Abstract

X-ray phase-contrast imaging is a technique that aims to reconstruct the projected absorption and refractive index distributions of an object. One common feature of reconstruction formulas for phase-contrast imaging is the presence of isolated Fourier domain singularities, which can greatly amplify the noise levels in the estimated Fourier domain and lead to noisy and/or distorted images in spatial domain. In this article, we develop a statistically optimal reconstruction method that employs multiple (>2) measurement states to mitigate the noise amplification effects due to singularities in the reconstruction formula. Computer-simulation studies are carried out to quantitatively and systematically investigate the developed method, within the context of propagation-based X-ray phase-contrast imaging. The reconstructed images are shown to possess dramatically reduced noise levels and greatly enhanced imaging contrast.

© 2007 Optical Society of America

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2007 (1)

Y. Huang and M. A. Anastasio, “Statistically principled use of in-line measurements in intensity diffraction tomography,” J. Opt. Soc. Am. A 24, 626–642 (2007).
[Crossref]

2006 (7)

T. E. Gureyev, Y. I. Nesterets, D. M. Paganin, A. Pogany, and S. W. Wilkins, “Linear algorithms for phase retrieval in the Fresnel region. 2. Partially coherent illumination,” Opt. Commun. 259, 569–580 (2006).
[Crossref]

T. E. Gureyev, D. M. Paganin, G. R. Myers, Y. I. Nesterest, and S. W. Wilkins, “Phase-and-amplitude computer tomography,” Appl. Phys. Lett. 89, 034102 (2006).
[Crossref]

Y. I. Nesterets, T. E. Gureyev, K. M. Pavlov, D. M. Paganin, and S. W. Wilkins, “Combined analyser-based and propagation-based phase-contrast imaging of weak objects,” Opt. Commun. 259, 19–31 (2006).
[Crossref]

C. Muehleman, J. Li, Z. Zhong, J. G. Brankov, and M. N. Wernick, “Multiple-image radiography for soft tissue of the foot and ankle,” J. Anat. 208, 115–124 (2006).
[Crossref] [PubMed]

J. G. Brankov, M. N. Wernick, Y. Yang, J. Li, C. Muehleman, Z. Zhong, and M. A. Anastasio, “A computed tomography implementation of multiple-image radiography,” Med. Phys. 33, 278–289 (2006).
[Crossref] [PubMed]

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

T. E. Gureyev, G. R. Myers, Y. I. Nesterets, D. Paganin, K. M. Pavlov, and S. W. Wilkins, “Stability and locality of amplitude and phase contrast tomographies,” Proc. SPIE 6318, 63180V (2006).

2005 (3)

W. Thomlinson, P. Suortti, and D. Chapman, “Recent advances in synchrotron radiation medical research,” Nucl. Instrum. Methods Phys. Res. A 543, 288–296 (2005).

T. Tanaka, C. Honda, S. Matsuo, K. Noma, H. Ohara, N. Nitta, S. Ota, K. Tsuchiya, Y. Sakashita, A. Yamada, M. Yamasaki, A. Furukawa, M. Takahashi, and K. Murata, “The first trial of phase contrast imaging for digital full-field mammography using a practical molybdenum x-ray tube,” Invest. Radiol. 40, 385–396 (2005).
[Crossref] [PubMed]

Y. I. Nesterets, T. E. Gureyev, and S.W. Wilkins, “Polychromaticity in the combined propagation-based/analyser-based phase-contrast imaging,” J. Phys. D 38, 4259–4271 (2005).

2004 (7)

K. M. Pavlov, T. E. Gureyev, D. Paganin, Y. Nesterets, M. J. Morgan, and R. A. Lewis, “Linear systems with slowly varying transfer functions and their application to X-ray phase-contrast imaging,” J. Phys. D 37, 2746–2750 (2004).

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

M. A. Anastasio, D. Shi, F. D. Carlo, and X. Pan, “Analytic image reconstruction in local phase-contrast tomography,” Phys. Med. Biol. 49, 121–144 (2004).
[Crossref] [PubMed]

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 37, 1262–1274 (2004).

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

R. Lewis, “Medical phase contrast x-ray imaging: current status and future prospects,” Phys. Med. Biol. 49, 3573–3583 (2004).
[Crossref] [PubMed]

M. Z. Kiss, D. E. Sayers, Z. Zhong, C. Parham, and E. D. Pisano, “Improved image contrast of calcifications in breast tissue specimens using diffraction enhanced imaging,” Phys. Med. Biol. 49, 3427–3439 (2004).
[Crossref] [PubMed]

2003 (6)

X. Wu and H. Liu, “Clinical implementation of X-ray phase-contrast imaging: Theoretical foundations and design considerations,” Med. Phys. 30, 2169–2179 (2003).
[Crossref] [PubMed]

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48, 3875–3895 (2003).
[Crossref]

E. F. Donnelly, R. R. Price, and D. R. Pickens, “Characterization of the phase-contrast radiography edge-enhancement effect in a cabinet x-ray system,” Med. Phys. 30, 2292–2296 (2003).
[Crossref] [PubMed]

H. Yamada, “Novel x-ray source based on a tabletop synchrotron and its unique features,” Nucl. Instrum. Methods Phys. Res. B 199, 509–516 (2003).

A. Bravin, “Exploiting the x-ray refraction contrast with an analyser: the state of the art,” J. Phys. D 36, A24–A29 (2003).

D. Paganin, A. Barty, P. J. Mcmahon, and K. A. Nugent, “Quantitative phase-amplitude microscopy III. The effects of noise,” J. Microsc. 214, 51–61 (2003).
[Crossref]

2002 (1)

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

2000 (3)

R. Waynant, “Toward practical coherent x-ray sources: Potential medical applications,” IEEE J. Quantum Electron. 6, 1465–1469 (2000).
[Crossref]

E. Pisano, R. Johnston, D. Chapman, J. Geradts, M. Iacocca, C. Livasy, D. Washburn, D. Sayers, Z. Zhong, M. Kiss, and W. Thomlinson, “Human Breast Cancer Specimens: Diffraction-enhanced Imaging with Histologic Correlation-Improved Conspicuity of Lesion Detail Compared with Digital Radiography,” Radiology 214, 895–901 (2000).
[PubMed]

F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. 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, 286–293 (2000).

1999 (3)

C. J. Kotre and I. P. Birch, “Phase contrast enhancement of x-ray mammography: a design study,” Phys. Med. Biol. 44, 2853–2866 (1999).
[Crossref] [PubMed]

P. Cloetens, W. Ludwig, J. Baruchel, D. Dyck, J. Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. lett. 75, 2912–2914 (1999).
[Crossref]

P. Spanne, C. Raven, I. Snigireva, and A. Snigirev, “In-line holography and phase-contrast microtomography with high energy x-rays,” Phys. Med. Biol. 44, 741–749 (1999).
[Crossref] [PubMed]

1998 (1)

F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, “Low-dose phase contrast x-ray medical imaging,” Phys. Med. Biol. 43, 2845–2852 (1998).
[Crossref] [PubMed]

1997 (3)

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmur, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42, 2015–2025 (1997).
[Crossref] [PubMed]

A. Krol, A. Ikhlef, J.-C. Kieffer, D. Bassano, C. C. Chamberlain, Z. Jiang, H. Pepin, and S. C. Prasad, “Laser-based microfocused X-ray source for mammography: feasibility study,” Med. Phys. 24, 725–732 (1997).
[Crossref] [PubMed]

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

1996 (2)

T. Davis, D. Gao, T. E. Gureyev, A. Stevenson, and S. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature (London) 373, 335–338 (1996).

K. A. Nugent, T. E. Gureyev, D. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard x-rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).
[Crossref] [PubMed]

1993 (1)

B.L. Henke, E.M. Gullikson, and J.C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50-30000 eV, Z=1-92,” At. Data Nucl. Data Tables 54, 181–342 (1993).
[Crossref]

1977 (1)

J.-P. Guigay, “Fourier transform analysis of Fresnel diffraction patterns and in-line holograms,” Optik 49, 121–125 (1977).

1970 (1)

Anastasio, M. A.

Y. Huang and M. A. Anastasio, “Statistically principled use of in-line measurements in intensity diffraction tomography,” J. Opt. Soc. Am. A 24, 626–642 (2007).
[Crossref]

J. G. Brankov, M. N. Wernick, Y. Yang, J. Li, C. Muehleman, Z. Zhong, and M. A. Anastasio, “A computed tomography implementation of multiple-image radiography,” Med. Phys. 33, 278–289 (2006).
[Crossref] [PubMed]

M. A. Anastasio, D. Shi, F. D. Carlo, and X. Pan, “Analytic image reconstruction in local phase-contrast tomography,” Phys. Med. Biol. 49, 121–144 (2004).
[Crossref] [PubMed]

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48, 3875–3895 (2003).
[Crossref]

Arfelli, F.

