Abstract

An advanced wave-optical approach for simulating a monochromator-analyzer set-up in Bragg geometry with high accuracy is presented. The polychromaticity of the incident wave on the monochromator is accounted for by using a distribution of incoherent point sources along the surface of the crystal. The resulting diffracted amplitude is modified by the sample and can be well represented by a scalar representation of the optical field where the limitations of the usual ‘weak object’ approximation are removed. The subsequent diffraction mechanism on the analyzer is described by the convolution of the incoming wave with the Green-Riemann function of the analyzer. The free space propagation up to the detector position is well reproduced by a classical Fresnel-Kirchhoff integral. The preliminary results of this innovative approach show an excellent agreement with experimental data.

© 2007 Optical Society of America

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  1. J. Keyriläinen, M. Fernández, S. Fiedler, A. Bravin, M. L. Karjalainen-Lindsberg, P. Virkkunen, E. M. Elo, M. Tenhunen, P. Suortti, and W. Thomlinson, "Visualisation of calcifications and thin collagen strands in human breast tumour specimens by the diffraction-enhanced imaging technique: a comparison with conventional mammography and histology," Eur. J. Radiol. 53 (2), 226 (2005).
    [CrossRef]
  2. F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. Dalla Palma, M. Di Michiel, M. Fabrizioli, R. Longo, R. -H. Menk, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, M. Ratti, L. Rigon, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, "Mammography with synchrotron radiation: Phase-detection techniques," Radiology 215, 286 (2000).
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    [CrossRef]
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    [CrossRef] [PubMed]
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  12. Y. Epelboin, V. Mocella, and A. Soyer, "Optical characteristics of synchrotron sources and their influence in the simulation of X-ray topographs," Philos. T. Roy. Soc. A 357, 2731 (1999).
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    [CrossRef]
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  17. V. Mocella, Y. Epelboin, and J. P. Guigay, "X-ray dynamical diffraction: the concept of a locally plane wave," Acta Cryst. A 56, 308 (2000).
    [CrossRef]
  18. V. Mocella, J. P. Guigay, Y. Epelboin, J. Haertwig, J. Baruchel, and A. Mazuelas, "Influence of the transverse and longitudinal coherence in the dynamical theory of X-ray diffraction," J. Phys. D: Appl. Phys. 32, A88 (1999).
    [CrossRef]
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    [CrossRef]
  21. S. Takagi, "A dynamical theory of diffraction for a distorted crystal," J. Phys. Soc. Jpn 26 (1969).
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    [CrossRef]
  26. P. Coan, E. Pagot, S. Fiedler, P. Cloetens, J. Baruchel, and A. Bravin, "Phase-contrast X-ray imaging combining free space propagation and Bragg diffraction," J. Synchrotron Radiat. 12, 241 (2005).
    [CrossRef] [PubMed]
  27. P. Coan, A. Peterzol, S. Fiedler, C. Ponchut, J. C. Labiche, and A , Bravin, "Evaluation of imaging performance of a taper optics CCD `FReLoN' camera designed for medical imaging," J. Synchrotron Radiat. 13, 260 (2006).
    [CrossRef] [PubMed]

2006 (3)

Y. I. Nesterets, T. E. Gureyev, K. M. Pavlov, D. Paganin, and S. W. Wilkins, "Combined analyser-based and propagation-based phase-contrast imaging of weak objects," Opt. Commun. 259, 19 (2006).
[CrossRef]

Y. I. Nesterets, P. Coan, T. E. Gureyev, A. Bravin, P. Cloetens, and S. W. Wilkins, "On qualitative and quantitative analysis in analyser-based imaging," Acta Cryst. A,  62296 (2006).
[CrossRef]

P. Coan, A. Peterzol, S. Fiedler, C. Ponchut, J. C. Labiche, and A , Bravin, "Evaluation of imaging performance of a taper optics CCD `FReLoN' camera designed for medical imaging," J. Synchrotron Radiat. 13, 260 (2006).
[CrossRef] [PubMed]

2005 (4)

P. Coan, E. Pagot, S. Fiedler, P. Cloetens, J. Baruchel, and A. Bravin, "Phase-contrast X-ray imaging combining free space propagation and Bragg diffraction," J. Synchrotron Radiat. 12, 241 (2005).
[CrossRef] [PubMed]

Y. I. Nesterets, T. E. Gureyev, and S. W. Wilkins, "Polychromaticity in the combined propagation-based/analyzer-based phase-contrast imaging," J. Phys. D: Appl. Phys. 38, 4259 (2005).
[CrossRef]

J. Keyriläinen, M. Fernández, S. Fiedler, A. Bravin, M. L. Karjalainen-Lindsberg, P. Virkkunen, E. M. Elo, M. Tenhunen, P. Suortti, and W. Thomlinson, "Visualisation of calcifications and thin collagen strands in human breast tumour specimens by the diffraction-enhanced imaging technique: a comparison with conventional mammography and histology," Eur. J. Radiol. 53 (2), 226 (2005).
[CrossRef]

A. Yoneyama, T. Takeda, Y. Tsuchiya, J. Wu, T. T. Lwin, K. Hyodo, and Y. Hirai, "High-energy phase-contrast X-ray imaging using a two-crystal X-ray interferometer," J. Synchrotron Radiat. 12, 534 (2005).
[CrossRef] [PubMed]

2004 (2)

Y. I. Nesterets, T. E. Gureyev, D. Paganin, K. M. Pavlov, and S. W. Wilkins, "Quantitative diffraction-enhanced X-ray imaging of weak objects," J. Phys. D: Appl. Phys. 37, 1262 (2004).
[CrossRef]

D. 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, 87 (2004).
[CrossRef]

2003 (1)

A. Bravin, "Exploiting the x-ray refraction contrast with an analyser: the state of the art," J. Phys. D: Appl. Phys. 36 (10A), A24 (2003).
[CrossRef]

2002 (1)

J. Keyriläinen, M. Fernández, and P. Suortti, "Refraction contrast X-ray imaging," Nucl. Instrum. Methods A 488, 419 (2002).
[CrossRef]

2000 (3)

F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. Dalla Palma, M. Di Michiel, M. Fabrizioli, R. Longo, R. -H. Menk, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, M. Ratti, L. Rigon, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, "Mammography with synchrotron radiation: Phase-detection techniques," Radiology 215, 286 (2000).

