Abstract

There is currently much interest in developing X-ray Phase Contrast Imaging (XPCI) systems which employ laboratory sources in order to deploy the technique in real world applications. The challenge faced by nearly all XPCI techniques is that of efficiently utilising the x-ray flux emitted by an x-ray tube which is polychromatic and possesses only partial spatial coherence. Techniques have, however, been developed which overcome these limitations. Such a technique, known as coded aperture XPCI, has been under development in our laboratories in recent years for application principally in medical imaging and security screening. In this paper we derive limitations imposed upon source polychromaticity and spatial extent by the coded aperture system. We also show that although other grating XPCI techniques employ a different physical principle, they satisfy design constraints similar to those of the coded aperture XPCI.

© 2010 Optical Society of America

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  1. E. Castelli, F. Arfelli, D. Dreossi, R. Longo, T. Rokvic, M. Cova, E. Quaia, M. Tonutti, F. Zanconati, A. Abrami, V. Chenda, R. Menk, E. Quai, G. Tromba, P. Bregant, and F. de Guarrini, "Clinical mammography at the SYRMEP beam line," Nucl. Instrum. Meth. A 572(1), 237-240 (2007).
    [CrossRef]
  2. A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, "Phase Tomography by X-ray Talbot Interferometry for Biological Imaging," Jpn. J. Appl. Phys. 45, 5254-5262 (2006).
    [CrossRef]
  3. 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(4), 258-261 (2006).
    [CrossRef]
  4. S. Wilkins, T. Gureyev, D. Gao, A. Pogany, and A. Stevenson, "Phase-contrast imaging using polychromatic hard X-rays," Nature 384, 335-338 (1996).
    [CrossRef]
  5. D. Chapman, W. Thomlinson, R. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, "Diffraction enhanced x-ray imaging," Phys. Med. Biol. 42(11), 2015 (1997).
    [CrossRef] [PubMed]
  6. Y. Suzuki, N. Yagi, and K. Uesugi, "X-ray refraction-enhanced imaging and a method for phase retrieval for a simple object," J. Synchrotron Radiat. 9(3), 160-165 (2002).
    [CrossRef] [PubMed]
  7. A. Olivo, and R. Speller, "Modelling of a novel x-ray phase contrast imaging technique based on coded apertures," Phys. Med. Biol. 52(22), 6555-6573 (2007).
    [CrossRef] [PubMed]
  8. A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, "Demonstration of X-Ray Talbot Interferometry," Jpn. J. Appl. Phys. 42(Part 2, No. 7B), L866-L868 (2003).
    [CrossRef]
  9. T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, "X-ray phase imaging with a grating interferometer," Opt. Express 13(16), 6296-6304 (2005).
    [CrossRef] [PubMed]
  10. F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Bronnimann, C. Grunzweig, and C. David, "Hard-X-ray dark-field imaging using a grating interferometer," Nat. Mater. 7(2), 134-137 (2008).
    [CrossRef] [PubMed]
  11. A. Olivo, and R. Speller, "A coded-aperture technique allowing x-ray phase contrast imaging with conventional sources," Appl. Phys. Lett. 91(7), 074106 (2007).
    [CrossRef]
  12. Z.-F. Huang, K.-J. Kang, L. Zhang, Z.-Q. Chen, F. Ding, Z.-T. Wang, and Q.-G. Fang, "Alternative method for differential phase-contrast imaging with weakly coherent hard x rays," Phys. Rev. A 79(1), 013815 (2009).
    [CrossRef]
  13. A. Olivo, and R. Speller, "Image formation principles in coded-aperture based x-ray phase contrast imaging," Phys. Med. Biol. 53(22), 6461-6474 (2008).
    [CrossRef] [PubMed]
  14. X. Wu, and H. Liu, "A new theory of phase-contrast x-ray imaging based on Wigner distributions," Med. Phys. 31(9), 2378-2384 (2004).
    [CrossRef] [PubMed]
  15. L. Mandel, and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, 1995).
  16. M. Born, and E. Wolf, Principles of Optics, seventh ed. (Cambridge University Press, Cambridge, 1999).
  17. Y. I. Nesterets, and S. W. Wilkins, "Phase-contrast imaging using a scanning-double grating configuration," Opt. Express 16(8), 5849-5867 (2008).
    [CrossRef] [PubMed]
  18. P. Munro, R. Ignatyev, K. Speller, and A. Olivo, "The relationship between wave and geometrical optics models of coded aperture type x-ray phase contrast imaging systems," Opt. Express 18(5), 4103-4117 (2010).
    [CrossRef] [PubMed]
  19. E. Chu, Discrete and Continuous Fourier Transforms: Analysis, Applications and Fast Algorithms (Chapman and Hall/CR, 2008).
  20. R. Nowotny, and A. Höfer, "A computer code for the calculation of diagnostic x-ray spectra," Fortschr Röntgenstr 142, 685-689 (1985).
    [CrossRef]
  21. M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, "The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources," J. Microsc. 232, 145-157 (2008).
    [CrossRef] [PubMed]

