Abstract

We demonstrate a fast, flexible, and accurate paraxial wave propagation model to serve as a forward model for propagation-based X-ray phase contrast imaging (XPCI) in parallel-beam or cone-beam geometry. This model incorporates geometric cone-beam effects into the multi-slice beam propagation method. It enables rapid prototyping and is well suited to serve as a forward model for propagation-based X-ray phase contrast tomographic reconstructions. Furthermore, it is capable of modeling arbitrary objects, including those that are strongly or multi-scattering. Simulation studies were conducted to compare our model to other forward models in the X-ray regime, such as the Mie and full-wave Rytov solutions.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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  1. A. Bravin, P. Coan, and P. Suortti, “X-ray phase-contrast imaging: from pre-clinical applications towards clinics,” Phys. Med. Biol. 58(1), R1–R35 (2013).
    [Crossref] [PubMed]
  2. T. E. Gureyev, S. C. Mayo, D. E. Myers, Y. I. Nesterets, D. M. Paganin, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “Refracting Röntgen’s rays: propagation-based x-ray phase contrast for biomedical imaging,” J. Appl. Phys. 105(10), 102005 (2009).
    [Crossref]
  3. M. Endrizzi, “X-ray phase-contrast imaging,” Nucl. Instrum. Methods Phys. Res. A 878, 88–98 (2018).
    [Crossref]
  4. T. E. Gureyev and K. A. Nugent, “Phase retrieval with the transport-of-intensity equation. II. Orthogonal series solution for nonuniform illumination,” J. Opt. Soc. Am. A 13(8), 1670–1682 (1996).
    [Crossref]
  5. D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206(Pt 1), 33–40 (2002).
    [Crossref] [PubMed]
  6. J. P. Guigay, M. Langer, R. Boistel, and P. Cloetens, “Mixed transfer function and transport of intensity approach for phase retrieval in the Fresnel region,” Opt. Lett. 32(12), 1617–1619 (2007).
    [Crossref] [PubMed]
  7. A. Horng, E. Brun, A. Mittone, S. Gasilov, L. Weber, T. Geith, S. Adam-Neumair, S. D. Auweter, A. Bravin, M. F. Reiser, and P. Coan, “Cartilage and soft tissue imaging using X-rays: propagation-based phase-contrast computed tomography of the human knee in comparison with clinical imaging techniques and histology,” Invest. Radiol. 49(9), 627–634 (2014).
    [Crossref] [PubMed]
  8. T. Geith, E. Brun, A. Mittone, S. Gasilov, L. Weber, S. Adam-Neumair, A. Bravin, M. Reiser, P. Coan, and A. Horng, “Quantitative Assessment of Degenerative Cartilage and Subchondral Bony Lesions in a Preserved Cadaveric Knee: Propagation-Based Phase-Contrast CT Versus Conventional MRI and CT,” AJR Am. J. Roentgenol. 210(6), 1317–1322 (2018).
    [Crossref] [PubMed]
  9. S. T. Taba, T. E. Gureyev, M. Alakhras, S. Lewis, D. Lockie, and P. C. Brennan, “X-ray phase-contrast technology in breast imaging: principles, options, and clinical application,” AJR Am. J. Roentgenol. 211(1), 133–145 (2018).
    [Crossref] [PubMed]
  10. L. C. P. Croton, K. S. Morgan, D. M. Paganin, L. T. Kerr, M. J. Wallace, K. J. Crossley, S. L. Miller, N. Yagi, K. Uesugi, S. B. Hooper, and M. J. Kitchen, “In situ phase contrast X-ray brain CT,” Sci. Rep. 8(1), 11412 (2018).
    [Crossref] [PubMed]
  11. F. Pfeiffer, O. Bunk, C. David, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “High-resolution brain tumor visualization using three-dimensional x-ray phase contrast tomography,” Phys. Med. Biol. 52(23), 6923–6930 (2007).
    [Crossref] [PubMed]
  12. G. Shinohara, K. Morita, M. Hoshino, Y. Ko, T. Tsukube, Y. Kaneko, H. Morishita, Y. Oshima, H. Matsuhisa, R. Iwaki, M. Takahashi, T. Matsuyama, K. Hashimoto, and N. Yagi, “Three dimensional visualization of human cardiac conduction tissue in whole heart specimens by high-resolution phase-contrast CT imaging using synchrotron radiation,” World J. Pediatr. Congenit. Heart Surg. 7(6), 700–705 (2016).