F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. 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, 286–293 (2000).

F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, “Low-dose phase contrast x-ray medical imaging,” Phys. Med. Biol. 43, 2845–2852 (1998).
[Crossref] [PubMed]

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmur, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42, 2015–2025 (1997).
[Crossref] [PubMed]

Arsenault, H.

Assante, M.

F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, “Low-dose phase contrast x-ray medical imaging,” Phys. Med. Biol. 43, 2845–2852 (1998).
[Crossref] [PubMed]

Barnea, Z.

K. A. Nugent, T. E. Gureyev, D. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard x-rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).
[Crossref] [PubMed]

Barty, A.

D. Paganin, A. Barty, P. J. Mcmahon, and K. A. Nugent, “Quantitative phase-amplitude microscopy III. The effects of noise,” J. Microsc. 214, 51–61 (2003).
[Crossref]

Baruchel, J.

P. Cloetens, W. Ludwig, J. Baruchel, D. Dyck, J. Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. lett. 75, 2912–2914 (1999).
[Crossref]

Bassano, D.

A. Krol, A. Ikhlef, J.-C. Kieffer, D. Bassano, C. C. Chamberlain, Z. Jiang, H. Pepin, and S. C. Prasad, “Laser-based microfocused X-ray source for mammography: feasibility study,” Med. Phys. 24, 725–732 (1997).
[Crossref] [PubMed]

Birch, I. P.

C. J. Kotre and I. P. Birch, “Phase contrast enhancement of x-ray mammography: a design study,” Phys. Med. Biol. 44, 2853–2866 (1999).
[Crossref] [PubMed]

Bonvicini, V.

F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. 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, 286–293 (2000).

F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, “Low-dose phase contrast x-ray medical imaging,” Phys. Med. Biol. 43, 2845–2852 (1998).
[Crossref] [PubMed]

Born, M.

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

Brankov, J. G.

C. Muehleman, J. Li, Z. Zhong, J. G. Brankov, and M. N. Wernick, “Multiple-image radiography for soft tissue of the foot and ankle,” J. Anat. 208, 115–124 (2006).
[Crossref] [PubMed]

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F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, “Low-dose phase contrast x-ray medical imaging,” Phys. Med. Biol. 43, 2845–2852 (1998).
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E. Pisano, R. Johnston, D. Chapman, J. Geradts, M. Iacocca, C. Livasy, D. Washburn, D. Sayers, Z. Zhong, M. Kiss, and W. Thomlinson, “Human Breast Cancer Specimens: Diffraction-enhanced Imaging with Histologic Correlation-Improved Conspicuity of Lesion Detail Compared with Digital Radiography,” Radiology 214, 895–901 (2000).
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K. M. Pavlov, T. E. Gureyev, D. Paganin, Y. Nesterets, M. J. Morgan, and R. A. Lewis, “Linear systems with slowly varying transfer functions and their application to X-ray phase-contrast imaging,” J. Phys. D 37, 2746–2750 (2004).

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 37, 1262–1274 (2004).

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D. M. Paganin, T. E. Gureyev, K. M. Pavlov, R. A. Lewis, and M. Kitchen, “Quantitative phase retrieval using coherent imaging systems with linear transfer functions,” Opt. Commun. 234, 87–105 (2004).
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K. A. Nugent, T. E. Gureyev, D. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard x-rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).
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B.L. Henke, E.M. Gullikson, and J.C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50-30000 eV, Z=1-92,” At. Data Nucl. Data Tables 54, 181–342 (1993).
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A. Krol, A. Ikhlef, J.-C. Kieffer, D. Bassano, C. C. Chamberlain, Z. Jiang, H. Pepin, and S. C. Prasad, “Laser-based microfocused X-ray source for mammography: feasibility study,” Med. Phys. 24, 725–732 (1997).
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E. Pisano, R. Johnston, D. Chapman, J. Geradts, M. Iacocca, C. Livasy, D. Washburn, D. Sayers, Z. Zhong, M. Kiss, and W. Thomlinson, “Human Breast Cancer Specimens: Diffraction-enhanced Imaging with Histologic Correlation-Improved Conspicuity of Lesion Detail Compared with Digital Radiography,” Radiology 214, 895–901 (2000).
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D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmur, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42, 2015–2025 (1997).
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E. Pisano, R. Johnston, D. Chapman, J. Geradts, M. Iacocca, C. Livasy, D. Washburn, D. Sayers, Z. Zhong, M. Kiss, and W. Thomlinson, “Human Breast Cancer Specimens: Diffraction-enhanced Imaging with Histologic Correlation-Improved Conspicuity of Lesion Detail Compared with Digital Radiography,” Radiology 214, 895–901 (2000).
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Landuyt, J.

P. Cloetens, W. Ludwig, J. Baruchel, D. Dyck, J. Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. lett. 75, 2912–2914 (1999).
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Lewis, R. A.

D. M. Paganin, T. E. Gureyev, K. M. Pavlov, R. A. Lewis, and M. Kitchen, “Quantitative phase retrieval using coherent imaging systems with linear transfer functions,” Opt. Commun. 234, 87–105 (2004).
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K. M. Pavlov, T. E. Gureyev, D. Paganin, Y. Nesterets, M. J. Morgan, and R. A. Lewis, “Linear systems with slowly varying transfer functions and their application to X-ray phase-contrast imaging,” J. Phys. D 37, 2746–2750 (2004).

Li, J.

C. Muehleman, J. Li, Z. Zhong, J. G. Brankov, and M. N. Wernick, “Multiple-image radiography for soft tissue of the foot and ankle,” J. Anat. 208, 115–124 (2006).
[Crossref] [PubMed]

J. G. Brankov, M. N. Wernick, Y. Yang, J. Li, C. Muehleman, Z. Zhong, and M. A. Anastasio, “A computed tomography implementation of multiple-image radiography,” Med. Phys. 33, 278–289 (2006).
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E. Pisano, R. Johnston, D. Chapman, J. Geradts, M. Iacocca, C. Livasy, D. Washburn, D. Sayers, Z. Zhong, M. Kiss, and W. Thomlinson, “Human Breast Cancer Specimens: Diffraction-enhanced Imaging with Histologic Correlation-Improved Conspicuity of Lesion Detail Compared with Digital Radiography,” Radiology 214, 895–901 (2000).
[PubMed]

Longo, R.

F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. 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, 286–293 (2000).

F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, “Low-dose phase contrast x-ray medical imaging,” Phys. Med. Biol. 43, 2845–2852 (1998).
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Ludwig, W.

P. Cloetens, W. Ludwig, J. Baruchel, D. Dyck, J. Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. lett. 75, 2912–2914 (1999).
[Crossref]

Matsuo, S.

T. Tanaka, C. Honda, S. Matsuo, K. Noma, H. Ohara, N. Nitta, S. Ota, K. Tsuchiya, Y. Sakashita, A. Yamada, M. Yamasaki, A. Furukawa, M. Takahashi, and K. Murata, “The first trial of phase contrast imaging for digital full-field mammography using a practical molybdenum x-ray tube,” Invest. Radiol. 40, 385–396 (2005).
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D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmur, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42, 2015–2025 (1997).
[Crossref] [PubMed]

Menk, R. H.

F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. 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, 286–293 (2000).

Michiel, M. D.

F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. 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, 286–293 (2000).

F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, “Low-dose phase contrast x-ray medical imaging,” Phys. Med. Biol. 43, 2845–2852 (1998).
[Crossref] [PubMed]

Morgan, M. J.

K. M. Pavlov, T. E. Gureyev, D. Paganin, Y. Nesterets, M. J. Morgan, and R. A. Lewis, “Linear systems with slowly varying transfer functions and their application to X-ray phase-contrast imaging,” J. Phys. D 37, 2746–2750 (2004).

Muehleman, C.

J. G. Brankov, M. N. Wernick, Y. Yang, J. Li, C. Muehleman, Z. Zhong, and M. A. Anastasio, “A computed tomography implementation of multiple-image radiography,” Med. Phys. 33, 278–289 (2006).
[Crossref] [PubMed]

C. Muehleman, J. Li, Z. Zhong, J. G. Brankov, and M. N. Wernick, “Multiple-image radiography for soft tissue of the foot and ankle,” J. Anat. 208, 115–124 (2006).
[Crossref] [PubMed]

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48, 3875–3895 (2003).
[Crossref]

Murata, K.

T. Tanaka, C. Honda, S. Matsuo, K. Noma, H. Ohara, N. Nitta, S. Ota, K. Tsuchiya, Y. Sakashita, A. Yamada, M. Yamasaki, A. Furukawa, M. Takahashi, and K. Murata, “The first trial of phase contrast imaging for digital full-field mammography using a practical molybdenum x-ray tube,” Invest. Radiol. 40, 385–396 (2005).
[Crossref] [PubMed]

Myers, G. R.

