Abstract

Image magnification via twofold asymmetric Bragg reflection (a setup called the ”Bragg Magnifier”) is a recently established technique allowing to achieve both sub-micrometer spatial resolution and phase contrast in X-ray imaging. The present article extends a previously developed theoretical formalism to account for partially coherent illumination. At a typical synchrotron setup polychromatic illumination is identified as the main influence of partial coherence and the implications on imaging characteristics are analyzed by numerical simulations. We show that contrast decreases by about 50% when compared to the monochromatic case, while sub-micrometer spatial resolution is preserved. The theoretical formalism is experimentally verified by correctly describing the dispersive interaction of the two orthogonal magnifier crystals, an effect that has to be taken into account for precise data evaluation.

© 2009 Optical Society of America

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    [Crossref]
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  3. T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S.W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373, 595–598 (1995).
    [Crossref]
  4. V. N. Ingal and E. A. Beliaevskaya, “Imaging of biological objects in the plane-wave diffraction scheme,” Nuovo Cimento 19, 553–560 (1997).
    [Crossref]
  5. K. Kobayashi, K. Izumi, H. Kimura, S. Kimura, T. Ibuki, Y. Yokoyama, Y. Tsusaka, Y. Kagoshima, and J. Matsui, “X-ray phase-contrast imaging with submicron resolution by using extremely asymmetric Bragg diffractions,” Appl. Phys. Lett. 78, 132–134 (2001).
    [Crossref]
  6. R. Köhler and P. Schäfer, “Asymmetric Bragg reflection as magnifying optics,” Cryst. Res. Technol. 37, 734–746 (2002).
    [Crossref]
  7. D. Korytár, P. Mikulík, C. Ferrari, J. Hrdý, T. Baumbach, A. Freund, and A. Kubena, “Two-dimensional x-ray magnification based on a monolithic beam conditioner,” J. Phys. D: Appl. Phys. 36, A65–A68 (2003).
    [Crossref]
  8. M. Stampanoni, G. Borchert, and R. Abela, “Towards nanotomography with asymmetrically cut crystals,” Nucl. Instrum. Meth. A 551, 119–124 (2005).
    [Crossref]
  9. M. G. Hönnicke and C. Cusatis, “Analyzer-based x-ray phase-contrast microscopy combining channel-cut and asymmetrically cut crystals,” Rev. Sci. Instrum. 78, 113708 (2007).
    [Crossref] [PubMed]
  10. R. Spal, “Submicrometer resolution hard X-Ray holography with the asymmetric Bragg diffraction microscope,” Phys. Rev. Lett. 86, 3044–3047 (2001).
    [Crossref] [PubMed]
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    [Crossref]
  12. Ya.I. Nesterets, T. E. Gureyev, D. Paganin, K. M. Pavlov, and S.W. Wilkins, “Quantitative diffraction-enhanced x-ray imaging of weak objects,” J. Phys. D: Appl. Phys. 371262–1274 (2004).
    [Crossref]
  13. P. Modregger, D. Lübbert, P. Schäfer, and R. Köhler, “Magnified x-ray phase imaging using asymmetric Bragg reflection: Experiment and theory,” Phys. Rev. B 74054107 (2006).
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  14. J.P. Guigay, E. Pagot, and P. Cloetens, “Fourier optics approach to X-ray analyser-based imaging,” Opt. Commun. 270, 180–188 (2007).
    [Crossref]
  15. A. Bravin, V. Mocella, P. Coan, A. Astolfo, and C. Ferrero, “A numerical wave-optical approach for the simulation of analyzer-based x-ray imaging,” Opt. Express 15, 5641–5648 (2007).
    [Crossref] [PubMed]
  16. Ya. I. Nesterets, T. E. Gureyev, and S. W. Wilkins, “Polychromaticity in the combined propagation-based/analyser-based phase-contrast imaging,” J. Phys. D: Appl. Phys. 38, 4259–4271 (2005).
    [Crossref]
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  18. P. Modregger, D. Lübbert, P. Schäfer, and R. Köhler, “Spatial resolution in Bragg-magnified X-ray images as determined by Fourier analysis,” Phys. Status Solidi (a) 204, 2746–2752 (2007).
    [Crossref]
  19. A. Rack, H. Riesemeier, S. Zabler, T. Weitkamp, B. Müller, G. Weidemann, P. Modregger, J. Banhart, L. Helfen, A. Danilewsky, H. Gräber, R. Heldele, B. Mayzel, J. Goebbels, and T. Baumbach, “The high resolution synchrotron-based imaging stations at the BAMline (BESSY) and TopoTomo (ANKA),” Proc. SPIE 7078, 70780X (2008).
    [Crossref]
  20. P. Coan, E. Pagot, S. Fiedler, P. Cloetens, J. Baruchel, and A. Bravin, “Phase-contrast X-ray imaging combining free space propagation and Bragg diffraction,” J. Synch. Rad. 12, 241–245 (2005)
    [Crossref]
  21. P. Cloetens, R. Barrett, J. Baruchel, J. P. Guigay, and M. Schlenker, “Phase objects in synchrotron radiation hard X-ray imaging,” J. Phys. D: Appl. Phys. 29, 133–146 (1996).
    [Crossref]
  22. T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13, 6296–6304 (2005).
    [Crossref] [PubMed]
  23. M. Kuriyama, W. J. Boettinger, and G. G. Cohen, “Synchrotron radiation topography,” Annu. Rev. Mater. Sci. 12, 23–50 (1982).
    [Crossref]
  24. J. Als-Niehlsen and D. McMorrowElements of modern x-ray physics, Wiley & Sons (2001).
  25. P. Modregger, D. Lübbert, P. Schäfer, R. Köhler, T. Weitkamp, M. Hanke, and T. Baumbach, “Fresnel diffraction in the case of an inclined image plane,” Opt. Express 16, 5141–5149 (2008).
    [Crossref] [PubMed]
  26. J. W. Goodman, Introduction to Fourier Optics, McGraw-Hill, San Fransisco, pp. 106–110 (1968).
  27. P. Modregger, D. Lübbert, P. Schäfer, and R. Köhler, “Two dimensional diffraction enhanced imaging algorithm,” Appl. Phys. Lett. 90, 193501 (2007).
    [Crossref]
  28. E. WilsonFourier Series and Optical Transform Techniques in Contemporary Optics, Wiley & Sons (1995).
  29. C. M. Sparrow, “On spectroscopic resolving power,” Astrophys. J. 44, 76–86 (1916).
    [Crossref]
  30. B. Batterman and H. Cole, “Dynamical diffraction of x rays by perfect crystals,” Rev. Mod. Phys. 36, 681–716 (1964).
    [Crossref]

2008 (2)

A. Rack, H. Riesemeier, S. Zabler, T. Weitkamp, B. Müller, G. Weidemann, P. Modregger, J. Banhart, L. Helfen, A. Danilewsky, H. Gräber, R. Heldele, B. Mayzel, J. Goebbels, and T. Baumbach, “The high resolution synchrotron-based imaging stations at the BAMline (BESSY) and TopoTomo (ANKA),” Proc. SPIE 7078, 70780X (2008).
[Crossref]

P. Modregger, D. Lübbert, P. Schäfer, R. Köhler, T. Weitkamp, M. Hanke, and T. Baumbach, “Fresnel diffraction in the case of an inclined image plane,” Opt. Express 16, 5141–5149 (2008).
[Crossref] [PubMed]

2007 (5)

