Abstract

Compared to phase retrieval from single sample-to-detector distance (SDD) image, phase retrieval with multiple SDD images could improve the precision in quantitative X-ray in-line phase contrast imaging (QXIPCI). Among all the related phase retrieval approaches, the two-SDD-image-based one is the simplest and well compromises between precision and dose. However, how to optimize the recording distances for the two images to achieve highest precision, remains unsolved. In this paper, the problem was investigated systematically based on digital simulation and related experiments. Spectral correlation degree (SCD) is introduced to evaluate the pertinence between the two SDD images. The simulation results show that the highest retrieving precision could be obtained while the SDD of the second image is three times that of the first image. The best retrieval could be achieved when SDD of the first image is selected properly, meanwhile the SCD occurs with a typical damping oscillation. Experiments, carried out at the X-ray imaging beamline of SSRF, demonstrated the simulation results.

© 2011 OSA

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  1. L. De Caro, F. Scattarella, C. Giannini, S. Tangaro, L. Rigon, R. Longo, and R. Bellotti, “Combined mixed approach algorithm for in-line phase-contrast x-ray imaging,” Med. Phys. 37(7), 3817–3827 (2010).
    [CrossRef] [PubMed]
  2. T. Xiao, A. Bergamaschi, D. Dreossi, R. Longo, A. Olivo, S. Pani, L. Rigon, T. Rokvic, C. Venanzi, and E. Castelli, “Effect of spatial coherence on application of in-line phase contrast imaging to synchrotron radiation mammography,” Nucl. Instrum. Meth. A 548(1-2), 155–162 (2005).
    [CrossRef]
  3. H. Ikeura-Sekiguchi, R. Kuroda, M. Yasumoto, H. Toyokawa, M. Koike, K. Yamada, F. Sakai, K. Mori, K. Maruyama, H. Oka, and T. Kimata, “In-line phase-contrast imaging of a biological specimen using a compact laser-Compton scattering-based x-ray source,” Appl. Phys. Lett. 92(13), 131107 (2008).
    [CrossRef]
  4. L. De Caro, A. Cedola, C. Giannini, I. Bukreeva, and S. Lagomarsino, “In-line phase-contrast imaging for strong absorbing objects,” Phys. Med. Biol. 53(22), 6619–6637 (2008).
    [CrossRef] [PubMed]
  5. B. Chen, P. Zhu, C. Chen, H. Shu, Y. Liu, Q. Yuan, J. Wang, W. Huang, H. Ming, and Z. Wu, “Theory and experiment of in-line phase contrast imaging on non-uniformly distributed source,” Spectrochim. Acta. B 62(6-7), 636–641 (2007).
    [CrossRef]
  6. Y. S. Kashyap, P. S. Yadav, T. Roy, P. S. Sarkar, M. Shukla, and A. Sinha, “Laboratory-based X-ray phase-contrast imaging technique for material and medical science applications,” Appl. Radiat. Isot. 66(8), 1083–1090 (2008).
    [CrossRef] [PubMed]
  7. S. C. Irvine, D. M. Paganin, S. Dubsky, R. A. Lewis, and A. Fouras, “Phase retrieval of improved three-dimensional velocimetry of dynamic x-ray blood speckle,” Appl. Phys. Lett. 93(15), 153901 (2008).
    [CrossRef]
  8. P. Cloetens, M. Pateyron-Salome, J. Y. Buffiere, 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(9), 5878–5886 (1997).
    [CrossRef]
  9. J. Y. Chen, D. J. Bottjer, G. Li, M. G. Hadfield, F. Gao, A. R. Cameron, C. Y. Zhang, D. C. Xian, P. Tafforeau, X. Liao, and Z. J. Yin, “Complex embryos displaying bilaterian characters from Precambrian Doushantuo phosphate deposits, Weng’an, Guizhou, China,” Proc. Natl. Acad. Sci. U.S.A. 106(45), 19056–19060 (2009).
    [CrossRef] [PubMed]
  10. X. Wei, T. Q. Xiao, L. X. Liu, G. H. Du, M. Chen, Y. Y. Luo, and H. J. Xu, “Application of x-ray phase contrast imaging to microscopic identification of Chinese medicines,” Phys. Med. Biol. 50(18), 4277–4286 (2005).
    [CrossRef] [PubMed]
  11. J. E. Adams, “Quantitative computed tomography,” Eur. J. Radiol. 71(3), 415–424 (2009).
    [CrossRef] [PubMed]
  12. N. M. Dragomir, X. M. Goh, and A. Roberts, “Three-dimensional refractive index reconstruction with quantitative phase tomography,” Microsc. Res. Tech. 71(1), 5–10 (2008).
    [CrossRef]
  13. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).
  14. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21(15), 2758–2769 (1982).
    [CrossRef] [PubMed]
  15. T. E. Gureyev and K. A. Nugent, “Rapid quantitative phase imaging using the transport of intensity equation,” Opt. Commun. 133(1-6), 339–346 (1997).
    [CrossRef]
  16. D. 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(1), 33–40 (2002).
    [CrossRef] [PubMed]
  17. 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(10), 4556–4566 (2008).
    [CrossRef] [PubMed]
  18. L.D. Turner, B. B. Dhal, J. P. Hayes, A. P. Mancuso, K. A. Nugent, D. Paterson, R. E. Scholten, C. Q. Tran, and A. G. Peele, “X-ray phase imaging: Demonstration of extended conditions for homogeneous objects,” Opt. Express 12(13), 2960–2965 (2004).
    [CrossRef] [PubMed]
  19. J. P. Guigay, M. Langer, R. Boistel, and P. Cloetens, “Mixed transfer function and transport of intensity approach for phase retrieval in the Fresnel region,” Opt. Lett. 32(12), 1617–1619 (2007).
    [CrossRef] [PubMed]
  20. T. E. Gureyev, A. Pogany, D. M. Paganin, and S. W. Wilkins, “Linear algorithms for phase retrieval in the Fresnel region,” Opt. Commun. 231(1-6), 53–70 (2004).
    [CrossRef]
  21. 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(12), 2418–2430 (2004).
    [CrossRef] [PubMed]
  22. 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(7), 6423–6436 (2010).
    [CrossRef] [PubMed]
  23. D. M. Paganin, T. E. Gureyev, K. M. Pavlov, R. A. Lewis, and M. Kitchen, “Phase retrieval using coherent imaging systems with linear transfer functions,” Opt. Commun. 234(1-6), 87–105 (2004).
    [CrossRef]
  24. M. R. Teague, “Deterministic phase retrieval: a Green’s function solution,” J. Opt. Soc. Am. 73(11), 1434–1441 (1983).
    [CrossRef]
  25. C. Y. Chou, Y. Huang, D. Shi, and M. A. Anastasio, “Image reconstruction in quantitative X-ray phase-contrast imaging employing multiple measurements,” Opt. Express 15(16), 10002–10025 (2007).
    [CrossRef] [PubMed]
  26. C. Y. Chou and M. A. Anastasio, “Influence of imaging geometry on noise texture in quantitative in-line X-ray phase-contrast imaging,” Opt. Express 17(17), 14466–14480 (2009).
    [CrossRef] [PubMed]
  27. D. Paganin, A. Barty, P. J. Mcmahon, and K. A. Nugent, “Quantitative phase-amplitude microscopy. III. The effect of noise,” J. Microsc. 214(1), 51–61 (2004).
    [CrossRef] [PubMed]
  28. M. Born, and E. Wolf, Principles of Optics: ElectromagneticTheory of Propagation, Interference and Diffraction of Light (Cambridge UniversityPress, 1999).
  29. O. K. Ersoy, Diffraction, Fourier Optics and Imaging (John Wiley& Sons, Inc., 2006).
  30. A. N. Tikhonov and V. Y. Arsenin, “Solutions of Ill-posed Problems,” SIAM Rev. 21(2), 266–267 (1979).
    [CrossRef]
  31. A. Groso, R. Abela, and M. Stampanoni, “Implementation of a fast method for high resolution phase contrast tomography,” Opt. Express 14(18), 8103–8110 (2006).
    [CrossRef] [PubMed]
  32. B. L. Henke, E. M. Cullikson, and J. C. Davis, “X-ray interactions: photo absorption, scattering, transmission, and reflection at E=50-30,000eV,Z=1-92,” At. Data Nucl. Data Tables 54(2), 181–342 (1993).
    [CrossRef]
  33. L. Mandel and E. Wolf, “Spectral coherence and the concept of cross-spectral purity,” J. Opt. Soc. Am. 66(6), 529–535 (1976).
    [CrossRef]
  34. J. Bigot, F. Gamboa, and M. Vimond, “Estimation of Translation, Rotation, and Scaling between Noisy Images Using the Fouier-Mellin Transform,” SIAM J. Imaging Sci. 2(2), 614–645 (2009).
    [CrossRef]
  35. Eastman Kodak Company, “CCD Image sensors noise sources,” Rev. 2.1 (2005).
  36. K. Irie, A. E. McKinnon, K. Unsworth, and I. M. Woodhead, “A model for measurement of noise in CCD digital-video cameras,” Meas. Sci. Technol. 19(4), 045207–045211 (2008).
    [CrossRef]
  37. Y. Zhang and X. Zhang, “Reconstruction of a complex object from two in-line holograms,” Opt. Express 11(6), 572–578 (2003).
    [CrossRef] [PubMed]
  38. M. S. Nixon, and A. S. Aguado, Feature Extraction and Image Processing (Academic Press, 2008).
  39. R. C. Gonzalez, and R. E. Woods, Digital Image Processing (Pearson Prentice Hall, 2008).
  40. D. Paganin, Coherent X-ray Optics (Oxford University Press, New York, 2006).