V. Mocella, Y. Epelboin, and J. P. Guigay, "X-ray dynamical diffraction: the concept of a locally plane wave," Acta Cryst. A 56, 308 (2000).
[CrossRef]

V. Mocella, Y. Epelboin, and J. P. Guigay, "X-ray dynamical diffraction: the concept of a locally plane wave," Acta Cryst. A 56, 308 (2000).
[CrossRef]

1999 (3)

V. Mocella, J. P. Guigay, Y. Epelboin, J. Haertwig, J. Baruchel, and A. Mazuelas, "Influence of the transverse and longitudinal coherence in the dynamical theory of X-ray diffraction," J. Phys. D: Appl. Phys. 32, A88 (1999).
[CrossRef]

Y. Epelboin, V. Mocella, and A. Soyer, "Optical characteristics of synchrotron sources and their influence in the simulation of X-ray topographs," Philos. T. Roy. Soc. A 357, 2731 (1999).
[CrossRef]

J. P. Guigay, "A simple view of the spherical wave in dynamical theory," Acta Cryst. A. 55, 561 (1999).
[CrossRef]

1995 (1)

T. J. Davis, T. E. Gureyev, D. Gao, A. W. Stevenson, and S. W. Wilkins, "X-ray image contrast from a simple phase object," Phys. Rev. Lett. 74, 3173 (1995).
[CrossRef] [PubMed]

1993 (1)

C. A. M. Carvalho, and Y. Epelboin, "Simulation of X-ray traverse topographs and synchrotron Laue topographs: application of the reciprocity theorem," Acta Cryst. A 49, 467 (1993).
[CrossRef]

1971 (1)

A. M. Afanas'ev, and V. G. Kohn, "Dynamical theory of X-ray diffraction in crystals with defects," Acta Cryst. A 27, 421 (1971).
[CrossRef]

1969 (2)

S. Takagi, "A dynamical theory of diffraction for a distorted crystal," J. Phys. Soc. Jpn 26 (1969).
[CrossRef]

T. Uragami, "Pendellösung fringes of X-rays in Bragg case," J. Phys. Soc. Jpn 27, 147 (1969).
[CrossRef]

1968 (1)

A. Autier and D. Simon, "Application de la théorie dynamique de S. Takagi au contraste d'un défaut plan en topographie par rayons X. I. Faute d'empilement," Acta Cryst. A 24, 517 (1968).
[CrossRef]

Afanas'ev, A. M.

A. M. Afanas'ev, and V. G. Kohn, "Dynamical theory of X-ray diffraction in crystals with defects," Acta Cryst. A 27, 421 (1971).
[CrossRef]

Arfelli, F.

F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. Dalla Palma, M. Di Michiel, M. Fabrizioli, R. Longo, R. -H. Menk, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, M. Ratti, L. Rigon, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, "Mammography with synchrotron radiation: Phase-detection techniques," Radiology 215, 286 (2000).

Autier, A.

A. Autier and D. Simon, "Application de la théorie dynamique de S. Takagi au contraste d'un défaut plan en topographie par rayons X. I. Faute d'empilement," Acta Cryst. A 24, 517 (1968).
[CrossRef]

Baruchel, J.

P. Coan, E. Pagot, S. Fiedler, P. Cloetens, J. Baruchel, and A. Bravin, "Phase-contrast X-ray imaging combining free space propagation and Bragg diffraction," J. Synchrotron Radiat. 12, 241 (2005).
[CrossRef] [PubMed]

V. Mocella, J. P. Guigay, Y. Epelboin, J. Haertwig, J. Baruchel, and A. Mazuelas, "Influence of the transverse and longitudinal coherence in the dynamical theory of X-ray diffraction," J. Phys. D: Appl. Phys. 32, A88 (1999).
[CrossRef]

Bonvicini, V.

F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. Dalla Palma, M. Di Michiel, M. Fabrizioli, R. Longo, R. -H. Menk, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, M. Ratti, L. Rigon, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, "Mammography with synchrotron radiation: Phase-detection techniques," Radiology 215, 286 (2000).

Bravin, A

P. Coan, A. Peterzol, S. Fiedler, C. Ponchut, J. C. Labiche, and A , Bravin, "Evaluation of imaging performance of a taper optics CCD `FReLoN' camera designed for medical imaging," J. Synchrotron Radiat. 13, 260 (2006).
[CrossRef] [PubMed]

Bravin, A.

