Abstract

Despite the extensive use of polycapillary x-ray optics for focusing and collimating applications, there remains a significant need for characterization of the coherence properties of the output wavefield. In this work, we present the first quantitative computational method for calculation of the spatial coherence effects of polycapillary x-ray optical devices. This method employs the coherent mode decomposition of an extended x-ray source, geometric optical propagation of individual wavefield modes through a polycapillary device, output wavefield calculation by ray data resampling onto a uniform grid, and the calculation of spatial coherence properties by way of the spectral degree of coherence.

© 2012 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. Schroer and B. Lengeler, “X-ray optics,” in Springer Handbook of Lasers and Optics, F. Träger, ed., (Springer-Verlag, 2007).
    [CrossRef]
  2. C. A. MacDonald and W. M. Gibson, “Applications and advances in polycapillary optics,” X-ray Spectrom.  32, 258–268 (2003).
    [CrossRef]
  3. Yu. M. Alexandrov, S. B. Dabagov, M. A. Kumakhov, V. A. Murashova, D. A. Fedin, R. V. Fedorchuk, and M. N. Yakimenko, “Peculiarities of photon transmission through capillary systems,” Nucl. Instrum. Methods Phys. Res., Sect. B 134, 174–180 (1998).
    [CrossRef]
  4. S. B. Dabagov and A. Marcelli, “Single-reflection regime of x rays that travel into a monocapillary,” Appl. Opt. 38, 7494–7497 (1999).
    [CrossRef]
  5. S. V. Kukhlevsky, F. Flora, A. Marinai, G. Nyitray, Zs. Kozma, A. Ritucci, L. Palladino, A. Reale, and G. Tomassetti, “Wave-optics treatment of x-rays passing through tapered capillary guides,” X-Ray Spectrom.  29, 354–359 (2000).
    [CrossRef]
  6. S. B. Dabagov, “Wave theory of x-ray scattering in capillary structures,” X-Ray Spectrom. 32, 223–228 (2003).
    [CrossRef]
  7. L. Vincze, K. Janssens, F. Adams, and A. Rindby, “Detained ray-tracing code for capillary optics,” X-Ray Spectrom. 24, 27–37 (1995).
    [CrossRef]
  8. S. V. Kukhlevsky, F. Flora, A. Marinai, G. Nyitray, A. Ritucci, L. Palladino, A. Reale, and G. Tomassetti, “Diffraction of X-ray beams in capillary waveguides,” Nucl. Instrum. Methods Phys. Res., Sect. B 168, 276–282 (2000).
    [CrossRef]
  9. S. V. Kukhlevsky, “Interference and diffraction in capillary x-ray optics,” X-Ray Spectrom. 32, 223–228 (2003).
    [CrossRef]
  10. Q. F. Xiao and S. V. Poturaev, “Polycapillary-based X-ray optics,” Nucl. Instrum. Methods Phys. Res., Sect. A 347, 376–383 (1994).
    [CrossRef]
  11. A. Liu, “The X-ray distribution after a focussing polycapillary a shadow simulation,” Nucl. Instrum. Methods Phys. Res., Sect. B 243, 223–226 (2006).
    [CrossRef]
  12. C. Welnak, G. J. Chen, and F. Cerrina, “Shadow: a synchrotron radiation and X-ray optics simulation tool,” Nucl. Instrum. Methods Phys. Res., Sect. A 347, 344–347 (1994).
    [CrossRef]
  13. D. Hampai, S. B. Dabagov, G. Cappuccio, and G. Cibin, “X-ray propagation through hollow channel: PolyCAD - a ray tracing code,” Nucl. Instrum. Methods Phys. Res., Sect. B 244, 481–488 (2006).
    [CrossRef]
  14. D. Hampai, S. B. Dabagov, G. Cappuccio, and G. Cibin, “X-ray propagation through polycapillary optics studied through a ray tracing approach,” Spectrochim. Acta, Part B 62, 608–614 (2007).
    [CrossRef]
  15. S. B. Dabagov, M. A. Kumakhov, S. V. Nikitina, V. A. Murashova, R. V. Fedorchuk, and M. N. Yakimenko, “Observation of interference effects at the focus of an x-ray lens,” J. Synchrotron Radiat. 2, 132–135 (1995).
    [CrossRef] [PubMed]
  16. S. B. Dabagov, M. A. Kumakhov, and S. V. Nikitina, “On the interference of X-rays in multiple reflection optics,” Phys. Lett. A 203, 279–282 (1995).
    [CrossRef]
  17. A. Bjeoumikhov, “Observation of peculiarities in angular distributions of X-ray radiation after propagation through polycapillary structures,” Phys. Lett. A 360, 405–410 (2007).
    [CrossRef]
  18. A. Bjeoumikhov, S. Bjeoumikhova, H. Riesemeier, M. Radtke, and R. Wedell, “Propagation of synchrotron radiation through nanocapillary structures,” Phys. Lett. A 366, 283–288 (2007).
    [CrossRef]
  19. S. B. Dabagov, R. V. Fedorchuk, V. A. Murashova, S. V. Nikitina, and M. N. Yakimenko, “Interference phenomenon under focusing of synchrotron radiation by a Kumakhov lens,” Nucl. Instrum. Methods Phys. Res., Sect. B 108, 213–218 (1996).
    [CrossRef]
  20. L. Vincze, K. Janssens, and S. V. Kukhlevsky, “Simulation of polycapillary lenses for coherent and partially coherent x-rays,” Proc. SPIE 5536, 81–85 (2004).
    [CrossRef]
  21. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).
  22. E. Wolf, “New spectral representation of random sources and of the partially coherent field that they generate,” Opt. Commun. 38, 3–6 (1981).
    [CrossRef]
  23. H. Liu, G. Mu, and L. Lin, “Propagation theories of partially coherent electromagnetic fields based on coherent or separated-coordinate mode decomposition,” J. Opt. Soc. Am. A 23, 2208–2218 (2006).
    [CrossRef]
  24. A. M. Zysk, P. S. Carney, and J. C. Schotland, “Eikonal method for calculation of coherence functions,” Phys. Rev. Lett. 95, 043904 (2005).
    [CrossRef] [PubMed]
  25. R. W. Schoonover, A. M. Zysk, and P. S. Carney, “Geometrical optics limit of stochastic electromagnetic fields,” Phys. Rev. A 77, 043831 (2008).
    [CrossRef]
  26. A. Liu, “Simulation of x-ray propagation in a straight capillary,” Math. Comput. Simulat. 65, 251–256 (2004).
    [CrossRef]
  27. A. Liu, “Simulation of x-ray beam collimation by polycapillaries,” Nucl. Instrum. Methods Phys. Res., Sect. B 234, 555–562 (2005).
    [CrossRef]
  28. Q. Xiao, I. Ponomarev, A. Kolomitsev, and J. Kimball, “Numerical simulations for capillary-based x-ray optics,” Proc. SPIE 1736, 227–238 (1992).
    [CrossRef]
  29. M. Popov, “A new method of computation of wave fields using gaussian beams,” Wave Motion 4, 85–97 (1982).
    [CrossRef]
  30. A. Norris, “Complex point-source representation of real point sources and the gaussian beam summation method,” J. Opt. Soc. Am. A 3, 2005–2010 (1986).
    [CrossRef]
  31. G. Forbes and M. Alonso, “Using rays better. I. theory for smoothly varying media,” J. Opt. Soc. Am. A 18, 1132–1145 (2001).
    [CrossRef]
  32. T. Heilpern, E. Heyman, and V. Timchenko, “A beam summation algorithm for wave radiation and guidance in stratified media,” J. Acoust. Soc. Am. 121, 1856–1864 (2007).
    [CrossRef] [PubMed]
  33. E. Svensson, “Gaussian beam summation in shallow waveguides,” Wave Motion 45, 445–456 (2008).
    [CrossRef]
  34. J. Jackson, C. Meyer, D. Nishimura, and A. Macovski, “Selection of a convolution function for fourier inversion using gridding [computerised tomography application],” IEEE Trans. Med. Imag. 10, 473–478 (1991).
    [CrossRef]
  35. S. Bollanti, P. Albertano, M. Belli, P. Di Lazzaro, A. Ya. Faenov, F. Flora, G. Giordano, A. Grilli, F. Ianzinni, S. V. Kukhlevsky, T. Letardi, A. Nottola, L. Palladino, T. Pikuz, A. Reale, L. Reale, A. Scafati, M. A. Tabocchini, I. C. E. Turcu, K. Vigli-Papadaki, and G. Schina, “Soft X-ray plasma source for atmospheric-pressure microscopy, radiobiology and other applications,” Il Nuovo Cimento 20, 1685–1701 (1998).
  36. B. Hargreaves and P. Beatty, “Gridding functions,” http://mrsrl.stanford.edu/brian/gridding/ .
  37. D. Hampai, S. B. Dabagov, G. Cappuccio, G. Cibin, and V. Sessa, “X-ray micro-imaging by capillary optics,” Spectrochim. Acta, Part B 64, 1180–1184 (2009).
    [CrossRef]

