Abstract

Interest in phase contrast imaging methods based on electromagnetic wave coherence has increased significantly recently, particularly at X-ray energies. This is giving rise to a demand for effective simulation methods. Coherent imaging approaches are usually based on wave optics, which require significant computational resources, particularly for producing 2D images. Monte Carlo (MC) methods, used to track individual particles/photons for particle physics, are not considered appropriate for describing coherence effects. Previous preliminary work has evaluated the possibility of incorporating coherence in Monte Carlo codes. However, in this paper, we present the implementation of refraction in a model that is based on time of flight calculations and the Huygens-Fresnel principle, which allow reproducing the formation of phase contrast images in partially and fully coherent experimental conditions. The model is implemented in the FLUKA Monte Carlo code and X-ray phase contrast imaging simulations are compared with experiments and wave optics calculations.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. B. Lengeler, “Coherence in X-ray physics,” Naturwissenschaften 88(6), 249–260 (2001).
    [Crossref] [PubMed]
  2. A. Bravin, P. Coan, and P. Suortti, “X-ray phase-contrast imaging: from pre-clinical applications towards clinics,” Phys. Med. Biol. 58(1), R1–R35 (2013).
    [Crossref] [PubMed]
  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(6515), 595–598 (1995).
    [Crossref]
  4. A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).
    [Crossref]
  5. C. David, B. Nohammer, H. H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81(17), 3287–3289 (2002).
    [Crossref]
  6. A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. H. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, “An innovative digital imaging set-up allowing a low-dose approach to phase contrast applications in the medical field,” Med. Phys. 28(8), 1610–1619 (2001).
    [Crossref] [PubMed]
  7. A. Olivo and R. Speller, “A coded-aperture technique allowing x-ray phase contrast imaging with conventional sources,” Appl. Phys. Lett. 91(7), 074106 (2007).
    [Crossref]
  8. A. Peterzol, A. Olivo, L. Rigon, S. Pani, and D. Dreossi, “The effects of the imaging system on the validity limits of the ray-optical approach to phase contrast imaging,” Med. Phys. 32(12), 3617–3627 (2005).
    [Crossref] [PubMed]
  9. T. E. Gureyev, Y. I. Nesterets, A. W. Stevenson, P. R. Miller, A. Pogany, and S. W. Wilkins, “Some simple rules for contrast, signal-to-noise and resolution in in-line x-ray phase-contrast imaging,” Opt. Express 16(5), 3223–3241 (2008).
    [Crossref] [PubMed]
  10. Z. Wang, Z. Huang, L. Zhang, Z. Chen, and K. Kang, “Implement X-ray refraction effect in Geant4 for phase contrast imaging,” IEEE Nuclear Science Symposium Conference Record, 2395 - 2398 (2009)
  11. A. Prodi, E. Knudsen, P. Willendrup, S. Schmitt, C. Ferrero, R. Feidenhans’l, and K. Lefmann, “A Monte Carlo approach for simulating the propagation of partially coherent x-ray beams,” Proc. SPIE 8141, 814108 (2011).
  12. E. Bergbäck Knudsen, A. Prodi, J. Baltser, M. Thomsen, P. Kjaer Willendrup, M. Sanchez del Rio, C. Ferrero, E. Farhi, K. Haldrup, A. Vickery, R. Feidenhans’l, K. Mortensen, M. Meedom Nielsen, H. Friis Poulsen, S. Schmidt, and K. Lefmann, “McXtrace: a Monte Carlo software package for simulating X-ray optics, beamlines and experiments,” J. Appl. Cryst. 46(3), 679–696 (2013).
    [Crossref]
  13. S. Peter, P. Modregger, M. K. Fix, W. Volken, D. Frei, P. Manser, and M. Stampanoni, “Combining Monte Carlo methods with coherent wave optics for the simulation of phase-sensitive X-ray imaging,” J. Synchrotron Radiat. 21(3), 613–622 (2014).
    [Crossref] [PubMed]
  14. G. Battistoni, F. Cerutti, A. Fasso, A. Ferrari, S. Muraro, J. Ranft, S. Roesler, and P. R. Sala, “The FLUKA code: description and benchmarking,” Hadronic Shower Simulation Workshop896,31–49 (2007).
    [Crossref]
  15. F. A. Vittoria, P. C. Diemoz, M. Endrizzi, L. Rigon, F. C. Lopez, D. Dreossi, P. R. T. Munro, and A. Olivo, “Strategies for efficient and fast wave optics simulation of coded-aperture and other x-ray phase-contrast imaging methods,” Appl. Opt. 52(28), 6940–6947 (2013).
    [PubMed]
  16. C. Huygens, Traite' de la lumiere (Leyden, 1690).
  17. A. Fresnel, Annales de chimie et physique28, (1816), p. 147.
  18. E. Hecht, Optics, fourth ed. (Pearson, Harlow, 2003).
  19. H. F. Talbot, “Facts relating to optical science,” Philos. Mag. 9, 401–407 (1836).
  20. 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(16), 6296–6304 (2005).
    [Crossref] [PubMed]
  21. A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-ray Talbot Interferometry,” Jpn. J. Appl. Phys. 42(Part 2, No. 7B), L866–L868 (2003).
    [Crossref]
  22. C. Theis, (personal communication).