P. Modregger, D. Lübbert, P. Schäfer, and R. Köhler, “Two dimensional diffraction enhanced imaging algorithm,” Appl. Phys. Lett. 90, 193501 (2007).
[Crossref]

M. G. Hönnicke and C. Cusatis, “Analyzer-based x-ray phase-contrast microscopy combining channel-cut and asymmetrically cut crystals,” Rev. Sci. Instrum. 78, 113708 (2007).
[Crossref] [PubMed]

J.P. Guigay, E. Pagot, and P. Cloetens, “Fourier optics approach to X-ray analyser-based imaging,” Opt. Commun. 270, 180–188 (2007).
[Crossref]

A. Bravin, V. Mocella, P. Coan, A. Astolfo, and C. Ferrero, “A numerical wave-optical approach for the simulation of analyzer-based x-ray imaging,” Opt. Express 15, 5641–5648 (2007).
[Crossref] [PubMed]

P. Modregger, D. Lübbert, P. Schäfer, and R. Köhler, “Spatial resolution in Bragg-magnified X-ray images as determined by Fourier analysis,” Phys. Status Solidi (a) 204, 2746–2752 (2007).
[Crossref]

2006 (1)

P. Modregger, D. Lübbert, P. Schäfer, and R. Köhler, “Magnified x-ray phase imaging using asymmetric Bragg reflection: Experiment and theory,” Phys. Rev. B 74054107 (2006).
[Crossref]

2005 (4)

Ya. I. Nesterets, T. E. Gureyev, and S. W. Wilkins, “Polychromaticity in the combined propagation-based/analyser-based phase-contrast imaging,” J. Phys. D: Appl. Phys. 38, 4259–4271 (2005).
[Crossref]

M. Stampanoni, G. Borchert, and R. Abela, “Towards nanotomography with asymmetrically cut crystals,” Nucl. Instrum. Meth. A 551, 119–124 (2005).
[Crossref]

P. Coan, E. Pagot, S. Fiedler, P. Cloetens, J. Baruchel, and A. Bravin, “Phase-contrast X-ray imaging combining free space propagation and Bragg diffraction,” J. Synch. Rad. 12, 241–245 (2005)
[Crossref]

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13, 6296–6304 (2005).
[Crossref] [PubMed]

2004 (1)

Ya.I. Nesterets, T. E. Gureyev, D. Paganin, K. M. Pavlov, and S.W. Wilkins, “Quantitative diffraction-enhanced x-ray imaging of weak objects,” J. Phys. D: Appl. Phys. 371262–1274 (2004).
[Crossref]

2003 (1)

D. Korytár, P. Mikulík, C. Ferrari, J. Hrdý, T. Baumbach, A. Freund, and A. Kubena, “Two-dimensional x-ray magnification based on a monolithic beam conditioner,” J. Phys. D: Appl. Phys. 36, A65–A68 (2003).
[Crossref]

2002 (2)

R. Köhler and P. Schäfer, “Asymmetric Bragg reflection as magnifying optics,” Cryst. Res. Technol. 37, 734–746 (2002).
[Crossref]

J. Keyriläinen, M. Fernandez, and P. Suortti, “Refraction contrast in x-ray imaging,” Nucl. Instrum. Meth. A 488, 419–427 (2002).
[Crossref]

2001 (2)

R. Spal, “Submicrometer resolution hard X-Ray holography with the asymmetric Bragg diffraction microscope,” Phys. Rev. Lett. 86, 3044–3047 (2001).
[Crossref] [PubMed]

K. Kobayashi, K. Izumi, H. Kimura, S. Kimura, T. Ibuki, Y. Yokoyama, Y. Tsusaka, Y. Kagoshima, and J. Matsui, “X-ray phase-contrast imaging with submicron resolution by using extremely asymmetric Bragg diffractions,” Appl. Phys. Lett. 78, 132–134 (2001).
[Crossref]

1997 (1)

V. N. Ingal and E. A. Beliaevskaya, “Imaging of biological objects in the plane-wave diffraction scheme,” Nuovo Cimento 19, 553–560 (1997).
[Crossref]

1996 (1)

P. Cloetens, R. Barrett, J. Baruchel, J. P. Guigay, and M. Schlenker, “Phase objects in synchrotron radiation hard X-ray imaging,” J. Phys. D: Appl. Phys. 29, 133–146 (1996).
[Crossref]

1995 (1)

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S.W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373, 595–598 (1995).
[Crossref]

1990 (1)

M. Kuriyama, R. C. Dobbyn, R. D. Spal, H. E. Burdette, and D.R. Black, “Hard x-ray microscope with submicrometer spatial resolution,” J. Res. Natl. Inst. Stand. Technol. 95, 559–574 (1990).

1982 (1)

M. Kuriyama, W. J. Boettinger, and G. G. Cohen, “Synchrotron radiation topography,” Annu. Rev. Mater. Sci. 12, 23–50 (1982).
[Crossref]

1980 (1)

E. Förster, K. Goetz, and P. Zaumseil, “Double crystal diffractometry for the characterization of targets for laser fusion experiments,” Krist. Tech. 15, 937–945 (1980).
[Crossref]

1964 (1)

B. Batterman and H. Cole, “Dynamical diffraction of x rays by perfect crystals,” Rev. Mod. Phys. 36, 681–716 (1964).
[Crossref]

1916 (1)

C. M. Sparrow, “On spectroscopic resolving power,” Astrophys. J. 44, 76–86 (1916).
[Crossref]

Abela, R.

M. Stampanoni, G. Borchert, and R. Abela, “Towards nanotomography with asymmetrically cut crystals,” Nucl. Instrum. Meth. A 551, 119–124 (2005).
[Crossref]

Als-Niehlsen, J.

J. Als-Niehlsen and D. McMorrowElements of modern x-ray physics, Wiley & Sons (2001).

Astolfo, A.

Authier, A.

A. AuthierDynamical Theory of X-Ray Diffraction, Vol. 11 of IUCr Monographs on Crystallography, 2nd ed. (Oxford University Press, Oxford2001).

Banhart, J.

A. Rack, H. Riesemeier, S. Zabler, T. Weitkamp, B. Müller, G. Weidemann, P. Modregger, J. Banhart, L. Helfen, A. Danilewsky, H. Gräber, R. Heldele, B. Mayzel, J. Goebbels, and T. Baumbach, “The high resolution synchrotron-based imaging stations at the BAMline (BESSY) and TopoTomo (ANKA),” Proc. SPIE 7078, 70780X (2008).
[Crossref]

Barrett, R.

P. Cloetens, R. Barrett, J. Baruchel, J. P. Guigay, and M. Schlenker, “Phase objects in synchrotron radiation hard X-ray imaging,” J. Phys. D: Appl. Phys. 29, 133–146 (1996).
[Crossref]

Baruchel, J.

P. Coan, E. Pagot, S. Fiedler, P. Cloetens, J. Baruchel, and A. Bravin, “Phase-contrast X-ray imaging combining free space propagation and Bragg diffraction,” J. Synch. Rad. 12, 241–245 (2005)
[Crossref]

P. Cloetens, R. Barrett, J. Baruchel, J. P. Guigay, and M. Schlenker, “Phase objects in synchrotron radiation hard X-ray imaging,” J. Phys. D: Appl. Phys. 29, 133–146 (1996).
[Crossref]

Batterman, B.

B. Batterman and H. Cole, “Dynamical diffraction of x rays by perfect crystals,” Rev. Mod. Phys. 36, 681–716 (1964).
[Crossref]

Baumbach, T.