2010 (1)

2009 (1)

Z.-F. Huang, K.-J. Kang, L. Zhang, Z.-Q. Chen, F. Ding, Z.-T. Wang, and Q.-G. Fang, "Alternative method for differential phase-contrast imaging with weakly coherent hard x rays," Phys. Rev. A 79(1), 013815 (2009).
[CrossRef]

2008 (4)

A. Olivo, and R. Speller, "Image formation principles in coded-aperture based x-ray phase contrast imaging," Phys. Med. Biol. 53(22), 6461-6474 (2008).
[CrossRef] [PubMed]

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Bronnimann, C. Grunzweig, and C. David, "Hard-X-ray dark-field imaging using a grating interferometer," Nat. Mater. 7(2), 134-137 (2008).
[CrossRef] [PubMed]

Y. I. Nesterets, and S. W. Wilkins, "Phase-contrast imaging using a scanning-double grating configuration," Opt. Express 16(8), 5849-5867 (2008).
[CrossRef] [PubMed]

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, "The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources," J. Microsc. 232, 145-157 (2008).
[CrossRef] [PubMed]

2007 (3)

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

E. Castelli, F. Arfelli, D. Dreossi, R. Longo, T. Rokvic, M. Cova, E. Quaia, M. Tonutti, F. Zanconati, A. Abrami, V. Chenda, R. Menk, E. Quai, G. Tromba, P. Bregant, and F. de Guarrini, "Clinical mammography at the SYRMEP beam line," Nucl. Instrum. Meth. A 572(1), 237-240 (2007).
[CrossRef]

A. Olivo, and R. Speller, "Modelling of a novel x-ray phase contrast imaging technique based on coded apertures," Phys. Med. Biol. 52(22), 6555-6573 (2007).
[CrossRef] [PubMed]

2006 (2)

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, "Phase Tomography by X-ray Talbot Interferometry for Biological Imaging," Jpn. J. Appl. Phys. 45, 5254-5262 (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(4), 258-261 (2006).
[CrossRef]

2005 (1)

2004 (1)

X. Wu, and H. Liu, "A new theory of phase-contrast x-ray imaging based on Wigner distributions," Med. Phys. 31(9), 2378-2384 (2004).
[CrossRef] [PubMed]

2003 (1)

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

2002 (1)

Y. Suzuki, N. Yagi, and K. Uesugi, "X-ray refraction-enhanced imaging and a method for phase retrieval for a simple object," J. Synchrotron Radiat. 9(3), 160-165 (2002).
[CrossRef] [PubMed]

1997 (1)

D. Chapman, W. Thomlinson, R. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, "Diffraction enhanced x-ray imaging," Phys. Med. Biol. 42(11), 2015 (1997).
[CrossRef] [PubMed]

1996 (1)

S. Wilkins, T. Gureyev, D. Gao, A. Pogany, and A. Stevenson, "Phase-contrast imaging using polychromatic hard X-rays," Nature 384, 335-338 (1996).
[CrossRef]

1985 (1)

R. Nowotny, and A. Höfer, "A computer code for the calculation of diagnostic x-ray spectra," Fortschr Röntgenstr 142, 685-689 (1985).
[CrossRef]

Abrami, A.

E. Castelli, F. Arfelli, D. Dreossi, R. Longo, T. Rokvic, M. Cova, E. Quaia, M. Tonutti, F. Zanconati, A. Abrami, V. Chenda, R. Menk, E. Quai, G. Tromba, P. Bregant, and F. de Guarrini, "Clinical mammography at the SYRMEP beam line," Nucl. Instrum. Meth. A 572(1), 237-240 (2007).
[CrossRef]

Arfelli, F.

E. Castelli, F. Arfelli, D. Dreossi, R. Longo, T. Rokvic, M. Cova, E. Quaia, M. Tonutti, F. Zanconati, A. Abrami, V. Chenda, R. Menk, E. Quai, G. Tromba, P. Bregant, and F. de Guarrini, "Clinical mammography at the SYRMEP beam line," Nucl. Instrum. Meth. A 572(1), 237-240 (2007).
[CrossRef]

D. Chapman, W. Thomlinson, R. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, "Diffraction enhanced x-ray imaging," Phys. Med. Biol. 42(11), 2015 (1997).
[CrossRef] [PubMed]

Baumann, J.

