Abstract

The attenuation of x-rays in a material forms the basis of x-ray radiography and tomography. By measuring the transmission of the x-rays over a large amount of raypaths, the three-dimensional (3D) distribution of the x-ray linear attenuation coefficient can be reconstructed in a 3D volume. In x-ray microtomography (μCT), however, the x-ray refraction yields a significant signal in the transmission image and the 3D distribution of the refractive index can be reconstructed in a 3D volume. To do so, several methods exist, on both a hardware and software level. In this paper, we compare two similar software methods, the modified Bronnikov algorithm and the simultaneous phase-and-amplitude retrieval. The first method assumes a pure phase object, whereas the latter assumes a homogeneous object. Although these assumptions seem very restrictive, both methods have proven to yield good results on experimental data.

© 2012 Optical Society of America

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  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 (London) 373, 595–598 (1995).
    [CrossRef]
  2. P. Cloetens, R. Barrett, J. Baruchel, J. P. Guigay, and M. Schlenker, “Phase objects in synchrotron radiation hard x-ray imaging,” J. Phys. D: Appl. Phys. 29, 133–146 (1996).
    [CrossRef]
  3. S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard x-rays,” Nature 384, 335–338 (1996).
    [CrossRef]
  4. F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance x-ray sources,” Nat. Phys. 2, 258–261 (2006).
    [CrossRef]
  5. C. David, T. Weitkamp, F. Pfeiffer, A. Diaz, J. Bruder, T. Rohbeck, A. Groso, O. Bunk, M. Stampanoni, and P. Cloetens, “Hard x-ray phase imaging and tomography using a grating interferometer,” Spectrochim. Acta: Part B 62, 626–630 (2007).
    [CrossRef]
  6. S. A. McDonald, F. Marone, C. Hintermuller, G. Mikuljan, C. David, F. Pfeiffer, and M. Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synchrotron Radiat. 16, 562–572 (2009).
    [CrossRef]
  7. P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyts, J. P. Guigay, and M. Schlenker, “Holotomography: quantitative phase tomography with micrometerresolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).
    [CrossRef]
  8. M. Langer, P. Cloetens, J. P. Guigay, and F. Peyrin, “Quantitative comparison of direct phase retrieval algorithms in in-line phase tomography,” Med. Phys. 35, 4556–4566 (2008).
    [CrossRef]
  9. P. Cloetens, M. Pateyron-Salom, J. Y. Buffire, G. Peix, J. Baruchel, F. Peyrin, and M. Schlenker, “Observation of microstructure and damage in materials by phase sensitive radiography and tomography,” J. Appl. Phys. 81, 5878–5886 (1997).
    [CrossRef]
  10. A. Pogany, D. Gao, and S. W. Wilkins, “Contrast and resolution in imaging with a microfocus x-ray source,” Rev. Sci. Instrum. 68, 2774–2782 (1997).
    [CrossRef]
  11. 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, 3617–3627 (2005).
    [CrossRef]
  12. C. M. Laperle, T. J. Hamilton, P. Wintermeyer, E. J. Walker, D. Shi, M. A. Anastasio, Z. Derdak, J. R. Wands, G. Diebold, and C. Rose-Petruck, “Low density contrast agents for x-ray phase contrast imaging: the use of ambient air for x-ray angiography of excised murine liver tissue,” Phys. Med. Biol. 53, 6911–6923 (2008).
    [CrossRef]
  13. E. M. Friis, P. R. Crane, K. R. Pedersen, S. Bengton, P. C. J. Donoghue, G. W. Grimm, and M. Stampanoni, “Phase-contrast x-ray microtomography links cretaceous seeds with gnetales and bennettitales,” Nature 450, 549–552 (2007).
    [CrossRef]
  14. P. Trtik, J. Dual, D. Keunecke, D. Mannes, P. Niemz, P. Stähli, A. Kaestner, A. Groso, and M. Stampanoni, “3d imaging of microstructure of spruce wood,” J. Struct. Biol. 159, 46–55 (2007).
    [CrossRef]
  15. P. Tafforeau and T. M. Smith, “Nondestructive imaging of hominoid dental microstructure using phase contrast x-ray synchrotron microtomography,” J. Hum. Evol. 54, 272–278 (2008).
    [CrossRef]
  16. M. R. Teague, “Deterministic phase retrieval: a Green’s function solution,” J. Opt. Soc. Am. 73, 1434–1441 (1983).
    [CrossRef]
  17. A. V. Bronnikov, “Theory of quantitative phase-contrast computed tomography,” J. Opt. Soc. Am. A 19, 472–480 (2002).
    [CrossRef]
  18. A. V. Bronnikov, “Phase-contrast CT: fundamental theorem and fast image reconstruction algorithms,” Proc. SPIE 6318, 63180Q (2006).
    [CrossRef]
  19. A. Groso, R. Abela, and M. Stampanoni, “Implementation of a fast method for high resolution phase contrast tomography,” Opt. Express 14, 8103–8110 (2006).
    [CrossRef]
  20. D. M. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206, 33–40 (2002).
    [CrossRef]
  21. S. C. Mayo, T. J. Davis, T. E. Gureyev, P. R. Miller, D. M. Paganin, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “X-ray phase-contrast microscopy and microtomography,” Opt. Express 11, 2289–2302 (2003).
    [CrossRef]
  22. T. E. Gureyev, T. J. Davis, A. Pogany, S. C. Mayo, and S. W. Wilkins, “Optical phase retrieval by use of first Born-and-Rytov-type approximations,” Appl. Opt. 43, 2418–2430 (2004).
    [CrossRef]
  23. X. Wu, H. Liu, and A. Yan, “X-ray phase-attenuation duality and phase retrieval,” Opt. Lett. 30, 379–381 (2005).
    [CrossRef]
  24. Y. De Witte, M. N. Boone, J. Vlassenbroeck, M. Dierick, and L. Van Hoorebeke, “Bronnikov-aided correction for x-ray computed tomography,” J. Opt. Soc. Am. A 26, 890–894 (2009).
    [CrossRef]
  25. A. Burvall, U. Lundstrm, P. A. C. Takman, D. H. Larsson, and H. M. Hertz, “Phase retreival in x-ray phase-contrast imaging suitable for tomography,” Opt. Express 19, 10359–10376 (2011).
    [CrossRef]
  26. M. N. Boone, Y. De Witte, M. Dierick, J. Van den Bulcke, J. Vlassenbroeck, and L. Van Hoorebeke, “Practical use of the modified Bronnikov algorithm in micro-CT,” Nucl. Instrum. Methods Phys. Res. Sect. B 267, 1182–1186 (2009).
    [CrossRef]
  27. T. Weitkamp, D. Haas, D. Wegrzynek, and A. Rack, “Ankaphase: software for single-distance phase retrieval from inline x-ray phase-contrast radiographs,” J. Synchrotron. Radiat. 18, 617–629 (2011).
    [CrossRef]
  28. R. C. Chen, H. L. Xie, L. Rigon, R. Longo, E. Castelli, and T. Q. Xiao, “Phase retrieval in quantitative x-ray microtomography with a single sample-to-detector distance,” Opt. Lett. 36, 1719–1721 (2011).
    [CrossRef]
  29. A. Almeida, S. Possemiers, M. N. Boone, T. De Beer, T. Quinten, L. Van Hoorebeke, J.-P. Remon, and C. Vervaet, “Ethylene vinyl acetate as matrix for oral sustained release dosage forms produced via hot-melt extrusion,” Eur. J. Pharm. Biopharm. 77, 297–305 (2011).
    [CrossRef]
  30. D. Derome, M. Griffa, M. Koebel, and J. Carmeliet, “Hysteretic swelling of wood at cellular scale probed by phase-contrast x-ray tomography,” J. Struct. Biol. 173, 180–190 (2011).
    [CrossRef]
  31. J. Vlassenbroeck, M. Dierick, B. Masschaele, V. Cnudde, L. Van Hoorebeke, and P. Jacobs, “Software tools for quantification of x-ray microtomography at the UGCT,” Nucl. Instrum. Methods Phys. Res.: Sect. A 580, 442–445 (2007).
    [CrossRef]
  32. B. D. Arhatari, W. P. Gates, N. Estiaghi, and A. G. Peele, “Phase retrieval tomography in the presence of noise,” J. Appl. Phys. 107, 034904 (2010).
    [CrossRef]
  33. M. N. Boone, Y. De Witte, M. Dierick, A. Almeida, and L. Van Hoorebeke, “Improved signal-to-noise ratio in laboratory-based phase contrast tomography,” Microsc. Microanal. 18, 399–405 (2012).
    [CrossRef]
  34. Y. De Witte, “Improved and practically feasible reconstruction methods for high resolution x-ray tomography,” Ph.D. thesis (Ghent University, 2010).
  35. B. Masschaele, V. Cnudde, M. Dierick, P. Jacobs, L. Van Hoorebeke, and J. Vlassenbroeck, “UGCT: new x-ray radiography and tomography facility,” Nucl. Instrum. Methods Phys. Res. Sect. A 580, 266–269 (2007).
    [CrossRef]
  36. M. N. Boone, J. Vlassenbroeck, S. Peetermans, D. Van Loo, M. Dierick, and L. Van Hoorebeke, “Secondary radiation in transmission-type x-ray tubes: simulation, practical issues and solution in the context of x-ray microtomography,” Nucl. Instrum. Methods Phys. Res. Sect. A 661, 7–12 (2012).
    [CrossRef]
  37. X. Wu and H. Liu, “A general theoretical formalism for x-ray phase contrast imaging,” J. X-ray Sci. Technol. 11, 33–42 (2003).
  38. T. E. Gureyev and S. W. Wilkins, “On x-ray phase imaging with a point source,” J. Opt. Soc. Am. A 15, 579–585 (1998).
    [CrossRef]
  39. H. Derluyn, M. Griffa, D. Mannes, I. Jerjen, J. Dewanckele, P. Vontobel, A. Sheppard, M. N. Boone, D. Derome, V. Cnudde, E. Lehmann, and J. Carmeliet, “Probing salt crystallization damage mechanisms in porous limestone with neutron radiography and x-ray tomography,” in 5th International Building Physics Conference (2012), pp. 95–102.
  40. M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R. Betemps, U. Frommherz, P. Bhler, D. Meister, M. Lange, and R. Abela, “Trends in synchrotron-based tomographic imaging: the SLS experience,” Proc. SPIE 6318, 63180M (2006).
    [CrossRef]
  41. F. Marone, C. Hintermuller, S. A. McDonald, R. Abela, G. Mikuljan, A. Isenegger, and M. Stampanoni, “X-ray tomographic microscopy at TOMCAT,” J. Phys.: Conf. Ser. 186, 012042 (2009).
    [CrossRef]
  42. NIST, “X-ray form factor, attenuation and scattering tables,” http://physics.nist.gov/PhysRefData/FFast/html/form.html .
  43. M. A. Beltran, D. M. Paganin, K. Uesugi, and M. J. Kitchen, “2D and 3D x-ray phase retrieval of multi-material objects using a single defocus distance,” Opt. Express 18, 6423–6436 (2010).
    [CrossRef]
  44. M. A. Beltran, D. M. Paganin, K. W. Siu, A. Fouras, S. B. Hooper, D. H. Reser, and M. J. Kitchen, “Interface-specific x-ray phase retrieval tomography of complex biological organs,” Phys. Med. Biol. 56, 7353–7369 (2011).
    [CrossRef]

