Abstract

An X-ray grating interferometer (GI) suitable for clinical mammography must comply with quite strict dose, scanning time and geometry limitations, while being able to detect tumors, microcalcifications and other abnormalities. Such a design task is not straightforward, since obtaining optimal phase-contrast and dark-field signals with clinically compatible doses and geometrical constraints is remarkably challenging. In this work, we present a wave propagation based optimization that uses the phase and dark-field sensitivities as figures of merit. This method was used to calculate the optimal interferometer designs for a commercial mammography setup. Its accuracy was validated by measuring the visibility of polycarbonate samples of different thicknesses on a Talbot-Lau interferometer installed on this device and considering some of the most common grating imperfections to be able to reproduce the experimental values. The optimization method outcomes indicate that small grating pitches are required to boost sensitivity in such a constrained setup and that there is a different optimal scenario for each signal type.

© 2017 Optical Society of America

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    [Crossref] [PubMed]

2016 (1)

2015 (3)

Z. Wang, N. Hauser, R. Kubik-Huch, F. D’Isidoro, and M. Stampanoni, “Quantitative volumetric breast density estimation using phase contrast mammography,” Phys. Med. Biol. 60, 4123–4135 (2015).
[Crossref] [PubMed]

K. Scherer, K. Willer, L. Gromann, L. Birnbacher, E. Braig, S. Grandl, A. SztrÃşkay-Gaul, J. Herzen, D. Mayr, K. Hellerhoff, and F. Pfeiffer, “Toward clinically compatible phase-contrast mammography,” PLoS ONE 10(6), e0130776 (2015).
[Crossref] [PubMed]

T. Koehler, H. Daerr, G. Martens, N. Kuhn, S. Loescher, U. van Stevendaal, and E. Roessl, “Slit-scanning differential x-ray phase-contrast mammography: Proof-of-concept experimental studies,” Med. Phys. 42(4), 1959–1965 (2015).
[Crossref] [PubMed]

2014 (7)

E. Roessl, H. Daerr, T. Koehler, G. Martens, and U. van Stevendaal, “Clinical boundary conditions for grating-based differential phase-contrast mammography,” Philos. Trans. R. Soc. London, Ser. A 372(2010), 20130033 (2014).
[Crossref]

K. Scherer, L. Birnbacher, M. Chabior, J. Herzen, D. Mayr, S. Grandl, A. Sztrokay-Gaul, K. Hellerhoff, F. Bamberg, and F. Pfeiffer, “Bi-Directional X-Ray Phase-Contrast Mammography,” PLoS ONE 9(5), e93502 (2014).
[Crossref] [PubMed]

S. D. Auweter, J. Herzen, M. Willner, S. Grandl, K. Scherer, F. Bamberg, M.F. Reiser, F. Pfeiffer, and K. Hellerhoff, “X-ray phase-contrast imaging of the breast-advances towards clinical implementation,” Br. J. Radiol. 87, 20130606 (2014).
[Crossref]

M. Strobl, “General solution for quantitative dark-field contrast imaging with grating interferometers,” Sci. Rep. 4, 72431 (2014).
[Crossref]

Z. Wang, N. Hauser, G. Singer, M. Trippel, R. Kubik-Huch, C. Schneider, and M. Stampanoni, “Non-invasive classification of microcalcifications with phase-contrast X-ray mammography,” Nat. Commun. 5, 1–9 (2014).

C. Arboleda, Z. Wang Z, and M. Stampanoni, “Tilted-grating approach for scanning-mode X-ray phase contrast imaging,” Opt. Express 22(13), 15447–15458 (2014).
[Crossref] [PubMed]

T. Thüring and M. Stampanoni, “Performance and optimization of X-ray grating interferometry,” Phil. Trans. Royal Soc. A 372(2010), 20130027 (2014).
[Crossref]

2013 (4)

N. Hauser, Z. Wang, R.A. Kubik-Huch, M. Trippel, G. Singer, M.K. Hohl, E. Roessl, T. Koehler, U. van Stevendaal, N. Wieberneit, and M. Stampanoni, “A Study on Mastectomy Samples to Evaluate Breast Imaging Quality and Potential Clinical Relevance of Differential Phase Contrast Mammography,” Invest. Radiol. 49(3), 131–137 (2013).
[Crossref] [PubMed]

G. Anton, F. Bayer, M.W. Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, T. Michel, G. Pelzer, M. Radicke, C. Rauh, J. Rieger, A. Ritter, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and L. Wucherer, “Grating-based dark-field imaging of human breast tissue,” Zeitschrift für Medizinische Physik 23(3), 228–235 (2013).
[Crossref]

A. Olivo, S. Gkoumas, M. Endrizzi, C. K. Hagen, M. B. Szafraniec, and P. C. Diemoz, “Low-dose phase contrast mammography with conventional x-ray sources,” Med. Phys. 40(9), 090701 (2013).
[Crossref] [PubMed]

T. Michel, J. Rieger, G. Anton, F. Bayer, M.W Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D.L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58(8), 2713–2732 (2013).
[Crossref] [PubMed]

2012 (1)

H. Ding and S. Molloi, “Quantification of breast density with spectral mammography based on a scanned multi-slit photon-counting detector: a feasibility study,” Phys. Med. Biol. 57, 4719–4738 (2012).
[Crossref] [PubMed]

2011 (3)

2010 (3)

P.R. Munro, K. Ignatyev, R.D. Speller, and A. Olivo, “Design of a novel phase contrast x-ray imaging system for mammography,” Phys. Med. Biol. 55, 4169–4185 (2010).
[Crossref] [PubMed]

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based X-ray differential phase contrast imaging,” Rev. Sci. Instrum. 81(7), 0737091–4 (2010).
[Crossref]

W. Yashiro, Y. Terui, K. Kawabata, and A. Momose, “On the origin of visibility contrast in x-ray Talbot interferometry,” Opt. Express 18(16), 16890–16901(2010).
[Crossref] [PubMed]

2009 (2)

Z. Wang, K. Kang, Z. Huang, and Z. Chen, “Quantitative grating-based x-ray dark-field computed tomography,” Appl. Phys. Lett. 95(9), 0941051 (2009).

T. Donath, M. Chabior, F. Pfeiffer, O. Bunk, E. Reznikova, J. Mohr, E. Hempel, S. Popescu, M. Hoheisel, M. Schuster, J. Baumann, and C. David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106, 0547031 (2009).
[Crossref]

2008 (1)

M. Fernandez, H. Suhonen, J. KeyrilÃd’inen, A. Bravin, S. Fiedler, M.L. Karjalainen-Lindsberg, M. Leidenius, K. von Smitten, and P. Suortti, “USAXS and SAXS from cancer-bearing breast tissue samples,” Eur. J. Radiology 68S, S89 (2008).

2007 (2)

M. Aslund, B. Cederström, M. Lundqvist, and M. Danielsson, “Physical characterization of a scanning photon counting digital mammography system based on Si-strip detectors,” Med. Phys. 34(6), 1918–1925 (2007).
[Crossref] [PubMed]

C. Kottler, F. Pfeiffer, O. Bunk, C. Grunzweig, and C. David, “Grating interferometer based scanning setup for hard x-ray phase contrast imaging,” Rev. Sci. Instrum. 78, 043710 (2007)
[Crossref] [PubMed]

2006 (1)

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys. 2(4), 258–261 (2006).
[Crossref]

2005 (2)

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

F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J. van der Veen, I. Vartanyants, and I. Robinson, “Shearing interferometer for quantifying the coherence of hard x-ray beams,” Phys. Rev. Lett. 94(16), 1648011–4 (2005).
[Crossref]

1997 (1)

J. Boone, T. Fewell, and R. Jennings, “Molybdenum, rhodium, and tungsten anode spectral models using interpolating polynomials with application to mammography,” Med. Phys. 24(12), 1863–1874 (1997).
[Crossref]

Anton, G.

G. Anton, F. Bayer, M.W. Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, T. Michel, G. Pelzer, M. Radicke, C. Rauh, J. Rieger, A. Ritter, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and L. Wucherer, “Grating-based dark-field imaging of human breast tissue,” Zeitschrift für Medizinische Physik 23(3), 228–235 (2013).
[Crossref]

T. Michel, J. Rieger, G. Anton, F. Bayer, M.W Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D.L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58(8), 2713–2732 (2013).
[Crossref] [PubMed]

Arboleda, C.

Aslund, M.

M. Aslund, B. Cederström, M. Lundqvist, and M. Danielsson, “Physical characterization of a scanning photon counting digital mammography system based on Si-strip detectors,” Med. Phys. 34(6), 1918–1925 (2007).
[Crossref] [PubMed]

Atwood, D.

D. Atwood, Soft X-Rays and Extreme Ultraviolet Radiation, Principles and Applications (Cambridge University, 2007).

Auweter, S. D.

S. D. Auweter, J. Herzen, M. Willner, S. Grandl, K. Scherer, F. Bamberg, M.F. Reiser, F. Pfeiffer, and K. Hellerhoff, “X-ray phase-contrast imaging of the breast-advances towards clinical implementation,” Br. J. Radiol. 87, 20130606 (2014).
[Crossref]

Auxier, J.

Bamberg, F.

S. D. Auweter, J. Herzen, M. Willner, S. Grandl, K. Scherer, F. Bamberg, M.F. Reiser, F. Pfeiffer, and K. Hellerhoff, “X-ray phase-contrast imaging of the breast-advances towards clinical implementation,” Br. J. Radiol. 87, 20130606 (2014).
[Crossref]

K. Scherer, L. Birnbacher, M. Chabior, J. Herzen, D. Mayr, S. Grandl, A. Sztrokay-Gaul, K. Hellerhoff, F. Bamberg, and F. Pfeiffer, “Bi-Directional X-Ray Phase-Contrast Mammography,” PLoS ONE 9(5), e93502 (2014).
[Crossref] [PubMed]

Baumann, J.

T. Donath, M. Chabior, F. Pfeiffer, O. Bunk, E. Reznikova, J. Mohr, E. Hempel, S. Popescu, M. Hoheisel, M. Schuster, J. Baumann, and C. David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106, 0547031 (2009).
[Crossref]

Bayer, F.

G. Anton, F. Bayer, M.W. Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, T. Michel, G. Pelzer, M. Radicke, C. Rauh, J. Rieger, A. Ritter, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and L. Wucherer, “Grating-based dark-field imaging of human breast tissue,” Zeitschrift für Medizinische Physik 23(3), 228–235 (2013).
[Crossref]

T. Michel, J. Rieger, G. Anton, F. Bayer, M.W Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D.L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58(8), 2713–2732 (2013).
[Crossref] [PubMed]

Beckmann, M.W

T. Michel, J. Rieger, G. Anton, F. Bayer, M.W Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D.L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58(8), 2713–2732 (2013).
[Crossref] [PubMed]

Beckmann, M.W.