Y. I. Nesterets, P. Coan, T. E. Gureyev, A. Bravin, P. Cloetens, and S. W. Wilkins, "On qualitative and quantitative analysis in analyser-based imaging," Acta Cryst. A,  62296 (2006).
[CrossRef]

J. Keyriläinen, M. Fernández, S. Fiedler, A. Bravin, M. L. Karjalainen-Lindsberg, P. Virkkunen, E. M. Elo, M. Tenhunen, P. Suortti, and W. Thomlinson, "Visualisation of calcifications and thin collagen strands in human breast tumour specimens by the diffraction-enhanced imaging technique: a comparison with conventional mammography and histology," Eur. J. Radiol. 53 (2), 226 (2005).
[CrossRef]

P. Coan, E. Pagot, S. Fiedler, P. Cloetens, J. Baruchel, and A. Bravin, "Phase-contrast X-ray imaging combining free space propagation and Bragg diffraction," J. Synchrotron Radiat. 12, 241 (2005).
[CrossRef] [PubMed]

A. Bravin, "Exploiting the x-ray refraction contrast with an analyser: the state of the art," J. Phys. D: Appl. Phys. 36 (10A), A24 (2003).
[CrossRef]

F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. Dalla Palma, M. Di Michiel, M. Fabrizioli, R. Longo, R. -H. Menk, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, M. Ratti, L. Rigon, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, "Mammography with synchrotron radiation: Phase-detection techniques," Radiology 215, 286 (2000).

Cantatore, G.

F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. Dalla Palma, M. Di Michiel, M. Fabrizioli, R. Longo, R. -H. Menk, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, M. Ratti, L. Rigon, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, "Mammography with synchrotron radiation: Phase-detection techniques," Radiology 215, 286 (2000).

Carvalho, C. A. M.

C. A. M. Carvalho, and Y. Epelboin, "Simulation of X-ray traverse topographs and synchrotron Laue topographs: application of the reciprocity theorem," Acta Cryst. A 49, 467 (1993).
[CrossRef]

Castelli, E.

F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. Dalla Palma, M. Di Michiel, M. Fabrizioli, R. Longo, R. -H. Menk, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, M. Ratti, L. Rigon, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, "Mammography with synchrotron radiation: Phase-detection techniques," Radiology 215, 286 (2000).

Cloetens, P.

Y. I. Nesterets, P. Coan, T. E. Gureyev, A. Bravin, P. Cloetens, and S. W. Wilkins, "On qualitative and quantitative analysis in analyser-based imaging," Acta Cryst. A,  62296 (2006).
[CrossRef]

P. Coan, E. Pagot, S. Fiedler, P. Cloetens, J. Baruchel, and A. Bravin, "Phase-contrast X-ray imaging combining free space propagation and Bragg diffraction," J. Synchrotron Radiat. 12, 241 (2005).
[CrossRef] [PubMed]

Coan, P.

P. Coan, A. Peterzol, S. Fiedler, C. Ponchut, J. C. Labiche, and A , Bravin, "Evaluation of imaging performance of a taper optics CCD `FReLoN' camera designed for medical imaging," J. Synchrotron Radiat. 13, 260 (2006).
[CrossRef] [PubMed]

Y. I. Nesterets, P. Coan, T. E. Gureyev, A. Bravin, P. Cloetens, and S. W. Wilkins, "On qualitative and quantitative analysis in analyser-based imaging," Acta Cryst. A,  62296 (2006).
[CrossRef]

P. Coan, E. Pagot, S. Fiedler, P. Cloetens, J. Baruchel, and A. Bravin, "Phase-contrast X-ray imaging combining free space propagation and Bragg diffraction," J. Synchrotron Radiat. 12, 241 (2005).
[CrossRef] [PubMed]

Dalla Palma, L.

F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. Dalla Palma, M. Di Michiel, M. Fabrizioli, R. Longo, R. -H. Menk, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, M. Ratti, L. Rigon, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, "Mammography with synchrotron radiation: Phase-detection techniques," Radiology 215, 286 (2000).

Davis, T. J.

T. J. Davis, T. E. Gureyev, D. Gao, A. W. Stevenson, and S. W. Wilkins, "X-ray image contrast from a simple phase object," Phys. Rev. Lett. 74, 3173 (1995).
[CrossRef] [PubMed]

Di Michiel, M.

F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. Dalla Palma, M. Di Michiel, M. Fabrizioli, R. Longo, R. -H. Menk, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, M. Ratti, L. Rigon, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, "Mammography with synchrotron radiation: Phase-detection techniques," Radiology 215, 286 (2000).

Elo, E. M.

J. Keyriläinen, M. Fernández, S. Fiedler, A. Bravin, M. L. Karjalainen-Lindsberg, P. Virkkunen, E. M. Elo, M. Tenhunen, P. Suortti, and W. Thomlinson, "Visualisation of calcifications and thin collagen strands in human breast tumour specimens by the diffraction-enhanced imaging technique: a comparison with conventional mammography and histology," Eur. J. Radiol. 53 (2), 226 (2005).
[CrossRef]

Epelboin, Y.

V. Mocella, Y. Epelboin, and J. P. Guigay, "X-ray dynamical diffraction: the concept of a locally plane wave," Acta Cryst. A 56, 308 (2000).
[CrossRef]

V. Mocella, Y. Epelboin, and J. P. Guigay, "X-ray dynamical diffraction: the concept of a locally plane wave," Acta Cryst. A 56, 308 (2000).
[CrossRef]

V. Mocella, J. P. Guigay, Y. Epelboin, J. Haertwig, J. Baruchel, and A. Mazuelas, "Influence of the transverse and longitudinal coherence in the dynamical theory of X-ray diffraction," J. Phys. D: Appl. Phys. 32, A88 (1999).
[CrossRef]

Y. Epelboin, V. Mocella, and A. Soyer, "Optical characteristics of synchrotron sources and their influence in the simulation of X-ray topographs," Philos. T. Roy. Soc. A 357, 2731 (1999).
[CrossRef]

C. A. M. Carvalho, and Y. Epelboin, "Simulation of X-ray traverse topographs and synchrotron Laue topographs: application of the reciprocity theorem," Acta Cryst. A 49, 467 (1993).
[CrossRef]

Fabrizioli, M.

F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. Dalla Palma, M. Di Michiel, M. Fabrizioli, R. Longo, R. -H. Menk, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, M. Ratti, L. Rigon, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, "Mammography with synchrotron radiation: Phase-detection techniques," Radiology 215, 286 (2000).