2010 (2)

L. De Caro, F. Scattarella, C. Giannini, S. Tangaro, L. Rigon, R. Longo, and R. Bellotti, “Combined mixed approach algorithm for in-line phase-contrast x-ray imaging,” Med. Phys. 37(7), 3817–3827 (2010).
[CrossRef] [PubMed]

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(7), 6423–6436 (2010).
[CrossRef] [PubMed]

2009 (4)

C. Y. Chou and M. A. Anastasio, “Influence of imaging geometry on noise texture in quantitative in-line X-ray phase-contrast imaging,” Opt. Express 17(17), 14466–14480 (2009).
[CrossRef] [PubMed]

J. Bigot, F. Gamboa, and M. Vimond, “Estimation of Translation, Rotation, and Scaling between Noisy Images Using the Fouier-Mellin Transform,” SIAM J. Imaging Sci. 2(2), 614–645 (2009).
[CrossRef]

J. Y. Chen, D. J. Bottjer, G. Li, M. G. Hadfield, F. Gao, A. R. Cameron, C. Y. Zhang, D. C. Xian, P. Tafforeau, X. Liao, and Z. J. Yin, “Complex embryos displaying bilaterian characters from Precambrian Doushantuo phosphate deposits, Weng’an, Guizhou, China,” Proc. Natl. Acad. Sci. U.S.A. 106(45), 19056–19060 (2009).
[CrossRef] [PubMed]

J. E. Adams, “Quantitative computed tomography,” Eur. J. Radiol. 71(3), 415–424 (2009).
[CrossRef] [PubMed]

2008 (7)

N. M. Dragomir, X. M. Goh, and A. Roberts, “Three-dimensional refractive index reconstruction with quantitative phase tomography,” Microsc. Res. Tech. 71(1), 5–10 (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(10), 4556–4566 (2008).
[CrossRef] [PubMed]

Y. S. Kashyap, P. S. Yadav, T. Roy, P. S. Sarkar, M. Shukla, and A. Sinha, “Laboratory-based X-ray phase-contrast imaging technique for material and medical science applications,” Appl. Radiat. Isot. 66(8), 1083–1090 (2008).
[CrossRef] [PubMed]

S. C. Irvine, D. M. Paganin, S. Dubsky, R. A. Lewis, and A. Fouras, “Phase retrieval of improved three-dimensional velocimetry of dynamic x-ray blood speckle,” Appl. Phys. Lett. 93(15), 153901 (2008).
[CrossRef]

H. Ikeura-Sekiguchi, R. Kuroda, M. Yasumoto, H. Toyokawa, M. Koike, K. Yamada, F. Sakai, K. Mori, K. Maruyama, H. Oka, and T. Kimata, “In-line phase-contrast imaging of a biological specimen using a compact laser-Compton scattering-based x-ray source,” Appl. Phys. Lett. 92(13), 131107 (2008).
[CrossRef]

L. De Caro, A. Cedola, C. Giannini, I. Bukreeva, and S. Lagomarsino, “In-line phase-contrast imaging for strong absorbing objects,” Phys. Med. Biol. 53(22), 6619–6637 (2008).
[CrossRef] [PubMed]

K. Irie, A. E. McKinnon, K. Unsworth, and I. M. Woodhead, “A model for measurement of noise in CCD digital-video cameras,” Meas. Sci. Technol. 19(4), 045207–045211 (2008).
[CrossRef]

2007 (3)

2006 (1)

2005 (2)

T. Xiao, A. Bergamaschi, D. Dreossi, R. Longo, A. Olivo, S. Pani, L. Rigon, T. Rokvic, C. Venanzi, and E. Castelli, “Effect of spatial coherence on application of in-line phase contrast imaging to synchrotron radiation mammography,” Nucl. Instrum. Meth. A 548(1-2), 155–162 (2005).
[CrossRef]

X. Wei, T. Q. Xiao, L. X. Liu, G. H. Du, M. Chen, Y. Y. Luo, and H. J. Xu, “Application of x-ray phase contrast imaging to microscopic identification of Chinese medicines,” Phys. Med. Biol. 50(18), 4277–4286 (2005).
[CrossRef] [PubMed]

2004 (5)

T. E. Gureyev, A. Pogany, D. M. Paganin, and S. W. Wilkins, “Linear algorithms for phase retrieval in the Fresnel region,” Opt. Commun. 231(1-6), 53–70 (2004).
[CrossRef]

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(12), 2418–2430 (2004).
[CrossRef] [PubMed]

L.D. Turner, B. B. Dhal, J. P. Hayes, A. P. Mancuso, K. A. Nugent, D. Paterson, R. E. Scholten, C. Q. Tran, and A. G. Peele, “X-ray phase imaging: Demonstration of extended conditions for homogeneous objects,” Opt. Express 12(13), 2960–2965 (2004).
[CrossRef] [PubMed]

D. Paganin, A. Barty, P. J. Mcmahon, and K. A. Nugent, “Quantitative phase-amplitude microscopy. III. The effect of noise,” J. Microsc. 214(1), 51–61 (2004).
[CrossRef] [PubMed]

D. M. Paganin, T. E. Gureyev, K. M. Pavlov, R. A. Lewis, and M. Kitchen, “Phase retrieval using coherent imaging systems with linear transfer functions,” Opt. Commun. 234(1-6), 87–105 (2004).
[CrossRef]

2003 (1)

2002 (1)

D. 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(1), 33–40 (2002).
[CrossRef] [PubMed]

1997 (2)

T. E. Gureyev and K. A. Nugent, “Rapid quantitative phase imaging using the transport of intensity equation,” Opt. Commun. 133(1-6), 339–346 (1997).
[CrossRef]

P. Cloetens, M. Pateyron-Salome, J. Y. Buffiere, 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(9), 5878–5886 (1997).
[CrossRef]

1993 (1)

B. L. Henke, E. M. Cullikson, and J. C. Davis, “X-ray interactions: photo absorption, scattering, transmission, and reflection at E=50-30,000eV,Z=1-92,” At. Data Nucl. Data Tables 54(2), 181–342 (1993).
[CrossRef]

1983 (1)

1982 (1)

1979 (1)

A. N. Tikhonov and V. Y. Arsenin, “Solutions of Ill-posed Problems,” SIAM Rev. 21(2), 266–267 (1979).
[CrossRef]

1976 (1)

1972 (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).

Abela, R.

Adams, J. E.

J. E. Adams, “Quantitative computed tomography,” Eur. J. Radiol. 71(3), 415–424 (2009).
[CrossRef] [PubMed]

Anastasio, M. A.

Arsenin, V. Y.

A. N. Tikhonov and V. Y. Arsenin, “Solutions of Ill-posed Problems,” SIAM Rev. 21(2), 266–267 (1979).
[CrossRef]

Barty, A.