P. Modregger, D. Lübbert, P. Schäfer, R. Köhler, T. Weitkamp, M. Hanke, and T. Baumbach, “Fresnel diffraction in the case of an inclined image plane,” Opt. Express 16, 5141–5149 (2008).
[Crossref] [PubMed]

A. Rack, H. Riesemeier, S. Zabler, T. Weitkamp, B. Müller, G. Weidemann, P. Modregger, J. Banhart, L. Helfen, A. Danilewsky, H. Gräber, R. Heldele, B. Mayzel, J. Goebbels, and T. Baumbach, “The high resolution synchrotron-based imaging stations at the BAMline (BESSY) and TopoTomo (ANKA),” Proc. SPIE 7078, 70780X (2008).
[Crossref]

D. Korytár, P. Mikulík, C. Ferrari, J. Hrdý, T. Baumbach, A. Freund, and A. Kubena, “Two-dimensional x-ray magnification based on a monolithic beam conditioner,” J. Phys. D: Appl. Phys. 36, A65–A68 (2003).
[Crossref]

Beliaevskaya, E. A.

V. N. Ingal and E. A. Beliaevskaya, “Imaging of biological objects in the plane-wave diffraction scheme,” Nuovo Cimento 19, 553–560 (1997).
[Crossref]

Black, D.R.

M. Kuriyama, R. C. Dobbyn, R. D. Spal, H. E. Burdette, and D.R. Black, “Hard x-ray microscope with submicrometer spatial resolution,” J. Res. Natl. Inst. Stand. Technol. 95, 559–574 (1990).

Boettinger, W. J.

M. Kuriyama, W. J. Boettinger, and G. G. Cohen, “Synchrotron radiation topography,” Annu. Rev. Mater. Sci. 12, 23–50 (1982).
[Crossref]

Borchert, G.

M. Stampanoni, G. Borchert, and R. Abela, “Towards nanotomography with asymmetrically cut crystals,” Nucl. Instrum. Meth. A 551, 119–124 (2005).
[Crossref]

Bravin, A.

A. Bravin, V. Mocella, P. Coan, A. Astolfo, and C. Ferrero, “A numerical wave-optical approach for the simulation of analyzer-based x-ray imaging,” Opt. Express 15, 5641–5648 (2007).
[Crossref] [PubMed]

P. Coan, E. Pagot, S. Fiedler, P. Cloetens, J. Baruchel, and A. Bravin, “Phase-contrast X-ray imaging combining free space propagation and Bragg diffraction,” J. Synch. Rad. 12, 241–245 (2005)
[Crossref]

Burdette, H. E.

M. Kuriyama, R. C. Dobbyn, R. D. Spal, H. E. Burdette, and D.R. Black, “Hard x-ray microscope with submicrometer spatial resolution,” J. Res. Natl. Inst. Stand. Technol. 95, 559–574 (1990).

Cloetens, P.

J.P. Guigay, E. Pagot, and P. Cloetens, “Fourier optics approach to X-ray analyser-based imaging,” Opt. Commun. 270, 180–188 (2007).
[Crossref]

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13, 6296–6304 (2005).
[Crossref] [PubMed]

P. Coan, E. Pagot, S. Fiedler, P. Cloetens, J. Baruchel, and A. Bravin, “Phase-contrast X-ray imaging combining free space propagation and Bragg diffraction,” J. Synch. Rad. 12, 241–245 (2005)
[Crossref]

P. Cloetens, R. Barrett, J. Baruchel, J. P. Guigay, and M. Schlenker, “Phase objects in synchrotron radiation hard X-ray imaging,” J. Phys. D: Appl. Phys. 29, 133–146 (1996).
[Crossref]

Coan, P.

A. Bravin, V. Mocella, P. Coan, A. Astolfo, and C. Ferrero, “A numerical wave-optical approach for the simulation of analyzer-based x-ray imaging,” Opt. Express 15, 5641–5648 (2007).
[Crossref] [PubMed]

P. Coan, E. Pagot, S. Fiedler, P. Cloetens, J. Baruchel, and A. Bravin, “Phase-contrast X-ray imaging combining free space propagation and Bragg diffraction,” J. Synch. Rad. 12, 241–245 (2005)
[Crossref]

Cohen, G. G.

M. Kuriyama, W. J. Boettinger, and G. G. Cohen, “Synchrotron radiation topography,” Annu. Rev. Mater. Sci. 12, 23–50 (1982).
[Crossref]

Cole, H.

B. Batterman and H. Cole, “Dynamical diffraction of x rays by perfect crystals,” Rev. Mod. Phys. 36, 681–716 (1964).
[Crossref]

Cusatis, C.

M. G. Hönnicke and C. Cusatis, “Analyzer-based x-ray phase-contrast microscopy combining channel-cut and asymmetrically cut crystals,” Rev. Sci. Instrum. 78, 113708 (2007).
[Crossref] [PubMed]

Danilewsky, A.

A. Rack, H. Riesemeier, S. Zabler, T. Weitkamp, B. Müller, G. Weidemann, P. Modregger, J. Banhart, L. Helfen, A. Danilewsky, H. Gräber, R. Heldele, B. Mayzel, J. Goebbels, and T. Baumbach, “The high resolution synchrotron-based imaging stations at the BAMline (BESSY) and TopoTomo (ANKA),” Proc. SPIE 7078, 70780X (2008).
[Crossref]

David, C.

Davis, T. J.

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S.W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373, 595–598 (1995).
[Crossref]

Diaz, A.

Dobbyn, R. C.

M. Kuriyama, R. C. Dobbyn, R. D. Spal, H. E. Burdette, and D.R. Black, “Hard x-ray microscope with submicrometer spatial resolution,” J. Res. Natl. Inst. Stand. Technol. 95, 559–574 (1990).

Fernandez, M.

J. Keyriläinen, M. Fernandez, and P. Suortti, “Refraction contrast in x-ray imaging,” Nucl. Instrum. Meth. A 488, 419–427 (2002).
[Crossref]

Ferrari, C.

D. Korytár, P. Mikulík, C. Ferrari, J. Hrdý, T. Baumbach, A. Freund, and A. Kubena, “Two-dimensional x-ray magnification based on a monolithic beam conditioner,” J. Phys. D: Appl. Phys. 36, A65–A68 (2003).
[Crossref]

Ferrero, C.

Fiedler, S.

P. Coan, E. Pagot, S. Fiedler, P. Cloetens, J. Baruchel, and A. Bravin, “Phase-contrast X-ray imaging combining free space propagation and Bragg diffraction,” J. Synch. Rad. 12, 241–245 (2005)
[Crossref]

Förster, E.

E. Förster, K. Goetz, and P. Zaumseil, “Double crystal diffractometry for the characterization of targets for laser fusion experiments,” Krist. Tech. 15, 937–945 (1980).
[Crossref]

Freund, A.

D. Korytár, P. Mikulík, C. Ferrari, J. Hrdý, T. Baumbach, A. Freund, and A. Kubena, “Two-dimensional x-ray magnification based on a monolithic beam conditioner,” J. Phys. D: Appl. Phys. 36, A65–A68 (2003).
[Crossref]

Gao, D.

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S.W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373, 595–598 (1995).
[Crossref]

Goebbels, J.

A. Rack, H. Riesemeier, S. Zabler, T. Weitkamp, B. Müller, G. Weidemann, P. Modregger, J. Banhart, L. Helfen, A. Danilewsky, H. Gräber, R. Heldele, B. Mayzel, J. Goebbels, and T. Baumbach, “The high resolution synchrotron-based imaging stations at the BAMline (BESSY) and TopoTomo (ANKA),” Proc. SPIE 7078, 70780X (2008).
[Crossref]

Goetz, K.

