
[PubMed]

A. Snigirev, I. Snigireva, M. Lyubomirskiy, V. Kohn, V. Yunkin, and S. Kuznetsov, “X-ray multilens interferometer based on Si refractive lenses,” Opt. Express 22(21), 25842–25852 (2014).
[PubMed]

P. Ershov, S. Kuznetsov, I. Snigireva, V. Yunkin, A. Goikhman, and A. Snigirev, “Fourier crystal diffractometry based on refractive optics,” J. Appl. Cryst. 46(5), 1475–1480 (2013).

A. Snigirev, I. Snigireva, V. Kohn, V. Yunkin, S. Kuznetsov, M. B. Grigoriev, T. Roth, G. Vaughan, and C. Detlefs, “X-ray nanointerferometer based on Si refractive bilenses,” Phys. Rev. Lett. 103(6), 064801 (2009).
[PubMed]

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).

Lengeler, B.

B. Lengeler, C. Schroer, J. Tummler, B. Benner, M. Richwin, A. Snigirev, I. Snigireva, and M. Drakopoulos, “Imaging by parabolic refractive lenses in the hard x-ray range,” J. Synchrotron Radiat. 6(6), 1153–1167 (1999).

A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, “A compound refractive lens for focusing high-energy X-rays,” Nature 384(6604), 49–51 (1996).

Lindblom, M.

Ludwig, W.

H. Simons, A. King, W. Ludwig, C. Detlefs, W. Pantleon, S. Schmidt, I. Snigireva, A. Snigirev, and H. F. Poulsen, “Dark-field X-ray microscopy for multiscale structural characterization,” Nat. Commun. 6, 6098 (2015).
[PubMed]

Lyubomirskiy, M.

M. Lyubomirskiy, I. Snigireva, V. Kohn, S. Kuznetsov, V. Yunkin, G. Vaughan, and A. Snigirev, “30-Lens interferometer for high-energy X-rays,” J. Synchrotron Radiat. 23(Pt 5), 1104–1109 (2016).
[PubMed]

A. Snigirev, I. Snigireva, M. Lyubomirskiy, V. Kohn, V. Yunkin, and S. Kuznetsov, “X-ray multilens interferometer based on Si refractive lenses,” Opt. Express 22(21), 25842–25852 (2014).
[PubMed]

Mathiesen, R. H.

K. V. Falch, D. Casari, M. Di Michiel, C. Detlefs, A. Snigirev, I. Snigireva, V. Honkimaki, and R. H. Mathiesen, “In situ hard X-ray transmission microscopy in material science,” J. Mater. Sci. 52(6), 3497–3507 (2017).

McGloin, D.

D. McGloin and K. Dholakia, “Bessel beams: diffraction in s new light,” Contemp. Phys. 46(1), 15–28 (2005).

McLeod, J. H.

Meijer, J.-M.

D. Byelov, J.-M. Meijer, I. Snigireva, A. Snigirev, L. Rossi, E. van den Pol, A. Kuijk, A. Phillipse, A. Imhof, A. van Blaaderen, G. J. Vroege, and A. Petukhov, “In-situ hard X-ray microscopy of self-assembly in colloidal suspentions,” RSC Advances 3(36), 15670–15677 (2013).

Miao, J.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400(6742), 342–344 (1999).

Mochrie, S. G. J.

M. Sutton, S. G. J. Mochrie, T. Greytak, S. E. Nagler, L. E. Berman, G. A. Held, and G. B. Stephenson, “Observation of speckle by diffraction with coherent X-rays,” Nature 352(6336), 608–610 (1991).

Mysyrowicz, A.

S. Akturk, B. Zhou, M. Franco, A. Couairon, and A. Mysyrowicz, “Generation of long plasma channels in air by focusing ulrashort laser pulses with an axicon,” Opt. Commun. 282(1), 129–134 (2009).

Nagler, S. E.

M. Sutton, S. G. J. Mochrie, T. Greytak, S. E. Nagler, L. E. Berman, G. A. Held, and G. B. Stephenson, “Observation of speckle by diffraction with coherent X-rays,” Nature 352(6336), 608–610 (1991).

Napolskii, K. S.