G. Anton, F. Bayer, M.W. Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, T. Michel, G. Pelzer, M. Radicke, C. Rauh, J. Rieger, A. Ritter, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and L. Wucherer, “Grating-based dark-field imaging of human breast tissue,” Zeitschrift für Medizinische Physik 23(3), 228–235 (2013).
[Crossref]

Bennett, E.C.

Beque, D.

Berger, M. J.

M. J. Berger, J. H. Hubbell, S. M. Seltzer, J. Chang, J. S. Coursey, R. Sukumar, D. S. Zucker, and K. Olsen, XCOM: Photon Cross Section Database (version 1.5) (National Institute of Standards and Technology, 1990).

Birnbacher, L.

L. Gromann, D. Beque, K. Scherer, K. Willer, L. Birnbacher, M. Willner, J. Herzen, S. Grandl, K. Hellerhoff, J. Sperl, F. Pfeiffer, and C. Cozzini, “Low-dose, phase-contrast mammography with high signal-to-noise ratio,” Biomed. Opt. Express 7, 381–391 (2016).
[Crossref] [PubMed]

K. Scherer, K. Willer, L. Gromann, L. Birnbacher, E. Braig, S. Grandl, A. SztrÃşkay-Gaul, J. Herzen, D. Mayr, K. Hellerhoff, and F. Pfeiffer, “Toward clinically compatible phase-contrast mammography,” PLoS ONE 10(6), e0130776 (2015).
[Crossref] [PubMed]

K. Scherer, L. Birnbacher, M. Chabior, J. Herzen, D. Mayr, S. Grandl, A. Sztrokay-Gaul, K. Hellerhoff, F. Bamberg, and F. Pfeiffer, “Bi-Directional X-Ray Phase-Contrast Mammography,” PLoS ONE 9(5), e93502 (2014).
[Crossref] [PubMed]

Boone, J.

J. Boone, T. Fewell, and R. Jennings, “Molybdenum, rhodium, and tungsten anode spectral models using interpolating polynomials with application to mammography,” Med. Phys. 24(12), 1863–1874 (1997).
[Crossref]

Braig, E.

K. Scherer, K. Willer, L. Gromann, L. Birnbacher, E. Braig, S. Grandl, A. SztrÃşkay-Gaul, J. Herzen, D. Mayr, K. Hellerhoff, and F. Pfeiffer, “Toward clinically compatible phase-contrast mammography,” PLoS ONE 10(6), e0130776 (2015).
[Crossref] [PubMed]

Bravin, A.

M. Fernandez, H. Suhonen, J. KeyrilÃd’inen, A. Bravin, S. Fiedler, M.L. Karjalainen-Lindsberg, M. Leidenius, K. von Smitten, and P. Suortti, “USAXS and SAXS from cancer-bearing breast tissue samples,” Eur. J. Radiology 68S, S89 (2008).

Broeders, M.

N. Perry, M. Broeders, C. de Wolf, S. Toernberg, R. Holland, and L von Karsa, European Guidelines for Quality Assurance in Breast Cancer Screening and Diagnosis, 4th ed. (European communities, 2006).

Bunk, O.

T. Donath, M. Chabior, F. Pfeiffer, O. Bunk, E. Reznikova, J. Mohr, E. Hempel, S. Popescu, M. Hoheisel, M. Schuster, J. Baumann, and C. David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106, 0547031 (2009).
[Crossref]

C. Kottler, F. Pfeiffer, O. Bunk, C. Grunzweig, and C. David, “Grating interferometer based scanning setup for hard x-ray phase contrast imaging,” Rev. Sci. Instrum. 78, 043710 (2007)
[Crossref] [PubMed]

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys. 2(4), 258–261 (2006).
[Crossref]

F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J. van der Veen, I. Vartanyants, and I. Robinson, “Shearing interferometer for quantifying the coherence of hard x-ray beams,” Phys. Rev. Lett. 94(16), 1648011–4 (2005).
[Crossref]

Cederström, B.

M. Aslund, B. Cederström, M. Lundqvist, and M. Danielsson, “Physical characterization of a scanning photon counting digital mammography system based on Si-strip detectors,” Med. Phys. 34(6), 1918–1925 (2007).
[Crossref] [PubMed]

Chabior, M.

K. Scherer, L. Birnbacher, M. Chabior, J. Herzen, D. Mayr, S. Grandl, A. Sztrokay-Gaul, K. Hellerhoff, F. Bamberg, and F. Pfeiffer, “Bi-Directional X-Ray Phase-Contrast Mammography,” PLoS ONE 9(5), e93502 (2014).
[Crossref] [PubMed]

T. Donath, M. Chabior, F. Pfeiffer, O. Bunk, E. Reznikova, J. Mohr, E. Hempel, S. Popescu, M. Hoheisel, M. Schuster, J. Baumann, and C. David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106, 0547031 (2009).
[Crossref]

Chang, J.

M. J. Berger, J. H. Hubbell, S. M. Seltzer, J. Chang, J. S. Coursey, R. Sukumar, D. S. Zucker, and K. Olsen, XCOM: Photon Cross Section Database (version 1.5) (National Institute of Standards and Technology, 1990).

Chen, Z.

Z. Wang, K. Kang, Z. Huang, and Z. Chen, “Quantitative grating-based x-ray dark-field computed tomography,” Appl. Phys. Lett. 95(9), 0941051 (2009).

Cloetens, P.

Coursey, J. S.

M. J. Berger, J. H. Hubbell, S. M. Seltzer, J. Chang, J. S. Coursey, R. Sukumar, D. S. Zucker, and K. Olsen, XCOM: Photon Cross Section Database (version 1.5) (National Institute of Standards and Technology, 1990).

Cozzini, C.

D’Isidoro, F.

Z. Wang, N. Hauser, R. Kubik-Huch, F. D’Isidoro, and M. Stampanoni, “Quantitative volumetric breast density estimation using phase contrast mammography,” Phys. Med. Biol. 60, 4123–4135 (2015).
[Crossref] [PubMed]

Daerr, H.

T. Koehler, H. Daerr, G. Martens, N. Kuhn, S. Loescher, U. van Stevendaal, and E. Roessl, “Slit-scanning differential x-ray phase-contrast mammography: Proof-of-concept experimental studies,” Med. Phys. 42(4), 1959–1965 (2015).
[Crossref] [PubMed]

E. Roessl, H. Daerr, T. Koehler, G. Martens, and U. van Stevendaal, “Clinical boundary conditions for grating-based differential phase-contrast mammography,” Philos. Trans. R. Soc. London, Ser. A 372(2010), 20130033 (2014).
[Crossref]

Danielsson, M.

M. Aslund, B. Cederström, M. Lundqvist, and M. Danielsson, “Physical characterization of a scanning photon counting digital mammography system based on Si-strip detectors,” Med. Phys. 34(6), 1918–1925 (2007).
[Crossref] [PubMed]

David, C.

P. Modregger, B. Pinzer, T. Thüring, S. Rutishauser, C. David, and M. Stampanoni, “Sensitivity of X-ray grating interferometry,” Opt. Express 19(19), 18324–18338 (2011).
[Crossref] [PubMed]

M. Stampanoni, Z. Wang, T. Thüring, C. David, E. Roessl, M. Trippel, R. Kubik-Huch, G. Singer, M. Hohl, and N. Hauser, “The First Analysis and Clinical Evaluation of Native Breast Tissue Using Differential Phase-Contrast Mammography,” Invest. Radiol. 46(12), 801–806 (2011).
[Crossref] [PubMed]

T. Donath, M. Chabior, F. Pfeiffer, O. Bunk, E. Reznikova, J. Mohr, E. Hempel, S. Popescu, M. Hoheisel, M. Schuster, J. Baumann, and C. David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106, 0547031 (2009).
[Crossref]

C. Kottler, F. Pfeiffer, O. Bunk, C. Grunzweig, and C. David, “Grating interferometer based scanning setup for hard x-ray phase contrast imaging,” Rev. Sci. Instrum. 78, 043710 (2007)
[Crossref] [PubMed]

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys. 2(4), 258–261 (2006).
[Crossref]

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

F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J. van der Veen, I. Vartanyants, and I. Robinson, “Shearing interferometer for quantifying the coherence of hard x-ray beams,” Phys. Rev. Lett. 94(16), 1648011–4 (2005).
[Crossref]

de Wolf, C.

N. Perry, M. Broeders, C. de Wolf, S. Toernberg, R. Holland, and L von Karsa, European Guidelines for Quality Assurance in Breast Cancer Screening and Diagnosis, 4th ed. (European communities, 2006).

Diaz, A.

F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J. van der Veen, I. Vartanyants, and I. Robinson, “Shearing interferometer for quantifying the coherence of hard x-ray beams,” Phys. Rev. Lett. 94(16), 1648011–4 (2005).
[Crossref]

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

Diemoz, P. C.

A. Olivo, S. Gkoumas, M. Endrizzi, C. K. Hagen, M. B. Szafraniec, and P. C. Diemoz, “Low-dose phase contrast mammography with conventional x-ray sources,” Med. Phys. 40(9), 090701 (2013).
[Crossref] [PubMed]

Ding, H.

H. Ding and S. Molloi, “Quantification of breast density with spectral mammography based on a scanned multi-slit photon-counting detector: a feasibility study,” Phys. Med. Biol. 57, 4719–4738 (2012).
[Crossref] [PubMed]

H. Johansson, M. von Tiedemann, K. Erhard, H. Heese, H. Ding, S. Molloi, and E. Fredenberg, “Volumetric breast-density measurement using photon-counting spectral mammography,” submitted to Med. Phys.(2016)

Donath, T.

T. Donath, M. Chabior, F. Pfeiffer, O. Bunk, E. Reznikova, J. Mohr, E. Hempel, S. Popescu, M. Hoheisel, M. Schuster, J. Baumann, and C. David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106, 0547031 (2009).
[Crossref]

Durst, J.

T. Michel, J. Rieger, G. Anton, F. Bayer, M.W Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D.L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58(8), 2713–2732 (2013).
[Crossref] [PubMed]

G. Anton, F. Bayer, M.W. Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, T. Michel, G. Pelzer, M. Radicke, C. Rauh, J. Rieger, A. Ritter, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and L. Wucherer, “Grating-based dark-field imaging of human breast tissue,” Zeitschrift für Medizinische Physik 23(3), 228–235 (2013).
[Crossref]

Endrizzi, M.