2014 (1)

S. Peter, P. Modregger, M. K. Fix, W. Volken, D. Frei, P. Manser, and M. Stampanoni, “Combining Monte Carlo methods with coherent wave optics for the simulation of phase-sensitive X-ray imaging,” J. Synchrotron Radiat. 21(3), 613–622 (2014).
[Crossref] [PubMed]

2013 (3)

F. A. Vittoria, P. C. Diemoz, M. Endrizzi, L. Rigon, F. C. Lopez, D. Dreossi, P. R. T. Munro, and A. Olivo, “Strategies for efficient and fast wave optics simulation of coded-aperture and other x-ray phase-contrast imaging methods,” Appl. Opt. 52(28), 6940–6947 (2013).
[PubMed]

E. Bergbäck Knudsen, A. Prodi, J. Baltser, M. Thomsen, P. Kjaer Willendrup, M. Sanchez del Rio, C. Ferrero, E. Farhi, K. Haldrup, A. Vickery, R. Feidenhans’l, K. Mortensen, M. Meedom Nielsen, H. Friis Poulsen, S. Schmidt, and K. Lefmann, “McXtrace: a Monte Carlo software package for simulating X-ray optics, beamlines and experiments,” J. Appl. Cryst. 46(3), 679–696 (2013).
[Crossref]

A. Bravin, P. Coan, and P. Suortti, “X-ray phase-contrast imaging: from pre-clinical applications towards clinics,” Phys. Med. Biol. 58(1), R1–R35 (2013).
[Crossref] [PubMed]

2011 (1)

A. Prodi, E. Knudsen, P. Willendrup, S. Schmitt, C. Ferrero, R. Feidenhans’l, and K. Lefmann, “A Monte Carlo approach for simulating the propagation of partially coherent x-ray beams,” Proc. SPIE 8141, 814108 (2011).

2008 (1)

2007 (1)

A. Olivo and R. Speller, “A coded-aperture technique allowing x-ray phase contrast imaging with conventional sources,” Appl. Phys. Lett. 91(7), 074106 (2007).
[Crossref]

2005 (2)

A. Peterzol, A. Olivo, L. Rigon, S. Pani, and D. Dreossi, “The effects of the imaging system on the validity limits of the ray-optical approach to phase contrast imaging,” Med. Phys. 32(12), 3617–3627 (2005).
[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(16), 6296–6304 (2005).
[Crossref] [PubMed]

2003 (1)

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-ray Talbot Interferometry,” Jpn. J. Appl. Phys. 42(Part 2, No. 7B), L866–L868 (2003).
[Crossref]

2002 (1)

C. David, B. Nohammer, H. H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81(17), 3287–3289 (2002).
[Crossref]

2001 (2)

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. H. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, “An innovative digital imaging set-up allowing a low-dose approach to phase contrast applications in the medical field,” Med. Phys. 28(8), 1610–1619 (2001).
[Crossref] [PubMed]

B. Lengeler, “Coherence in X-ray physics,” Naturwissenschaften 88(6), 249–260 (2001).
[Crossref] [PubMed]

1995 (2)

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(6515), 595–598 (1995).
[Crossref]

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).
[Crossref]

1836 (1)

H. F. Talbot, “Facts relating to optical science,” Philos. Mag. 9, 401–407 (1836).

Arfelli, F.

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. H. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, “An innovative digital imaging set-up allowing a low-dose approach to phase contrast applications in the medical field,” Med. Phys. 28(8), 1610–1619 (2001).
[Crossref] [PubMed]

Baltser, J.

E. Bergbäck Knudsen, A. Prodi, J. Baltser, M. Thomsen, P. Kjaer Willendrup, M. Sanchez del Rio, C. Ferrero, E. Farhi, K. Haldrup, A. Vickery, R. Feidenhans’l, K. Mortensen, M. Meedom Nielsen, H. Friis Poulsen, S. Schmidt, and K. Lefmann, “McXtrace: a Monte Carlo software package for simulating X-ray optics, beamlines and experiments,” J. Appl. Cryst. 46(3), 679–696 (2013).
[Crossref]

Battistoni, G.

G. Battistoni, F. Cerutti, A. Fasso, A. Ferrari, S. Muraro, J. Ranft, S. Roesler, and P. R. Sala, “The FLUKA code: description and benchmarking,” Hadronic Shower Simulation Workshop896,31–49 (2007).
[Crossref]

Bergbäck Knudsen, E.

E. Bergbäck Knudsen, A. Prodi, J. Baltser, M. Thomsen, P. Kjaer Willendrup, M. Sanchez del Rio, C. Ferrero, E. Farhi, K. Haldrup, A. Vickery, R. Feidenhans’l, K. Mortensen, M. Meedom Nielsen, H. Friis Poulsen, S. Schmidt, and K. Lefmann, “McXtrace: a Monte Carlo software package for simulating X-ray optics, beamlines and experiments,” J. Appl. Cryst. 46(3), 679–696 (2013).
[Crossref]

Bravin, A.

A. Bravin, P. Coan, and P. Suortti, “X-ray phase-contrast imaging: from pre-clinical applications towards clinics,” Phys. Med. Biol. 58(1), R1–R35 (2013).
[Crossref] [PubMed]

Cantatore, G.

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. H. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, “An innovative digital imaging set-up allowing a low-dose approach to phase contrast applications in the medical field,” Med. Phys. 28(8), 1610–1619 (2001).
[Crossref] [PubMed]

Castelli, E.