2012 (2)

M. N. Boone, Y. De Witte, M. Dierick, A. Almeida, and L. Van Hoorebeke, “Improved signal-to-noise ratio in laboratory-based phase contrast tomography,” Microsc. Microanal. 18, 399–405 (2012).
[CrossRef]

M. N. Boone, J. Vlassenbroeck, S. Peetermans, D. Van Loo, M. Dierick, and L. Van Hoorebeke, “Secondary radiation in transmission-type x-ray tubes: simulation, practical issues and solution in the context of x-ray microtomography,” Nucl. Instrum. Methods Phys. Res. Sect. A 661, 7–12 (2012).
[CrossRef]

2011 (6)

T. Weitkamp, D. Haas, D. Wegrzynek, and A. Rack, “Ankaphase: software for single-distance phase retrieval from inline x-ray phase-contrast radiographs,” J. Synchrotron. Radiat. 18, 617–629 (2011).
[CrossRef]

A. Almeida, S. Possemiers, M. N. Boone, T. De Beer, T. Quinten, L. Van Hoorebeke, J.-P. Remon, and C. Vervaet, “Ethylene vinyl acetate as matrix for oral sustained release dosage forms produced via hot-melt extrusion,” Eur. J. Pharm. Biopharm. 77, 297–305 (2011).
[CrossRef]

D. Derome, M. Griffa, M. Koebel, and J. Carmeliet, “Hysteretic swelling of wood at cellular scale probed by phase-contrast x-ray tomography,” J. Struct. Biol. 173, 180–190 (2011).
[CrossRef]

M. A. Beltran, D. M. Paganin, K. W. Siu, A. Fouras, S. B. Hooper, D. H. Reser, and M. J. Kitchen, “Interface-specific x-ray phase retrieval tomography of complex biological organs,” Phys. Med. Biol. 56, 7353–7369 (2011).
[CrossRef]

R. C. Chen, H. L. Xie, L. Rigon, R. Longo, E. Castelli, and T. Q. Xiao, “Phase retrieval in quantitative x-ray microtomography with a single sample-to-detector distance,” Opt. Lett. 36, 1719–1721 (2011).
[CrossRef]

A. Burvall, U. Lundstrm, P. A. C. Takman, D. H. Larsson, and H. M. Hertz, “Phase retreival in x-ray phase-contrast imaging suitable for tomography,” Opt. Express 19, 10359–10376 (2011).
[CrossRef]

2010 (2)

M. A. Beltran, D. M. Paganin, K. Uesugi, and M. J. Kitchen, “2D and 3D x-ray phase retrieval of multi-material objects using a single defocus distance,” Opt. Express 18, 6423–6436 (2010).
[CrossRef]

B. D. Arhatari, W. P. Gates, N. Estiaghi, and A. G. Peele, “Phase retrieval tomography in the presence of noise,” J. Appl. Phys. 107, 034904 (2010).
[CrossRef]

2009 (4)

F. Marone, C. Hintermuller, S. A. McDonald, R. Abela, G. Mikuljan, A. Isenegger, and M. Stampanoni, “X-ray tomographic microscopy at TOMCAT,” J. Phys.: Conf. Ser. 186, 012042 (2009).
[CrossRef]

S. A. McDonald, F. Marone, C. Hintermuller, G. Mikuljan, C. David, F. Pfeiffer, and M. Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synchrotron Radiat. 16, 562–572 (2009).
[CrossRef]

M. N. Boone, Y. De Witte, M. Dierick, J. Van den Bulcke, J. Vlassenbroeck, and L. Van Hoorebeke, “Practical use of the modified Bronnikov algorithm in micro-CT,” Nucl. Instrum. Methods Phys. Res. Sect. B 267, 1182–1186 (2009).
[CrossRef]

Y. De Witte, M. N. Boone, J. Vlassenbroeck, M. Dierick, and L. Van Hoorebeke, “Bronnikov-aided correction for x-ray computed tomography,” J. Opt. Soc. Am. A 26, 890–894 (2009).
[CrossRef]

2008 (3)

P. Tafforeau and T. M. Smith, “Nondestructive imaging of hominoid dental microstructure using phase contrast x-ray synchrotron microtomography,” J. Hum. Evol. 54, 272–278 (2008).
[CrossRef]

C. M. Laperle, T. J. Hamilton, P. Wintermeyer, E. J. Walker, D. Shi, M. A. Anastasio, Z. Derdak, J. R. Wands, G. Diebold, and C. Rose-Petruck, “Low density contrast agents for x-ray phase contrast imaging: the use of ambient air for x-ray angiography of excised murine liver tissue,” Phys. Med. Biol. 53, 6911–6923 (2008).
[CrossRef]

M. Langer, P. Cloetens, J. P. Guigay, and F. Peyrin, “Quantitative comparison of direct phase retrieval algorithms in in-line phase tomography,” Med. Phys. 35, 4556–4566 (2008).
[CrossRef]

2007 (5)

E. M. Friis, P. R. Crane, K. R. Pedersen, S. Bengton, P. C. J. Donoghue, G. W. Grimm, and M. Stampanoni, “Phase-contrast x-ray microtomography links cretaceous seeds with gnetales and bennettitales,” Nature 450, 549–552 (2007).
[CrossRef]

P. Trtik, J. Dual, D. Keunecke, D. Mannes, P. Niemz, P. Stähli, A. Kaestner, A. Groso, and M. Stampanoni, “3d imaging of microstructure of spruce wood,” J. Struct. Biol. 159, 46–55 (2007).
[CrossRef]

C. David, T. Weitkamp, F. Pfeiffer, A. Diaz, J. Bruder, T. Rohbeck, A. Groso, O. Bunk, M. Stampanoni, and P. Cloetens, “Hard x-ray phase imaging and tomography using a grating interferometer,” Spectrochim. Acta: Part B 62, 626–630 (2007).
[CrossRef]

J. Vlassenbroeck, M. Dierick, B. Masschaele, V. Cnudde, L. Van Hoorebeke, and P. Jacobs, “Software tools for quantification of x-ray microtomography at the UGCT,” Nucl. Instrum. Methods Phys. Res.: Sect. A 580, 442–445 (2007).
[CrossRef]

B. Masschaele, V. Cnudde, M. Dierick, P. Jacobs, L. Van Hoorebeke, and J. Vlassenbroeck, “UGCT: new x-ray radiography and tomography facility,” Nucl. Instrum. Methods Phys. Res. Sect. A 580, 266–269 (2007).
[CrossRef]

2006 (4)

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R. Betemps, U. Frommherz, P. Bhler, D. Meister, M. Lange, and R. Abela, “Trends in synchrotron-based tomographic imaging: the SLS experience,” Proc. SPIE 6318, 63180M (2006).
[CrossRef]

A. V. Bronnikov, “Phase-contrast CT: fundamental theorem and fast image reconstruction algorithms,” Proc. SPIE 6318, 63180Q (2006).
[CrossRef]

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance x-ray sources,” Nat. Phys. 2, 258–261 (2006).
[CrossRef]

A. Groso, R. Abela, and M. Stampanoni, “Implementation of a fast method for high resolution phase contrast tomography,” Opt. Express 14, 8103–8110 (2006).
[CrossRef]

2005 (2)

X. Wu, H. Liu, and A. Yan, “X-ray phase-attenuation duality and phase retrieval,” Opt. Lett. 30, 379–381 (2005).
[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, 3617–3627 (2005).
[CrossRef]

2004 (1)

2003 (2)

2002 (2)

A. V. Bronnikov, “Theory of quantitative phase-contrast computed tomography,” J. Opt. Soc. Am. A 19, 472–480 (2002).
[CrossRef]

D. M. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206, 33–40 (2002).
[CrossRef]

1999 (1)

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyts, J. P. Guigay, and M. Schlenker, “Holotomography: quantitative phase tomography with micrometerresolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).
[CrossRef]

1998 (1)

1997 (2)

P. Cloetens, M. Pateyron-Salom, J. Y. Buffire, G. Peix, J. Baruchel, F. Peyrin, and M. Schlenker, “Observation of microstructure and damage in materials by phase sensitive radiography and tomography,” J. Appl. Phys. 81, 5878–5886 (1997).
[CrossRef]

A. Pogany, D. Gao, and S. W. Wilkins, “Contrast and resolution in imaging with a microfocus x-ray source,” Rev. Sci. Instrum. 68, 2774–2782 (1997).
[CrossRef]

1996 (2)

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

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard x-rays,” Nature 384, 335–338 (1996).
[CrossRef]

1995 (1)

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

1983 (1)

Abela, R.

F. Marone, C. Hintermuller, S. A. McDonald, R. Abela, G. Mikuljan, A. Isenegger, and M. Stampanoni, “X-ray tomographic microscopy at TOMCAT,” J. Phys.: Conf. Ser. 186, 012042 (2009).
[CrossRef]

A. Groso, R. Abela, and M. Stampanoni, “Implementation of a fast method for high resolution phase contrast tomography,” Opt. Express 14, 8103–8110 (2006).
[CrossRef]

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R. Betemps, U. Frommherz, P. Bhler, D. Meister, M. Lange, and R. Abela, “Trends in synchrotron-based tomographic imaging: the SLS experience,” Proc. SPIE 6318, 63180M (2006).
[CrossRef]

Almeida, A.

M. N. Boone, Y. De Witte, M. Dierick, A. Almeida, and L. Van Hoorebeke, “Improved signal-to-noise ratio in laboratory-based phase contrast tomography,” Microsc. Microanal. 18, 399–405 (2012).
[CrossRef]

A. Almeida, S. Possemiers, M. N. Boone, T. De Beer, T. Quinten, L. Van Hoorebeke, J.-P. Remon, and C. Vervaet, “Ethylene vinyl acetate as matrix for oral sustained release dosage forms produced via hot-melt extrusion,” Eur. J. Pharm. Biopharm. 77, 297–305 (2011).
[CrossRef]

Anastasio, M. A.

C. M. Laperle, T. J. Hamilton, P. Wintermeyer, E. J. Walker, D. Shi, M. A. Anastasio, Z. Derdak, J. R. Wands, G. Diebold, and C. Rose-Petruck, “Low density contrast agents for x-ray phase contrast imaging: the use of ambient air for x-ray angiography of excised murine liver tissue,” Phys. Med. Biol. 53, 6911–6923 (2008).
[CrossRef]

Arhatari, B. D.

