Abstract

Refractive X-ray lenses are in use at a large number of synchrotron experiments. Several materials and fabrication techniques are available for their production, each having their own strengths and drawbacks. We present a grating interferometer for the quantitative analysis of single refractive X-ray lenses and employ it for the study of a beryllium point focus lens and a polymer line focus lens, highlighting the differences in the outcome of the fabrication methods. The residuals of a line fit to the phase gradient are used to quantify local lens defects, while shape aberrations are quantified by the decomposition of the retrieved wavefront phase profile into either Zernike or Legendre polynomials, depending on the focus and aperture shape. While the polymer lens shows better material homogeneity, the beryllium lens shows higher shape accuracy.

© 2016 Optical Society of America

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References

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  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).
    [Crossref]
  2. T. Roth, L. Helfen, J. Hallmann, L. Samoylova, P. Kwaśniewski, B. Lengeler, and A. Madsen, “X-ray laminography and SAXS on beryllium grades and lenses and wavefront propagation through imperfect compound refractive lenses,” Proc. SPIE 9207, 920702 (2014).
    [Crossref]
  3. 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]
  4. 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]
  5. K. S. Morgan, D. M. Paganin, and K. K. W. Siu, “Quantitative x-ray phase-contrast imaging using a single grating of comparable pitch to sample feature size,” Opt. Lett. 36(1), 55–57 (2011).
    [Crossref] [PubMed]
  6. H. H. Wen, E. E. Bennett, R. Kopace, A. F. Stein, and V. Pai, “Single-shot x-ray differential phase-contrast and diffraction imaging using two-dimensional transmission gratings,” Opt. Lett. 35(12), 1932–1934 (2010).
    [Crossref] [PubMed]
  7. P. Zhou and J. H. Burge, “Analysis of wavefront propagation using the Talbot effect,” Appl. Opt. 49(28), 5351–5359 (2010).
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  8. W. Yashiro, S. Harasse, A. Takeuchi, Y. Suzuki, and A. Momose, “Hard-x-ray phase-imaging microscopy using the self-imaging phenomenon of a transmission grating,” Phys. Rev. A 82(4), 043822 (2010).
    [Crossref]
  9. F. Uhlén, J. Rahomäki, D. Nilsson, F. Seiboth, C. Sanz, U. Wagner, C. Rau, C. G. Schroer, and U. Vogt, “Ronchi test for characterization of X-ray nanofocusing optics and beamlines,” J. Synchrotron Radiat. 21(5), 1105–1109 (2014).
    [Crossref] [PubMed]
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    [Crossref]
  11. F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  13. F. Zernike, “Beugungstheorie des Schneidenverfahrens und seiner verbesserten Form, der Phasenkontrastmethode,” Physica 1(7–12), 689–704 (1934).
    [Crossref]
  14. J. Ye, Z. Gao, S. Wang, J. Cheng, W. Wang, and W. Sun, “Comparative assessment of orthogonal polynomials for wavefront reconstruction over the square aperture,” J. Opt. Soc. Am. A 31(10), 2304–2311 (2014).
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  15. A. Last, O. Márkus, S. Georgi, and J. Mohr, “Röntgenoptische Messung des Seitenwandwinkels direktlithografischer refraktiver Röntgenlinsen,” in MikroSystemTechnik Kongress (2015).
  16. M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk, and C. David, “Inspection of refractive X-ray lenses using high-resolution differential phase contrast imaging with a microfocus X-ray source,” Rev. Sci. Instrum. 78(9), 093707 (2007).
    [Crossref] [PubMed]

2014 (3)

T. Roth, L. Helfen, J. Hallmann, L. Samoylova, P. Kwaśniewski, B. Lengeler, and A. Madsen, “X-ray laminography and SAXS on beryllium grades and lenses and wavefront propagation through imperfect compound refractive lenses,” Proc. SPIE 9207, 920702 (2014).
[Crossref]