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. H. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, “An innovative digital imaging set-up allowing a low-dose approach to phase contrast applications in the medical field,” Med. Phys. 28(8), 1610–1619 (2001).
[Crossref] [PubMed]

Cerutti, F.

G. Battistoni, F. Cerutti, A. Fasso, A. Ferrari, S. Muraro, J. Ranft, S. Roesler, and P. R. Sala, “The FLUKA code: description and benchmarking,” Hadronic Shower Simulation Workshop896,31–49 (2007).
[Crossref]

Chen, Z.

Z. Wang, Z. Huang, L. Zhang, Z. Chen, and K. Kang, “Implement X-ray refraction effect in Geant4 for phase contrast imaging,” IEEE Nuclear Science Symposium Conference Record, 2395 - 2398 (2009)

Cloetens, P.

Coan, P.

A. Bravin, P. Coan, and P. Suortti, “X-ray phase-contrast imaging: from pre-clinical applications towards clinics,” Phys. Med. Biol. 58(1), R1–R35 (2013).
[Crossref] [PubMed]

David, C.

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(16), 6296–6304 (2005).
[Crossref] [PubMed]

C. David, B. Nohammer, H. H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81(17), 3287–3289 (2002).
[Crossref]

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(6515), 595–598 (1995).
[Crossref]

Diaz, A.

Diemoz, P. C.

Dreossi, D.

F. A. Vittoria, P. C. Diemoz, M. Endrizzi, L. Rigon, F. C. Lopez, D. Dreossi, P. R. T. Munro, and A. Olivo, “Strategies for efficient and fast wave optics simulation of coded-aperture and other x-ray phase-contrast imaging methods,” Appl. Opt. 52(28), 6940–6947 (2013).
[PubMed]

A. Peterzol, A. Olivo, L. Rigon, S. Pani, and D. Dreossi, “The effects of the imaging system on the validity limits of the ray-optical approach to phase contrast imaging,” Med. Phys. 32(12), 3617–3627 (2005).
[Crossref] [PubMed]

Endrizzi, M.

Farhi, E.

E. Bergbäck Knudsen, A. Prodi, J. Baltser, M. Thomsen, P. Kjaer Willendrup, M. Sanchez del Rio, C. Ferrero, E. Farhi, K. Haldrup, A. Vickery, R. Feidenhans’l, K. Mortensen, M. Meedom Nielsen, H. Friis Poulsen, S. Schmidt, and K. Lefmann, “McXtrace: a Monte Carlo software package for simulating X-ray optics, beamlines and experiments,” J. Appl. Cryst. 46(3), 679–696 (2013).
[Crossref]

Fasso, A.

G. Battistoni, F. Cerutti, A. Fasso, A. Ferrari, S. Muraro, J. Ranft, S. Roesler, and P. R. Sala, “The FLUKA code: description and benchmarking,” Hadronic Shower Simulation Workshop896,31–49 (2007).
[Crossref]

Feidenhans’l, R.

E. Bergbäck Knudsen, A. Prodi, J. Baltser, M. Thomsen, P. Kjaer Willendrup, M. Sanchez del Rio, C. Ferrero, E. Farhi, K. Haldrup, A. Vickery, R. Feidenhans’l, K. Mortensen, M. Meedom Nielsen, H. Friis Poulsen, S. Schmidt, and K. Lefmann, “McXtrace: a Monte Carlo software package for simulating X-ray optics, beamlines and experiments,” J. Appl. Cryst. 46(3), 679–696 (2013).
[Crossref]

A. Prodi, E. Knudsen, P. Willendrup, S. Schmitt, C. Ferrero, R. Feidenhans’l, and K. Lefmann, “A Monte Carlo approach for simulating the propagation of partially coherent x-ray beams,” Proc. SPIE 8141, 814108 (2011).

Ferrari, A.

G. Battistoni, F. Cerutti, A. Fasso, A. Ferrari, S. Muraro, J. Ranft, S. Roesler, and P. R. Sala, “The FLUKA code: description and benchmarking,” Hadronic Shower Simulation Workshop896,31–49 (2007).
[Crossref]

Ferrero, C.

E. Bergbäck Knudsen, A. Prodi, J. Baltser, M. Thomsen, P. Kjaer Willendrup, M. Sanchez del Rio, C. Ferrero, E. Farhi, K. Haldrup, A. Vickery, R. Feidenhans’l, K. Mortensen, M. Meedom Nielsen, H. Friis Poulsen, S. Schmidt, and K. Lefmann, “McXtrace: a Monte Carlo software package for simulating X-ray optics, beamlines and experiments,” J. Appl. Cryst. 46(3), 679–696 (2013).
[Crossref]

A. Prodi, E. Knudsen, P. Willendrup, S. Schmitt, C. Ferrero, R. Feidenhans’l, and K. Lefmann, “A Monte Carlo approach for simulating the propagation of partially coherent x-ray beams,” Proc. SPIE 8141, 814108 (2011).

Fix, M. K.

S. Peter, P. Modregger, M. K. Fix, W. Volken, D. Frei, P. Manser, and M. Stampanoni, “Combining Monte Carlo methods with coherent wave optics for the simulation of phase-sensitive X-ray imaging,” J. Synchrotron Radiat. 21(3), 613–622 (2014).
[Crossref] [PubMed]

Frei, D.

S. Peter, P. Modregger, M. K. Fix, W. Volken, D. Frei, P. Manser, and M. Stampanoni, “Combining Monte Carlo methods with coherent wave optics for the simulation of phase-sensitive X-ray imaging,” J. Synchrotron Radiat. 21(3), 613–622 (2014).
[Crossref] [PubMed]

Friis Poulsen, H.

