Abstract

We propose an innovative method to extend the utilization of the phase space downstream of a synchrotron light source for X-ray transmission microscopy. Based on the dynamical theory of X-ray diffraction, asymmetrically cut perfect crystals are applied to reshape the position–angle–wavelength space of the light source, by which the usable phase space of the source can be magnified by over one hundred times, thereby “phase-space-matching” the source with the objective lens of the microscope. The method’s validity is confirmed using SHADOW code simulations, and aberration through an optical lens such as a Fresnel zone plate is examined via matrix optics for nano-resolution X-ray images.

© 2015 Optical Society of America

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References

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  1. D. Attwood, Soft X-rays and Extreme Ultraviolet Radiation - Principles and Applications (Cambridge University, 2000), Chap. 9.
  2. M. Feser, M. R. Howells, J. Kirz, J. Rudati, and W. Yun, “Advantages of a synchrotron bending magnet as the sample illuminator for a wide-field X-ray microscope,” J. Synchrotron Radiat. 19(5), 751–758 (2012).
    [Crossref] [PubMed]
  3. R. Falcone, C. Jacobsen, J. Kirz, S. Marchesini, D. Shapiro, and J. Spence, “New directions in X-ray microscopy,” Contemp. Phys. 52(4), 293–318 (2011).
    [Crossref]
  4. Q. Shen, “X-ray flux, brilliance and coherence of the proposed Cornell energy-recovery synchrotron source,” CHESS Technical Memo 01–002 (2001).
  5. J. W. M. DuMond, “Theory of the use of more than two successive x-ray crystal reflection to obtain increased resolving power,” Phys. Rev. 52(8), 872–883 (1937).
    [Crossref]
  6. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd ed. (John Wiley & Sons, Inc., 2007), Chap. 3.
  7. Y. Shvyd’ko, X-Ray Optics – High Energy Resolution Applications (Springer-Verlag, 2004), Chaps. 1–3.
  8. A. Authier, Dynamical Theory of X-Ray Diffraction (Oxford University, 2001), Chap. 4.
  9. J. Als-Nielsen, Elements of Modern X-ray Physics (John Wiley & Sons Ltd., 2011).
  10. T. Matsushita and U. Kaminaga, “A systematic method of estimating the performance of X-ray optical systems for synchrotron radiation. I. Description of various optical elements in position-angle for ideally monochromatic X-rays,” J. Appl. Cryst. 13(6), 465–471 (1980).
    [Crossref]
  11. T. Matsushita, U. Kamanaga, and K. Kohra, “A generalized phase space optical analysis of X-ray optical systems using crystal monochromators,” Jpn. J. Appl. Phys. 17(S2Suppl.), 449–452 (1978).
    [Crossref]
  12. C. Ferrero, D.-M. Smilgies, C. Riekel, G. Gatta, and P. Daly, “Extending the possibilities in phase space analysis of synchrotron radiation x-ray optics,” Appl. Opt. 47(22), E116–E124 (2008).
    [Crossref] [PubMed]
  13. D.-M. Smilgies, “Compact matrix formalism for phase space analysis of complex optical systems,” Appl. Opt. 47(22), E106–E115 (2008).
    [Crossref] [PubMed]
  14. M. Sanchez del Rio and R. J. Dejus, “X-ray Oriented Programs – Graphical user interfaces for synchrotron radiation spectral, optics, and analysis calculations,” http://www.esrf.eu/computing/scientific/xop2.1/intro.html .
  15. M. Sanchez del Rio, “SHADOWVUI – A visual user interface to SHADOW under IDL,” http://www.esrf.eu/computing/scientific/xop2.1/shadowvui/ .
  16. M. Sanchez del Rio and F. Cerrina, “Asymmetrically cut crystals for synchrotron radiation monochromators,” Rev. Sci. Instrum. 63(1), 936–940 (1992).
    [Crossref]
  17. H. Takano, Y. Suzuki, and A. Takeuchi, “Sub-100 nm hard X-Ray microbeam generation with Fresnel zone plate Optics,” Jpn. J. Appl. Phys. 42(Part 2, No. 2A), L132–L134 (2003).
    [Crossref]
  18. Y. Suzuki, A. Takeuchi, H. Takano, and H. Takenaka, “Performance test of Fresnel zone plate with 50 nm outermost zone width in hard X-ray region,” Jpn. J. Appl. Phys. 44(4A), 1994–1998 (2005).
    [Crossref]
  19. K. Codling and P. Mitchell, “A constant deviation grazing incidence monochromator,” J. Phys. E Sci. Instrum. 3(9), 685–689 (1970).
    [Crossref]
  20. M. Wieland, Ch. Spielmann, U. Kleineberg, T. Westerwalbesloh, U. Heinzmann, and T. Wilhein, “Toward time-resolved soft X-ray microscopy using pulsed fs-high-harmonic radiation,” Ultramicroscopy 102(2), 93–100 (2005).
    [Crossref] [PubMed]
  21. D. Guay, J. Stewart-Ornstein, X. Zhang, and A. P. Hitchcock, “In situ spatial and time-resolved studies of electrochemical reactions by scanning transmission X-ray microscopy,” Anal. Chem. 77(11), 3479–3487 (2005).
    [Crossref] [PubMed]
  22. S. Brauer, G. B. Stephenson, and M. Sutton, “Perfect crystals in the asymmetric Bragg geometry as optical elements for coherent X-ray beams,” J. Synchrotron Radiat. 2(4), 163–173 (1995).
    [Crossref] [PubMed]
  23. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (The McGraw-Hill Companies, Inc., 2004), Chap. 6.