2009 (1)

D. Hampai, S. B. Dabagov, G. Cappuccio, G. Cibin, and V. Sessa, “X-ray micro-imaging by capillary optics,” Spectrochim. Acta, Part B 64, 1180–1184 (2009).
[CrossRef]

2008 (2)

E. Svensson, “Gaussian beam summation in shallow waveguides,” Wave Motion 45, 445–456 (2008).
[CrossRef]

R. W. Schoonover, A. M. Zysk, and P. S. Carney, “Geometrical optics limit of stochastic electromagnetic fields,” Phys. Rev. A 77, 043831 (2008).
[CrossRef]

2007 (4)

T. Heilpern, E. Heyman, and V. Timchenko, “A beam summation algorithm for wave radiation and guidance in stratified media,” J. Acoust. Soc. Am. 121, 1856–1864 (2007).
[CrossRef] [PubMed]

D. Hampai, S. B. Dabagov, G. Cappuccio, and G. Cibin, “X-ray propagation through polycapillary optics studied through a ray tracing approach,” Spectrochim. Acta, Part B 62, 608–614 (2007).
[CrossRef]

A. Bjeoumikhov, “Observation of peculiarities in angular distributions of X-ray radiation after propagation through polycapillary structures,” Phys. Lett. A 360, 405–410 (2007).
[CrossRef]

A. Bjeoumikhov, S. Bjeoumikhova, H. Riesemeier, M. Radtke, and R. Wedell, “Propagation of synchrotron radiation through nanocapillary structures,” Phys. Lett. A 366, 283–288 (2007).
[CrossRef]

2006 (3)

A. Liu, “The X-ray distribution after a focussing polycapillary a shadow simulation,” Nucl. Instrum. Methods Phys. Res., Sect. B 243, 223–226 (2006).
[CrossRef]

D. Hampai, S. B. Dabagov, G. Cappuccio, and G. Cibin, “X-ray propagation through hollow channel: PolyCAD - a ray tracing code,” Nucl. Instrum. Methods Phys. Res., Sect. B 244, 481–488 (2006).
[CrossRef]

H. Liu, G. Mu, and L. Lin, “Propagation theories of partially coherent electromagnetic fields based on coherent or separated-coordinate mode decomposition,” J. Opt. Soc. Am. A 23, 2208–2218 (2006).
[CrossRef]

2005 (2)

A. M. Zysk, P. S. Carney, and J. C. Schotland, “Eikonal method for calculation of coherence functions,” Phys. Rev. Lett. 95, 043904 (2005).
[CrossRef] [PubMed]

A. Liu, “Simulation of x-ray beam collimation by polycapillaries,” Nucl. Instrum. Methods Phys. Res., Sect. B 234, 555–562 (2005).
[CrossRef]

2004 (2)

A. Liu, “Simulation of x-ray propagation in a straight capillary,” Math. Comput. Simulat. 65, 251–256 (2004).
[CrossRef]

L. Vincze, K. Janssens, and S. V. Kukhlevsky, “Simulation of polycapillary lenses for coherent and partially coherent x-rays,” Proc. SPIE 5536, 81–85 (2004).
[CrossRef]

2003 (3)

C. A. MacDonald and W. M. Gibson, “Applications and advances in polycapillary optics,” X-ray Spectrom.  32, 258–268 (2003).
[CrossRef]

S. B. Dabagov, “Wave theory of x-ray scattering in capillary structures,” X-Ray Spectrom. 32, 223–228 (2003).
[CrossRef]

S. V. Kukhlevsky, “Interference and diffraction in capillary x-ray optics,” X-Ray Spectrom. 32, 223–228 (2003).
[CrossRef]

2001 (1)

2000 (2)

S. V. Kukhlevsky, F. Flora, A. Marinai, G. Nyitray, Zs. Kozma, A. Ritucci, L. Palladino, A. Reale, and G. Tomassetti, “Wave-optics treatment of x-rays passing through tapered capillary guides,” X-Ray Spectrom.  29, 354–359 (2000).
[CrossRef]

S. V. Kukhlevsky, F. Flora, A. Marinai, G. Nyitray, A. Ritucci, L. Palladino, A. Reale, and G. Tomassetti, “Diffraction of X-ray beams in capillary waveguides,” Nucl. Instrum. Methods Phys. Res., Sect. B 168, 276–282 (2000).
[CrossRef]

1999 (1)

1998 (2)

Yu. M. Alexandrov, S. B. Dabagov, M. A. Kumakhov, V. A. Murashova, D. A. Fedin, R. V. Fedorchuk, and M. N. Yakimenko, “Peculiarities of photon transmission through capillary systems,” Nucl. Instrum. Methods Phys. Res., Sect. B 134, 174–180 (1998).
[CrossRef]

S. Bollanti, P. Albertano, M. Belli, P. Di Lazzaro, A. Ya. Faenov, F. Flora, G. Giordano, A. Grilli, F. Ianzinni, S. V. Kukhlevsky, T. Letardi, A. Nottola, L. Palladino, T. Pikuz, A. Reale, L. Reale, A. Scafati, M. A. Tabocchini, I. C. E. Turcu, K. Vigli-Papadaki, and G. Schina, “Soft X-ray plasma source for atmospheric-pressure microscopy, radiobiology and other applications,” Il Nuovo Cimento 20, 1685–1701 (1998).

1996 (1)

S. B. Dabagov, R. V. Fedorchuk, V. A. Murashova, S. V. Nikitina, and M. N. Yakimenko, “Interference phenomenon under focusing of synchrotron radiation by a Kumakhov lens,” Nucl. Instrum. Methods Phys. Res., Sect. B 108, 213–218 (1996).
[CrossRef]

1995 (3)

S. B. Dabagov, M. A. Kumakhov, S. V. Nikitina, V. A. Murashova, R. V. Fedorchuk, and M. N. Yakimenko, “Observation of interference effects at the focus of an x-ray lens,” J. Synchrotron Radiat. 2, 132–135 (1995).
[CrossRef] [PubMed]

S. B. Dabagov, M. A. Kumakhov, and S. V. Nikitina, “On the interference of X-rays in multiple reflection optics,” Phys. Lett. A 203, 279–282 (1995).
[CrossRef]

L. Vincze, K. Janssens, F. Adams, and A. Rindby, “Detained ray-tracing code for capillary optics,” X-Ray Spectrom. 24, 27–37 (1995).
[CrossRef]

1994 (2)

Q. F. Xiao and S. V. Poturaev, “Polycapillary-based X-ray optics,” Nucl. Instrum. Methods Phys. Res., Sect. A 347, 376–383 (1994).
[CrossRef]

C. Welnak, G. J. Chen, and F. Cerrina, “Shadow: a synchrotron radiation and X-ray optics simulation tool,” Nucl. Instrum. Methods Phys. Res., Sect. A 347, 344–347 (1994).
[CrossRef]

1992 (1)

Q. Xiao, I. Ponomarev, A. Kolomitsev, and J. Kimball, “Numerical simulations for capillary-based x-ray optics,” Proc. SPIE 1736, 227–238 (1992).
[CrossRef]

1991 (1)

J. Jackson, C. Meyer, D. Nishimura, and A. Macovski, “Selection of a convolution function for fourier inversion using gridding [computerised tomography application],” IEEE Trans. Med. Imag. 10, 473–478 (1991).
[CrossRef]

1986 (1)

1982 (1)

M. Popov, “A new method of computation of wave fields using gaussian beams,” Wave Motion 4, 85–97 (1982).
[CrossRef]

1981 (1)

E. Wolf, “New spectral representation of random sources and of the partially coherent field that they generate,” Opt. Commun. 38, 3–6 (1981).
[CrossRef]

Adams, F.