Fernández, M.

J. Keyriläinen, M. Fernández, S. Fiedler, A. Bravin, M. L. Karjalainen-Lindsberg, P. Virkkunen, E. M. Elo, M. Tenhunen, P. Suortti, and W. Thomlinson, "Visualisation of calcifications and thin collagen strands in human breast tumour specimens by the diffraction-enhanced imaging technique: a comparison with conventional mammography and histology," Eur. J. Radiol. 53 (2), 226 (2005).
[CrossRef]

J. Keyriläinen, M. Fernández, and P. Suortti, "Refraction contrast X-ray imaging," Nucl. Instrum. Methods A 488, 419 (2002).
[CrossRef]

Fiedler, S.

P. Coan, A. Peterzol, S. Fiedler, C. Ponchut, J. C. Labiche, and A , Bravin, "Evaluation of imaging performance of a taper optics CCD `FReLoN' camera designed for medical imaging," J. Synchrotron Radiat. 13, 260 (2006).
[CrossRef] [PubMed]

P. Coan, E. Pagot, S. Fiedler, P. Cloetens, J. Baruchel, and A. Bravin, "Phase-contrast X-ray imaging combining free space propagation and Bragg diffraction," J. Synchrotron Radiat. 12, 241 (2005).
[CrossRef] [PubMed]

J. Keyriläinen, M. Fernández, S. Fiedler, A. Bravin, M. L. Karjalainen-Lindsberg, P. Virkkunen, E. M. Elo, M. Tenhunen, P. Suortti, and W. Thomlinson, "Visualisation of calcifications and thin collagen strands in human breast tumour specimens by the diffraction-enhanced imaging technique: a comparison with conventional mammography and histology," Eur. J. Radiol. 53 (2), 226 (2005).
[CrossRef]

Gao, D.

T. J. Davis, T. E. Gureyev, D. Gao, A. W. Stevenson, and S. W. Wilkins, "X-ray image contrast from a simple phase object," Phys. Rev. Lett. 74, 3173 (1995).
[CrossRef] [PubMed]

Guigay, J. P.

V. Mocella, Y. Epelboin, and J. P. Guigay, "X-ray dynamical diffraction: the concept of a locally plane wave," Acta Cryst. A 56, 308 (2000).
[CrossRef]

V. Mocella, Y. Epelboin, and J. P. Guigay, "X-ray dynamical diffraction: the concept of a locally plane wave," Acta Cryst. A 56, 308 (2000).
[CrossRef]

V. Mocella, J. P. Guigay, Y. Epelboin, J. Haertwig, J. Baruchel, and A. Mazuelas, "Influence of the transverse and longitudinal coherence in the dynamical theory of X-ray diffraction," J. Phys. D: Appl. Phys. 32, A88 (1999).
[CrossRef]

J. P. Guigay, "A simple view of the spherical wave in dynamical theory," Acta Cryst. A. 55, 561 (1999).
[CrossRef]

Gureyev, T. E.

Y. I. Nesterets, P. Coan, T. E. Gureyev, A. Bravin, P. Cloetens, and S. W. Wilkins, "On qualitative and quantitative analysis in analyser-based imaging," Acta Cryst. A,  62296 (2006).
[CrossRef]

Y. I. Nesterets, T. E. Gureyev, K. M. Pavlov, D. Paganin, and S. W. Wilkins, "Combined analyser-based and propagation-based phase-contrast imaging of weak objects," Opt. Commun. 259, 19 (2006).
[CrossRef]

Y. I. Nesterets, T. E. Gureyev, and S. W. Wilkins, "Polychromaticity in the combined propagation-based/analyzer-based phase-contrast imaging," J. Phys. D: Appl. Phys. 38, 4259 (2005).
[CrossRef]

Y. I. Nesterets, T. E. Gureyev, D. Paganin, K. M. Pavlov, and S. W. Wilkins, "Quantitative diffraction-enhanced X-ray imaging of weak objects," J. Phys. D: Appl. Phys. 37, 1262 (2004).
[CrossRef]

D. 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, 87 (2004).
[CrossRef]

T. J. Davis, T. E. Gureyev, D. Gao, A. W. Stevenson, and S. W. Wilkins, "X-ray image contrast from a simple phase object," Phys. Rev. Lett. 74, 3173 (1995).
[CrossRef] [PubMed]

Haertwig, J.

V. Mocella, J. P. Guigay, Y. Epelboin, J. Haertwig, J. Baruchel, and A. Mazuelas, "Influence of the transverse and longitudinal coherence in the dynamical theory of X-ray diffraction," J. Phys. D: Appl. Phys. 32, A88 (1999).
[CrossRef]

Hirai, Y.

A. Yoneyama, T. Takeda, Y. Tsuchiya, J. Wu, T. T. Lwin, K. Hyodo, and Y. Hirai, "High-energy phase-contrast X-ray imaging using a two-crystal X-ray interferometer," J. Synchrotron Radiat. 12, 534 (2005).
[CrossRef] [PubMed]

Hyodo, K.

A. Yoneyama, T. Takeda, Y. Tsuchiya, J. Wu, T. T. Lwin, K. Hyodo, and Y. Hirai, "High-energy phase-contrast X-ray imaging using a two-crystal X-ray interferometer," J. Synchrotron Radiat. 12, 534 (2005).
[CrossRef] [PubMed]

Karjalainen-Lindsberg, M. L.

J. Keyriläinen, M. Fernández, S. Fiedler, A. Bravin, M. L. Karjalainen-Lindsberg, P. Virkkunen, E. M. Elo, M. Tenhunen, P. Suortti, and W. Thomlinson, "Visualisation of calcifications and thin collagen strands in human breast tumour specimens by the diffraction-enhanced imaging technique: a comparison with conventional mammography and histology," Eur. J. Radiol. 53 (2), 226 (2005).
[CrossRef]

Keyriläinen, J.