F. Uhlén, J. Rahomäki, D. Nilsson, F. Seiboth, C. Sanz, U. Wagner, C. Rau, C. G. Schroer, and U. Vogt, “Ronchi test for characterization of X-ray nanofocusing optics and beamlines,” J. Synchrotron Radiat. 21(5), 1105–1109 (2014).
[Crossref] [PubMed]

J. Ye, Z. Gao, S. Wang, J. Cheng, W. Wang, and W. Sun, “Comparative assessment of orthogonal polynomials for wavefront reconstruction over the square aperture,” J. Opt. Soc. Am. A 31(10), 2304–2311 (2014).
[Crossref] [PubMed]

2011 (2)

K. S. Morgan, D. M. Paganin, and K. K. W. Siu, “Quantitative x-ray phase-contrast imaging using a single grating of comparable pitch to sample feature size,” Opt. Lett. 36(1), 55–57 (2011).
[Crossref] [PubMed]

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]

2010 (3)

2008 (1)

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[Crossref] [PubMed]

2007 (2)

M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk, and C. David, “Inspection of refractive X-ray lenses using high-resolution differential phase contrast imaging with a microfocus X-ray source,” Rev. Sci. Instrum. 78(9), 093707 (2007).
[Crossref] [PubMed]

C. Kottler, C. David, F. Pfeiffer, and O. Bunk, “A two-directional approach for grating based differential phase contrast imaging using hard x-rays,” Opt. Express 15(3), 1175–1181 (2007).
[Crossref] [PubMed]

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]

2004 (1)

V. Nazmov, E. Reznikova, J. Mohr, A. Snigirev, I. Snigireva, S. Achenbach, and V. Saile, “Fabrication and preliminary testing of X-ray lenses in thick SU-8 resist layers,” Microsyst. Technol. 10(10), 716–721 (2004).
[Crossref]

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).
[Crossref]

1934 (1)

F. Zernike, “Beugungstheorie des Schneidenverfahrens und seiner verbesserten Form, der Phasenkontrastmethode,” Physica 1(7–12), 689–704 (1934).
[Crossref]

Achenbach, S.

V. Nazmov, E. Reznikova, J. Mohr, A. Snigirev, I. Snigireva, S. Achenbach, and V. Saile, “Fabrication and preliminary testing of X-ray lenses in thick SU-8 resist layers,” Microsyst. Technol. 10(10), 716–721 (2004).
[Crossref]

Baumann, J.

M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk, and C. David, “Inspection of refractive X-ray lenses using high-resolution differential phase contrast imaging with a microfocus X-ray source,” Rev. Sci. Instrum. 78(9), 093707 (2007).
[Crossref] [PubMed]

Bech, M.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[Crossref] [PubMed]

Bennett, E. E.

Brönnimann, Ch.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[Crossref] [PubMed]

Bunk, O.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[Crossref] [PubMed]

C. Kottler, C. David, F. Pfeiffer, and O. Bunk, “A two-directional approach for grating based differential phase contrast imaging using hard x-rays,” Opt. Express 15(3), 1175–1181 (2007).
[Crossref] [PubMed]

M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk, and C. David, “Inspection of refractive X-ray lenses using high-resolution differential phase contrast imaging with a microfocus X-ray source,” Rev. Sci. Instrum. 78(9), 093707 (2007).
[Crossref] [PubMed]

Burge, J. H.

Cheng, J.

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]

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[Crossref] [PubMed]

M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk, and C. David, “Inspection of refractive X-ray lenses using high-resolution differential phase contrast imaging with a microfocus X-ray source,” Rev. Sci. Instrum. 78(9), 093707 (2007).
[Crossref] [PubMed]

C. Kottler, C. David, F. Pfeiffer, and O. Bunk, “A two-directional approach for grating based differential phase contrast imaging using hard x-rays,” Opt. Express 15(3), 1175–1181 (2007).
[Crossref] [PubMed]

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]

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]

Eikenberry, E. F.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[Crossref] [PubMed]

Engelhardt, M.