L. Vincze, K. Janssens, F. Adams, and A. Rindby, “Detained ray-tracing code for capillary optics,” X-Ray Spectrom. 24, 27–37 (1995).
[CrossRef]

Albertano, P.

S. Bollanti, P. Albertano, M. Belli, P. Di Lazzaro, A. Ya. Faenov, F. Flora, G. Giordano, A. Grilli, F. Ianzinni, S. V. Kukhlevsky, T. Letardi, A. Nottola, L. Palladino, T. Pikuz, A. Reale, L. Reale, A. Scafati, M. A. Tabocchini, I. C. E. Turcu, K. Vigli-Papadaki, and G. Schina, “Soft X-ray plasma source for atmospheric-pressure microscopy, radiobiology and other applications,” Il Nuovo Cimento 20, 1685–1701 (1998).

Alexandrov, Yu. M.

Yu. M. Alexandrov, S. B. Dabagov, M. A. Kumakhov, V. A. Murashova, D. A. Fedin, R. V. Fedorchuk, and M. N. Yakimenko, “Peculiarities of photon transmission through capillary systems,” Nucl. Instrum. Methods Phys. Res., Sect. B 134, 174–180 (1998).
[CrossRef]

Alonso, M.

Belli, M.

S. Bollanti, P. Albertano, M. Belli, P. Di Lazzaro, A. Ya. Faenov, F. Flora, G. Giordano, A. Grilli, F. Ianzinni, S. V. Kukhlevsky, T. Letardi, A. Nottola, L. Palladino, T. Pikuz, A. Reale, L. Reale, A. Scafati, M. A. Tabocchini, I. C. E. Turcu, K. Vigli-Papadaki, and G. Schina, “Soft X-ray plasma source for atmospheric-pressure microscopy, radiobiology and other applications,” Il Nuovo Cimento 20, 1685–1701 (1998).

Bjeoumikhov, A.

A. Bjeoumikhov, “Observation of peculiarities in angular distributions of X-ray radiation after propagation through polycapillary structures,” Phys. Lett. A 360, 405–410 (2007).
[CrossRef]

A. Bjeoumikhov, S. Bjeoumikhova, H. Riesemeier, M. Radtke, and R. Wedell, “Propagation of synchrotron radiation through nanocapillary structures,” Phys. Lett. A 366, 283–288 (2007).
[CrossRef]

Bjeoumikhova, S.

A. Bjeoumikhov, S. Bjeoumikhova, H. Riesemeier, M. Radtke, and R. Wedell, “Propagation of synchrotron radiation through nanocapillary structures,” Phys. Lett. A 366, 283–288 (2007).
[CrossRef]

Bollanti, S.

S. Bollanti, P. Albertano, M. Belli, P. Di Lazzaro, A. Ya. Faenov, F. Flora, G. Giordano, A. Grilli, F. Ianzinni, S. V. Kukhlevsky, T. Letardi, A. Nottola, L. Palladino, T. Pikuz, A. Reale, L. Reale, A. Scafati, M. A. Tabocchini, I. C. E. Turcu, K. Vigli-Papadaki, and G. Schina, “Soft X-ray plasma source for atmospheric-pressure microscopy, radiobiology and other applications,” Il Nuovo Cimento 20, 1685–1701 (1998).

Cappuccio, G.

D. Hampai, S. B. Dabagov, G. Cappuccio, G. Cibin, and V. Sessa, “X-ray micro-imaging by capillary optics,” Spectrochim. Acta, Part B 64, 1180–1184 (2009).
[CrossRef]

D. Hampai, S. B. Dabagov, G. Cappuccio, and G. Cibin, “X-ray propagation through polycapillary optics studied through a ray tracing approach,” Spectrochim. Acta, Part B 62, 608–614 (2007).
[CrossRef]

D. Hampai, S. B. Dabagov, G. Cappuccio, and G. Cibin, “X-ray propagation through hollow channel: PolyCAD - a ray tracing code,” Nucl. Instrum. Methods Phys. Res., Sect. B 244, 481–488 (2006).
[CrossRef]

Carney, P. S.

R. W. Schoonover, A. M. Zysk, and P. S. Carney, “Geometrical optics limit of stochastic electromagnetic fields,” Phys. Rev. A 77, 043831 (2008).
[CrossRef]

A. M. Zysk, P. S. Carney, and J. C. Schotland, “Eikonal method for calculation of coherence functions,” Phys. Rev. Lett. 95, 043904 (2005).
[CrossRef] [PubMed]

Cerrina, F.

C. Welnak, G. J. Chen, and F. Cerrina, “Shadow: a synchrotron radiation and X-ray optics simulation tool,” Nucl. Instrum. Methods Phys. Res., Sect. A 347, 344–347 (1994).
[CrossRef]

Chen, G. J.

C. Welnak, G. J. Chen, and F. Cerrina, “Shadow: a synchrotron radiation and X-ray optics simulation tool,” Nucl. Instrum. Methods Phys. Res., Sect. A 347, 344–347 (1994).
[CrossRef]

Cibin, G.

D. Hampai, S. B. Dabagov, G. Cappuccio, G. Cibin, and V. Sessa, “X-ray micro-imaging by capillary optics,” Spectrochim. Acta, Part B 64, 1180–1184 (2009).
[CrossRef]

D. Hampai, S. B. Dabagov, G. Cappuccio, and G. Cibin, “X-ray propagation through polycapillary optics studied through a ray tracing approach,” Spectrochim. Acta, Part B 62, 608–614 (2007).
[CrossRef]

D. Hampai, S. B. Dabagov, G. Cappuccio, and G. Cibin, “X-ray propagation through hollow channel: PolyCAD - a ray tracing code,” Nucl. Instrum. Methods Phys. Res., Sect. B 244, 481–488 (2006).
[CrossRef]

Dabagov, S. B.

D. Hampai, S. B. Dabagov, G. Cappuccio, G. Cibin, and V. Sessa, “X-ray micro-imaging by capillary optics,” Spectrochim. Acta, Part B 64, 1180–1184 (2009).
[CrossRef]

D. Hampai, S. B. Dabagov, G. Cappuccio, and G. Cibin, “X-ray propagation through polycapillary optics studied through a ray tracing approach,” Spectrochim. Acta, Part B 62, 608–614 (2007).
[CrossRef]

D. Hampai, S. B. Dabagov, G. Cappuccio, and G. Cibin, “X-ray propagation through hollow channel: PolyCAD - a ray tracing code,” Nucl. Instrum. Methods Phys. Res., Sect. B 244, 481–488 (2006).
[CrossRef]

S. B. Dabagov, “Wave theory of x-ray scattering in capillary structures,” X-Ray Spectrom. 32, 223–228 (2003).
[CrossRef]

S. B. Dabagov and A. Marcelli, “Single-reflection regime of x rays that travel into a monocapillary,” Appl. Opt. 38, 7494–7497 (1999).
[CrossRef]

Yu. M. Alexandrov, S. B. Dabagov, M. A. Kumakhov, V. A. Murashova, D. A. Fedin, R. V. Fedorchuk, and M. N. Yakimenko, “Peculiarities of photon transmission through capillary systems,” Nucl. Instrum. Methods Phys. Res., Sect. B 134, 174–180 (1998).
[CrossRef]

S. B. Dabagov, R. V. Fedorchuk, V. A. Murashova, S. V. Nikitina, and M. N. Yakimenko, “Interference phenomenon under focusing of synchrotron radiation by a Kumakhov lens,” Nucl. Instrum. Methods Phys. Res., Sect. B 108, 213–218 (1996).
[CrossRef]

S. B. Dabagov, M. A. Kumakhov, and S. V. Nikitina, “On the interference of X-rays in multiple reflection optics,” Phys. Lett. A 203, 279–282 (1995).
[CrossRef]

S. B. Dabagov, M. A. Kumakhov, S. V. Nikitina, V. A. Murashova, R. V. Fedorchuk, and M. N. Yakimenko, “Observation of interference effects at the focus of an x-ray lens,” J. Synchrotron Radiat. 2, 132–135 (1995).
[CrossRef] [PubMed]

Di Lazzaro, P.