A. Olivo, S. Gkoumas, M. Endrizzi, C. K. Hagen, M. B. Szafraniec, and P. C. Diemoz, “Low-dose phase contrast mammography with conventional x-ray sources,” Med. Phys. 40(9), 090701 (2013).
[Crossref] [PubMed]

Erhard, K.

K. Erhard, E. Fredenberg, H. Homann, and E. Roessl, “Spectral lesion characterization on a photon-counting mammography system,” Proc. SPIE Medical Imaging9033 (2014).

H. Johansson, M. von Tiedemann, K. Erhard, H. Heese, H. Ding, S. Molloi, and E. Fredenberg, “Volumetric breast-density measurement using photon-counting spectral mammography,” submitted to Med. Phys.(2016)

Fasching, P. A.

T. Michel, J. Rieger, G. Anton, F. Bayer, M.W Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D.L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58(8), 2713–2732 (2013).
[Crossref] [PubMed]

G. Anton, F. Bayer, M.W. Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, T. Michel, G. Pelzer, M. Radicke, C. Rauh, J. Rieger, A. Ritter, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and L. Wucherer, “Grating-based dark-field imaging of human breast tissue,” Zeitschrift für Medizinische Physik 23(3), 228–235 (2013).
[Crossref]

Fernandez, M.

M. Fernandez, H. Suhonen, J. KeyrilÃd’inen, A. Bravin, S. Fiedler, M.L. Karjalainen-Lindsberg, M. Leidenius, K. von Smitten, and P. Suortti, “USAXS and SAXS from cancer-bearing breast tissue samples,” Eur. J. Radiology 68S, S89 (2008).

Fewell, T.

J. Boone, T. Fewell, and R. Jennings, “Molybdenum, rhodium, and tungsten anode spectral models using interpolating polynomials with application to mammography,” Med. Phys. 24(12), 1863–1874 (1997).
[Crossref]

Fiedler, S.

M. Fernandez, H. Suhonen, J. KeyrilÃd’inen, A. Bravin, S. Fiedler, M.L. Karjalainen-Lindsberg, M. Leidenius, K. von Smitten, and P. Suortti, “USAXS and SAXS from cancer-bearing breast tissue samples,” Eur. J. Radiology 68S, S89 (2008).

Fredenberg, E.

K. Erhard, E. Fredenberg, H. Homann, and E. Roessl, “Spectral lesion characterization on a photon-counting mammography system,” Proc. SPIE Medical Imaging9033 (2014).

H. Johansson, M. von Tiedemann, K. Erhard, H. Heese, H. Ding, S. Molloi, and E. Fredenberg, “Volumetric breast-density measurement using photon-counting spectral mammography,” submitted to Med. Phys.(2016)

Gkoumas, S.

A. Olivo, S. Gkoumas, M. Endrizzi, C. K. Hagen, M. B. Szafraniec, and P. C. Diemoz, “Low-dose phase contrast mammography with conventional x-ray sources,” Med. Phys. 40(9), 090701 (2013).
[Crossref] [PubMed]

Grandl, S.

L. Gromann, D. Beque, K. Scherer, K. Willer, L. Birnbacher, M. Willner, J. Herzen, S. Grandl, K. Hellerhoff, J. Sperl, F. Pfeiffer, and C. Cozzini, “Low-dose, phase-contrast mammography with high signal-to-noise ratio,” Biomed. Opt. Express 7, 381–391 (2016).
[Crossref] [PubMed]

K. Scherer, K. Willer, L. Gromann, L. Birnbacher, E. Braig, S. Grandl, A. SztrÃşkay-Gaul, J. Herzen, D. Mayr, K. Hellerhoff, and F. Pfeiffer, “Toward clinically compatible phase-contrast mammography,” PLoS ONE 10(6), e0130776 (2015).
[Crossref] [PubMed]

K. Scherer, L. Birnbacher, M. Chabior, J. Herzen, D. Mayr, S. Grandl, A. Sztrokay-Gaul, K. Hellerhoff, F. Bamberg, and F. Pfeiffer, “Bi-Directional X-Ray Phase-Contrast Mammography,” PLoS ONE 9(5), e93502 (2014).
[Crossref] [PubMed]

S. D. Auweter, J. Herzen, M. Willner, S. Grandl, K. Scherer, F. Bamberg, M.F. Reiser, F. Pfeiffer, and K. Hellerhoff, “X-ray phase-contrast imaging of the breast-advances towards clinical implementation,” Br. J. Radiol. 87, 20130606 (2014).
[Crossref]

Gromann, L.

L. Gromann, D. Beque, K. Scherer, K. Willer, L. Birnbacher, M. Willner, J. Herzen, S. Grandl, K. Hellerhoff, J. Sperl, F. Pfeiffer, and C. Cozzini, “Low-dose, phase-contrast mammography with high signal-to-noise ratio,” Biomed. Opt. Express 7, 381–391 (2016).
[Crossref] [PubMed]

K. Scherer, K. Willer, L. Gromann, L. Birnbacher, E. Braig, S. Grandl, A. SztrÃşkay-Gaul, J. Herzen, D. Mayr, K. Hellerhoff, and F. Pfeiffer, “Toward clinically compatible phase-contrast mammography,” PLoS ONE 10(6), e0130776 (2015).
[Crossref] [PubMed]

Grunzweig, C.

C. Kottler, F. Pfeiffer, O. Bunk, C. Grunzweig, and C. David, “Grating interferometer based scanning setup for hard x-ray phase contrast imaging,” Rev. Sci. Instrum. 78, 043710 (2007)
[Crossref] [PubMed]

Haas, W.

T. Michel, J. Rieger, G. Anton, F. Bayer, M.W Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D.L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58(8), 2713–2732 (2013).
[Crossref] [PubMed]

G. Anton, F. Bayer, M.W. Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, T. Michel, G. Pelzer, M. Radicke, C. Rauh, J. Rieger, A. Ritter, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and L. Wucherer, “Grating-based dark-field imaging of human breast tissue,” Zeitschrift für Medizinische Physik 23(3), 228–235 (2013).
[Crossref]

Hagen, C. K.

A. Olivo, S. Gkoumas, M. Endrizzi, C. K. Hagen, M. B. Szafraniec, and P. C. Diemoz, “Low-dose phase contrast mammography with conventional x-ray sources,” Med. Phys. 40(9), 090701 (2013).
[Crossref] [PubMed]

Hartmann, A.

T. Michel, J. Rieger, G. Anton, F. Bayer, M.W Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D.L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58(8), 2713–2732 (2013).
[Crossref] [PubMed]

G. Anton, F. Bayer, M.W. Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, T. Michel, G. Pelzer, M. Radicke, C. Rauh, J. Rieger, A. Ritter, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and L. Wucherer, “Grating-based dark-field imaging of human breast tissue,” Zeitschrift für Medizinische Physik 23(3), 228–235 (2013).
[Crossref]

Hauser, N.

Z. Wang, N. Hauser, R. Kubik-Huch, F. D’Isidoro, and M. Stampanoni, “Quantitative volumetric breast density estimation using phase contrast mammography,” Phys. Med. Biol. 60, 4123–4135 (2015).
[Crossref] [PubMed]

Z. Wang, N. Hauser, G. Singer, M. Trippel, R. Kubik-Huch, C. Schneider, and M. Stampanoni, “Non-invasive classification of microcalcifications with phase-contrast X-ray mammography,” Nat. Commun. 5, 1–9 (2014).

N. Hauser, Z. Wang, R.A. Kubik-Huch, M. Trippel, G. Singer, M.K. Hohl, E. Roessl, T. Koehler, U. van Stevendaal, N. Wieberneit, and M. Stampanoni, “A Study on Mastectomy Samples to Evaluate Breast Imaging Quality and Potential Clinical Relevance of Differential Phase Contrast Mammography,” Invest. Radiol. 49(3), 131–137 (2013).
[Crossref] [PubMed]

M. Stampanoni, Z. Wang, T. Thüring, C. David, E. Roessl, M. Trippel, R. Kubik-Huch, G. Singer, M. Hohl, and N. Hauser, “The First Analysis and Clinical Evaluation of Native Breast Tissue Using Differential Phase-Contrast Mammography,” Invest. Radiol. 46(12), 801–806 (2011).
[Crossref] [PubMed]

Heese, H.

H. Johansson, M. von Tiedemann, K. Erhard, H. Heese, H. Ding, S. Molloi, and E. Fredenberg, “Volumetric breast-density measurement using photon-counting spectral mammography,” submitted to Med. Phys.(2016)

Hellerhoff, K.

L. Gromann, D. Beque, K. Scherer, K. Willer, L. Birnbacher, M. Willner, J. Herzen, S. Grandl, K. Hellerhoff, J. Sperl, F. Pfeiffer, and C. Cozzini, “Low-dose, phase-contrast mammography with high signal-to-noise ratio,” Biomed. Opt. Express 7, 381–391 (2016).
[Crossref] [PubMed]

K. Scherer, K. Willer, L. Gromann, L. Birnbacher, E. Braig, S. Grandl, A. SztrÃşkay-Gaul, J. Herzen, D. Mayr, K. Hellerhoff, and F. Pfeiffer, “Toward clinically compatible phase-contrast mammography,” PLoS ONE 10(6), e0130776 (2015).
[Crossref] [PubMed]

K. Scherer, L. Birnbacher, M. Chabior, J. Herzen, D. Mayr, S. Grandl, A. Sztrokay-Gaul, K. Hellerhoff, F. Bamberg, and F. Pfeiffer, “Bi-Directional X-Ray Phase-Contrast Mammography,” PLoS ONE 9(5), e93502 (2014).
[Crossref] [PubMed]

S. D. Auweter, J. Herzen, M. Willner, S. Grandl, K. Scherer, F. Bamberg, M.F. Reiser, F. Pfeiffer, and K. Hellerhoff, “X-ray phase-contrast imaging of the breast-advances towards clinical implementation,” Br. J. Radiol. 87, 20130606 (2014).
[Crossref]

Hempel, E.

T. Donath, M. Chabior, F. Pfeiffer, O. Bunk, E. Reznikova, J. Mohr, E. Hempel, S. Popescu, M. Hoheisel, M. Schuster, J. Baumann, and C. David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106, 0547031 (2009).
[Crossref]

Herzen, J.