E. Förster, K. Goetz, and P. Zaumseil, “Double crystal diffractometry for the characterization of targets for laser fusion experiments,” Krist. Tech. 15, 937–945 (1980).
[Crossref]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, McGraw-Hill, San Fransisco, pp. 106–110 (1968).

Gräber, H.

A. Rack, H. Riesemeier, S. Zabler, T. Weitkamp, B. Müller, G. Weidemann, P. Modregger, J. Banhart, L. Helfen, A. Danilewsky, H. Gräber, R. Heldele, B. Mayzel, J. Goebbels, and T. Baumbach, “The high resolution synchrotron-based imaging stations at the BAMline (BESSY) and TopoTomo (ANKA),” Proc. SPIE 7078, 70780X (2008).
[Crossref]

Guigay, J. P.

P. Cloetens, R. Barrett, J. Baruchel, J. P. Guigay, and M. Schlenker, “Phase objects in synchrotron radiation hard X-ray imaging,” J. Phys. D: Appl. Phys. 29, 133–146 (1996).
[Crossref]

Guigay, J.P.

J.P. Guigay, E. Pagot, and P. Cloetens, “Fourier optics approach to X-ray analyser-based imaging,” Opt. Commun. 270, 180–188 (2007).
[Crossref]

Gureyev, T. E.

Ya. I. Nesterets, T. E. Gureyev, and S. W. Wilkins, “Polychromaticity in the combined propagation-based/analyser-based phase-contrast imaging,” J. Phys. D: Appl. Phys. 38, 4259–4271 (2005).
[Crossref]

Ya.I. Nesterets, T. E. Gureyev, D. Paganin, K. M. Pavlov, and S.W. Wilkins, “Quantitative diffraction-enhanced x-ray imaging of weak objects,” J. Phys. D: Appl. Phys. 371262–1274 (2004).
[Crossref]

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S.W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373, 595–598 (1995).
[Crossref]

Hanke, M.

Heldele, R.

A. Rack, H. Riesemeier, S. Zabler, T. Weitkamp, B. Müller, G. Weidemann, P. Modregger, J. Banhart, L. Helfen, A. Danilewsky, H. Gräber, R. Heldele, B. Mayzel, J. Goebbels, and T. Baumbach, “The high resolution synchrotron-based imaging stations at the BAMline (BESSY) and TopoTomo (ANKA),” Proc. SPIE 7078, 70780X (2008).
[Crossref]

Helfen, L.

A. Rack, H. Riesemeier, S. Zabler, T. Weitkamp, B. Müller, G. Weidemann, P. Modregger, J. Banhart, L. Helfen, A. Danilewsky, H. Gräber, R. Heldele, B. Mayzel, J. Goebbels, and T. Baumbach, “The high resolution synchrotron-based imaging stations at the BAMline (BESSY) and TopoTomo (ANKA),” Proc. SPIE 7078, 70780X (2008).
[Crossref]

Hönnicke, M. G.

M. G. Hönnicke and C. Cusatis, “Analyzer-based x-ray phase-contrast microscopy combining channel-cut and asymmetrically cut crystals,” Rev. Sci. Instrum. 78, 113708 (2007).
[Crossref] [PubMed]

Hrdý, J.

D. Korytár, P. Mikulík, C. Ferrari, J. Hrdý, T. Baumbach, A. Freund, and A. Kubena, “Two-dimensional x-ray magnification based on a monolithic beam conditioner,” J. Phys. D: Appl. Phys. 36, A65–A68 (2003).
[Crossref]

Ibuki, T.

K. Kobayashi, K. Izumi, H. Kimura, S. Kimura, T. Ibuki, Y. Yokoyama, Y. Tsusaka, Y. Kagoshima, and J. Matsui, “X-ray phase-contrast imaging with submicron resolution by using extremely asymmetric Bragg diffractions,” Appl. Phys. Lett. 78, 132–134 (2001).
[Crossref]

Ingal, V. N.

V. N. Ingal and E. A. Beliaevskaya, “Imaging of biological objects in the plane-wave diffraction scheme,” Nuovo Cimento 19, 553–560 (1997).
[Crossref]

Izumi, K.

K. Kobayashi, K. Izumi, H. Kimura, S. Kimura, T. Ibuki, Y. Yokoyama, Y. Tsusaka, Y. Kagoshima, and J. Matsui, “X-ray phase-contrast imaging with submicron resolution by using extremely asymmetric Bragg diffractions,” Appl. Phys. Lett. 78, 132–134 (2001).
[Crossref]

Kagoshima, Y.

K. Kobayashi, K. Izumi, H. Kimura, S. Kimura, T. Ibuki, Y. Yokoyama, Y. Tsusaka, Y. Kagoshima, and J. Matsui, “X-ray phase-contrast imaging with submicron resolution by using extremely asymmetric Bragg diffractions,” Appl. Phys. Lett. 78, 132–134 (2001).
[Crossref]

Keyriläinen, J.

J. Keyriläinen, M. Fernandez, and P. Suortti, “Refraction contrast in x-ray imaging,” Nucl. Instrum. Meth. A 488, 419–427 (2002).
[Crossref]

Kimura, H.

K. Kobayashi, K. Izumi, H. Kimura, S. Kimura, T. Ibuki, Y. Yokoyama, Y. Tsusaka, Y. Kagoshima, and J. Matsui, “X-ray phase-contrast imaging with submicron resolution by using extremely asymmetric Bragg diffractions,” Appl. Phys. Lett. 78, 132–134 (2001).
[Crossref]

Kimura, S.

K. Kobayashi, K. Izumi, H. Kimura, S. Kimura, T. Ibuki, Y. Yokoyama, Y. Tsusaka, Y. Kagoshima, and J. Matsui, “X-ray phase-contrast imaging with submicron resolution by using extremely asymmetric Bragg diffractions,” Appl. Phys. Lett. 78, 132–134 (2001).
[Crossref]

Kobayashi, K.

K. Kobayashi, K. Izumi, H. Kimura, S. Kimura, T. Ibuki, Y. Yokoyama, Y. Tsusaka, Y. Kagoshima, and J. Matsui, “X-ray phase-contrast imaging with submicron resolution by using extremely asymmetric Bragg diffractions,” Appl. Phys. Lett. 78, 132–134 (2001).
[Crossref]

Köhler, R.

P. Modregger, D. Lübbert, P. Schäfer, R. Köhler, T. Weitkamp, M. Hanke, and T. Baumbach, “Fresnel diffraction in the case of an inclined image plane,” Opt. Express 16, 5141–5149 (2008).
[Crossref] [PubMed]

P. Modregger, D. Lübbert, P. Schäfer, and R. Köhler, “Two dimensional diffraction enhanced imaging algorithm,” Appl. Phys. Lett. 90, 193501 (2007).
[Crossref]

P. Modregger, D. Lübbert, P. Schäfer, and R. Köhler, “Spatial resolution in Bragg-magnified X-ray images as determined by Fourier analysis,” Phys. Status Solidi (a) 204, 2746–2752 (2007).
[Crossref]

P. Modregger, D. Lübbert, P. Schäfer, and R. Köhler, “Magnified x-ray phase imaging using asymmetric Bragg reflection: Experiment and theory,” Phys. Rev. B 74054107 (2006).
[Crossref]

R. Köhler and P. Schäfer, “Asymmetric Bragg reflection as magnifying optics,” Cryst. Res. Technol. 37, 734–746 (2002).
[Crossref]

Korytár, D.