2012 (1)

M. Feser, M. R. Howells, J. Kirz, J. Rudati, and W. Yun, “Advantages of a synchrotron bending magnet as the sample illuminator for a wide-field X-ray microscope,” J. Synchrotron Radiat. 19(5), 751–758 (2012).
[Crossref] [PubMed]

2011 (1)

R. Falcone, C. Jacobsen, J. Kirz, S. Marchesini, D. Shapiro, and J. Spence, “New directions in X-ray microscopy,” Contemp. Phys. 52(4), 293–318 (2011).
[Crossref]

2008 (2)

2005 (3)

Y. Suzuki, A. Takeuchi, H. Takano, and H. Takenaka, “Performance test of Fresnel zone plate with 50 nm outermost zone width in hard X-ray region,” Jpn. J. Appl. Phys. 44(4A), 1994–1998 (2005).
[Crossref]

M. Wieland, Ch. Spielmann, U. Kleineberg, T. Westerwalbesloh, U. Heinzmann, and T. Wilhein, “Toward time-resolved soft X-ray microscopy using pulsed fs-high-harmonic radiation,” Ultramicroscopy 102(2), 93–100 (2005).
[Crossref] [PubMed]

D. Guay, J. Stewart-Ornstein, X. Zhang, and A. P. Hitchcock, “In situ spatial and time-resolved studies of electrochemical reactions by scanning transmission X-ray microscopy,” Anal. Chem. 77(11), 3479–3487 (2005).
[Crossref] [PubMed]

2003 (1)

H. Takano, Y. Suzuki, and A. Takeuchi, “Sub-100 nm hard X-Ray microbeam generation with Fresnel zone plate Optics,” Jpn. J. Appl. Phys. 42(Part 2, No. 2A), L132–L134 (2003).
[Crossref]

1995 (1)

S. Brauer, G. B. Stephenson, and M. Sutton, “Perfect crystals in the asymmetric Bragg geometry as optical elements for coherent X-ray beams,” J. Synchrotron Radiat. 2(4), 163–173 (1995).
[Crossref] [PubMed]

1992 (1)

M. Sanchez del Rio and F. Cerrina, “Asymmetrically cut crystals for synchrotron radiation monochromators,” Rev. Sci. Instrum. 63(1), 936–940 (1992).
[Crossref]

1980 (1)

T. Matsushita and U. Kaminaga, “A systematic method of estimating the performance of X-ray optical systems for synchrotron radiation. I. Description of various optical elements in position-angle for ideally monochromatic X-rays,” J. Appl. Cryst. 13(6), 465–471 (1980).
[Crossref]

1978 (1)

T. Matsushita, U. Kamanaga, and K. Kohra, “A generalized phase space optical analysis of X-ray optical systems using crystal monochromators,” Jpn. J. Appl. Phys. 17(S2Suppl.), 449–452 (1978).
[Crossref]

1970 (1)

K. Codling and P. Mitchell, “A constant deviation grazing incidence monochromator,” J. Phys. E Sci. Instrum. 3(9), 685–689 (1970).
[Crossref]

1937 (1)

J. W. M. DuMond, “Theory of the use of more than two successive x-ray crystal reflection to obtain increased resolving power,” Phys. Rev. 52(8), 872–883 (1937).
[Crossref]

Brauer, S.