M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk, and C. David, “Inspection of refractive X-ray lenses using high-resolution differential phase contrast imaging with a microfocus X-ray source,” Rev. Sci. Instrum. 78(9), 093707 (2007).
[Crossref] [PubMed]

Gao, Z.

Grünzweig, C.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[Crossref] [PubMed]

Hallmann, J.

T. Roth, L. Helfen, J. Hallmann, L. Samoylova, P. Kwaśniewski, B. Lengeler, and A. Madsen, “X-ray laminography and SAXS on beryllium grades and lenses and wavefront propagation through imperfect compound refractive lenses,” Proc. SPIE 9207, 920702 (2014).
[Crossref]

Harasse, S.

W. Yashiro, S. Harasse, A. Takeuchi, Y. Suzuki, and A. Momose, “Hard-x-ray phase-imaging microscopy using the self-imaging phenomenon of a transmission grating,” Phys. Rev. A 82(4), 043822 (2010).
[Crossref]

Helfen, L.

T. Roth, L. Helfen, J. Hallmann, L. Samoylova, P. Kwaśniewski, B. Lengeler, and A. Madsen, “X-ray laminography and SAXS on beryllium grades and lenses and wavefront propagation through imperfect compound refractive lenses,” Proc. SPIE 9207, 920702 (2014).
[Crossref]

Kohn, V.

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).
[Crossref]

Kopace, R.

Kottler, C.

C. Kottler, C. David, F. Pfeiffer, and O. Bunk, “A two-directional approach for grating based differential phase contrast imaging using hard x-rays,” Opt. Express 15(3), 1175–1181 (2007).
[Crossref] [PubMed]

M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk, and C. David, “Inspection of refractive X-ray lenses using high-resolution differential phase contrast imaging with a microfocus X-ray source,” Rev. Sci. Instrum. 78(9), 093707 (2007).
[Crossref] [PubMed]

Kraft, P.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[Crossref] [PubMed]

Kwasniewski, P.

T. Roth, L. Helfen, J. Hallmann, L. Samoylova, P. Kwaśniewski, B. Lengeler, and A. Madsen, “X-ray laminography and SAXS on beryllium grades and lenses and wavefront propagation through imperfect compound refractive lenses,” Proc. SPIE 9207, 920702 (2014).
[Crossref]

Lengeler, B.

T. Roth, L. Helfen, J. Hallmann, L. Samoylova, P. Kwaśniewski, B. Lengeler, and A. Madsen, “X-ray laminography and SAXS on beryllium grades and lenses and wavefront propagation through imperfect compound refractive lenses,” Proc. SPIE 9207, 920702 (2014).
[Crossref]

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).
[Crossref]

Madsen, A.

T. Roth, L. Helfen, J. Hallmann, L. Samoylova, P. Kwaśniewski, B. Lengeler, and A. Madsen, “X-ray laminography and SAXS on beryllium grades and lenses and wavefront propagation through imperfect compound refractive lenses,” Proc. SPIE 9207, 920702 (2014).
[Crossref]

Mohr, J.

V. Nazmov, E. Reznikova, J. Mohr, A. Snigirev, I. Snigireva, S. Achenbach, and V. Saile, “Fabrication and preliminary testing of X-ray lenses in thick SU-8 resist layers,” Microsyst. Technol. 10(10), 716–721 (2004).
[Crossref]

Momose, A.

W. Yashiro, S. Harasse, A. Takeuchi, Y. Suzuki, and A. Momose, “Hard-x-ray phase-imaging microscopy using the self-imaging phenomenon of a transmission grating,” Phys. Rev. A 82(4), 043822 (2010).
[Crossref]

Morgan, K. S.

Nazmov, V.