J. Keyriläinen, M. Fernández, S. Fiedler, A. Bravin, M. L. Karjalainen-Lindsberg, P. Virkkunen, E. M. Elo, M. Tenhunen, P. Suortti, and W. Thomlinson, "Visualisation of calcifications and thin collagen strands in human breast tumour specimens by the diffraction-enhanced imaging technique: a comparison with conventional mammography and histology," Eur. J. Radiol. 53 (2), 226 (2005).
[CrossRef]

J. Keyriläinen, M. Fernández, and P. Suortti, "Refraction contrast X-ray imaging," Nucl. Instrum. Methods A 488, 419 (2002).
[CrossRef]

Kitchen, M.

D. 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, 87 (2004).
[CrossRef]

Kohn, V. G.

A. M. Afanas'ev, and V. G. Kohn, "Dynamical theory of X-ray diffraction in crystals with defects," Acta Cryst. A 27, 421 (1971).
[CrossRef]

Labiche, J. C.

P. Coan, A. Peterzol, S. Fiedler, C. Ponchut, J. C. Labiche, and A , Bravin, "Evaluation of imaging performance of a taper optics CCD `FReLoN' camera designed for medical imaging," J. Synchrotron Radiat. 13, 260 (2006).
[CrossRef] [PubMed]

Lewis, R. A.

D. 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, 87 (2004).
[CrossRef]

Longo, R.

F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. Dalla Palma, M. Di Michiel, M. Fabrizioli, R. Longo, R. -H. Menk, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, M. Ratti, L. Rigon, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, "Mammography with synchrotron radiation: Phase-detection techniques," Radiology 215, 286 (2000).

Lwin, T. T.

A. Yoneyama, T. Takeda, Y. Tsuchiya, J. Wu, T. T. Lwin, K. Hyodo, and Y. Hirai, "High-energy phase-contrast X-ray imaging using a two-crystal X-ray interferometer," J. Synchrotron Radiat. 12, 534 (2005).
[CrossRef] [PubMed]

Mazuelas, A.

V. Mocella, J. P. Guigay, Y. Epelboin, J. Haertwig, J. Baruchel, and A. Mazuelas, "Influence of the transverse and longitudinal coherence in the dynamical theory of X-ray diffraction," J. Phys. D: Appl. Phys. 32, A88 (1999).
[CrossRef]

Menk, R. -H.

F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. Dalla Palma, M. Di Michiel, M. Fabrizioli, R. Longo, R. -H. Menk, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, M. Ratti, L. Rigon, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, "Mammography with synchrotron radiation: Phase-detection techniques," Radiology 215, 286 (2000).

Mocella, V.

V. Mocella, Y. Epelboin, and J. P. Guigay, "X-ray dynamical diffraction: the concept of a locally plane wave," Acta Cryst. A 56, 308 (2000).
[CrossRef]

V. Mocella, Y. Epelboin, and J. P. Guigay, "X-ray dynamical diffraction: the concept of a locally plane wave," Acta Cryst. A 56, 308 (2000).
[CrossRef]

V. Mocella, J. P. Guigay, Y. Epelboin, J. Haertwig, J. Baruchel, and A. Mazuelas, "Influence of the transverse and longitudinal coherence in the dynamical theory of X-ray diffraction," J. Phys. D: Appl. Phys. 32, A88 (1999).
[CrossRef]

Y. Epelboin, V. Mocella, and A. Soyer, "Optical characteristics of synchrotron sources and their influence in the simulation of X-ray topographs," Philos. T. Roy. Soc. A 357, 2731 (1999).
[CrossRef]

Nesterets, Y. I.

Y. I. Nesterets, T. E. Gureyev, K. M. Pavlov, D. Paganin, and S. W. Wilkins, "Combined analyser-based and propagation-based phase-contrast imaging of weak objects," Opt. Commun. 259, 19 (2006).
[CrossRef]

Y. I. Nesterets, P. Coan, T. E. Gureyev, A. Bravin, P. Cloetens, and S. W. Wilkins, "On qualitative and quantitative analysis in analyser-based imaging," Acta Cryst. A,  62296 (2006).
[CrossRef]

Y. I. Nesterets, T. E. Gureyev, and S. W. Wilkins, "Polychromaticity in the combined propagation-based/analyzer-based phase-contrast imaging," J. Phys. D: Appl. Phys. 38, 4259 (2005).
[CrossRef]

Y. I. Nesterets, T. E. Gureyev, D. Paganin, K. M. Pavlov, and S. W. Wilkins, "Quantitative diffraction-enhanced X-ray imaging of weak objects," J. Phys. D: Appl. Phys. 37, 1262 (2004).
[CrossRef]

Olivo, A.

F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. Dalla Palma, M. Di Michiel, M. Fabrizioli, R. Longo, R. -H. Menk, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, M. Ratti, L. Rigon, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, "Mammography with synchrotron radiation: Phase-detection techniques," Radiology 215, 286 (2000).

Paganin, D.

Y. I. Nesterets, T. E. Gureyev, K. M. Pavlov, D. Paganin, and S. W. Wilkins, "Combined analyser-based and propagation-based phase-contrast imaging of weak objects," Opt. Commun. 259, 19 (2006).
[CrossRef]

D. 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, 87 (2004).
[CrossRef]

Y. I. Nesterets, T. E. Gureyev, D. Paganin, K. M. Pavlov, and S. W. Wilkins, "Quantitative diffraction-enhanced X-ray imaging of weak objects," J. Phys. D: Appl. Phys. 37, 1262 (2004).
[CrossRef]

Pagot, E.