L. Gromann, D. Beque, K. Scherer, K. Willer, L. Birnbacher, M. Willner, J. Herzen, S. Grandl, K. Hellerhoff, J. Sperl, F. Pfeiffer, and C. Cozzini, “Low-dose, phase-contrast mammography with high signal-to-noise ratio,” Biomed. Opt. Express 7, 381–391 (2016).
[Crossref] [PubMed]

K. Scherer, K. Willer, L. Gromann, L. Birnbacher, E. Braig, S. Grandl, A. SztrÃşkay-Gaul, J. Herzen, D. Mayr, K. Hellerhoff, and F. Pfeiffer, “Toward clinically compatible phase-contrast mammography,” PLoS ONE 10(6), e0130776 (2015).
[Crossref] [PubMed]

K. Scherer, L. Birnbacher, M. Chabior, J. Herzen, D. Mayr, S. Grandl, A. Sztrokay-Gaul, K. Hellerhoff, F. Bamberg, and F. Pfeiffer, “Bi-Directional X-Ray Phase-Contrast Mammography,” PLoS ONE 9(5), e93502 (2014).
[Crossref] [PubMed]

S. D. Auweter, J. Herzen, M. Willner, S. Grandl, K. Scherer, F. Bamberg, M.F. Reiser, F. Pfeiffer, and K. Hellerhoff, “X-ray phase-contrast imaging of the breast-advances towards clinical implementation,” Br. J. Radiol. 87, 20130606 (2014).
[Crossref]

Hoheisel, M.

T. Donath, M. Chabior, F. Pfeiffer, O. Bunk, E. Reznikova, J. Mohr, E. Hempel, S. Popescu, M. Hoheisel, M. Schuster, J. Baumann, and C. David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106, 0547031 (2009).
[Crossref]

Hohl, M.

M. Stampanoni, Z. Wang, T. Thüring, C. David, E. Roessl, M. Trippel, R. Kubik-Huch, G. Singer, M. Hohl, and N. Hauser, “The First Analysis and Clinical Evaluation of Native Breast Tissue Using Differential Phase-Contrast Mammography,” Invest. Radiol. 46(12), 801–806 (2011).
[Crossref] [PubMed]

Hohl, M.K.

N. Hauser, Z. Wang, R.A. Kubik-Huch, M. Trippel, G. Singer, M.K. Hohl, E. Roessl, T. Koehler, U. van Stevendaal, N. Wieberneit, and M. Stampanoni, “A Study on Mastectomy Samples to Evaluate Breast Imaging Quality and Potential Clinical Relevance of Differential Phase Contrast Mammography,” Invest. Radiol. 49(3), 131–137 (2013).
[Crossref] [PubMed]

Holland, R.

N. Perry, M. Broeders, C. de Wolf, S. Toernberg, R. Holland, and L von Karsa, European Guidelines for Quality Assurance in Breast Cancer Screening and Diagnosis, 4th ed. (European communities, 2006).

Homann, H.

K. Erhard, E. Fredenberg, H. Homann, and E. Roessl, “Spectral lesion characterization on a photon-counting mammography system,” Proc. SPIE Medical Imaging9033 (2014).

Huang, Z.

Z. Wang, K. Kang, Z. Huang, and Z. Chen, “Quantitative grating-based x-ray dark-field computed tomography,” Appl. Phys. Lett. 95(9), 0941051 (2009).

Hubbell, J. H.

M. J. Berger, J. H. Hubbell, S. M. Seltzer, J. Chang, J. S. Coursey, R. Sukumar, D. S. Zucker, and K. Olsen, XCOM: Photon Cross Section Database (version 1.5) (National Institute of Standards and Technology, 1990).

Ignatyev, K.

P.R. Munro, K. Ignatyev, R.D. Speller, and A. Olivo, “Design of a novel phase contrast x-ray imaging system for mammography,” Phys. Med. Biol. 55, 4169–4185 (2010).
[Crossref] [PubMed]

Jennings, R.

J. Boone, T. Fewell, and R. Jennings, “Molybdenum, rhodium, and tungsten anode spectral models using interpolating polynomials with application to mammography,” Med. Phys. 24(12), 1863–1874 (1997).
[Crossref]

Johansson, H.

H. Johansson, M. von Tiedemann, K. Erhard, H. Heese, H. Ding, S. Molloi, and E. Fredenberg, “Volumetric breast-density measurement using photon-counting spectral mammography,” submitted to Med. Phys.(2016)

Kang, K.

Z. Wang, K. Kang, Z. Huang, and Z. Chen, “Quantitative grating-based x-ray dark-field computed tomography,” Appl. Phys. Lett. 95(9), 0941051 (2009).

Karjalainen-Lindsberg, M.L.

M. Fernandez, H. Suhonen, J. KeyrilÃd’inen, A. Bravin, S. Fiedler, M.L. Karjalainen-Lindsberg, M. Leidenius, K. von Smitten, and P. Suortti, “USAXS and SAXS from cancer-bearing breast tissue samples,” Eur. J. Radiology 68S, S89 (2008).

Kaufmann, R.

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based X-ray differential phase contrast imaging,” Rev. Sci. Instrum. 81(7), 0737091–4 (2010).
[Crossref]

Kawabata, K.

Kemble, C.K.

KeyrilÃd’inen, J.

M. Fernandez, H. Suhonen, J. KeyrilÃd’inen, A. Bravin, S. Fiedler, M.L. Karjalainen-Lindsberg, M. Leidenius, K. von Smitten, and P. Suortti, “USAXS and SAXS from cancer-bearing breast tissue samples,” Eur. J. Radiology 68S, S89 (2008).

Koehler, T.

T. Koehler, H. Daerr, G. Martens, N. Kuhn, S. Loescher, U. van Stevendaal, and E. Roessl, “Slit-scanning differential x-ray phase-contrast mammography: Proof-of-concept experimental studies,” Med. Phys. 42(4), 1959–1965 (2015).
[Crossref] [PubMed]

E. Roessl, H. Daerr, T. Koehler, G. Martens, and U. van Stevendaal, “Clinical boundary conditions for grating-based differential phase-contrast mammography,” Philos. Trans. R. Soc. London, Ser. A 372(2010), 20130033 (2014).
[Crossref]

N. Hauser, Z. Wang, R.A. Kubik-Huch, M. Trippel, G. Singer, M.K. Hohl, E. Roessl, T. Koehler, U. van Stevendaal, N. Wieberneit, and M. Stampanoni, “A Study on Mastectomy Samples to Evaluate Breast Imaging Quality and Potential Clinical Relevance of Differential Phase Contrast Mammography,” Invest. Radiol. 49(3), 131–137 (2013).
[Crossref] [PubMed]

Kottler, C.

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based X-ray differential phase contrast imaging,” Rev. Sci. Instrum. 81(7), 0737091–4 (2010).
[Crossref]

C. Kottler, F. Pfeiffer, O. Bunk, C. Grunzweig, and C. David, “Grating interferometer based scanning setup for hard x-ray phase contrast imaging,” Rev. Sci. Instrum. 78, 043710 (2007)
[Crossref] [PubMed]

Kubik-Huch, R.

Z. Wang, N. Hauser, R. Kubik-Huch, F. D’Isidoro, and M. Stampanoni, “Quantitative volumetric breast density estimation using phase contrast mammography,” Phys. Med. Biol. 60, 4123–4135 (2015).
[Crossref] [PubMed]

Z. Wang, N. Hauser, G. Singer, M. Trippel, R. Kubik-Huch, C. Schneider, and M. Stampanoni, “Non-invasive classification of microcalcifications with phase-contrast X-ray mammography,” Nat. Commun. 5, 1–9 (2014).

M. Stampanoni, Z. Wang, T. Thüring, C. David, E. Roessl, M. Trippel, R. Kubik-Huch, G. Singer, M. Hohl, and N. Hauser, “The First Analysis and Clinical Evaluation of Native Breast Tissue Using Differential Phase-Contrast Mammography,” Invest. Radiol. 46(12), 801–806 (2011).
[Crossref] [PubMed]

Kubik-Huch, R.A.

N. Hauser, Z. Wang, R.A. Kubik-Huch, M. Trippel, G. Singer, M.K. Hohl, E. Roessl, T. Koehler, U. van Stevendaal, N. Wieberneit, and M. Stampanoni, “A Study on Mastectomy Samples to Evaluate Breast Imaging Quality and Potential Clinical Relevance of Differential Phase Contrast Mammography,” Invest. Radiol. 49(3), 131–137 (2013).
[Crossref] [PubMed]

Kuhn, N.

T. Koehler, H. Daerr, G. Martens, N. Kuhn, S. Loescher, U. van Stevendaal, and E. Roessl, “Slit-scanning differential x-ray phase-contrast mammography: Proof-of-concept experimental studies,” Med. Phys. 42(4), 1959–1965 (2015).
[Crossref] [PubMed]

Lee, W.

Leidenius, M.

M. Fernandez, H. Suhonen, J. KeyrilÃd’inen, A. Bravin, S. Fiedler, M.L. Karjalainen-Lindsberg, M. Leidenius, K. von Smitten, and P. Suortti, “USAXS and SAXS from cancer-bearing breast tissue samples,” Eur. J. Radiology 68S, S89 (2008).

Loescher, S.

T. Koehler, H. Daerr, G. Martens, N. Kuhn, S. Loescher, U. van Stevendaal, and E. Roessl, “Slit-scanning differential x-ray phase-contrast mammography: Proof-of-concept experimental studies,” Med. Phys. 42(4), 1959–1965 (2015).
[Crossref] [PubMed]

Lundqvist, M.

M. Aslund, B. Cederström, M. Lundqvist, and M. Danielsson, “Physical characterization of a scanning photon counting digital mammography system based on Si-strip detectors,” Med. Phys. 34(6), 1918–1925 (2007).
[Crossref] [PubMed]

Lynch, S. K.

Martens, G.

T. Koehler, H. Daerr, G. Martens, N. Kuhn, S. Loescher, U. van Stevendaal, and E. Roessl, “Slit-scanning differential x-ray phase-contrast mammography: Proof-of-concept experimental studies,” Med. Phys. 42(4), 1959–1965 (2015).
[Crossref] [PubMed]

E. Roessl, H. Daerr, T. Koehler, G. Martens, and U. van Stevendaal, “Clinical boundary conditions for grating-based differential phase-contrast mammography,” Philos. Trans. R. Soc. London, Ser. A 372(2010), 20130033 (2014).
[Crossref]

Mayr, D.