    [Crossref] [PubMed]
  13. P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75(19), 2912–2914 (1999).
    [Crossref]
  14. S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative X-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207(Pt 2), 79–96 (2002).
    [Crossref] [PubMed]
  15. R. Mokso, P. Cloetens, E. Maire, W. Ludwig, and J. Y. Buffière, “Nanoscale zoom tomography with hard x rays using Kirkpatrick-Baez optics,” Appl. Phys. Lett. 90(14), 144104 (2007).
    [Crossref]
  16. E. Maire and P. J. Withers, “Quantitative X-ray tomography,” Int. Mater. Rev. 59(1), 1–43 (2014).
    [Crossref]
  17. A. Beerlink, S. Thutupalli, M. Mell, M. Bartels, P. Cloetens, S. Herminghaus, and T. Salditt, “X-ray propagation imaging of a lipid bilayer in solution,” Soft Matter 8(17), 4595–4601 (2012).
    [Crossref]
  18. M. Krenkel, M. Töpperwien, C. Dullin, F. Alves, and T. Salditt, “Propagation-based phase-contrast tomography for high-resolution lung imaging with laboratory sources,” AIP Adv. 6(3), 035007 (2016).
    [Crossref]
  19. M. Langer, A. Pacureanu, H. Suhonen, Q. Grimal, P. Cloetens, and F. Peyrin, “X-ray phase nanotomography resolves the 3D human bone ultrastructure,” PLoS One 7(8), e35691 (2012).
    [Crossref] [PubMed]
  20. M. Langer and F. Peyrin, “3D X-ray ultra-microscopy of bone tissue,” Osteoporos. Int. 27(2), 441–455 (2016).
    [Crossref] [PubMed]
  21. A. Khimchenko, C. Bikis, A. Pacureanu, S. E. Hieber, P. Thalmann, H. Deyhle, G. Schweighauser, J. Hench, S. Frank, M. Müller-Gerbl, G. Schulz, P. Cloetens, and B. Müller, “Hard x-ray nanoholotomography: large-scale, label-free, 3D neuroimaging beyond optical limit,” Adv. Sci. (Weinh.) 5(6), 1700694 (2018).
    [Crossref] [PubMed]
  22. C. Olendrowitz, M. Bartels, M. Krenkel, A. Beerlink, R. Mokso, M. Sprung, and T. Salditt, “Phase-contrast x-ray imaging and tomography of the nematode Caenorhabditis elegans,” Phys. Med. Biol. 57(16), 5309–5323 (2012).
    [Crossref] [PubMed]
  23. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).
  24. M. I. Mishchenko, L. D. Travis, and D. W. Mackowski, “T-matrix computations of light scattering nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transf. 55(5), 535–575 (1996).
    [Crossref]
  25. G. Gouesbet, J. A. Lock, and G. Grehan, “Generalized Lorenz–Mie theories and description of electromagnetic arbitrary shaped beams: localized approximations and localized beam models, a review,” J. Quant. Spectrosc. Radiat. Transf. 112(1), 1–27 (2011).
    [Crossref]
  26. Y. Sung and G. Barbastathis, “Rytov approximation for x-ray phase imaging,” Opt. Express 21(3), 2674–2682 (2013).
    [Crossref] [PubMed]
  27. Y. Sung, C. J. R. Sheppard, G. Barbastathis, M. Ando, and R. Gupta, “Full-wave approach for x-ray phase imaging,” Opt. Express 21(15), 17547–17557 (2013).
    [Crossref] [PubMed]
  28. Y. Sung, W. P. Segars, A. Pan, M. Ando, C. J. R. Sheppard, and R. Gupta, “Realistic wave-optics simulation of X-ray phase-contrast imaging at a human scale,” Sci. Rep. 5(1), 12011 (2015).
    [Crossref] [PubMed]
  29. Y. Sung, R. Gupta, B. Nelson, S. Leng, C. H. McCollough, and W. S. Graves, “Phase-contrast imaging with a compact x-ray light source: system design,” J. Med. Imaging (Bellingham) 4(4), 043503 (2017).
    [Crossref] [PubMed]
  30. D. M. Paganin, Coherent X-Ray Optics (Oxford University, 2006).
  31. J. A. Fleck, J. R. Morris, and M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. (Berl.) 10(2), 129–160 (1976).
    [Crossref]
  32. J. M. Cowley and A. F. Moodie, “The scattering of electrons by atoms and crystals. I. A new theoretical approach,” Acta Crystallogr. 10(10), 609–619 (1957).
    [Crossref]
  33. U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical tomographic image reconstruction based on beam propagation and sparse regularization,” IEEE Trans. Comput. Imaging 2(1), 59–70 (2016).
