Abstract

Quality of a refractive compound X-ray lens can be limited by imperfections in surfaces of unit lenses and stacking precision. In general case both the lens transmission and optical aberrations define properties of a beam in the lens exit plane; together they can be expressed in terms of the generalized pupil function. In this work we measure this function for a diamond single crystal compound refractive lens. Consequently, we apply the pupil function to evaluate the performance of the examined compound refractive X-ray lens. A number of practically important conclusions can be drawn from such analysis.

© 2017 Optical Society of America

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  1. A. Snigirev, V. Kohn, I. Snigireva, A. Souvorov, and B. Lengeler, “Focusing high-energy x rays by compound refractive lenses,” Appl. Opt. 37(4), 653–662 (1998).
    [Crossref] [PubMed]
  2. B. Lengeler, J. Tümmler, A. Snigirev, I. Snigireva, and C. Raven, “Transmission and gain of singly and doubly focusing refractive x-ray lenses,” J. Appl. Phys. 84(11), 5855–5861 (1998).
    [Crossref]
  3. A. Snigirev, Y. Yunkin, I. Snigireva, M. Di Michiel, M. Drakopoulos, S. Kouznetsov, L. Shabel’nikov, M. Grigoriev, V. Ralchenko, I. Sychov, M. Hoffmann, and E. I. Voges, “Design and microfabrication of novel X-ray optics,” Proc. SPIE 4783, 1–9 (2002).
    [Crossref]
  4. S. Terentyev, V. Blank, S. Polyakov, S. Zholudev, A. Snigirev, M. Polikarpov, T. Kolodziej, J. Qian, H. Zhou, and Y. Shvyd’ko, “Parabolic single-crystal diamond lenses for coherent x-ray imaging,” Appl. Phys. Lett. 107(11), 111108 (2015).
    [Crossref]
  5. P. Heimann, M. MacDonald, B. Nagler, H. J. Lee, E. Galtier, B. Arnold, and Z. Xing, “Compound refractive lenses as prefocusing optics for X-ray FEL radiation,” J. Synchrotron Radiat. 23(2), 425–429 (2016).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
  10. F. J. Koch, C. Detlefs, T. J. Schröter, D. Kunka, A. Last, and J. Mohr, “Quantitative characterization of X-ray lenses from two fabrication techniques with grating Interferometry,” Opt. Express 24(9), 9168–9177 (2016).
    [Crossref] [PubMed]
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    [Crossref]
  12. M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
    [Crossref] [PubMed]
  13. S. Gasilov, A. Mittone, E. Brun, A. Bravin, S. Grandl, A. Mirone, and P. Coan, “Tomographic reconstruction of the refractive index with hard X-rays: an efficient method based on the gradient vector-field approach,” Opt. Express 22(5), 5216–5227 (2014).
    [Crossref] [PubMed]
  14. J. C. Wyant and K. Creath, “Basic wavefront Aberration theory for Optical Metrology,” Appl. Opt. Opt. Eng. 11, 2–53 (1992).
  15. F. Seiboth, A. Schropp, M. Scholz, F. Wittwer, C. Rödel, M. Wünsche, T. Ullsperger, S. Nolte, J. Rahomäki, K. Parfeniukas, S. Giakoumidis, U. Vogt, U. Wagner, C. Rau, U. Boesenberg, J. Garrevoet, G. Falkenberg, E. C. Galtier, H. Ja Lee, B. Nagler, and C. G. Schroer, “Perfect X-ray focusing via fitting corrective glasses to aberrated optics,” Nat. Commun. 8, 14623 (2017).
    [Crossref] [PubMed]

2017 (1)

F. Seiboth, A. Schropp, M. Scholz, F. Wittwer, C. Rödel, M. Wünsche, T. Ullsperger, S. Nolte, J. Rahomäki, K. Parfeniukas, S. Giakoumidis, U. Vogt, U. Wagner, C. Rau, U. Boesenberg, J. Garrevoet, G. Falkenberg, E. C. Galtier, H. Ja Lee, B. Nagler, and C. G. Schroer, “Perfect X-ray focusing via fitting corrective glasses to aberrated optics,” Nat. Commun. 8, 14623 (2017).
[Crossref] [PubMed]

2016 (2)

P. Heimann, M. MacDonald, B. Nagler, H. J. Lee, E. Galtier, B. Arnold, and Z. Xing, “Compound refractive lenses as prefocusing optics for X-ray FEL radiation,” J. Synchrotron Radiat. 23(2), 425–429 (2016).
[Crossref] [PubMed]

F. J. Koch, C. Detlefs, T. J. Schröter, D. Kunka, A. Last, and J. Mohr, “Quantitative characterization of X-ray lenses from two fabrication techniques with grating Interferometry,” Opt. Express 24(9), 9168–9177 (2016).
[Crossref] [PubMed]

2015 (1)

S. Terentyev, V. Blank, S. Polyakov, S. Zholudev, A. Snigirev, M. Polikarpov, T. Kolodziej, J. Qian, H. Zhou, and Y. Shvyd’ko, “Parabolic single-crystal diamond lenses for coherent x-ray imaging,” Appl. Phys. Lett. 107(11), 111108 (2015).
[Crossref]

2014 (1)

2011 (1)

S. Rutishauser, I. Zanette, T. Weitkamp, T. Donath, and C. David, “At-wavelength characterization of refractive x-ray lenses using a two-dimensional grating interferometer,” Appl. Phys. Lett. 99(22), 221104 (2011).
[Crossref]