S. Bollanti, P. Albertano, M. Belli, P. Di Lazzaro, A. Ya. Faenov, F. Flora, G. Giordano, A. Grilli, F. Ianzinni, S. V. Kukhlevsky, T. Letardi, A. Nottola, L. Palladino, T. Pikuz, A. Reale, L. Reale, A. Scafati, M. A. Tabocchini, I. C. E. Turcu, K. Vigli-Papadaki, and G. Schina, “Soft X-ray plasma source for atmospheric-pressure microscopy, radiobiology and other applications,” Il Nuovo Cimento 20, 1685–1701 (1998).

Faenov, A. Ya.

S. Bollanti, P. Albertano, M. Belli, P. Di Lazzaro, A. Ya. Faenov, F. Flora, G. Giordano, A. Grilli, F. Ianzinni, S. V. Kukhlevsky, T. Letardi, A. Nottola, L. Palladino, T. Pikuz, A. Reale, L. Reale, A. Scafati, M. A. Tabocchini, I. C. E. Turcu, K. Vigli-Papadaki, and G. Schina, “Soft X-ray plasma source for atmospheric-pressure microscopy, radiobiology and other applications,” Il Nuovo Cimento 20, 1685–1701 (1998).

Fedin, D. A.

Yu. M. Alexandrov, S. B. Dabagov, M. A. Kumakhov, V. A. Murashova, D. A. Fedin, R. V. Fedorchuk, and M. N. Yakimenko, “Peculiarities of photon transmission through capillary systems,” Nucl. Instrum. Methods Phys. Res., Sect. B 134, 174–180 (1998).
[CrossRef]

Fedorchuk, R. V.

Yu. M. Alexandrov, S. B. Dabagov, M. A. Kumakhov, V. A. Murashova, D. A. Fedin, R. V. Fedorchuk, and M. N. Yakimenko, “Peculiarities of photon transmission through capillary systems,” Nucl. Instrum. Methods Phys. Res., Sect. B 134, 174–180 (1998).
[CrossRef]

S. B. Dabagov, R. V. Fedorchuk, V. A. Murashova, S. V. Nikitina, and M. N. Yakimenko, “Interference phenomenon under focusing of synchrotron radiation by a Kumakhov lens,” Nucl. Instrum. Methods Phys. Res., Sect. B 108, 213–218 (1996).
[CrossRef]

S. B. Dabagov, M. A. Kumakhov, S. V. Nikitina, V. A. Murashova, R. V. Fedorchuk, and M. N. Yakimenko, “Observation of interference effects at the focus of an x-ray lens,” J. Synchrotron Radiat. 2, 132–135 (1995).
[CrossRef] [PubMed]

Flora, F.

S. V. Kukhlevsky, F. Flora, A. Marinai, G. Nyitray, Zs. Kozma, A. Ritucci, L. Palladino, A. Reale, and G. Tomassetti, “Wave-optics treatment of x-rays passing through tapered capillary guides,” X-Ray Spectrom.  29, 354–359 (2000).
[CrossRef]

S. V. Kukhlevsky, F. Flora, A. Marinai, G. Nyitray, A. Ritucci, L. Palladino, A. Reale, and G. Tomassetti, “Diffraction of X-ray beams in capillary waveguides,” Nucl. Instrum. Methods Phys. Res., Sect. B 168, 276–282 (2000).
[CrossRef]

S. Bollanti, P. Albertano, M. Belli, P. Di Lazzaro, A. Ya. Faenov, F. Flora, G. Giordano, A. Grilli, F. Ianzinni, S. V. Kukhlevsky, T. Letardi, A. Nottola, L. Palladino, T. Pikuz, A. Reale, L. Reale, A. Scafati, M. A. Tabocchini, I. C. E. Turcu, K. Vigli-Papadaki, and G. Schina, “Soft X-ray plasma source for atmospheric-pressure microscopy, radiobiology and other applications,” Il Nuovo Cimento 20, 1685–1701 (1998).

Forbes, G.

Gibson, W. M.

C. A. MacDonald and W. M. Gibson, “Applications and advances in polycapillary optics,” X-ray Spectrom.  32, 258–268 (2003).
[CrossRef]

Giordano, G.

S. Bollanti, P. Albertano, M. Belli, P. Di Lazzaro, A. Ya. Faenov, F. Flora, G. Giordano, A. Grilli, F. Ianzinni, S. V. Kukhlevsky, T. Letardi, A. Nottola, L. Palladino, T. Pikuz, A. Reale, L. Reale, A. Scafati, M. A. Tabocchini, I. C. E. Turcu, K. Vigli-Papadaki, and G. Schina, “Soft X-ray plasma source for atmospheric-pressure microscopy, radiobiology and other applications,” Il Nuovo Cimento 20, 1685–1701 (1998).

Grilli, A.

S. Bollanti, P. Albertano, M. Belli, P. Di Lazzaro, A. Ya. Faenov, F. Flora, G. Giordano, A. Grilli, F. Ianzinni, S. V. Kukhlevsky, T. Letardi, A. Nottola, L. Palladino, T. Pikuz, A. Reale, L. Reale, A. Scafati, M. A. Tabocchini, I. C. E. Turcu, K. Vigli-Papadaki, and G. Schina, “Soft X-ray plasma source for atmospheric-pressure microscopy, radiobiology and other applications,” Il Nuovo Cimento 20, 1685–1701 (1998).

Hampai, D.

D. Hampai, S. B. Dabagov, G. Cappuccio, G. Cibin, and V. Sessa, “X-ray micro-imaging by capillary optics,” Spectrochim. Acta, Part B 64, 1180–1184 (2009).
[CrossRef]

D. Hampai, S. B. Dabagov, G. Cappuccio, and G. Cibin, “X-ray propagation through polycapillary optics studied through a ray tracing approach,” Spectrochim. Acta, Part B 62, 608–614 (2007).
[CrossRef]

D. Hampai, S. B. Dabagov, G. Cappuccio, and G. Cibin, “X-ray propagation through hollow channel: PolyCAD - a ray tracing code,” Nucl. Instrum. Methods Phys. Res., Sect. B 244, 481–488 (2006).
[CrossRef]

Heilpern, T.

T. Heilpern, E. Heyman, and V. Timchenko, “A beam summation algorithm for wave radiation and guidance in stratified media,” J. Acoust. Soc. Am. 121, 1856–1864 (2007).
[CrossRef] [PubMed]

Heyman, E.

T. Heilpern, E. Heyman, and V. Timchenko, “A beam summation algorithm for wave radiation and guidance in stratified media,” J. Acoust. Soc. Am. 121, 1856–1864 (2007).
[CrossRef] [PubMed]

Ianzinni, F.

S. Bollanti, P. Albertano, M. Belli, P. Di Lazzaro, A. Ya. Faenov, F. Flora, G. Giordano, A. Grilli, F. Ianzinni, S. V. Kukhlevsky, T. Letardi, A. Nottola, L. Palladino, T. Pikuz, A. Reale, L. Reale, A. Scafati, M. A. Tabocchini, I. C. E. Turcu, K. Vigli-Papadaki, and G. Schina, “Soft X-ray plasma source for atmospheric-pressure microscopy, radiobiology and other applications,” Il Nuovo Cimento 20, 1685–1701 (1998).

Jackson, J.

J. Jackson, C. Meyer, D. Nishimura, and A. Macovski, “Selection of a convolution function for fourier inversion using gridding [computerised tomography application],” IEEE Trans. Med. Imag. 10, 473–478 (1991).
[CrossRef]

Janssens, K.

L. Vincze, K. Janssens, and S. V. Kukhlevsky, “Simulation of polycapillary lenses for coherent and partially coherent x-rays,” Proc. SPIE 5536, 81–85 (2004).
[CrossRef]

L. Vincze, K. Janssens, F. Adams, and A. Rindby, “Detained ray-tracing code for capillary optics,” X-Ray Spectrom. 24, 27–37 (1995).
[CrossRef]

Kimball, J.

Q. Xiao, I. Ponomarev, A. Kolomitsev, and J. Kimball, “Numerical simulations for capillary-based x-ray optics,” Proc. SPIE 1736, 227–238 (1992).
[CrossRef]

Kolomitsev, A.

Q. Xiao, I. Ponomarev, A. Kolomitsev, and J. Kimball, “Numerical simulations for capillary-based x-ray optics,” Proc. SPIE 1736, 227–238 (1992).
[CrossRef]

Kozma, Zs.

S. V. Kukhlevsky, F. Flora, A. Marinai, G. Nyitray, Zs. Kozma, A. Ritucci, L. Palladino, A. Reale, and G. Tomassetti, “Wave-optics treatment of x-rays passing through tapered capillary guides,” X-Ray Spectrom.  29, 354–359 (2000).
[CrossRef]

Kukhlevsky, S. V.