K. Scherer, K. Willer, L. Gromann, L. Birnbacher, E. Braig, S. Grandl, A. SztrÃşkay-Gaul, J. Herzen, D. Mayr, K. Hellerhoff, and F. Pfeiffer, “Toward clinically compatible phase-contrast mammography,” PLoS ONE 10(6), e0130776 (2015).
[Crossref] [PubMed]

K. Scherer, L. Birnbacher, M. Chabior, J. Herzen, D. Mayr, S. Grandl, A. Sztrokay-Gaul, K. Hellerhoff, F. Bamberg, and F. Pfeiffer, “Bi-Directional X-Ray Phase-Contrast Mammography,” PLoS ONE 9(5), e93502 (2014).
[Crossref] [PubMed]

Michel, T.

G. Anton, F. Bayer, M.W. Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, T. Michel, G. Pelzer, M. Radicke, C. Rauh, J. Rieger, A. Ritter, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and L. Wucherer, “Grating-based dark-field imaging of human breast tissue,” Zeitschrift für Medizinische Physik 23(3), 228–235 (2013).
[Crossref]

T. Michel, J. Rieger, G. Anton, F. Bayer, M.W Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D.L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58(8), 2713–2732 (2013).
[Crossref] [PubMed]

Modregger, P.

Mohr, J.

T. Donath, M. Chabior, F. Pfeiffer, O. Bunk, E. Reznikova, J. Mohr, E. Hempel, S. Popescu, M. Hoheisel, M. Schuster, J. Baumann, and C. David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106, 0547031 (2009).
[Crossref]

Molloi, S.

H. Ding and S. Molloi, “Quantification of breast density with spectral mammography based on a scanned multi-slit photon-counting detector: a feasibility study,” Phys. Med. Biol. 57, 4719–4738 (2012).
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H. Johansson, M. von Tiedemann, K. Erhard, H. Heese, H. Ding, S. Molloi, and E. Fredenberg, “Volumetric breast-density measurement using photon-counting spectral mammography,” submitted to Med. Phys.(2016)

Momose, A.

Morgan, N.Y.

Munro, P.R.

P.R. Munro, K. Ignatyev, R.D. Speller, and A. Olivo, “Design of a novel phase contrast x-ray imaging system for mammography,” Phys. Med. Biol. 55, 4169–4185 (2010).
[Crossref] [PubMed]

Olivo, A.

A. Olivo, S. Gkoumas, M. Endrizzi, C. K. Hagen, M. B. Szafraniec, and P. C. Diemoz, “Low-dose phase contrast mammography with conventional x-ray sources,” Med. Phys. 40(9), 090701 (2013).
[Crossref] [PubMed]

P.R. Munro, K. Ignatyev, R.D. Speller, and A. Olivo, “Design of a novel phase contrast x-ray imaging system for mammography,” Phys. Med. Biol. 55, 4169–4185 (2010).
[Crossref] [PubMed]

Olsen, K.

M. J. Berger, J. H. Hubbell, S. M. Seltzer, J. Chang, J. S. Coursey, R. Sukumar, D. S. Zucker, and K. Olsen, XCOM: Photon Cross Section Database (version 1.5) (National Institute of Standards and Technology, 1990).

Pai, V.

Pelzer, G.

T. Michel, J. Rieger, G. Anton, F. Bayer, M.W Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D.L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58(8), 2713–2732 (2013).
[Crossref] [PubMed]

G. Anton, F. Bayer, M.W. Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, T. Michel, G. Pelzer, M. Radicke, C. Rauh, J. Rieger, A. Ritter, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and L. Wucherer, “Grating-based dark-field imaging of human breast tissue,” Zeitschrift für Medizinische Physik 23(3), 228–235 (2013).
[Crossref]

Perry, N.

N. Perry, M. Broeders, C. de Wolf, S. Toernberg, R. Holland, and L von Karsa, European Guidelines for Quality Assurance in Breast Cancer Screening and Diagnosis, 4th ed. (European communities, 2006).

Pfeiffer, F.

L. Gromann, D. Beque, K. Scherer, K. Willer, L. Birnbacher, M. Willner, J. Herzen, S. Grandl, K. Hellerhoff, J. Sperl, F. Pfeiffer, and C. Cozzini, “Low-dose, phase-contrast mammography with high signal-to-noise ratio,” Biomed. Opt. Express 7, 381–391 (2016).
[Crossref] [PubMed]

K. Scherer, K. Willer, L. Gromann, L. Birnbacher, E. Braig, S. Grandl, A. SztrÃşkay-Gaul, J. Herzen, D. Mayr, K. Hellerhoff, and F. Pfeiffer, “Toward clinically compatible phase-contrast mammography,” PLoS ONE 10(6), e0130776 (2015).
[Crossref] [PubMed]

K. Scherer, L. Birnbacher, M. Chabior, J. Herzen, D. Mayr, S. Grandl, A. Sztrokay-Gaul, K. Hellerhoff, F. Bamberg, and F. Pfeiffer, “Bi-Directional X-Ray Phase-Contrast Mammography,” PLoS ONE 9(5), e93502 (2014).
[Crossref] [PubMed]

S. D. Auweter, J. Herzen, M. Willner, S. Grandl, K. Scherer, F. Bamberg, M.F. Reiser, F. Pfeiffer, and K. Hellerhoff, “X-ray phase-contrast imaging of the breast-advances towards clinical implementation,” Br. J. Radiol. 87, 20130606 (2014).
[Crossref]

T. Donath, M. Chabior, F. Pfeiffer, O. Bunk, E. Reznikova, J. Mohr, E. Hempel, S. Popescu, M. Hoheisel, M. Schuster, J. Baumann, and C. David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106, 0547031 (2009).
[Crossref]

C. Kottler, F. Pfeiffer, O. Bunk, C. Grunzweig, and C. David, “Grating interferometer based scanning setup for hard x-ray phase contrast imaging,” Rev. Sci. Instrum. 78, 043710 (2007)
[Crossref] [PubMed]

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys. 2(4), 258–261 (2006).
[Crossref]

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

F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J. van der Veen, I. Vartanyants, and I. Robinson, “Shearing interferometer for quantifying the coherence of hard x-ray beams,” Phys. Rev. Lett. 94(16), 1648011–4 (2005).
[Crossref]

Pinzer, B.

Popescu, S.

T. Donath, M. Chabior, F. Pfeiffer, O. Bunk, E. Reznikova, J. Mohr, E. Hempel, S. Popescu, M. Hoheisel, M. Schuster, J. Baumann, and C. David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106, 0547031 (2009).
[Crossref]

Radicke, M.

T. Michel, J. Rieger, G. Anton, F. Bayer, M.W Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D.L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58(8), 2713–2732 (2013).
[Crossref] [PubMed]

G. Anton, F. Bayer, M.W. Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, T. Michel, G. Pelzer, M. Radicke, C. Rauh, J. Rieger, A. Ritter, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and L. Wucherer, “Grating-based dark-field imaging of human breast tissue,” Zeitschrift für Medizinische Physik 23(3), 228–235 (2013).
[Crossref]

Rauh, C.

G. Anton, F. Bayer, M.W. Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, T. Michel, G. Pelzer, M. Radicke, C. Rauh, J. Rieger, A. Ritter, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and L. Wucherer, “Grating-based dark-field imaging of human breast tissue,” Zeitschrift für Medizinische Physik 23(3), 228–235 (2013).
[Crossref]

T. Michel, J. Rieger, G. Anton, F. Bayer, M.W Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D.L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58(8), 2713–2732 (2013).
[Crossref] [PubMed]

Reiser, M.F.

S. D. Auweter, J. Herzen, M. Willner, S. Grandl, K. Scherer, F. Bamberg, M.F. Reiser, F. Pfeiffer, and K. Hellerhoff, “X-ray phase-contrast imaging of the breast-advances towards clinical implementation,” Br. J. Radiol. 87, 20130606 (2014).
[Crossref]

Revol, V.

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based X-ray differential phase contrast imaging,” Rev. Sci. Instrum. 81(7), 0737091–4 (2010).
[Crossref]

Reznikova, E.

T. Donath, M. Chabior, F. Pfeiffer, O. Bunk, E. Reznikova, J. Mohr, E. Hempel, S. Popescu, M. Hoheisel, M. Schuster, J. Baumann, and C. David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106, 0547031 (2009).
[Crossref]

Rieger, J.

T. Michel, J. Rieger, G. Anton, F. Bayer, M.W Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D.L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58(8), 2713–2732 (2013).
[Crossref] [PubMed]

G. Anton, F. Bayer, M.W. Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, T. Michel, G. Pelzer, M. Radicke, C. Rauh, J. Rieger, A. Ritter, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and L. Wucherer, “Grating-based dark-field imaging of human breast tissue,” Zeitschrift für Medizinische Physik 23(3), 228–235 (2013).
[Crossref]

Ritter, A.

G. Anton, F. Bayer, M.W. Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, T. Michel, G. Pelzer, M. Radicke, C. Rauh, J. Rieger, A. Ritter, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and L. Wucherer, “Grating-based dark-field imaging of human breast tissue,” Zeitschrift für Medizinische Physik 23(3), 228–235 (2013).
[Crossref]

T. Michel, J. Rieger, G. Anton, F. Bayer, M.W Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D.L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58(8), 2713–2732 (2013).
[Crossref] [PubMed]

Robinson, I.

F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J. van der Veen, I. Vartanyants, and I. Robinson, “Shearing interferometer for quantifying the coherence of hard x-ray beams,” Phys. Rev. Lett. 94(16), 1648011–4 (2005).
[Crossref]

Roessl, E.

T. Koehler, H. Daerr, G. Martens, N. Kuhn, S. Loescher, U. van Stevendaal, and E. Roessl, “Slit-scanning differential x-ray phase-contrast mammography: Proof-of-concept experimental studies,” Med. Phys. 42(4), 1959–1965 (2015).
[Crossref] [PubMed]

E. Roessl, H. Daerr, T. Koehler, G. Martens, and U. van Stevendaal, “Clinical boundary conditions for grating-based differential phase-contrast mammography,” Philos. Trans. R. Soc. London, Ser. A 372(2010), 20130033 (2014).
[Crossref]

N. Hauser, Z. Wang, R.A. Kubik-Huch, M. Trippel, G. Singer, M.K. Hohl, E. Roessl, T. Koehler, U. van Stevendaal, N. Wieberneit, and M. Stampanoni, “A Study on Mastectomy Samples to Evaluate Breast Imaging Quality and Potential Clinical Relevance of Differential Phase Contrast Mammography,” Invest. Radiol. 49(3), 131–137 (2013).
[Crossref] [PubMed]

M. Stampanoni, Z. Wang, T. Thüring, C. David, E. Roessl, M. Trippel, R. Kubik-Huch, G. Singer, M. Hohl, and N. Hauser, “The First Analysis and Clinical Evaluation of Native Breast Tissue Using Differential Phase-Contrast Mammography,” Invest. Radiol. 46(12), 801–806 (2011).
[Crossref] [PubMed]

K. Erhard, E. Fredenberg, H. Homann, and E. Roessl, “Spectral lesion characterization on a photon-counting mammography system,” Proc. SPIE Medical Imaging9033 (2014).