2005 (1)

T. Weitkamp, B. Nöhammer, A. Diaz, C. David, and E. Ziegler, “X-ray wavefront analysis and optics characterization with a grating interferometer,” Appl. Phys. Lett. 86(5), 054101 (2005).
[Crossref]

2003 (1)

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[Crossref] [PubMed]

2002 (1)

A. Snigirev, Y. Yunkin, I. Snigireva, M. Di Michiel, M. Drakopoulos, S. Kouznetsov, L. Shabel’nikov, M. Grigoriev, V. Ralchenko, I. Sychov, M. Hoffmann, and E. I. Voges, “Design and microfabrication of novel X-ray optics,” Proc. SPIE 4783, 1–9 (2002).
[Crossref]

1998 (2)

A. Snigirev, V. Kohn, I. Snigireva, A. Souvorov, and B. Lengeler, “Focusing high-energy x rays by compound refractive lenses,” Appl. Opt. 37(4), 653–662 (1998).
[Crossref] [PubMed]

B. Lengeler, J. Tümmler, A. Snigirev, I. Snigireva, and C. Raven, “Transmission and gain of singly and doubly focusing refractive x-ray lenses,” J. Appl. Phys. 84(11), 5855–5861 (1998).
[Crossref]

1992 (1)

J. C. Wyant and K. Creath, “Basic wavefront Aberration theory for Optical Metrology,” Appl. Opt. Opt. Eng. 11, 2–53 (1992).

1926 (1)

C. M. Slack, “The refraction of X-rays in prisms of various materials,” Phys. Rev. 27(6), 691–695 (1926).
[Crossref]

Anastasio, M. A.

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[Crossref] [PubMed]

Arnold, B.

P. Heimann, M. MacDonald, B. Nagler, H. J. Lee, E. Galtier, B. Arnold, and Z. Xing, “Compound refractive lenses as prefocusing optics for X-ray FEL radiation,” J. Synchrotron Radiat. 23(2), 425–429 (2016).
[Crossref] [PubMed]

Blank, V.

S. Terentyev, V. Blank, S. Polyakov, S. Zholudev, A. Snigirev, M. Polikarpov, T. Kolodziej, J. Qian, H. Zhou, and Y. Shvyd’ko, “Parabolic single-crystal diamond lenses for coherent x-ray imaging,” Appl. Phys. Lett. 107(11), 111108 (2015).
[Crossref]

Boesenberg, U.

F. Seiboth, A. Schropp, M. Scholz, F. Wittwer, C. Rödel, M. Wünsche, T. Ullsperger, S. Nolte, J. Rahomäki, K. Parfeniukas, S. Giakoumidis, U. Vogt, U. Wagner, C. Rau, U. Boesenberg, J. Garrevoet, G. Falkenberg, E. C. Galtier, H. Ja Lee, B. Nagler, and C. G. Schroer, “Perfect X-ray focusing via fitting corrective glasses to aberrated optics,” Nat. Commun. 8, 14623 (2017).
[Crossref] [PubMed]

Brankov, J. G.

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[Crossref] [PubMed]

Bravin, A.

Brun, E.

Chapman, D.

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[Crossref] [PubMed]

Coan, P.

Creath, K.

J. C. Wyant and K. Creath, “Basic wavefront Aberration theory for Optical Metrology,” Appl. Opt. Opt. Eng. 11, 2–53 (1992).

David, C.

S. Rutishauser, I. Zanette, T. Weitkamp, T. Donath, and C. David, “At-wavelength characterization of refractive x-ray lenses using a two-dimensional grating interferometer,” Appl. Phys. Lett. 99(22), 221104 (2011).
[Crossref]

T. Weitkamp, B. Nöhammer, A. Diaz, C. David, and E. Ziegler, “X-ray wavefront analysis and optics characterization with a grating interferometer,” Appl. Phys. Lett. 86(5), 054101 (2005).
[Crossref]

Detlefs, C.

Di Michiel, M.

A. Snigirev, Y. Yunkin, I. Snigireva, M. Di Michiel, M. Drakopoulos, S. Kouznetsov, L. Shabel’nikov, M. Grigoriev, V. Ralchenko, I. Sychov, M. Hoffmann, and E. I. Voges, “Design and microfabrication of novel X-ray optics,” Proc. SPIE 4783, 1–9 (2002).
[Crossref]

Diaz, A.

T. Weitkamp, B. Nöhammer, A. Diaz, C. David, and E. Ziegler, “X-ray wavefront analysis and optics characterization with a grating interferometer,” Appl. Phys. Lett. 86(5), 054101 (2005).
[Crossref]

Donath, T.

S. Rutishauser, I. Zanette, T. Weitkamp, T. Donath, and C. David, “At-wavelength characterization of refractive x-ray lenses using a two-dimensional grating interferometer,” Appl. Phys. Lett. 99(22), 221104 (2011).
[Crossref]

Drakopoulos, M.

A. Snigirev, Y. Yunkin, I. Snigireva, M. Di Michiel, M. Drakopoulos, S. Kouznetsov, L. Shabel’nikov, M. Grigoriev, V. Ralchenko, I. Sychov, M. Hoffmann, and E. I. Voges, “Design and microfabrication of novel X-ray optics,” Proc. SPIE 4783, 1–9 (2002).
[Crossref]

Falkenberg, G.