E. Bergbäck Knudsen, A. Prodi, J. Baltser, M. Thomsen, P. Kjaer Willendrup, M. Sanchez del Rio, C. Ferrero, E. Farhi, K. Haldrup, A. Vickery, R. Feidenhans’l, K. Mortensen, M. Meedom Nielsen, H. Friis Poulsen, S. Schmidt, and K. Lefmann, “McXtrace: a Monte Carlo software package for simulating X-ray optics, beamlines and experiments,” J. Appl. Cryst. 46(3), 679–696 (2013).
[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(6515), 595–598 (1995).
[Crossref]

Gureyev, T. E.

T. E. Gureyev, Y. I. Nesterets, A. W. Stevenson, P. R. Miller, A. Pogany, and S. W. Wilkins, “Some simple rules for contrast, signal-to-noise and resolution in in-line x-ray phase-contrast imaging,” Opt. Express 16(5), 3223–3241 (2008).
[Crossref] [PubMed]

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(6515), 595–598 (1995).
[Crossref]

Haldrup, K.

E. Bergbäck Knudsen, A. Prodi, J. Baltser, M. Thomsen, P. Kjaer Willendrup, M. Sanchez del Rio, C. Ferrero, E. Farhi, K. Haldrup, A. Vickery, R. Feidenhans’l, K. Mortensen, M. Meedom Nielsen, H. Friis Poulsen, S. Schmidt, and K. Lefmann, “McXtrace: a Monte Carlo software package for simulating X-ray optics, beamlines and experiments,” J. Appl. Cryst. 46(3), 679–696 (2013).
[Crossref]

Hamaishi, Y.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-ray Talbot Interferometry,” Jpn. J. Appl. Phys. 42(Part 2, No. 7B), L866–L868 (2003).
[Crossref]

Huang, Z.

Z. Wang, Z. Huang, L. Zhang, Z. Chen, and K. Kang, “Implement X-ray refraction effect in Geant4 for phase contrast imaging,” IEEE Nuclear Science Symposium Conference Record, 2395 - 2398 (2009)

Kang, K.

Z. Wang, Z. Huang, L. Zhang, Z. Chen, and K. Kang, “Implement X-ray refraction effect in Geant4 for phase contrast imaging,” IEEE Nuclear Science Symposium Conference Record, 2395 - 2398 (2009)

Kawamoto, S.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-ray Talbot Interferometry,” Jpn. J. Appl. Phys. 42(Part 2, No. 7B), L866–L868 (2003).
[Crossref]

Kjaer Willendrup, P.

E. Bergbäck Knudsen, A. Prodi, J. Baltser, M. Thomsen, P. Kjaer Willendrup, M. Sanchez del Rio, C. Ferrero, E. Farhi, K. Haldrup, A. Vickery, R. Feidenhans’l, K. Mortensen, M. Meedom Nielsen, H. Friis Poulsen, S. Schmidt, and K. Lefmann, “McXtrace: a Monte Carlo software package for simulating X-ray optics, beamlines and experiments,” J. Appl. Cryst. 46(3), 679–696 (2013).
[Crossref]

Knudsen, E.

A. Prodi, E. Knudsen, P. Willendrup, S. Schmitt, C. Ferrero, R. Feidenhans’l, and K. Lefmann, “A Monte Carlo approach for simulating the propagation of partially coherent x-ray beams,” Proc. SPIE 8141, 814108 (2011).

Kohn, V.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).
[Crossref]

Koyama, I.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-ray Talbot Interferometry,” Jpn. J. Appl. Phys. 42(Part 2, No. 7B), L866–L868 (2003).
[Crossref]

Kuznetsov, S.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).
[Crossref]

Lefmann, K.

E. Bergbäck Knudsen, A. Prodi, J. Baltser, M. Thomsen, P. Kjaer Willendrup, M. Sanchez del Rio, C. Ferrero, E. Farhi, K. Haldrup, A. Vickery, R. Feidenhans’l, K. Mortensen, M. Meedom Nielsen, H. Friis Poulsen, S. Schmidt, and K. Lefmann, “McXtrace: a Monte Carlo software package for simulating X-ray optics, beamlines and experiments,” J. Appl. Cryst. 46(3), 679–696 (2013).
[Crossref]

A. Prodi, E. Knudsen, P. Willendrup, S. Schmitt, C. Ferrero, R. Feidenhans’l, and K. Lefmann, “A Monte Carlo approach for simulating the propagation of partially coherent x-ray beams,” Proc. SPIE 8141, 814108 (2011).

Lengeler, B.

B. Lengeler, “Coherence in X-ray physics,” Naturwissenschaften 88(6), 249–260 (2001).
[Crossref] [PubMed]

Longo, R.

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. H. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, “An innovative digital imaging set-up allowing a low-dose approach to phase contrast applications in the medical field,” Med. Phys. 28(8), 1610–1619 (2001).
[Crossref] [PubMed]

Lopez, F. C.

Manser, P.

S. Peter, P. Modregger, M. K. Fix, W. Volken, D. Frei, P. Manser, and M. Stampanoni, “Combining Monte Carlo methods with coherent wave optics for the simulation of phase-sensitive X-ray imaging,” J. Synchrotron Radiat. 21(3), 613–622 (2014).
[Crossref] [PubMed]

Meedom Nielsen, M.