D. Paganin, A. Barty, P. J. Mcmahon, and K. A. Nugent, “Quantitative phase-amplitude microscopy. III. The effect of noise,” J. Microsc. 214(1), 51–61 (2004).
[CrossRef] [PubMed]

Baruchel, J.

P. Cloetens, M. Pateyron-Salome, J. Y. Buffiere, 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(9), 5878–5886 (1997).
[CrossRef]

Bellotti, R.

L. De Caro, F. Scattarella, C. Giannini, S. Tangaro, L. Rigon, R. Longo, and R. Bellotti, “Combined mixed approach algorithm for in-line phase-contrast x-ray imaging,” Med. Phys. 37(7), 3817–3827 (2010).
[CrossRef] [PubMed]

Beltran, M. A.

Bergamaschi, A.

T. Xiao, A. Bergamaschi, D. Dreossi, R. Longo, A. Olivo, S. Pani, L. Rigon, T. Rokvic, C. Venanzi, and E. Castelli, “Effect of spatial coherence on application of in-line phase contrast imaging to synchrotron radiation mammography,” Nucl. Instrum. Meth. A 548(1-2), 155–162 (2005).
[CrossRef]

Bigot, J.

J. Bigot, F. Gamboa, and M. Vimond, “Estimation of Translation, Rotation, and Scaling between Noisy Images Using the Fouier-Mellin Transform,” SIAM J. Imaging Sci. 2(2), 614–645 (2009).
[CrossRef]

Boistel, R.

Bottjer, D. J.

J. Y. Chen, D. J. Bottjer, G. Li, M. G. Hadfield, F. Gao, A. R. Cameron, C. Y. Zhang, D. C. Xian, P. Tafforeau, X. Liao, and Z. J. Yin, “Complex embryos displaying bilaterian characters from Precambrian Doushantuo phosphate deposits, Weng’an, Guizhou, China,” Proc. Natl. Acad. Sci. U.S.A. 106(45), 19056–19060 (2009).
[CrossRef] [PubMed]

Buffiere, J. Y.

P. Cloetens, M. Pateyron-Salome, J. Y. Buffiere, 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(9), 5878–5886 (1997).
[CrossRef]

Bukreeva, I.

L. De Caro, A. Cedola, C. Giannini, I. Bukreeva, and S. Lagomarsino, “In-line phase-contrast imaging for strong absorbing objects,” Phys. Med. Biol. 53(22), 6619–6637 (2008).
[CrossRef] [PubMed]

Cameron, A. R.

J. Y. Chen, D. J. Bottjer, G. Li, M. G. Hadfield, F. Gao, A. R. Cameron, C. Y. Zhang, D. C. Xian, P. Tafforeau, X. Liao, and Z. J. Yin, “Complex embryos displaying bilaterian characters from Precambrian Doushantuo phosphate deposits, Weng’an, Guizhou, China,” Proc. Natl. Acad. Sci. U.S.A. 106(45), 19056–19060 (2009).
[CrossRef] [PubMed]

Castelli, E.

T. Xiao, A. Bergamaschi, D. Dreossi, R. Longo, A. Olivo, S. Pani, L. Rigon, T. Rokvic, C. Venanzi, and E. Castelli, “Effect of spatial coherence on application of in-line phase contrast imaging to synchrotron radiation mammography,” Nucl. Instrum. Meth. A 548(1-2), 155–162 (2005).
[CrossRef]

Cedola, A.

L. De Caro, A. Cedola, C. Giannini, I. Bukreeva, and S. Lagomarsino, “In-line phase-contrast imaging for strong absorbing objects,” Phys. Med. Biol. 53(22), 6619–6637 (2008).
[CrossRef] [PubMed]

Chen, B.

B. Chen, P. Zhu, C. Chen, H. Shu, Y. Liu, Q. Yuan, J. Wang, W. Huang, H. Ming, and Z. Wu, “Theory and experiment of in-line phase contrast imaging on non-uniformly distributed source,” Spectrochim. Acta. B 62(6-7), 636–641 (2007).
[CrossRef]

Chen, C.

B. Chen, P. Zhu, C. Chen, H. Shu, Y. Liu, Q. Yuan, J. Wang, W. Huang, H. Ming, and Z. Wu, “Theory and experiment of in-line phase contrast imaging on non-uniformly distributed source,” Spectrochim. Acta. B 62(6-7), 636–641 (2007).
[CrossRef]

Chen, J. Y.

J. Y. Chen, D. J. Bottjer, G. Li, M. G. Hadfield, F. Gao, A. R. Cameron, C. Y. Zhang, D. C. Xian, P. Tafforeau, X. Liao, and Z. J. Yin, “Complex embryos displaying bilaterian characters from Precambrian Doushantuo phosphate deposits, Weng’an, Guizhou, China,” Proc. Natl. Acad. Sci. U.S.A. 106(45), 19056–19060 (2009).
[CrossRef] [PubMed]

Chen, M.

X. Wei, T. Q. Xiao, L. X. Liu, G. H. Du, M. Chen, Y. Y. Luo, and H. J. Xu, “Application of x-ray phase contrast imaging to microscopic identification of Chinese medicines,” Phys. Med. Biol. 50(18), 4277–4286 (2005).
[CrossRef] [PubMed]

Chou, C. Y.

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(10), 4556–4566 (2008).
[CrossRef] [PubMed]

J. P. Guigay, M. Langer, R. Boistel, and P. Cloetens, “Mixed transfer function and transport of intensity approach for phase retrieval in the Fresnel region,” Opt. Lett. 32(12), 1617–1619 (2007).
[CrossRef] [PubMed]

P. Cloetens, M. Pateyron-Salome, J. Y. Buffiere, 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(9), 5878–5886 (1997).
[CrossRef]

Cullikson, E. M.

B. L. Henke, E. M. Cullikson, and J. C. Davis, “X-ray interactions: photo absorption, scattering, transmission, and reflection at E=50-30,000eV,Z=1-92,” At. Data Nucl. Data Tables 54(2), 181–342 (1993).
[CrossRef]

Davis, J. C.

B. L. Henke, E. M. Cullikson, and J. C. Davis, “X-ray interactions: photo absorption, scattering, transmission, and reflection at E=50-30,000eV,Z=1-92,” At. Data Nucl. Data Tables 54(2), 181–342 (1993).
[CrossRef]

Davis, T. J.

De Caro, L.

L. De Caro, F. Scattarella, C. Giannini, S. Tangaro, L. Rigon, R. Longo, and R. Bellotti, “Combined mixed approach algorithm for in-line phase-contrast x-ray imaging,” Med. Phys. 37(7), 3817–3827 (2010).
[CrossRef] [PubMed]

L. De Caro, A. Cedola, C. Giannini, I. Bukreeva, and S. Lagomarsino, “In-line phase-contrast imaging for strong absorbing objects,” Phys. Med. Biol. 53(22), 6619–6637 (2008).
[CrossRef] [PubMed]

Dhal, B. B.

Dragomir, N. M.

N. M. Dragomir, X. M. Goh, and A. Roberts, “Three-dimensional refractive index reconstruction with quantitative phase tomography,” Microsc. Res. Tech. 71(1), 5–10 (2008).
[CrossRef]

Dreossi, D.

T. Xiao, A. Bergamaschi, D. Dreossi, R. Longo, A. Olivo, S. Pani, L. Rigon, T. Rokvic, C. Venanzi, and E. Castelli, “Effect of spatial coherence on application of in-line phase contrast imaging to synchrotron radiation mammography,” Nucl. Instrum. Meth. A 548(1-2), 155–162 (2005).
[CrossRef]

Du, G. H.

X. Wei, T. Q. Xiao, L. X. Liu, G. H. Du, M. Chen, Y. Y. Luo, and H. J. Xu, “Application of x-ray phase contrast imaging to microscopic identification of Chinese medicines,” Phys. Med. Biol. 50(18), 4277–4286 (2005).
[CrossRef] [PubMed]

Dubsky, S.

S. C. Irvine, D. M. Paganin, S. Dubsky, R. A. Lewis, and A. Fouras, “Phase retrieval of improved three-dimensional velocimetry of dynamic x-ray blood speckle,” Appl. Phys. Lett. 93(15), 153901 (2008).
[CrossRef]

Fienup, J. R.

Fouras, A.