V. Nazmov, E. Reznikova, J. Mohr, A. Snigirev, I. Snigireva, S. Achenbach, and V. Saile, “Fabrication and preliminary testing of X-ray lenses in thick SU-8 resist layers,” Microsyst. Technol. 10(10), 716–721 (2004).
[Crossref]

Nilsson, D.

F. Uhlén, J. Rahomäki, D. Nilsson, F. Seiboth, C. Sanz, U. Wagner, C. Rau, C. G. Schroer, and U. Vogt, “Ronchi test for characterization of X-ray nanofocusing optics and beamlines,” J. Synchrotron Radiat. 21(5), 1105–1109 (2014).
[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]

Paganin, D. M.

Pai, V.

Pfeiffer, F.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[Crossref] [PubMed]

M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk, and C. David, “Inspection of refractive X-ray lenses using high-resolution differential phase contrast imaging with a microfocus X-ray source,” Rev. Sci. Instrum. 78(9), 093707 (2007).
[Crossref] [PubMed]

C. Kottler, C. David, F. Pfeiffer, and O. Bunk, “A two-directional approach for grating based differential phase contrast imaging using hard x-rays,” Opt. Express 15(3), 1175–1181 (2007).
[Crossref] [PubMed]

Rahomäki, J.

F. Uhlén, J. Rahomäki, D. Nilsson, F. Seiboth, C. Sanz, U. Wagner, C. Rau, C. G. Schroer, and U. Vogt, “Ronchi test for characterization of X-ray nanofocusing optics and beamlines,” J. Synchrotron Radiat. 21(5), 1105–1109 (2014).
[Crossref] [PubMed]

Rau, C.

F. Uhlén, J. Rahomäki, D. Nilsson, F. Seiboth, C. Sanz, U. Wagner, C. Rau, C. G. Schroer, and U. Vogt, “Ronchi test for characterization of X-ray nanofocusing optics and beamlines,” J. Synchrotron Radiat. 21(5), 1105–1109 (2014).
[Crossref] [PubMed]

Reznikova, E.

V. Nazmov, E. Reznikova, J. Mohr, A. Snigirev, I. Snigireva, S. Achenbach, and V. Saile, “Fabrication and preliminary testing of X-ray lenses in thick SU-8 resist layers,” Microsyst. Technol. 10(10), 716–721 (2004).
[Crossref]

Roth, T.

T. Roth, L. Helfen, J. Hallmann, L. Samoylova, P. Kwaśniewski, B. Lengeler, and A. Madsen, “X-ray laminography and SAXS on beryllium grades and lenses and wavefront propagation through imperfect compound refractive lenses,” Proc. SPIE 9207, 920702 (2014).
[Crossref]

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]

Saile, V.

V. Nazmov, E. Reznikova, J. Mohr, A. Snigirev, I. Snigireva, S. Achenbach, and V. Saile, “Fabrication and preliminary testing of X-ray lenses in thick SU-8 resist layers,” Microsyst. Technol. 10(10), 716–721 (2004).
[Crossref]

Samoylova, L.

T. Roth, L. Helfen, J. Hallmann, L. Samoylova, P. Kwaśniewski, B. Lengeler, and A. Madsen, “X-ray laminography and SAXS on beryllium grades and lenses and wavefront propagation through imperfect compound refractive lenses,” Proc. SPIE 9207, 920702 (2014).
[Crossref]

Sanz, C.

F. Uhlén, J. Rahomäki, D. Nilsson, F. Seiboth, C. Sanz, U. Wagner, C. Rau, C. G. Schroer, and U. Vogt, “Ronchi test for characterization of X-ray nanofocusing optics and beamlines,” J. Synchrotron Radiat. 21(5), 1105–1109 (2014).
[Crossref] [PubMed]

Schroer, C. G.

F. Uhlén, J. Rahomäki, D. Nilsson, F. Seiboth, C. Sanz, U. Wagner, C. Rau, C. G. Schroer, and U. Vogt, “Ronchi test for characterization of X-ray nanofocusing optics and beamlines,” J. Synchrotron Radiat. 21(5), 1105–1109 (2014).
[Crossref] [PubMed]

Schuster, M.

