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

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]

Appl. Opt.

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

IEEE Trans. Med. Imag.

• 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

• 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.

• 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

• 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]
• 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]
• G. Forbes and M. Alonso, “Using rays better. I. theory for smoothly varying media,” J. Opt. Soc. Am. A 18, 1132–1145 (2001). [CrossRef]

J. Synchrotron Radiat.

• 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.

• 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

• 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

• 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.

• 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

• 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

• 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.

• 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

• 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

• 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

• 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

• 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.

• 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

• 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).

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