D. Korytár, P. Mikulík, C. Ferrari, J. Hrdý, T. Baumbach, A. Freund, and A. Kubena, “Two-dimensional x-ray magnification based on a monolithic beam conditioner,” J. Phys. D: Appl. Phys. 36, A65–A68 (2003).
[Crossref]

Kubena, A.

D. Korytár, P. Mikulík, C. Ferrari, J. Hrdý, T. Baumbach, A. Freund, and A. Kubena, “Two-dimensional x-ray magnification based on a monolithic beam conditioner,” J. Phys. D: Appl. Phys. 36, A65–A68 (2003).
[Crossref]

Kuriyama, M.

M. Kuriyama, R. C. Dobbyn, R. D. Spal, H. E. Burdette, and D.R. Black, “Hard x-ray microscope with submicrometer spatial resolution,” J. Res. Natl. Inst. Stand. Technol. 95, 559–574 (1990).

M. Kuriyama, W. J. Boettinger, and G. G. Cohen, “Synchrotron radiation topography,” Annu. Rev. Mater. Sci. 12, 23–50 (1982).
[Crossref]

Lübbert, D.

P. Modregger, D. Lübbert, P. Schäfer, R. Köhler, T. Weitkamp, M. Hanke, and T. Baumbach, “Fresnel diffraction in the case of an inclined image plane,” Opt. Express 16, 5141–5149 (2008).
[Crossref] [PubMed]

P. Modregger, D. Lübbert, P. Schäfer, and R. Köhler, “Two dimensional diffraction enhanced imaging algorithm,” Appl. Phys. Lett. 90, 193501 (2007).
[Crossref]

P. Modregger, D. Lübbert, P. Schäfer, and R. Köhler, “Spatial resolution in Bragg-magnified X-ray images as determined by Fourier analysis,” Phys. Status Solidi (a) 204, 2746–2752 (2007).
[Crossref]

P. Modregger, D. Lübbert, P. Schäfer, and R. Köhler, “Magnified x-ray phase imaging using asymmetric Bragg reflection: Experiment and theory,” Phys. Rev. B 74054107 (2006).
[Crossref]

Matsui, J.

K. Kobayashi, K. Izumi, H. Kimura, S. Kimura, T. Ibuki, Y. Yokoyama, Y. Tsusaka, Y. Kagoshima, and J. Matsui, “X-ray phase-contrast imaging with submicron resolution by using extremely asymmetric Bragg diffractions,” Appl. Phys. Lett. 78, 132–134 (2001).
[Crossref]

Mayzel, B.

A. Rack, H. Riesemeier, S. Zabler, T. Weitkamp, B. Müller, G. Weidemann, P. Modregger, J. Banhart, L. Helfen, A. Danilewsky, H. Gräber, R. Heldele, B. Mayzel, J. Goebbels, and T. Baumbach, “The high resolution synchrotron-based imaging stations at the BAMline (BESSY) and TopoTomo (ANKA),” Proc. SPIE 7078, 70780X (2008).
[Crossref]

McMorrow, D.

J. Als-Niehlsen and D. McMorrowElements of modern x-ray physics, Wiley & Sons (2001).

Mikulík, P.

D. Korytár, P. Mikulík, C. Ferrari, J. Hrdý, T. Baumbach, A. Freund, and A. Kubena, “Two-dimensional x-ray magnification based on a monolithic beam conditioner,” J. Phys. D: Appl. Phys. 36, A65–A68 (2003).
[Crossref]

Mocella, V.

Modregger, P.

P. Modregger, D. Lübbert, P. Schäfer, R. Köhler, T. Weitkamp, M. Hanke, and T. Baumbach, “Fresnel diffraction in the case of an inclined image plane,” Opt. Express 16, 5141–5149 (2008).
[Crossref] [PubMed]

A. Rack, H. Riesemeier, S. Zabler, T. Weitkamp, B. Müller, G. Weidemann, P. Modregger, J. Banhart, L. Helfen, A. Danilewsky, H. Gräber, R. Heldele, B. Mayzel, J. Goebbels, and T. Baumbach, “The high resolution synchrotron-based imaging stations at the BAMline (BESSY) and TopoTomo (ANKA),” Proc. SPIE 7078, 70780X (2008).
[Crossref]

P. Modregger, D. Lübbert, P. Schäfer, and R. Köhler, “Two dimensional diffraction enhanced imaging algorithm,” Appl. Phys. Lett. 90, 193501 (2007).
[Crossref]

P. Modregger, D. Lübbert, P. Schäfer, and R. Köhler, “Spatial resolution in Bragg-magnified X-ray images as determined by Fourier analysis,” Phys. Status Solidi (a) 204, 2746–2752 (2007).
[Crossref]

P. Modregger, D. Lübbert, P. Schäfer, and R. Köhler, “Magnified x-ray phase imaging using asymmetric Bragg reflection: Experiment and theory,” Phys. Rev. B 74054107 (2006).
[Crossref]

Müller, B.

A. Rack, H. Riesemeier, S. Zabler, T. Weitkamp, B. Müller, G. Weidemann, P. Modregger, J. Banhart, L. Helfen, A. Danilewsky, H. Gräber, R. Heldele, B. Mayzel, J. Goebbels, and T. Baumbach, “The high resolution synchrotron-based imaging stations at the BAMline (BESSY) and TopoTomo (ANKA),” Proc. SPIE 7078, 70780X (2008).
[Crossref]

Nesterets, Ya. I.

Ya. I. Nesterets, T. E. Gureyev, and S. W. Wilkins, “Polychromaticity in the combined propagation-based/analyser-based phase-contrast imaging,” J. Phys. D: Appl. Phys. 38, 4259–4271 (2005).
[Crossref]

Nesterets, Ya.I.

Ya.I. Nesterets, T. E. Gureyev, D. Paganin, K. M. Pavlov, and S.W. Wilkins, “Quantitative diffraction-enhanced x-ray imaging of weak objects,” J. Phys. D: Appl. Phys. 371262–1274 (2004).
[Crossref]

Paganin, D.

Ya.I. Nesterets, T. E. Gureyev, D. Paganin, K. M. Pavlov, and S.W. Wilkins, “Quantitative diffraction-enhanced x-ray imaging of weak objects,” J. Phys. D: Appl. Phys. 371262–1274 (2004).
[Crossref]

Pagot, E.

J.P. Guigay, E. Pagot, and P. Cloetens, “Fourier optics approach to X-ray analyser-based imaging,” Opt. Commun. 270, 180–188 (2007).
[Crossref]

P. Coan, E. Pagot, S. Fiedler, P. Cloetens, J. Baruchel, and A. Bravin, “Phase-contrast X-ray imaging combining free space propagation and Bragg diffraction,” J. Synch. Rad. 12, 241–245 (2005)
[Crossref]

Pavlov, K. M.

Ya.I. Nesterets, T. E. Gureyev, D. Paganin, K. M. Pavlov, and S.W. Wilkins, “Quantitative diffraction-enhanced x-ray imaging of weak objects,” J. Phys. D: Appl. Phys. 371262–1274 (2004).
[Crossref]

Pfeiffer, F.

Rack, A.

A. Rack, H. Riesemeier, S. Zabler, T. Weitkamp, B. Müller, G. Weidemann, P. Modregger, J. Banhart, L. Helfen, A. Danilewsky, H. Gräber, R. Heldele, B. Mayzel, J. Goebbels, and T. Baumbach, “The high resolution synchrotron-based imaging stations at the BAMline (BESSY) and TopoTomo (ANKA),” Proc. SPIE 7078, 70780X (2008).
[Crossref]

Riesemeier, H.