E. Bergbäck Knudsen, A. Prodi, J. Baltser, M. Thomsen, P. Kjaer Willendrup, M. Sanchez del Rio, C. Ferrero, E. Farhi, K. Haldrup, A. Vickery, R. Feidenhans’l, K. Mortensen, M. Meedom Nielsen, H. Friis Poulsen, S. Schmidt, and K. Lefmann, “McXtrace: a Monte Carlo software package for simulating X-ray optics, beamlines and experiments,” J. Appl. Cryst. 46(3), 679–696 (2013).
[Crossref]

Menk, R. H.

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. H. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, “An innovative digital imaging set-up allowing a low-dose approach to phase contrast applications in the medical field,” Med. Phys. 28(8), 1610–1619 (2001).
[Crossref] [PubMed]

Miller, P. R.

Modregger, P.

S. Peter, P. Modregger, M. K. Fix, W. Volken, D. Frei, P. Manser, and M. Stampanoni, “Combining Monte Carlo methods with coherent wave optics for the simulation of phase-sensitive X-ray imaging,” J. Synchrotron Radiat. 21(3), 613–622 (2014).
[Crossref] [PubMed]

Momose, A.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-ray Talbot Interferometry,” Jpn. J. Appl. Phys. 42(Part 2, No. 7B), L866–L868 (2003).
[Crossref]

Mortensen, K.

E. Bergbäck Knudsen, A. Prodi, J. Baltser, M. Thomsen, P. Kjaer Willendrup, M. Sanchez del Rio, C. Ferrero, E. Farhi, K. Haldrup, A. Vickery, R. Feidenhans’l, K. Mortensen, M. Meedom Nielsen, H. Friis Poulsen, S. Schmidt, and K. Lefmann, “McXtrace: a Monte Carlo software package for simulating X-ray optics, beamlines and experiments,” J. Appl. Cryst. 46(3), 679–696 (2013).
[Crossref]

Munro, P. R. T.

Muraro, S.

G. Battistoni, F. Cerutti, A. Fasso, A. Ferrari, S. Muraro, J. Ranft, S. Roesler, and P. R. Sala, “The FLUKA code: description and benchmarking,” Hadronic Shower Simulation Workshop896,31–49 (2007).
[Crossref]

Nesterets, Y. I.

Nohammer, B.

C. David, B. Nohammer, H. H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81(17), 3287–3289 (2002).
[Crossref]

Olivo, A.

F. A. Vittoria, P. C. Diemoz, M. Endrizzi, L. Rigon, F. C. Lopez, D. Dreossi, P. R. T. Munro, and A. Olivo, “Strategies for efficient and fast wave optics simulation of coded-aperture and other x-ray phase-contrast imaging methods,” Appl. Opt. 52(28), 6940–6947 (2013).
[PubMed]

A. Olivo and R. Speller, “A coded-aperture technique allowing x-ray phase contrast imaging with conventional sources,” Appl. Phys. Lett. 91(7), 074106 (2007).
[Crossref]

A. Peterzol, A. Olivo, L. Rigon, S. Pani, and D. Dreossi, “The effects of the imaging system on the validity limits of the ray-optical approach to phase contrast imaging,” Med. Phys. 32(12), 3617–3627 (2005).
[Crossref] [PubMed]

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. H. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, “An innovative digital imaging set-up allowing a low-dose approach to phase contrast applications in the medical field,” Med. Phys. 28(8), 1610–1619 (2001).
[Crossref] [PubMed]

Pani, S.

A. Peterzol, A. Olivo, L. Rigon, S. Pani, and D. Dreossi, “The effects of the imaging system on the validity limits of the ray-optical approach to phase contrast imaging,” Med. Phys. 32(12), 3617–3627 (2005).
[Crossref] [PubMed]

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. H. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, “An innovative digital imaging set-up allowing a low-dose approach to phase contrast applications in the medical field,” Med. Phys. 28(8), 1610–1619 (2001).
[Crossref] [PubMed]

Peter, S.

S. Peter, P. Modregger, M. K. Fix, W. Volken, D. Frei, P. Manser, and M. Stampanoni, “Combining Monte Carlo methods with coherent wave optics for the simulation of phase-sensitive X-ray imaging,” J. Synchrotron Radiat. 21(3), 613–622 (2014).
[Crossref] [PubMed]

Peterzol, A.

A. Peterzol, A. Olivo, L. Rigon, S. Pani, and D. Dreossi, “The effects of the imaging system on the validity limits of the ray-optical approach to phase contrast imaging,” Med. Phys. 32(12), 3617–3627 (2005).
[Crossref] [PubMed]

Pfeiffer, F.

Pogany, A.

Poropat, P.

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. H. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, “An innovative digital imaging set-up allowing a low-dose approach to phase contrast applications in the medical field,” Med. Phys. 28(8), 1610–1619 (2001).
[Crossref] [PubMed]

Prest, M.

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. H. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, “An innovative digital imaging set-up allowing a low-dose approach to phase contrast applications in the medical field,” Med. Phys. 28(8), 1610–1619 (2001).
[Crossref] [PubMed]

Prodi, A.