A. Bosak, I. Snigireva, K. S. Napolskii, and A. Snigirev, “High-resolution transmission X-ray microscopy: a new tool for mesoscopic materials,” Adv. Mater. 22(30), 3256–3259 (2010).
[PubMed]

Pantleon, W.

H. Simons, A. King, W. Ludwig, C. Detlefs, W. Pantleon, S. Schmidt, I. Snigireva, A. Snigirev, and H. F. Poulsen, “Dark-field X-ray microscopy for multiscale structural characterization,” Nat. Commun. 6, 6098 (2015).
[PubMed]

Petukhov, A.

D. Byelov, J.-M. Meijer, I. Snigireva, A. Snigirev, L. Rossi, E. van den Pol, A. Kuijk, A. Phillipse, A. Imhof, A. van Blaaderen, G. J. Vroege, and A. Petukhov, “In-situ hard X-ray microscopy of self-assembly in colloidal suspentions,” RSC Advances 3(36), 15670–15677 (2013).

Phillipse, A.

D. Byelov, J.-M. Meijer, I. Snigireva, A. Snigirev, L. Rossi, E. van den Pol, A. Kuijk, A. Phillipse, A. Imhof, A. van Blaaderen, G. J. Vroege, and A. Petukhov, “In-situ hard X-ray microscopy of self-assembly in colloidal suspentions,” RSC Advances 3(36), 15670–15677 (2013).

Polikarpov, M.

M. Polikarpov, I. Snigireva, and A. Snigirev, “X-ray harmonics rejection on third-generation synchrotron sources using compound refractive lenses,” J. Synchrotron Radiat. 21(Pt 3), 484–487 (2014).
[PubMed]

Poulsen, H. F.

H. Simons, A. King, W. Ludwig, C. Detlefs, W. Pantleon, S. Schmidt, I. Snigireva, A. Snigirev, and H. F. Poulsen, “Dark-field X-ray microscopy for multiscale structural characterization,” Nat. Commun. 6, 6098 (2015).
[PubMed]

Ren, O.

O. Ren and R. Birngruber, “Axicon: a new laser beam delivery system for corneal surgery,” IEEE J. Quantum Electron. 26(12), 2305–2308 (1990).

Richwin, M.

B. Lengeler, C. Schroer, J. Tummler, B. Benner, M. Richwin, A. Snigirev, I. Snigireva, and M. Drakopoulos, “Imaging by parabolic refractive lenses in the hard x-ray range,” J. Synchrotron Radiat. 6(6), 1153–1167 (1999).

Rossi, L.

D. Byelov, J.-M. Meijer, I. Snigireva, A. Snigirev, L. Rossi, E. van den Pol, A. Kuijk, A. Phillipse, A. Imhof, A. van Blaaderen, G. J. Vroege, and A. Petukhov, “In-situ hard X-ray microscopy of self-assembly in colloidal suspentions,” RSC Advances 3(36), 15670–15677 (2013).

Roth, T.

A. Snigirev, I. Snigireva, V. Kohn, V. Yunkin, S. Kuznetsov, M. B. Grigoriev, T. Roth, G. Vaughan, and C. Detlefs, “X-ray nanointerferometer based on Si refractive bilenses,” Phys. Rev. Lett. 103(6), 064801 (2009).
[PubMed]

Sayre, D.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400(6742), 342–344 (1999).

Schelokov, I.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).

Schilling, J.

M. Drakopoulos, A. Snigirev, I. Snigireva, and J. Schilling, “X-ray high-resolution diffraction using refractive lenses,” Appl. Phys. Lett. 86(1), 014102 (2005).

Schmidt, S.

H. Simons, A. King, W. Ludwig, C. Detlefs, W. Pantleon, S. Schmidt, I. Snigireva, A. Snigirev, and H. F. Poulsen, “Dark-field X-ray microscopy for multiscale structural characterization,” Nat. Commun. 6, 6098 (2015).
[PubMed]

Schroer, C.

B. Lengeler, C. Schroer, J. Tummler, B. Benner, M. Richwin, A. Snigirev, I. Snigireva, and M. Drakopoulos, “Imaging by parabolic refractive lenses in the hard x-ray range,” J. Synchrotron Radiat. 6(6), 1153–1167 (1999).

Shabelnikov, L.