    [Crossref]
  34. U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “A learning approach to optical tomography,” Optica 2(6), 517–522 (2015).
    [Crossref]
  35. W. G. Tam, “Split-step Fourier-transform analysis for laser-pulse propagation in particulate media,” J. Opt. Soc. Am. A 72(10), 1311–1316 (1982).
    [Crossref]
  36. A. M. Maiden, M. J. Humphry, and J. M. Rodenburg, “Ptychographic transmission microscopy in three dimensions using a multi-slice approach,” J. Opt. Soc. Am. A 29(8), 1606–1614 (2012).
    [Crossref] [PubMed]
  37. X. Ma, W. Xiao, and F. Pan, “Optical tomographic reconstruction based on multi-slice wave propagation method,” Opt. Express 25(19), 22595–22607 (2017).
    [Crossref] [PubMed]
  38. T. M. Godden, R. Suman, M. J. Humphry, J. M. Rodenburg, and A. M. Maiden, “Ptychographic microscope for three-dimensional imaging,” Opt. Express 22(10), 12513–12523 (2014).
    [Crossref] [PubMed]
  39. K. Li, M. Wojcik, and C. Jacobsen, “Multislice does it all-calculating the performance of nanofocusing X-ray optics,” Opt. Express 25(3), 1831–1846 (2017).
    [Crossref] [PubMed]
  40. J. Lim, A. Goy, M. H. Shoreh, M. Unser, and D. Psaltis, “Learning tomography assessed using Mie theory,” Phys. Rev. Appl. 9(3), 34027 (2018).
    [Crossref]
  41. E. Maire and P. J. Withers, “Quantitative x-ray tomography,” Int. Mater. Rev. 59(1), 1–43 (2014).
    [Crossref]
  42. M. Krenkel, A. Markus, M. Bartels, C. Dullin, F. Alves, and T. Salditt, “Phase-contrast zoom tomography reveals precise locations of macrophages in mouse lungs,” Sci. Rep. 5(1), 9973 (2015).
    [Crossref] [PubMed]
  43. M. Guizar-Sicairos, J. J. Boon, K. Mader, A. Diaz, A. Menzel, and O. Bunk, “Quantitative interior x-ray nanotomography by a hybrid imaging technique,” Optica 2(3), 259–266 (2015).
    [Crossref]
  44. M. Bartels, M. Krenkel, P. Cloetens, W. Möbius, and T. Salditt, “Myelinated mouse nerves studied by X-ray phase contrast zoom tomography,” J. Struct. Biol. 192(3), 561–568 (2015).
    [Crossref] [PubMed]
  45. S. Steckmann, M. Knaup, and M. Kachelriess, “Algorithm for hyperfast cone-beam spiral backprojection,” Comput. Methods Programs Biomed. 98(3), 253–260 (2010).
    [Crossref] [PubMed]
  46. M. Beister, D. Kolditz, and W. A. Kalender, “Iterative reconstruction methods in X-ray CT,” Phys. Med. 28(2), 94–108 (2012).
    [Crossref] [PubMed]
  47. M. Nilchian, Z. Wang, T. Thuering, M. Unser, and M. Stampanoni, “Spline based iterative phase retrieval algorithm for X-ray differential phase contrast radiography,” Opt. Express 23(8), 10631–10642 (2015).
    [Crossref] [PubMed]
  48. J. A. Lock and G. Gouesbet, “Generalized Lorenz–Mie theory and applications,” J. Quant. Spectrosc. Radiat. Transf. 110(11), 800–807 (2009).
    [Crossref]
  49. N. J. Moore and M. A. Alonso, “Closed form formula for Mie scattering of nonparaxial analogues of Gaussian beams,” Opt. Express 16(8), 5926–5933 (2008).
    [Crossref] [PubMed]
  50. P. C. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53(8), 805–812 (1965).
    [Crossref]
  51. M. I. Mishchenko, “Light scattering by randomly oriented axially symmetric particles,” J. Opt. Soc. Am. A 8(6), 871–882 (1991).
    [Crossref]
  52. F. M. Kahnert, “Numerical methods in electromagnetic scattering theory,” J. Quant. Spectrosc. Radiat. Transf. 79–80(1), 775–824 (2003).
    [Crossref]
  53. J. Schäfer, S. C. Lee, and A. Kienle, “Calculation of the near fields for the scattering of electromagnetic waves by multiple infinite cylinders at perpendicular incidence,” J. Quant. Spectrosc. Radiat. Transf. 113(16), 2113–2123 (2012).
    [Crossref]
  54. S.-C. Lee, “Dependent scattering of an obliquely incident plane wave by a collection of parallel cylinders,” J. Appl. Phys. 68(10), 4952–4957 (1990).