L. Vincze, K. Janssens, and S. V. Kukhlevsky, “Simulation of polycapillary lenses for coherent and partially coherent x-rays,” Proc. SPIE 5536, 81–85 (2004).
[CrossRef]

S. V. Kukhlevsky, “Interference and diffraction in capillary x-ray optics,” X-Ray Spectrom. 32, 223–228 (2003).
[CrossRef]

S. V. Kukhlevsky, F. Flora, A. Marinai, G. Nyitray, A. Ritucci, L. Palladino, A. Reale, and G. Tomassetti, “Diffraction of X-ray beams in capillary waveguides,” Nucl. Instrum. Methods Phys. Res., Sect. B 168, 276–282 (2000).
[CrossRef]

S. V. Kukhlevsky, F. Flora, A. Marinai, G. Nyitray, Zs. Kozma, A. Ritucci, L. Palladino, A. Reale, and G. Tomassetti, “Wave-optics treatment of x-rays passing through tapered capillary guides,” X-Ray Spectrom.  29, 354–359 (2000).
[CrossRef]

S. Bollanti, P. Albertano, M. Belli, P. Di Lazzaro, A. Ya. Faenov, F. Flora, G. Giordano, A. Grilli, F. Ianzinni, S. V. Kukhlevsky, T. Letardi, A. Nottola, L. Palladino, T. Pikuz, A. Reale, L. Reale, A. Scafati, M. A. Tabocchini, I. C. E. Turcu, K. Vigli-Papadaki, and G. Schina, “Soft X-ray plasma source for atmospheric-pressure microscopy, radiobiology and other applications,” Il Nuovo Cimento 20, 1685–1701 (1998).

Kumakhov, M. A.

Yu. M. Alexandrov, S. B. Dabagov, M. A. Kumakhov, V. A. Murashova, D. A. Fedin, R. V. Fedorchuk, and M. N. Yakimenko, “Peculiarities of photon transmission through capillary systems,” Nucl. Instrum. Methods Phys. Res., Sect. B 134, 174–180 (1998).
[CrossRef]

S. B. Dabagov, M. A. Kumakhov, and S. V. Nikitina, “On the interference of X-rays in multiple reflection optics,” Phys. Lett. A 203, 279–282 (1995).
[CrossRef]

S. B. Dabagov, M. A. Kumakhov, S. V. Nikitina, V. A. Murashova, R. V. Fedorchuk, and M. N. Yakimenko, “Observation of interference effects at the focus of an x-ray lens,” J. Synchrotron Radiat. 2, 132–135 (1995).
[CrossRef] [PubMed]

Lengeler, B.

C. Schroer and B. Lengeler, “X-ray optics,” in Springer Handbook of Lasers and Optics, F. Träger, ed., (Springer-Verlag, 2007).
[CrossRef]

Letardi, T.

S. Bollanti, P. Albertano, M. Belli, P. Di Lazzaro, A. Ya. Faenov, F. Flora, G. Giordano, A. Grilli, F. Ianzinni, S. V. Kukhlevsky, T. Letardi, A. Nottola, L. Palladino, T. Pikuz, A. Reale, L. Reale, A. Scafati, M. A. Tabocchini, I. C. E. Turcu, K. Vigli-Papadaki, and G. Schina, “Soft X-ray plasma source for atmospheric-pressure microscopy, radiobiology and other applications,” Il Nuovo Cimento 20, 1685–1701 (1998).

Lin, L.

Liu, A.

A. Liu, “The X-ray distribution after a focussing polycapillary a shadow simulation,” Nucl. Instrum. Methods Phys. Res., Sect. B 243, 223–226 (2006).
[CrossRef]

A. Liu, “Simulation of x-ray beam collimation by polycapillaries,” Nucl. Instrum. Methods Phys. Res., Sect. B 234, 555–562 (2005).
[CrossRef]

A. Liu, “Simulation of x-ray propagation in a straight capillary,” Math. Comput. Simulat. 65, 251–256 (2004).
[CrossRef]

Liu, H.

MacDonald, C. A.

C. A. MacDonald and W. M. Gibson, “Applications and advances in polycapillary optics,” X-ray Spectrom.  32, 258–268 (2003).
[CrossRef]

Macovski, A.

J. Jackson, C. Meyer, D. Nishimura, and A. Macovski, “Selection of a convolution function for fourier inversion using gridding [computerised tomography application],” IEEE Trans. Med. Imag. 10, 473–478 (1991).
[CrossRef]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).

Marcelli, A.

Marinai, A.

S. V. Kukhlevsky, F. Flora, A. Marinai, G. Nyitray, A. Ritucci, L. Palladino, A. Reale, and G. Tomassetti, “Diffraction of X-ray beams in capillary waveguides,” Nucl. Instrum. Methods Phys. Res., Sect. B 168, 276–282 (2000).
[CrossRef]

S. V. Kukhlevsky, F. Flora, A. Marinai, G. Nyitray, Zs. Kozma, A. Ritucci, L. Palladino, A. Reale, and G. Tomassetti, “Wave-optics treatment of x-rays passing through tapered capillary guides,” X-Ray Spectrom.  29, 354–359 (2000).
[CrossRef]

Meyer, C.

J. Jackson, C. Meyer, D. Nishimura, and A. Macovski, “Selection of a convolution function for fourier inversion using gridding [computerised tomography application],” IEEE Trans. Med. Imag. 10, 473–478 (1991).
[CrossRef]

Mu, G.

Murashova, V. A.

Yu. M. Alexandrov, S. B. Dabagov, M. A. Kumakhov, V. A. Murashova, D. A. Fedin, R. V. Fedorchuk, and M. N. Yakimenko, “Peculiarities of photon transmission through capillary systems,” Nucl. Instrum. Methods Phys. Res., Sect. B 134, 174–180 (1998).
[CrossRef]

S. B. Dabagov, R. V. Fedorchuk, V. A. Murashova, S. V. Nikitina, and M. N. Yakimenko, “Interference phenomenon under focusing of synchrotron radiation by a Kumakhov lens,” Nucl. Instrum. Methods Phys. Res., Sect. B 108, 213–218 (1996).
[CrossRef]

S. B. Dabagov, M. A. Kumakhov, S. V. Nikitina, V. A. Murashova, R. V. Fedorchuk, and M. N. Yakimenko, “Observation of interference effects at the focus of an x-ray lens,” J. Synchrotron Radiat. 2, 132–135 (1995).
[CrossRef] [PubMed]

Nikitina, S. V.

S. B. Dabagov, R. V. Fedorchuk, V. A. Murashova, S. V. Nikitina, and M. N. Yakimenko, “Interference phenomenon under focusing of synchrotron radiation by a Kumakhov lens,” Nucl. Instrum. Methods Phys. Res., Sect. B 108, 213–218 (1996).
[CrossRef]

S. B. Dabagov, M. A. Kumakhov, and S. V. Nikitina, “On the interference of X-rays in multiple reflection optics,” Phys. Lett. A 203, 279–282 (1995).
[CrossRef]

S. B. Dabagov, M. A. Kumakhov, S. V. Nikitina, V. A. Murashova, R. V. Fedorchuk, and M. N. Yakimenko, “Observation of interference effects at the focus of an x-ray lens,” J. Synchrotron Radiat. 2, 132–135 (1995).
[CrossRef] [PubMed]

Nishimura, D.

J. Jackson, C. Meyer, D. Nishimura, and A. Macovski, “Selection of a convolution function for fourier inversion using gridding [computerised tomography application],” IEEE Trans. Med. Imag. 10, 473–478 (1991).
[CrossRef]

Norris, A.

Nottola, A.

S. Bollanti, P. Albertano, M. Belli, P. Di Lazzaro, A. Ya. Faenov, F. Flora, G. Giordano, A. Grilli, F. Ianzinni, S. V. Kukhlevsky, T. Letardi, A. Nottola, L. Palladino, T. Pikuz, A. Reale, L. Reale, A. Scafati, M. A. Tabocchini, I. C. E. Turcu, K. Vigli-Papadaki, and G. Schina, “Soft X-ray plasma source for atmospheric-pressure microscopy, radiobiology and other applications,” Il Nuovo Cimento 20, 1685–1701 (1998).