Rutishauser, S.

Scherer, K.

L. Gromann, D. Beque, K. Scherer, K. Willer, L. Birnbacher, M. Willner, J. Herzen, S. Grandl, K. Hellerhoff, J. Sperl, F. Pfeiffer, and C. Cozzini, “Low-dose, phase-contrast mammography with high signal-to-noise ratio,” Biomed. Opt. Express 7, 381–391 (2016).
[Crossref] [PubMed]

K. Scherer, K. Willer, L. Gromann, L. Birnbacher, E. Braig, S. Grandl, A. SztrÃşkay-Gaul, J. Herzen, D. Mayr, K. Hellerhoff, and F. Pfeiffer, “Toward clinically compatible phase-contrast mammography,” PLoS ONE 10(6), e0130776 (2015).
[Crossref] [PubMed]

K. Scherer, L. Birnbacher, M. Chabior, J. Herzen, D. Mayr, S. Grandl, A. Sztrokay-Gaul, K. Hellerhoff, F. Bamberg, and F. Pfeiffer, “Bi-Directional X-Ray Phase-Contrast Mammography,” PLoS ONE 9(5), e93502 (2014).
[Crossref] [PubMed]

S. D. Auweter, J. Herzen, M. Willner, S. Grandl, K. Scherer, F. Bamberg, M.F. Reiser, F. Pfeiffer, and K. Hellerhoff, “X-ray phase-contrast imaging of the breast-advances towards clinical implementation,” Br. J. Radiol. 87, 20130606 (2014).
[Crossref]

Schneider, C.

Z. Wang, N. Hauser, G. Singer, M. Trippel, R. Kubik-Huch, C. Schneider, and M. Stampanoni, “Non-invasive classification of microcalcifications with phase-contrast X-ray mammography,” Nat. Commun. 5, 1–9 (2014).

Schulze-Briese, C.

F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J. van der Veen, I. Vartanyants, and I. Robinson, “Shearing interferometer for quantifying the coherence of hard x-ray beams,” Phys. Rev. Lett. 94(16), 1648011–4 (2005).
[Crossref]

Schulz-Wendtland, R.

T. Michel, J. Rieger, G. Anton, F. Bayer, M.W Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D.L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58(8), 2713–2732 (2013).
[Crossref] [PubMed]

G. Anton, F. Bayer, M.W. Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, T. Michel, G. Pelzer, M. Radicke, C. Rauh, J. Rieger, A. Ritter, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and L. Wucherer, “Grating-based dark-field imaging of human breast tissue,” Zeitschrift für Medizinische Physik 23(3), 228–235 (2013).
[Crossref]

Schuster, M.

T. Donath, M. Chabior, F. Pfeiffer, O. Bunk, E. Reznikova, J. Mohr, E. Hempel, S. Popescu, M. Hoheisel, M. Schuster, J. Baumann, and C. David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106, 0547031 (2009).
[Crossref]

Seltzer, S. M.

M. J. Berger, J. H. Hubbell, S. M. Seltzer, J. Chang, J. S. Coursey, R. Sukumar, D. S. Zucker, and K. Olsen, XCOM: Photon Cross Section Database (version 1.5) (National Institute of Standards and Technology, 1990).

Sievers, P.

T. Michel, J. Rieger, G. Anton, F. Bayer, M.W Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D.L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58(8), 2713–2732 (2013).
[Crossref] [PubMed]

Singer, G.

Z. Wang, N. Hauser, G. Singer, M. Trippel, R. Kubik-Huch, C. Schneider, and M. Stampanoni, “Non-invasive classification of microcalcifications with phase-contrast X-ray mammography,” Nat. Commun. 5, 1–9 (2014).

N. Hauser, Z. Wang, R.A. Kubik-Huch, M. Trippel, G. Singer, M.K. Hohl, E. Roessl, T. Koehler, U. van Stevendaal, N. Wieberneit, and M. Stampanoni, “A Study on Mastectomy Samples to Evaluate Breast Imaging Quality and Potential Clinical Relevance of Differential Phase Contrast Mammography,” Invest. Radiol. 49(3), 131–137 (2013).
[Crossref] [PubMed]

M. Stampanoni, Z. Wang, T. Thüring, C. David, E. Roessl, M. Trippel, R. Kubik-Huch, G. Singer, M. Hohl, and N. Hauser, “The First Analysis and Clinical Evaluation of Native Breast Tissue Using Differential Phase-Contrast Mammography,” Invest. Radiol. 46(12), 801–806 (2011).
[Crossref] [PubMed]

Speller, R.D.

P.R. Munro, K. Ignatyev, R.D. Speller, and A. Olivo, “Design of a novel phase contrast x-ray imaging system for mammography,” Phys. Med. Biol. 55, 4169–4185 (2010).
[Crossref] [PubMed]

Sperl, J.

Stampanoni, M.

Z. Wang, N. Hauser, R. Kubik-Huch, F. D’Isidoro, and M. Stampanoni, “Quantitative volumetric breast density estimation using phase contrast mammography,” Phys. Med. Biol. 60, 4123–4135 (2015).
[Crossref] [PubMed]

C. Arboleda, Z. Wang Z, and M. Stampanoni, “Tilted-grating approach for scanning-mode X-ray phase contrast imaging,” Opt. Express 22(13), 15447–15458 (2014).
[Crossref] [PubMed]

T. Thüring and M. Stampanoni, “Performance and optimization of X-ray grating interferometry,” Phil. Trans. Royal Soc. A 372(2010), 20130027 (2014).
[Crossref]

Z. Wang, N. Hauser, G. Singer, M. Trippel, R. Kubik-Huch, C. Schneider, and M. Stampanoni, “Non-invasive classification of microcalcifications with phase-contrast X-ray mammography,” Nat. Commun. 5, 1–9 (2014).

N. Hauser, Z. Wang, R.A. Kubik-Huch, M. Trippel, G. Singer, M.K. Hohl, E. Roessl, T. Koehler, U. van Stevendaal, N. Wieberneit, and M. Stampanoni, “A Study on Mastectomy Samples to Evaluate Breast Imaging Quality and Potential Clinical Relevance of Differential Phase Contrast Mammography,” Invest. Radiol. 49(3), 131–137 (2013).
[Crossref] [PubMed]

M. Stampanoni, Z. Wang, T. Thüring, C. David, E. Roessl, M. Trippel, R. Kubik-Huch, G. Singer, M. Hohl, and N. Hauser, “The First Analysis and Clinical Evaluation of Native Breast Tissue Using Differential Phase-Contrast Mammography,” Invest. Radiol. 46(12), 801–806 (2011).
[Crossref] [PubMed]

P. Modregger, B. Pinzer, T. Thüring, S. Rutishauser, C. David, and M. Stampanoni, “Sensitivity of X-ray grating interferometry,” Opt. Express 19(19), 18324–18338 (2011).
[Crossref] [PubMed]

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

Stein, A.F.

Straumann, U.

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based X-ray differential phase contrast imaging,” Rev. Sci. Instrum. 81(7), 0737091–4 (2010).
[Crossref]

Strobl, M.

M. Strobl, “General solution for quantitative dark-field contrast imaging with grating interferometers,” Sci. Rep. 4, 72431 (2014).
[Crossref]

Suhonen, H.

M. Fernandez, H. Suhonen, J. KeyrilÃd’inen, A. Bravin, S. Fiedler, M.L. Karjalainen-Lindsberg, M. Leidenius, K. von Smitten, and P. Suortti, “USAXS and SAXS from cancer-bearing breast tissue samples,” Eur. J. Radiology 68S, S89 (2008).

Sukumar, R.

M. J. Berger, J. H. Hubbell, S. M. Seltzer, J. Chang, J. S. Coursey, R. Sukumar, D. S. Zucker, and K. Olsen, XCOM: Photon Cross Section Database (version 1.5) (National Institute of Standards and Technology, 1990).

Suortti, P.

M. Fernandez, H. Suhonen, J. KeyrilÃd’inen, A. Bravin, S. Fiedler, M.L. Karjalainen-Lindsberg, M. Leidenius, K. von Smitten, and P. Suortti, “USAXS and SAXS from cancer-bearing breast tissue samples,” Eur. J. Radiology 68S, S89 (2008).

Szafraniec, M. B.

A. Olivo, S. Gkoumas, M. Endrizzi, C. K. Hagen, M. B. Szafraniec, and P. C. Diemoz, “Low-dose phase contrast mammography with conventional x-ray sources,” Med. Phys. 40(9), 090701 (2013).
[Crossref] [PubMed]

SztrÃskay-Gaul, A.

K. Scherer, K. Willer, L. Gromann, L. Birnbacher, E. Braig, S. Grandl, A. SztrÃşkay-Gaul, J. Herzen, D. Mayr, K. Hellerhoff, and F. Pfeiffer, “Toward clinically compatible phase-contrast mammography,” PLoS ONE 10(6), e0130776 (2015).
[Crossref] [PubMed]

Sztrokay-Gaul, A.

K. Scherer, L. Birnbacher, M. Chabior, J. Herzen, D. Mayr, S. Grandl, A. Sztrokay-Gaul, K. Hellerhoff, F. Bamberg, and F. Pfeiffer, “Bi-Directional X-Ray Phase-Contrast Mammography,” PLoS ONE 9(5), e93502 (2014).
[Crossref] [PubMed]

Terui, Y.

Thüring, T.

T. Thüring and M. Stampanoni, “Performance and optimization of X-ray grating interferometry,” Phil. Trans. Royal Soc. A 372(2010), 20130027 (2014).
[Crossref]

M. Stampanoni, Z. Wang, T. Thüring, C. David, E. Roessl, M. Trippel, R. Kubik-Huch, G. Singer, M. Hohl, and N. Hauser, “The First Analysis and Clinical Evaluation of Native Breast Tissue Using Differential Phase-Contrast Mammography,” Invest. Radiol. 46(12), 801–806 (2011).
[Crossref] [PubMed]

P. Modregger, B. Pinzer, T. Thüring, S. Rutishauser, C. David, and M. Stampanoni, “Sensitivity of X-ray grating interferometry,” Opt. Express 19(19), 18324–18338 (2011).
[Crossref] [PubMed]

T. Thüring, Compact X-ray grating interferometry for phase and dark-field computed tomography in the diagnostic energy range, ETH PhD thesis (2013).