E. Bergbäck Knudsen, A. Prodi, J. Baltser, M. Thomsen, P. Kjaer Willendrup, M. Sanchez del Rio, C. Ferrero, E. Farhi, K. Haldrup, A. Vickery, R. Feidenhans’l, K. Mortensen, M. Meedom Nielsen, H. Friis Poulsen, S. Schmidt, and K. Lefmann, “McXtrace: a Monte Carlo software package for simulating X-ray optics, beamlines and experiments,” J. Appl. Cryst. 46(3), 679–696 (2013).
[Crossref]

A. Prodi, E. Knudsen, P. Willendrup, S. Schmitt, C. Ferrero, R. Feidenhans’l, and K. Lefmann, “A Monte Carlo approach for simulating the propagation of partially coherent x-ray beams,” Proc. SPIE 8141, 814108 (2011).

Ranft, J.

G. Battistoni, F. Cerutti, A. Fasso, A. Ferrari, S. Muraro, J. Ranft, S. Roesler, and P. R. Sala, “The FLUKA code: description and benchmarking,” Hadronic Shower Simulation Workshop896,31–49 (2007).
[Crossref]

Rigon, L.

F. A. Vittoria, P. C. Diemoz, M. Endrizzi, L. Rigon, F. C. Lopez, D. Dreossi, P. R. T. Munro, and A. Olivo, “Strategies for efficient and fast wave optics simulation of coded-aperture and other x-ray phase-contrast imaging methods,” Appl. Opt. 52(28), 6940–6947 (2013).
[PubMed]

A. Peterzol, A. Olivo, L. Rigon, S. Pani, and D. Dreossi, “The effects of the imaging system on the validity limits of the ray-optical approach to phase contrast imaging,” Med. Phys. 32(12), 3617–3627 (2005).
[Crossref] [PubMed]

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. H. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, “An innovative digital imaging set-up allowing a low-dose approach to phase contrast applications in the medical field,” Med. Phys. 28(8), 1610–1619 (2001).
[Crossref] [PubMed]

Roesler, S.

G. Battistoni, F. Cerutti, A. Fasso, A. Ferrari, S. Muraro, J. Ranft, S. Roesler, and P. R. Sala, “The FLUKA code: description and benchmarking,” Hadronic Shower Simulation Workshop896,31–49 (2007).
[Crossref]

Sala, P. R.

G. Battistoni, F. Cerutti, A. Fasso, A. Ferrari, S. Muraro, J. Ranft, S. Roesler, and P. R. Sala, “The FLUKA code: description and benchmarking,” Hadronic Shower Simulation Workshop896,31–49 (2007).
[Crossref]

Sanchez del Rio, M.

E. Bergbäck Knudsen, A. Prodi, J. Baltser, M. Thomsen, P. Kjaer Willendrup, M. Sanchez del Rio, C. Ferrero, E. Farhi, K. Haldrup, A. Vickery, R. Feidenhans’l, K. Mortensen, M. Meedom Nielsen, H. Friis Poulsen, S. Schmidt, and K. Lefmann, “McXtrace: a Monte Carlo software package for simulating X-ray optics, beamlines and experiments,” J. Appl. Cryst. 46(3), 679–696 (2013).
[Crossref]

Schelokov, I.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).
[Crossref]

Schmidt, S.

E. Bergbäck Knudsen, A. Prodi, J. Baltser, M. Thomsen, P. Kjaer Willendrup, M. Sanchez del Rio, C. Ferrero, E. Farhi, K. Haldrup, A. Vickery, R. Feidenhans’l, K. Mortensen, M. Meedom Nielsen, H. Friis Poulsen, S. Schmidt, and K. Lefmann, “McXtrace: a Monte Carlo software package for simulating X-ray optics, beamlines and experiments,” J. Appl. Cryst. 46(3), 679–696 (2013).
[Crossref]

Schmitt, S.

A. Prodi, E. Knudsen, P. Willendrup, S. Schmitt, C. Ferrero, R. Feidenhans’l, and K. Lefmann, “A Monte Carlo approach for simulating the propagation of partially coherent x-ray beams,” Proc. SPIE 8141, 814108 (2011).

Snigirev, A.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).
[Crossref]

Snigireva, I.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).
[Crossref]

Solak, H. H.

C. David, B. Nohammer, H. H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81(17), 3287–3289 (2002).
[Crossref]

Speller, R.

A. Olivo and R. Speller, “A coded-aperture technique allowing x-ray phase contrast imaging with conventional sources,” Appl. Phys. Lett. 91(7), 074106 (2007).
[Crossref]

Stampanoni, M.

S. Peter, P. Modregger, M. K. Fix, W. Volken, D. Frei, P. Manser, and M. Stampanoni, “Combining Monte Carlo methods with coherent wave optics for the simulation of phase-sensitive X-ray imaging,” J. Synchrotron Radiat. 21(3), 613–622 (2014).
[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(16), 6296–6304 (2005).
[Crossref] [PubMed]

Stevenson, A. W.

T. E. Gureyev, Y. I. Nesterets, A. W. Stevenson, P. R. Miller, A. Pogany, and S. W. Wilkins, “Some simple rules for contrast, signal-to-noise and resolution in in-line x-ray phase-contrast imaging,” Opt. Express 16(5), 3223–3241 (2008).
[Crossref] [PubMed]

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(6515), 595–598 (1995).
[Crossref]

Suortti, P.