    [Crossref]
  55. G. A. Tsihrintzis and A. J. Devaney, “Higher order (nonlinear) diffraction tomography: inversion of the Rytov series,” IEEE Trans. Inf. Theory 46(5), 1748–1761 (2000).
    [Crossref]
  56. A. J. Devaney, “Inverse-scattering theory within the Rytov approximation,” Opt. Lett. 6(8), 374–376 (1981).
    [Crossref] [PubMed]
  57. E. Soubies, T.-A. Pham, and M. Unser, “Efficient inversion of multiple-scattering model for optical diffraction tomography,” Opt. Express 25(18), 21786–21800 (2017).
    [Crossref] [PubMed]
  58. M. Lee, S. Shin, and Y. Park, “Reconstructions of refractive index tomograms via a discrete algebraic reconstruction technique,” Opt. Express 25(22), 27415–27430 (2017).
    [Crossref] [PubMed]
  59. C. T. Putkunz, M. A. Pfeifer, A. G. Peele, G. J. Williams, H. M. Quiney, B. Abbey, K. A. Nugent, and I. McNulty, “Fresnel coherent diffraction tomography,” Opt. Express 18(11), 11746–11753 (2010).
    [Crossref] [PubMed]
  60. M. Chen, L. Tian, and L. Waller, “3D differential phase contrast microscopy,” Biomed. Opt. Express 7(10), 3940–3950 (2016).
    [Crossref] [PubMed]
  61. M. R. Teague, “Deterministic phase retrieval: a Green’s function solution,” J. Opt. Soc. Am. 73(11), 1434–1441 (1983).
    [Crossref]
  62. X. Wu and H. Liu, “A general theoretical formalism for X-ray phase contrast imaging,” J. XRay Sci. Technol. 11(1), 33–42 (2003).
    [PubMed]
  63. J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company Publishers, 2005).
  64. J. Miao, T. Ishikawa, I. K. Robinson, and M. M. Murnane, “Beyond crystallography: diffractive imaging using coherent x-ray light sources,” Science 348(6234), 530–535 (2015).
    [Crossref] [PubMed]
  65. W. S. Graves, J. Bessuille, P. Brown, S. Carbajo, V. Dolgashev, K.-H. Hong, E. Ihloff, B. Khaykovich, H. Lin, K. Murari, E. A. Nanni, G. Resta, S. Tantawi, L. E. Zapata, F. X. Kärtner, and D. E. Moncton, “Compact x-ray source based on burst-mode inverse Compton scattering at 100 kHz,” Phys. Rev. Spec. Top. Accel. Beams 17(12), 120701 (2014).
    [Crossref]
  66. 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(2), 181–342 (1993).
    [Crossref]
  67. K. S. Morgan, K. K. W. Siu, and D. M. Paganin, “The projection approximation and edge contrast for x-ray propagation-based phase contrast imaging of a cylindrical edge,” Opt. Express 18(10), 9865–9878 (2010).
    [Crossref] [PubMed]
  68. K. S. Morgan, K. K. W. Siu, and D. M. Paganin, “The projection approximation versus an exact solution for x-ray phase contrast imaging, with a plane wave scattered by a dielectric cylinder,” Opt. Commun. 283(23), 4601–4608 (2010).
    [Crossref]
  69. C. M. Li, W. P. Segars, G. D. Tourassi, J. M. Boone, and J. T. Dobbins, “Methodology for generating a 3D computerized breast phantom from empirical data,” Med. Phys. 36(7), 3122–3131 (2009).
    [Crossref] [PubMed]
  70. D. W. Erickson, J. R. Wells, G. M. Sturgeon, E. Samei, J. T. Dobbins, W. P. Segars, and J. Y. Lo, “Population of 224 realistic human subject-based computational breast phantoms,” Med. Phys. 43(1), 23–32 (2016).
    [Crossref] [PubMed]
  71. G. M. Sturgeon, N. Kiarashi, J. Y. Lo, E. Samei, and W. P. Segars, “Finite-element modeling of compression and gravity on a population of breast phantoms for multimodality imaging simulation,” Med. Phys. 43(5), 2207–2217 (2016).
    [Crossref] [PubMed]
  72. D. R. White, R. V. Griffith, and I. J. Wilson, “ICRU Report 46: photon, electron, proton, and neutron interaction data for body tissues,” J. ICRUos24(1), (1992).
  73. J. Hsieh, Computed Tomography Principles, Design, Artifacts, and Recent Advances, 3rd ed. (SPIE Press, 2015).
  74. G. Gbur and E. Wolf, “Relation between computed tomography and diffraction tomography,” J. Opt. Soc. Am. A 18(9), 2132–2137 (2001).
    [Crossref] [PubMed]