Toernberg, S.

N. Perry, M. Broeders, C. de Wolf, S. Toernberg, R. Holland, and L von Karsa, European Guidelines for Quality Assurance in Breast Cancer Screening and Diagnosis, 4th ed. (European communities, 2006).

Trippel, M.

Z. Wang, N. Hauser, G. Singer, M. Trippel, R. Kubik-Huch, C. Schneider, and M. Stampanoni, “Non-invasive classification of microcalcifications with phase-contrast X-ray mammography,” Nat. Commun. 5, 1–9 (2014).

N. Hauser, Z. Wang, R.A. Kubik-Huch, M. Trippel, G. Singer, M.K. Hohl, E. Roessl, T. Koehler, U. van Stevendaal, N. Wieberneit, and M. Stampanoni, “A Study on Mastectomy Samples to Evaluate Breast Imaging Quality and Potential Clinical Relevance of Differential Phase Contrast Mammography,” Invest. Radiol. 49(3), 131–137 (2013).
[Crossref] [PubMed]

M. Stampanoni, Z. Wang, T. Thüring, C. David, E. Roessl, M. Trippel, R. Kubik-Huch, G. Singer, M. Hohl, and N. Hauser, “The First Analysis and Clinical Evaluation of Native Breast Tissue Using Differential Phase-Contrast Mammography,” Invest. Radiol. 46(12), 801–806 (2011).
[Crossref] [PubMed]

Uder, M.

G. Anton, F. Bayer, M.W. Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, T. Michel, G. Pelzer, M. Radicke, C. Rauh, J. Rieger, A. Ritter, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and L. Wucherer, “Grating-based dark-field imaging of human breast tissue,” Zeitschrift für Medizinische Physik 23(3), 228–235 (2013).
[Crossref]

T. Michel, J. Rieger, G. Anton, F. Bayer, M.W Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D.L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58(8), 2713–2732 (2013).
[Crossref] [PubMed]

Urban, C.

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based X-ray differential phase contrast imaging,” Rev. Sci. Instrum. 81(7), 0737091–4 (2010).
[Crossref]

van der Veen, J.

F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J. van der Veen, I. Vartanyants, and I. Robinson, “Shearing interferometer for quantifying the coherence of hard x-ray beams,” Phys. Rev. Lett. 94(16), 1648011–4 (2005).
[Crossref]

van Stevendaal, U.

T. Koehler, H. Daerr, G. Martens, N. Kuhn, S. Loescher, U. van Stevendaal, and E. Roessl, “Slit-scanning differential x-ray phase-contrast mammography: Proof-of-concept experimental studies,” Med. Phys. 42(4), 1959–1965 (2015).
[Crossref] [PubMed]

E. Roessl, H. Daerr, T. Koehler, G. Martens, and U. van Stevendaal, “Clinical boundary conditions for grating-based differential phase-contrast mammography,” Philos. Trans. R. Soc. London, Ser. A 372(2010), 20130033 (2014).
[Crossref]

N. Hauser, Z. Wang, R.A. Kubik-Huch, M. Trippel, G. Singer, M.K. Hohl, E. Roessl, T. Koehler, U. van Stevendaal, N. Wieberneit, and M. Stampanoni, “A Study on Mastectomy Samples to Evaluate Breast Imaging Quality and Potential Clinical Relevance of Differential Phase Contrast Mammography,” Invest. Radiol. 49(3), 131–137 (2013).
[Crossref] [PubMed]

Vartanyants, I.

F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J. van der Veen, I. Vartanyants, and I. Robinson, “Shearing interferometer for quantifying the coherence of hard x-ray beams,” Phys. Rev. Lett. 94(16), 1648011–4 (2005).
[Crossref]

von Karsa, L

N. Perry, M. Broeders, C. de Wolf, S. Toernberg, R. Holland, and L von Karsa, European Guidelines for Quality Assurance in Breast Cancer Screening and Diagnosis, 4th ed. (European communities, 2006).

von Smitten, K.

M. Fernandez, H. Suhonen, J. KeyrilÃd’inen, A. Bravin, S. Fiedler, M.L. Karjalainen-Lindsberg, M. Leidenius, K. von Smitten, and P. Suortti, “USAXS and SAXS from cancer-bearing breast tissue samples,” Eur. J. Radiology 68S, S89 (2008).

von Tiedemann, M.

H. Johansson, M. von Tiedemann, K. Erhard, H. Heese, H. Ding, S. Molloi, and E. Fredenberg, “Volumetric breast-density measurement using photon-counting spectral mammography,” submitted to Med. Phys.(2016)

Wachter, D. L.

G. Anton, F. Bayer, M.W. Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, T. Michel, G. Pelzer, M. Radicke, C. Rauh, J. Rieger, A. Ritter, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and L. Wucherer, “Grating-based dark-field imaging of human breast tissue,” Zeitschrift für Medizinische Physik 23(3), 228–235 (2013).
[Crossref]

Wachter, D.L.

T. Michel, J. Rieger, G. Anton, F. Bayer, M.W Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D.L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58(8), 2713–2732 (2013).
[Crossref] [PubMed]

Wang, Z.

Z. Wang, N. Hauser, R. Kubik-Huch, F. D’Isidoro, and M. Stampanoni, “Quantitative volumetric breast density estimation using phase contrast mammography,” Phys. Med. Biol. 60, 4123–4135 (2015).
[Crossref] [PubMed]

Z. Wang, N. Hauser, G. Singer, M. Trippel, R. Kubik-Huch, C. Schneider, and M. Stampanoni, “Non-invasive classification of microcalcifications with phase-contrast X-ray mammography,” Nat. Commun. 5, 1–9 (2014).

N. Hauser, Z. Wang, R.A. Kubik-Huch, M. Trippel, G. Singer, M.K. Hohl, E. Roessl, T. Koehler, U. van Stevendaal, N. Wieberneit, and M. Stampanoni, “A Study on Mastectomy Samples to Evaluate Breast Imaging Quality and Potential Clinical Relevance of Differential Phase Contrast Mammography,” Invest. Radiol. 49(3), 131–137 (2013).
[Crossref] [PubMed]

M. Stampanoni, Z. Wang, T. Thüring, C. David, E. Roessl, M. Trippel, R. Kubik-Huch, G. Singer, M. Hohl, and N. Hauser, “The First Analysis and Clinical Evaluation of Native Breast Tissue Using Differential Phase-Contrast Mammography,” Invest. Radiol. 46(12), 801–806 (2011).
[Crossref] [PubMed]

Z. Wang, K. Kang, Z. Huang, and Z. Chen, “Quantitative grating-based x-ray dark-field computed tomography,” Appl. Phys. Lett. 95(9), 0941051 (2009).

Wang Z, Z.

Weber, T.

G. Anton, F. Bayer, M.W. Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, T. Michel, G. Pelzer, M. Radicke, C. Rauh, J. Rieger, A. Ritter, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and L. Wucherer, “Grating-based dark-field imaging of human breast tissue,” Zeitschrift für Medizinische Physik 23(3), 228–235 (2013).
[Crossref]

T. Michel, J. Rieger, G. Anton, F. Bayer, M.W Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D.L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58(8), 2713–2732 (2013).
[Crossref] [PubMed]

Weitkamp, T.

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys. 2(4), 258–261 (2006).
[Crossref]

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

F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J. van der Veen, I. Vartanyants, and I. Robinson, “Shearing interferometer for quantifying the coherence of hard x-ray beams,” Phys. Rev. Lett. 94(16), 1648011–4 (2005).
[Crossref]

Wen, H.H.

Wenkel, E.

T. Michel, J. Rieger, G. Anton, F. Bayer, M.W Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D.L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58(8), 2713–2732 (2013).
[Crossref] [PubMed]

G. Anton, F. Bayer, M.W. Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, T. Michel, G. Pelzer, M. Radicke, C. Rauh, J. Rieger, A. Ritter, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and L. Wucherer, “Grating-based dark-field imaging of human breast tissue,” Zeitschrift für Medizinische Physik 23(3), 228–235 (2013).
[Crossref]

Wieberneit, N.

N. Hauser, Z. Wang, R.A. Kubik-Huch, M. Trippel, G. Singer, M.K. Hohl, E. Roessl, T. Koehler, U. van Stevendaal, N. Wieberneit, and M. Stampanoni, “A Study on Mastectomy Samples to Evaluate Breast Imaging Quality and Potential Clinical Relevance of Differential Phase Contrast Mammography,” Invest. Radiol. 49(3), 131–137 (2013).
[Crossref] [PubMed]

Willer, K.

L. Gromann, D. Beque, K. Scherer, K. Willer, L. Birnbacher, M. Willner, J. Herzen, S. Grandl, K. Hellerhoff, J. Sperl, F. Pfeiffer, and C. Cozzini, “Low-dose, phase-contrast mammography with high signal-to-noise ratio,” Biomed. Opt. Express 7, 381–391 (2016).
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K. Scherer, K. Willer, L. Gromann, L. Birnbacher, E. Braig, S. Grandl, A. SztrÃşkay-Gaul, J. Herzen, D. Mayr, K. Hellerhoff, and F. Pfeiffer, “Toward clinically compatible phase-contrast mammography,” PLoS ONE 10(6), e0130776 (2015).
[Crossref] [PubMed]

Willner, M.

L. Gromann, D. Beque, K. Scherer, K. Willer, L. Birnbacher, M. Willner, J. Herzen, S. Grandl, K. Hellerhoff, J. Sperl, F. Pfeiffer, and C. Cozzini, “Low-dose, phase-contrast mammography with high signal-to-noise ratio,” Biomed. Opt. Express 7, 381–391 (2016).
[Crossref] [PubMed]

S. D. Auweter, J. Herzen, M. Willner, S. Grandl, K. Scherer, F. Bamberg, M.F. Reiser, F. Pfeiffer, and K. Hellerhoff, “X-ray phase-contrast imaging of the breast-advances towards clinical implementation,” Br. J. Radiol. 87, 20130606 (2014).
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Wucherer, L.

G. Anton, F. Bayer, M.W. Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, T. Michel, G. Pelzer, M. Radicke, C. Rauh, J. Rieger, A. Ritter, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and L. Wucherer, “Grating-based dark-field imaging of human breast tissue,” Zeitschrift für Medizinische Physik 23(3), 228–235 (2013).
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Xiao, X.

Yashiro, W.

Zang, A.

T. Michel, J. Rieger, G. Anton, F. Bayer, M.W Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D.L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58(8), 2713–2732 (2013).
[Crossref] [PubMed]

Ziegler, E.