T. E. Gureyev, G. R. Myers, Y. I. Nesterets, D. Paganin, K. M. Pavlov, and S. W. Wilkins, “Stability and locality of amplitude and phase contrast tomographies,” Proc. SPIE 6318, 63180V (2006).

T. E. Gureyev, D. M. Paganin, G. R. Myers, Y. I. Nesterest, and S. W. Wilkins, “Phase-and-amplitude computer tomography,” Appl. Phys. Lett. 89, 034102 (2006).
[Crossref]

Nesterest, Y. I.

T. E. Gureyev, D. M. Paganin, G. R. Myers, Y. I. Nesterest, and S. W. Wilkins, “Phase-and-amplitude computer tomography,” Appl. Phys. Lett. 89, 034102 (2006).
[Crossref]

Nesterets, Y.

K. M. Pavlov, T. E. Gureyev, D. Paganin, Y. Nesterets, M. J. Morgan, and R. A. Lewis, “Linear systems with slowly varying transfer functions and their application to X-ray phase-contrast imaging,” J. Phys. D 37, 2746–2750 (2004).

Nesterets, Y. I.

T. E. Gureyev, Y. I. Nesterets, D. M. Paganin, A. Pogany, and S. W. Wilkins, “Linear algorithms for phase retrieval in the Fresnel region. 2. Partially coherent illumination,” Opt. Commun. 259, 569–580 (2006).
[Crossref]

T. E. Gureyev, G. R. Myers, Y. I. Nesterets, D. Paganin, K. M. Pavlov, and S. W. Wilkins, “Stability and locality of amplitude and phase contrast tomographies,” Proc. SPIE 6318, 63180V (2006).

Y. I. Nesterets, T. E. Gureyev, K. M. Pavlov, D. M. Paganin, and S. W. Wilkins, “Combined analyser-based and propagation-based phase-contrast imaging of weak objects,” Opt. Commun. 259, 19–31 (2006).
[Crossref]

Y. I. Nesterets, T. E. Gureyev, and S.W. Wilkins, “Polychromaticity in the combined propagation-based/analyser-based phase-contrast imaging,” J. Phys. D 38, 4259–4271 (2005).

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 37, 1262–1274 (2004).

Nitta, N.

T. Tanaka, C. Honda, S. Matsuo, K. Noma, H. Ohara, N. Nitta, S. Ota, K. Tsuchiya, Y. Sakashita, A. Yamada, M. Yamasaki, A. Furukawa, M. Takahashi, and K. Murata, “The first trial of phase contrast imaging for digital full-field mammography using a practical molybdenum x-ray tube,” Invest. Radiol. 40, 385–396 (2005).
[Crossref] [PubMed]

Noma, K.

T. Tanaka, C. Honda, S. Matsuo, K. Noma, H. Ohara, N. Nitta, S. Ota, K. Tsuchiya, Y. Sakashita, A. Yamada, M. Yamasaki, A. Furukawa, M. Takahashi, and K. Murata, “The first trial of phase contrast imaging for digital full-field mammography using a practical molybdenum x-ray tube,” Invest. Radiol. 40, 385–396 (2005).
[Crossref] [PubMed]

Nugent, K. A.

D. Paganin, A. Barty, P. J. Mcmahon, and K. A. Nugent, “Quantitative phase-amplitude microscopy III. The effects of noise,” J. Microsc. 214, 51–61 (2003).
[Crossref]

K. A. Nugent, T. E. Gureyev, D. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard x-rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).
[Crossref] [PubMed]

Ohara, H.

T. Tanaka, C. Honda, S. Matsuo, K. Noma, H. Ohara, N. Nitta, S. Ota, K. Tsuchiya, Y. Sakashita, A. Yamada, M. Yamasaki, A. Furukawa, M. Takahashi, and K. Murata, “The first trial of phase contrast imaging for digital full-field mammography using a practical molybdenum x-ray tube,” Invest. Radiol. 40, 385–396 (2005).
[Crossref] [PubMed]

Olivo, A.

F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. 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, 286–293 (2000).

F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, “Low-dose phase contrast x-ray medical imaging,” Phys. Med. Biol. 43, 2845–2852 (1998).
[Crossref] [PubMed]

Oltulu, O.

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48, 3875–3895 (2003).
[Crossref]

Ota, S.

T. Tanaka, C. Honda, S. Matsuo, K. Noma, H. Ohara, N. Nitta, S. Ota, K. Tsuchiya, Y. Sakashita, A. Yamada, M. Yamasaki, A. Furukawa, M. Takahashi, and K. Murata, “The first trial of phase contrast imaging for digital full-field mammography using a practical molybdenum x-ray tube,” Invest. Radiol. 40, 385–396 (2005).
[Crossref] [PubMed]

Paganin, D.

T. E. Gureyev, G. R. Myers, Y. I. Nesterets, D. Paganin, K. M. Pavlov, and S. W. Wilkins, “Stability and locality of amplitude and phase contrast tomographies,” Proc. SPIE 6318, 63180V (2006).

K. M. Pavlov, T. E. Gureyev, D. Paganin, Y. Nesterets, M. J. Morgan, and R. A. Lewis, “Linear systems with slowly varying transfer functions and their application to X-ray phase-contrast imaging,” J. Phys. D 37, 2746–2750 (2004).

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 37, 1262–1274 (2004).

D. Paganin, A. Barty, P. J. Mcmahon, and K. A. Nugent, “Quantitative phase-amplitude microscopy III. The effects of noise,” J. Microsc. 214, 51–61 (2003).
[Crossref]

K. A. Nugent, T. E. Gureyev, D. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard x-rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).
[Crossref] [PubMed]

Paganin, D. M.

T. E. Gureyev, Y. I. Nesterets, D. M. Paganin, A. Pogany, and S. W. Wilkins, “Linear algorithms for phase retrieval in the Fresnel region. 2. Partially coherent illumination,” Opt. Commun. 259, 569–580 (2006).
[Crossref]

Y. I. Nesterets, T. E. Gureyev, K. M. Pavlov, D. M. Paganin, and S. W. Wilkins, “Combined analyser-based and propagation-based phase-contrast imaging of weak objects,” Opt. Commun. 259, 19–31 (2006).
[Crossref]

T. E. Gureyev, D. M. Paganin, G. R. Myers, Y. I. Nesterest, and S. W. Wilkins, “Phase-and-amplitude computer tomography,” Appl. Phys. Lett. 89, 034102 (2006).
[Crossref]

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

D. M. Paganin, Coherent X-Ray Optics (Oxford University Press, 2006).
[Crossref]

Paganin, D.M.

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

Palma, L. D.

F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. 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, 286–293 (2000).

F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, “Low-dose phase contrast x-ray medical imaging,” Phys. Med. Biol. 43, 2845–2852 (1998).
[Crossref] [PubMed]

Pan, X.

M. A. Anastasio, D. Shi, F. D. Carlo, and X. Pan, “Analytic image reconstruction in local phase-contrast tomography,” Phys. Med. Biol. 49, 121–144 (2004).
[Crossref] [PubMed]

Pani, S.

F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. 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, 286–293 (2000).

F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, “Low-dose phase contrast x-ray medical imaging,” Phys. Med. Biol. 43, 2845–2852 (1998).
[Crossref] [PubMed]

Parham, C.

M. Z. Kiss, D. E. Sayers, Z. Zhong, C. Parham, and E. D. Pisano, “Improved image contrast of calcifications in breast tissue specimens using diffraction enhanced imaging,” Phys. Med. Biol. 49, 3427–3439 (2004).
[Crossref] [PubMed]

Pavlov, K. M.

Y. I. Nesterets, T. E. Gureyev, K. M. Pavlov, D. M. Paganin, and S. W. Wilkins, “Combined analyser-based and propagation-based phase-contrast imaging of weak objects,” Opt. Commun. 259, 19–31 (2006).
[Crossref]

T. E. Gureyev, G. R. Myers, Y. I. Nesterets, D. Paganin, K. M. Pavlov, and S. W. Wilkins, “Stability and locality of amplitude and phase contrast tomographies,” Proc. SPIE 6318, 63180V (2006).

K. M. Pavlov, T. E. Gureyev, D. Paganin, Y. Nesterets, M. J. Morgan, and R. A. Lewis, “Linear systems with slowly varying transfer functions and their application to X-ray phase-contrast imaging,” J. Phys. D 37, 2746–2750 (2004).

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 37, 1262–1274 (2004).

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

Pepin, H.

A. Krol, A. Ikhlef, J.-C. Kieffer, D. Bassano, C. C. Chamberlain, Z. Jiang, H. Pepin, and S. C. Prasad, “Laser-based microfocused X-ray source for mammography: feasibility study,” Med. Phys. 24, 725–732 (1997).
[Crossref] [PubMed]

Pfeiffer, F.

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

Pickens, D. R.