M. Drakopoulos, J. Zegenhagen, A. Snigirev, I. Snigireva, M. Hauser, K. Eberl, V. Aristov, L. Shabelnikov, and V. Yunkin, “X-ray standing wave microscopy: Chemical microanalysis with atomic resolution,” Appl. Phys. Lett. 81(12), 2279–2281 (2002).

Simons, H.

H. Simons, A. King, W. Ludwig, C. Detlefs, W. Pantleon, S. Schmidt, I. Snigireva, A. Snigirev, and H. F. Poulsen, “Dark-field X-ray microscopy for multiscale structural characterization,” Nat. Commun. 6, 6098 (2015).
[PubMed]

Skinner, G. K.

G. K. Skinner and J. F. Krizmanic, “X-ray interferometry with transmissive beam combiners for ultra-high angular resolution astronomy,” Exp. Astron. 27(1–2), 61–76 (2009).

Snigirev, A.

K. V. Falch, D. Casari, M. Di Michiel, C. Detlefs, A. Snigirev, I. Snigireva, V. Honkimaki, and R. H. Mathiesen, “In situ hard X-ray transmission microscopy in material science,” J. Mater. Sci. 52(6), 3497–3507 (2017).

M. Lyubomirskiy, I. Snigireva, V. Kohn, S. Kuznetsov, V. Yunkin, G. Vaughan, and A. Snigirev, “30-Lens interferometer for high-energy X-rays,” J. Synchrotron Radiat. 23(Pt 5), 1104–1109 (2016).
[PubMed]

H. Simons, A. King, W. Ludwig, C. Detlefs, W. Pantleon, S. Schmidt, I. Snigireva, A. Snigirev, and H. F. Poulsen, “Dark-field X-ray microscopy for multiscale structural characterization,” Nat. Commun. 6, 6098 (2015).
[PubMed]

A. Snigirev, I. Snigireva, M. Lyubomirskiy, V. Kohn, V. Yunkin, and S. Kuznetsov, “X-ray multilens interferometer based on Si refractive lenses,” Opt. Express 22(21), 25842–25852 (2014).
[PubMed]

M. Polikarpov, I. Snigireva, and A. Snigirev, “X-ray harmonics rejection on third-generation synchrotron sources using compound refractive lenses,” J. Synchrotron Radiat. 21(Pt 3), 484–487 (2014).
[PubMed]

D. Byelov, J.-M. Meijer, I. Snigireva, A. Snigirev, L. Rossi, E. van den Pol, A. Kuijk, A. Phillipse, A. Imhof, A. van Blaaderen, G. J. Vroege, and A. Petukhov, “In-situ hard X-ray microscopy of self-assembly in colloidal suspentions,” RSC Advances 3(36), 15670–15677 (2013).

P. Ershov, S. Kuznetsov, I. Snigireva, V. Yunkin, A. Goikhman, and A. Snigirev, “Fourier crystal diffractometry based on refractive optics,” J. Appl. Cryst. 46(5), 1475–1480 (2013).

A. Bosak, I. Snigireva, K. S. Napolskii, and A. Snigirev, “High-resolution transmission X-ray microscopy: a new tool for mesoscopic materials,” Adv. Mater. 22(30), 3256–3259 (2010).
[PubMed]

A. Snigirev, I. Snigireva, V. Kohn, V. Yunkin, S. Kuznetsov, M. B. Grigoriev, T. Roth, G. Vaughan, and C. Detlefs, “X-ray nanointerferometer based on Si refractive bilenses,” Phys. Rev. Lett. 103(6), 064801 (2009).
[PubMed]

A. Snigirev and I. Snigireva, “High energy X-ray micro-optics,” C. R. Phys. 9(5–6), 507–516 (2008).

A. Snigirev, A. Bjeoumikhov, A. Erko, I. Snigireva, M. Grigoriev, V. Yunkin, M. Erko, and S. Bjeoumikhova, “Two-step hard X-ray focusing combining Fresnel zone plate and single-bounce ellipsoidal capillary,” J. Synchrotron Radiat. 14(Pt 4), 326–330 (2007).
[PubMed]

M. Drakopoulos, A. Snigirev, I. Snigireva, and J. Schilling, “X-ray high-resolution diffraction using refractive lenses,” Appl. Phys. Lett. 86(1), 014102 (2005).