F. Seiboth, A. Schropp, M. Scholz, F. Wittwer, C. Rödel, M. Wünsche, T. Ullsperger, S. Nolte, J. Rahomäki, K. Parfeniukas, S. Giakoumidis, U. Vogt, U. Wagner, C. Rau, U. Boesenberg, J. Garrevoet, G. Falkenberg, E. C. Galtier, H. Ja Lee, B. Nagler, and C. G. Schroer, “Perfect X-ray focusing via fitting corrective glasses to aberrated optics,” Nat. Commun. 8, 14623 (2017).
[Crossref] [PubMed]

Galatsanos, N. P.

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[Crossref] [PubMed]

Galtier, E.

P. Heimann, M. MacDonald, B. Nagler, H. J. Lee, E. Galtier, B. Arnold, and Z. Xing, “Compound refractive lenses as prefocusing optics for X-ray FEL radiation,” J. Synchrotron Radiat. 23(2), 425–429 (2016).
[Crossref] [PubMed]

Galtier, E. C.

F. Seiboth, A. Schropp, M. Scholz, F. Wittwer, C. Rödel, M. Wünsche, T. Ullsperger, S. Nolte, J. Rahomäki, K. Parfeniukas, S. Giakoumidis, U. Vogt, U. Wagner, C. Rau, U. Boesenberg, J. Garrevoet, G. Falkenberg, E. C. Galtier, H. Ja Lee, B. Nagler, and C. G. Schroer, “Perfect X-ray focusing via fitting corrective glasses to aberrated optics,” Nat. Commun. 8, 14623 (2017).
[Crossref] [PubMed]

Garrevoet, J.

F. Seiboth, A. Schropp, M. Scholz, F. Wittwer, C. Rödel, M. Wünsche, T. Ullsperger, S. Nolte, J. Rahomäki, K. Parfeniukas, S. Giakoumidis, U. Vogt, U. Wagner, C. Rau, U. Boesenberg, J. Garrevoet, G. Falkenberg, E. C. Galtier, H. Ja Lee, B. Nagler, and C. G. Schroer, “Perfect X-ray focusing via fitting corrective glasses to aberrated optics,” Nat. Commun. 8, 14623 (2017).
[Crossref] [PubMed]

Gasilov, S.

Giakoumidis, S.

F. Seiboth, A. Schropp, M. Scholz, F. Wittwer, C. Rödel, M. Wünsche, T. Ullsperger, S. Nolte, J. Rahomäki, K. Parfeniukas, S. Giakoumidis, U. Vogt, U. Wagner, C. Rau, U. Boesenberg, J. Garrevoet, G. Falkenberg, E. C. Galtier, H. Ja Lee, B. Nagler, and C. G. Schroer, “Perfect X-ray focusing via fitting corrective glasses to aberrated optics,” Nat. Commun. 8, 14623 (2017).
[Crossref] [PubMed]

Grandl, S.

Grigoriev, M.

A. Snigirev, Y. Yunkin, I. Snigireva, M. Di Michiel, M. Drakopoulos, S. Kouznetsov, L. Shabel’nikov, M. Grigoriev, V. Ralchenko, I. Sychov, M. Hoffmann, and E. I. Voges, “Design and microfabrication of novel X-ray optics,” Proc. SPIE 4783, 1–9 (2002).
[Crossref]

Heimann, P.

P. Heimann, M. MacDonald, B. Nagler, H. J. Lee, E. Galtier, B. Arnold, and Z. Xing, “Compound refractive lenses as prefocusing optics for X-ray FEL radiation,” J. Synchrotron Radiat. 23(2), 425–429 (2016).
[Crossref] [PubMed]

Hoffmann, M.

A. Snigirev, Y. Yunkin, I. Snigireva, M. Di Michiel, M. Drakopoulos, S. Kouznetsov, L. Shabel’nikov, M. Grigoriev, V. Ralchenko, I. Sychov, M. Hoffmann, and E. I. Voges, “Design and microfabrication of novel X-ray optics,” Proc. SPIE 4783, 1–9 (2002).
[Crossref]

Ja Lee, H.

F. Seiboth, A. Schropp, M. Scholz, F. Wittwer, C. Rödel, M. Wünsche, T. Ullsperger, S. Nolte, J. Rahomäki, K. Parfeniukas, S. Giakoumidis, U. Vogt, U. Wagner, C. Rau, U. Boesenberg, J. Garrevoet, G. Falkenberg, E. C. Galtier, H. Ja Lee, B. Nagler, and C. G. Schroer, “Perfect X-ray focusing via fitting corrective glasses to aberrated optics,” Nat. Commun. 8, 14623 (2017).
[Crossref] [PubMed]

Koch, F. J.

Kohn, V.

Kolodziej, T.

S. Terentyev, V. Blank, S. Polyakov, S. Zholudev, A. Snigirev, M. Polikarpov, T. Kolodziej, J. Qian, H. Zhou, and Y. Shvyd’ko, “Parabolic single-crystal diamond lenses for coherent x-ray imaging,” Appl. Phys. Lett. 107(11), 111108 (2015).
[Crossref]

Kouznetsov, S.