2018 (6)

T. Geith, E. Brun, A. Mittone, S. Gasilov, L. Weber, S. Adam-Neumair, A. Bravin, M. Reiser, P. Coan, and A. Horng, “Quantitative Assessment of Degenerative Cartilage and Subchondral Bony Lesions in a Preserved Cadaveric Knee: Propagation-Based Phase-Contrast CT Versus Conventional MRI and CT,” AJR Am. J. Roentgenol. 210(6), 1317–1322 (2018).
[Crossref] [PubMed]

S. T. Taba, T. E. Gureyev, M. Alakhras, S. Lewis, D. Lockie, and P. C. Brennan, “X-ray phase-contrast technology in breast imaging: principles, options, and clinical application,” AJR Am. J. Roentgenol. 211(1), 133–145 (2018).
[Crossref] [PubMed]

L. C. P. Croton, K. S. Morgan, D. M. Paganin, L. T. Kerr, M. J. Wallace, K. J. Crossley, S. L. Miller, N. Yagi, K. Uesugi, S. B. Hooper, and M. J. Kitchen, “In situ phase contrast X-ray brain CT,” Sci. Rep. 8(1), 11412 (2018).
[Crossref] [PubMed]

A. Khimchenko, C. Bikis, A. Pacureanu, S. E. Hieber, P. Thalmann, H. Deyhle, G. Schweighauser, J. Hench, S. Frank, M. Müller-Gerbl, G. Schulz, P. Cloetens, and B. Müller, “Hard x-ray nanoholotomography: large-scale, label-free, 3D neuroimaging beyond optical limit,” Adv. Sci. (Weinh.) 5(6), 1700694 (2018).
[Crossref] [PubMed]

M. Endrizzi, “X-ray phase-contrast imaging,” Nucl. Instrum. Methods Phys. Res. A 878, 88–98 (2018).
[Crossref]

J. Lim, A. Goy, M. H. Shoreh, M. Unser, and D. Psaltis, “Learning tomography assessed using Mie theory,” Phys. Rev. Appl. 9(3), 34027 (2018).
[Crossref]

2017 (5)

2016 (7)

M. Chen, L. Tian, and L. Waller, “3D differential phase contrast microscopy,” Biomed. Opt. Express 7(10), 3940–3950 (2016).
[Crossref] [PubMed]

D. W. Erickson, J. R. Wells, G. M. Sturgeon, E. Samei, J. T. Dobbins, W. P. Segars, and J. Y. Lo, “Population of 224 realistic human subject-based computational breast phantoms,” Med. Phys. 43(1), 23–32 (2016).
[Crossref] [PubMed]

G. M. Sturgeon, N. Kiarashi, J. Y. Lo, E. Samei, and W. P. Segars, “Finite-element modeling of compression and gravity on a population of breast phantoms for multimodality imaging simulation,” Med. Phys. 43(5), 2207–2217 (2016).
[Crossref] [PubMed]

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical tomographic image reconstruction based on beam propagation and sparse regularization,” IEEE Trans. Comput. Imaging 2(1), 59–70 (2016).
[Crossref]