E. F. Donnelly, R. R. Price, and D. R. Pickens, “Characterization of the phase-contrast radiography edge-enhancement effect in a cabinet x-ray system,” Med. Phys. 30, 2292–2296 (2003).
[Crossref] [PubMed]

Pisano, E.

E. Pisano, R. Johnston, D. Chapman, J. Geradts, M. Iacocca, C. Livasy, D. Washburn, D. Sayers, Z. Zhong, M. Kiss, and W. Thomlinson, “Human Breast Cancer Specimens: Diffraction-enhanced Imaging with Histologic Correlation-Improved Conspicuity of Lesion Detail Compared with Digital Radiography,” Radiology 214, 895–901 (2000).
[PubMed]

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmur, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42, 2015–2025 (1997).
[Crossref] [PubMed]

Pisano, E. D.

M. Z. Kiss, D. E. Sayers, Z. Zhong, C. Parham, and E. D. Pisano, “Improved image contrast of calcifications in breast tissue specimens using diffraction enhanced imaging,” Phys. Med. Biol. 49, 3427–3439 (2004).
[Crossref] [PubMed]

Pogany, A.

T. E. Gureyev, Y. I. Nesterets, D. M. Paganin, A. Pogany, and S. W. Wilkins, “Linear algorithms for phase retrieval in the Fresnel region. 2. Partially coherent illumination,” Opt. Commun. 259, 569–580 (2006).
[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, 53–70 (2004).
[Crossref]

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

Pontoni, D.

F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. 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, 286–293 (2000).

F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, “Low-dose phase contrast x-ray medical imaging,” Phys. Med. Biol. 43, 2845–2852 (1998).
[Crossref] [PubMed]

Poropat, P.

F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. 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, 286–293 (2000).

F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, “Low-dose phase contrast x-ray medical imaging,” Phys. Med. Biol. 43, 2845–2852 (1998).
[Crossref] [PubMed]

Prasad, S. C.

A. Krol, A. Ikhlef, J.-C. Kieffer, D. Bassano, C. C. Chamberlain, Z. Jiang, H. Pepin, and S. C. Prasad, “Laser-based microfocused X-ray source for mammography: feasibility study,” Med. Phys. 24, 725–732 (1997).
[Crossref] [PubMed]

Prest, M.

F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. 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, 286–293 (2000).

F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, “Low-dose phase contrast x-ray medical imaging,” Phys. Med. Biol. 43, 2845–2852 (1998).
[Crossref] [PubMed]

Price, R. R.

E. F. Donnelly, R. R. Price, and D. R. Pickens, “Characterization of the phase-contrast radiography edge-enhancement effect in a cabinet x-ray system,” Med. Phys. 30, 2292–2296 (2003).
[Crossref] [PubMed]

Rashevsky, A.

F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. 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, 286–293 (2000).

F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, “Low-dose phase contrast x-ray medical imaging,” Phys. Med. Biol. 43, 2845–2852 (1998).
[Crossref] [PubMed]

Ratti, M.

F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. 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, 286–293 (2000).

Raven, C.

P. Spanne, C. Raven, I. Snigireva, and A. Snigirev, “In-line holography and phase-contrast microtomography with high energy x-rays,” Phys. Med. Biol. 44, 741–749 (1999).
[Crossref] [PubMed]

Rigon, L.

F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. 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, 286–293 (2000).

Sakashita, Y.

T. Tanaka, C. Honda, S. Matsuo, K. Noma, H. Ohara, N. Nitta, S. Ota, K. Tsuchiya, Y. Sakashita, A. Yamada, M. Yamasaki, A. Furukawa, M. Takahashi, and K. Murata, “The first trial of phase contrast imaging for digital full-field mammography using a practical molybdenum x-ray tube,” Invest. Radiol. 40, 385–396 (2005).
[Crossref] [PubMed]

Sayers, D.

E. Pisano, R. Johnston, D. Chapman, J. Geradts, M. Iacocca, C. Livasy, D. Washburn, D. Sayers, Z. Zhong, M. Kiss, and W. Thomlinson, “Human Breast Cancer Specimens: Diffraction-enhanced Imaging with Histologic Correlation-Improved Conspicuity of Lesion Detail Compared with Digital Radiography,” Radiology 214, 895–901 (2000).
[PubMed]

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmur, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42, 2015–2025 (1997).
[Crossref] [PubMed]

Sayers, D. E.

M. Z. Kiss, D. E. Sayers, Z. Zhong, C. Parham, and E. D. Pisano, “Improved image contrast of calcifications in breast tissue specimens using diffraction enhanced imaging,” Phys. Med. Biol. 49, 3427–3439 (2004).
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P. Cloetens, W. Ludwig, J. Baruchel, D. Dyck, J. Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. lett. 75, 2912–2914 (1999).
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Shi, D.

M. A. Anastasio, D. Shi, F. D. Carlo, and X. Pan, “Analytic image reconstruction in local phase-contrast tomography,” Phys. Med. Biol. 49, 121–144 (2004).
[Crossref] [PubMed]

Snigirev, A.

P. Spanne, C. Raven, I. Snigireva, and A. Snigirev, “In-line holography and phase-contrast microtomography with high energy x-rays,” Phys. Med. Biol. 44, 741–749 (1999).
[Crossref] [PubMed]

Snigireva, I.

P. Spanne, C. Raven, I. Snigireva, and A. Snigirev, “In-line holography and phase-contrast microtomography with high energy x-rays,” Phys. Med. Biol. 44, 741–749 (1999).
[Crossref] [PubMed]

Spanne, P.

P. Spanne, C. Raven, I. Snigireva, and A. Snigirev, “In-line holography and phase-contrast microtomography with high energy x-rays,” Phys. Med. Biol. 44, 741–749 (1999).
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W. Thomlinson, P. Suortti, and D. Chapman, “Recent advances in synchrotron radiation medical research,” Nucl. Instrum. Methods Phys. Res. A 543, 288–296 (2005).

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T. Tanaka, C. Honda, S. Matsuo, K. Noma, H. Ohara, N. Nitta, S. Ota, K. Tsuchiya, Y. Sakashita, A. Yamada, M. Yamasaki, A. Furukawa, M. Takahashi, and K. Murata, “The first trial of phase contrast imaging for digital full-field mammography using a practical molybdenum x-ray tube,” Invest. Radiol. 40, 385–396 (2005).
[Crossref] [PubMed]

Tanaka, T.

T. Tanaka, C. Honda, S. Matsuo, K. Noma, H. Ohara, N. Nitta, S. Ota, K. Tsuchiya, Y. Sakashita, A. Yamada, M. Yamasaki, A. Furukawa, M. Takahashi, and K. Murata, “The first trial of phase contrast imaging for digital full-field mammography using a practical molybdenum x-ray tube,” Invest. Radiol. 40, 385–396 (2005).
[Crossref] [PubMed]

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W. Thomlinson, P. Suortti, and D. Chapman, “Recent advances in synchrotron radiation medical research,” Nucl. Instrum. Methods Phys. Res. A 543, 288–296 (2005).

E. Pisano, R. Johnston, D. Chapman, J. Geradts, M. Iacocca, C. Livasy, D. Washburn, D. Sayers, Z. Zhong, M. Kiss, and W. Thomlinson, “Human Breast Cancer Specimens: Diffraction-enhanced Imaging with Histologic Correlation-Improved Conspicuity of Lesion Detail Compared with Digital Radiography,” Radiology 214, 895–901 (2000).
[PubMed]

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmur, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42, 2015–2025 (1997).
[Crossref] [PubMed]

Tromba, G.

F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. 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, 286–293 (2000).

F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, “Low-dose phase contrast x-ray medical imaging,” Phys. Med. Biol. 43, 2845–2852 (1998).
[Crossref] [PubMed]

Tsuchiya, K.

T. Tanaka, C. Honda, S. Matsuo, K. Noma, H. Ohara, N. Nitta, S. Ota, K. Tsuchiya, Y. Sakashita, A. Yamada, M. Yamasaki, A. Furukawa, M. Takahashi, and K. Murata, “The first trial of phase contrast imaging for digital full-field mammography using a practical molybdenum x-ray tube,” Invest. Radiol. 40, 385–396 (2005).
[Crossref] [PubMed]

Vacchi, A.

F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. 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, 286–293 (2000).

F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, “Low-dose phase contrast x-ray medical imaging,” Phys. Med. Biol. 43, 2845–2852 (1998).
[Crossref] [PubMed]

Vallazza, E.

F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. 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, 286–293 (2000).

F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, “Low-dose phase contrast x-ray medical imaging,” Phys. Med. Biol. 43, 2845–2852 (1998).
[Crossref] [PubMed]

Washburn, D.

E. Pisano, R. Johnston, D. Chapman, J. Geradts, M. Iacocca, C. Livasy, D. Washburn, D. Sayers, Z. Zhong, M. Kiss, and W. Thomlinson, “Human Breast Cancer Specimens: Diffraction-enhanced Imaging with Histologic Correlation-Improved Conspicuity of Lesion Detail Compared with Digital Radiography,” Radiology 214, 895–901 (2000).
[PubMed]

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmur, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42, 2015–2025 (1997).
[Crossref] [PubMed]

Waynant, R.