B. D. Arhatari, W. P. Gates, N. Estiaghi, and A. G. Peele, “Phase retrieval tomography in the presence of noise,” J. Appl. Phys. 107, 034904 (2010).
[CrossRef]

Barrett, R.

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

Baruchel, J.

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyts, J. P. Guigay, and M. Schlenker, “Holotomography: quantitative phase tomography with micrometerresolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).
[CrossRef]

P. Cloetens, M. Pateyron-Salom, J. Y. Buffire, G. Peix, J. Baruchel, F. Peyrin, and M. Schlenker, “Observation of microstructure and damage in materials by phase sensitive radiography and tomography,” J. Appl. Phys. 81, 5878–5886 (1997).
[CrossRef]

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

Beltran, M. A.

M. A. Beltran, D. M. Paganin, K. W. Siu, A. Fouras, S. B. Hooper, D. H. Reser, and M. J. Kitchen, “Interface-specific x-ray phase retrieval tomography of complex biological organs,” Phys. Med. Biol. 56, 7353–7369 (2011).
[CrossRef]

M. A. Beltran, D. M. Paganin, K. Uesugi, and M. J. Kitchen, “2D and 3D x-ray phase retrieval of multi-material objects using a single defocus distance,” Opt. Express 18, 6423–6436 (2010).
[CrossRef]

Bengton, S.

E. M. Friis, P. R. Crane, K. R. Pedersen, S. Bengton, P. C. J. Donoghue, G. W. Grimm, and M. Stampanoni, “Phase-contrast x-ray microtomography links cretaceous seeds with gnetales and bennettitales,” Nature 450, 549–552 (2007).
[CrossRef]

Bertrand, A.

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R. Betemps, U. Frommherz, P. Bhler, D. Meister, M. Lange, and R. Abela, “Trends in synchrotron-based tomographic imaging: the SLS experience,” Proc. SPIE 6318, 63180M (2006).
[CrossRef]

Betemps, R.

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R. Betemps, U. Frommherz, P. Bhler, D. Meister, M. Lange, and R. Abela, “Trends in synchrotron-based tomographic imaging: the SLS experience,” Proc. SPIE 6318, 63180M (2006).
[CrossRef]

Bhler, P.

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R. Betemps, U. Frommherz, P. Bhler, D. Meister, M. Lange, and R. Abela, “Trends in synchrotron-based tomographic imaging: the SLS experience,” Proc. SPIE 6318, 63180M (2006).
[CrossRef]

Boone, M. N.

M. N. Boone, Y. De Witte, M. Dierick, A. Almeida, and L. Van Hoorebeke, “Improved signal-to-noise ratio in laboratory-based phase contrast tomography,” Microsc. Microanal. 18, 399–405 (2012).
[CrossRef]

M. N. Boone, J. Vlassenbroeck, S. Peetermans, D. Van Loo, M. Dierick, and L. Van Hoorebeke, “Secondary radiation in transmission-type x-ray tubes: simulation, practical issues and solution in the context of x-ray microtomography,” Nucl. Instrum. Methods Phys. Res. Sect. A 661, 7–12 (2012).
[CrossRef]

A. Almeida, S. Possemiers, M. N. Boone, T. De Beer, T. Quinten, L. Van Hoorebeke, J.-P. Remon, and C. Vervaet, “Ethylene vinyl acetate as matrix for oral sustained release dosage forms produced via hot-melt extrusion,” Eur. J. Pharm. Biopharm. 77, 297–305 (2011).
[CrossRef]

M. N. Boone, Y. De Witte, M. Dierick, J. Van den Bulcke, J. Vlassenbroeck, and L. Van Hoorebeke, “Practical use of the modified Bronnikov algorithm in micro-CT,” Nucl. Instrum. Methods Phys. Res. Sect. B 267, 1182–1186 (2009).
[CrossRef]

Y. De Witte, M. N. Boone, J. Vlassenbroeck, M. Dierick, and L. Van Hoorebeke, “Bronnikov-aided correction for x-ray computed tomography,” J. Opt. Soc. Am. A 26, 890–894 (2009).
[CrossRef]

H. Derluyn, M. Griffa, D. Mannes, I. Jerjen, J. Dewanckele, P. Vontobel, A. Sheppard, M. N. Boone, D. Derome, V. Cnudde, E. Lehmann, and J. Carmeliet, “Probing salt crystallization damage mechanisms in porous limestone with neutron radiography and x-ray tomography,” in 5th International Building Physics Conference (2012), pp. 95–102.

Bronnikov, A. V.

A. V. Bronnikov, “Phase-contrast CT: fundamental theorem and fast image reconstruction algorithms,” Proc. SPIE 6318, 63180Q (2006).
[CrossRef]

A. V. Bronnikov, “Theory of quantitative phase-contrast computed tomography,” J. Opt. Soc. Am. A 19, 472–480 (2002).
[CrossRef]

Bruder, J.

C. David, T. Weitkamp, F. Pfeiffer, A. Diaz, J. Bruder, T. Rohbeck, A. Groso, O. Bunk, M. Stampanoni, and P. Cloetens, “Hard x-ray phase imaging and tomography using a grating interferometer,” Spectrochim. Acta: Part B 62, 626–630 (2007).
[CrossRef]

Buffire, J. Y.

P. Cloetens, M. Pateyron-Salom, J. Y. Buffire, G. Peix, J. Baruchel, F. Peyrin, and M. Schlenker, “Observation of microstructure and damage in materials by phase sensitive radiography and tomography,” J. Appl. Phys. 81, 5878–5886 (1997).
[CrossRef]

Bunk, O.

C. David, T. Weitkamp, F. Pfeiffer, A. Diaz, J. Bruder, T. Rohbeck, A. Groso, O. Bunk, M. Stampanoni, and P. Cloetens, “Hard x-ray phase imaging and tomography using a grating interferometer,” Spectrochim. Acta: Part B 62, 626–630 (2007).
[CrossRef]

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance x-ray sources,” Nat. Phys. 2, 258–261 (2006).
[CrossRef]

Burvall, A.

Carmeliet, J.

D. Derome, M. Griffa, M. Koebel, and J. Carmeliet, “Hysteretic swelling of wood at cellular scale probed by phase-contrast x-ray tomography,” J. Struct. Biol. 173, 180–190 (2011).
[CrossRef]

H. Derluyn, M. Griffa, D. Mannes, I. Jerjen, J. Dewanckele, P. Vontobel, A. Sheppard, M. N. Boone, D. Derome, V. Cnudde, E. Lehmann, and J. Carmeliet, “Probing salt crystallization damage mechanisms in porous limestone with neutron radiography and x-ray tomography,” in 5th International Building Physics Conference (2012), pp. 95–102.

Castelli, E.

Chen, Q.

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R. Betemps, U. Frommherz, P. Bhler, D. Meister, M. Lange, and R. Abela, “Trends in synchrotron-based tomographic imaging: the SLS experience,” Proc. SPIE 6318, 63180M (2006).
[CrossRef]

Chen, R. C.

Cloetens, P.

M. Langer, P. Cloetens, J. P. Guigay, and F. Peyrin, “Quantitative comparison of direct phase retrieval algorithms in in-line phase tomography,” Med. Phys. 35, 4556–4566 (2008).
[CrossRef]

C. David, T. Weitkamp, F. Pfeiffer, A. Diaz, J. Bruder, T. Rohbeck, A. Groso, O. Bunk, M. Stampanoni, and P. Cloetens, “Hard x-ray phase imaging and tomography using a grating interferometer,” Spectrochim. Acta: Part B 62, 626–630 (2007).
[CrossRef]

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyts, J. P. Guigay, and M. Schlenker, “Holotomography: quantitative phase tomography with micrometerresolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).
[CrossRef]

P. Cloetens, M. Pateyron-Salom, J. Y. Buffire, G. Peix, J. Baruchel, F. Peyrin, and M. Schlenker, “Observation of microstructure and damage in materials by phase sensitive radiography and tomography,” J. Appl. Phys. 81, 5878–5886 (1997).
[CrossRef]

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

Cnudde, V.

B. Masschaele, V. Cnudde, M. Dierick, P. Jacobs, L. Van Hoorebeke, and J. Vlassenbroeck, “UGCT: new x-ray radiography and tomography facility,” Nucl. Instrum. Methods Phys. Res. Sect. A 580, 266–269 (2007).
[CrossRef]

J. Vlassenbroeck, M. Dierick, B. Masschaele, V. Cnudde, L. Van Hoorebeke, and P. Jacobs, “Software tools for quantification of x-ray microtomography at the UGCT,” Nucl. Instrum. Methods Phys. Res.: Sect. A 580, 442–445 (2007).
[CrossRef]

H. Derluyn, M. Griffa, D. Mannes, I. Jerjen, J. Dewanckele, P. Vontobel, A. Sheppard, M. N. Boone, D. Derome, V. Cnudde, E. Lehmann, and J. Carmeliet, “Probing salt crystallization damage mechanisms in porous limestone with neutron radiography and x-ray tomography,” in 5th International Building Physics Conference (2012), pp. 95–102.

Crane, P. R.

E. M. Friis, P. R. Crane, K. R. Pedersen, S. Bengton, P. C. J. Donoghue, G. W. Grimm, and M. Stampanoni, “Phase-contrast x-ray microtomography links cretaceous seeds with gnetales and bennettitales,” Nature 450, 549–552 (2007).
[CrossRef]

David, C.

S. A. McDonald, F. Marone, C. Hintermuller, G. Mikuljan, C. David, F. Pfeiffer, and M. Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synchrotron Radiat. 16, 562–572 (2009).
[CrossRef]

C. David, T. Weitkamp, F. Pfeiffer, A. Diaz, J. Bruder, T. Rohbeck, A. Groso, O. Bunk, M. Stampanoni, and P. Cloetens, “Hard x-ray phase imaging and tomography using a grating interferometer,” Spectrochim. Acta: Part B 62, 626–630 (2007).
[CrossRef]

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance x-ray sources,” Nat. Phys. 2, 258–261 (2006).
[CrossRef]

Davis, T. J.

De Beer, T.

A. Almeida, S. Possemiers, M. N. Boone, T. De Beer, T. Quinten, L. Van Hoorebeke, J.-P. Remon, and C. Vervaet, “Ethylene vinyl acetate as matrix for oral sustained release dosage forms produced via hot-melt extrusion,” Eur. J. Pharm. Biopharm. 77, 297–305 (2011).
[CrossRef]

De Witte, Y.

M. N. Boone, Y. De Witte, M. Dierick, A. Almeida, and L. Van Hoorebeke, “Improved signal-to-noise ratio in laboratory-based phase contrast tomography,” Microsc. Microanal. 18, 399–405 (2012).
[CrossRef]

M. N. Boone, Y. De Witte, M. Dierick, J. Van den Bulcke, J. Vlassenbroeck, and L. Van Hoorebeke, “Practical use of the modified Bronnikov algorithm in micro-CT,” Nucl. Instrum. Methods Phys. Res. Sect. B 267, 1182–1186 (2009).
[CrossRef]

Y. De Witte, M. N. Boone, J. Vlassenbroeck, M. Dierick, and L. Van Hoorebeke, “Bronnikov-aided correction for x-ray computed tomography,” J. Opt. Soc. Am. A 26, 890–894 (2009).
[CrossRef]

Y. De Witte, “Improved and practically feasible reconstruction methods for high resolution x-ray tomography,” Ph.D. thesis (Ghent University, 2010).