Nyitray, G.

S. V. Kukhlevsky, F. Flora, A. Marinai, G. Nyitray, Zs. Kozma, A. Ritucci, L. Palladino, A. Reale, and G. Tomassetti, “Wave-optics treatment of x-rays passing through tapered capillary guides,” X-Ray Spectrom.  29, 354–359 (2000).
[CrossRef]

S. V. Kukhlevsky, F. Flora, A. Marinai, G. Nyitray, A. Ritucci, L. Palladino, A. Reale, and G. Tomassetti, “Diffraction of X-ray beams in capillary waveguides,” Nucl. Instrum. Methods Phys. Res., Sect. B 168, 276–282 (2000).
[CrossRef]

Palladino, L.

S. V. Kukhlevsky, F. Flora, A. Marinai, G. Nyitray, Zs. Kozma, A. Ritucci, L. Palladino, A. Reale, and G. Tomassetti, “Wave-optics treatment of x-rays passing through tapered capillary guides,” X-Ray Spectrom.  29, 354–359 (2000).
[CrossRef]

S. V. Kukhlevsky, F. Flora, A. Marinai, G. Nyitray, A. Ritucci, L. Palladino, A. Reale, and G. Tomassetti, “Diffraction of X-ray beams in capillary waveguides,” Nucl. Instrum. Methods Phys. Res., Sect. B 168, 276–282 (2000).
[CrossRef]

S. Bollanti, P. Albertano, M. Belli, P. Di Lazzaro, A. Ya. Faenov, F. Flora, G. Giordano, A. Grilli, F. Ianzinni, S. V. Kukhlevsky, T. Letardi, A. Nottola, L. Palladino, T. Pikuz, A. Reale, L. Reale, A. Scafati, M. A. Tabocchini, I. C. E. Turcu, K. Vigli-Papadaki, and G. Schina, “Soft X-ray plasma source for atmospheric-pressure microscopy, radiobiology and other applications,” Il Nuovo Cimento 20, 1685–1701 (1998).

Pikuz, T.

S. Bollanti, P. Albertano, M. Belli, P. Di Lazzaro, A. Ya. Faenov, F. Flora, G. Giordano, A. Grilli, F. Ianzinni, S. V. Kukhlevsky, T. Letardi, A. Nottola, L. Palladino, T. Pikuz, A. Reale, L. Reale, A. Scafati, M. A. Tabocchini, I. C. E. Turcu, K. Vigli-Papadaki, and G. Schina, “Soft X-ray plasma source for atmospheric-pressure microscopy, radiobiology and other applications,” Il Nuovo Cimento 20, 1685–1701 (1998).

Ponomarev, I.

Q. Xiao, I. Ponomarev, A. Kolomitsev, and J. Kimball, “Numerical simulations for capillary-based x-ray optics,” Proc. SPIE 1736, 227–238 (1992).
[CrossRef]

Popov, M.

M. Popov, “A new method of computation of wave fields using gaussian beams,” Wave Motion 4, 85–97 (1982).
[CrossRef]

Poturaev, S. V.

Q. F. Xiao and S. V. Poturaev, “Polycapillary-based X-ray optics,” Nucl. Instrum. Methods Phys. Res., Sect. A 347, 376–383 (1994).
[CrossRef]

Radtke, M.

A. Bjeoumikhov, S. Bjeoumikhova, H. Riesemeier, M. Radtke, and R. Wedell, “Propagation of synchrotron radiation through nanocapillary structures,” Phys. Lett. A 366, 283–288 (2007).
[CrossRef]

Reale, A.

S. V. Kukhlevsky, F. Flora, A. Marinai, G. Nyitray, A. Ritucci, L. Palladino, A. Reale, and G. Tomassetti, “Diffraction of X-ray beams in capillary waveguides,” Nucl. Instrum. Methods Phys. Res., Sect. B 168, 276–282 (2000).
[CrossRef]

S. V. Kukhlevsky, F. Flora, A. Marinai, G. Nyitray, Zs. Kozma, A. Ritucci, L. Palladino, A. Reale, and G. Tomassetti, “Wave-optics treatment of x-rays passing through tapered capillary guides,” X-Ray Spectrom.  29, 354–359 (2000).
[CrossRef]

S. Bollanti, P. Albertano, M. Belli, P. Di Lazzaro, A. Ya. Faenov, F. Flora, G. Giordano, A. Grilli, F. Ianzinni, S. V. Kukhlevsky, T. Letardi, A. Nottola, L. Palladino, T. Pikuz, A. Reale, L. Reale, A. Scafati, M. A. Tabocchini, I. C. E. Turcu, K. Vigli-Papadaki, and G. Schina, “Soft X-ray plasma source for atmospheric-pressure microscopy, radiobiology and other applications,” Il Nuovo Cimento 20, 1685–1701 (1998).

Reale, L.

S. Bollanti, P. Albertano, M. Belli, P. Di Lazzaro, A. Ya. Faenov, F. Flora, G. Giordano, A. Grilli, F. Ianzinni, S. V. Kukhlevsky, T. Letardi, A. Nottola, L. Palladino, T. Pikuz, A. Reale, L. Reale, A. Scafati, M. A. Tabocchini, I. C. E. Turcu, K. Vigli-Papadaki, and G. Schina, “Soft X-ray plasma source for atmospheric-pressure microscopy, radiobiology and other applications,” Il Nuovo Cimento 20, 1685–1701 (1998).

Riesemeier, H.

A. Bjeoumikhov, S. Bjeoumikhova, H. Riesemeier, M. Radtke, and R. Wedell, “Propagation of synchrotron radiation through nanocapillary structures,” Phys. Lett. A 366, 283–288 (2007).
[CrossRef]

Rindby, A.

L. Vincze, K. Janssens, F. Adams, and A. Rindby, “Detained ray-tracing code for capillary optics,” X-Ray Spectrom. 24, 27–37 (1995).
[CrossRef]

Ritucci, A.

S. V. Kukhlevsky, F. Flora, A. Marinai, G. Nyitray, A. Ritucci, L. Palladino, A. Reale, and G. Tomassetti, “Diffraction of X-ray beams in capillary waveguides,” Nucl. Instrum. Methods Phys. Res., Sect. B 168, 276–282 (2000).
[CrossRef]

S. V. Kukhlevsky, F. Flora, A. Marinai, G. Nyitray, Zs. Kozma, A. Ritucci, L. Palladino, A. Reale, and G. Tomassetti, “Wave-optics treatment of x-rays passing through tapered capillary guides,” X-Ray Spectrom.  29, 354–359 (2000).
[CrossRef]

Scafati, A.

S. Bollanti, P. Albertano, M. Belli, P. Di Lazzaro, A. Ya. Faenov, F. Flora, G. Giordano, A. Grilli, F. Ianzinni, S. V. Kukhlevsky, T. Letardi, A. Nottola, L. Palladino, T. Pikuz, A. Reale, L. Reale, A. Scafati, M. A. Tabocchini, I. C. E. Turcu, K. Vigli-Papadaki, and G. Schina, “Soft X-ray plasma source for atmospheric-pressure microscopy, radiobiology and other applications,” Il Nuovo Cimento 20, 1685–1701 (1998).

Schina, G.

S. Bollanti, P. Albertano, M. Belli, P. Di Lazzaro, A. Ya. Faenov, F. Flora, G. Giordano, A. Grilli, F. Ianzinni, S. V. Kukhlevsky, T. Letardi, A. Nottola, L. Palladino, T. Pikuz, A. Reale, L. Reale, A. Scafati, M. A. Tabocchini, I. C. E. Turcu, K. Vigli-Papadaki, and G. Schina, “Soft X-ray plasma source for atmospheric-pressure microscopy, radiobiology and other applications,” Il Nuovo Cimento 20, 1685–1701 (1998).

Schoonover, R. W.

R. W. Schoonover, A. M. Zysk, and P. S. Carney, “Geometrical optics limit of stochastic electromagnetic fields,” Phys. Rev. A 77, 043831 (2008).
[CrossRef]

Schotland, J. C.

A. M. Zysk, P. S. Carney, and J. C. Schotland, “Eikonal method for calculation of coherence functions,” Phys. Rev. Lett. 95, 043904 (2005).
[CrossRef] [PubMed]

Schroer, C.

C. Schroer and B. Lengeler, “X-ray optics,” in Springer Handbook of Lasers and Optics, F. Träger, ed., (Springer-Verlag, 2007).
[CrossRef]

Sessa, V.