M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk, and C. David, “Inspection of refractive X-ray lenses using high-resolution differential phase contrast imaging with a microfocus X-ray source,” Rev. Sci. Instrum. 78(9), 093707 (2007).
[Crossref] [PubMed]

Seiboth, F.

F. Uhlén, J. Rahomäki, D. Nilsson, F. Seiboth, C. Sanz, U. Wagner, C. Rau, C. G. Schroer, and U. Vogt, “Ronchi test for characterization of X-ray nanofocusing optics and beamlines,” J. Synchrotron Radiat. 21(5), 1105–1109 (2014).
[Crossref] [PubMed]

Siu, K. K. W.

Snigirev, A.

V. Nazmov, E. Reznikova, J. Mohr, A. Snigirev, I. Snigireva, S. Achenbach, and V. Saile, “Fabrication and preliminary testing of X-ray lenses in thick SU-8 resist layers,” Microsyst. Technol. 10(10), 716–721 (2004).
[Crossref]

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).
[Crossref]

Snigireva, I.

V. Nazmov, E. Reznikova, J. Mohr, A. Snigirev, I. Snigireva, S. Achenbach, and V. Saile, “Fabrication and preliminary testing of X-ray lenses in thick SU-8 resist layers,” Microsyst. Technol. 10(10), 716–721 (2004).
[Crossref]

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).
[Crossref]

Stein, A. F.

Sun, W.

Suzuki, Y.

W. Yashiro, S. Harasse, A. Takeuchi, Y. Suzuki, and A. Momose, “Hard-x-ray phase-imaging microscopy using the self-imaging phenomenon of a transmission grating,” Phys. Rev. A 82(4), 043822 (2010).
[Crossref]

Takeuchi, A.

W. Yashiro, S. Harasse, A. Takeuchi, Y. Suzuki, and A. Momose, “Hard-x-ray phase-imaging microscopy using the self-imaging phenomenon of a transmission grating,” Phys. Rev. A 82(4), 043822 (2010).
[Crossref]

Uhlén, F.

F. Uhlén, J. Rahomäki, D. Nilsson, F. Seiboth, C. Sanz, U. Wagner, C. Rau, C. G. Schroer, and U. Vogt, “Ronchi test for characterization of X-ray nanofocusing optics and beamlines,” J. Synchrotron Radiat. 21(5), 1105–1109 (2014).
[Crossref] [PubMed]

Vogt, U.

F. Uhlén, J. Rahomäki, D. Nilsson, F. Seiboth, C. Sanz, U. Wagner, C. Rau, C. G. Schroer, and U. Vogt, “Ronchi test for characterization of X-ray nanofocusing optics and beamlines,” J. Synchrotron Radiat. 21(5), 1105–1109 (2014).
[Crossref] [PubMed]

Wagner, U.

F. Uhlén, J. Rahomäki, D. Nilsson, F. Seiboth, C. Sanz, U. Wagner, C. Rau, C. G. Schroer, and U. Vogt, “Ronchi test for characterization of X-ray nanofocusing optics and beamlines,” J. Synchrotron Radiat. 21(5), 1105–1109 (2014).
[Crossref] [PubMed]

Wang, S.

Wang, W.

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]

Wen, H. H.

Yashiro, W.

W. Yashiro, S. Harasse, A. Takeuchi, Y. Suzuki, and A. Momose, “Hard-x-ray phase-imaging microscopy using the self-imaging phenomenon of a transmission grating,” Phys. Rev. A 82(4), 043822 (2010).
[Crossref]

Ye, J.

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]

Zernike, F.

F. Zernike, “Beugungstheorie des Schneidenverfahrens und seiner verbesserten Form, der Phasenkontrastmethode,” Physica 1(7–12), 689–704 (1934).
[Crossref]

Zhou, P.