Derdak, Z.

C. M. Laperle, T. J. Hamilton, P. Wintermeyer, E. J. Walker, D. Shi, M. A. Anastasio, Z. Derdak, J. R. Wands, G. Diebold, and C. Rose-Petruck, “Low density contrast agents for x-ray phase contrast imaging: the use of ambient air for x-ray angiography of excised murine liver tissue,” Phys. Med. Biol. 53, 6911–6923 (2008).
[CrossRef]

Derluyn, H.

H. Derluyn, M. Griffa, D. Mannes, I. Jerjen, J. Dewanckele, P. Vontobel, A. Sheppard, M. N. Boone, D. Derome, V. Cnudde, E. Lehmann, and J. Carmeliet, “Probing salt crystallization damage mechanisms in porous limestone with neutron radiography and x-ray tomography,” in 5th International Building Physics Conference (2012), pp. 95–102.

Derome, D.

D. Derome, M. Griffa, M. Koebel, and J. Carmeliet, “Hysteretic swelling of wood at cellular scale probed by phase-contrast x-ray tomography,” J. Struct. Biol. 173, 180–190 (2011).
[CrossRef]

H. Derluyn, M. Griffa, D. Mannes, I. Jerjen, J. Dewanckele, P. Vontobel, A. Sheppard, M. N. Boone, D. Derome, V. Cnudde, E. Lehmann, and J. Carmeliet, “Probing salt crystallization damage mechanisms in porous limestone with neutron radiography and x-ray tomography,” in 5th International Building Physics Conference (2012), pp. 95–102.

Dewanckele, J.

H. Derluyn, M. Griffa, D. Mannes, I. Jerjen, J. Dewanckele, P. Vontobel, A. Sheppard, M. N. Boone, D. Derome, V. Cnudde, E. Lehmann, and J. Carmeliet, “Probing salt crystallization damage mechanisms in porous limestone with neutron radiography and x-ray tomography,” in 5th International Building Physics Conference (2012), pp. 95–102.

Diaz, A.

C. David, T. Weitkamp, F. Pfeiffer, A. Diaz, J. Bruder, T. Rohbeck, A. Groso, O. Bunk, M. Stampanoni, and P. Cloetens, “Hard x-ray phase imaging and tomography using a grating interferometer,” Spectrochim. Acta: Part B 62, 626–630 (2007).
[CrossRef]

Diebold, G.

C. M. Laperle, T. J. Hamilton, P. Wintermeyer, E. J. Walker, D. Shi, M. A. Anastasio, Z. Derdak, J. R. Wands, G. Diebold, and C. Rose-Petruck, “Low density contrast agents for x-ray phase contrast imaging: the use of ambient air for x-ray angiography of excised murine liver tissue,” Phys. Med. Biol. 53, 6911–6923 (2008).
[CrossRef]

Dierick, M.

M. N. Boone, Y. De Witte, M. Dierick, A. Almeida, and L. Van Hoorebeke, “Improved signal-to-noise ratio in laboratory-based phase contrast tomography,” Microsc. Microanal. 18, 399–405 (2012).
[CrossRef]

M. N. Boone, J. Vlassenbroeck, S. Peetermans, D. Van Loo, M. Dierick, and L. Van Hoorebeke, “Secondary radiation in transmission-type x-ray tubes: simulation, practical issues and solution in the context of x-ray microtomography,” Nucl. Instrum. Methods Phys. Res. Sect. A 661, 7–12 (2012).
[CrossRef]

M. N. Boone, Y. De Witte, M. Dierick, J. Van den Bulcke, J. Vlassenbroeck, and L. Van Hoorebeke, “Practical use of the modified Bronnikov algorithm in micro-CT,” Nucl. Instrum. Methods Phys. Res. Sect. B 267, 1182–1186 (2009).
[CrossRef]

Y. De Witte, M. N. Boone, J. Vlassenbroeck, M. Dierick, and L. Van Hoorebeke, “Bronnikov-aided correction for x-ray computed tomography,” J. Opt. Soc. Am. A 26, 890–894 (2009).
[CrossRef]

B. Masschaele, V. Cnudde, M. Dierick, P. Jacobs, L. Van Hoorebeke, and J. Vlassenbroeck, “UGCT: new x-ray radiography and tomography facility,” Nucl. Instrum. Methods Phys. Res. Sect. A 580, 266–269 (2007).
[CrossRef]

J. Vlassenbroeck, M. Dierick, B. Masschaele, V. Cnudde, L. Van Hoorebeke, and P. Jacobs, “Software tools for quantification of x-ray microtomography at the UGCT,” Nucl. Instrum. Methods Phys. Res.: Sect. A 580, 442–445 (2007).
[CrossRef]

Donoghue, P. C. J.

E. M. Friis, P. R. Crane, K. R. Pedersen, S. Bengton, P. C. J. Donoghue, G. W. Grimm, and M. Stampanoni, “Phase-contrast x-ray microtomography links cretaceous seeds with gnetales and bennettitales,” Nature 450, 549–552 (2007).
[CrossRef]

Dreossi, D.

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, 3617–3627 (2005).
[CrossRef]

Dual, J.

P. Trtik, J. Dual, D. Keunecke, D. Mannes, P. Niemz, P. Stähli, A. Kaestner, A. Groso, and M. Stampanoni, “3d imaging of microstructure of spruce wood,” J. Struct. Biol. 159, 46–55 (2007).
[CrossRef]

Estiaghi, N.

B. D. Arhatari, W. P. Gates, N. Estiaghi, and A. G. Peele, “Phase retrieval tomography in the presence of noise,” J. Appl. Phys. 107, 034904 (2010).
[CrossRef]

Fouras, A.

M. A. Beltran, D. M. Paganin, K. W. Siu, A. Fouras, S. B. Hooper, D. H. Reser, and M. J. Kitchen, “Interface-specific x-ray phase retrieval tomography of complex biological organs,” Phys. Med. Biol. 56, 7353–7369 (2011).
[CrossRef]

Friis, E. M.

E. M. Friis, P. R. Crane, K. R. Pedersen, S. Bengton, P. C. J. Donoghue, G. W. Grimm, and M. Stampanoni, “Phase-contrast x-ray microtomography links cretaceous seeds with gnetales and bennettitales,” Nature 450, 549–552 (2007).
[CrossRef]

Frommherz, U.

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R. Betemps, U. Frommherz, P. Bhler, D. Meister, M. Lange, and R. Abela, “Trends in synchrotron-based tomographic imaging: the SLS experience,” Proc. SPIE 6318, 63180M (2006).
[CrossRef]

Gao, D.

A. Pogany, D. Gao, and S. W. Wilkins, “Contrast and resolution in imaging with a microfocus x-ray source,” Rev. Sci. Instrum. 68, 2774–2782 (1997).
[CrossRef]

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard x-rays,” Nature 384, 335–338 (1996).
[CrossRef]

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

Gates, W. P.

B. D. Arhatari, W. P. Gates, N. Estiaghi, and A. G. Peele, “Phase retrieval tomography in the presence of noise,” J. Appl. Phys. 107, 034904 (2010).
[CrossRef]

Griffa, M.

D. Derome, M. Griffa, M. Koebel, and J. Carmeliet, “Hysteretic swelling of wood at cellular scale probed by phase-contrast x-ray tomography,” J. Struct. Biol. 173, 180–190 (2011).
[CrossRef]

H. Derluyn, M. Griffa, D. Mannes, I. Jerjen, J. Dewanckele, P. Vontobel, A. Sheppard, M. N. Boone, D. Derome, V. Cnudde, E. Lehmann, and J. Carmeliet, “Probing salt crystallization damage mechanisms in porous limestone with neutron radiography and x-ray tomography,” in 5th International Building Physics Conference (2012), pp. 95–102.

Grimm, G. W.

E. M. Friis, P. R. Crane, K. R. Pedersen, S. Bengton, P. C. J. Donoghue, G. W. Grimm, and M. Stampanoni, “Phase-contrast x-ray microtomography links cretaceous seeds with gnetales and bennettitales,” Nature 450, 549–552 (2007).
[CrossRef]

Groso, A.

C. David, T. Weitkamp, F. Pfeiffer, A. Diaz, J. Bruder, T. Rohbeck, A. Groso, O. Bunk, M. Stampanoni, and P. Cloetens, “Hard x-ray phase imaging and tomography using a grating interferometer,” Spectrochim. Acta: Part B 62, 626–630 (2007).
[CrossRef]

P. Trtik, J. Dual, D. Keunecke, D. Mannes, P. Niemz, P. Stähli, A. Kaestner, A. Groso, and M. Stampanoni, “3d imaging of microstructure of spruce wood,” J. Struct. Biol. 159, 46–55 (2007).
[CrossRef]

A. Groso, R. Abela, and M. Stampanoni, “Implementation of a fast method for high resolution phase contrast tomography,” Opt. Express 14, 8103–8110 (2006).
[CrossRef]

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R. Betemps, U. Frommherz, P. Bhler, D. Meister, M. Lange, and R. Abela, “Trends in synchrotron-based tomographic imaging: the SLS experience,” Proc. SPIE 6318, 63180M (2006).
[CrossRef]

Guigay, J. P.

M. Langer, P. Cloetens, J. P. Guigay, and F. Peyrin, “Quantitative comparison of direct phase retrieval algorithms in in-line phase tomography,” Med. Phys. 35, 4556–4566 (2008).
[CrossRef]

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyts, J. P. Guigay, and M. Schlenker, “Holotomography: quantitative phase tomography with micrometerresolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).
[CrossRef]

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

Gureyev, T. E.

T. E. Gureyev, T. J. Davis, A. Pogany, S. C. Mayo, and S. W. Wilkins, “Optical phase retrieval by use of first Born-and-Rytov-type approximations,” Appl. Opt. 43, 2418–2430 (2004).
[CrossRef]

S. C. Mayo, T. J. Davis, T. E. Gureyev, P. R. Miller, D. M. Paganin, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “X-ray phase-contrast microscopy and microtomography,” Opt. Express 11, 2289–2302 (2003).
[CrossRef]

D. M. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206, 33–40 (2002).
[CrossRef]

T. E. Gureyev and S. W. Wilkins, “On x-ray phase imaging with a point source,” J. Opt. Soc. Am. A 15, 579–585 (1998).
[CrossRef]

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard x-rays,” Nature 384, 335–338 (1996).
[CrossRef]

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

Haas, D.