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, "The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources," J. Microsc. 232, 145-157 (2008).
[CrossRef] [PubMed]

Bech, M.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Bronnimann, C. Grunzweig, and C. David, "Hard-X-ray dark-field imaging using a grating interferometer," Nat. Mater. 7(2), 134-137 (2008).
[CrossRef] [PubMed]

Bregant, P.

E. Castelli, F. Arfelli, D. Dreossi, R. Longo, T. Rokvic, M. Cova, E. Quaia, M. Tonutti, F. Zanconati, A. Abrami, V. Chenda, R. Menk, E. Quai, G. Tromba, P. Bregant, and F. de Guarrini, "Clinical mammography at the SYRMEP beam line," Nucl. Instrum. Meth. A 572(1), 237-240 (2007).
[CrossRef]

Bronnimann, C.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Bronnimann, C. Grunzweig, and C. David, "Hard-X-ray dark-field imaging using a grating interferometer," Nat. Mater. 7(2), 134-137 (2008).
[CrossRef] [PubMed]

Bunk, O.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Bronnimann, C. Grunzweig, and C. David, "Hard-X-ray dark-field imaging using a grating interferometer," Nat. Mater. 7(2), 134-137 (2008).
[CrossRef] [PubMed]

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, "The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources," J. Microsc. 232, 145-157 (2008).
[CrossRef] [PubMed]

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(4), 258-261 (2006).
[CrossRef]

Castelli, E.

E. Castelli, F. Arfelli, D. Dreossi, R. Longo, T. Rokvic, M. Cova, E. Quaia, M. Tonutti, F. Zanconati, A. Abrami, V. Chenda, R. Menk, E. Quai, G. Tromba, P. Bregant, and F. de Guarrini, "Clinical mammography at the SYRMEP beam line," Nucl. Instrum. Meth. A 572(1), 237-240 (2007).
[CrossRef]

Chapman, D.

D. Chapman, W. Thomlinson, R. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, "Diffraction enhanced x-ray imaging," Phys. Med. Biol. 42(11), 2015 (1997).
[CrossRef] [PubMed]

Chen, Z.-Q.

Z.-F. Huang, K.-J. Kang, L. Zhang, Z.-Q. Chen, F. Ding, Z.-T. Wang, and Q.-G. Fang, "Alternative method for differential phase-contrast imaging with weakly coherent hard x rays," Phys. Rev. A 79(1), 013815 (2009).
[CrossRef]

Chenda, V.

E. Castelli, F. Arfelli, D. Dreossi, R. Longo, T. Rokvic, M. Cova, E. Quaia, M. Tonutti, F. Zanconati, A. Abrami, V. Chenda, R. Menk, E. Quai, G. Tromba, P. Bregant, and F. de Guarrini, "Clinical mammography at the SYRMEP beam line," Nucl. Instrum. Meth. A 572(1), 237-240 (2007).
[CrossRef]

Cloetens, P.

Cova, M.

E. Castelli, F. Arfelli, D. Dreossi, R. Longo, T. Rokvic, M. Cova, E. Quaia, M. Tonutti, F. Zanconati, A. Abrami, V. Chenda, R. Menk, E. Quai, G. Tromba, P. Bregant, and F. de Guarrini, "Clinical mammography at the SYRMEP beam line," Nucl. Instrum. Meth. A 572(1), 237-240 (2007).
[CrossRef]

David, C.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Bronnimann, C. Grunzweig, and C. David, "Hard-X-ray dark-field imaging using a grating interferometer," Nat. Mater. 7(2), 134-137 (2008).
[CrossRef] [PubMed]

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, "The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources," J. Microsc. 232, 145-157 (2008).
[CrossRef] [PubMed]

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(4), 258-261 (2006).
[CrossRef]

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, "X-ray phase imaging with a grating interferometer," Opt. Express 13(16), 6296-6304 (2005).
[CrossRef] [PubMed]

de Guarrini, F.

E. Castelli, F. Arfelli, D. Dreossi, R. Longo, T. Rokvic, M. Cova, E. Quaia, M. Tonutti, F. Zanconati, A. Abrami, V. Chenda, R. Menk, E. Quai, G. Tromba, P. Bregant, and F. de Guarrini, "Clinical mammography at the SYRMEP beam line," Nucl. Instrum. Meth. A 572(1), 237-240 (2007).
[CrossRef]

Diaz, A.

Ding, F.

Z.-F. Huang, K.-J. Kang, L. Zhang, Z.-Q. Chen, F. Ding, Z.-T. Wang, and Q.-G. Fang, "Alternative method for differential phase-contrast imaging with weakly coherent hard x rays," Phys. Rev. A 79(1), 013815 (2009).
[CrossRef]

Dreossi, D.