Zucker, D. S.

M. J. Berger, J. H. Hubbell, S. M. Seltzer, J. Chang, J. S. Coursey, R. Sukumar, D. S. Zucker, and K. Olsen, XCOM: Photon Cross Section Database (version 1.5) (National Institute of Standards and Technology, 1990).

Appl. Opt. (1)

Appl. Phys. Lett. (1)

Z. Wang, K. Kang, Z. Huang, and Z. Chen, “Quantitative grating-based x-ray dark-field computed tomography,” Appl. Phys. Lett. 95(9), 0941051 (2009).

Biomed. Opt. Express (1)

Br. J. Radiol. (1)

S. D. Auweter, J. Herzen, M. Willner, S. Grandl, K. Scherer, F. Bamberg, M.F. Reiser, F. Pfeiffer, and K. Hellerhoff, “X-ray phase-contrast imaging of the breast-advances towards clinical implementation,” Br. J. Radiol. 87, 20130606 (2014).
[Crossref]

Eur. J. Radiology (1)

M. Fernandez, H. Suhonen, J. KeyrilÃd’inen, A. Bravin, S. Fiedler, M.L. Karjalainen-Lindsberg, M. Leidenius, K. von Smitten, and P. Suortti, “USAXS and SAXS from cancer-bearing breast tissue samples,” Eur. J. Radiology 68S, S89 (2008).

Invest. Radiol. (2)

M. Stampanoni, Z. Wang, T. Thüring, C. David, E. Roessl, M. Trippel, R. Kubik-Huch, G. Singer, M. Hohl, and N. Hauser, “The First Analysis and Clinical Evaluation of Native Breast Tissue Using Differential Phase-Contrast Mammography,” Invest. Radiol. 46(12), 801–806 (2011).
[Crossref] [PubMed]

N. Hauser, Z. Wang, R.A. Kubik-Huch, M. Trippel, G. Singer, M.K. Hohl, E. Roessl, T. Koehler, U. van Stevendaal, N. Wieberneit, and M. Stampanoni, “A Study on Mastectomy Samples to Evaluate Breast Imaging Quality and Potential Clinical Relevance of Differential Phase Contrast Mammography,” Invest. Radiol. 49(3), 131–137 (2013).
[Crossref] [PubMed]

J. Appl. Phys. (1)

T. Donath, M. Chabior, F. Pfeiffer, O. Bunk, E. Reznikova, J. Mohr, E. Hempel, S. Popescu, M. Hoheisel, M. Schuster, J. Baumann, and C. David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106, 0547031 (2009).
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Med. Phys. (4)

J. Boone, T. Fewell, and R. Jennings, “Molybdenum, rhodium, and tungsten anode spectral models using interpolating polynomials with application to mammography,” Med. Phys. 24(12), 1863–1874 (1997).
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M. Aslund, B. Cederström, M. Lundqvist, and M. Danielsson, “Physical characterization of a scanning photon counting digital mammography system based on Si-strip detectors,” Med. Phys. 34(6), 1918–1925 (2007).
[Crossref] [PubMed]

A. Olivo, S. Gkoumas, M. Endrizzi, C. K. Hagen, M. B. Szafraniec, and P. C. Diemoz, “Low-dose phase contrast mammography with conventional x-ray sources,” Med. Phys. 40(9), 090701 (2013).
[Crossref] [PubMed]

T. Koehler, H. Daerr, G. Martens, N. Kuhn, S. Loescher, U. van Stevendaal, and E. Roessl, “Slit-scanning differential x-ray phase-contrast mammography: Proof-of-concept experimental studies,” Med. Phys. 42(4), 1959–1965 (2015).
[Crossref] [PubMed]

Nat. Commun. (1)

Z. Wang, N. Hauser, G. Singer, M. Trippel, R. Kubik-Huch, C. Schneider, and M. Stampanoni, “Non-invasive classification of microcalcifications with phase-contrast X-ray mammography,” Nat. Commun. 5, 1–9 (2014).

Nat. Phys. (1)

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys. 2(4), 258–261 (2006).
[Crossref]

Opt. Express (4)

Phil. Trans. Royal Soc. A (1)

T. Thüring and M. Stampanoni, “Performance and optimization of X-ray grating interferometry,” Phil. Trans. Royal Soc. A 372(2010), 20130027 (2014).
[Crossref]

Philos. Trans. R. Soc. London, Ser. A (1)

E. Roessl, H. Daerr, T. Koehler, G. Martens, and U. van Stevendaal, “Clinical boundary conditions for grating-based differential phase-contrast mammography,” Philos. Trans. R. Soc. London, Ser. A 372(2010), 20130033 (2014).
[Crossref]

Phys. Med. Biol. (4)

P.R. Munro, K. Ignatyev, R.D. Speller, and A. Olivo, “Design of a novel phase contrast x-ray imaging system for mammography,” Phys. Med. Biol. 55, 4169–4185 (2010).
[Crossref] [PubMed]

T. Michel, J. Rieger, G. Anton, F. Bayer, M.W Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D.L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58(8), 2713–2732 (2013).
[Crossref] [PubMed]

H. Ding and S. Molloi, “Quantification of breast density with spectral mammography based on a scanned multi-slit photon-counting detector: a feasibility study,” Phys. Med. Biol. 57, 4719–4738 (2012).
[Crossref] [PubMed]

Z. Wang, N. Hauser, R. Kubik-Huch, F. D’Isidoro, and M. Stampanoni, “Quantitative volumetric breast density estimation using phase contrast mammography,” Phys. Med. Biol. 60, 4123–4135 (2015).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J. van der Veen, I. Vartanyants, and I. Robinson, “Shearing interferometer for quantifying the coherence of hard x-ray beams,” Phys. Rev. Lett. 94(16), 1648011–4 (2005).
[Crossref]

PLoS ONE (2)

K. Scherer, L. Birnbacher, M. Chabior, J. Herzen, D. Mayr, S. Grandl, A. Sztrokay-Gaul, K. Hellerhoff, F. Bamberg, and F. Pfeiffer, “Bi-Directional X-Ray Phase-Contrast Mammography,” PLoS ONE 9(5), e93502 (2014).
[Crossref] [PubMed]

K. Scherer, K. Willer, L. Gromann, L. Birnbacher, E. Braig, S. Grandl, A. SztrÃşkay-Gaul, J. Herzen, D. Mayr, K. Hellerhoff, and F. Pfeiffer, “Toward clinically compatible phase-contrast mammography,” PLoS ONE 10(6), e0130776 (2015).
[Crossref] [PubMed]

Rev. Sci. Instrum. (2)

C. Kottler, F. Pfeiffer, O. Bunk, C. Grunzweig, and C. David, “Grating interferometer based scanning setup for hard x-ray phase contrast imaging,” Rev. Sci. Instrum. 78, 043710 (2007)
[Crossref] [PubMed]

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based X-ray differential phase contrast imaging,” Rev. Sci. Instrum. 81(7), 0737091–4 (2010).
[Crossref]

Sci. Rep. (1)

M. Strobl, “General solution for quantitative dark-field contrast imaging with grating interferometers,” Sci. Rep. 4, 72431 (2014).
[Crossref]

Zeitschrift für Medizinische Physik (1)

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[Crossref]

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K. Erhard, E. Fredenberg, H. Homann, and E. Roessl, “Spectral lesion characterization on a photon-counting mammography system,” Proc. SPIE Medical Imaging9033 (2014).

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Figures (8)

Fig. 1
Fig. 1

Sketch of a Talbot-Lau interferometer installed on the Philips Microdose Mammography.

Fig. 2
Fig. 2

Simulated spectra after all the GI elements (gratings plus grating wafers) on the beam path assuming 250 µm thick grating wafers for an exposure time of 15 s.

Fig. 3
Fig. 3

Summary of the wave propagation simulation

Fig. 4
Fig. 4

Summary of the optimization algorithm. An optimal scenario for the phase sensitivity and another for the dark-field SNR are the outcomes of this method.

Fig. 5
Fig. 5

Experimental (pink) and simulated (black bars) visibility values (%) for different Polycarbonate (PC) thicknesses and spectra. The standard deviation in the simulated values accounts for the potential grating height and duty cycle imperfections, while it refers to the noise in the experimental results.

Fig. 6
Fig. 6

Dark-field extinction coefficient (µd) for breast tissue as a function of the auto-correlation length. It can be seen that the detected visibility reduction changes with the auto-correlation length in a sigmoid manner for auto-correlation lengths below 20 µm, which suggests that the scatterers in the breast have roughly this size.

Fig. 7
Fig. 7

Dark-field extinction coefficients (μd) for our fresh mastectomy database.

Fig. 8
Fig. 8

Dark-field (top) and electron density (bottom) sensitivity vs. design energy for an inter-grating distance of 4 cm.

Tables (4)

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Table 1 Philips Microdose Mammography boundary conditions for the GI design.

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Table 2 Optimal scenarios for each Talbot order. For orders 1, 3 and 7, the optimal scenarios for both signals are the same, whereas for order 5 there are diffierent optimal scenarios for phase1 and dark field2.

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Table 3 Visibility values (%) predicted by Thüring’s formula and obtained from wave-optics simulations for the optimal dark-field sensitivity design energy (23 keV).

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Table 4 Phase and dark-field sensitivities for the optimal design scenario at each available Microdose spectrum.

Equations (14)

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S N R ϕ = ϕ Δ ϕ = α 2 π d p 2 1 Δ ϕ ,
ϕ = ϕ b a c k g r o u n d ϕ s a m p l e ,
Δ ϕ = Δ ϕ b a c k g r o u n d 2 + Δ ϕ s a m p l e 2 ,
α m i n = p 2 2 π d Δ ϕ ,
Δ 2 ϕ = 2 V r 2 N ( 1 + 1 T V 2 ) ,
Δ ρ e , m i n = 2 π r e λ eff 2 α m i n ,
S N R d f = l n ( V ) Δ l n ( V ) ,
l n ( V ) = μ d t = Σ t ( G ( ξ ) 1 ) ,
ξ = λ eff L s p 2 ,
f ( x ) = 1 σ 2 π exp [ 1 2 σ 2 ( x d ) 2 ] ,
σ = Σ t ( G ( ξ ) 1 ) 2 π 2 ( d p 2 ) 2 ,
Δ l n ( V ) = ( Δ V s 2 V s 2 ) + ( Δ V r 2 V r 2 ) ,
Δ 2 l n ( V ) = 2 V r 2 N ( 1 + 1 T V 2 ) + 1 N ( 1 + 1 T ) ,
D = K c g s ,

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