M. Langer and F. Peyrin, “3D X-ray ultra-microscopy of bone tissue,” Osteoporos. Int. 27(2), 441–455 (2016).
[Crossref] [PubMed]

M. Krenkel, M. Töpperwien, C. Dullin, F. Alves, and T. Salditt, “Propagation-based phase-contrast tomography for high-resolution lung imaging with laboratory sources,” AIP Adv. 6(3), 035007 (2016).
[Crossref]

G. Shinohara, K. Morita, M. Hoshino, Y. Ko, T. Tsukube, Y. Kaneko, H. Morishita, Y. Oshima, H. Matsuhisa, R. Iwaki, M. Takahashi, T. Matsuyama, K. Hashimoto, and N. Yagi, “Three dimensional visualization of human cardiac conduction tissue in whole heart specimens by high-resolution phase-contrast CT imaging using synchrotron radiation,” World J. Pediatr. Congenit. Heart Surg. 7(6), 700–705 (2016).
[Crossref] [PubMed]

2015 (7)

Y. Sung, W. P. Segars, A. Pan, M. Ando, C. J. R. Sheppard, and R. Gupta, “Realistic wave-optics simulation of X-ray phase-contrast imaging at a human scale,” Sci. Rep. 5(1), 12011 (2015).
[Crossref] [PubMed]

M. Krenkel, A. Markus, M. Bartels, C. Dullin, F. Alves, and T. Salditt, “Phase-contrast zoom tomography reveals precise locations of macrophages in mouse lungs,” Sci. Rep. 5(1), 9973 (2015).
[Crossref] [PubMed]

M. Bartels, M. Krenkel, P. Cloetens, W. Möbius, and T. Salditt, “Myelinated mouse nerves studied by X-ray phase contrast zoom tomography,” J. Struct. Biol. 192(3), 561–568 (2015).
[Crossref] [PubMed]

J. Miao, T. Ishikawa, I. K. Robinson, and M. M. Murnane, “Beyond crystallography: diffractive imaging using coherent x-ray light sources,” Science 348(6234), 530–535 (2015).
[Crossref] [PubMed]

M. Guizar-Sicairos, J. J. Boon, K. Mader, A. Diaz, A. Menzel, and O. Bunk, “Quantitative interior x-ray nanotomography by a hybrid imaging technique,” Optica 2(3), 259–266 (2015).
[Crossref]

M. Nilchian, Z. Wang, T. Thuering, M. Unser, and M. Stampanoni, “Spline based iterative phase retrieval algorithm for X-ray differential phase contrast radiography,” Opt. Express 23(8), 10631–10642 (2015).
[Crossref] [PubMed]

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “A learning approach to optical tomography,” Optica 2(6), 517–522 (2015).
[Crossref]

2014 (5)

T. M. Godden, R. Suman, M. J. Humphry, J. M. Rodenburg, and A. M. Maiden, “Ptychographic microscope for three-dimensional imaging,” Opt. Express 22(10), 12513–12523 (2014).
[Crossref] [PubMed]

W. S. Graves, J. Bessuille, P. Brown, S. Carbajo, V. Dolgashev, K.-H. Hong, E. Ihloff, B. Khaykovich, H. Lin, K. Murari, E. A. Nanni, G. Resta, S. Tantawi, L. E. Zapata, F. X. Kärtner, and D. E. Moncton, “Compact x-ray source based on burst-mode inverse Compton scattering at 100 kHz,” Phys. Rev. Spec. Top. Accel. Beams 17(12), 120701 (2014).
[Crossref]

E. Maire and P. J. Withers, “Quantitative x-ray tomography,” Int. Mater. Rev. 59(1), 1–43 (2014).
[Crossref]

A. Horng, E. Brun, A. Mittone, S. Gasilov, L. Weber, T. Geith, S. Adam-Neumair, S. D. Auweter, A. Bravin, M. F. Reiser, and P. Coan, “Cartilage and soft tissue imaging using X-rays: propagation-based phase-contrast computed tomography of the human knee in comparison with clinical imaging techniques and histology,” Invest. Radiol. 49(9), 627–634 (2014).
[Crossref] [PubMed]

E. Maire and P. J. Withers, “Quantitative X-ray tomography,” Int. Mater. Rev. 59(1), 1–43 (2014).
[Crossref]

2013 (3)

2012 (6)