E. Castelli, F. Arfelli, D. Dreossi, R. Longo, T. Rokvic, M. Cova, E. Quaia, M. Tonutti, F. Zanconati, A. Abrami, V. Chenda, R. Menk, E. Quai, G. Tromba, P. Bregant, and F. de Guarrini, "Clinical mammography at the SYRMEP beam line," Nucl. Instrum. Meth. A 572(1), 237-240 (2007).
[CrossRef]

Eikenberry, E. F.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Bronnimann, C. Grunzweig, and C. David, "Hard-X-ray dark-field imaging using a grating interferometer," Nat. Mater. 7(2), 134-137 (2008).
[CrossRef] [PubMed]

Engelhardt, M.

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, "The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources," J. Microsc. 232, 145-157 (2008).
[CrossRef] [PubMed]

Fang, Q.-G.

Z.-F. Huang, K.-J. Kang, L. Zhang, Z.-Q. Chen, F. Ding, Z.-T. Wang, and Q.-G. Fang, "Alternative method for differential phase-contrast imaging with weakly coherent hard x rays," Phys. Rev. A 79(1), 013815 (2009).
[CrossRef]

Gao, D.

S. Wilkins, T. Gureyev, D. Gao, A. Pogany, and A. Stevenson, "Phase-contrast imaging using polychromatic hard X-rays," Nature 384, 335-338 (1996).
[CrossRef]

Gmür, N.

D. Chapman, W. Thomlinson, R. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, "Diffraction enhanced x-ray imaging," Phys. Med. Biol. 42(11), 2015 (1997).
[CrossRef] [PubMed]

Grunzweig, C.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Bronnimann, C. Grunzweig, and C. David, "Hard-X-ray dark-field imaging using a grating interferometer," Nat. Mater. 7(2), 134-137 (2008).
[CrossRef] [PubMed]

Gureyev, T.

S. Wilkins, T. Gureyev, D. Gao, A. Pogany, and A. Stevenson, "Phase-contrast imaging using polychromatic hard X-rays," Nature 384, 335-338 (1996).
[CrossRef]

Hamaishi, Y.

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

Hattori, T.

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, "Phase Tomography by X-ray Talbot Interferometry for Biological Imaging," Jpn. J. Appl. Phys. 45, 5254-5262 (2006).
[CrossRef]

Höfer, A.

R. Nowotny, and A. Höfer, "A computer code for the calculation of diagnostic x-ray spectra," Fortschr Röntgenstr 142, 685-689 (1985).
[CrossRef]

Huang, Z.-F.

Z.-F. Huang, K.-J. Kang, L. Zhang, Z.-Q. Chen, F. Ding, Z.-T. Wang, and Q.-G. Fang, "Alternative method for differential phase-contrast imaging with weakly coherent hard x rays," Phys. Rev. A 79(1), 013815 (2009).
[CrossRef]

Ignatyev, R.

Johnston, R.

D. Chapman, W. Thomlinson, R. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, "Diffraction enhanced x-ray imaging," Phys. Med. Biol. 42(11), 2015 (1997).
[CrossRef] [PubMed]

Kang, K.-J.

Z.-F. Huang, K.-J. Kang, L. Zhang, Z.-Q. Chen, F. Ding, Z.-T. Wang, and Q.-G. Fang, "Alternative method for differential phase-contrast imaging with weakly coherent hard x rays," Phys. Rev. A 79(1), 013815 (2009).
[CrossRef]

Kawamoto, S.

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

Kottler, C.

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, "The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources," J. Microsc. 232, 145-157 (2008).
[CrossRef] [PubMed]

Koyama, I.

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

Kraft, P.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Bronnimann, C. Grunzweig, and C. David, "Hard-X-ray dark-field imaging using a grating interferometer," Nat. Mater. 7(2), 134-137 (2008).
[CrossRef] [PubMed]

Liu, H.

X. Wu, and H. Liu, "A new theory of phase-contrast x-ray imaging based on Wigner distributions," Med. Phys. 31(9), 2378-2384 (2004).
[CrossRef] [PubMed]

Longo, R.

E. Castelli, F. Arfelli, D. Dreossi, R. Longo, T. Rokvic, M. Cova, E. Quaia, M. Tonutti, F. Zanconati, A. Abrami, V. Chenda, R. Menk, E. Quai, G. Tromba, P. Bregant, and F. de Guarrini, "Clinical mammography at the SYRMEP beam line," Nucl. Instrum. Meth. A 572(1), 237-240 (2007).
[CrossRef]

Menk, R.