R. Waynant, “Toward practical coherent x-ray sources: Potential medical applications,” IEEE J. Quantum Electron. 6, 1465–1469 (2000).
[Crossref]

Weitkamp, T.

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

Wernick, M. N.

J. G. Brankov, M. N. Wernick, Y. Yang, J. Li, C. Muehleman, Z. Zhong, and M. A. Anastasio, “A computed tomography implementation of multiple-image radiography,” Med. Phys. 33, 278–289 (2006).
[Crossref] [PubMed]

C. Muehleman, J. Li, Z. Zhong, J. G. Brankov, and M. N. Wernick, “Multiple-image radiography for soft tissue of the foot and ankle,” J. Anat. 208, 115–124 (2006).
[Crossref] [PubMed]

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48, 3875–3895 (2003).
[Crossref]

Wilkins, S.

T. Davis, D. Gao, T. E. Gureyev, A. Stevenson, and S. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature (London) 373, 335–338 (1996).

Wilkins, S. W.

T. E. Gureyev, G. R. Myers, Y. I. Nesterets, D. Paganin, K. M. Pavlov, and S. W. Wilkins, “Stability and locality of amplitude and phase contrast tomographies,” Proc. SPIE 6318, 63180V (2006).

T. E. Gureyev, Y. I. Nesterets, D. M. Paganin, A. Pogany, and S. W. Wilkins, “Linear algorithms for phase retrieval in the Fresnel region. 2. Partially coherent illumination,” Opt. Commun. 259, 569–580 (2006).
[Crossref]

T. E. Gureyev, D. M. Paganin, G. R. Myers, Y. I. Nesterest, and S. W. Wilkins, “Phase-and-amplitude computer tomography,” Appl. Phys. Lett. 89, 034102 (2006).
[Crossref]

Y. I. Nesterets, T. E. Gureyev, K. M. Pavlov, D. M. Paganin, and S. W. Wilkins, “Combined analyser-based and propagation-based phase-contrast imaging of weak objects,” Opt. Commun. 259, 19–31 (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 37, 1262–1274 (2004).

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

Wilkins, S.W.

Y. I. Nesterets, T. E. Gureyev, and S.W. Wilkins, “Polychromaticity in the combined propagation-based/analyser-based phase-contrast imaging,” J. Phys. D 38, 4259–4271 (2005).

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

Wirjadi, O.

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48, 3875–3895 (2003).
[Crossref]

Wolf, E.

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

Wu, X.

X. Wu and H. Liu, “Clinical implementation of X-ray phase-contrast imaging: Theoretical foundations and design considerations,” Med. Phys. 30, 2169–2179 (2003).
[Crossref] [PubMed]

Yamada, A.

T. Tanaka, C. Honda, S. Matsuo, K. Noma, H. Ohara, N. Nitta, S. Ota, K. Tsuchiya, Y. Sakashita, A. Yamada, M. Yamasaki, A. Furukawa, M. Takahashi, and K. Murata, “The first trial of phase contrast imaging for digital full-field mammography using a practical molybdenum x-ray tube,” Invest. Radiol. 40, 385–396 (2005).
[Crossref] [PubMed]

Yamada, H.

H. Yamada, “Novel x-ray source based on a tabletop synchrotron and its unique features,” Nucl. Instrum. Methods Phys. Res. B 199, 509–516 (2003).

Yamasaki, M.

T. Tanaka, C. Honda, S. Matsuo, K. Noma, H. Ohara, N. Nitta, S. Ota, K. Tsuchiya, Y. Sakashita, A. Yamada, M. Yamasaki, A. Furukawa, M. Takahashi, and K. Murata, “The first trial of phase contrast imaging for digital full-field mammography using a practical molybdenum x-ray tube,” Invest. Radiol. 40, 385–396 (2005).
[Crossref] [PubMed]

Yang, Y.

J. G. Brankov, M. N. Wernick, Y. Yang, J. Li, C. Muehleman, Z. Zhong, and M. A. Anastasio, “A computed tomography implementation of multiple-image radiography,” Med. Phys. 33, 278–289 (2006).
[Crossref] [PubMed]

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48, 3875–3895 (2003).
[Crossref]

Zanconati, F.

F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. 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, 286–293 (2000).

F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, “Low-dose phase contrast x-ray medical imaging,” Phys. Med. Biol. 43, 2845–2852 (1998).
[Crossref] [PubMed]

Zhong, Z.

C. Muehleman, J. Li, Z. Zhong, J. G. Brankov, and M. N. Wernick, “Multiple-image radiography for soft tissue of the foot and ankle,” J. Anat. 208, 115–124 (2006).
[Crossref] [PubMed]

J. G. Brankov, M. N. Wernick, Y. Yang, J. Li, C. Muehleman, Z. Zhong, and M. A. Anastasio, “A computed tomography implementation of multiple-image radiography,” Med. Phys. 33, 278–289 (2006).
[Crossref] [PubMed]

M. Z. Kiss, D. E. Sayers, Z. Zhong, C. Parham, and E. D. Pisano, “Improved image contrast of calcifications in breast tissue specimens using diffraction enhanced imaging,” Phys. Med. Biol. 49, 3427–3439 (2004).
[Crossref] [PubMed]

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48, 3875–3895 (2003).
[Crossref]

E. Pisano, R. Johnston, D. Chapman, J. Geradts, M. Iacocca, C. Livasy, D. Washburn, D. Sayers, Z. Zhong, M. Kiss, and W. Thomlinson, “Human Breast Cancer Specimens: Diffraction-enhanced Imaging with Histologic Correlation-Improved Conspicuity of Lesion Detail Compared with Digital Radiography,” Radiology 214, 895–901 (2000).
[PubMed]

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmur, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42, 2015–2025 (1997).
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Appl. Phys. lett. (1)

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T. E. Gureyev, D. M. Paganin, G. R. Myers, Y. I. Nesterest, and S. W. Wilkins, “Phase-and-amplitude computer tomography,” Appl. Phys. Lett. 89, 034102 (2006).
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At. Data Nucl. Data Tables (1)

B.L. Henke, E.M. Gullikson, and J.C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50-30000 eV, Z=1-92,” At. Data Nucl. Data Tables 54, 181–342 (1993).
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IEEE J. Quantum Electron. (1)

R. Waynant, “Toward practical coherent x-ray sources: Potential medical applications,” IEEE J. Quantum Electron. 6, 1465–1469 (2000).
[Crossref]

Invest. Radiol. (1)

T. Tanaka, C. Honda, S. Matsuo, K. Noma, H. Ohara, N. Nitta, S. Ota, K. Tsuchiya, Y. Sakashita, A. Yamada, M. Yamasaki, A. Furukawa, M. Takahashi, and K. Murata, “The first trial of phase contrast imaging for digital full-field mammography using a practical molybdenum x-ray tube,” Invest. Radiol. 40, 385–396 (2005).
[Crossref] [PubMed]

J. Anat. (1)

C. Muehleman, J. Li, Z. Zhong, J. G. Brankov, and M. N. Wernick, “Multiple-image radiography for soft tissue of the foot and ankle,” J. Anat. 208, 115–124 (2006).
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D. Paganin, A. Barty, P. J. Mcmahon, and K. A. Nugent, “Quantitative phase-amplitude microscopy III. The effects of noise,” J. Microsc. 214, 51–61 (2003).
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Y. I. Nesterets, T. E. Gureyev, and S.W. Wilkins, “Polychromaticity in the combined propagation-based/analyser-based phase-contrast imaging,” J. Phys. D 38, 4259–4271 (2005).

K. M. Pavlov, T. E. Gureyev, D. Paganin, Y. Nesterets, M. J. Morgan, and R. A. Lewis, “Linear systems with slowly varying transfer functions and their application to X-ray phase-contrast imaging,” J. Phys. D 37, 2746–2750 (2004).

A. Bravin, “Exploiting the x-ray refraction contrast with an analyser: the state of the art,” J. Phys. D 36, A24–A29 (2003).

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 37, 1262–1274 (2004).

Med. Phys. (4)

J. G. Brankov, M. N. Wernick, Y. Yang, J. Li, C. Muehleman, Z. Zhong, and M. A. Anastasio, “A computed tomography implementation of multiple-image radiography,” Med. Phys. 33, 278–289 (2006).
[Crossref] [PubMed]

A. Krol, A. Ikhlef, J.-C. Kieffer, D. Bassano, C. C. Chamberlain, Z. Jiang, H. Pepin, and S. C. Prasad, “Laser-based microfocused X-ray source for mammography: feasibility study,” Med. Phys. 24, 725–732 (1997).
[Crossref] [PubMed]

X. Wu and H. Liu, “Clinical implementation of X-ray phase-contrast imaging: Theoretical foundations and design considerations,” Med. Phys. 30, 2169–2179 (2003).
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E. F. Donnelly, R. R. Price, and D. R. Pickens, “Characterization of the phase-contrast radiography edge-enhancement effect in a cabinet x-ray system,” Med. Phys. 30, 2292–2296 (2003).
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Nature (London) (1)

T. Davis, D. Gao, T. E. Gureyev, A. Stevenson, and S. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature (London) 373, 335–338 (1996).