S. Brauer, G. B. Stephenson, and M. Sutton, “Perfect crystals in the asymmetric Bragg geometry as optical elements for coherent X-ray beams,” J. Synchrotron Radiat. 2(4), 163–173 (1995).
[Crossref] [PubMed]

Cerrina, F.

M. Sanchez del Rio and F. Cerrina, “Asymmetrically cut crystals for synchrotron radiation monochromators,” Rev. Sci. Instrum. 63(1), 936–940 (1992).
[Crossref]

Codling, K.

K. Codling and P. Mitchell, “A constant deviation grazing incidence monochromator,” J. Phys. E Sci. Instrum. 3(9), 685–689 (1970).
[Crossref]

Daly, P.

DuMond, J. W. M.

J. W. M. DuMond, “Theory of the use of more than two successive x-ray crystal reflection to obtain increased resolving power,” Phys. Rev. 52(8), 872–883 (1937).
[Crossref]

Falcone, R.

R. Falcone, C. Jacobsen, J. Kirz, S. Marchesini, D. Shapiro, and J. Spence, “New directions in X-ray microscopy,” Contemp. Phys. 52(4), 293–318 (2011).
[Crossref]

Ferrero, C.

Feser, M.

M. Feser, M. R. Howells, J. Kirz, J. Rudati, and W. Yun, “Advantages of a synchrotron bending magnet as the sample illuminator for a wide-field X-ray microscope,” J. Synchrotron Radiat. 19(5), 751–758 (2012).
[Crossref] [PubMed]

Gatta, G.

Guay, D.

D. Guay, J. Stewart-Ornstein, X. Zhang, and A. P. Hitchcock, “In situ spatial and time-resolved studies of electrochemical reactions by scanning transmission X-ray microscopy,” Anal. Chem. 77(11), 3479–3487 (2005).
[Crossref] [PubMed]

Heinzmann, U.

M. Wieland, Ch. Spielmann, U. Kleineberg, T. Westerwalbesloh, U. Heinzmann, and T. Wilhein, “Toward time-resolved soft X-ray microscopy using pulsed fs-high-harmonic radiation,” Ultramicroscopy 102(2), 93–100 (2005).
[Crossref] [PubMed]

Hitchcock, A. P.

D. Guay, J. Stewart-Ornstein, X. Zhang, and A. P. Hitchcock, “In situ spatial and time-resolved studies of electrochemical reactions by scanning transmission X-ray microscopy,” Anal. Chem. 77(11), 3479–3487 (2005).
[Crossref] [PubMed]

Howells, M. R.

M. Feser, M. R. Howells, J. Kirz, J. Rudati, and W. Yun, “Advantages of a synchrotron bending magnet as the sample illuminator for a wide-field X-ray microscope,” J. Synchrotron Radiat. 19(5), 751–758 (2012).
[Crossref] [PubMed]

Jacobsen, C.

R. Falcone, C. Jacobsen, J. Kirz, S. Marchesini, D. Shapiro, and J. Spence, “New directions in X-ray microscopy,” Contemp. Phys. 52(4), 293–318 (2011).
[Crossref]

Kamanaga, U.

T. Matsushita, U. Kamanaga, and K. Kohra, “A generalized phase space optical analysis of X-ray optical systems using crystal monochromators,” Jpn. J. Appl. Phys. 17(S2Suppl.), 449–452 (1978).
[Crossref]

Kaminaga, U.

T. Matsushita and U. Kaminaga, “A systematic method of estimating the performance of X-ray optical systems for synchrotron radiation. I. Description of various optical elements in position-angle for ideally monochromatic X-rays,” J. Appl. Cryst. 13(6), 465–471 (1980).
[Crossref]

Kirz, J.