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. Phys. Lett. (2)

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]

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]

J. Opt. Soc. Am. A (1)

J. Synchrotron Radiat. (1)

F. Uhlén, J. Rahomäki, D. Nilsson, F. Seiboth, C. Sanz, U. Wagner, C. Rau, C. G. Schroer, and U. Vogt, “Ronchi test for characterization of X-ray nanofocusing optics and beamlines,” J. Synchrotron Radiat. 21(5), 1105–1109 (2014).
[Crossref] [PubMed]

Microsyst. Technol. (1)

V. Nazmov, E. Reznikova, J. Mohr, A. Snigirev, I. Snigireva, S. Achenbach, and V. Saile, “Fabrication and preliminary testing of X-ray lenses in thick SU-8 resist layers,” Microsyst. Technol. 10(10), 716–721 (2004).
[Crossref]

Nat. Mater. (1)

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[Crossref] [PubMed]

Nature (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).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. A (1)

W. Yashiro, S. Harasse, A. Takeuchi, Y. Suzuki, and A. Momose, “Hard-x-ray phase-imaging microscopy using the self-imaging phenomenon of a transmission grating,” Phys. Rev. A 82(4), 043822 (2010).
[Crossref]

Physica (1)

F. Zernike, “Beugungstheorie des Schneidenverfahrens und seiner verbesserten Form, der Phasenkontrastmethode,” Physica 1(7–12), 689–704 (1934).
[Crossref]

Proc. SPIE (1)

T. Roth, L. Helfen, J. Hallmann, L. Samoylova, P. Kwaśniewski, B. Lengeler, and A. Madsen, “X-ray laminography and SAXS on beryllium grades and lenses and wavefront propagation through imperfect compound refractive lenses,” Proc. SPIE 9207, 920702 (2014).
[Crossref]

Rev. Sci. Instrum. (1)

M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk, and C. David, “Inspection of refractive X-ray lenses using high-resolution differential phase contrast imaging with a microfocus X-ray source,” Rev. Sci. Instrum. 78(9), 093707 (2007).
[Crossref] [PubMed]

Other (1)

A. Last, O. Márkus, S. Georgi, and J. Mohr, “Röntgenoptische Messung des Seitenwandwinkels direktlithografischer refraktiver Röntgenlinsen,” in MikroSystemTechnik Kongress (2015).

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Figures (5)

Fig. 1
Fig. 1

Phase gradient in orthogonal directions for a beryllium point focus lens with apex radius 50 µm (A) and a polymer line focus lens with apex radius 300 µm (B). No structure is visible in the non-focusing direction of the line focus lens.

Fig. 2
Fig. 2

Deviation from ideal refraction angle for Be (left) and polymer lens (right). Plotted is the magnitude of the 2d angular deviation vector.

Fig. 3
Fig. 3

Profile of the focal length of the polymer line focus length over the height of the aperture.

Fig. 4
Fig. 4

Magnified area of the angular deviation map of the polymer lens seen in Fig. 2. calculated with (from left to right) 12, 4 and 2 scans at different azimuthal angles.

Fig. 5
Fig. 5

Magnified area of the angular deviation map of the beryllium lens seen in Fig. 2 calculated with (from left to right) 10, 4 and 2 scans at different azimuthal angles.

Tables (2)

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Table 1 Zernike Coefficients for the Point Focus Be Lens

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Table 2 Legendre Coefficients for the Polymer Line Focus Lens

Equations (7)

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f min = (d+a)p/ Ms p/ Ms 1 .
L e = (fa)d fad .
Δφ= λd p det Φ x =α 2πd p det .
γ α x = 1 f = 2δ R .
γ= l d l d +Δ φ t .
L j (x,y)= P n (x) P m (y).
1 1 1 1 L j (x,y) L k (x,y) dxdy=4 δ jk ,

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