Nature Phys. (1)

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

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

W. Thomlinson, P. Suortti, and D. Chapman, “Recent advances in synchrotron radiation medical research,” Nucl. Instrum. Methods Phys. Res. A 543, 288–296 (2005).

H. Yamada, “Novel x-ray source based on a tabletop synchrotron and its unique features,” Nucl. Instrum. Methods Phys. Res. B 199, 509–516 (2003).

Opt. Commun. (4)

Y. I. Nesterets, T. E. Gureyev, K. M. Pavlov, D. M. Paganin, and S. W. Wilkins, “Combined analyser-based and propagation-based phase-contrast imaging of weak objects,” Opt. Commun. 259, 19–31 (2006).
[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, 53–70 (2004).
[Crossref]

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

T. E. Gureyev, Y. I. Nesterets, D. M. Paganin, A. Pogany, and S. W. Wilkins, “Linear algorithms for phase retrieval in the Fresnel region. 2. Partially coherent illumination,” Opt. Commun. 259, 569–580 (2006).
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J.-P. Guigay, “Fourier transform analysis of Fresnel diffraction patterns and in-line holograms,” Optik 49, 121–125 (1977).

Phys. Med. Biol. (8)

M. A. Anastasio, D. Shi, F. D. Carlo, and X. Pan, “Analytic image reconstruction in local phase-contrast tomography,” Phys. Med. Biol. 49, 121–144 (2004).
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P. Spanne, C. Raven, I. Snigireva, and A. Snigirev, “In-line holography and phase-contrast microtomography with high energy x-rays,” Phys. Med. Biol. 44, 741–749 (1999).
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R. Lewis, “Medical phase contrast x-ray imaging: current status and future prospects,” Phys. Med. Biol. 49, 3573–3583 (2004).
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D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmur, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42, 2015–2025 (1997).
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C. J. Kotre and I. P. Birch, “Phase contrast enhancement of x-ray mammography: a design study,” Phys. Med. Biol. 44, 2853–2866 (1999).
[Crossref] [PubMed]

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48, 3875–3895 (2003).
[Crossref]

F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, “Low-dose phase contrast x-ray medical imaging,” Phys. Med. Biol. 43, 2845–2852 (1998).
[Crossref] [PubMed]

M. Z. Kiss, D. E. Sayers, Z. Zhong, C. Parham, and E. D. Pisano, “Improved image contrast of calcifications in breast tissue specimens using diffraction enhanced imaging,” Phys. Med. Biol. 49, 3427–3439 (2004).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

K. A. Nugent, T. E. Gureyev, D. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard x-rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).
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Proc. SPIE (1)

T. E. Gureyev, G. R. Myers, Y. I. Nesterets, D. Paganin, K. M. Pavlov, and S. W. Wilkins, “Stability and locality of amplitude and phase contrast tomographies,” Proc. SPIE 6318, 63180V (2006).

Radiology (2)

E. Pisano, R. Johnston, D. Chapman, J. Geradts, M. Iacocca, C. Livasy, D. Washburn, D. Sayers, Z. Zhong, M. Kiss, and W. Thomlinson, “Human Breast Cancer Specimens: Diffraction-enhanced Imaging with Histologic Correlation-Improved Conspicuity of Lesion Detail Compared with Digital Radiography,” Radiology 214, 895–901 (2000).
[PubMed]

F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. 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, 286–293 (2000).

Rev. Sci. Instrum. (1)

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

Other (5)

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

P. Cloetens, “Contribution to Phase Contrast Imaging, Reconstruction and Tomography with Hard Synchrotron Radiation: Principles, Implementation and Applications,” Ph.D. thesis, Vrije Universiteit Brussel (1999).

D. M. Paganin, Coherent X-Ray Optics (Oxford University Press, 2006).
[Crossref]

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company Publishers, 2004).

W. D. Stanley, G. R. Dougherty, and R. Dougherty, Digital Signal Processing (Reston Publishing Company, Inc., 1984).

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Figures (12)

Fig. 1.
Fig. 1.

A schematic of a generic X-ray phase-contrast imaging system.

Fig. 2.
Fig. 2.

The measurement geometry of propagation-based X-ray phase-contrast imaging employing multiple detector-planes.

Fig. 3.
Fig. 3.

Images of the true object properties (a) A(x,y) and (b) ϕ(x,y).

Fig. 4.
Fig. 4.

Images of theoretical and empirical estimates of Var{Ã(u, v)} measured in Geometry ‘A’ are displayed logarithmically in subfigures (a)–(b), respectively. The corresponding variance maps of ϕ̃(u, v) are contained in subfigures (c)–(d), respectively.

Fig. 5.
Fig. 5.

Variance profiles of images in Fig. 4. Subfigure (a) contains the theoretically and empirically determined variance profiles of Ã(u, v), which are depicted by solid and dashed curves, respectively. The corresponding variance profiles of ϕ̃(u, v) are shown in subfigure (b).

Fig. 6.
Fig. 6.

Images of theoretical and empirical estimates of Var{Ã(u, v)} measured in Geometry ‘B’ are displayed logarithmically in subfigures (a)–(b), respectively. The corresponding variance maps of ϕ̃(u, v) are contained in subfigures (c)–(d), respectively.

Fig. 7.
Fig. 7.

Variance profiles of images in Fig. 6. Subfigure (a) contains the theoretically and empirically determined variance profiles of Ã(u, v), which are depicted by solid and dashed curves, respectively. The corresponding variance profiles of ϕ̃(u, v) are shown in subfigure (b).

Fig. 8.
Fig. 8.

Estimates of A(x, y) reconstructed from noisy intensity data measured in Geometry ‘A’ by use of detector-planes (a)(1,2), (b)(1,3), (c)(2,3), and (d) an optimally-weighted combination of all three detector-planes. The corresponding estimates of ϕ(x, y) are shown in subfigures (e)–(h).

Fig. 9.
Fig. 9.

Empirical variance profiles of Ã(u, v) and ϕ̃(u, v) measured in Geometry ‘A’ are displayed in subfigures (a)–(b), respectively. Each subfigure contains profiles corresponding to the Fourier variances estimated by use of detector-planes (1,2) (dashed curve), detector-planes (1,3) (dashdotted curve), detector-planes (2,3) (dotted curve), and the optimal one (solid curve). Subfigures (c) and (d) display empirical variance profiles of the corresponding images in the spatial domain.

Fig. 10.
Fig. 10.

Estimates of A(x, y) reconstructed from noisy intensity data measured in Geometry ‘B’ by use of detector-planes (a)(1,2), (b)(1,3), (c)(2,3), and (d) an optimally-weighted combination of all three detector-planes. The corresponding estimates of ϕ(x, y) are shown in subfigures (e)–(h).

Fig. 11.
Fig. 11.

Empirical variance profiles of Ã(u, v) and ϕ̃(u, v) measured in Geometry ‘B’ are displayed in subfigures (a)–(b), respectively. Each subfigure contains profiles corresponding to the Fourier variances estimated by use of detector-planes (1,2) (dashed curve), detectorplanes (1,3) (dashdotted curve), detector-planes (2,3) (dotted curve), and the optimal one (solid curve). Subfigures (c) and (d) display empirical variance profiles of the corresponding images in the spatial domain.

Fig. 12.
Fig. 12.

The optimally determined estimates of A(x, y) are reconstructed from noisy intensity data measured in Geometry ‘A’ with detector position uncertainty of (a) error level 1, (b) error level 2, and (c) error level 3. The corresponding estimates of ϕ(x, y) are contained in subfigures (d)–(f).

Tables (1)

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Table 1. Error levels in the detector positions in Geometry ‘A’.