T. Weitkamp, D. Haas, D. Wegrzynek, and A. Rack, “Ankaphase: software for single-distance phase retrieval from inline x-ray phase-contrast radiographs,” J. Synchrotron. Radiat. 18, 617–629 (2011).
[CrossRef]

Hamilton, T. J.

C. M. Laperle, T. J. Hamilton, P. Wintermeyer, E. J. Walker, D. Shi, M. A. Anastasio, Z. Derdak, J. R. Wands, G. Diebold, and C. Rose-Petruck, “Low density contrast agents for x-ray phase contrast imaging: the use of ambient air for x-ray angiography of excised murine liver tissue,” Phys. Med. Biol. 53, 6911–6923 (2008).
[CrossRef]

Henein, S.

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R. Betemps, U. Frommherz, P. Bhler, D. Meister, M. Lange, and R. Abela, “Trends in synchrotron-based tomographic imaging: the SLS experience,” Proc. SPIE 6318, 63180M (2006).
[CrossRef]

Hertz, H. M.

Hintermuller, C.

F. Marone, C. Hintermuller, S. A. McDonald, R. Abela, G. Mikuljan, A. Isenegger, and M. Stampanoni, “X-ray tomographic microscopy at TOMCAT,” J. Phys.: Conf. Ser. 186, 012042 (2009).
[CrossRef]

S. A. McDonald, F. Marone, C. Hintermuller, G. Mikuljan, C. David, F. Pfeiffer, and M. Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synchrotron Radiat. 16, 562–572 (2009).
[CrossRef]

Hooper, S. B.

M. A. Beltran, D. M. Paganin, K. W. Siu, A. Fouras, S. B. Hooper, D. H. Reser, and M. J. Kitchen, “Interface-specific x-ray phase retrieval tomography of complex biological organs,” Phys. Med. Biol. 56, 7353–7369 (2011).
[CrossRef]

Isenegger, A.

F. Marone, C. Hintermuller, S. A. McDonald, R. Abela, G. Mikuljan, A. Isenegger, and M. Stampanoni, “X-ray tomographic microscopy at TOMCAT,” J. Phys.: Conf. Ser. 186, 012042 (2009).
[CrossRef]

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R. Betemps, U. Frommherz, P. Bhler, D. Meister, M. Lange, and R. Abela, “Trends in synchrotron-based tomographic imaging: the SLS experience,” Proc. SPIE 6318, 63180M (2006).
[CrossRef]

Jacobs, P.

J. Vlassenbroeck, M. Dierick, B. Masschaele, V. Cnudde, L. Van Hoorebeke, and P. Jacobs, “Software tools for quantification of x-ray microtomography at the UGCT,” Nucl. Instrum. Methods Phys. Res.: Sect. A 580, 442–445 (2007).
[CrossRef]

B. Masschaele, V. Cnudde, M. Dierick, P. Jacobs, L. Van Hoorebeke, and J. Vlassenbroeck, “UGCT: new x-ray radiography and tomography facility,” Nucl. Instrum. Methods Phys. Res. Sect. A 580, 266–269 (2007).
[CrossRef]

Jerjen, I.

H. Derluyn, M. Griffa, D. Mannes, I. Jerjen, J. Dewanckele, P. Vontobel, A. Sheppard, M. N. Boone, D. Derome, V. Cnudde, E. Lehmann, and J. Carmeliet, “Probing salt crystallization damage mechanisms in porous limestone with neutron radiography and x-ray tomography,” in 5th International Building Physics Conference (2012), pp. 95–102.

Kaestner, A.

P. Trtik, J. Dual, D. Keunecke, D. Mannes, P. Niemz, P. Stähli, A. Kaestner, A. Groso, and M. Stampanoni, “3d imaging of microstructure of spruce wood,” J. Struct. Biol. 159, 46–55 (2007).
[CrossRef]

Keunecke, D.

P. Trtik, J. Dual, D. Keunecke, D. Mannes, P. Niemz, P. Stähli, A. Kaestner, A. Groso, and M. Stampanoni, “3d imaging of microstructure of spruce wood,” J. Struct. Biol. 159, 46–55 (2007).
[CrossRef]

Kitchen, M. J.

M. A. Beltran, D. M. Paganin, K. W. Siu, A. Fouras, S. B. Hooper, D. H. Reser, and M. J. Kitchen, “Interface-specific x-ray phase retrieval tomography of complex biological organs,” Phys. Med. Biol. 56, 7353–7369 (2011).
[CrossRef]

M. A. Beltran, D. M. Paganin, K. Uesugi, and M. J. Kitchen, “2D and 3D x-ray phase retrieval of multi-material objects using a single defocus distance,” Opt. Express 18, 6423–6436 (2010).
[CrossRef]

Koebel, M.

D. Derome, M. Griffa, M. Koebel, and J. Carmeliet, “Hysteretic swelling of wood at cellular scale probed by phase-contrast x-ray tomography,” J. Struct. Biol. 173, 180–190 (2011).
[CrossRef]

Lange, M.

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R. Betemps, U. Frommherz, P. Bhler, D. Meister, M. Lange, and R. Abela, “Trends in synchrotron-based tomographic imaging: the SLS experience,” Proc. SPIE 6318, 63180M (2006).
[CrossRef]

Langer, M.

M. Langer, P. Cloetens, J. P. Guigay, and F. Peyrin, “Quantitative comparison of direct phase retrieval algorithms in in-line phase tomography,” Med. Phys. 35, 4556–4566 (2008).
[CrossRef]

Laperle, C. M.

C. M. Laperle, T. J. Hamilton, P. Wintermeyer, E. J. Walker, D. Shi, M. A. Anastasio, Z. Derdak, J. R. Wands, G. Diebold, and C. Rose-Petruck, “Low density contrast agents for x-ray phase contrast imaging: the use of ambient air for x-ray angiography of excised murine liver tissue,” Phys. Med. Biol. 53, 6911–6923 (2008).
[CrossRef]

Larsson, D. H.

Lehmann, E.

H. Derluyn, M. Griffa, D. Mannes, I. Jerjen, J. Dewanckele, P. Vontobel, A. Sheppard, M. N. Boone, D. Derome, V. Cnudde, E. Lehmann, and J. Carmeliet, “Probing salt crystallization damage mechanisms in porous limestone with neutron radiography and x-ray tomography,” in 5th International Building Physics Conference (2012), pp. 95–102.

Liu, H.

X. Wu, H. Liu, and A. Yan, “X-ray phase-attenuation duality and phase retrieval,” Opt. Lett. 30, 379–381 (2005).
[CrossRef]

X. Wu and H. Liu, “A general theoretical formalism for x-ray phase contrast imaging,” J. X-ray Sci. Technol. 11, 33–42 (2003).

Longo, R.

Ludwig, W.

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyts, J. P. Guigay, and M. Schlenker, “Holotomography: quantitative phase tomography with micrometerresolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).
[CrossRef]

Lundstrm, U.

Mannes, D.

P. Trtik, J. Dual, D. Keunecke, D. Mannes, P. Niemz, P. Stähli, A. Kaestner, A. Groso, and M. Stampanoni, “3d imaging of microstructure of spruce wood,” J. Struct. Biol. 159, 46–55 (2007).
[CrossRef]

H. Derluyn, M. Griffa, D. Mannes, I. Jerjen, J. Dewanckele, P. Vontobel, A. Sheppard, M. N. Boone, D. Derome, V. Cnudde, E. Lehmann, and J. Carmeliet, “Probing salt crystallization damage mechanisms in porous limestone with neutron radiography and x-ray tomography,” in 5th International Building Physics Conference (2012), pp. 95–102.

Marone, F.

F. Marone, C. Hintermuller, S. A. McDonald, R. Abela, G. Mikuljan, A. Isenegger, and M. Stampanoni, “X-ray tomographic microscopy at TOMCAT,” J. Phys.: Conf. Ser. 186, 012042 (2009).
[CrossRef]

S. A. McDonald, F. Marone, C. Hintermuller, G. Mikuljan, C. David, F. Pfeiffer, and M. Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synchrotron Radiat. 16, 562–572 (2009).
[CrossRef]

Masschaele, B.

J. Vlassenbroeck, M. Dierick, B. Masschaele, V. Cnudde, L. Van Hoorebeke, and P. Jacobs, “Software tools for quantification of x-ray microtomography at the UGCT,” Nucl. Instrum. Methods Phys. Res.: Sect. A 580, 442–445 (2007).
[CrossRef]

B. Masschaele, V. Cnudde, M. Dierick, P. Jacobs, L. Van Hoorebeke, and J. Vlassenbroeck, “UGCT: new x-ray radiography and tomography facility,” Nucl. Instrum. Methods Phys. Res. Sect. A 580, 266–269 (2007).
[CrossRef]

Mayo, S. C.

McDonald, S. A.

S. A. McDonald, F. Marone, C. Hintermuller, G. Mikuljan, C. David, F. Pfeiffer, and M. Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synchrotron Radiat. 16, 562–572 (2009).
[CrossRef]

F. Marone, C. Hintermuller, S. A. McDonald, R. Abela, G. Mikuljan, A. Isenegger, and M. Stampanoni, “X-ray tomographic microscopy at TOMCAT,” J. Phys.: Conf. Ser. 186, 012042 (2009).
[CrossRef]

Meister, D.

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R. Betemps, U. Frommherz, P. Bhler, D. Meister, M. Lange, and R. Abela, “Trends in synchrotron-based tomographic imaging: the SLS experience,” Proc. SPIE 6318, 63180M (2006).
[CrossRef]

Mikuljan, G.

F. Marone, C. Hintermuller, S. A. McDonald, R. Abela, G. Mikuljan, A. Isenegger, and M. Stampanoni, “X-ray tomographic microscopy at TOMCAT,” J. Phys.: Conf. Ser. 186, 012042 (2009).
[CrossRef]

S. A. McDonald, F. Marone, C. Hintermuller, G. Mikuljan, C. David, F. Pfeiffer, and M. Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synchrotron Radiat. 16, 562–572 (2009).
[CrossRef]

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R. Betemps, U. Frommherz, P. Bhler, D. Meister, M. Lange, and R. Abela, “Trends in synchrotron-based tomographic imaging: the SLS experience,” Proc. SPIE 6318, 63180M (2006).
[CrossRef]

Miller, P. R.

S. C. Mayo, T. J. Davis, T. E. Gureyev, P. R. Miller, D. M. Paganin, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “X-ray phase-contrast microscopy and microtomography,” Opt. Express 11, 2289–2302 (2003).
[CrossRef]

D. M. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206, 33–40 (2002).
[CrossRef]

Niemz, P.

P. Trtik, J. Dual, D. Keunecke, D. Mannes, P. Niemz, P. Stähli, A. Kaestner, A. Groso, and M. Stampanoni, “3d imaging of microstructure of spruce wood,” J. Struct. Biol. 159, 46–55 (2007).
[CrossRef]

Olivo, 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, 3617–3627 (2005).
[CrossRef]

Paganin, D. M.