A. Bravin, P. Coan, and P. Suortti, “X-ray phase-contrast imaging: from pre-clinical applications towards clinics,” Phys. Med. Biol. 58(1), R1–R35 (2013).
[Crossref] [PubMed]

Suzuki, Y.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-ray Talbot Interferometry,” Jpn. J. Appl. Phys. 42(Part 2, No. 7B), L866–L868 (2003).
[Crossref]

Takai, K.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-ray Talbot Interferometry,” Jpn. J. Appl. Phys. 42(Part 2, No. 7B), L866–L868 (2003).
[Crossref]

Talbot, H. F.

H. F. Talbot, “Facts relating to optical science,” Philos. Mag. 9, 401–407 (1836).

Thomsen, M.

E. Bergbäck Knudsen, A. Prodi, J. Baltser, M. Thomsen, P. Kjaer Willendrup, M. Sanchez del Rio, C. Ferrero, E. Farhi, K. Haldrup, A. Vickery, R. Feidenhans’l, K. Mortensen, M. Meedom Nielsen, H. Friis Poulsen, S. Schmidt, and K. Lefmann, “McXtrace: a Monte Carlo software package for simulating X-ray optics, beamlines and experiments,” J. Appl. Cryst. 46(3), 679–696 (2013).
[Crossref]

Tromba, G.

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. H. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, “An innovative digital imaging set-up allowing a low-dose approach to phase contrast applications in the medical field,” Med. Phys. 28(8), 1610–1619 (2001).
[Crossref] [PubMed]

Vallazza, E.

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. H. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, “An innovative digital imaging set-up allowing a low-dose approach to phase contrast applications in the medical field,” Med. Phys. 28(8), 1610–1619 (2001).
[Crossref] [PubMed]

Vickery, A.

E. Bergbäck Knudsen, A. Prodi, J. Baltser, M. Thomsen, P. Kjaer Willendrup, M. Sanchez del Rio, C. Ferrero, E. Farhi, K. Haldrup, A. Vickery, R. Feidenhans’l, K. Mortensen, M. Meedom Nielsen, H. Friis Poulsen, S. Schmidt, and K. Lefmann, “McXtrace: a Monte Carlo software package for simulating X-ray optics, beamlines and experiments,” J. Appl. Cryst. 46(3), 679–696 (2013).
[Crossref]

Vittoria, F. A.

Volken, W.

S. Peter, P. Modregger, M. K. Fix, W. Volken, D. Frei, P. Manser, and M. Stampanoni, “Combining Monte Carlo methods with coherent wave optics for the simulation of phase-sensitive X-ray imaging,” J. Synchrotron Radiat. 21(3), 613–622 (2014).
[Crossref] [PubMed]

Wang, Z.

Z. Wang, Z. Huang, L. Zhang, Z. Chen, and K. Kang, “Implement X-ray refraction effect in Geant4 for phase contrast imaging,” IEEE Nuclear Science Symposium Conference Record, 2395 - 2398 (2009)

Weitkamp, T.

Wilkins, S. W.

T. E. Gureyev, Y. I. Nesterets, A. W. Stevenson, P. R. Miller, A. Pogany, and S. W. Wilkins, “Some simple rules for contrast, signal-to-noise and resolution in in-line x-ray phase-contrast imaging,” Opt. Express 16(5), 3223–3241 (2008).
[Crossref] [PubMed]

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(6515), 595–598 (1995).
[Crossref]

Willendrup, P.

A. Prodi, E. Knudsen, P. Willendrup, S. Schmitt, C. Ferrero, R. Feidenhans’l, and K. Lefmann, “A Monte Carlo approach for simulating the propagation of partially coherent x-ray beams,” Proc. SPIE 8141, 814108 (2011).

Zhang, L.

Z. Wang, Z. Huang, L. Zhang, Z. Chen, and K. Kang, “Implement X-ray refraction effect in Geant4 for phase contrast imaging,” IEEE Nuclear Science Symposium Conference Record, 2395 - 2398 (2009)

Ziegler, E.

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(16), 6296–6304 (2005).
[Crossref] [PubMed]

C. David, B. Nohammer, H. H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81(17), 3287–3289 (2002).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

C. David, B. Nohammer, H. H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81(17), 3287–3289 (2002).
[Crossref]

A. Olivo and R. Speller, “A coded-aperture technique allowing x-ray phase contrast imaging with conventional sources,” Appl. Phys. Lett. 91(7), 074106 (2007).
[Crossref]

J. Appl. Cryst. (1)

E. Bergbäck Knudsen, A. Prodi, J. Baltser, M. Thomsen, P. Kjaer Willendrup, M. Sanchez del Rio, C. Ferrero, E. Farhi, K. Haldrup, A. Vickery, R. Feidenhans’l, K. Mortensen, M. Meedom Nielsen, H. Friis Poulsen, S. Schmidt, and K. Lefmann, “McXtrace: a Monte Carlo software package for simulating X-ray optics, beamlines and experiments,” J. Appl. Cryst. 46(3), 679–696 (2013).
[Crossref]

J. Synchrotron Radiat. (1)

S. Peter, P. Modregger, M. K. Fix, W. Volken, D. Frei, P. Manser, and M. Stampanoni, “Combining Monte Carlo methods with coherent wave optics for the simulation of phase-sensitive X-ray imaging,” J. Synchrotron Radiat. 21(3), 613–622 (2014).
[Crossref] [PubMed]

Jpn. J. Appl. Phys. (1)

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-ray Talbot Interferometry,” Jpn. J. Appl. Phys. 42(Part 2, No. 7B), L866–L868 (2003).
[Crossref]

Med. Phys. (2)