Equations (97)

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n ( r ) 1 δ ( r ) + j β ( r ) ,
μ ( r ) = 2 k β ( r ) ,
U o ( x , y ) = T ( x , y ) U i
T ( x , y ) = M ( x , y ) exp [ j ϕ ( x , y ) ] .
A ( x , y ) = k d z β ( r )
ϕ ( x , y ) = k d z δ ( r )
U m ( x , y ) = G m ( x , y ) * U o ( x , y ) ,
K m ( x , y ) 1 I m ( x , y ) I i ,
K ˜ m ( u , v ) = d x d y K m ( x , y ) exp [ j 2 π ( ux + vy ) ] .
K ˜ m ( u , v ) = 2 G ˜ m a ( u , v ) A ˜ ( u , v ) + 2 G ˜ m p ( u , v ) ϕ ˜ ( u , v )
G ˜ m a ( u , v ) = 1 2 [ G ˜ m ( u , v ) + G ˜ m * ( u , v ) ] ,
G ˜ m p ( u , v ) = 1 2 j [ G ˜ m ( u , v ) G ˜ m * ( u , v ) ] .
A ˜ ( u , v ) = G ˜ n p ( u , v ) K ˜ m ( u , v ) G ˜ m p ( u , v ) K ˜ n ( u , v ) 2 [ G ˜ m a ( u , v ) G ˜ n p ( u , v ) G ˜ n a ( u , v ) G ˜ m p ( u , v ) ]
ϕ ˜ ( u , v ) = G ˜ n a ( u , v ) K ˜ m ( u , v ) + G ˜ m a ( u , v ) K ˜ n ( u , v ) 2 [ G ˜ m a ( u , v ) G ˜ n p ( u , v ) G ˜ n a ( u , v ) G ˜ m p ( u , v ) ] .
G ˜ m a ( u , v ) G ˜ n p ( u , v ) G ˜ n a ( u , v ) G ˜ m p ( u , v ) = 0 .
ϕ ˜ m , n ( u , v ) = α l , m ϕ ( u , v ) ϕ ˜ l , m ( u , v ) + α l , n ϕ ( u , v ) ϕ ˜ l , n ( u , v )
A ˜ m , n ( u , v ) = α l , m a ( u , v ) A ˜ l , m ( u , v ) + α l , n a ( u , v ) A ˜ l , n ( u , v )
α l , m ϕ ( u , v ) = G ˜ n a ( u , v ) [ G ˜ l a ( u , v ) G ˜ m p ( u , v ) G ˜ m a ( u , v ) G ˜ l p ( u , v ) ] G ˜ l a ( u , v ) [ G ˜ m a ( u , v ) G ˜ n p ( u , v ) G ˜ n a ( u , v ) G ˜ m p ( u , v ) ]
α l , n ϕ ( u , v ) = G ˜ m a ( u , v ) [ G ˜ l a ( u , v ) G ˜ n p ( u , v ) G ˜ n a ( u , v ) G ˜ l p ( u , v ) ] G ˜ l a ( u , v ) [ G ˜ m a ( u , v ) G ˜ n p ( u , v ) G ˜ n a ( u , v ) G ˜ m p ( u , v ) ] ,
α l , m a ( u , v ) = G ˜ n p ( u , v ) [ G ˜ l a ( u , v ) G ˜ m p ( u , v ) G ˜ m a ( u , v ) G ˜ l p ( u , v ) ] G ˜ l p ( u , v ) [ G ˜ m a ( u , v ) G ˜ n p ( u , v ) G ˜ n a ( u , v ) G ˜ m p ( u , v ) ] ,
α l , n a ( u , v ) = G ˜ m p ( u , v ) [ G ˜ l a ( u , v ) G ˜ n p ( u , v ) G ˜ n a ( u , v ) G ˜ l p ( u , v ) ] G ˜ l p ( u , v ) [ G ˜ m a ( u , v ) G ˜ n p ( u , v ) G ˜ n a ( u , v ) G ˜ m p ( u , v ) ] ,
α l , m ϕ ( u , v ) + α l , n ϕ ( u , v ) 1
α l , m a ( u , v ) + α l , n a ( u , v ) 1 .
ϕ ˜ ( u , v ) = ω 1 , 2 ϕ ( u , v ) ϕ ˜ 1 , 2 ( u , v ) + ω 1 , 3 ϕ ( u , v ) ϕ ˜ 1 , 3 ( u , v )
A ˜ ( u , v ) = ω 1 , 2 a ( u , v ) A ˜ 1 , 2 ( u , v ) + ω 1 , 3 a ( u , v ) A ˜ 1 , 3 ( u , v ) ,
ω 1 , 2 ϕ + ω 1 , 3 ϕ = 1
ω 1 , 2 a + ω 1 , 3 a = 1 .
σ m , n 2 ( u , v ) Var { ϕ ˜ m , n ( u , v ) }
ρ k , l ; m , n ( r ) ( u , v ) + j ρ k , l ; m , n ( i ) ( u , v ) Cov { ϕ ˜ k , l ( u , v ) , ϕ ˜ m , n ( u , v ) }
R m , n ( u , v ) + j I m , n ( u , v ) ω m , n ϕ ( u , v ) ,
Var { ϕ ˜ ( u , v ) } = ω 1 , 2 ϕ ( u , v ) 2 σ 1 , 2 2 + ω 1 , 3 ϕ ( u , v ) 2 σ 1 , 3 2
+ 2 Re [ ω 1 , 2 ϕ ( u , v ) [ ω 1 , 3 ϕ ( u , v ) ] * Cov { ϕ ˜ 1 , 2 ( u , v ) , ϕ ˜ 1 , 3 ( u , v ) } ]
Var { ϕ ˜ } R 1 , 2 R 1 , 2 ( op ) = 0
Var { ϕ ˜ } I 1 , 2 I 1 , 2 ( op ) = 0 ,
R 1 , 2 ( op ) ( u , v ) = σ 1 , 3 2 ρ 1 , 2 ; 1 , 3 ( r ) σ 1 , 2 2 + σ 1 , 3 2 2 ρ 1 , 2 ; 1 , 3 ( r )
I 1 , 2 ( op ) ( u , v ) = ρ 1 , 2 ; 1 , 3 ( i ) σ 1 , 2 2 + σ 1 , 3 2 2 ρ 1 , 2 ; 1 , 3 ( r ) .
G m ( x , y ) = exp [ j kz m ] j λ z m exp [ j π x 2 + y 2 λ z m ] ,
G ˜ m ( u , v ) = exp [ j kz m j π λ z m ( u 2 + v 2 ) ] .
ϕ ˜ m , n ( u , v ) = cos ( π λ z n f 2 ) K ˜ m ( u , v ) + cos ( π λ z m f 2 ) K ˜ n ( u , v ) D m , n
A ˜ m , n ( u , v ) = sin ( π λ z m f 2 ) K ˜ n ( u , v ) + sin ( π λ z n f 2 ) K ˜ m ( u , v ) D m , n ,
D m , n ( u , v ) 2 sin ( π λ f 2 ( z m z n ) ) .
u 2 + v 2 = l λ ( z m z n ) ,
u M 2 + v M 2 1 λ ( z m z n ) .
Var { ϕ ˜ m , n ( u , v ) } = cos 2 ( π λ z n f 2 ) Var { I ˜ m ( u , v ) } + cos 2 ( π λ z m f 2 ) Var { I ˜ n ( u , v ) } D m , n 2
Var { A ˜ m , n ( u , v ) } = sin 2 ( π λ z n f 2 ) Var { I ˜ m ( u , v ) } + sin 2 ( π λ z m f 2 ) Var { I ˜ n ( u , v ) } D m , n 2
Cov { ϕ ˜ 1 , 2 ( u , v ) , ϕ ˜ 1 , 3 ( u , v ) } = cos ( π λ z 2 f 2 ) cos ( π λ z 3 f 2 ) Var { I ˜ 1 ( u , v ) } D 1 , 2 D 1 , 3
Cov { A ˜ 1 , 2 ( u , v ) , A ˜ 1 , 3 ( u , v ) } = sin ( π λ z 2 f 2 ) sin ( π λ z 3 f 2 ) Var { I ˜ 1 ( u , v ) } D 1 , 2 D 1 , 3
Var { ϕ ˜ m , n ( u , v ) } 1 D m , n 2 ( u , v )
Var { A ˜ m , n ( u , v ) } 1 D m , n 2 ( u , v ) .
ω 1 , 2 heur ( u , v ) = D 1 , 2 2 + α 1 , 2 ϕ D 2 , 3 2 D 1 , 2 2 + D 1 , 3 2 + D 2 , 3 2
ω 1 , 3 heur ( u , v ) = D 1 , 3 2 + α 1 , 3 ϕ D 2 , 3 2 D 1 , 2 2 + D 1 , 3 2 + D 2 , 3 2 ,
I m [ r , s ] = I m ( x , y ) x = r Δ x , y = s Δ y ,