M. Feser, M. R. Howells, J. Kirz, J. Rudati, and W. Yun, “Advantages of a synchrotron bending magnet as the sample illuminator for a wide-field X-ray microscope,” J. Synchrotron Radiat. 19(5), 751–758 (2012).
[Crossref] [PubMed]

R. Falcone, C. Jacobsen, J. Kirz, S. Marchesini, D. Shapiro, and J. Spence, “New directions in X-ray microscopy,” Contemp. Phys. 52(4), 293–318 (2011).
[Crossref]

Kleineberg, U.

M. Wieland, Ch. Spielmann, U. Kleineberg, T. Westerwalbesloh, U. Heinzmann, and T. Wilhein, “Toward time-resolved soft X-ray microscopy using pulsed fs-high-harmonic radiation,” Ultramicroscopy 102(2), 93–100 (2005).
[Crossref] [PubMed]

Kohra, K.

T. Matsushita, U. Kamanaga, and K. Kohra, “A generalized phase space optical analysis of X-ray optical systems using crystal monochromators,” Jpn. J. Appl. Phys. 17(S2Suppl.), 449–452 (1978).
[Crossref]

Marchesini, S.

R. Falcone, C. Jacobsen, J. Kirz, S. Marchesini, D. Shapiro, and J. Spence, “New directions in X-ray microscopy,” Contemp. Phys. 52(4), 293–318 (2011).
[Crossref]

Matsushita, T.

T. Matsushita and U. Kaminaga, “A systematic method of estimating the performance of X-ray optical systems for synchrotron radiation. I. Description of various optical elements in position-angle for ideally monochromatic X-rays,” J. Appl. Cryst. 13(6), 465–471 (1980).
[Crossref]

T. Matsushita, U. Kamanaga, and K. Kohra, “A generalized phase space optical analysis of X-ray optical systems using crystal monochromators,” Jpn. J. Appl. Phys. 17(S2Suppl.), 449–452 (1978).
[Crossref]

Mitchell, P.

K. Codling and P. Mitchell, “A constant deviation grazing incidence monochromator,” J. Phys. E Sci. Instrum. 3(9), 685–689 (1970).
[Crossref]

Riekel, C.

Rudati, J.

M. Feser, M. R. Howells, J. Kirz, J. Rudati, and W. Yun, “Advantages of a synchrotron bending magnet as the sample illuminator for a wide-field X-ray microscope,” J. Synchrotron Radiat. 19(5), 751–758 (2012).
[Crossref] [PubMed]

Sanchez del Rio, M.

M. Sanchez del Rio and F. Cerrina, “Asymmetrically cut crystals for synchrotron radiation monochromators,” Rev. Sci. Instrum. 63(1), 936–940 (1992).
[Crossref]

Shapiro, D.

R. Falcone, C. Jacobsen, J. Kirz, S. Marchesini, D. Shapiro, and J. Spence, “New directions in X-ray microscopy,” Contemp. Phys. 52(4), 293–318 (2011).
[Crossref]

Smilgies, D.-M.

Spence, J.

R. Falcone, C. Jacobsen, J. Kirz, S. Marchesini, D. Shapiro, and J. Spence, “New directions in X-ray microscopy,” Contemp. Phys. 52(4), 293–318 (2011).
[Crossref]

Spielmann, Ch.

M. Wieland, Ch. Spielmann, U. Kleineberg, T. Westerwalbesloh, U. Heinzmann, and T. Wilhein, “Toward time-resolved soft X-ray microscopy using pulsed fs-high-harmonic radiation,” Ultramicroscopy 102(2), 93–100 (2005).
[Crossref] [PubMed]

Stephenson, G. B.

S. Brauer, G. B. Stephenson, and M. Sutton, “Perfect crystals in the asymmetric Bragg geometry as optical elements for coherent X-ray beams,” J. Synchrotron Radiat. 2(4), 163–173 (1995).
[Crossref] [PubMed]

Stewart-Ornstein, J.

D. Guay, J. Stewart-Ornstein, X. Zhang, and A. P. Hitchcock, “In situ spatial and time-resolved studies of electrochemical reactions by scanning transmission X-ray microscopy,” Anal. Chem. 77(11), 3479–3487 (2005).
[Crossref] [PubMed]

Sutton, M.