A. Rack, H. Riesemeier, S. Zabler, T. Weitkamp, B. Müller, G. Weidemann, P. Modregger, J. Banhart, L. Helfen, A. Danilewsky, H. Gräber, R. Heldele, B. Mayzel, J. Goebbels, and T. Baumbach, “The high resolution synchrotron-based imaging stations at the BAMline (BESSY) and TopoTomo (ANKA),” Proc. SPIE 7078, 70780X (2008).
[Crossref]

Schäfer, P.

P. Modregger, D. Lübbert, P. Schäfer, R. Köhler, T. Weitkamp, M. Hanke, and T. Baumbach, “Fresnel diffraction in the case of an inclined image plane,” Opt. Express 16, 5141–5149 (2008).
[Crossref] [PubMed]

P. Modregger, D. Lübbert, P. Schäfer, and R. Köhler, “Two dimensional diffraction enhanced imaging algorithm,” Appl. Phys. Lett. 90, 193501 (2007).
[Crossref]

P. Modregger, D. Lübbert, P. Schäfer, and R. Köhler, “Spatial resolution in Bragg-magnified X-ray images as determined by Fourier analysis,” Phys. Status Solidi (a) 204, 2746–2752 (2007).
[Crossref]

P. Modregger, D. Lübbert, P. Schäfer, and R. Köhler, “Magnified x-ray phase imaging using asymmetric Bragg reflection: Experiment and theory,” Phys. Rev. B 74054107 (2006).
[Crossref]

R. Köhler and P. Schäfer, “Asymmetric Bragg reflection as magnifying optics,” Cryst. Res. Technol. 37, 734–746 (2002).
[Crossref]

Schlenker, M.

P. Cloetens, R. Barrett, J. Baruchel, J. P. Guigay, and M. Schlenker, “Phase objects in synchrotron radiation hard X-ray imaging,” J. Phys. D: Appl. Phys. 29, 133–146 (1996).
[Crossref]

Spal, R.

R. Spal, “Submicrometer resolution hard X-Ray holography with the asymmetric Bragg diffraction microscope,” Phys. Rev. Lett. 86, 3044–3047 (2001).
[Crossref] [PubMed]

Spal, R. D.

M. Kuriyama, R. C. Dobbyn, R. D. Spal, H. E. Burdette, and D.R. Black, “Hard x-ray microscope with submicrometer spatial resolution,” J. Res. Natl. Inst. Stand. Technol. 95, 559–574 (1990).

Sparrow, C. M.

C. M. Sparrow, “On spectroscopic resolving power,” Astrophys. J. 44, 76–86 (1916).
[Crossref]

Stampanoni, M.

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13, 6296–6304 (2005).
[Crossref] [PubMed]

M. Stampanoni, G. Borchert, and R. Abela, “Towards nanotomography with asymmetrically cut crystals,” Nucl. Instrum. Meth. A 551, 119–124 (2005).
[Crossref]

Stevenson, A. W.

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S.W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373, 595–598 (1995).
[Crossref]

Suortti, P.

J. Keyriläinen, M. Fernandez, and P. Suortti, “Refraction contrast in x-ray imaging,” Nucl. Instrum. Meth. A 488, 419–427 (2002).
[Crossref]

Tsusaka, Y.

K. Kobayashi, K. Izumi, H. Kimura, S. Kimura, T. Ibuki, Y. Yokoyama, Y. Tsusaka, Y. Kagoshima, and J. Matsui, “X-ray phase-contrast imaging with submicron resolution by using extremely asymmetric Bragg diffractions,” Appl. Phys. Lett. 78, 132–134 (2001).
[Crossref]

Weidemann, G.

A. Rack, H. Riesemeier, S. Zabler, T. Weitkamp, B. Müller, G. Weidemann, P. Modregger, J. Banhart, L. Helfen, A. Danilewsky, H. Gräber, R. Heldele, B. Mayzel, J. Goebbels, and T. Baumbach, “The high resolution synchrotron-based imaging stations at the BAMline (BESSY) and TopoTomo (ANKA),” Proc. SPIE 7078, 70780X (2008).
[Crossref]

Weitkamp, T.

A. Rack, H. Riesemeier, S. Zabler, T. Weitkamp, B. Müller, G. Weidemann, P. Modregger, J. Banhart, L. Helfen, A. Danilewsky, H. Gräber, R. Heldele, B. Mayzel, J. Goebbels, and T. Baumbach, “The high resolution synchrotron-based imaging stations at the BAMline (BESSY) and TopoTomo (ANKA),” Proc. SPIE 7078, 70780X (2008).
[Crossref]

P. Modregger, D. Lübbert, P. Schäfer, R. Köhler, T. Weitkamp, M. Hanke, and T. Baumbach, “Fresnel diffraction in the case of an inclined image plane,” Opt. Express 16, 5141–5149 (2008).
[Crossref] [PubMed]

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13, 6296–6304 (2005).
[Crossref] [PubMed]

Wilkins, S. W.

Ya. I. Nesterets, T. E. Gureyev, and S. W. Wilkins, “Polychromaticity in the combined propagation-based/analyser-based phase-contrast imaging,” J. Phys. D: Appl. Phys. 38, 4259–4271 (2005).
[Crossref]

Wilkins, S.W.

Ya.I. Nesterets, T. E. Gureyev, D. Paganin, K. M. Pavlov, and S.W. Wilkins, “Quantitative diffraction-enhanced x-ray imaging of weak objects,” J. Phys. D: Appl. Phys. 371262–1274 (2004).
[Crossref]

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S.W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373, 595–598 (1995).
[Crossref]

Wilson, E.

E. WilsonFourier Series and Optical Transform Techniques in Contemporary Optics, Wiley & Sons (1995).

Yokoyama, Y.

K. Kobayashi, K. Izumi, H. Kimura, S. Kimura, T. Ibuki, Y. Yokoyama, Y. Tsusaka, Y. Kagoshima, and J. Matsui, “X-ray phase-contrast imaging with submicron resolution by using extremely asymmetric Bragg diffractions,” Appl. Phys. Lett. 78, 132–134 (2001).
[Crossref]

Zabler, S.

A. Rack, H. Riesemeier, S. Zabler, T. Weitkamp, B. Müller, G. Weidemann, P. Modregger, J. Banhart, L. Helfen, A. Danilewsky, H. Gräber, R. Heldele, B. Mayzel, J. Goebbels, and T. Baumbach, “The high resolution synchrotron-based imaging stations at the BAMline (BESSY) and TopoTomo (ANKA),” Proc. SPIE 7078, 70780X (2008).
[Crossref]

Zaumseil, P.

E. Förster, K. Goetz, and P. Zaumseil, “Double crystal diffractometry for the characterization of targets for laser fusion experiments,” Krist. Tech. 15, 937–945 (1980).
[Crossref]

Ziegler, E.