I m [ r , s ] = I m 0 [ r , s ] + n m [ r , s ] ,
Var { n m [ r , s ] } = ( I m 0 [ r , s ] ) 2 σ 2 ( z m ) ,
Cov { n m [ r , s ] , n m [ r , s ] } = Var { n m [ r , s ] } δ rr δ ss δ mm ,
I ˜ m [ p , q ] = I m 0 ˜ [ p , q ] + n ˜ m [ p , q ]
I ˜ m [ p , q ] = r = 0 N 1 s = 0 N 1 I m [ r , s ] exp [ j 2 π N ( pr + qs ) ]
I m 0 ˜ [ p , q ] = r = 0 N 1 s = 0 N 1 I m 0 [ r , s ] exp [ j 2 π N ( pr + qs ) ]
n ˜ m [ p , q ] = r = 0 N 1 s = 0 N 1 n m [ r , s ] exp [ j 2 π N ( pr + qs ) ] ,
Var { n ˜ m [ p , q ] } = r , r = 0 N 1 s , s = 0 N 1 exp [ j 2 π N ( p ( r r ) + q ( s s ) ) ] Cov { n m [ r , s ] , n m [ r , s ] }
= r = 0 N 1 s = 0 N 1 E { ( n m [ r , s ] ) 2 } = r = 0 N 1 s = 0 N 1 ( I m 0 [ r , s ] ) 2 σ 2 ( z m ) ,
I ˜ m ( u , v ) u = p Δ u , v = q Δ v L 2 N 2 I ˜ m [ p , q ] ,
Var { I ˜ m ( u , v ) } u = p Δ u , v = q Δ v L 4 N 4 Var { I ˜ m [ p , q ] } = L 4 N 4 σ 2 ( z m ) r = 0 N 1 s = 0 N 1 ( I m 0 [ r , s ] ) 2 .
Var { ϕ ˜ m , n ( u , v ) } u = p Δ u , v = q Δ v
L 4 N 4 cos 2 ( π λ z n f 2 ) r = 0 N 1 s = 0 N 1 ( I 0 [ r , s ; z m ] ) 2 σ 2 ( z m ) + cos 2 ( π λ z m f 2 ) r = 0 N 1 s = 0 N 1 ( I 0 [ r , s ; z n ] ) 2 σ 2 ( z n ) D m , n 2
Var { A ˜ m , n ( u , v ) } u = p Δ u , v = q Δ v
L 4 N 4 sin 2 ( π λ z n f 2 ) r = 0 N 1 s = 0 N 1 ( I 0 [ r , s ; z m ] ) 2 σ 2 ( z m ) + sin 2 ( π λ z m f 2 ) r = 0 N 1 s = 0 N 1 ( I 0 [ r , s ; z n ] ) 2 σ 2 ( z n ) D m , n 2
Cov { ϕ ˜ 1 , 2 , ϕ ˜ 1 , 3 } L 4 N 4 cos ( π λ z 2 f 2 ) cos ( π λ z 3 f 2 ) r = 0 N 1 s = 0 N 1 ( I 0 [ r , s ; z 1 ] ) 2 σ 2 ( z 1 ) D 1 , 2 D 1 , 3 u = p Δ u , v = q Δ v
Cov { A ˜ 1 , 2 , A ˜ 1 , 3 } L 4 N 4 sin ( π λ z 2 f 2 ) sin ( π λ z 3 f 2 ) r = 0 N 1 s = 0 N 1 ( I 0 [ r , s ; z 1 ] ) 2 σ 2 ( z 1 ) D 1 , 2 D 1 , 3 u = p Δ u , v = q Δ v .
ω 1 , 2 ϕ ( u , v ) = K 1 ϕ K 2 ϕ K 1 ϕ + K 3 ϕ 2 K 2 ϕ
ω 1 , 2 ϕ ( u , v ) = K 1 a K 2 a K 1 a + K 3 a 2 K 2 a
K 1 ϕ = D 1 , 2 2 [ cos 2 ( π λ z 3 f 2 ) r = 0 N 1 s = 0 N 1 ( I 0 [ r , s ; z 1 ] ) 2 σ 1 2 + cos 2 ( π λ z 1 f 2 ) r = 0 N 1 s = 0 N 1 ( I 0 [ r , s ; z 3 ] ) 2 σ 3 2 ]
K 2 ϕ = D 1 , 2 D 1 , 3 [ cos ( π λ z 2 f 2 ) cos ( π λ z 3 f 2 ) r = 0 N 1 s = 0 N 1 ( I 0 [ r , s ; z 1 ] ) 2 σ 1 2 ]
K 3 ϕ = D 1 , 3 2 [ cos 2 ( π λ z 2 f 2 ) r = 0 N 1 s = 0 N 1 ( I 0 [ r , s ; z 1 ] ) 2 σ 1 2 + cos 2 ( π λ z 1 f 2 ) r = 0 N 1 s = 0 N 1 ( I 0 [ r , s ; z 2 ] ) 2 σ 2 2 ] ,
K 1 a = D 1 , 2 2 [ sin 2 ( π λ z 3 f 2 ) r = 0 N 1 s = 0 N 1 ( I 0 [ r , s ; z 1 ] ) 2 σ 1 2 + sin 2 ( π λ z 1 f 2 ) r = 0 N 1 s = 0 N 1 ( I 0 [ r , s ; z 3 ] ) 2 σ 3 2 ]
K 2 a = D 1 , 2 D 1 , 3 [ sin ( π λ z 2 f 2 ) sin ( π λ z 3 f 2 ) r = 0 N 1 s = 0 N 1 ( I 0 [ r , s ; z 1 ] ) 2 σ 1 2 ]
K 3 a = D 1 , 3 2 [ sin 2 ( π λ z 2 f 2 ) r = 0 N 1 s = 0 N 1 ( I 0 [ r , s ; z 1 ] ) 2 σ 1 2 + sin 2 ( π λ z 1 f 2 ) r = 0 N 1 s = 0 N 1 ( I 0 [ r , s ; z 2 ] ) 2 σ 2 2 ] ,
ω 1 , 2 ϕ ( u , v )
D 1 , 2 2 [ cos 2 ( π λ z 3 f 2 ) σ 1 2 + cos 2 ( π λ z 1 f 2 ) σ 3 2 ] D 1 , 2 D 1 , 3 [ cos ( π λ z 2 f 2 ) cos ( π λ z 3 f 2 ) σ 1 2 ] m , n = 2 m n 3 D 1 , m 2 [ cos 2 ( π λ z n f 2 ) σ 1 2 + cos 2 ( π λ z 1 f 2 ) σ n 2 ] 2 D 1 D 1 , 3 [ cos ( π λ z 2 f 2 ) cos ( π λ z 3 f 2 ) σ 1 2 ] .
ϕ ˜ ( u , v ) = m = 1 M 1 n = m + 1 M ω ̂ m , n ϕ ( u , v ) ϕ ̂ m , n ( u , v ) ,
m = 1 M 1 n = m + 1 M ω ̂ m , n ϕ ( u , v ) = 1 .
ϕ ˜ ( u , v ) = m = 2 M ω 1 , m ϕ ( u , v ) ϕ ˜ 1 , m ( u , v ) .
Var { ϕ ˜ ( u , v ) } = l = 2 M ω 1 , l ϕ ( u , v ) 2 Var { ϕ ˜ 1 , l ( u , v ) }
+ 2 Re [ m = 2 M 1 n = m + 1 M ω 1 , m ϕ ( u , v ) ω 1 , n ϕ * ( u , v ) Cov { ϕ ˜ 1 , m ( u , v ) ϕ ˜ 1 , n ( u , v ) } ] ,
σ 1 , m 2 ( u , v ) Var { ϕ ˜ 1 , m [ u , v ] } ,
ρ 1 , m ; 1 , n ( r ) ( u , v ) + j ρ 1 , m ; 1 , n ( i ) ( u , v ) Cov { ϕ ˜ 1 , m [ u , v ] , ϕ ˜ 1 , n [ u , v ] } ,
R 1 , m ( u , v ) + j I 1 , m ( u , v ) ω 1 , m ϕ ( u , v ) .
Var { ϕ ˜ } = l = 2 M ( R 1 , l 2 + I 1 , l 2 ) σ 1 , l 2
+ 2 { m = 2 M 1 n = m + 1 M [ ρ 1 , m ; 1 , n ( r ) ( R 1 , m R 1 , n + I 1 , m I 1 , n ) ρ 1 , m ; 1 , n ( i ) ( R 1 , n I 1 , m R 1 , m I 1 , n ) ] } .
Var { ϕ ˜ } R 1 , m R 1 , m ( op ) = 0
Var { ϕ ˜ } I 1 , m I 1 , m ( op ) = 0 ,
Hx = b
H = ( h 11 h 12 h 1 , 2 M 4 h 2 M 4 , 1 h 2 M 4 , 2 h 2 M 4 , 2 M 4 ) ,
x = ( R 1 , 2 ( op ) I 1 , 2 ( op ) R 1 , 3 ( op ) I 1 , 3 ( op ) R 1 , M 1 ( op ) I 1 , M 1 ( op ) ) T ,
b = ( b 1 b 2 b 2 M 4 ) T ,
x m ( u , v ) = det ( H m ) det ( H ) m = 1 , 2 , 3 , , 2 M 4
ω 1 , m heur ( u , v ) = D 1 , m 2 + α 1 , m n = 2 n m M D m , n 2 l = 1 M 1 m = l + 1 M D l , m 2

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