E. Castelli, F. Arfelli, D. Dreossi, R. Longo, T. Rokvic, M. Cova, E. Quaia, M. Tonutti, F. Zanconati, A. Abrami, V. Chenda, R. Menk, E. Quai, G. Tromba, P. Bregant, and F. de Guarrini, "Clinical mammography at the SYRMEP beam line," Nucl. Instrum. Meth. A 572(1), 237-240 (2007).
[CrossRef]

D. Chapman, W. Thomlinson, R. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, "Diffraction enhanced x-ray imaging," Phys. Med. Biol. 42(11), 2015 (1997).
[CrossRef] [PubMed]

Momose, A.

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, "Phase Tomography by X-ray Talbot Interferometry for Biological Imaging," Jpn. J. Appl. Phys. 45, 5254-5262 (2006).
[CrossRef]

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

Munro, P.

Nesterets, Y. I.

Nowotny, R.

R. Nowotny, and A. Höfer, "A computer code for the calculation of diagnostic x-ray spectra," Fortschr Röntgenstr 142, 685-689 (1985).
[CrossRef]

Olivo, A.

P. Munro, R. Ignatyev, K. Speller, and A. Olivo, "The relationship between wave and geometrical optics models of coded aperture type x-ray phase contrast imaging systems," Opt. Express 18(5), 4103-4117 (2010).
[CrossRef] [PubMed]

A. Olivo, and R. Speller, "Image formation principles in coded-aperture based x-ray phase contrast imaging," Phys. Med. Biol. 53(22), 6461-6474 (2008).
[CrossRef] [PubMed]

A. Olivo, and R. Speller, "Modelling of a novel x-ray phase contrast imaging technique based on coded apertures," Phys. Med. Biol. 52(22), 6555-6573 (2007).
[CrossRef] [PubMed]

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

Pfeiffer, F.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Bronnimann, C. Grunzweig, and C. David, "Hard-X-ray dark-field imaging using a grating interferometer," Nat. Mater. 7(2), 134-137 (2008).
[CrossRef] [PubMed]

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, "The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources," J. Microsc. 232, 145-157 (2008).
[CrossRef] [PubMed]

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(4), 258-261 (2006).
[CrossRef]

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, "X-ray phase imaging with a grating interferometer," Opt. Express 13(16), 6296-6304 (2005).
[CrossRef] [PubMed]

Pisano, E.

D. Chapman, W. Thomlinson, R. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, "Diffraction enhanced x-ray imaging," Phys. Med. Biol. 42(11), 2015 (1997).
[CrossRef] [PubMed]

Pogany, A.

S. Wilkins, T. Gureyev, D. Gao, A. Pogany, and A. Stevenson, "Phase-contrast imaging using polychromatic hard X-rays," Nature 384, 335-338 (1996).
[CrossRef]

Quai, E.

E. Castelli, F. Arfelli, D. Dreossi, R. Longo, T. Rokvic, M. Cova, E. Quaia, M. Tonutti, F. Zanconati, A. Abrami, V. Chenda, R. Menk, E. Quai, G. Tromba, P. Bregant, and F. de Guarrini, "Clinical mammography at the SYRMEP beam line," Nucl. Instrum. Meth. A 572(1), 237-240 (2007).
[CrossRef]

Quaia, E.

E. Castelli, F. Arfelli, D. Dreossi, R. Longo, T. Rokvic, M. Cova, E. Quaia, M. Tonutti, F. Zanconati, A. Abrami, V. Chenda, R. Menk, E. Quai, G. Tromba, P. Bregant, and F. de Guarrini, "Clinical mammography at the SYRMEP beam line," Nucl. Instrum. Meth. A 572(1), 237-240 (2007).
[CrossRef]

Rokvic, T.

E. Castelli, F. Arfelli, D. Dreossi, R. Longo, T. Rokvic, M. Cova, E. Quaia, M. Tonutti, F. Zanconati, A. Abrami, V. Chenda, R. Menk, E. Quai, G. Tromba, P. Bregant, and F. de Guarrini, "Clinical mammography at the SYRMEP beam line," Nucl. Instrum. Meth. A 572(1), 237-240 (2007).
[CrossRef]

Sayers, D.

D. Chapman, W. Thomlinson, R. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, "Diffraction enhanced x-ray imaging," Phys. Med. Biol. 42(11), 2015 (1997).
[CrossRef] [PubMed]

Schroer, C.

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, "The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources," J. Microsc. 232, 145-157 (2008).
[CrossRef] [PubMed]

Schuster, M.

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, "The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources," J. Microsc. 232, 145-157 (2008).
[CrossRef] [PubMed]

Speller, K.

Speller, R.