P. Coan, E. Pagot, S. Fiedler, P. Cloetens, J. Baruchel, and A. Bravin, "Phase-contrast X-ray imaging combining free space propagation and Bragg diffraction," J. Synchrotron Radiat. 12, 241 (2005).
[CrossRef] [PubMed]

Pani, S.

F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. Dalla Palma, M. Di Michiel, M. Fabrizioli, R. Longo, R. -H. Menk, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, M. Ratti, L. Rigon, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, "Mammography with synchrotron radiation: Phase-detection techniques," Radiology 215, 286 (2000).

Pavlov, K. M.

Y. I. Nesterets, T. E. Gureyev, K. M. Pavlov, D. Paganin, and S. W. Wilkins, "Combined analyser-based and propagation-based phase-contrast imaging of weak objects," Opt. Commun. 259, 19 (2006).
[CrossRef]

Y. I. Nesterets, T. E. Gureyev, D. Paganin, K. M. Pavlov, and S. W. Wilkins, "Quantitative diffraction-enhanced X-ray imaging of weak objects," J. Phys. D: Appl. Phys. 37, 1262 (2004).
[CrossRef]

D. 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, 87 (2004).
[CrossRef]

Peterzol, A.

P. Coan, A. Peterzol, S. Fiedler, C. Ponchut, J. C. Labiche, and A , Bravin, "Evaluation of imaging performance of a taper optics CCD `FReLoN' camera designed for medical imaging," J. Synchrotron Radiat. 13, 260 (2006).
[CrossRef] [PubMed]

Ponchut, C.

P. Coan, A. Peterzol, S. Fiedler, C. Ponchut, J. C. Labiche, and A , Bravin, "Evaluation of imaging performance of a taper optics CCD `FReLoN' camera designed for medical imaging," J. Synchrotron Radiat. 13, 260 (2006).
[CrossRef] [PubMed]

Pontoni, D.

F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. Dalla Palma, M. Di Michiel, M. Fabrizioli, R. Longo, R. -H. Menk, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, M. Ratti, L. Rigon, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, "Mammography with synchrotron radiation: Phase-detection techniques," Radiology 215, 286 (2000).

Poropat, P.

F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. Dalla Palma, M. Di Michiel, M. Fabrizioli, R. Longo, R. -H. Menk, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, M. Ratti, L. Rigon, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, "Mammography with synchrotron radiation: Phase-detection techniques," Radiology 215, 286 (2000).

Prest, M.

F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. Dalla Palma, M. Di Michiel, M. Fabrizioli, R. Longo, R. -H. Menk, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, M. Ratti, L. Rigon, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, "Mammography with synchrotron radiation: Phase-detection techniques," Radiology 215, 286 (2000).

Rashevsky, A.

F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. Dalla Palma, M. Di Michiel, M. Fabrizioli, R. Longo, R. -H. Menk, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, M. Ratti, L. Rigon, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, "Mammography with synchrotron radiation: Phase-detection techniques," Radiology 215, 286 (2000).

Ratti, M.

F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. Dalla Palma, M. Di Michiel, M. Fabrizioli, R. Longo, R. -H. Menk, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, M. Ratti, L. Rigon, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, "Mammography with synchrotron radiation: Phase-detection techniques," Radiology 215, 286 (2000).

Rigon, L.

F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. Dalla Palma, M. Di Michiel, M. Fabrizioli, R. Longo, R. -H. Menk, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, M. Ratti, L. Rigon, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, "Mammography with synchrotron radiation: Phase-detection techniques," Radiology 215, 286 (2000).

Simon, D.

A. Autier and D. Simon, "Application de la théorie dynamique de S. Takagi au contraste d'un défaut plan en topographie par rayons X. I. Faute d'empilement," Acta Cryst. A 24, 517 (1968).
[CrossRef]

Soyer, A.

Y. Epelboin, V. Mocella, and A. Soyer, "Optical characteristics of synchrotron sources and their influence in the simulation of X-ray topographs," Philos. T. Roy. Soc. A 357, 2731 (1999).
[CrossRef]

Stevenson, A. W.

T. J. Davis, T. E. Gureyev, D. Gao, A. W. Stevenson, and S. W. Wilkins, "X-ray image contrast from a simple phase object," Phys. Rev. Lett. 74, 3173 (1995).
[CrossRef] [PubMed]

Suortti, P.

J. Keyriläinen, M. Fernández, S. Fiedler, A. Bravin, M. L. Karjalainen-Lindsberg, P. Virkkunen, E. M. Elo, M. Tenhunen, P. Suortti, and W. Thomlinson, "Visualisation of calcifications and thin collagen strands in human breast tumour specimens by the diffraction-enhanced imaging technique: a comparison with conventional mammography and histology," Eur. J. Radiol. 53 (2), 226 (2005).
[CrossRef]

J. Keyriläinen, M. Fernández, and P. Suortti, "Refraction contrast X-ray imaging," Nucl. Instrum. Methods A 488, 419 (2002).
[CrossRef]

Takagi, S.

S. Takagi, "A dynamical theory of diffraction for a distorted crystal," J. Phys. Soc. Jpn 26 (1969).
[CrossRef]

Takeda, T.

A. Yoneyama, T. Takeda, Y. Tsuchiya, J. Wu, T. T. Lwin, K. Hyodo, and Y. Hirai, "High-energy phase-contrast X-ray imaging using a two-crystal X-ray interferometer," J. Synchrotron Radiat. 12, 534 (2005).
[CrossRef] [PubMed]

Tenhunen, M.