V. Kohn, I. Snigireva, and A. Snigirev, “Diffraction theory of imaging with X-ray compound refractive lens,” Opt. Commun. 216(4–6), 247–260 (2003).

M. Drakopoulos, J. Zegenhagen, A. Snigirev, I. Snigireva, M. Hauser, K. Eberl, V. Aristov, L. Shabelnikov, and V. Yunkin, “X-ray standing wave microscopy: Chemical microanalysis with atomic resolution,” Appl. Phys. Lett. 81(12), 2279–2281 (2002).

B. Lengeler, C. Schroer, J. Tummler, B. Benner, M. Richwin, A. Snigirev, I. Snigireva, and M. Drakopoulos, “Imaging by parabolic refractive lenses in the hard x-ray range,” J. Synchrotron Radiat. 6(6), 1153–1167 (1999).

A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, “A compound refractive lens for focusing high-energy X-rays,” Nature 384(6604), 49–51 (1996).

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).

Snigireva, I.

K. V. Falch, D. Casari, M. Di Michiel, C. Detlefs, A. Snigirev, I. Snigireva, V. Honkimaki, and R. H. Mathiesen, “In situ hard X-ray transmission microscopy in material science,” J. Mater. Sci. 52(6), 3497–3507 (2017).

M. Lyubomirskiy, I. Snigireva, V. Kohn, S. Kuznetsov, V. Yunkin, G. Vaughan, and A. Snigirev, “30-Lens interferometer for high-energy X-rays,” J. Synchrotron Radiat. 23(Pt 5), 1104–1109 (2016).
[PubMed]

H. Simons, A. King, W. Ludwig, C. Detlefs, W. Pantleon, S. Schmidt, I. Snigireva, A. Snigirev, and H. F. Poulsen, “Dark-field X-ray microscopy for multiscale structural characterization,” Nat. Commun. 6, 6098 (2015).
[PubMed]

A. Snigirev, I. Snigireva, M. Lyubomirskiy, V. Kohn, V. Yunkin, and S. Kuznetsov, “X-ray multilens interferometer based on Si refractive lenses,” Opt. Express 22(21), 25842–25852 (2014).
[PubMed]

M. Polikarpov, I. Snigireva, and A. Snigirev, “X-ray harmonics rejection on third-generation synchrotron sources using compound refractive lenses,” J. Synchrotron Radiat. 21(Pt 3), 484–487 (2014).
[PubMed]

D. Byelov, J.-M. Meijer, I. Snigireva, A. Snigirev, L. Rossi, E. van den Pol, A. Kuijk, A. Phillipse, A. Imhof, A. van Blaaderen, G. J. Vroege, and A. Petukhov, “In-situ hard X-ray microscopy of self-assembly in colloidal suspentions,” RSC Advances 3(36), 15670–15677 (2013).

P. Ershov, S. Kuznetsov, I. Snigireva, V. Yunkin, A. Goikhman, and A. Snigirev, “Fourier crystal diffractometry based on refractive optics,” J. Appl. Cryst. 46(5), 1475–1480 (2013).

A. Bosak, I. Snigireva, K. S. Napolskii, and A. Snigirev, “High-resolution transmission X-ray microscopy: a new tool for mesoscopic materials,” Adv. Mater. 22(30), 3256–3259 (2010).
[PubMed]

A. Snigirev, I. Snigireva, V. Kohn, V. Yunkin, S. Kuznetsov, M. B. Grigoriev, T. Roth, G. Vaughan, and C. Detlefs, “X-ray nanointerferometer based on Si refractive bilenses,” Phys. Rev. Lett. 103(6), 064801 (2009).
[PubMed]

A. Snigirev and I. Snigireva, “High energy X-ray micro-optics,” C. R. Phys. 9(5–6), 507–516 (2008).

A. Snigirev, A. Bjeoumikhov, A. Erko, I. Snigireva, M. Grigoriev, V. Yunkin, M. Erko, and S. Bjeoumikhova, “Two-step hard X-ray focusing combining Fresnel zone plate and single-bounce ellipsoidal capillary,” J. Synchrotron Radiat. 14(Pt 4), 326–330 (2007).
[PubMed]

M. Drakopoulos, A. Snigirev, I. Snigireva, and J. Schilling, “X-ray high-resolution diffraction using refractive lenses,” Appl. Phys. Lett. 86(1), 014102 (2005).