D. Hampai, S. B. Dabagov, G. Cappuccio, G. Cibin, and V. Sessa, “X-ray micro-imaging by capillary optics,” Spectrochim. Acta, Part B 64, 1180–1184 (2009).
[CrossRef]

Svensson, E.

E. Svensson, “Gaussian beam summation in shallow waveguides,” Wave Motion 45, 445–456 (2008).
[CrossRef]

Tabocchini, M. A.

S. Bollanti, P. Albertano, M. Belli, P. Di Lazzaro, A. Ya. Faenov, F. Flora, G. Giordano, A. Grilli, F. Ianzinni, S. V. Kukhlevsky, T. Letardi, A. Nottola, L. Palladino, T. Pikuz, A. Reale, L. Reale, A. Scafati, M. A. Tabocchini, I. C. E. Turcu, K. Vigli-Papadaki, and G. Schina, “Soft X-ray plasma source for atmospheric-pressure microscopy, radiobiology and other applications,” Il Nuovo Cimento 20, 1685–1701 (1998).

Timchenko, V.

T. Heilpern, E. Heyman, and V. Timchenko, “A beam summation algorithm for wave radiation and guidance in stratified media,” J. Acoust. Soc. Am. 121, 1856–1864 (2007).
[CrossRef] [PubMed]

Tomassetti, G.

S. V. Kukhlevsky, F. Flora, A. Marinai, G. Nyitray, Zs. Kozma, A. Ritucci, L. Palladino, A. Reale, and G. Tomassetti, “Wave-optics treatment of x-rays passing through tapered capillary guides,” X-Ray Spectrom.  29, 354–359 (2000).
[CrossRef]

S. V. Kukhlevsky, F. Flora, A. Marinai, G. Nyitray, A. Ritucci, L. Palladino, A. Reale, and G. Tomassetti, “Diffraction of X-ray beams in capillary waveguides,” Nucl. Instrum. Methods Phys. Res., Sect. B 168, 276–282 (2000).
[CrossRef]

Turcu, I. C. E.

S. Bollanti, P. Albertano, M. Belli, P. Di Lazzaro, A. Ya. Faenov, F. Flora, G. Giordano, A. Grilli, F. Ianzinni, S. V. Kukhlevsky, T. Letardi, A. Nottola, L. Palladino, T. Pikuz, A. Reale, L. Reale, A. Scafati, M. A. Tabocchini, I. C. E. Turcu, K. Vigli-Papadaki, and G. Schina, “Soft X-ray plasma source for atmospheric-pressure microscopy, radiobiology and other applications,” Il Nuovo Cimento 20, 1685–1701 (1998).

Vigli-Papadaki, K.

S. Bollanti, P. Albertano, M. Belli, P. Di Lazzaro, A. Ya. Faenov, F. Flora, G. Giordano, A. Grilli, F. Ianzinni, S. V. Kukhlevsky, T. Letardi, A. Nottola, L. Palladino, T. Pikuz, A. Reale, L. Reale, A. Scafati, M. A. Tabocchini, I. C. E. Turcu, K. Vigli-Papadaki, and G. Schina, “Soft X-ray plasma source for atmospheric-pressure microscopy, radiobiology and other applications,” Il Nuovo Cimento 20, 1685–1701 (1998).

Vincze, L.

L. Vincze, K. Janssens, and S. V. Kukhlevsky, “Simulation of polycapillary lenses for coherent and partially coherent x-rays,” Proc. SPIE 5536, 81–85 (2004).
[CrossRef]

L. Vincze, K. Janssens, F. Adams, and A. Rindby, “Detained ray-tracing code for capillary optics,” X-Ray Spectrom. 24, 27–37 (1995).
[CrossRef]

Wedell, R.

A. Bjeoumikhov, S. Bjeoumikhova, H. Riesemeier, M. Radtke, and R. Wedell, “Propagation of synchrotron radiation through nanocapillary structures,” Phys. Lett. A 366, 283–288 (2007).
[CrossRef]

Welnak, C.

C. Welnak, G. J. Chen, and F. Cerrina, “Shadow: a synchrotron radiation and X-ray optics simulation tool,” Nucl. Instrum. Methods Phys. Res., Sect. A 347, 344–347 (1994).
[CrossRef]

Wolf, E.

E. Wolf, “New spectral representation of random sources and of the partially coherent field that they generate,” Opt. Commun. 38, 3–6 (1981).
[CrossRef]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).

Xiao, Q.

Q. Xiao, I. Ponomarev, A. Kolomitsev, and J. Kimball, “Numerical simulations for capillary-based x-ray optics,” Proc. SPIE 1736, 227–238 (1992).
[CrossRef]

Xiao, Q. F.

Q. F. Xiao and S. V. Poturaev, “Polycapillary-based X-ray optics,” Nucl. Instrum. Methods Phys. Res., Sect. A 347, 376–383 (1994).
[CrossRef]

Yakimenko, M. N.

Yu. M. Alexandrov, S. B. Dabagov, M. A. Kumakhov, V. A. Murashova, D. A. Fedin, R. V. Fedorchuk, and M. N. Yakimenko, “Peculiarities of photon transmission through capillary systems,” Nucl. Instrum. Methods Phys. Res., Sect. B 134, 174–180 (1998).
[CrossRef]

S. B. Dabagov, R. V. Fedorchuk, V. A. Murashova, S. V. Nikitina, and M. N. Yakimenko, “Interference phenomenon under focusing of synchrotron radiation by a Kumakhov lens,” Nucl. Instrum. Methods Phys. Res., Sect. B 108, 213–218 (1996).
[CrossRef]

S. B. Dabagov, M. A. Kumakhov, S. V. Nikitina, V. A. Murashova, R. V. Fedorchuk, and M. N. Yakimenko, “Observation of interference effects at the focus of an x-ray lens,” J. Synchrotron Radiat. 2, 132–135 (1995).
[CrossRef] [PubMed]

Zysk, A. M.

R. W. Schoonover, A. M. Zysk, and P. S. Carney, “Geometrical optics limit of stochastic electromagnetic fields,” Phys. Rev. A 77, 043831 (2008).
[CrossRef]

A. M. Zysk, P. S. Carney, and J. C. Schotland, “Eikonal method for calculation of coherence functions,” Phys. Rev. Lett. 95, 043904 (2005).
[CrossRef] [PubMed]

Appl. Opt. (1)

IEEE Trans. Med. Imag. (1)

J. Jackson, C. Meyer, D. Nishimura, and A. Macovski, “Selection of a convolution function for fourier inversion using gridding [computerised tomography application],” IEEE Trans. Med. Imag. 10, 473–478 (1991).
[CrossRef]

Il Nuovo Cimento (1)

S. Bollanti, P. Albertano, M. Belli, P. Di Lazzaro, A. Ya. Faenov, F. Flora, G. Giordano, A. Grilli, F. Ianzinni, S. V. Kukhlevsky, T. Letardi, A. Nottola, L. Palladino, T. Pikuz, A. Reale, L. Reale, A. Scafati, M. A. Tabocchini, I. C. E. Turcu, K. Vigli-Papadaki, and G. Schina, “Soft X-ray plasma source for atmospheric-pressure microscopy, radiobiology and other applications,” Il Nuovo Cimento 20, 1685–1701 (1998).