A. Snigirev, Y. Yunkin, I. Snigireva, M. Di Michiel, M. Drakopoulos, S. Kouznetsov, L. Shabel’nikov, M. Grigoriev, V. Ralchenko, I. Sychov, M. Hoffmann, and E. I. Voges, “Design and microfabrication of novel X-ray optics,” Proc. SPIE 4783, 1–9 (2002).
[Crossref]

Kunka, D.

Last, A.

Lee, H. J.

P. Heimann, M. MacDonald, B. Nagler, H. J. Lee, E. Galtier, B. Arnold, and Z. Xing, “Compound refractive lenses as prefocusing optics for X-ray FEL radiation,” J. Synchrotron Radiat. 23(2), 425–429 (2016).
[Crossref] [PubMed]

Lengeler, B.

B. Lengeler, J. Tümmler, A. Snigirev, I. Snigireva, and C. Raven, “Transmission and gain of singly and doubly focusing refractive x-ray lenses,” J. Appl. Phys. 84(11), 5855–5861 (1998).
[Crossref]

A. Snigirev, V. Kohn, I. Snigireva, A. Souvorov, and B. Lengeler, “Focusing high-energy x rays by compound refractive lenses,” Appl. Opt. 37(4), 653–662 (1998).
[Crossref] [PubMed]

MacDonald, M.

P. Heimann, M. MacDonald, B. Nagler, H. J. Lee, E. Galtier, B. Arnold, and Z. Xing, “Compound refractive lenses as prefocusing optics for X-ray FEL radiation,” J. Synchrotron Radiat. 23(2), 425–429 (2016).
[Crossref] [PubMed]

Mirone, A.

Mittone, A.

Mohr, J.

Muehleman, C.

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[Crossref] [PubMed]

Nagler, B.

F. Seiboth, A. Schropp, M. Scholz, F. Wittwer, C. Rödel, M. Wünsche, T. Ullsperger, S. Nolte, J. Rahomäki, K. Parfeniukas, S. Giakoumidis, U. Vogt, U. Wagner, C. Rau, U. Boesenberg, J. Garrevoet, G. Falkenberg, E. C. Galtier, H. Ja Lee, B. Nagler, and C. G. Schroer, “Perfect X-ray focusing via fitting corrective glasses to aberrated optics,” Nat. Commun. 8, 14623 (2017).
[Crossref] [PubMed]

P. Heimann, M. MacDonald, B. Nagler, H. J. Lee, E. Galtier, B. Arnold, and Z. Xing, “Compound refractive lenses as prefocusing optics for X-ray FEL radiation,” J. Synchrotron Radiat. 23(2), 425–429 (2016).
[Crossref] [PubMed]

Nöhammer, B.

T. Weitkamp, B. Nöhammer, A. Diaz, C. David, and E. Ziegler, “X-ray wavefront analysis and optics characterization with a grating interferometer,” Appl. Phys. Lett. 86(5), 054101 (2005).
[Crossref]

Nolte, S.

F. Seiboth, A. Schropp, M. Scholz, F. Wittwer, C. Rödel, M. Wünsche, T. Ullsperger, S. Nolte, J. Rahomäki, K. Parfeniukas, S. Giakoumidis, U. Vogt, U. Wagner, C. Rau, U. Boesenberg, J. Garrevoet, G. Falkenberg, E. C. Galtier, H. Ja Lee, B. Nagler, and C. G. Schroer, “Perfect X-ray focusing via fitting corrective glasses to aberrated optics,” Nat. Commun. 8, 14623 (2017).
[Crossref] [PubMed]

Oltulu, O.

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[Crossref] [PubMed]

Parfeniukas, K.

F. Seiboth, A. Schropp, M. Scholz, F. Wittwer, C. Rödel, M. Wünsche, T. Ullsperger, S. Nolte, J. Rahomäki, K. Parfeniukas, S. Giakoumidis, U. Vogt, U. Wagner, C. Rau, U. Boesenberg, J. Garrevoet, G. Falkenberg, E. C. Galtier, H. Ja Lee, B. Nagler, and C. G. Schroer, “Perfect X-ray focusing via fitting corrective glasses to aberrated optics,” Nat. Commun. 8, 14623 (2017).
[Crossref] [PubMed]

Polikarpov, M.

S. Terentyev, V. Blank, S. Polyakov, S. Zholudev, A. Snigirev, M. Polikarpov, T. Kolodziej, J. Qian, H. Zhou, and Y. Shvyd’ko, “Parabolic single-crystal diamond lenses for coherent x-ray imaging,” Appl. Phys. Lett. 107(11), 111108 (2015).
[Crossref]

Polyakov, S.

S. Terentyev, V. Blank, S. Polyakov, S. Zholudev, A. Snigirev, M. Polikarpov, T. Kolodziej, J. Qian, H. Zhou, and Y. Shvyd’ko, “Parabolic single-crystal diamond lenses for coherent x-ray imaging,” Appl. Phys. Lett. 107(11), 111108 (2015).
[Crossref]

Qian, J.

S. Terentyev, V. Blank, S. Polyakov, S. Zholudev, A. Snigirev, M. Polikarpov, T. Kolodziej, J. Qian, H. Zhou, and Y. Shvyd’ko, “Parabolic single-crystal diamond lenses for coherent x-ray imaging,” Appl. Phys. Lett. 107(11), 111108 (2015).
[Crossref]

Rahomäki, J.