M. A. Beltran, D. M. Paganin, K. W. Siu, A. Fouras, S. B. Hooper, D. H. Reser, and M. J. Kitchen, “Interface-specific x-ray phase retrieval tomography of complex biological organs,” Phys. Med. Biol. 56, 7353–7369 (2011).
[CrossRef]

M. A. Beltran, D. M. Paganin, K. Uesugi, and M. J. Kitchen, “2D and 3D x-ray phase retrieval of multi-material objects using a single defocus distance,” Opt. Express 18, 6423–6436 (2010).
[CrossRef]

S. C. Mayo, T. J. Davis, T. E. Gureyev, P. R. Miller, D. M. Paganin, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “X-ray phase-contrast microscopy and microtomography,” Opt. Express 11, 2289–2302 (2003).
[CrossRef]

D. M. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206, 33–40 (2002).
[CrossRef]

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, 3617–3627 (2005).
[CrossRef]

Pateyron-Salom, M.

P. Cloetens, M. Pateyron-Salom, J. Y. Buffire, G. Peix, J. Baruchel, F. Peyrin, and M. Schlenker, “Observation of microstructure and damage in materials by phase sensitive radiography and tomography,” J. Appl. Phys. 81, 5878–5886 (1997).
[CrossRef]

Pedersen, K. R.

E. M. Friis, P. R. Crane, K. R. Pedersen, S. Bengton, P. C. J. Donoghue, G. W. Grimm, and M. Stampanoni, “Phase-contrast x-ray microtomography links cretaceous seeds with gnetales and bennettitales,” Nature 450, 549–552 (2007).
[CrossRef]

Peele, A. G.

B. D. Arhatari, W. P. Gates, N. Estiaghi, and A. G. Peele, “Phase retrieval tomography in the presence of noise,” J. Appl. Phys. 107, 034904 (2010).
[CrossRef]

Peetermans, S.

M. N. Boone, J. Vlassenbroeck, S. Peetermans, D. Van Loo, M. Dierick, and L. Van Hoorebeke, “Secondary radiation in transmission-type x-ray tubes: simulation, practical issues and solution in the context of x-ray microtomography,” Nucl. Instrum. Methods Phys. Res. Sect. A 661, 7–12 (2012).
[CrossRef]

Peix, G.

P. Cloetens, M. Pateyron-Salom, J. Y. Buffire, G. Peix, J. Baruchel, F. Peyrin, and M. Schlenker, “Observation of microstructure and damage in materials by phase sensitive radiography and tomography,” J. Appl. Phys. 81, 5878–5886 (1997).
[CrossRef]

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, 3617–3627 (2005).
[CrossRef]

Peyrin, F.

M. Langer, P. Cloetens, J. P. Guigay, and F. Peyrin, “Quantitative comparison of direct phase retrieval algorithms in in-line phase tomography,” Med. Phys. 35, 4556–4566 (2008).
[CrossRef]

P. Cloetens, M. Pateyron-Salom, J. Y. Buffire, G. Peix, J. Baruchel, F. Peyrin, and M. Schlenker, “Observation of microstructure and damage in materials by phase sensitive radiography and tomography,” J. Appl. Phys. 81, 5878–5886 (1997).
[CrossRef]

Pfeiffer, F.

S. A. McDonald, F. Marone, C. Hintermuller, G. Mikuljan, C. David, F. Pfeiffer, and M. Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synchrotron Radiat. 16, 562–572 (2009).
[CrossRef]

C. David, T. Weitkamp, F. Pfeiffer, A. Diaz, J. Bruder, T. Rohbeck, A. Groso, O. Bunk, M. Stampanoni, and P. Cloetens, “Hard x-ray phase imaging and tomography using a grating interferometer,” Spectrochim. Acta: Part B 62, 626–630 (2007).
[CrossRef]

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance x-ray sources,” Nat. Phys. 2, 258–261 (2006).
[CrossRef]

Pogany, A.

T. E. Gureyev, T. J. Davis, A. Pogany, S. C. Mayo, and S. W. Wilkins, “Optical phase retrieval by use of first Born-and-Rytov-type approximations,” Appl. Opt. 43, 2418–2430 (2004).
[CrossRef]

S. C. Mayo, T. J. Davis, T. E. Gureyev, P. R. Miller, D. M. Paganin, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “X-ray phase-contrast microscopy and microtomography,” Opt. Express 11, 2289–2302 (2003).
[CrossRef]

A. Pogany, D. Gao, and S. W. Wilkins, “Contrast and resolution in imaging with a microfocus x-ray source,” Rev. Sci. Instrum. 68, 2774–2782 (1997).
[CrossRef]

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard x-rays,” Nature 384, 335–338 (1996).
[CrossRef]

Possemiers, S.

A. Almeida, S. Possemiers, M. N. Boone, T. De Beer, T. Quinten, L. Van Hoorebeke, J.-P. Remon, and C. Vervaet, “Ethylene vinyl acetate as matrix for oral sustained release dosage forms produced via hot-melt extrusion,” Eur. J. Pharm. Biopharm. 77, 297–305 (2011).
[CrossRef]

Quinten, T.

A. Almeida, S. Possemiers, M. N. Boone, T. De Beer, T. Quinten, L. Van Hoorebeke, J.-P. Remon, and C. Vervaet, “Ethylene vinyl acetate as matrix for oral sustained release dosage forms produced via hot-melt extrusion,” Eur. J. Pharm. Biopharm. 77, 297–305 (2011).
[CrossRef]

Rack, A.

T. Weitkamp, D. Haas, D. Wegrzynek, and A. Rack, “Ankaphase: software for single-distance phase retrieval from inline x-ray phase-contrast radiographs,” J. Synchrotron. Radiat. 18, 617–629 (2011).
[CrossRef]

Remon, J.-P.

A. Almeida, S. Possemiers, M. N. Boone, T. De Beer, T. Quinten, L. Van Hoorebeke, J.-P. Remon, and C. Vervaet, “Ethylene vinyl acetate as matrix for oral sustained release dosage forms produced via hot-melt extrusion,” Eur. J. Pharm. Biopharm. 77, 297–305 (2011).
[CrossRef]

Reser, D. H.

M. A. Beltran, D. M. Paganin, K. W. Siu, A. Fouras, S. B. Hooper, D. H. Reser, and M. J. Kitchen, “Interface-specific x-ray phase retrieval tomography of complex biological organs,” Phys. Med. Biol. 56, 7353–7369 (2011).
[CrossRef]

Rigon, L.

R. C. Chen, H. L. Xie, L. Rigon, R. Longo, E. Castelli, and T. Q. Xiao, “Phase retrieval in quantitative x-ray microtomography with a single sample-to-detector distance,” Opt. Lett. 36, 1719–1721 (2011).
[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, 3617–3627 (2005).
[CrossRef]

Rohbeck, T.

C. David, T. Weitkamp, F. Pfeiffer, A. Diaz, J. Bruder, T. Rohbeck, A. Groso, O. Bunk, M. Stampanoni, and P. Cloetens, “Hard x-ray phase imaging and tomography using a grating interferometer,” Spectrochim. Acta: Part B 62, 626–630 (2007).
[CrossRef]

Rose-Petruck, C.

C. M. Laperle, T. J. Hamilton, P. Wintermeyer, E. J. Walker, D. Shi, M. A. Anastasio, Z. Derdak, J. R. Wands, G. Diebold, and C. Rose-Petruck, “Low density contrast agents for x-ray phase contrast imaging: the use of ambient air for x-ray angiography of excised murine liver tissue,” Phys. Med. Biol. 53, 6911–6923 (2008).
[CrossRef]

Schlenker, M.

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyts, J. P. Guigay, and M. Schlenker, “Holotomography: quantitative phase tomography with micrometerresolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).
[CrossRef]

P. Cloetens, M. Pateyron-Salom, J. Y. Buffire, G. Peix, J. Baruchel, F. Peyrin, and M. Schlenker, “Observation of microstructure and damage in materials by phase sensitive radiography and tomography,” J. Appl. Phys. 81, 5878–5886 (1997).
[CrossRef]

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

Sheppard, A.

H. Derluyn, M. Griffa, D. Mannes, I. Jerjen, J. Dewanckele, P. Vontobel, A. Sheppard, M. N. Boone, D. Derome, V. Cnudde, E. Lehmann, and J. Carmeliet, “Probing salt crystallization damage mechanisms in porous limestone with neutron radiography and x-ray tomography,” in 5th International Building Physics Conference (2012), pp. 95–102.

Shi, D.

C. M. Laperle, T. J. Hamilton, P. Wintermeyer, E. J. Walker, D. Shi, M. A. Anastasio, Z. Derdak, J. R. Wands, G. Diebold, and C. Rose-Petruck, “Low density contrast agents for x-ray phase contrast imaging: the use of ambient air for x-ray angiography of excised murine liver tissue,” Phys. Med. Biol. 53, 6911–6923 (2008).
[CrossRef]

Siu, K. W.

M. A. Beltran, D. M. Paganin, K. W. Siu, A. Fouras, S. B. Hooper, D. H. Reser, and M. J. Kitchen, “Interface-specific x-ray phase retrieval tomography of complex biological organs,” Phys. Med. Biol. 56, 7353–7369 (2011).
[CrossRef]

Smith, T. M.

P. Tafforeau and T. M. Smith, “Nondestructive imaging of hominoid dental microstructure using phase contrast x-ray synchrotron microtomography,” J. Hum. Evol. 54, 272–278 (2008).
[CrossRef]

Stähli, P.

P. Trtik, J. Dual, D. Keunecke, D. Mannes, P. Niemz, P. Stähli, A. Kaestner, A. Groso, and M. Stampanoni, “3d imaging of microstructure of spruce wood,” J. Struct. Biol. 159, 46–55 (2007).
[CrossRef]

Stampanoni, M.

F. Marone, C. Hintermuller, S. A. McDonald, R. Abela, G. Mikuljan, A. Isenegger, and M. Stampanoni, “X-ray tomographic microscopy at TOMCAT,” J. Phys.: Conf. Ser. 186, 012042 (2009).
[CrossRef]

S. A. McDonald, F. Marone, C. Hintermuller, G. Mikuljan, C. David, F. Pfeiffer, and M. Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synchrotron Radiat. 16, 562–572 (2009).
[CrossRef]

E. M. Friis, P. R. Crane, K. R. Pedersen, S. Bengton, P. C. J. Donoghue, G. W. Grimm, and M. Stampanoni, “Phase-contrast x-ray microtomography links cretaceous seeds with gnetales and bennettitales,” Nature 450, 549–552 (2007).
[CrossRef]

C. David, T. Weitkamp, F. Pfeiffer, A. Diaz, J. Bruder, T. Rohbeck, A. Groso, O. Bunk, M. Stampanoni, and P. Cloetens, “Hard x-ray phase imaging and tomography using a grating interferometer,” Spectrochim. Acta: Part B 62, 626–630 (2007).
[CrossRef]

P. Trtik, J. Dual, D. Keunecke, D. Mannes, P. Niemz, P. Stähli, A. Kaestner, A. Groso, and M. Stampanoni, “3d imaging of microstructure of spruce wood,” J. Struct. Biol. 159, 46–55 (2007).
[CrossRef]

A. Groso, R. Abela, and M. Stampanoni, “Implementation of a fast method for high resolution phase contrast tomography,” Opt. Express 14, 8103–8110 (2006).
[CrossRef]

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R. Betemps, U. Frommherz, P. Bhler, D. Meister, M. Lange, and R. Abela, “Trends in synchrotron-based tomographic imaging: the SLS experience,” Proc. SPIE 6318, 63180M (2006).
[CrossRef]

Stevenson, A. W.