J. Keyriläinen, M. Fernández, S. Fiedler, A. Bravin, M. L. Karjalainen-Lindsberg, P. Virkkunen, E. M. Elo, M. Tenhunen, P. Suortti, and W. Thomlinson, "Visualisation of calcifications and thin collagen strands in human breast tumour specimens by the diffraction-enhanced imaging technique: a comparison with conventional mammography and histology," Eur. J. Radiol. 53 (2), 226 (2005).
[CrossRef]

Thomlinson, W.

J. Keyriläinen, M. Fernández, S. Fiedler, A. Bravin, M. L. Karjalainen-Lindsberg, P. Virkkunen, E. M. Elo, M. Tenhunen, P. Suortti, and W. Thomlinson, "Visualisation of calcifications and thin collagen strands in human breast tumour specimens by the diffraction-enhanced imaging technique: a comparison with conventional mammography and histology," Eur. J. Radiol. 53 (2), 226 (2005).
[CrossRef]

Tromba, G.

F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. Dalla Palma, M. Di Michiel, M. Fabrizioli, R. Longo, R. -H. Menk, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, M. Ratti, L. Rigon, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, "Mammography with synchrotron radiation: Phase-detection techniques," Radiology 215, 286 (2000).

Tsuchiya, Y.

A. Yoneyama, T. Takeda, Y. Tsuchiya, J. Wu, T. T. Lwin, K. Hyodo, and Y. Hirai, "High-energy phase-contrast X-ray imaging using a two-crystal X-ray interferometer," J. Synchrotron Radiat. 12, 534 (2005).
[CrossRef] [PubMed]

Uragami, T.

T. Uragami, "Pendellösung fringes of X-rays in Bragg case," J. Phys. Soc. Jpn 27, 147 (1969).
[CrossRef]

Vacchi, A.

F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. Dalla Palma, M. Di Michiel, M. Fabrizioli, R. Longo, R. -H. Menk, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, M. Ratti, L. Rigon, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, "Mammography with synchrotron radiation: Phase-detection techniques," Radiology 215, 286 (2000).

Vallazza, E.

F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. Dalla Palma, M. Di Michiel, M. Fabrizioli, R. Longo, R. -H. Menk, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, M. Ratti, L. Rigon, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, "Mammography with synchrotron radiation: Phase-detection techniques," Radiology 215, 286 (2000).

Virkkunen, P.

J. Keyriläinen, M. Fernández, S. Fiedler, A. Bravin, M. L. Karjalainen-Lindsberg, P. Virkkunen, E. M. Elo, M. Tenhunen, P. Suortti, and W. Thomlinson, "Visualisation of calcifications and thin collagen strands in human breast tumour specimens by the diffraction-enhanced imaging technique: a comparison with conventional mammography and histology," Eur. J. Radiol. 53 (2), 226 (2005).
[CrossRef]

Wilkins, S. W.

Y. I. Nesterets, T. E. Gureyev, K. M. Pavlov, D. Paganin, and S. W. Wilkins, "Combined analyser-based and propagation-based phase-contrast imaging of weak objects," Opt. Commun. 259, 19 (2006).
[CrossRef]

Y. I. Nesterets, P. Coan, T. E. Gureyev, A. Bravin, P. Cloetens, and S. W. Wilkins, "On qualitative and quantitative analysis in analyser-based imaging," Acta Cryst. A,  62296 (2006).
[CrossRef]

Y. I. Nesterets, T. E. Gureyev, and S. W. Wilkins, "Polychromaticity in the combined propagation-based/analyzer-based phase-contrast imaging," J. Phys. D: Appl. Phys. 38, 4259 (2005).
[CrossRef]

Y. I. Nesterets, T. E. Gureyev, D. Paganin, K. M. Pavlov, and S. W. Wilkins, "Quantitative diffraction-enhanced X-ray imaging of weak objects," J. Phys. D: Appl. Phys. 37, 1262 (2004).
[CrossRef]

T. J. Davis, T. E. Gureyev, D. Gao, A. W. Stevenson, and S. W. Wilkins, "X-ray image contrast from a simple phase object," Phys. Rev. Lett. 74, 3173 (1995).
[CrossRef] [PubMed]

Wu, J.

A. Yoneyama, T. Takeda, Y. Tsuchiya, J. Wu, T. T. Lwin, K. Hyodo, and Y. Hirai, "High-energy phase-contrast X-ray imaging using a two-crystal X-ray interferometer," J. Synchrotron Radiat. 12, 534 (2005).
[CrossRef] [PubMed]

Yoneyama, A.

A. Yoneyama, T. Takeda, Y. Tsuchiya, J. Wu, T. T. Lwin, K. Hyodo, and Y. Hirai, "High-energy phase-contrast X-ray imaging using a two-crystal X-ray interferometer," J. Synchrotron Radiat. 12, 534 (2005).
[CrossRef] [PubMed]

Zanconati, F.

F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. Dalla Palma, M. Di Michiel, M. Fabrizioli, R. Longo, R. -H. Menk, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, M. Ratti, L. Rigon, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, "Mammography with synchrotron radiation: Phase-detection techniques," Radiology 215, 286 (2000).