S. C. Irvine, D. M. Paganin, S. Dubsky, R. A. Lewis, and A. Fouras, “Phase retrieval of improved three-dimensional velocimetry of dynamic x-ray blood speckle,” Appl. Phys. Lett. 93(15), 153901 (2008).
[CrossRef]

Gamboa, F.

J. Bigot, F. Gamboa, and M. Vimond, “Estimation of Translation, Rotation, and Scaling between Noisy Images Using the Fouier-Mellin Transform,” SIAM J. Imaging Sci. 2(2), 614–645 (2009).
[CrossRef]

Gao, F.

J. Y. Chen, D. J. Bottjer, G. Li, M. G. Hadfield, F. Gao, A. R. Cameron, C. Y. Zhang, D. C. Xian, P. Tafforeau, X. Liao, and Z. J. Yin, “Complex embryos displaying bilaterian characters from Precambrian Doushantuo phosphate deposits, Weng’an, Guizhou, China,” Proc. Natl. Acad. Sci. U.S.A. 106(45), 19056–19060 (2009).
[CrossRef] [PubMed]

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).

Giannini, C.

L. De Caro, F. Scattarella, C. Giannini, S. Tangaro, L. Rigon, R. Longo, and R. Bellotti, “Combined mixed approach algorithm for in-line phase-contrast x-ray imaging,” Med. Phys. 37(7), 3817–3827 (2010).
[CrossRef] [PubMed]

L. De Caro, A. Cedola, C. Giannini, I. Bukreeva, and S. Lagomarsino, “In-line phase-contrast imaging for strong absorbing objects,” Phys. Med. Biol. 53(22), 6619–6637 (2008).
[CrossRef] [PubMed]

Goh, X. M.

N. M. Dragomir, X. M. Goh, and A. Roberts, “Three-dimensional refractive index reconstruction with quantitative phase tomography,” Microsc. Res. Tech. 71(1), 5–10 (2008).
[CrossRef]

Groso, A.

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(10), 4556–4566 (2008).
[CrossRef] [PubMed]

J. P. Guigay, M. Langer, R. Boistel, and P. Cloetens, “Mixed transfer function and transport of intensity approach for phase retrieval in the Fresnel region,” Opt. Lett. 32(12), 1617–1619 (2007).
[CrossRef] [PubMed]

Gureyev, T. E.

T. E. Gureyev, A. Pogany, D. M. Paganin, and S. W. Wilkins, “Linear algorithms for phase retrieval in the Fresnel region,” Opt. Commun. 231(1-6), 53–70 (2004).
[CrossRef]

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(12), 2418–2430 (2004).
[CrossRef] [PubMed]

D. M. Paganin, T. E. Gureyev, K. M. Pavlov, R. A. Lewis, and M. Kitchen, “Phase retrieval using coherent imaging systems with linear transfer functions,” Opt. Commun. 234(1-6), 87–105 (2004).
[CrossRef]

D. 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(1), 33–40 (2002).
[CrossRef] [PubMed]

T. E. Gureyev and K. A. Nugent, “Rapid quantitative phase imaging using the transport of intensity equation,” Opt. Commun. 133(1-6), 339–346 (1997).
[CrossRef]

Hadfield, M. G.

J. Y. Chen, D. J. Bottjer, G. Li, M. G. Hadfield, F. Gao, A. R. Cameron, C. Y. Zhang, D. C. Xian, P. Tafforeau, X. Liao, and Z. J. Yin, “Complex embryos displaying bilaterian characters from Precambrian Doushantuo phosphate deposits, Weng’an, Guizhou, China,” Proc. Natl. Acad. Sci. U.S.A. 106(45), 19056–19060 (2009).
[CrossRef] [PubMed]

Hayes, J. P.

Henke, B. L.

B. L. Henke, E. M. Cullikson, and J. C. Davis, “X-ray interactions: photo absorption, scattering, transmission, and reflection at E=50-30,000eV,Z=1-92,” At. Data Nucl. Data Tables 54(2), 181–342 (1993).
[CrossRef]

Huang, W.

B. Chen, P. Zhu, C. Chen, H. Shu, Y. Liu, Q. Yuan, J. Wang, W. Huang, H. Ming, and Z. Wu, “Theory and experiment of in-line phase contrast imaging on non-uniformly distributed source,” Spectrochim. Acta. B 62(6-7), 636–641 (2007).
[CrossRef]

Huang, Y.

Ikeura-Sekiguchi, H.

H. Ikeura-Sekiguchi, R. Kuroda, M. Yasumoto, H. Toyokawa, M. Koike, K. Yamada, F. Sakai, K. Mori, K. Maruyama, H. Oka, and T. Kimata, “In-line phase-contrast imaging of a biological specimen using a compact laser-Compton scattering-based x-ray source,” Appl. Phys. Lett. 92(13), 131107 (2008).
[CrossRef]

Irie, K.

K. Irie, A. E. McKinnon, K. Unsworth, and I. M. Woodhead, “A model for measurement of noise in CCD digital-video cameras,” Meas. Sci. Technol. 19(4), 045207–045211 (2008).
[CrossRef]

Irvine, S. C.

S. C. Irvine, D. M. Paganin, S. Dubsky, R. A. Lewis, and A. Fouras, “Phase retrieval of improved three-dimensional velocimetry of dynamic x-ray blood speckle,” Appl. Phys. Lett. 93(15), 153901 (2008).
[CrossRef]

Kashyap, Y. S.

Y. S. Kashyap, P. S. Yadav, T. Roy, P. S. Sarkar, M. Shukla, and A. Sinha, “Laboratory-based X-ray phase-contrast imaging technique for material and medical science applications,” Appl. Radiat. Isot. 66(8), 1083–1090 (2008).
[CrossRef] [PubMed]

Kimata, T.

H. Ikeura-Sekiguchi, R. Kuroda, M. Yasumoto, H. Toyokawa, M. Koike, K. Yamada, F. Sakai, K. Mori, K. Maruyama, H. Oka, and T. Kimata, “In-line phase-contrast imaging of a biological specimen using a compact laser-Compton scattering-based x-ray source,” Appl. Phys. Lett. 92(13), 131107 (2008).
[CrossRef]

Kitchen, M.

D. M. Paganin, T. E. Gureyev, K. M. Pavlov, R. A. Lewis, and M. Kitchen, “Phase retrieval using coherent imaging systems with linear transfer functions,” Opt. Commun. 234(1-6), 87–105 (2004).
[CrossRef]

Kitchen, M. J.

Koike, M.

H. Ikeura-Sekiguchi, R. Kuroda, M. Yasumoto, H. Toyokawa, M. Koike, K. Yamada, F. Sakai, K. Mori, K. Maruyama, H. Oka, and T. Kimata, “In-line phase-contrast imaging of a biological specimen using a compact laser-Compton scattering-based x-ray source,” Appl. Phys. Lett. 92(13), 131107 (2008).
[CrossRef]

Kuroda, R.

H. Ikeura-Sekiguchi, R. Kuroda, M. Yasumoto, H. Toyokawa, M. Koike, K. Yamada, F. Sakai, K. Mori, K. Maruyama, H. Oka, and T. Kimata, “In-line phase-contrast imaging of a biological specimen using a compact laser-Compton scattering-based x-ray source,” Appl. Phys. Lett. 92(13), 131107 (2008).
[CrossRef]

Lagomarsino, S.

L. De Caro, A. Cedola, C. Giannini, I. Bukreeva, and S. Lagomarsino, “In-line phase-contrast imaging for strong absorbing objects,” Phys. Med. Biol. 53(22), 6619–6637 (2008).
[CrossRef] [PubMed]

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(10), 4556–4566 (2008).
[CrossRef] [PubMed]

J. P. Guigay, M. Langer, R. Boistel, and P. Cloetens, “Mixed transfer function and transport of intensity approach for phase retrieval in the Fresnel region,” Opt. Lett. 32(12), 1617–1619 (2007).
[CrossRef] [PubMed]

Lewis, R. A.

S. C. Irvine, D. M. Paganin, S. Dubsky, R. A. Lewis, and A. Fouras, “Phase retrieval of improved three-dimensional velocimetry of dynamic x-ray blood speckle,” Appl. Phys. Lett. 93(15), 153901 (2008).
[CrossRef]

D. M. Paganin, T. E. Gureyev, K. M. Pavlov, R. A. Lewis, and M. Kitchen, “Phase retrieval using coherent imaging systems with linear transfer functions,” Opt. Commun. 234(1-6), 87–105 (2004).
[CrossRef]

Li, G.