S. C. Mayo, T. J. Davis, T. E. Gureyev, P. R. Miller, D. M. Paganin, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “X-ray phase-contrast microscopy and microtomography,” Opt. Express 11, 2289–2302 (2003).
[CrossRef]

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard x-rays,” Nature 384, 335–338 (1996).
[CrossRef]

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

Tafforeau, P.

P. Tafforeau and T. M. Smith, “Nondestructive imaging of hominoid dental microstructure using phase contrast x-ray synchrotron microtomography,” J. Hum. Evol. 54, 272–278 (2008).
[CrossRef]

Takman, P. A. C.

Teague, M. R.

Trtik, P.

P. Trtik, J. Dual, D. Keunecke, D. Mannes, P. Niemz, P. Stähli, A. Kaestner, A. Groso, and M. Stampanoni, “3d imaging of microstructure of spruce wood,” J. Struct. Biol. 159, 46–55 (2007).
[CrossRef]

Uesugi, K.

Van den Bulcke, J.

M. N. Boone, Y. De Witte, M. Dierick, J. Van den Bulcke, J. Vlassenbroeck, and L. Van Hoorebeke, “Practical use of the modified Bronnikov algorithm in micro-CT,” Nucl. Instrum. Methods Phys. Res. Sect. B 267, 1182–1186 (2009).
[CrossRef]

Van Dyck, D.

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyts, J. P. Guigay, and M. Schlenker, “Holotomography: quantitative phase tomography with micrometerresolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).
[CrossRef]

Van Hoorebeke, L.

M. N. Boone, Y. De Witte, M. Dierick, A. Almeida, and L. Van Hoorebeke, “Improved signal-to-noise ratio in laboratory-based phase contrast tomography,” Microsc. Microanal. 18, 399–405 (2012).
[CrossRef]

M. N. Boone, J. Vlassenbroeck, S. Peetermans, D. Van Loo, M. Dierick, and L. Van Hoorebeke, “Secondary radiation in transmission-type x-ray tubes: simulation, practical issues and solution in the context of x-ray microtomography,” Nucl. Instrum. Methods Phys. Res. Sect. A 661, 7–12 (2012).
[CrossRef]

A. Almeida, S. Possemiers, M. N. Boone, T. De Beer, T. Quinten, L. Van Hoorebeke, J.-P. Remon, and C. Vervaet, “Ethylene vinyl acetate as matrix for oral sustained release dosage forms produced via hot-melt extrusion,” Eur. J. Pharm. Biopharm. 77, 297–305 (2011).
[CrossRef]

Y. De Witte, M. N. Boone, J. Vlassenbroeck, M. Dierick, and L. Van Hoorebeke, “Bronnikov-aided correction for x-ray computed tomography,” J. Opt. Soc. Am. A 26, 890–894 (2009).
[CrossRef]

M. N. Boone, Y. De Witte, M. Dierick, J. Van den Bulcke, J. Vlassenbroeck, and L. Van Hoorebeke, “Practical use of the modified Bronnikov algorithm in micro-CT,” Nucl. Instrum. Methods Phys. Res. Sect. B 267, 1182–1186 (2009).
[CrossRef]

B. Masschaele, V. Cnudde, M. Dierick, P. Jacobs, L. Van Hoorebeke, and J. Vlassenbroeck, “UGCT: new x-ray radiography and tomography facility,” Nucl. Instrum. Methods Phys. Res. Sect. A 580, 266–269 (2007).
[CrossRef]

J. Vlassenbroeck, M. Dierick, B. Masschaele, V. Cnudde, L. Van Hoorebeke, and P. Jacobs, “Software tools for quantification of x-ray microtomography at the UGCT,” Nucl. Instrum. Methods Phys. Res.: Sect. A 580, 442–445 (2007).
[CrossRef]

Van Landuyts, J.

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyts, J. P. Guigay, and M. Schlenker, “Holotomography: quantitative phase tomography with micrometerresolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).
[CrossRef]

Van Loo, D.

M. N. Boone, J. Vlassenbroeck, S. Peetermans, D. Van Loo, M. Dierick, and L. Van Hoorebeke, “Secondary radiation in transmission-type x-ray tubes: simulation, practical issues and solution in the context of x-ray microtomography,” Nucl. Instrum. Methods Phys. Res. Sect. A 661, 7–12 (2012).
[CrossRef]

Vervaet, C.

A. Almeida, S. Possemiers, M. N. Boone, T. De Beer, T. Quinten, L. Van Hoorebeke, J.-P. Remon, and C. Vervaet, “Ethylene vinyl acetate as matrix for oral sustained release dosage forms produced via hot-melt extrusion,” Eur. J. Pharm. Biopharm. 77, 297–305 (2011).
[CrossRef]

Vlassenbroeck, J.

M. N. Boone, J. Vlassenbroeck, S. Peetermans, D. Van Loo, M. Dierick, and L. Van Hoorebeke, “Secondary radiation in transmission-type x-ray tubes: simulation, practical issues and solution in the context of x-ray microtomography,” Nucl. Instrum. Methods Phys. Res. Sect. A 661, 7–12 (2012).
[CrossRef]

Y. De Witte, M. N. Boone, J. Vlassenbroeck, M. Dierick, and L. Van Hoorebeke, “Bronnikov-aided correction for x-ray computed tomography,” J. Opt. Soc. Am. A 26, 890–894 (2009).
[CrossRef]

M. N. Boone, Y. De Witte, M. Dierick, J. Van den Bulcke, J. Vlassenbroeck, and L. Van Hoorebeke, “Practical use of the modified Bronnikov algorithm in micro-CT,” Nucl. Instrum. Methods Phys. Res. Sect. B 267, 1182–1186 (2009).
[CrossRef]

J. Vlassenbroeck, M. Dierick, B. Masschaele, V. Cnudde, L. Van Hoorebeke, and P. Jacobs, “Software tools for quantification of x-ray microtomography at the UGCT,” Nucl. Instrum. Methods Phys. Res.: Sect. A 580, 442–445 (2007).
[CrossRef]

B. Masschaele, V. Cnudde, M. Dierick, P. Jacobs, L. Van Hoorebeke, and J. Vlassenbroeck, “UGCT: new x-ray radiography and tomography facility,” Nucl. Instrum. Methods Phys. Res. Sect. A 580, 266–269 (2007).
[CrossRef]

Vontobel, P.

H. Derluyn, M. Griffa, D. Mannes, I. Jerjen, J. Dewanckele, P. Vontobel, A. Sheppard, M. N. Boone, D. Derome, V. Cnudde, E. Lehmann, and J. Carmeliet, “Probing salt crystallization damage mechanisms in porous limestone with neutron radiography and x-ray tomography,” in 5th International Building Physics Conference (2012), pp. 95–102.

Walker, E. J.

C. M. Laperle, T. J. Hamilton, P. Wintermeyer, E. J. Walker, D. Shi, M. A. Anastasio, Z. Derdak, J. R. Wands, G. Diebold, and C. Rose-Petruck, “Low density contrast agents for x-ray phase contrast imaging: the use of ambient air for x-ray angiography of excised murine liver tissue,” Phys. Med. Biol. 53, 6911–6923 (2008).
[CrossRef]

Wands, J. R.

C. M. Laperle, T. J. Hamilton, P. Wintermeyer, E. J. Walker, D. Shi, M. A. Anastasio, Z. Derdak, J. R. Wands, G. Diebold, and C. Rose-Petruck, “Low density contrast agents for x-ray phase contrast imaging: the use of ambient air for x-ray angiography of excised murine liver tissue,” Phys. Med. Biol. 53, 6911–6923 (2008).
[CrossRef]

Wegrzynek, D.

T. Weitkamp, D. Haas, D. Wegrzynek, and A. Rack, “Ankaphase: software for single-distance phase retrieval from inline x-ray phase-contrast radiographs,” J. Synchrotron. Radiat. 18, 617–629 (2011).
[CrossRef]

Weitkamp, T.

T. Weitkamp, D. Haas, D. Wegrzynek, and A. Rack, “Ankaphase: software for single-distance phase retrieval from inline x-ray phase-contrast radiographs,” J. Synchrotron. Radiat. 18, 617–629 (2011).
[CrossRef]

C. David, T. Weitkamp, F. Pfeiffer, A. Diaz, J. Bruder, T. Rohbeck, A. Groso, O. Bunk, M. Stampanoni, and P. Cloetens, “Hard x-ray phase imaging and tomography using a grating interferometer,” Spectrochim. Acta: Part B 62, 626–630 (2007).
[CrossRef]

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance x-ray sources,” Nat. Phys. 2, 258–261 (2006).
[CrossRef]

Wilkins, S. W.

T. E. Gureyev, T. J. Davis, A. Pogany, S. C. Mayo, and S. W. Wilkins, “Optical phase retrieval by use of first Born-and-Rytov-type approximations,” Appl. Opt. 43, 2418–2430 (2004).
[CrossRef]

S. C. Mayo, T. J. Davis, T. E. Gureyev, P. R. Miller, D. M. Paganin, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “X-ray phase-contrast microscopy and microtomography,” Opt. Express 11, 2289–2302 (2003).
[CrossRef]

D. M. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206, 33–40 (2002).
[CrossRef]

T. E. Gureyev and S. W. Wilkins, “On x-ray phase imaging with a point source,” J. Opt. Soc. Am. A 15, 579–585 (1998).
[CrossRef]

A. Pogany, D. Gao, and S. W. Wilkins, “Contrast and resolution in imaging with a microfocus x-ray source,” Rev. Sci. Instrum. 68, 2774–2782 (1997).
[CrossRef]

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard x-rays,” Nature 384, 335–338 (1996).
[CrossRef]

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

Wintermeyer, P.

C. M. Laperle, T. J. Hamilton, P. Wintermeyer, E. J. Walker, D. Shi, M. A. Anastasio, Z. Derdak, J. R. Wands, G. Diebold, and C. Rose-Petruck, “Low density contrast agents for x-ray phase contrast imaging: the use of ambient air for x-ray angiography of excised murine liver tissue,” Phys. Med. Biol. 53, 6911–6923 (2008).
[CrossRef]

Wu, X.