A. Peterzol, A. Olivo, L. Rigon, S. Pani, and D. Dreossi, “The effects of the imaging system on the validity limits of the ray-optical approach to phase contrast imaging,” Med. Phys. 32(12), 3617–3627 (2005).
[Crossref] [PubMed]

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. H. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, “An innovative digital imaging set-up allowing a low-dose approach to phase contrast applications in the medical field,” Med. Phys. 28(8), 1610–1619 (2001).
[Crossref] [PubMed]

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(6515), 595–598 (1995).
[Crossref]

Naturwissenschaften (1)

B. Lengeler, “Coherence in X-ray physics,” Naturwissenschaften 88(6), 249–260 (2001).
[Crossref] [PubMed]

Opt. Express (2)

Philos. Mag. (1)

H. F. Talbot, “Facts relating to optical science,” Philos. Mag. 9, 401–407 (1836).

Phys. Med. Biol. (1)

A. Bravin, P. Coan, and P. Suortti, “X-ray phase-contrast imaging: from pre-clinical applications towards clinics,” Phys. Med. Biol. 58(1), R1–R35 (2013).
[Crossref] [PubMed]

Proc. SPIE (1)

A. Prodi, E. Knudsen, P. Willendrup, S. Schmitt, C. Ferrero, R. Feidenhans’l, and K. Lefmann, “A Monte Carlo approach for simulating the propagation of partially coherent x-ray beams,” Proc. SPIE 8141, 814108 (2011).

Rev. Sci. Instrum. (1)

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).
[Crossref]

Other (6)

Z. Wang, Z. Huang, L. Zhang, Z. Chen, and K. Kang, “Implement X-ray refraction effect in Geant4 for phase contrast imaging,” IEEE Nuclear Science Symposium Conference Record, 2395 - 2398 (2009)

C. Theis, (personal communication).

G. Battistoni, F. Cerutti, A. Fasso, A. Ferrari, S. Muraro, J. Ranft, S. Roesler, and P. R. Sala, “The FLUKA code: description and benchmarking,” Hadronic Shower Simulation Workshop896,31–49 (2007).
[Crossref]

C. Huygens, Traite' de la lumiere (Leyden, 1690).

A. Fresnel, Annales de chimie et physique28, (1816), p. 147.

E. Hecht, Optics, fourth ed. (Pearson, Harlow, 2003).

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 (10)

Fig. 1
Fig. 1

Schematic of the ray-tracing approach for phase contrast imaging.

Fig. 2
Fig. 2

Comparison of FLUKA simulations with experimental data. Red dots: experimental data: a) PEEK wire in water: δ PEEK = 2.98 × 10−6, δ WATER = 2.46 × 10−6. b) nylon wire: δ NYLON = 5.53 × 10−7. For both simulations the number of particles simulated is 5 x 108, the computational time per particle is ~1 x 10−6 s.

Fig. 3
Fig. 3

Double slit setup simulated in FLUKA. d is the slit distance, a the slit width. The photons after the slits are scattered isotropically within an angle ± D/L.

Fig. 4
Fig. 4

Double slit experiment. The analytic interference pattern (black dotted line) is compared with that produced using FLUKA (blue solid line) for a 20 keV X-ray beam transmitted through two slits with a = 5 μm d = 35 μm and L = 20 m. Number of simulated particle 2 x 108, processing time 1.2 x 10−5 s per particle.

Fig. 5
Fig. 5

(a) Flow chart summarizing the steps to implement refraction in FLUKA. (b) Illustration of photon propagation in FLUKA corresponding to the steps in the flow chart.

Fig. 6
Fig. 6

Wave-optical approach interference pattern obtained using FLUKA (blue line) and by numerically solving the Fresnel/Kirchhoff integral (black line) using 20 keV monochromatic X-rays to image 50 μm radius PEEK wire, δ PEEK = 7.15 × 10−7 (a) and 50 μm tungsten wire, δ W = 8.03 × 10−6 (b). The number of simulated particles is 1x109, processing time 0.8 x 10−5 s per particle.

Fig. 7
Fig. 7

Edge-illumination XPCI (not to scale). The figure extends in the plane of the drawing sufficiently to laterally cover the full sample, which is scanned along one direction only. With non-laminar (e.g. cone) beams, multiple beams are created through masks and scanning is avoided.

Fig. 8
Fig. 8

EIXPCI experiment: a) PEEK wire profile, δ PEEK = 7.15 × 10−7 and b) titanium wire profile, δ TITANIUM = 21.9 × 10−7. The experimental step size is 10 μm, the simulated scanning step 1 μm. The figures show FLUKA results compared to the experimental data. The simulated number of particle is 5 x 107 per scanning step. The number of steps is 520 and 290 for figure a) and b) respectively. The computational time is 1.2 x 10−5 s per particle.

Fig. 9
Fig. 9

Schematic of the Talbot interferometer implemented in FLUKA. The distance between the phase and the absorption gratings is 12.5 cm, corresponding to half the first Talbot distance.

Fig. 10
Fig. 10

FLUKA simulations of the Talbot interferometer. a) Reference phase stepping signal recorded without object (solid red line), which appears shifted when an object is introduced (dashed black line). b) Reconstructed differential phase signal due to the object (250 μm radius PEEK wire).

Equations (3)

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

π λ r 1 M [ 2 F g ] 2 1 ,
sin θ 1 sin θ 2 = ( n 2 ) ( n 1 ) ,
t o f t o f + d i o c ( δ ) ,

Metrics