S. Brauer, G. B. Stephenson, and M. Sutton, “Perfect crystals in the asymmetric Bragg geometry as optical elements for coherent X-ray beams,” J. Synchrotron Radiat. 2(4), 163–173 (1995).
[Crossref] [PubMed]

Suzuki, Y.

Y. Suzuki, A. Takeuchi, H. Takano, and H. Takenaka, “Performance test of Fresnel zone plate with 50 nm outermost zone width in hard X-ray region,” Jpn. J. Appl. Phys. 44(4A), 1994–1998 (2005).
[Crossref]

H. Takano, Y. Suzuki, and A. Takeuchi, “Sub-100 nm hard X-Ray microbeam generation with Fresnel zone plate Optics,” Jpn. J. Appl. Phys. 42(Part 2, No. 2A), L132–L134 (2003).
[Crossref]

Takano, H.

Y. Suzuki, A. Takeuchi, H. Takano, and H. Takenaka, “Performance test of Fresnel zone plate with 50 nm outermost zone width in hard X-ray region,” Jpn. J. Appl. Phys. 44(4A), 1994–1998 (2005).
[Crossref]

H. Takano, Y. Suzuki, and A. Takeuchi, “Sub-100 nm hard X-Ray microbeam generation with Fresnel zone plate Optics,” Jpn. J. Appl. Phys. 42(Part 2, No. 2A), L132–L134 (2003).
[Crossref]

Takenaka, H.

Y. Suzuki, A. Takeuchi, H. Takano, and H. Takenaka, “Performance test of Fresnel zone plate with 50 nm outermost zone width in hard X-ray region,” Jpn. J. Appl. Phys. 44(4A), 1994–1998 (2005).
[Crossref]

Takeuchi, A.

Y. Suzuki, A. Takeuchi, H. Takano, and H. Takenaka, “Performance test of Fresnel zone plate with 50 nm outermost zone width in hard X-ray region,” Jpn. J. Appl. Phys. 44(4A), 1994–1998 (2005).
[Crossref]

H. Takano, Y. Suzuki, and A. Takeuchi, “Sub-100 nm hard X-Ray microbeam generation with Fresnel zone plate Optics,” Jpn. J. Appl. Phys. 42(Part 2, No. 2A), L132–L134 (2003).
[Crossref]

Westerwalbesloh, T.

M. Wieland, Ch. Spielmann, U. Kleineberg, T. Westerwalbesloh, U. Heinzmann, and T. Wilhein, “Toward time-resolved soft X-ray microscopy using pulsed fs-high-harmonic radiation,” Ultramicroscopy 102(2), 93–100 (2005).
[Crossref] [PubMed]

Wieland, M.

M. Wieland, Ch. Spielmann, U. Kleineberg, T. Westerwalbesloh, U. Heinzmann, and T. Wilhein, “Toward time-resolved soft X-ray microscopy using pulsed fs-high-harmonic radiation,” Ultramicroscopy 102(2), 93–100 (2005).
[Crossref] [PubMed]

Wilhein, T.

M. Wieland, Ch. Spielmann, U. Kleineberg, T. Westerwalbesloh, U. Heinzmann, and T. Wilhein, “Toward time-resolved soft X-ray microscopy using pulsed fs-high-harmonic radiation,” Ultramicroscopy 102(2), 93–100 (2005).
[Crossref] [PubMed]

Yun, W.

M. Feser, M. R. Howells, J. Kirz, J. Rudati, and W. Yun, “Advantages of a synchrotron bending magnet as the sample illuminator for a wide-field X-ray microscope,” J. Synchrotron Radiat. 19(5), 751–758 (2012).
[Crossref] [PubMed]

Zhang, X.