Annu. Rev. Mater. Sci. (1)

M. Kuriyama, W. J. Boettinger, and G. G. Cohen, “Synchrotron radiation topography,” Annu. Rev. Mater. Sci. 12, 23–50 (1982).
[Crossref]

Appl. Phys. Lett. (2)

P. Modregger, D. Lübbert, P. Schäfer, and R. Köhler, “Two dimensional diffraction enhanced imaging algorithm,” Appl. Phys. Lett. 90, 193501 (2007).
[Crossref]

K. Kobayashi, K. Izumi, H. Kimura, S. Kimura, T. Ibuki, Y. Yokoyama, Y. Tsusaka, Y. Kagoshima, and J. Matsui, “X-ray phase-contrast imaging with submicron resolution by using extremely asymmetric Bragg diffractions,” Appl. Phys. Lett. 78, 132–134 (2001).
[Crossref]

Astrophys. J. (1)

C. M. Sparrow, “On spectroscopic resolving power,” Astrophys. J. 44, 76–86 (1916).
[Crossref]

Cryst. Res. Technol. (1)

R. Köhler and P. Schäfer, “Asymmetric Bragg reflection as magnifying optics,” Cryst. Res. Technol. 37, 734–746 (2002).
[Crossref]

J. Phys. D: Appl. Phys. (4)

D. Korytár, P. Mikulík, C. Ferrari, J. Hrdý, T. Baumbach, A. Freund, and A. Kubena, “Two-dimensional x-ray magnification based on a monolithic beam conditioner,” J. Phys. D: Appl. Phys. 36, A65–A68 (2003).
[Crossref]

Ya.I. Nesterets, T. E. Gureyev, D. Paganin, K. M. Pavlov, and S.W. Wilkins, “Quantitative diffraction-enhanced x-ray imaging of weak objects,” J. Phys. D: Appl. Phys. 371262–1274 (2004).
[Crossref]

Ya. I. Nesterets, T. E. Gureyev, and S. W. Wilkins, “Polychromaticity in the combined propagation-based/analyser-based phase-contrast imaging,” J. Phys. D: Appl. Phys. 38, 4259–4271 (2005).
[Crossref]

P. Cloetens, R. Barrett, J. Baruchel, J. P. Guigay, and M. Schlenker, “Phase objects in synchrotron radiation hard X-ray imaging,” J. Phys. D: Appl. Phys. 29, 133–146 (1996).
[Crossref]

J. Res. Natl. Inst. Stand. Technol. (1)

M. Kuriyama, R. C. Dobbyn, R. D. Spal, H. E. Burdette, and D.R. Black, “Hard x-ray microscope with submicrometer spatial resolution,” J. Res. Natl. Inst. Stand. Technol. 95, 559–574 (1990).

J. Synch. Rad. (1)

P. Coan, E. Pagot, S. Fiedler, P. Cloetens, J. Baruchel, and A. Bravin, “Phase-contrast X-ray imaging combining free space propagation and Bragg diffraction,” J. Synch. Rad. 12, 241–245 (2005)
[Crossref]

Krist. Tech. (1)

E. Förster, K. Goetz, and P. Zaumseil, “Double crystal diffractometry for the characterization of targets for laser fusion experiments,” Krist. Tech. 15, 937–945 (1980).
[Crossref]

Nature (1)

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S.W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373, 595–598 (1995).
[Crossref]

Nucl. Instrum. Meth. A (2)

M. Stampanoni, G. Borchert, and R. Abela, “Towards nanotomography with asymmetrically cut crystals,” Nucl. Instrum. Meth. A 551, 119–124 (2005).
[Crossref]

J. Keyriläinen, M. Fernandez, and P. Suortti, “Refraction contrast in x-ray imaging,” Nucl. Instrum. Meth. A 488, 419–427 (2002).
[Crossref]

Nuovo Cimento (1)

V. N. Ingal and E. A. Beliaevskaya, “Imaging of biological objects in the plane-wave diffraction scheme,” Nuovo Cimento 19, 553–560 (1997).
[Crossref]

Opt. Commun. (1)

J.P. Guigay, E. Pagot, and P. Cloetens, “Fourier optics approach to X-ray analyser-based imaging,” Opt. Commun. 270, 180–188 (2007).
[Crossref]

Opt. Express (3)

Phys. Rev. B (1)

P. Modregger, D. Lübbert, P. Schäfer, and R. Köhler, “Magnified x-ray phase imaging using asymmetric Bragg reflection: Experiment and theory,” Phys. Rev. B 74054107 (2006).
[Crossref]

Phys. Rev. Lett. (1)

R. Spal, “Submicrometer resolution hard X-Ray holography with the asymmetric Bragg diffraction microscope,” Phys. Rev. Lett. 86, 3044–3047 (2001).
[Crossref] [PubMed]

Phys. Status Solidi (a) (1)

P. Modregger, D. Lübbert, P. Schäfer, and R. Köhler, “Spatial resolution in Bragg-magnified X-ray images as determined by Fourier analysis,” Phys. Status Solidi (a) 204, 2746–2752 (2007).
[Crossref]

Proc. SPIE (1)

A. Rack, H. Riesemeier, S. Zabler, T. Weitkamp, B. Müller, G. Weidemann, P. Modregger, J. Banhart, L. Helfen, A. Danilewsky, H. Gräber, R. Heldele, B. Mayzel, J. Goebbels, and T. Baumbach, “The high resolution synchrotron-based imaging stations at the BAMline (BESSY) and TopoTomo (ANKA),” Proc. SPIE 7078, 70780X (2008).
[Crossref]

Rev. Mod. Phys. (1)

B. Batterman and H. Cole, “Dynamical diffraction of x rays by perfect crystals,” Rev. Mod. Phys. 36, 681–716 (1964).
[Crossref]

Rev. Sci. Instrum. (1)

M. G. Hönnicke and C. Cusatis, “Analyzer-based x-ray phase-contrast microscopy combining channel-cut and asymmetrically cut crystals,” Rev. Sci. Instrum. 78, 113708 (2007).
[Crossref] [PubMed]

Other (4)

A. AuthierDynamical Theory of X-Ray Diffraction, Vol. 11 of IUCr Monographs on Crystallography, 2nd ed. (Oxford University Press, Oxford2001).

E. WilsonFourier Series and Optical Transform Techniques in Contemporary Optics, Wiley & Sons (1995).

J. W. Goodman, Introduction to Fourier Optics, McGraw-Hill, San Fransisco, pp. 106–110 (1968).

J. Als-Niehlsen and D. McMorrowElements of modern x-ray physics, Wiley & Sons (2001).

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Figures (12)

Fig. 1.
Fig. 1.

Scheme of the Bragg Magnifier. The arrows labeled s and p indicate the corresponding polarization directions. The mean propagation distances in the used experimental setup are d 1=35 mm sample to first analyzer, d 2=45 mm first to second analyzer and d 3=150 mm second analyzer to CCD camera.

Fig. 2.
Fig. 2.

The figure illustrates that for imaging the incident divergence σinc as seen from the sample is of importance - not the intrinsic angular size of the source. More generally, the spectral and angular distribution of the beam at the location of the sample (Ib α,λ); see also Sec. 4.3) defines the possible effects of partially coherent illumination. The dotted rectangles named DCM and BM indicate the position of the double crystal monochromator and the Bragg Magnifier. The kink of beam fan at the position of the Bragg Magnifier illustrates the fact that the divergence of the beam is reduced after asymmetric Bragg reflection according to Eq. (1).

Fig. 3.
Fig. 3.

Ewald sphere construction for two wave vectors with fixed incident direction but different wavelengths for an asymmetric Bragg reflection. α and α′ are the glancing incidence and exit angles of the reference beam (thick arrows) respectively. The exit angle of the wavelength corresponding to kk is defined by the intersection of its Ewald sphere and the crystal truncation rod (CTR). Its obvious that the exit angle depends on the wavelength. Thus, even a perfectly collimated but polychromatic beam will be divergent after asymmetric reflection, an effect that is well known from dynamical theory and may be called dispersion induced divergence.