X. Wu, H. Liu, and A. Yan, “X-ray phase-attenuation duality and phase retrieval,” Opt. Lett. 30, 379–381 (2005).
[CrossRef]

X. Wu and H. Liu, “A general theoretical formalism for x-ray phase contrast imaging,” J. X-ray Sci. Technol. 11, 33–42 (2003).

Xiao, T. Q.

Xie, H. L.

Yan, A.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyts, J. P. Guigay, and M. Schlenker, “Holotomography: quantitative phase tomography with micrometerresolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).
[CrossRef]

Eur. J. Pharm. Biopharm. (1)

A. Almeida, S. Possemiers, M. N. Boone, T. De Beer, T. Quinten, L. Van Hoorebeke, J.-P. Remon, and C. Vervaet, “Ethylene vinyl acetate as matrix for oral sustained release dosage forms produced via hot-melt extrusion,” Eur. J. Pharm. Biopharm. 77, 297–305 (2011).
[CrossRef]

J. Appl. Phys. (2)

B. D. Arhatari, W. P. Gates, N. Estiaghi, and A. G. Peele, “Phase retrieval tomography in the presence of noise,” J. Appl. Phys. 107, 034904 (2010).
[CrossRef]

P. Cloetens, M. Pateyron-Salom, J. Y. Buffire, G. Peix, J. Baruchel, F. Peyrin, and M. Schlenker, “Observation of microstructure and damage in materials by phase sensitive radiography and tomography,” J. Appl. Phys. 81, 5878–5886 (1997).
[CrossRef]

J. Hum. Evol. (1)

P. Tafforeau and T. M. Smith, “Nondestructive imaging of hominoid dental microstructure using phase contrast x-ray synchrotron microtomography,” J. Hum. Evol. 54, 272–278 (2008).
[CrossRef]

J. Microsc. (1)

D. M. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206, 33–40 (2002).
[CrossRef]

J. Opt. Soc. Am. (1)

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

J. Phys. D: Appl. Phys. (1)

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

J. Phys.: Conf. Ser. (1)

F. Marone, C. Hintermuller, S. A. McDonald, R. Abela, G. Mikuljan, A. Isenegger, and M. Stampanoni, “X-ray tomographic microscopy at TOMCAT,” J. Phys.: Conf. Ser. 186, 012042 (2009).
[CrossRef]

J. Struct. Biol. (2)

D. Derome, M. Griffa, M. Koebel, and J. Carmeliet, “Hysteretic swelling of wood at cellular scale probed by phase-contrast x-ray tomography,” J. Struct. Biol. 173, 180–190 (2011).
[CrossRef]

P. Trtik, J. Dual, D. Keunecke, D. Mannes, P. Niemz, P. Stähli, A. Kaestner, A. Groso, and M. Stampanoni, “3d imaging of microstructure of spruce wood,” J. Struct. Biol. 159, 46–55 (2007).
[CrossRef]

J. Synchrotron Radiat. (1)

S. A. McDonald, F. Marone, C. Hintermuller, G. Mikuljan, C. David, F. Pfeiffer, and M. Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synchrotron Radiat. 16, 562–572 (2009).
[CrossRef]

J. Synchrotron. Radiat. (1)

T. Weitkamp, D. Haas, D. Wegrzynek, and A. Rack, “Ankaphase: software for single-distance phase retrieval from inline x-ray phase-contrast radiographs,” J. Synchrotron. Radiat. 18, 617–629 (2011).
[CrossRef]

J. X-ray Sci. Technol. (1)

X. Wu and H. Liu, “A general theoretical formalism for x-ray phase contrast imaging,” J. X-ray Sci. Technol. 11, 33–42 (2003).

Med. Phys. (2)

M. Langer, P. Cloetens, J. P. Guigay, and F. Peyrin, “Quantitative comparison of direct phase retrieval algorithms in in-line phase tomography,” Med. Phys. 35, 4556–4566 (2008).
[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, 3617–3627 (2005).
[CrossRef]

Microsc. Microanal. (1)

M. N. Boone, Y. De Witte, M. Dierick, A. Almeida, and L. Van Hoorebeke, “Improved signal-to-noise ratio in laboratory-based phase contrast tomography,” Microsc. Microanal. 18, 399–405 (2012).
[CrossRef]

Nat. Phys. (1)

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance x-ray sources,” Nat. Phys. 2, 258–261 (2006).
[CrossRef]

Nature (2)

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard x-rays,” Nature 384, 335–338 (1996).
[CrossRef]

E. M. Friis, P. R. Crane, K. R. Pedersen, S. Bengton, P. C. J. Donoghue, G. W. Grimm, and M. Stampanoni, “Phase-contrast x-ray microtomography links cretaceous seeds with gnetales and bennettitales,” Nature 450, 549–552 (2007).
[CrossRef]

Nature (London) (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 (London) 373, 595–598 (1995).
[CrossRef]

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

B. Masschaele, V. Cnudde, M. Dierick, P. Jacobs, L. Van Hoorebeke, and J. Vlassenbroeck, “UGCT: new x-ray radiography and tomography facility,” Nucl. Instrum. Methods Phys. Res. Sect. A 580, 266–269 (2007).
[CrossRef]

M. N. Boone, J. Vlassenbroeck, S. Peetermans, D. Van Loo, M. Dierick, and L. Van Hoorebeke, “Secondary radiation in transmission-type x-ray tubes: simulation, practical issues and solution in the context of x-ray microtomography,” Nucl. Instrum. Methods Phys. Res. Sect. A 661, 7–12 (2012).
[CrossRef]

Nucl. Instrum. Methods Phys. Res. Sect. B (1)

M. N. Boone, Y. De Witte, M. Dierick, J. Van den Bulcke, J. Vlassenbroeck, and L. Van Hoorebeke, “Practical use of the modified Bronnikov algorithm in micro-CT,” Nucl. Instrum. Methods Phys. Res. Sect. B 267, 1182–1186 (2009).
[CrossRef]

Nucl. Instrum. Methods Phys. Res.: Sect. A (1)

J. Vlassenbroeck, M. Dierick, B. Masschaele, V. Cnudde, L. Van Hoorebeke, and P. Jacobs, “Software tools for quantification of x-ray microtomography at the UGCT,” Nucl. Instrum. Methods Phys. Res.: Sect. A 580, 442–445 (2007).
[CrossRef]

Opt. Express (4)

Opt. Lett. (2)

Phys. Med. Biol. (2)

M. A. Beltran, D. M. Paganin, K. W. Siu, A. Fouras, S. B. Hooper, D. H. Reser, and M. J. Kitchen, “Interface-specific x-ray phase retrieval tomography of complex biological organs,” Phys. Med. Biol. 56, 7353–7369 (2011).
[CrossRef]

C. M. Laperle, T. J. Hamilton, P. Wintermeyer, E. J. Walker, D. Shi, M. A. Anastasio, Z. Derdak, J. R. Wands, G. Diebold, and C. Rose-Petruck, “Low density contrast agents for x-ray phase contrast imaging: the use of ambient air for x-ray angiography of excised murine liver tissue,” Phys. Med. Biol. 53, 6911–6923 (2008).
[CrossRef]

Proc. SPIE (2)

A. V. Bronnikov, “Phase-contrast CT: fundamental theorem and fast image reconstruction algorithms,” Proc. SPIE 6318, 63180Q (2006).
[CrossRef]

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R. Betemps, U. Frommherz, P. Bhler, D. Meister, M. Lange, and R. Abela, “Trends in synchrotron-based tomographic imaging: the SLS experience,” Proc. SPIE 6318, 63180M (2006).
[CrossRef]

Rev. Sci. Instrum. (1)

A. Pogany, D. Gao, and S. W. Wilkins, “Contrast and resolution in imaging with a microfocus x-ray source,” Rev. Sci. Instrum. 68, 2774–2782 (1997).
[CrossRef]

Spectrochim. Acta: Part B (1)

C. David, T. Weitkamp, F. Pfeiffer, A. Diaz, J. Bruder, T. Rohbeck, A. Groso, O. Bunk, M. Stampanoni, and P. Cloetens, “Hard x-ray phase imaging and tomography using a grating interferometer,” Spectrochim. Acta: Part B 62, 626–630 (2007).
[CrossRef]

Other (3)

H. Derluyn, M. Griffa, D. Mannes, I. Jerjen, J. Dewanckele, P. Vontobel, A. Sheppard, M. N. Boone, D. Derome, V. Cnudde, E. Lehmann, and J. Carmeliet, “Probing salt crystallization damage mechanisms in porous limestone with neutron radiography and x-ray tomography,” in 5th International Building Physics Conference (2012), pp. 95–102.

NIST, “X-ray form factor, attenuation and scattering tables,” http://physics.nist.gov/PhysRefData/FFast/html/form.html .

Y. De Witte, “Improved and practically feasible reconstruction methods for high resolution x-ray tomography,” Ph.D. thesis (Ghent University, 2010).

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Figures (5)

Fig. 1.
Fig. 1.

(a) Original phantom, where black indicates air, gray indicates the matrix material with parameters μ1 and δ1, and white indicates the inclusions with parameters μ2 and δ2. (b) MBA reconstruction of the homogeneous object at 75% attenuation. (c) MBA reconstruction of the semihomogeneous object at 75% attenuation. (d) SPAR reconstruction of the semihomogeneous object at 75% attenuation. (e) SPAR reconstruction of the object with phase inclusions at 25% attenuation. (f) SPAR reconstruction of the object with attenuation inclusions at 25% attenuation, reconstructed using SPAR.

Fig. 2.
Fig. 2.

NRMSE for (a) homogeneous and semihomogeneous object. (b) Object with phase inclusion. (c) Object with attenuation inclusion.

Fig. 3.
Fig. 3.

Calculated MTF50% for the homogeneous sample at varying attenuation level.

Fig. 4.
Fig. 4.

Line profile through the real homogeneous object scanned at 50kVp, 90kVp, and 120kVp, respectively. (a) MBA reconstructions and (b) SPAR reconstructions.

Fig. 5.
Fig. 5.

Reconstruction using SPAR of a rock sample showing the remaining phase effects due to sample inhomogeneity.

Tables (1)

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Table 1. Experimental Settings for the Epoxy Cylinder Scans

Equations (10)

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

2πλIθ(r,z)z=[Iθ(r,z)ϕθ(r,λ)],
ϕθ(r,λ)=2πλraypathδ(x,y,z,λ)xyz,
n(λ)=1δ(λ)+iβ(δ).
μ(x,y,z,λ)=2πλβ(x,y,z,λ).
μθ(r,λ)=raypathμ(x,y,z,λ)xyz.
Iθ(z=d)Iθ(z=0)[1λz2πM2ϕθ+λz2πM(μθxϕθx+μθyϕθy)],
Iθ(z=d)Iθ(z=0)(1λz2πM2ϕθ).
Q(ξ,η)=|ξ|ξ2+η2+α,
gθ(r)=Iθ(r,z)Iθ(r,z=0)1,
Tθ(r)=1μln[F1(μF{M2Iθ(Mr,z)}zδ(ξ2+η2)/M+μ)],

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