F. Seiboth, A. Schropp, M. Scholz, F. Wittwer, C. Rödel, M. Wünsche, T. Ullsperger, S. Nolte, J. Rahomäki, K. Parfeniukas, S. Giakoumidis, U. Vogt, U. Wagner, C. Rau, U. Boesenberg, J. Garrevoet, G. Falkenberg, E. C. Galtier, H. Ja Lee, B. Nagler, and C. G. Schroer, “Perfect X-ray focusing via fitting corrective glasses to aberrated optics,” Nat. Commun. 8, 14623 (2017).
[Crossref] [PubMed]

Ralchenko, V.

A. Snigirev, Y. Yunkin, I. Snigireva, M. Di Michiel, M. Drakopoulos, S. Kouznetsov, L. Shabel’nikov, M. Grigoriev, V. Ralchenko, I. Sychov, M. Hoffmann, and E. I. Voges, “Design and microfabrication of novel X-ray optics,” Proc. SPIE 4783, 1–9 (2002).
[Crossref]

Rau, C.

F. Seiboth, A. Schropp, M. Scholz, F. Wittwer, C. Rödel, M. Wünsche, T. Ullsperger, S. Nolte, J. Rahomäki, K. Parfeniukas, S. Giakoumidis, U. Vogt, U. Wagner, C. Rau, U. Boesenberg, J. Garrevoet, G. Falkenberg, E. C. Galtier, H. Ja Lee, B. Nagler, and C. G. Schroer, “Perfect X-ray focusing via fitting corrective glasses to aberrated optics,” Nat. Commun. 8, 14623 (2017).
[Crossref] [PubMed]

Raven, C.

B. Lengeler, J. Tümmler, A. Snigirev, I. Snigireva, and C. Raven, “Transmission and gain of singly and doubly focusing refractive x-ray lenses,” J. Appl. Phys. 84(11), 5855–5861 (1998).
[Crossref]

Rödel, C.

F. Seiboth, A. Schropp, M. Scholz, F. Wittwer, C. Rödel, M. Wünsche, T. Ullsperger, S. Nolte, J. Rahomäki, K. Parfeniukas, S. Giakoumidis, U. Vogt, U. Wagner, C. Rau, U. Boesenberg, J. Garrevoet, G. Falkenberg, E. C. Galtier, H. Ja Lee, B. Nagler, and C. G. Schroer, “Perfect X-ray focusing via fitting corrective glasses to aberrated optics,” Nat. Commun. 8, 14623 (2017).
[Crossref] [PubMed]

Rutishauser, S.

S. Rutishauser, I. Zanette, T. Weitkamp, T. Donath, and C. David, “At-wavelength characterization of refractive x-ray lenses using a two-dimensional grating interferometer,” Appl. Phys. Lett. 99(22), 221104 (2011).
[Crossref]

Scholz, M.

F. Seiboth, A. Schropp, M. Scholz, F. Wittwer, C. Rödel, M. Wünsche, T. Ullsperger, S. Nolte, J. Rahomäki, K. Parfeniukas, S. Giakoumidis, U. Vogt, U. Wagner, C. Rau, U. Boesenberg, J. Garrevoet, G. Falkenberg, E. C. Galtier, H. Ja Lee, B. Nagler, and C. G. Schroer, “Perfect X-ray focusing via fitting corrective glasses to aberrated optics,” Nat. Commun. 8, 14623 (2017).
[Crossref] [PubMed]

Schroer, C. G.

F. Seiboth, A. Schropp, M. Scholz, F. Wittwer, C. Rödel, M. Wünsche, T. Ullsperger, S. Nolte, J. Rahomäki, K. Parfeniukas, S. Giakoumidis, U. Vogt, U. Wagner, C. Rau, U. Boesenberg, J. Garrevoet, G. Falkenberg, E. C. Galtier, H. Ja Lee, B. Nagler, and C. G. Schroer, “Perfect X-ray focusing via fitting corrective glasses to aberrated optics,” Nat. Commun. 8, 14623 (2017).
[Crossref] [PubMed]

Schropp, A.

F. Seiboth, A. Schropp, M. Scholz, F. Wittwer, C. Rödel, M. Wünsche, T. Ullsperger, S. Nolte, J. Rahomäki, K. Parfeniukas, S. Giakoumidis, U. Vogt, U. Wagner, C. Rau, U. Boesenberg, J. Garrevoet, G. Falkenberg, E. C. Galtier, H. Ja Lee, B. Nagler, and C. G. Schroer, “Perfect X-ray focusing via fitting corrective glasses to aberrated optics,” Nat. Commun. 8, 14623 (2017).
[Crossref] [PubMed]

Schröter, T. J.

Seiboth, F.

F. Seiboth, A. Schropp, M. Scholz, F. Wittwer, C. Rödel, M. Wünsche, T. Ullsperger, S. Nolte, J. Rahomäki, K. Parfeniukas, S. Giakoumidis, U. Vogt, U. Wagner, C. Rau, U. Boesenberg, J. Garrevoet, G. Falkenberg, E. C. Galtier, H. Ja Lee, B. Nagler, and C. G. Schroer, “Perfect X-ray focusing via fitting corrective glasses to aberrated optics,” Nat. Commun. 8, 14623 (2017).
[Crossref] [PubMed]

Shabel’nikov, L.

A. Snigirev, Y. Yunkin, I. Snigireva, M. Di Michiel, M. Drakopoulos, S. Kouznetsov, L. Shabel’nikov, M. Grigoriev, V. Ralchenko, I. Sychov, M. Hoffmann, and E. I. Voges, “Design and microfabrication of novel X-ray optics,” Proc. SPIE 4783, 1–9 (2002).
[Crossref]

Shvyd’ko, Y.