V. Kohn, I. Snigireva, and A. Snigirev, “Diffraction theory of imaging with X-ray compound refractive lens,” Opt. Commun. 216(4–6), 247–260 (2003).

M. Drakopoulos, J. Zegenhagen, A. Snigirev, I. Snigireva, M. Hauser, K. Eberl, V. Aristov, L. Shabelnikov, and V. Yunkin, “X-ray standing wave microscopy: Chemical microanalysis with atomic resolution,” Appl. Phys. Lett. 81(12), 2279–2281 (2002).

B. Lengeler, C. Schroer, J. Tummler, B. Benner, M. Richwin, A. Snigirev, I. Snigireva, and M. Drakopoulos, “Imaging by parabolic refractive lenses in the hard x-ray range,” J. Synchrotron Radiat. 6(6), 1153–1167 (1999).

A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, “A compound refractive lens for focusing high-energy X-rays,” Nature 384(6604), 49–51 (1996).

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).

Stampanoni, M.

K. Jefimovs, J. Vila-Comamala, M. Stampanoni, B. Kaulich, and C. David, “Beam-shaping condenser lenses for full-field transmission X-ray microscopy,” J. Synchrotron Radiat. 15(Pt 1), 106–108 (2008).
[PubMed]

Stephenson, G. B.

M. Sutton, S. G. J. Mochrie, T. Greytak, S. E. Nagler, L. E. Berman, G. A. Held, and G. B. Stephenson, “Observation of speckle by diffraction with coherent X-rays,” Nature 352(6336), 608–610 (1991).

Susini, J.

Sutton, M.

M. Sutton, S. G. J. Mochrie, T. Greytak, S. E. Nagler, L. E. Berman, G. A. Held, and G. B. Stephenson, “Observation of speckle by diffraction with coherent X-rays,” Nature 352(6336), 608–610 (1991).

Tummler, J.

B. Lengeler, C. Schroer, J. Tummler, B. Benner, M. Richwin, A. Snigirev, I. Snigireva, and M. Drakopoulos, “Imaging by parabolic refractive lenses in the hard x-ray range,” J. Synchrotron Radiat. 6(6), 1153–1167 (1999).

van Blaaderen, A.

D. Byelov, J.-M. Meijer, I. Snigireva, A. Snigirev, L. Rossi, E. van den Pol, A. Kuijk, A. Phillipse, A. Imhof, A. van Blaaderen, G. J. Vroege, and A. Petukhov, “In-situ hard X-ray microscopy of self-assembly in colloidal suspentions,” RSC Advances 3(36), 15670–15677 (2013).

van den Pol, E.

D. Byelov, J.-M. Meijer, I. Snigireva, A. Snigirev, L. Rossi, E. van den Pol, A. Kuijk, A. Phillipse, A. Imhof, A. van Blaaderen, G. J. Vroege, and A. Petukhov, “In-situ hard X-ray microscopy of self-assembly in colloidal suspentions,” RSC Advances 3(36), 15670–15677 (2013).

Vaughan, G.

M. Lyubomirskiy, I. Snigireva, V. Kohn, S. Kuznetsov, V. Yunkin, G. Vaughan, and A. Snigirev, “30-Lens interferometer for high-energy X-rays,” J. Synchrotron Radiat. 23(Pt 5), 1104–1109 (2016).
[PubMed]

A. Snigirev, I. Snigireva, V. Kohn, V. Yunkin, S. Kuznetsov, M. B. Grigoriev, T. Roth, G. Vaughan, and C. Detlefs, “X-ray nanointerferometer based on Si refractive bilenses,” Phys. Rev. Lett. 103(6), 064801 (2009).
[PubMed]

Vila-Comamala, J.

K. Jefimovs, J. Vila-Comamala, M. Stampanoni, B. Kaulich, and C. David, “Beam-shaping condenser lenses for full-field transmission X-ray microscopy,” J. Synchrotron Radiat. 15(Pt 1), 106–108 (2008).
[PubMed]

Vogt, S.