D. Guay, J. Stewart-Ornstein, X. Zhang, and A. P. Hitchcock, “In situ spatial and time-resolved studies of electrochemical reactions by scanning transmission X-ray microscopy,” Anal. Chem. 77(11), 3479–3487 (2005).
[Crossref] [PubMed]

Anal. Chem. (1)

D. Guay, J. Stewart-Ornstein, X. Zhang, and A. P. Hitchcock, “In situ spatial and time-resolved studies of electrochemical reactions by scanning transmission X-ray microscopy,” Anal. Chem. 77(11), 3479–3487 (2005).
[Crossref] [PubMed]

Appl. Opt. (2)

Contemp. Phys. (1)

R. Falcone, C. Jacobsen, J. Kirz, S. Marchesini, D. Shapiro, and J. Spence, “New directions in X-ray microscopy,” Contemp. Phys. 52(4), 293–318 (2011).
[Crossref]

J. Appl. Cryst. (1)

T. Matsushita and U. Kaminaga, “A systematic method of estimating the performance of X-ray optical systems for synchrotron radiation. I. Description of various optical elements in position-angle for ideally monochromatic X-rays,” J. Appl. Cryst. 13(6), 465–471 (1980).
[Crossref]

J. Phys. E Sci. Instrum. (1)

K. Codling and P. Mitchell, “A constant deviation grazing incidence monochromator,” J. Phys. E Sci. Instrum. 3(9), 685–689 (1970).
[Crossref]

J. Synchrotron Radiat. (2)

S. Brauer, G. B. Stephenson, and M. Sutton, “Perfect crystals in the asymmetric Bragg geometry as optical elements for coherent X-ray beams,” J. Synchrotron Radiat. 2(4), 163–173 (1995).
[Crossref] [PubMed]

M. Feser, M. R. Howells, J. Kirz, J. Rudati, and W. Yun, “Advantages of a synchrotron bending magnet as the sample illuminator for a wide-field X-ray microscope,” J. Synchrotron Radiat. 19(5), 751–758 (2012).
[Crossref] [PubMed]

Jpn. J. Appl. Phys. (3)

T. Matsushita, U. Kamanaga, and K. Kohra, “A generalized phase space optical analysis of X-ray optical systems using crystal monochromators,” Jpn. J. Appl. Phys. 17(S2Suppl.), 449–452 (1978).
[Crossref]

H. Takano, Y. Suzuki, and A. Takeuchi, “Sub-100 nm hard X-Ray microbeam generation with Fresnel zone plate Optics,” Jpn. J. Appl. Phys. 42(Part 2, No. 2A), L132–L134 (2003).
[Crossref]

Y. Suzuki, A. Takeuchi, H. Takano, and H. Takenaka, “Performance test of Fresnel zone plate with 50 nm outermost zone width in hard X-ray region,” Jpn. J. Appl. Phys. 44(4A), 1994–1998 (2005).
[Crossref]

Phys. Rev. (1)

J. W. M. DuMond, “Theory of the use of more than two successive x-ray crystal reflection to obtain increased resolving power,” Phys. Rev. 52(8), 872–883 (1937).
[Crossref]

Rev. Sci. Instrum. (1)

M. Sanchez del Rio and F. Cerrina, “Asymmetrically cut crystals for synchrotron radiation monochromators,” Rev. Sci. Instrum. 63(1), 936–940 (1992).
[Crossref]

Ultramicroscopy (1)

M. Wieland, Ch. Spielmann, U. Kleineberg, T. Westerwalbesloh, U. Heinzmann, and T. Wilhein, “Toward time-resolved soft X-ray microscopy using pulsed fs-high-harmonic radiation,” Ultramicroscopy 102(2), 93–100 (2005).
[Crossref] [PubMed]

Other (9)

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (The McGraw-Hill Companies, Inc., 2004), Chap. 6.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd ed. (John Wiley & Sons, Inc., 2007), Chap. 3.

Y. Shvyd’ko, X-Ray Optics – High Energy Resolution Applications (Springer-Verlag, 2004), Chaps. 1–3.

A. Authier, Dynamical Theory of X-Ray Diffraction (Oxford University, 2001), Chap. 4.

J. Als-Nielsen, Elements of Modern X-ray Physics (John Wiley & Sons Ltd., 2011).

D. Attwood, Soft X-rays and Extreme Ultraviolet Radiation - Principles and Applications (Cambridge University, 2000), Chap. 9.

Q. Shen, “X-ray flux, brilliance and coherence of the proposed Cornell energy-recovery synchrotron source,” CHESS Technical Memo 01–002 (2001).