A. Olivo, and R. Speller, "Image formation principles in coded-aperture based x-ray phase contrast imaging," Phys. Med. Biol. 53(22), 6461-6474 (2008).
[CrossRef] [PubMed]

A. Olivo, and R. Speller, "Modelling of a novel x-ray phase contrast imaging technique based on coded apertures," Phys. Med. Biol. 52(22), 6555-6573 (2007).
[CrossRef] [PubMed]

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

Stampanoni, M.

Stevenson, A.

S. Wilkins, T. Gureyev, D. Gao, A. Pogany, and A. Stevenson, "Phase-contrast imaging using polychromatic hard X-rays," Nature 384, 335-338 (1996).
[CrossRef]

Suzuki, Y.

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, "Phase Tomography by X-ray Talbot Interferometry for Biological Imaging," Jpn. J. Appl. Phys. 45, 5254-5262 (2006).
[CrossRef]

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

Y. Suzuki, N. Yagi, and K. Uesugi, "X-ray refraction-enhanced imaging and a method for phase retrieval for a simple object," J. Synchrotron Radiat. 9(3), 160-165 (2002).
[CrossRef] [PubMed]

Takai, K.

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

Takeda, Y.

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, "Phase Tomography by X-ray Talbot Interferometry for Biological Imaging," Jpn. J. Appl. Phys. 45, 5254-5262 (2006).
[CrossRef]

Thomlinson, W.

D. Chapman, W. Thomlinson, R. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, "Diffraction enhanced x-ray imaging," Phys. Med. Biol. 42(11), 2015 (1997).
[CrossRef] [PubMed]

Tonutti, M.

E. Castelli, F. Arfelli, D. Dreossi, R. Longo, T. Rokvic, M. Cova, E. Quaia, M. Tonutti, F. Zanconati, A. Abrami, V. Chenda, R. Menk, E. Quai, G. Tromba, P. Bregant, and F. de Guarrini, "Clinical mammography at the SYRMEP beam line," Nucl. Instrum. Meth. A 572(1), 237-240 (2007).
[CrossRef]

Tromba, G.

E. Castelli, F. Arfelli, D. Dreossi, R. Longo, T. Rokvic, M. Cova, E. Quaia, M. Tonutti, F. Zanconati, A. Abrami, V. Chenda, R. Menk, E. Quai, G. Tromba, P. Bregant, and F. de Guarrini, "Clinical mammography at the SYRMEP beam line," Nucl. Instrum. Meth. A 572(1), 237-240 (2007).
[CrossRef]

Uesugi, K.

Y. Suzuki, N. Yagi, and K. Uesugi, "X-ray refraction-enhanced imaging and a method for phase retrieval for a simple object," J. Synchrotron Radiat. 9(3), 160-165 (2002).
[CrossRef] [PubMed]

Wang, Z.-T.

Z.-F. Huang, K.-J. Kang, L. Zhang, Z.-Q. Chen, F. Ding, Z.-T. Wang, and Q.-G. Fang, "Alternative method for differential phase-contrast imaging with weakly coherent hard x rays," Phys. Rev. A 79(1), 013815 (2009).
[CrossRef]

Washburn, D.

D. Chapman, W. Thomlinson, R. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, "Diffraction enhanced x-ray imaging," Phys. Med. Biol. 42(11), 2015 (1997).
[CrossRef] [PubMed]

Weitkamp, T.

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(4), 258-261 (2006).
[CrossRef]

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, "X-ray phase imaging with a grating interferometer," Opt. Express 13(16), 6296-6304 (2005).
[CrossRef] [PubMed]

Wilkins, S.

S. Wilkins, T. Gureyev, D. Gao, A. Pogany, and A. Stevenson, "Phase-contrast imaging using polychromatic hard X-rays," Nature 384, 335-338 (1996).
[CrossRef]

Wilkins, S. W.

Wu, X.

X. Wu, and H. Liu, "A new theory of phase-contrast x-ray imaging based on Wigner distributions," Med. Phys. 31(9), 2378-2384 (2004).
[CrossRef] [PubMed]

Yagi, N.

Y. Suzuki, N. Yagi, and K. Uesugi, "X-ray refraction-enhanced imaging and a method for phase retrieval for a simple object," J. Synchrotron Radiat. 9(3), 160-165 (2002).
[CrossRef] [PubMed]

Yashiro, W.

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, "Phase Tomography by X-ray Talbot Interferometry for Biological Imaging," Jpn. J. Appl. Phys. 45, 5254-5262 (2006).
[CrossRef]

Zanconati, F.

E. Castelli, F. Arfelli, D. Dreossi, R. Longo, T. Rokvic, M. Cova, E. Quaia, M. Tonutti, F. Zanconati, A. Abrami, V. Chenda, R. Menk, E. Quai, G. Tromba, P. Bregant, and F. de Guarrini, "Clinical mammography at the SYRMEP beam line," Nucl. Instrum. Meth. A 572(1), 237-240 (2007).
[CrossRef]

Zhang, L.