C. Holzner, M. Feser, S. Vogt, B. Hornberger, S. B. Baines, and C. Jacobsen, “Zernike phase contrast in scanning microscopy with X-rays,” Nat. Phys. 6(11), 883–887 (2010).
[PubMed]

Vogt, U.

Vroege, G. J.

D. Byelov, J.-M. Meijer, I. Snigireva, A. Snigirev, L. Rossi, E. van den Pol, A. Kuijk, A. Phillipse, A. Imhof, A. van Blaaderen, G. J. Vroege, and A. Petukhov, “In-situ hard X-ray microscopy of self-assembly in colloidal suspentions,” RSC Advances 3(36), 15670–15677 (2013).

Wilhein, T.

Yunkin, V.

M. Lyubomirskiy, I. Snigireva, V. Kohn, S. Kuznetsov, V. Yunkin, G. Vaughan, and A. Snigirev, “30-Lens interferometer for high-energy X-rays,” J. Synchrotron Radiat. 23(Pt 5), 1104–1109 (2016).
[PubMed]

A. Snigirev, I. Snigireva, M. Lyubomirskiy, V. Kohn, V. Yunkin, and S. Kuznetsov, “X-ray multilens interferometer based on Si refractive lenses,” Opt. Express 22(21), 25842–25852 (2014).
[PubMed]

P. Ershov, S. Kuznetsov, I. Snigireva, V. Yunkin, A. Goikhman, and A. Snigirev, “Fourier crystal diffractometry based on refractive optics,” J. Appl. Cryst. 46(5), 1475–1480 (2013).

A. Snigirev, I. Snigireva, V. Kohn, V. Yunkin, S. Kuznetsov, M. B. Grigoriev, T. Roth, G. Vaughan, and C. Detlefs, “X-ray nanointerferometer based on Si refractive bilenses,” Phys. Rev. Lett. 103(6), 064801 (2009).
[PubMed]

A. Snigirev, A. Bjeoumikhov, A. Erko, I. Snigireva, M. Grigoriev, V. Yunkin, M. Erko, and S. Bjeoumikhova, “Two-step hard X-ray focusing combining Fresnel zone plate and single-bounce ellipsoidal capillary,” J. Synchrotron Radiat. 14(Pt 4), 326–330 (2007).
[PubMed]

M. Drakopoulos, J. Zegenhagen, A. Snigirev, I. Snigireva, M. Hauser, K. Eberl, V. Aristov, L. Shabelnikov, and V. Yunkin, “X-ray standing wave microscopy: Chemical microanalysis with atomic resolution,” Appl. Phys. Lett. 81(12), 2279–2281 (2002).

Zegenhagen, J.

M. Drakopoulos, J. Zegenhagen, A. Snigirev, I. Snigireva, M. Hauser, K. Eberl, V. Aristov, L. Shabelnikov, and V. Yunkin, “X-ray standing wave microscopy: Chemical microanalysis with atomic resolution,” Appl. Phys. Lett. 81(12), 2279–2281 (2002).

Zhang, J.

F. Courvoisier, J. Zhang, M. K. Bhuyan, M. Jacquot, and J. M. Dudley, “Applications of femtosecond Bessel beams to laser ablation,” Appl. Phys., A Mater. Sci. Process. 112(1), 29–34 (2013).

Zhou, B.

S. Akturk, B. Zhou, M. Franco, A. Couairon, and A. Mysyrowicz, “Generation of long plasma channels in air by focusing ulrashort laser pulses with an axicon,” Opt. Commun. 282(1), 129–134 (2009).

Adv. Mater. (1)

A. Bosak, I. Snigireva, K. S. Napolskii, and A. Snigirev, “High-resolution transmission X-ray microscopy: a new tool for mesoscopic materials,” Adv. Mater. 22(30), 3256–3259 (2010).
[PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

M. Drakopoulos, J. Zegenhagen, A. Snigirev, I. Snigireva, M. Hauser, K. Eberl, V. Aristov, L. Shabelnikov, and V. Yunkin, “X-ray standing wave microscopy: Chemical microanalysis with atomic resolution,” Appl. Phys. Lett. 81(12), 2279–2281 (2002).