S. Terentyev, V. Blank, S. Polyakov, S. Zholudev, A. Snigirev, M. Polikarpov, T. Kolodziej, J. Qian, H. Zhou, and Y. Shvyd’ko, “Parabolic single-crystal diamond lenses for coherent x-ray imaging,” Appl. Phys. Lett. 107(11), 111108 (2015).
[Crossref]

Slack, C. M.

C. M. Slack, “The refraction of X-rays in prisms of various materials,” Phys. Rev. 27(6), 691–695 (1926).
[Crossref]

Snigirev, A.

S. Terentyev, V. Blank, S. Polyakov, S. Zholudev, A. Snigirev, M. Polikarpov, T. Kolodziej, J. Qian, H. Zhou, and Y. Shvyd’ko, “Parabolic single-crystal diamond lenses for coherent x-ray imaging,” Appl. Phys. Lett. 107(11), 111108 (2015).
[Crossref]

A. Snigirev, Y. Yunkin, I. Snigireva, M. Di Michiel, M. Drakopoulos, S. Kouznetsov, L. Shabel’nikov, M. Grigoriev, V. Ralchenko, I. Sychov, M. Hoffmann, and E. I. Voges, “Design and microfabrication of novel X-ray optics,” Proc. SPIE 4783, 1–9 (2002).
[Crossref]

B. Lengeler, J. Tümmler, A. Snigirev, I. Snigireva, and C. Raven, “Transmission and gain of singly and doubly focusing refractive x-ray lenses,” J. Appl. Phys. 84(11), 5855–5861 (1998).
[Crossref]

A. Snigirev, V. Kohn, I. Snigireva, A. Souvorov, and B. Lengeler, “Focusing high-energy x rays by compound refractive lenses,” Appl. Opt. 37(4), 653–662 (1998).
[Crossref] [PubMed]

Snigireva, I.

A. Snigirev, Y. Yunkin, I. Snigireva, M. Di Michiel, M. Drakopoulos, S. Kouznetsov, L. Shabel’nikov, M. Grigoriev, V. Ralchenko, I. Sychov, M. Hoffmann, and E. I. Voges, “Design and microfabrication of novel X-ray optics,” Proc. SPIE 4783, 1–9 (2002).
[Crossref]

B. Lengeler, J. Tümmler, A. Snigirev, I. Snigireva, and C. Raven, “Transmission and gain of singly and doubly focusing refractive x-ray lenses,” J. Appl. Phys. 84(11), 5855–5861 (1998).
[Crossref]

A. Snigirev, V. Kohn, I. Snigireva, A. Souvorov, and B. Lengeler, “Focusing high-energy x rays by compound refractive lenses,” Appl. Opt. 37(4), 653–662 (1998).
[Crossref] [PubMed]

Souvorov, A.

Sychov, I.

A. Snigirev, Y. Yunkin, I. Snigireva, M. Di Michiel, M. Drakopoulos, S. Kouznetsov, L. Shabel’nikov, M. Grigoriev, V. Ralchenko, I. Sychov, M. Hoffmann, and E. I. Voges, “Design and microfabrication of novel X-ray optics,” Proc. SPIE 4783, 1–9 (2002).
[Crossref]

Terentyev, S.

S. Terentyev, V. Blank, S. Polyakov, S. Zholudev, A. Snigirev, M. Polikarpov, T. Kolodziej, J. Qian, H. Zhou, and Y. Shvyd’ko, “Parabolic single-crystal diamond lenses for coherent x-ray imaging,” Appl. Phys. Lett. 107(11), 111108 (2015).
[Crossref]

Tümmler, J.

B. Lengeler, J. Tümmler, A. Snigirev, I. Snigireva, and C. Raven, “Transmission and gain of singly and doubly focusing refractive x-ray lenses,” J. Appl. Phys. 84(11), 5855–5861 (1998).
[Crossref]

Ullsperger, T.

F. Seiboth, A. Schropp, M. Scholz, F. Wittwer, C. Rödel, M. Wünsche, T. Ullsperger, S. Nolte, J. Rahomäki, K. Parfeniukas, S. Giakoumidis, U. Vogt, U. Wagner, C. Rau, U. Boesenberg, J. Garrevoet, G. Falkenberg, E. C. Galtier, H. Ja Lee, B. Nagler, and C. G. Schroer, “Perfect X-ray focusing via fitting corrective glasses to aberrated optics,” Nat. Commun. 8, 14623 (2017).
[Crossref] [PubMed]

Voges, E. I.

A. Snigirev, Y. Yunkin, I. Snigireva, M. Di Michiel, M. Drakopoulos, S. Kouznetsov, L. Shabel’nikov, M. Grigoriev, V. Ralchenko, I. Sychov, M. Hoffmann, and E. I. Voges, “Design and microfabrication of novel X-ray optics,” Proc. SPIE 4783, 1–9 (2002).
[Crossref]

Vogt, U.