Acta Cryst. A (6)

C. A. M. Carvalho, and Y. Epelboin, "Simulation of X-ray traverse topographs and synchrotron Laue topographs: application of the reciprocity theorem," Acta Cryst. A 49, 467 (1993).
[CrossRef]

V. Mocella, Y. Epelboin, and J. P. Guigay, "X-ray dynamical diffraction: the concept of a locally plane wave," Acta Cryst. A 56, 308 (2000).
[CrossRef]

V. Mocella, Y. Epelboin, and J. P. Guigay, "X-ray dynamical diffraction: the concept of a locally plane wave," Acta Cryst. A 56, 308 (2000).
[CrossRef]

Y. I. Nesterets, P. Coan, T. E. Gureyev, A. Bravin, P. Cloetens, and S. W. Wilkins, "On qualitative and quantitative analysis in analyser-based imaging," Acta Cryst. A,  62296 (2006).
[CrossRef]

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A. Autier and D. Simon, "Application de la théorie dynamique de S. Takagi au contraste d'un défaut plan en topographie par rayons X. I. Faute d'empilement," Acta Cryst. A 24, 517 (1968).
[CrossRef]

Acta Cryst. A. (1)

J. P. Guigay, "A simple view of the spherical wave in dynamical theory," Acta Cryst. A. 55, 561 (1999).
[CrossRef]

Eur. J. Radiol. (1)

J. Keyriläinen, M. Fernández, S. Fiedler, A. Bravin, M. L. Karjalainen-Lindsberg, P. Virkkunen, E. M. Elo, M. Tenhunen, P. Suortti, and W. Thomlinson, "Visualisation of calcifications and thin collagen strands in human breast tumour specimens by the diffraction-enhanced imaging technique: a comparison with conventional mammography and histology," Eur. J. Radiol. 53 (2), 226 (2005).
[CrossRef]

J. Phys. D: Appl. Phys. (4)

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[CrossRef]

V. Mocella, J. P. Guigay, Y. Epelboin, J. Haertwig, J. Baruchel, and A. Mazuelas, "Influence of the transverse and longitudinal coherence in the dynamical theory of X-ray diffraction," J. Phys. D: Appl. Phys. 32, A88 (1999).
[CrossRef]

Y. I. Nesterets, T. E. Gureyev, D. Paganin, K. M. Pavlov, and S. W. Wilkins, "Quantitative diffraction-enhanced X-ray imaging of weak objects," J. Phys. D: Appl. Phys. 37, 1262 (2004).
[CrossRef]

Y. I. Nesterets, T. E. Gureyev, and S. W. Wilkins, "Polychromaticity in the combined propagation-based/analyzer-based phase-contrast imaging," J. Phys. D: Appl. Phys. 38, 4259 (2005).
[CrossRef]

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[CrossRef]

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[CrossRef]

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A. Yoneyama, T. Takeda, Y. Tsuchiya, J. Wu, T. T. Lwin, K. Hyodo, and Y. Hirai, "High-energy phase-contrast X-ray imaging using a two-crystal X-ray interferometer," J. Synchrotron Radiat. 12, 534 (2005).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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J. Keyriläinen, M. Fernández, and P. Suortti, "Refraction contrast X-ray imaging," Nucl. Instrum. Methods A 488, 419 (2002).
[CrossRef]

Opt. Commun. (2)

D. 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, 87 (2004).
[CrossRef]

Y. I. Nesterets, T. E. Gureyev, K. M. Pavlov, D. Paganin, and S. W. Wilkins, "Combined analyser-based and propagation-based phase-contrast imaging of weak objects," Opt. Commun. 259, 19 (2006).
[CrossRef]

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[PubMed]

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Figures (5)

Fig. 1.
Fig. 1.

Schematic layout of the experimental set-up for analyzer-based imaging with synchrotron radiation. The premonochromator is not shown. x, x’, ξ and ξ’: coordinate directions (see text).

Fig. 2.
Fig. 2.

(a). Intensity pattern (a. u.): experimental (red), geometrical (blue) wave-optical (dashed green): Si(111) reflection, θa = 0 μrad, nylon, R = 175 μm, L = 0.5 m; (b) Intensity pattern (a.u.); experimental (red), geometrical (blue) wave-optical (dashed green): Si(111) reflection, θa = -11.7 μrad, nylon, R = 175 μm, L = 0.5 m.

Fig. 3.
Fig. 3.

(a). Intensity pattern (a.u.); experimental (red), geometrical (blue) wave-optical (dashed green): Si(111) reflection, θa = 0 μrad, Kevlar, R = 50 μm, L = 5.5 m; (b) Intensity pattern (a.u.); experimental (red), geometrical (blue) wave-optical (dashed green): Si(111) reflection, θa = -11.7 μrad, Kevlar, R = 50 μm, L = 5.5 m.

Fig. 4.
Fig. 4.

(a). Triangular plexiglas wedge; a=3 mm, b=2.6 mm, c=1.5 mm, α= 30°, β= 60°.; (b) Trapezoidal plexiglas wedge; a=b=1.5 mm, c= 2 mm, d= 4.12 mm, α= 45°, β= 135°. The arrows indicate the incident X-ray beam direction.

Fig. 5.
Fig. 5.

(a). Intensity pattern (a.u.): experimental (red) and wave-optical (dashed green) for the triangular wedge as in Fig. 4(a), Si(111) reflection, θa = 3.404 μrad, L=2.2 m; (b) Intensity pattern (a.u.): experimental (red) and wave-optical (dashed green) for the trapezoidal wedge as in Fig. 4(b), Si(111) reflection, θa = -3.404 μrad, L=2.2 m.

Equations (10)

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R h x S = iπCk χ h [ J 0 ( ( x S ) πkC sin θ B χ h ¯ χ h ) + J 2 ( ( x S ) πkC sin θ B χ h ¯ χ h ) ]
1 n x z = δ x z + x z
Φ ( x ) = 2 π λ ( δ x z + x z ) dz
A ( x ) = e i Φ ( x ) = A 0 ( x ) e ( x )
A 0 ( x ) = e 2 π λ β x z dz
φ ( x ) = 2 π λ δ x z dz
ψ x S = R h x S A ( x )
ϒ ( ξ ' , S ) = ψ τ S R h ( ξ τ , S )
Ψ ξ S = ϒ τ S e iπk ( ξ τ ) 2 L
I ( ξ ) = Ψ ξ S 2 dS

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