M. Drakopoulos, A. Snigirev, I. Snigireva, and J. Schilling, “X-ray high-resolution diffraction using refractive lenses,” Appl. Phys. Lett. 86(1), 014102 (2005).

Appl. Phys., A Mater. Sci. Process. (1)

F. Courvoisier, J. Zhang, M. K. Bhuyan, M. Jacquot, and J. M. Dudley, “Applications of femtosecond Bessel beams to laser ablation,” Appl. Phys., A Mater. Sci. Process. 112(1), 29–34 (2013).

C. R. Phys. (1)

A. Snigirev and I. Snigireva, “High energy X-ray micro-optics,” C. R. Phys. 9(5–6), 507–516 (2008).

Contemp. Phys. (1)

D. McGloin and K. Dholakia, “Bessel beams: diffraction in s new light,” Contemp. Phys. 46(1), 15–28 (2005).

Exp. Astron. (1)

G. K. Skinner and J. F. Krizmanic, “X-ray interferometry with transmissive beam combiners for ultra-high angular resolution astronomy,” Exp. Astron. 27(1–2), 61–76 (2009).

IEEE J. Quantum Electron. (1)

O. Ren and R. Birngruber, “Axicon: a new laser beam delivery system for corneal surgery,” IEEE J. Quantum Electron. 26(12), 2305–2308 (1990).

J. Appl. Cryst. (1)

P. Ershov, S. Kuznetsov, I. Snigireva, V. Yunkin, A. Goikhman, and A. Snigirev, “Fourier crystal diffractometry based on refractive optics,” J. Appl. Cryst. 46(5), 1475–1480 (2013).

J. Mater. Sci. (1)

K. V. Falch, D. Casari, M. Di Michiel, C. Detlefs, A. Snigirev, I. Snigireva, V. Honkimaki, and R. H. Mathiesen, “In situ hard X-ray transmission microscopy in material science,” J. Mater. Sci. 52(6), 3497–3507 (2017).

J. Opt. Soc. Am. (2)

J. Synchrotron Radiat. (5)

B. Lengeler, C. Schroer, J. Tummler, B. Benner, M. Richwin, A. Snigirev, I. Snigireva, and M. Drakopoulos, “Imaging by parabolic refractive lenses in the hard x-ray range,” J. Synchrotron Radiat. 6(6), 1153–1167 (1999).

A. Snigirev, A. Bjeoumikhov, A. Erko, I. Snigireva, M. Grigoriev, V. Yunkin, M. Erko, and S. Bjeoumikhova, “Two-step hard X-ray focusing combining Fresnel zone plate and single-bounce ellipsoidal capillary,” J. Synchrotron Radiat. 14(Pt 4), 326–330 (2007).
[PubMed]

M. Polikarpov, I. Snigireva, and A. Snigirev, “X-ray harmonics rejection on third-generation synchrotron sources using compound refractive lenses,” J. Synchrotron Radiat. 21(Pt 3), 484–487 (2014).
[PubMed]

M. Lyubomirskiy, I. Snigireva, V. Kohn, S. Kuznetsov, V. Yunkin, G. Vaughan, and A. Snigirev, “30-Lens interferometer for high-energy X-rays,” J. Synchrotron Radiat. 23(Pt 5), 1104–1109 (2016).
[PubMed]

K. Jefimovs, J. Vila-Comamala, M. Stampanoni, B. Kaulich, and C. David, “Beam-shaping condenser lenses for full-field transmission X-ray microscopy,” J. Synchrotron Radiat. 15(Pt 1), 106–108 (2008).
[PubMed]

Laser Photonics Rev. (1)

M. Duocastella and C. B. Arnold, “Bessel and annular beams for materials processing,” Laser Photonics Rev. 6(5), 607–621 (2012).

Nat. Commun. (1)

H. Simons, A. King, W. Ludwig, C. Detlefs, W. Pantleon, S. Schmidt, I. Snigireva, A. Snigirev, and H. F. Poulsen, “Dark-field X-ray microscopy for multiscale structural characterization,” Nat. Commun. 6, 6098 (2015).
[PubMed]

Nat. Phys. (1)

C. Holzner, M. Feser, S. Vogt, B. Hornberger, S. B. Baines, and C. Jacobsen, “Zernike phase contrast in scanning microscopy with X-rays,” Nat. Phys. 6(11), 883–887 (2010).
[PubMed]

Nature (3)

M. Sutton, S. G. J. Mochrie, T. Greytak, S. E. Nagler, L. E. Berman, G. A. Held, and G. B. Stephenson, “Observation of speckle by diffraction with coherent X-rays,” Nature 352(6336), 608–610 (1991).