F. Seiboth, A. Schropp, M. Scholz, F. Wittwer, C. Rödel, M. Wünsche, T. Ullsperger, S. Nolte, J. Rahomäki, K. Parfeniukas, S. Giakoumidis, U. Vogt, U. Wagner, C. Rau, U. Boesenberg, J. Garrevoet, G. Falkenberg, E. C. Galtier, H. Ja Lee, B. Nagler, and C. G. Schroer, “Perfect X-ray focusing via fitting corrective glasses to aberrated optics,” Nat. Commun. 8, 14623 (2017).
[Crossref] [PubMed]

Wagner, U.

F. Seiboth, A. Schropp, M. Scholz, F. Wittwer, C. Rödel, M. Wünsche, T. Ullsperger, S. Nolte, J. Rahomäki, K. Parfeniukas, S. Giakoumidis, U. Vogt, U. Wagner, C. Rau, U. Boesenberg, J. Garrevoet, G. Falkenberg, E. C. Galtier, H. Ja Lee, B. Nagler, and C. G. Schroer, “Perfect X-ray focusing via fitting corrective glasses to aberrated optics,” Nat. Commun. 8, 14623 (2017).
[Crossref] [PubMed]

Weitkamp, T.

S. Rutishauser, I. Zanette, T. Weitkamp, T. Donath, and C. David, “At-wavelength characterization of refractive x-ray lenses using a two-dimensional grating interferometer,” Appl. Phys. Lett. 99(22), 221104 (2011).
[Crossref]

T. Weitkamp, B. Nöhammer, A. Diaz, C. David, and E. Ziegler, “X-ray wavefront analysis and optics characterization with a grating interferometer,” Appl. Phys. Lett. 86(5), 054101 (2005).
[Crossref]

Wernick, M. N.

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[Crossref] [PubMed]

Wirjadi, O.

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[Crossref] [PubMed]

Wittwer, F.

F. Seiboth, A. Schropp, M. Scholz, F. Wittwer, C. Rödel, M. Wünsche, T. Ullsperger, S. Nolte, J. Rahomäki, K. Parfeniukas, S. Giakoumidis, U. Vogt, U. Wagner, C. Rau, U. Boesenberg, J. Garrevoet, G. Falkenberg, E. C. Galtier, H. Ja Lee, B. Nagler, and C. G. Schroer, “Perfect X-ray focusing via fitting corrective glasses to aberrated optics,” Nat. Commun. 8, 14623 (2017).
[Crossref] [PubMed]

Wünsche, M.

F. Seiboth, A. Schropp, M. Scholz, F. Wittwer, C. Rödel, M. Wünsche, T. Ullsperger, S. Nolte, J. Rahomäki, K. Parfeniukas, S. Giakoumidis, U. Vogt, U. Wagner, C. Rau, U. Boesenberg, J. Garrevoet, G. Falkenberg, E. C. Galtier, H. Ja Lee, B. Nagler, and C. G. Schroer, “Perfect X-ray focusing via fitting corrective glasses to aberrated optics,” Nat. Commun. 8, 14623 (2017).
[Crossref] [PubMed]

Wyant, J. C.

J. C. Wyant and K. Creath, “Basic wavefront Aberration theory for Optical Metrology,” Appl. Opt. Opt. Eng. 11, 2–53 (1992).

Xing, Z.

P. Heimann, M. MacDonald, B. Nagler, H. J. Lee, E. Galtier, B. Arnold, and Z. Xing, “Compound refractive lenses as prefocusing optics for X-ray FEL radiation,” J. Synchrotron Radiat. 23(2), 425–429 (2016).
[Crossref] [PubMed]

Yang, Y.

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[Crossref] [PubMed]

Yunkin, Y.

A. Snigirev, Y. Yunkin, I. Snigireva, M. Di Michiel, M. Drakopoulos, S. Kouznetsov, L. Shabel’nikov, M. Grigoriev, V. Ralchenko, I. Sychov, M. Hoffmann, and E. I. Voges, “Design and microfabrication of novel X-ray optics,” Proc. SPIE 4783, 1–9 (2002).
[Crossref]

Zanette, I.

S. Rutishauser, I. Zanette, T. Weitkamp, T. Donath, and C. David, “At-wavelength characterization of refractive x-ray lenses using a two-dimensional grating interferometer,” Appl. Phys. Lett. 99(22), 221104 (2011).
[Crossref]

Zholudev, S.

S. Terentyev, V. Blank, S. Polyakov, S. Zholudev, A. Snigirev, M. Polikarpov, T. Kolodziej, J. Qian, H. Zhou, and Y. Shvyd’ko, “Parabolic single-crystal diamond lenses for coherent x-ray imaging,” Appl. Phys. Lett. 107(11), 111108 (2015).
[Crossref]

Zhong, Z.

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[Crossref] [PubMed]

Zhou, H.

S. Terentyev, V. Blank, S. Polyakov, S. Zholudev, A. Snigirev, M. Polikarpov, T. Kolodziej, J. Qian, H. Zhou, and Y. Shvyd’ko, “Parabolic single-crystal diamond lenses for coherent x-ray imaging,” Appl. Phys. Lett. 107(11), 111108 (2015).
[Crossref]

Ziegler, E.

T. Weitkamp, B. Nöhammer, A. Diaz, C. David, and E. Ziegler, “X-ray wavefront analysis and optics characterization with a grating interferometer,” Appl. Phys. Lett. 86(5), 054101 (2005).
[Crossref]

Appl. Opt. (1)

Appl. Opt. Opt. Eng. (1)

J. C. Wyant and K. Creath, “Basic wavefront Aberration theory for Optical Metrology,” Appl. Opt. Opt. Eng. 11, 2–53 (1992).