Fig. 4.
Fig. 4.

Definition of quantities for the theoretical formalism: the angle of incidence α of the beam on the analyzer crystal, the coordinate system for the output wave field (x; z), the position on the analyzer surface s, the mean propagation distance between sample and analyzer crystal z 0 and the additional propagation distance z(x) that is dependent on the position of the analyzer surface. Note: Since the influence of free-space propagation after reflection is practically negligible, the observable wave field at the detector (not shown) equals the output wave field after reflection on the surface of the analyzer crystal.

Fig. 5.
Fig. 5.

Numerically calculated polychromatic response function (RF poly ) and the monochromatic response function (i.e. ζ=0) for the first reflection and a free-space propagation distance of 5 mm.

Fig. 6.
Fig. 6.

(a) Numerically calculated contrast of a Gaussian-shaped sample in dependence of the relative spectral width ζ. While the contrast clearly decreases with increasing ζ the general shape of the intensity distribution is preserved. (b) Contrast ratio between monochromatic and polychromatic case for the 224 reflection (first analyzer) and the 004 reflection (second analyzer) in dependence on ζ. While the full lines indicate the spectral widths corresponding to 50% contrast loss, the dashed lines reflect the typical experimental situation with a spectral width of ζ=1.3×10-4.

Fig. 7.
Fig. 7.

Spatial resolution of the Bragg Magnifier as determined by the Sparrow criterion for the monochromatic and dispersive cases. The numerical calculations were performed for the first reflection (Si-224, σ) at 8.048 keV, corresponding to a magnification factor of 40. The working point was chosen on the left slope. As expected the resolution decreases in the dispersive case but is still well in the sub-micrometer regime.

Fig. 8.
Fig. 8.

Intensity maps with the two working points ω 1 and ω 2 on the analyzer crystals of the Bragg Magnifier as parameters: (a) experiment and (b) theory. In order to improve the comparability a background value was added in (b) corresponding to a background present in the experiment.

Fig. 9.
Fig. 9.

Observable halfwidths of the experimental intensity map in Fig. 8(a). The FWHMs of each horizontal line (corresponding to the half width in ω 1) and each vertical line (corresponding to the half width in ω 2) in the intensity map was determined. The resulting FWHMs are in each case shown in dependence of the other working point. It is clearly visible that the half width of one rocking curve depends on the working point position of the other rocking curve. This can be understood as a dispersive effect.

Fig. 10.
Fig. 10.

Schematic visualization of the integral in Eq. 32 used to explain the dependence of FWHMω 2 on ω 1 (bottom line in Fig. 9). In this case the integral describes a convolution of the second reflection curve |R̂2|2 with the function |W×R̂1|2. The figures show the intensity distribution of the quantities as indicated in the legend with increasing ω 1. It is obvious that the width of the function |W×R̂1|2 depends on the chosen working point ω 1.

Fig. 11.
Fig. 11.

Dispersion at the monochromator with asymmetric Bragg reflection (here: b<1). A fixed exit direction expressed with respect to the angular deviation ϕ from the reference beam is traced through the crystal via the vacuum dispersion surfaces. Δθd λ/λ tan θm denotes the angular offset for a symmetric reflection (i.e. b=1). The inset in the middle bottom part of the figure describes the relative orientations of the incident wave vector k0, the exit wave vector k⃗h and the lattice vector h⃗, respectively. Bearing in mind that an angular deviation on the exit side Δθout transforms to an angular deviation on the incident side Δθin via Δθin =bΔθout , it is possible to retrieve Eq. (34) and Eq. (35) from this figure.

Fig. 12.
Fig. 12.

Ray-tracing at one monochromator crystal.

Tables (2)

Tables Icon

Table 1. Experimental parameters of a typical monochromator and the Bragg Magnifier. The index of reflection and the corresponding polarization is given by hkl. θB is the Bragg angle, b the magnification factor, ωD the theoretical Darwin width and ζ is the corresponding relative spectral width (or spectral acceptance) according to Eq. (6). All values apply for a x-ray photon energy of 8:048 keV.

Tables Icon

Table 2. Spatial coherence lengths and incident divergences of two beamlines: the TOPO-TOMO beamline at ANKA [19] and the ID19 beamline at the ESRF [20]. The values apply for a wavelength of 1.5 Å and are valid under the assumption that no additional optical elements (e.g. windows) deteriorate the beam coherence.

Equations (40)

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σout=σinb
Δxver=σverd1+σverb(d2+d3){0.18μm(TOPOTOMO)0.008μm(ID19)
Δxhor=σhor(d1+d2)+σhorbd3{1.4μm(TOPOTOMO)0.07μm(ID19)
b=sinα′sinα=sin(θB+ρ)sin(θBρ)
Δθd=ΔλλtanθB
ζ=ωDcotθB.
Δθad=(11b)ΔλλtanθB
Δx=dΔθad=d (11b)ζtanθB.
Dout(x)= dq D̂in (q)R̂1(qK+ω1)exp(iqxiz0+z(x)2Kq2)
x=ssinαandz=s cos α
q(f)=KtanαK2tan2α2Kcosαf.
Dout(s)= d f P̂ (q(f))D̂in(q(f))eifs
P̂(f)=exp(iz02Kq(f)2)sinαcosαKq(f)R̂(q(f)K+ω1).
I(x)= d λ d Δ α Ib (Δα,λ) DΔα,λ(x)2
Δα=1Kϕx
Din (x)exp (iΔαKx)Din(x)
D̂in(q)D̂in(qq0).
q(f)=KtanαK2tan2α2Kcosαfq0
P̂Δα(f)=exp(iz02K(q(f)+q0)2)sinαcosαK(q(f)+q0)R̂(q(f)K+ω1Δα)
Δθλi=tan θi λλrefλref (i=1,2)
P̂Δα,λ(f)=exp(iz02K(q(f)+q0)2)sinαcosαK(q(f)+q0)R̂(q(f)K+ω1Δα+Δθλi).
Ib(Δα,λ)δD(Δα)W(λ)
P̂λ(f)=exp(iz02Kq(f)2)sinαcosαKq(f)R̂(q(f)K+ω1+Δθλ1).
Dλ(s)= d f P̂λ (f)D̂in(q(f))eifs
Idisp(s)= d λ W (λ)Dλ(s)2 .
RFpoly(s)= d λ W (λ)dfP̂λ(q(f))eifs2
h(x)=h1(1exp(x22σ2))
Din(x)=exp (ih(x)(n1)K)
Din(x)=1D̂in(q)=δD(q).
Iλ(x;λ)=R̂1(Δθλ1+ω1)2.
Iλ(λ)=R̂1(Δθλ1+ω1)2R̂2(Δθλ2+ω2)2,
I(ω1,ω2)= d λ W (λ)R̂1(ω1+Δθλ1)2R̂2(ω2+Δθλ2)2
FWHMout=FWHMWR12+FWHMR22
Δθm=bm(ϕ+Δλλtanθm)
ϕ′=bmϕ+(bm1)Δλλtanθm.
x′=1b1(x+z1ϕ)+z2ϕ′
x″=1b2(x′+z3ϕ′)+z4ϕ″
ϕ″=b2b1ϕ+(b2b11)ΔλλtanθB
Ib(ϕ,λ,x)=R̂c1(Δθ1)2R̂c2(Δθ2)2Is(ϕ″,λ,x″)
Δλλ=xzgcotθB

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