J. Y. Chen, D. J. Bottjer, G. Li, M. G. Hadfield, F. Gao, A. R. Cameron, C. Y. Zhang, D. C. Xian, P. Tafforeau, X. Liao, and Z. J. Yin, “Complex embryos displaying bilaterian characters from Precambrian Doushantuo phosphate deposits, Weng’an, Guizhou, China,” Proc. Natl. Acad. Sci. U.S.A. 106(45), 19056–19060 (2009).
[CrossRef] [PubMed]

Liao, X.

J. Y. Chen, D. J. Bottjer, G. Li, M. G. Hadfield, F. Gao, A. R. Cameron, C. Y. Zhang, D. C. Xian, P. Tafforeau, X. Liao, and Z. J. Yin, “Complex embryos displaying bilaterian characters from Precambrian Doushantuo phosphate deposits, Weng’an, Guizhou, China,” Proc. Natl. Acad. Sci. U.S.A. 106(45), 19056–19060 (2009).
[CrossRef] [PubMed]

Liu, L. X.

X. Wei, T. Q. Xiao, L. X. Liu, G. H. Du, M. Chen, Y. Y. Luo, and H. J. Xu, “Application of x-ray phase contrast imaging to microscopic identification of Chinese medicines,” Phys. Med. Biol. 50(18), 4277–4286 (2005).
[CrossRef] [PubMed]

Liu, Y.

B. Chen, P. Zhu, C. Chen, H. Shu, Y. Liu, Q. Yuan, J. Wang, W. Huang, H. Ming, and Z. Wu, “Theory and experiment of in-line phase contrast imaging on non-uniformly distributed source,” Spectrochim. Acta. B 62(6-7), 636–641 (2007).
[CrossRef]

Longo, R.

L. De Caro, F. Scattarella, C. Giannini, S. Tangaro, L. Rigon, R. Longo, and R. Bellotti, “Combined mixed approach algorithm for in-line phase-contrast x-ray imaging,” Med. Phys. 37(7), 3817–3827 (2010).
[CrossRef] [PubMed]

T. Xiao, A. Bergamaschi, D. Dreossi, R. Longo, A. Olivo, S. Pani, L. Rigon, T. Rokvic, C. Venanzi, and E. Castelli, “Effect of spatial coherence on application of in-line phase contrast imaging to synchrotron radiation mammography,” Nucl. Instrum. Meth. A 548(1-2), 155–162 (2005).
[CrossRef]

Luo, Y. Y.

X. Wei, T. Q. Xiao, L. X. Liu, G. H. Du, M. Chen, Y. Y. Luo, and H. J. Xu, “Application of x-ray phase contrast imaging to microscopic identification of Chinese medicines,” Phys. Med. Biol. 50(18), 4277–4286 (2005).
[CrossRef] [PubMed]

Mancuso, A. P.

Mandel, L.

Maruyama, K.

H. Ikeura-Sekiguchi, R. Kuroda, M. Yasumoto, H. Toyokawa, M. Koike, K. Yamada, F. Sakai, K. Mori, K. Maruyama, H. Oka, and T. Kimata, “In-line phase-contrast imaging of a biological specimen using a compact laser-Compton scattering-based x-ray source,” Appl. Phys. Lett. 92(13), 131107 (2008).
[CrossRef]

Mayo, S. C.

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(12), 2418–2430 (2004).
[CrossRef] [PubMed]

D. 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(1), 33–40 (2002).
[CrossRef] [PubMed]

McKinnon, A. E.

K. Irie, A. E. McKinnon, K. Unsworth, and I. M. Woodhead, “A model for measurement of noise in CCD digital-video cameras,” Meas. Sci. Technol. 19(4), 045207–045211 (2008).
[CrossRef]

Mcmahon, P. J.

D. Paganin, A. Barty, P. J. Mcmahon, and K. A. Nugent, “Quantitative phase-amplitude microscopy. III. The effect of noise,” J. Microsc. 214(1), 51–61 (2004).
[CrossRef] [PubMed]

Miller, P. R.

D. 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(1), 33–40 (2002).
[CrossRef] [PubMed]

Ming, H.

B. Chen, P. Zhu, C. Chen, H. Shu, Y. Liu, Q. Yuan, J. Wang, W. Huang, H. Ming, and Z. Wu, “Theory and experiment of in-line phase contrast imaging on non-uniformly distributed source,” Spectrochim. Acta. B 62(6-7), 636–641 (2007).
[CrossRef]

Mori, K.

H. Ikeura-Sekiguchi, R. Kuroda, M. Yasumoto, H. Toyokawa, M. Koike, K. Yamada, F. Sakai, K. Mori, K. Maruyama, H. Oka, and T. Kimata, “In-line phase-contrast imaging of a biological specimen using a compact laser-Compton scattering-based x-ray source,” Appl. Phys. Lett. 92(13), 131107 (2008).
[CrossRef]

Nugent, K. A.

L.D. Turner, B. B. Dhal, J. P. Hayes, A. P. Mancuso, K. A. Nugent, D. Paterson, R. E. Scholten, C. Q. Tran, and A. G. Peele, “X-ray phase imaging: Demonstration of extended conditions for homogeneous objects,” Opt. Express 12(13), 2960–2965 (2004).
[CrossRef] [PubMed]

D. Paganin, A. Barty, P. J. Mcmahon, and K. A. Nugent, “Quantitative phase-amplitude microscopy. III. The effect of noise,” J. Microsc. 214(1), 51–61 (2004).
[CrossRef] [PubMed]

T. E. Gureyev and K. A. Nugent, “Rapid quantitative phase imaging using the transport of intensity equation,” Opt. Commun. 133(1-6), 339–346 (1997).
[CrossRef]

Oka, H.

H. Ikeura-Sekiguchi, R. Kuroda, M. Yasumoto, H. Toyokawa, M. Koike, K. Yamada, F. Sakai, K. Mori, K. Maruyama, H. Oka, and T. Kimata, “In-line phase-contrast imaging of a biological specimen using a compact laser-Compton scattering-based x-ray source,” Appl. Phys. Lett. 92(13), 131107 (2008).
[CrossRef]

Olivo, A.

T. Xiao, A. Bergamaschi, D. Dreossi, R. Longo, A. Olivo, S. Pani, L. Rigon, T. Rokvic, C. Venanzi, and E. Castelli, “Effect of spatial coherence on application of in-line phase contrast imaging to synchrotron radiation mammography,” Nucl. Instrum. Meth. A 548(1-2), 155–162 (2005).
[CrossRef]

Paganin, D.

D. Paganin, A. Barty, P. J. Mcmahon, and K. A. Nugent, “Quantitative phase-amplitude microscopy. III. The effect of noise,” J. Microsc. 214(1), 51–61 (2004).
[CrossRef] [PubMed]

D. 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(1), 33–40 (2002).
[CrossRef] [PubMed]

Paganin, D. M.

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(7), 6423–6436 (2010).
[CrossRef] [PubMed]

S. C. Irvine, D. M. Paganin, S. Dubsky, R. A. Lewis, and A. Fouras, “Phase retrieval of improved three-dimensional velocimetry of dynamic x-ray blood speckle,” Appl. Phys. Lett. 93(15), 153901 (2008).
[CrossRef]

D. M. Paganin, T. E. Gureyev, K. M. Pavlov, R. A. Lewis, and M. Kitchen, “Phase retrieval using coherent imaging systems with linear transfer functions,” Opt. Commun. 234(1-6), 87–105 (2004).
[CrossRef]

T. E. Gureyev, A. Pogany, D. M. Paganin, and S. W. Wilkins, “Linear algorithms for phase retrieval in the Fresnel region,” Opt. Commun. 231(1-6), 53–70 (2004).
[CrossRef]

Pani, S.

T. Xiao, A. Bergamaschi, D. Dreossi, R. Longo, A. Olivo, S. Pani, L. Rigon, T. Rokvic, C. Venanzi, and E. Castelli, “Effect of spatial coherence on application of in-line phase contrast imaging to synchrotron radiation mammography,” Nucl. Instrum. Meth. A 548(1-2), 155–162 (2005).
[CrossRef]

Paterson, D.

Pateyron-Salome, M.