Appl. Phys. Lett. (3)

S. Terentyev, V. Blank, S. Polyakov, S. Zholudev, A. Snigirev, M. Polikarpov, T. Kolodziej, J. Qian, H. Zhou, and Y. Shvyd’ko, “Parabolic single-crystal diamond lenses for coherent x-ray imaging,” Appl. Phys. Lett. 107(11), 111108 (2015).
[Crossref]

S. Rutishauser, I. Zanette, T. Weitkamp, T. Donath, and C. David, “At-wavelength characterization of refractive x-ray lenses using a two-dimensional grating interferometer,” Appl. Phys. Lett. 99(22), 221104 (2011).
[Crossref]

T. Weitkamp, B. Nöhammer, A. Diaz, C. David, and E. Ziegler, “X-ray wavefront analysis and optics characterization with a grating interferometer,” Appl. Phys. Lett. 86(5), 054101 (2005).
[Crossref]

J. Appl. Phys. (1)

B. Lengeler, J. Tümmler, A. Snigirev, I. Snigireva, and C. Raven, “Transmission and gain of singly and doubly focusing refractive x-ray lenses,” J. Appl. Phys. 84(11), 5855–5861 (1998).
[Crossref]

J. Synchrotron Radiat. (1)

P. Heimann, M. MacDonald, B. Nagler, H. J. Lee, E. Galtier, B. Arnold, and Z. Xing, “Compound refractive lenses as prefocusing optics for X-ray FEL radiation,” J. Synchrotron Radiat. 23(2), 425–429 (2016).
[Crossref] [PubMed]

Nat. Commun. (1)

F. Seiboth, A. Schropp, M. Scholz, F. Wittwer, C. Rödel, M. Wünsche, T. Ullsperger, S. Nolte, J. Rahomäki, K. Parfeniukas, S. Giakoumidis, U. Vogt, U. Wagner, C. Rau, U. Boesenberg, J. Garrevoet, G. Falkenberg, E. C. Galtier, H. Ja Lee, B. Nagler, and C. G. Schroer, “Perfect X-ray focusing via fitting corrective glasses to aberrated optics,” Nat. Commun. 8, 14623 (2017).
[Crossref] [PubMed]

Opt. Express (2)

Phys. Med. Biol. (1)

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[Crossref] [PubMed]

Phys. Rev. (1)

C. M. Slack, “The refraction of X-rays in prisms of various materials,” Phys. Rev. 27(6), 691–695 (1926).
[Crossref]

Proc. SPIE (1)

A. Snigirev, Y. Yunkin, I. Snigireva, M. Di Michiel, M. Drakopoulos, S. Kouznetsov, L. Shabel’nikov, M. Grigoriev, V. Ralchenko, I. Sychov, M. Hoffmann, and E. I. Voges, “Design and microfabrication of novel X-ray optics,” Proc. SPIE 4783, 1–9 (2002).
[Crossref]

Other (2)

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts and Company Publishers, 2005).

A. Momose, W. Yashiro, and Y. Takeda, “X-Ray Phase Imaging with Talbot Interferometry,” in Imaging, Therapy Planning, and Inverse Problems in Biomedical Mathematics: Promising Directions (Medical Physics Publishing, 2009), p. 292.

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Figures (3)

Fig. 1
Fig. 1 Experimental setup: in-vacuum Si (111) Laue monochromator reduces relative energy bandwidth to ∆E/E~10−3; the first Si (333) crystal of DCS reduces ∆E/E to ~10−5. Divergence of the beam in the CRL entrance pupil is ~6 × 10−6 µrad owing to the large distance to the source. Divergence of the beam in the analyzed 21 × 21 µm2 wavefront samples is much smaller than the rocking curve width of the Si (333) reflection. Inset (a) shows X-ray images of the CRL versus position of the second, analyzer crystal. An optical image of the CRL pupil is shown in (b).
Fig. 2
Fig. 2 Experimental results. Two-D maps of the vertical component of the X-rays’ deflection angle (a) and transmission T (b). Panels (c) and (d) show with different markers deflection angle profiles and T measured at points in sagittal and meridional planes of the CRL; deflection and T produced by ideal parabolic profile are shown by solid lines. Right y-axis in panel (c) shows the magnitude of the deflection error plotted with red color. Reconstructed phase delays and deviation ϕ of the phase from a perfect parabolic figure are shown in panels (e) and (f).
Fig. 3
Fig. 3 Applications of the generalized pupil function: panels (a) and (b) show the PSF of the CRL calculated with and without optical aberrations taken into account; 1D profiles of the PSF are compared in (c). Panels (d-g) demonstrate the simulated propagation of the 15 keV photon beam after the CRL. Evolution of the beam intensity along the propagation axis z (d); intensity in the plane z = 710 cm calculated using GO (e) and wave optics (g). To illustrate that peripheral aberrations limit the gain, intensity of the beam in the focal plane is shown in (f) for the case of fully open CRL aperture. All results are displayed on a uniform grid with 4 µm spacing. Panels (d-f) share the colorbar shown on their right. The intensity of the transmitted beam integrated in the focal plane is equal to 400 a. u. for panels (e,g) and 880 for the case (f). The fraction of the encircled beam intensity in the focal plane against the spot radius is shown in (h). Log scale is shown in all 2D maps.

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