Z.-F. Huang, K.-J. Kang, L. Zhang, Z.-Q. Chen, F. Ding, Z.-T. Wang, and Q.-G. Fang, "Alternative method for differential phase-contrast imaging with weakly coherent hard x rays," Phys. Rev. A 79(1), 013815 (2009).
[CrossRef]

Zhong, Z.

D. Chapman, W. Thomlinson, R. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, "Diffraction enhanced x-ray imaging," Phys. Med. Biol. 42(11), 2015 (1997).
[CrossRef] [PubMed]

Ziegler, E.

Appl. Phys. Lett. (1)

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

Fortschr Röntgenstr (1)

R. Nowotny, and A. Höfer, "A computer code for the calculation of diagnostic x-ray spectra," Fortschr Röntgenstr 142, 685-689 (1985).
[CrossRef]

J. Microsc. (1)

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, "The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources," J. Microsc. 232, 145-157 (2008).
[CrossRef] [PubMed]

J. Synchrotron Radiat. (1)

Y. Suzuki, N. Yagi, and K. Uesugi, "X-ray refraction-enhanced imaging and a method for phase retrieval for a simple object," J. Synchrotron Radiat. 9(3), 160-165 (2002).
[CrossRef] [PubMed]

Jpn. J. Appl. Phys. (2)

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

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, "Phase Tomography by X-ray Talbot Interferometry for Biological Imaging," Jpn. J. Appl. Phys. 45, 5254-5262 (2006).
[CrossRef]

Med. Phys. (1)

X. Wu, and H. Liu, "A new theory of phase-contrast x-ray imaging based on Wigner distributions," Med. Phys. 31(9), 2378-2384 (2004).
[CrossRef] [PubMed]

Nat. Mater. (1)

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Bronnimann, C. Grunzweig, and C. David, "Hard-X-ray dark-field imaging using a grating interferometer," Nat. Mater. 7(2), 134-137 (2008).
[CrossRef] [PubMed]

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(4), 258-261 (2006).
[CrossRef]

Nature (1)

S. Wilkins, T. Gureyev, D. Gao, A. Pogany, and A. Stevenson, "Phase-contrast imaging using polychromatic hard X-rays," Nature 384, 335-338 (1996).
[CrossRef]

Nucl. Instrum. Meth. A (1)

E. Castelli, F. Arfelli, D. Dreossi, R. Longo, T. Rokvic, M. Cova, E. Quaia, M. Tonutti, F. Zanconati, A. Abrami, V. Chenda, R. Menk, E. Quai, G. Tromba, P. Bregant, and F. de Guarrini, "Clinical mammography at the SYRMEP beam line," Nucl. Instrum. Meth. A 572(1), 237-240 (2007).
[CrossRef]

Opt. Express (3)

Phys. Med. Biol. (3)

A. Olivo, and R. Speller, "Modelling of a novel x-ray phase contrast imaging technique based on coded apertures," Phys. Med. Biol. 52(22), 6555-6573 (2007).
[CrossRef] [PubMed]

D. Chapman, W. Thomlinson, R. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, "Diffraction enhanced x-ray imaging," Phys. Med. Biol. 42(11), 2015 (1997).
[CrossRef] [PubMed]

A. Olivo, and R. Speller, "Image formation principles in coded-aperture based x-ray phase contrast imaging," Phys. Med. Biol. 53(22), 6461-6474 (2008).
[CrossRef] [PubMed]

Phys. Rev. A (1)

Z.-F. Huang, K.-J. Kang, L. Zhang, Z.-Q. Chen, F. Ding, Z.-T. Wang, and Q.-G. Fang, "Alternative method for differential phase-contrast imaging with weakly coherent hard x rays," Phys. Rev. A 79(1), 013815 (2009).
[CrossRef]

Other (3)

E. Chu, Discrete and Continuous Fourier Transforms: Analysis, Applications and Fast Algorithms (Chapman and Hall/CR, 2008).

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

M. Born, and E. Wolf, Principles of Optics, seventh ed. (Cambridge University Press, Cambridge, 1999).

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Figures (8)

Fig. 1.
Fig. 1.

Schematic diagrams of a CAXPCI system. The diagram on the right is a top-down version of the left. G1 and G2 are both transmission gratings. G1 creates x-ray beams which are incident upon G2 which is used to achieve partial pixel illumination.

Fig. 2.
Fig. 2.