P. Cloetens, M. Pateyron-Salome, J. Y. Buffiere, 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(9), 5878–5886 (1997).
[CrossRef]

Pavlov, K. M.

D. M. Paganin, T. E. Gureyev, K. M. Pavlov, R. A. Lewis, and M. Kitchen, “Phase retrieval using coherent imaging systems with linear transfer functions,” Opt. Commun. 234(1-6), 87–105 (2004).
[CrossRef]

Peele, A. G.

Peix, G.

P. Cloetens, M. Pateyron-Salome, J. Y. Buffiere, 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(9), 5878–5886 (1997).
[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(10), 4556–4566 (2008).
[CrossRef] [PubMed]

P. Cloetens, M. Pateyron-Salome, J. Y. Buffiere, 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(9), 5878–5886 (1997).
[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(12), 2418–2430 (2004).
[CrossRef] [PubMed]

T. E. Gureyev, A. Pogany, D. M. Paganin, and S. W. Wilkins, “Linear algorithms for phase retrieval in the Fresnel region,” Opt. Commun. 231(1-6), 53–70 (2004).
[CrossRef]

Rigon, L.

L. De Caro, F. Scattarella, C. Giannini, S. Tangaro, L. Rigon, R. Longo, and R. Bellotti, “Combined mixed approach algorithm for in-line phase-contrast x-ray imaging,” Med. Phys. 37(7), 3817–3827 (2010).
[CrossRef] [PubMed]

T. Xiao, A. Bergamaschi, D. Dreossi, R. Longo, A. Olivo, S. Pani, L. Rigon, T. Rokvic, C. Venanzi, and E. Castelli, “Effect of spatial coherence on application of in-line phase contrast imaging to synchrotron radiation mammography,” Nucl. Instrum. Meth. A 548(1-2), 155–162 (2005).
[CrossRef]

Roberts, A.

N. M. Dragomir, X. M. Goh, and A. Roberts, “Three-dimensional refractive index reconstruction with quantitative phase tomography,” Microsc. Res. Tech. 71(1), 5–10 (2008).
[CrossRef]

Rokvic, T.

T. Xiao, A. Bergamaschi, D. Dreossi, R. Longo, A. Olivo, S. Pani, L. Rigon, T. Rokvic, C. Venanzi, and E. Castelli, “Effect of spatial coherence on application of in-line phase contrast imaging to synchrotron radiation mammography,” Nucl. Instrum. Meth. A 548(1-2), 155–162 (2005).
[CrossRef]

Roy, T.

Y. S. Kashyap, P. S. Yadav, T. Roy, P. S. Sarkar, M. Shukla, and A. Sinha, “Laboratory-based X-ray phase-contrast imaging technique for material and medical science applications,” Appl. Radiat. Isot. 66(8), 1083–1090 (2008).
[CrossRef] [PubMed]

Sakai, F.

H. Ikeura-Sekiguchi, R. Kuroda, M. Yasumoto, H. Toyokawa, M. Koike, K. Yamada, F. Sakai, K. Mori, K. Maruyama, H. Oka, and T. Kimata, “In-line phase-contrast imaging of a biological specimen using a compact laser-Compton scattering-based x-ray source,” Appl. Phys. Lett. 92(13), 131107 (2008).
[CrossRef]

Sarkar, P. S.

Y. S. Kashyap, P. S. Yadav, T. Roy, P. S. Sarkar, M. Shukla, and A. Sinha, “Laboratory-based X-ray phase-contrast imaging technique for material and medical science applications,” Appl. Radiat. Isot. 66(8), 1083–1090 (2008).
[CrossRef] [PubMed]

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).

Scattarella, F.

L. De Caro, F. Scattarella, C. Giannini, S. Tangaro, L. Rigon, R. Longo, and R. Bellotti, “Combined mixed approach algorithm for in-line phase-contrast x-ray imaging,” Med. Phys. 37(7), 3817–3827 (2010).
[CrossRef] [PubMed]

Schlenker, M.

P. Cloetens, M. Pateyron-Salome, J. Y. Buffiere, 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(9), 5878–5886 (1997).
[CrossRef]

Scholten, R. E.

Shi, D.

Shu, H.

B. Chen, P. Zhu, C. Chen, H. Shu, Y. Liu, Q. Yuan, J. Wang, W. Huang, H. Ming, and Z. Wu, “Theory and experiment of in-line phase contrast imaging on non-uniformly distributed source,” Spectrochim. Acta. B 62(6-7), 636–641 (2007).
[CrossRef]

Shukla, M.

Y. S. Kashyap, P. S. Yadav, T. Roy, P. S. Sarkar, M. Shukla, and A. Sinha, “Laboratory-based X-ray phase-contrast imaging technique for material and medical science applications,” Appl. Radiat. Isot. 66(8), 1083–1090 (2008).
[CrossRef] [PubMed]

Sinha, A.

Y. S. Kashyap, P. S. Yadav, T. Roy, P. S. Sarkar, M. Shukla, and A. Sinha, “Laboratory-based X-ray phase-contrast imaging technique for material and medical science applications,” Appl. Radiat. Isot. 66(8), 1083–1090 (2008).
[CrossRef] [PubMed]

Stampanoni, M.

Tafforeau, P.

J. Y. Chen, D. J. Bottjer, G. Li, M. G. Hadfield, F. Gao, A. R. Cameron, C. Y. Zhang, D. C. Xian, P. Tafforeau, X. Liao, and Z. J. Yin, “Complex embryos displaying bilaterian characters from Precambrian Doushantuo phosphate deposits, Weng’an, Guizhou, China,” Proc. Natl. Acad. Sci. U.S.A. 106(45), 19056–19060 (2009).
[CrossRef] [PubMed]

Tangaro, S.

L. De Caro, F. Scattarella, C. Giannini, S. Tangaro, L. Rigon, R. Longo, and R. Bellotti, “Combined mixed approach algorithm for in-line phase-contrast x-ray imaging,” Med. Phys. 37(7), 3817–3827 (2010).
[CrossRef] [PubMed]

Teague, M. R.

Tikhonov, A. N.

A. N. Tikhonov and V. Y. Arsenin, “Solutions of Ill-posed Problems,” SIAM Rev. 21(2), 266–267 (1979).
[CrossRef]

Toyokawa, H.

H. Ikeura-Sekiguchi, R. Kuroda, M. Yasumoto, H. Toyokawa, M. Koike, K. Yamada, F. Sakai, K. Mori, K. Maruyama, H. Oka, and T. Kimata, “In-line phase-contrast imaging of a biological specimen using a compact laser-Compton scattering-based x-ray source,” Appl. Phys. Lett. 92(13), 131107 (2008).
[CrossRef]

Tran, C. Q.

Turner, L.D.

Uesugi, K.

Unsworth, K.

K. Irie, A. E. McKinnon, K. Unsworth, and I. M. Woodhead, “A model for measurement of noise in CCD digital-video cameras,” Meas. Sci. Technol. 19(4), 045207–045211 (2008).
[CrossRef]

Venanzi, C.

T. Xiao, A. Bergamaschi, D. Dreossi, R. Longo, A. Olivo, S. Pani, L. Rigon, T. Rokvic, C. Venanzi, and E. Castelli, “Effect of spatial coherence on application of in-line phase contrast imaging to synchrotron radiation mammography,” Nucl. Instrum. Meth. A 548(1-2), 155–162 (2005).
[CrossRef]

Vimond, M.

J. Bigot, F. Gamboa, and M. Vimond, “Estimation of Translation, Rotation, and Scaling between Noisy Images Using the Fouier-Mellin Transform,” SIAM J. Imaging Sci. 2(2), 614–645 (2009).
[CrossRef]

Wang, J.

B. Chen, P. Zhu, C. Chen, H. Shu, Y. Liu, Q. Yuan, J. Wang, W. Huang, H. Ming, and Z. Wu, “Theory and experiment of in-line phase contrast imaging on non-uniformly distributed source,” Spectrochim. Acta. B 62(6-7), 636–641 (2007).
[CrossRef]

Wei, X.