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400(6742), 342–344 (1999).

A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, “A compound refractive lens for focusing high-energy X-rays,” Nature 384(6604), 49–51 (1996).

Opt. Commun. (2)

V. Kohn, I. Snigireva, and A. Snigirev, “Diffraction theory of imaging with X-ray compound refractive lens,” Opt. Commun. 216(4–6), 247–260 (2003).

S. Akturk, B. Zhou, M. Franco, A. Couairon, and A. Mysyrowicz, “Generation of long plasma channels in air by focusing ulrashort laser pulses with an axicon,” Opt. Commun. 282(1), 129–134 (2009).

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

A. Snigirev, I. Snigireva, V. Kohn, V. Yunkin, S. Kuznetsov, M. B. Grigoriev, T. Roth, G. Vaughan, and C. Detlefs, “X-ray nanointerferometer based on Si refractive bilenses,” Phys. Rev. Lett. 103(6), 064801 (2009).
[PubMed]

Rev. Sci. Instrum. (1)

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).

RSC Advances (1)

D. Byelov, J.-M. Meijer, I. Snigireva, A. Snigirev, L. Rossi, E. van den Pol, A. Kuijk, A. Phillipse, A. Imhof, A. van Blaaderen, G. J. Vroege, and A. Petukhov, “In-situ hard X-ray microscopy of self-assembly in colloidal suspentions,” RSC Advances 3(36), 15670–15677 (2013).

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 (5)

Fig. 1
Fig. 1 (a) Schematic construction of the profile of a parabolic axicon refractive surface. (b) Cross-section of the single parabolic axicon lens.
Fig. 2
Fig. 2 Schematic view of the shaped beam produced by X-ray parabolic axicon lens. (a) The beam propagation through the axicon lens and the intensity distribution along the optical axis. Transformed beam forms an interference area in the near field and a ring area in far field. (b) The intensity distribution of the ring-shaped beam in the focusing position f and its cross-section. (c) The typical pattern of the Bessel beam produced at the interference area and its cross-section.
Fig. 3
Fig. 3 Experimental layout for the test of X-ray parabolic axicon lenses. The axicon lenses are illuminated by synchrotron radiation and generate shaped beam registered by CCD detector.
Fig. 4
Fig. 4 The Bessel beam generated by X-ray parabolic axicon lense in interference area, recorded with 10 keV X-rays at 1.4 m from the lens. (a) Transverse intensity distribution of the Bessel beam (inverted grayscale). (b) Intensity profile obtained for the vertical cross-section through the centre of the Bessel beam pattern.
Fig. 5
Fig. 5 The ring-shaped beam generated by X-ray parabolic axicon lens in the ring area, recorded with 12.4 keV X-rays. (a) Transverse intensity distribution of the beam with elliptical shape obtained while horizontal slit was closed to 30 μm (inverted grayscale). The intensity profiles along the (b) vertical major and (c) horizontal minor axes of the elliptical form of the beam. (d) Transverse intensity distribution of the ring-shaped beam obtained at the focusing position with secondary point-like source generated by horizontal and vertical slits (inverted grayscale).

Equations (7)

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

z(r,φ)= 1 2R r 2 + b R r.
F(ρ,z)= k iz exp( ikz )exp( ik ρ 2 2z ) 0 τ(r) exp( ik r 2 2z ) J 0 ( krρ z )rdr,
τ(r)=exp[ 2N( μ 2 +ikδ )( 1 2R r 2 + b R r ) ],
I(ρ,z) I 0 (z) J 0 2 ( kb fz ρ ),
d ρ (z) 2.4λ π fz b ,
I 0 (z)= 2πkf b 2 z ( fz ) 3 exp[ μ b 2 fδ ( z 2 2fz ( fz ) 2 ) ].
I(ρ,z) J 0 2 ( 1 A kb fz ρ ),

Metrics