M. Sanchez del Rio and R. J. Dejus, “X-ray Oriented Programs – Graphical user interfaces for synchrotron radiation spectral, optics, and analysis calculations,” http://www.esrf.eu/computing/scientific/xop2.1/intro.html .

M. Sanchez del Rio, “SHADOWVUI – A visual user interface to SHADOW under IDL,” http://www.esrf.eu/computing/scientific/xop2.1/shadowvui/ .

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Figures (6)

Fig. 1
Fig. 1 (a) Schematic of full-field transmission X-ray microscope. (b) Dispersion by symmetrical (left panel) and asymmetrically cut (right panel) crystals. (c) Divergences for symmetric (left) and asymmetric (right) diffraction. Asymmetric diffraction causes the incident beam to be dispersed. However, for Fresnel zone plates (FZPs) with relatively low resolving power, the diffraction is not dependent on the energy distribution (shown as rays of various colors), and the result is a divergent beam.
Fig. 2
Fig. 2 Phase space volume conservation. (a) Volume shape (gray area) intercepted according to beam parameters and the crystal’s Darwin width. (b), (c) Projections of the phase volume onto y λ space (DuMond diagram) and y y space (phase space), respectively. (d), (e), (f) Phase volume and projections after diffraction corresponding to (a), (b), (c), respectively. The yellow area represents the incident-beam phase space area and the teal blue represents the exit-beam phase space area. This figure is valid for the case of b < 1.
Fig. 3
Fig. 3 Angular dispersion contour calculated using Eq. (10) for transfer ratios of 1, 1.1, 2, 5, 10, 20, and 40 for Si(111) at 10 keV. Color in log scale.
Fig. 4
Fig. 4 (a) Simple schematic of our simulation setup. (b)-(e) Phase space plots at different distances along the optical axis: (b) Gaussian profile with uniform energy distribution. (c) Profile after beam has propagated 2 m downstream of the source. (d) and (e) Collimated beam and asymmetric diffraction with asymmetric angle α = −4.8°, respectively.
Fig. 5
Fig. 5 Phase space obtained for three crystals with miscut angles of (a) −4.8°, (b) −7.6°, and (c) −9.5°. The frames at the center indicate the “usable” region with the full-width at half maximum (FWHM) length and width in μm and μrad, respectively. (d) 3D map of (c) showing the intensity distribution as a function of the total dispersive divergence.
Fig. 6
Fig. 6 Transformation of phase volume obtained with ray tracing for Figs. 2(a) and 2(d). (a) and (b) Ray distributions in 3D phase space for source and diffracted beam, respectively.

Tables (2)

Tables Icon

Table 1 Parameters of the Taiwan photon source

Tables Icon

Table 2 Simulation summary.

Equations (19)

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

b= sin θ i sin θ e = sin( θ B +α) sin( θ B -α) .
Δ θ i = w (S) b = w (A)
Δ θ e = w (S) b =b w (A)
Δ y e =bΔ y i
Δ y e = 1 b Δ y i
Δλ λ c =cot θ B Δθ=cot θ B ( w (A) +Δ y i )
D= w (S) ( 1 b b )
D t = [ D 2 + ( Δ y e ) 2 ] 1/2 = { [ w (S) ( 1 b b ) ] 2 + ( bΔ y i ) 2 } 1/2 .
ε e =Δ y e D t = 1 b Δ y i D t
TR= ε e ε i = 1 b D t Δ y i
[ x x p ]=[ 1 d 2 0 1 ][ 1 0 1 /f 1 ][ 1 d 1 0 1 ][ x x p ]
x =x( 1 d 2 f )+ x p ( 1 d 1 + 1 d 2 1 f ) d 1 d 2 .
x = d 2 d 1 x d 1 d 2 δλ 4N ( Δr ) 2 x p
x p = δλ λ c ( 1| b | )tan θ c
δ x = d 1 d 2 ( δλ λ c ) 2 1 f c (1| b |)tan θ c
Δ y e = b 1 b 2 Δ y i
Δ y e = 1 b 1 b 2 Δ y i
D= w (S) b 1 ( 1 b 1 b 2 )
TR= 1 b 1 b 2 ( D 2 +Δ y e 2 ) 1/2 Δ y i = 1 b 1 b 2 D t Δ y i

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