X. Wei, T. Q. Xiao, L. X. Liu, G. H. Du, M. Chen, Y. Y. Luo, and H. J. Xu, “Application of x-ray phase contrast imaging to microscopic identification of Chinese medicines,” Phys. Med. Biol. 50(18), 4277–4286 (2005).
[CrossRef] [PubMed]

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(12), 2418–2430 (2004).
[CrossRef] [PubMed]

T. E. Gureyev, A. Pogany, D. M. Paganin, and S. W. Wilkins, “Linear algorithms for phase retrieval in the Fresnel region,” Opt. Commun. 231(1-6), 53–70 (2004).
[CrossRef]

D. 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(1), 33–40 (2002).
[CrossRef] [PubMed]

Wolf, E.

Woodhead, I. M.

K. Irie, A. E. McKinnon, K. Unsworth, and I. M. Woodhead, “A model for measurement of noise in CCD digital-video cameras,” Meas. Sci. Technol. 19(4), 045207–045211 (2008).
[CrossRef]

Wu, Z.

B. Chen, P. Zhu, C. Chen, H. Shu, Y. Liu, Q. Yuan, J. Wang, W. Huang, H. Ming, and Z. Wu, “Theory and experiment of in-line phase contrast imaging on non-uniformly distributed source,” Spectrochim. Acta. B 62(6-7), 636–641 (2007).
[CrossRef]

Xian, D. C.

J. Y. Chen, D. J. Bottjer, G. Li, M. G. Hadfield, F. Gao, A. R. Cameron, C. Y. Zhang, D. C. Xian, P. Tafforeau, X. Liao, and Z. J. Yin, “Complex embryos displaying bilaterian characters from Precambrian Doushantuo phosphate deposits, Weng’an, Guizhou, China,” Proc. Natl. Acad. Sci. U.S.A. 106(45), 19056–19060 (2009).
[CrossRef] [PubMed]

Xiao, T.

T. Xiao, A. Bergamaschi, D. Dreossi, R. Longo, A. Olivo, S. Pani, L. Rigon, T. Rokvic, C. Venanzi, and E. Castelli, “Effect of spatial coherence on application of in-line phase contrast imaging to synchrotron radiation mammography,” Nucl. Instrum. Meth. A 548(1-2), 155–162 (2005).
[CrossRef]

Xiao, T. Q.

X. Wei, T. Q. Xiao, L. X. Liu, G. H. Du, M. Chen, Y. Y. Luo, and H. J. Xu, “Application of x-ray phase contrast imaging to microscopic identification of Chinese medicines,” Phys. Med. Biol. 50(18), 4277–4286 (2005).
[CrossRef] [PubMed]

Xu, H. J.

X. Wei, T. Q. Xiao, L. X. Liu, G. H. Du, M. Chen, Y. Y. Luo, and H. J. Xu, “Application of x-ray phase contrast imaging to microscopic identification of Chinese medicines,” Phys. Med. Biol. 50(18), 4277–4286 (2005).
[CrossRef] [PubMed]

Yadav, P. S.

Y. S. Kashyap, P. S. Yadav, T. Roy, P. S. Sarkar, M. Shukla, and A. Sinha, “Laboratory-based X-ray phase-contrast imaging technique for material and medical science applications,” Appl. Radiat. Isot. 66(8), 1083–1090 (2008).
[CrossRef] [PubMed]

Yamada, K.

H. Ikeura-Sekiguchi, R. Kuroda, M. Yasumoto, H. Toyokawa, M. Koike, K. Yamada, F. Sakai, K. Mori, K. Maruyama, H. Oka, and T. Kimata, “In-line phase-contrast imaging of a biological specimen using a compact laser-Compton scattering-based x-ray source,” Appl. Phys. Lett. 92(13), 131107 (2008).
[CrossRef]

Yasumoto, M.

H. Ikeura-Sekiguchi, R. Kuroda, M. Yasumoto, H. Toyokawa, M. Koike, K. Yamada, F. Sakai, K. Mori, K. Maruyama, H. Oka, and T. Kimata, “In-line phase-contrast imaging of a biological specimen using a compact laser-Compton scattering-based x-ray source,” Appl. Phys. Lett. 92(13), 131107 (2008).
[CrossRef]

Yin, Z. J.

J. Y. Chen, D. J. Bottjer, G. Li, M. G. Hadfield, F. Gao, A. R. Cameron, C. Y. Zhang, D. C. Xian, P. Tafforeau, X. Liao, and Z. J. Yin, “Complex embryos displaying bilaterian characters from Precambrian Doushantuo phosphate deposits, Weng’an, Guizhou, China,” Proc. Natl. Acad. Sci. U.S.A. 106(45), 19056–19060 (2009).
[CrossRef] [PubMed]

Yuan, Q.

B. Chen, P. Zhu, C. Chen, H. Shu, Y. Liu, Q. Yuan, J. Wang, W. Huang, H. Ming, and Z. Wu, “Theory and experiment of in-line phase contrast imaging on non-uniformly distributed source,” Spectrochim. Acta. B 62(6-7), 636–641 (2007).
[CrossRef]

Zhang, C. Y.

J. Y. Chen, D. J. Bottjer, G. Li, M. G. Hadfield, F. Gao, A. R. Cameron, C. Y. Zhang, D. C. Xian, P. Tafforeau, X. Liao, and Z. J. Yin, “Complex embryos displaying bilaterian characters from Precambrian Doushantuo phosphate deposits, Weng’an, Guizhou, China,” Proc. Natl. Acad. Sci. U.S.A. 106(45), 19056–19060 (2009).
[CrossRef] [PubMed]

Zhang, X.

Zhang, Y.

Zhu, P.

B. Chen, P. Zhu, C. Chen, H. Shu, Y. Liu, Q. Yuan, J. Wang, W. Huang, H. Ming, and Z. Wu, “Theory and experiment of in-line phase contrast imaging on non-uniformly distributed source,” Spectrochim. Acta. B 62(6-7), 636–641 (2007).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (2)

H. Ikeura-Sekiguchi, R. Kuroda, M. Yasumoto, H. Toyokawa, M. Koike, K. Yamada, F. Sakai, K. Mori, K. Maruyama, H. Oka, and T. Kimata, “In-line phase-contrast imaging of a biological specimen using a compact laser-Compton scattering-based x-ray source,” Appl. Phys. Lett. 92(13), 131107 (2008).
[CrossRef]

S. C. Irvine, D. M. Paganin, S. Dubsky, R. A. Lewis, and A. Fouras, “Phase retrieval of improved three-dimensional velocimetry of dynamic x-ray blood speckle,” Appl. Phys. Lett. 93(15), 153901 (2008).
[CrossRef]

Appl. Radiat. Isot. (1)

Y. S. Kashyap, P. S. Yadav, T. Roy, P. S. Sarkar, M. Shukla, and A. Sinha, “Laboratory-based X-ray phase-contrast imaging technique for material and medical science applications,” Appl. Radiat. Isot. 66(8), 1083–1090 (2008).
[CrossRef] [PubMed]

At. Data Nucl. Data Tables (1)

B. L. Henke, E. M. Cullikson, and J. C. Davis, “X-ray interactions: photo absorption, scattering, transmission, and reflection at E=50-30,000eV,Z=1-92,” At. Data Nucl. Data Tables 54(2), 181–342 (1993).
[CrossRef]

Eur. J. Radiol. (1)

J. E. Adams, “Quantitative computed tomography,” Eur. J. Radiol. 71(3), 415–424 (2009).
[CrossRef] [PubMed]

J. Appl. Phys. (1)

P. Cloetens, M. Pateyron-Salome, J. Y. Buffiere, 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(9), 5878–5886 (1997).
[CrossRef]

J. Microsc. (2)

D. 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(1), 33–40 (2002).
[CrossRef] [PubMed]

D. Paganin, A. Barty, P. J. Mcmahon, and K. A. Nugent, “Quantitative phase-amplitude microscopy. III. The effect of noise,” J. Microsc. 214(1), 51–61 (2004).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (2)

Meas. Sci. Technol. (1)

K. Irie, A. E. McKinnon, K. Unsworth, and I. M. Woodhead, “A model for measurement of noise in CCD digital-video cameras,” Meas. Sci. Technol. 19(4), 045207–045211 (2008).
[CrossRef]

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(10), 4556–4566 (2008).
[CrossRef] [PubMed]

L. De Caro, F. Scattarella, C. Giannini, S. Tangaro, L. Rigon, R. Longo, and R. Bellotti, “Combined mixed approach algorithm for in-line phase-contrast x-ray imaging,” Med. Phys. 37(7), 3817–3827 (2010).
[CrossRef] [PubMed]