J. Acoust. Soc. Am. (1)

T. Heilpern, E. Heyman, and V. Timchenko, “A beam summation algorithm for wave radiation and guidance in stratified media,” J. Acoust. Soc. Am. 121, 1856–1864 (2007).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (3)

J. Synchrotron Radiat. (1)

S. B. Dabagov, M. A. Kumakhov, S. V. Nikitina, V. A. Murashova, R. V. Fedorchuk, and M. N. Yakimenko, “Observation of interference effects at the focus of an x-ray lens,” J. Synchrotron Radiat. 2, 132–135 (1995).
[CrossRef] [PubMed]

Math. Comput. Simulat. (1)

A. Liu, “Simulation of x-ray propagation in a straight capillary,” Math. Comput. Simulat. 65, 251–256 (2004).
[CrossRef]

Nucl. Instrum. Methods Phys. Res., Sect. A (2)

Q. F. Xiao and S. V. Poturaev, “Polycapillary-based X-ray optics,” Nucl. Instrum. Methods Phys. Res., Sect. A 347, 376–383 (1994).
[CrossRef]

C. Welnak, G. J. Chen, and F. Cerrina, “Shadow: a synchrotron radiation and X-ray optics simulation tool,” Nucl. Instrum. Methods Phys. Res., Sect. A 347, 344–347 (1994).
[CrossRef]

Nucl. Instrum. Methods Phys. Res., Sect. B (6)

D. Hampai, S. B. Dabagov, G. Cappuccio, and G. Cibin, “X-ray propagation through hollow channel: PolyCAD - a ray tracing code,” Nucl. Instrum. Methods Phys. Res., Sect. B 244, 481–488 (2006).
[CrossRef]

A. Liu, “The X-ray distribution after a focussing polycapillary a shadow simulation,” Nucl. Instrum. Methods Phys. Res., Sect. B 243, 223–226 (2006).
[CrossRef]

S. V. Kukhlevsky, F. Flora, A. Marinai, G. Nyitray, A. Ritucci, L. Palladino, A. Reale, and G. Tomassetti, “Diffraction of X-ray beams in capillary waveguides,” Nucl. Instrum. Methods Phys. Res., Sect. B 168, 276–282 (2000).
[CrossRef]

A. Liu, “Simulation of x-ray beam collimation by polycapillaries,” Nucl. Instrum. Methods Phys. Res., Sect. B 234, 555–562 (2005).
[CrossRef]

S. B. Dabagov, R. V. Fedorchuk, V. A. Murashova, S. V. Nikitina, and M. N. Yakimenko, “Interference phenomenon under focusing of synchrotron radiation by a Kumakhov lens,” Nucl. Instrum. Methods Phys. Res., Sect. B 108, 213–218 (1996).
[CrossRef]

Yu. M. Alexandrov, S. B. Dabagov, M. A. Kumakhov, V. A. Murashova, D. A. Fedin, R. V. Fedorchuk, and M. N. Yakimenko, “Peculiarities of photon transmission through capillary systems,” Nucl. Instrum. Methods Phys. Res., Sect. B 134, 174–180 (1998).
[CrossRef]

Opt. Commun. (1)

E. Wolf, “New spectral representation of random sources and of the partially coherent field that they generate,” Opt. Commun. 38, 3–6 (1981).
[CrossRef]

Phys. Lett. A (3)

S. B. Dabagov, M. A. Kumakhov, and S. V. Nikitina, “On the interference of X-rays in multiple reflection optics,” Phys. Lett. A 203, 279–282 (1995).
[CrossRef]

A. Bjeoumikhov, “Observation of peculiarities in angular distributions of X-ray radiation after propagation through polycapillary structures,” Phys. Lett. A 360, 405–410 (2007).
[CrossRef]

A. Bjeoumikhov, S. Bjeoumikhova, H. Riesemeier, M. Radtke, and R. Wedell, “Propagation of synchrotron radiation through nanocapillary structures,” Phys. Lett. A 366, 283–288 (2007).
[CrossRef]

Phys. Rev. A (1)

R. W. Schoonover, A. M. Zysk, and P. S. Carney, “Geometrical optics limit of stochastic electromagnetic fields,” Phys. Rev. A 77, 043831 (2008).
[CrossRef]

Phys. Rev. Lett. (1)

A. M. Zysk, P. S. Carney, and J. C. Schotland, “Eikonal method for calculation of coherence functions,” Phys. Rev. Lett. 95, 043904 (2005).
[CrossRef] [PubMed]

Proc. SPIE (2)

L. Vincze, K. Janssens, and S. V. Kukhlevsky, “Simulation of polycapillary lenses for coherent and partially coherent x-rays,” Proc. SPIE 5536, 81–85 (2004).
[CrossRef]

Q. Xiao, I. Ponomarev, A. Kolomitsev, and J. Kimball, “Numerical simulations for capillary-based x-ray optics,” Proc. SPIE 1736, 227–238 (1992).
[CrossRef]

Spectrochim. Acta, Part B (2)

D. Hampai, S. B. Dabagov, G. Cappuccio, and G. Cibin, “X-ray propagation through polycapillary optics studied through a ray tracing approach,” Spectrochim. Acta, Part B 62, 608–614 (2007).
[CrossRef]

D. Hampai, S. B. Dabagov, G. Cappuccio, G. Cibin, and V. Sessa, “X-ray micro-imaging by capillary optics,” Spectrochim. Acta, Part B 64, 1180–1184 (2009).
[CrossRef]

Wave Motion (2)

M. Popov, “A new method of computation of wave fields using gaussian beams,” Wave Motion 4, 85–97 (1982).
[CrossRef]

E. Svensson, “Gaussian beam summation in shallow waveguides,” Wave Motion 45, 445–456 (2008).
[CrossRef]

X-ray Spectrom (1)

C. A. MacDonald and W. M. Gibson, “Applications and advances in polycapillary optics,” X-ray Spectrom.  32, 258–268 (2003).
[CrossRef]

S. V. Kukhlevsky, F. Flora, A. Marinai, G. Nyitray, Zs. Kozma, A. Ritucci, L. Palladino, A. Reale, and G. Tomassetti, “Wave-optics treatment of x-rays passing through tapered capillary guides,” X-Ray Spectrom.  29, 354–359 (2000).
[CrossRef]

X-Ray Spectrom. (3)

S. B. Dabagov, “Wave theory of x-ray scattering in capillary structures,” X-Ray Spectrom. 32, 223–228 (2003).
[CrossRef]

L. Vincze, K. Janssens, F. Adams, and A. Rindby, “Detained ray-tracing code for capillary optics,” X-Ray Spectrom. 24, 27–37 (1995).
[CrossRef]

S. V. Kukhlevsky, “Interference and diffraction in capillary x-ray optics,” X-Ray Spectrom. 32, 223–228 (2003).
[CrossRef]

Other (3)

C. Schroer and B. Lengeler, “X-ray optics,” in Springer Handbook of Lasers and Optics, F. Träger, ed., (Springer-Verlag, 2007).
[CrossRef]

B. Hargreaves and P. Beatty, “Gridding functions,” http://mrsrl.stanford.edu/brian/gridding/ .

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).

Supplementary Material (3)

» Media 1: AVI (2225 KB)     
» Media 2: AVI (2367 KB)     
» Media 3: AVI (2364 KB)     

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

The transverse intensity response from a parallel-plane waveguide illuminated by a soft x-ray laser source. The simulation results using the techniques in this work (B) are compared to simulated results (C) and experimental measurements (A) from the literature [8]. Portions of this figure are reprinted from Nuclear Instruments and Methods in Physics Reseach B, Vol. 168, S.V. Kukhlevsky, et al., “Diffraction of X-ray beams in capillary waveguides,” Pages 276–282, Copyright 2000, with permission from Elsevier.

Fig. 2
Fig. 2

Simulation results showing the spatial distribution of ray locations at the polycapillary device output plane with varying input anode source point locations. The panels show (from left to right) the anode source point locations (−6.4 μm, 0), (−3.2 μm, 0), and (0, 0).

Fig. 3
Fig. 3

Simulation results showing the log intensity of the polycapillary device wavefield output at distances (d = 0–10 cm with 0.5 cm increments) from the output plane ( Media 1). As the wavefield propagates, the response from individual capillaries diverges and overlaps.

Fig. 4
Fig. 4

Simulation results showing the spectral degree of coherence of the polycapillary device output wavefield. The spectral degree of coherence is a two-point quantity, and these data are shown as a function of r2 with r1 = (0, 0) on the left ( Media 2) and r1 = (63.8 μm, 0) on the right ( Media 3). r1 corresponds to the center point (left) and to the center point of the first capillary right of the center in the device output plane (right). Data are shown at distances (d = 0–10 cm with 0.5 cm increments) from the output plane.

Equations (3)

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

W s ( r 1 , r 2 , ω ) = n = 1 β n ( ω ) ϕ n * ( r 1 , ω ) ϕ n ( r 2 , ω ) ,
W ( r 1 , r 2 , ω ) = U ˜ * ( r 1 , ω ) U ˜ ( r 2 , ω ) = n = 1 β n ( ω ) ψ n * ( r 1 , ω ) ψ n ( r 2 , ω ) ,
μ ( r 1 , r 2 , ω ) = W ( r 1 , r 2 , ω ) W ( r 1 , r 1 , ω ) W ( r 2 , r 2 , ω ) .

Metrics