Diagrams showing the principle of pixel edge illumination with a cylindrical sample. The pixel edge refers to the edge of the region of the pixel not covered by G2. The left diagram would result in an increased detector signal whilst the right would result in a reduced signal. It is assumed that the real part of the refractive index of the cylinder is less than unity as is typical for materials of interest at x-ray photon energies. The arrows are intended to indicate the fraction of photons and note that the divergence of the x-ray beam has been neglected for simplicity.

Fig. 3.
Fig. 3.

Spectrum of x-rays emitted by an x-ray source with tube voltage of 40 kV for a tungsten anode, 2mm of aluminium filtration, an anode angle of 17° at a distance of 10cm from the source. Data was calculated by code developed by Nowotny and Höfer [20]. The mean photon energy is 27.4keV corresponding to wavelength 45pm.

Fig. 4.
Fig. 4.

Plots of x-ray intensity at the detector grating when a point source with the spectrum of Fig. 3 is employed for three values of L, zso = 1.6m and zod = 0.4m. λ 0 is 45pm, the wavelength of the mean photon energy.

Fig. 5.
Fig. 5.

Plots of the real (ℜ) and imaginary (ℑ) parts of K 3 calculated for three values of L, zso = 1.6m and zod = 0.4m for the spectrum shown in Fig. 3. λ 0 is 45pm, the wavelength of the mean photon energy. The chosen values of L result in values for γt of 3.5 × 103, 3.2 × 10−2 and 1.3 × 10−3 respectively.

Fig. 6.
Fig. 6.

Plot of minimum achievable IPF versus γt for a point source with spectrum as shown in Fig. 3. zso and zod were varied whilst maintaining zso + zod = 2m.

Fig. 7.
Fig. 7.

Plot of K 1 for three typical values of L: 40µm, 68µm and 80µm with zso = 1.6m, zod = 0.4m and a source FWHM of 75µm.

Fig. 8.
Fig. 8.

Plot of minimum achievable IPF against γs . The IPF was calculated for combinations of P=50, 85 and 100µm, zso varying between 1 and 1.9m, total system length equal to 2m, source FWHM varying between 50 and 100µm and the spectrum shown in Fig. 3. All resultant data points were found to lie on the line plotted in the figure.

Equations (16)

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

W ( x d 1 , x d 2 , ω ) = U * ( x d 1 , ω ; z o d ) U ( x d 2 , ω ; z o d ) ω
= σ σ K * ( x d 1 , x s 1 , ω ; z o s , z o d ) K ( x d 2 , x s 2 , ω ; z o s , z o d ) U * ( x s 1 , ω ; z s o ) U ( x s 2 , ω ; z s o ) ω d x s 1 d x x 2
W ( x s 1 , x s 2 , ω ) = U ( x s 1 , ω ) 2 ω δ ( x s 1 x s 2 )
= I ( x s 1 , ω ) δ ( x s 1 x s 2 )
I ( x d 1 ) = 1 2 π 0 σ K ( x d 1 , x s 1 , ω ; z o s , z o d ) 2 I ( x s 1 , ω ) d x s 1 d ω
K ( x d 1 , x s 1 , ω ; z o s , z o d ) = exp ( ik ( z s o + z o d ) ) z s o + z o d exp ( ik ( x d 1 x s 1 ) 2 2 ( z s o + z o d ) ) .
n = exp ( i π λ ( n L ) 2 z s o z o d z s o + z o d ) C n exp ( i 2 π n L x z s o z s o + z o d )
I ( x s , ω ) = 1 σ x π exp [ ( x s σ x ) 2 ] I ( ω )
I ( x d ) = 1 ( z s o + z o d ) 2 n 1 = n 2 = [ exp ( π 2 σ x 2 ( n 1 n 2 L ) 2 ( z o d z s o + z o d ) 2 )
· exp ( i 2 π ( n 1 L n 2 L ) ( x d z s o z s o + z o d ) )
· C n 1 C n 2 * c λ s λ l exp ( i π λ ( ( n 1 L ) 2 ( n 2 L ) 2 ) z s o z o d z s o + z o d ) I ( λ ) λ 2 d λ ]
K 1 ( σ x , n 1 , n 2 ) = exp ( π 2 σ x 2 ( n 1 n 2 L ) 2 ( z o d z s o + z o d ) 2 )
K 2 ( x d , n 1 , n 2 ) = exp ( i 2 π ( n 1 L n 2 L ) ( x d z s o z s o + z o d ) )
K 3 ( n 1 , n 2 ) = c λ s λ l exp ( i π λ ( ( n 1 L ) 2 ( n 2 L ) 2 ) z s o z o d z s o + z o d ) I ( λ ) λ 2 d λ
Δ λ 2 ( n L ) 2 z s o z o d z s o + z o d < 1
γ s = σ x P z o d z s o + z o d = σ x P z o d z s o

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