Microsc. Res. Tech. (1)

N. M. Dragomir, X. M. Goh, and A. Roberts, “Three-dimensional refractive index reconstruction with quantitative phase tomography,” Microsc. Res. Tech. 71(1), 5–10 (2008).
[CrossRef]

Nucl. Instrum. Meth. A (1)

T. Xiao, A. Bergamaschi, D. Dreossi, R. Longo, A. Olivo, S. Pani, L. Rigon, T. Rokvic, C. Venanzi, and E. Castelli, “Effect of spatial coherence on application of in-line phase contrast imaging to synchrotron radiation mammography,” Nucl. Instrum. Meth. A 548(1-2), 155–162 (2005).
[CrossRef]

Opt. Commun. (3)

T. E. Gureyev and K. A. Nugent, “Rapid quantitative phase imaging using the transport of intensity equation,” Opt. Commun. 133(1-6), 339–346 (1997).
[CrossRef]

T. E. Gureyev, A. Pogany, D. M. Paganin, and S. W. Wilkins, “Linear algorithms for phase retrieval in the Fresnel region,” Opt. Commun. 231(1-6), 53–70 (2004).
[CrossRef]

D. M. Paganin, T. E. Gureyev, K. M. Pavlov, R. A. Lewis, and M. Kitchen, “Phase retrieval using coherent imaging systems with linear transfer functions,” Opt. Commun. 234(1-6), 87–105 (2004).
[CrossRef]

Opt. Express (6)

Opt. Lett. (1)

Optik (Stuttg.) (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).

Phys. Med. Biol. (2)

L. De Caro, A. Cedola, C. Giannini, I. Bukreeva, and S. Lagomarsino, “In-line phase-contrast imaging for strong absorbing objects,” Phys. Med. Biol. 53(22), 6619–6637 (2008).
[CrossRef] [PubMed]

X. Wei, T. Q. Xiao, L. X. Liu, G. H. Du, M. Chen, Y. Y. Luo, and H. J. Xu, “Application of x-ray phase contrast imaging to microscopic identification of Chinese medicines,” Phys. Med. Biol. 50(18), 4277–4286 (2005).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. U.S.A. (1)

J. Y. Chen, D. J. Bottjer, G. Li, M. G. Hadfield, F. Gao, A. R. Cameron, C. Y. Zhang, D. C. Xian, P. Tafforeau, X. Liao, and Z. J. Yin, “Complex embryos displaying bilaterian characters from Precambrian Doushantuo phosphate deposits, Weng’an, Guizhou, China,” Proc. Natl. Acad. Sci. U.S.A. 106(45), 19056–19060 (2009).
[CrossRef] [PubMed]

SIAM J. Imaging Sci. (1)

J. Bigot, F. Gamboa, and M. Vimond, “Estimation of Translation, Rotation, and Scaling between Noisy Images Using the Fouier-Mellin Transform,” SIAM J. Imaging Sci. 2(2), 614–645 (2009).
[CrossRef]

SIAM Rev. (1)

A. N. Tikhonov and V. Y. Arsenin, “Solutions of Ill-posed Problems,” SIAM Rev. 21(2), 266–267 (1979).
[CrossRef]

Spectrochim. Acta. B (1)

B. Chen, P. Zhu, C. Chen, H. Shu, Y. Liu, Q. Yuan, J. Wang, W. Huang, H. Ming, and Z. Wu, “Theory and experiment of in-line phase contrast imaging on non-uniformly distributed source,” Spectrochim. Acta. B 62(6-7), 636–641 (2007).
[CrossRef]

Other (6)

Eastman Kodak Company, “CCD Image sensors noise sources,” Rev. 2.1 (2005).

M. S. Nixon, and A. S. Aguado, Feature Extraction and Image Processing (Academic Press, 2008).

R. C. Gonzalez, and R. E. Woods, Digital Image Processing (Pearson Prentice Hall, 2008).

D. Paganin, Coherent X-ray Optics (Oxford University Press, New York, 2006).

M. Born, and E. Wolf, Principles of Optics: ElectromagneticTheory of Propagation, Interference and Diffraction of Light (Cambridge UniversityPress, 1999).

O. K. Ersoy, Diffraction, Fourier Optics and Imaging (John Wiley& Sons, Inc., 2006).

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Figures (9)

Fig. 1
Fig. 1

Schematic diagram for the quantitative in-line phase contrast imaging system, where the distances between the object plane and the two image planes are z 1 and z 2 , respectively.

Fig. 2
Fig. 2

Phantom for simulation (a) nylon fiber with a diameter of 100μm and (b) corresponding profile at the white line marked in Fig. 2(a).

Fig. 3
Fig. 3

Retrieving errors vs. z2, while z1 was set to (a) 50cm, (b) 100cm, (c) 120cm and (d) 150cm, respectively. The photon energy is set to 15keV and the diameter for the fiber sample is 100μm.

Fig. 4
Fig. 4

Retrieved image profiles by the triple rules at the white line as marked in Fig. 2, (a) profiles with different SDD-pair, (b) profiles at different z2 while z1 fixed to 120cm. The photon energy is set to 15keV and the diameter for the fiber sample is 100μm.

Fig. 5
Fig. 5

Spectral correlation degree vs. z2 when z1 was set to (a) 50cm, (b) 100cm, (c) 120cm and (d) 150cm, respectively. The photon energy is set to 15keV and the diameter for the fiber sample is 100μm.

Fig. 6
Fig. 6

Picture for experimental facilities at SSRF BL13W beamline (a) sample stage, (b) CCD and (c) slide rails.

Fig. 7
Fig. 7

In-line phase contrast images at SDD of 50cm in (a), retrieved image with single image at SDD of 50cm is shown in (b) and retrieved image with images at SDD pair of 50cm and 150cm in (c). Profiles of retrieved images with single image at 50cm, SDD-pair 50-150cm and 120-360cm are displayed in (d).

Fig. 8
Fig. 8

The simulation results for the retrieved image profiles at different SDD pairs with the triple rules, with the same parameters as that employed in the experiment, i.e., the photon energy 15keV, the diameter for the fiber sample 128μm and the effective pixel size 1.85μm.

Fig. 9
Fig. 9

Experimental results with SDD for the first image fixed to 50cm, where (a) RMS errors of the retrieved images vs. z2. (b) Spectral correlation degree vs. z2.

Tables (1)

Tables Icon

Table 1 Relative RMS Errors for the Retrieved Images at a Series of SDD-Pairs Following the Triple Relations

Equations (10)

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n = 1 δ + i β
U z ( x , y ) exp ( i k z ) i λ z U o ( x , y ) exp { i k 2 z [ ( x x ) 2 + ( y y ) 2 ] } d x d y
I z ( x , y ) = | h ( x , y ; x , y ) U o ( x , y ) | 2
F { ( I z / I o 1 ) / 2 } = cos ( χ z ) F { Re φ o } + sin ( χ z ) F { Im φ o }
( F { Re φ o } F { Im φ o } ) = 1 sin [ ( z 2 z 1 ) χ ] × [ sin ( z 2 χ ) cos ( z 2 χ ) sin ( z 1 χ ) cos ( z 1 χ ) ] × ( F { ( I z 1 / I o 1 ) / 2 } F { ( I z 2 / I o 1 ) / 2 } )
( z 2 z 1 ) λ ( u 2 + v 2 ) = m , ( m = 0 , ± 1 , ± 2 , ... )
( F { Re φ o } F { Im φ o } ) = sin [ ( z 2 z 1 ) χ ] sin 2 [ ( z 2 z 1 ) χ ] + α × [ sin ( z 2 χ ) cos ( z 2 χ ) sin ( z 1 χ ) cos ( z 1 χ ) ] × ( F { ( I z 1 / I o 1 ) / 2 } F { ( I z 2 / I o 1 ) / 2 } )
Δ z = z 2 z 1 m λ ( u 2 + v 2 ) , ( m = 0 , ± 1 , ± 2 , ... )
R M S = ( i , j | g ( i , j ) f ( i , j ) | 2 / i , j | f ( i , j ) | 2 ) 1 2 × 100 %
ρ 12 = R 1 ( u , v ) R 2 ( u , v ) d u d v [ R 1 2 ( u , v ) d u d v R 2 2 ( u , v ) d u d v ] 1 2

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