A. M. Maiden, M. J. Humphry, and J. M. Rodenburg, “Ptychographic transmission microscopy in three dimensions using a multi-slice approach,” J. Opt. Soc. Am. A 29(8), 1606–1614 (2012).
[Crossref] [PubMed]

M. Beister, D. Kolditz, and W. A. Kalender, “Iterative reconstruction methods in X-ray CT,” Phys. Med. 28(2), 94–108 (2012).
[Crossref] [PubMed]

J. Schäfer, S. C. Lee, and A. Kienle, “Calculation of the near fields for the scattering of electromagnetic waves by multiple infinite cylinders at perpendicular incidence,” J. Quant. Spectrosc. Radiat. Transf. 113(16), 2113–2123 (2012).
[Crossref]

A. Beerlink, S. Thutupalli, M. Mell, M. Bartels, P. Cloetens, S. Herminghaus, and T. Salditt, “X-ray propagation imaging of a lipid bilayer in solution,” Soft Matter 8(17), 4595–4601 (2012).
[Crossref]

M. Langer, A. Pacureanu, H. Suhonen, Q. Grimal, P. Cloetens, and F. Peyrin, “X-ray phase nanotomography resolves the 3D human bone ultrastructure,” PLoS One 7(8), e35691 (2012).
[Crossref] [PubMed]

C. Olendrowitz, M. Bartels, M. Krenkel, A. Beerlink, R. Mokso, M. Sprung, and T. Salditt, “Phase-contrast x-ray imaging and tomography of the nematode Caenorhabditis elegans,” Phys. Med. Biol. 57(16), 5309–5323 (2012).
[Crossref] [PubMed]

2011 (1)

G. Gouesbet, J. A. Lock, and G. Grehan, “Generalized Lorenz–Mie theories and description of electromagnetic arbitrary shaped beams: localized approximations and localized beam models, a review,” J. Quant. Spectrosc. Radiat. Transf. 112(1), 1–27 (2011).
[Crossref]

2010 (4)

K. S. Morgan, K. K. W. Siu, and D. M. Paganin, “The projection approximation versus an exact solution for x-ray phase contrast imaging, with a plane wave scattered by a dielectric cylinder,” Opt. Commun. 283(23), 4601–4608 (2010).
[Crossref]

K. S. Morgan, K. K. W. Siu, and D. M. Paganin, “The projection approximation and edge contrast for x-ray propagation-based phase contrast imaging of a cylindrical edge,” Opt. Express 18(10), 9865–9878 (2010).
[Crossref] [PubMed]

C. T. Putkunz, M. A. Pfeifer, A. G. Peele, G. J. Williams, H. M. Quiney, B. Abbey, K. A. Nugent, and I. McNulty, “Fresnel coherent diffraction tomography,” Opt. Express 18(11), 11746–11753 (2010).
[Crossref] [PubMed]

S. Steckmann, M. Knaup, and M. Kachelriess, “Algorithm for hyperfast cone-beam spiral backprojection,” Comput. Methods Programs Biomed. 98(3), 253–260 (2010).
[Crossref] [PubMed]

2009 (3)

J. A. Lock and G. Gouesbet, “Generalized Lorenz–Mie theory and applications,” J. Quant. Spectrosc. Radiat. Transf. 110(11), 800–807 (2009).
[Crossref]

T. E. Gureyev, S. C. Mayo, D. E. Myers, Y. I. Nesterets, D. M. Paganin, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “Refracting Röntgen’s rays: propagation-based x-ray phase contrast for biomedical imaging,” J. Appl. Phys. 105(10), 102005 (2009).
[Crossref]

C. M. Li, W. P. Segars, G. D. Tourassi, J. M. Boone, and J. T. Dobbins, “Methodology for generating a 3D computerized breast phantom from empirical data,” Med. Phys. 36(7), 3122–3131 (2009).
[Crossref] [PubMed]

2008 (1)

2007 (3)

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

R. Mokso, P. Cloetens, E. Maire, W. Ludwig, and J. Y. Buffière, “Nanoscale zoom tomography with hard x rays using Kirkpatrick-Baez optics,” Appl. Phys. Lett. 90(14), 144104 (2007).
[Crossref]

F. Pfeiffer, O. Bunk, C. David, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “High-resolution brain tumor visualization using three-dimensional x-ray phase contrast tomography,” Phys. Med. Biol. 52(23), 6923–6930 (2007).
[Crossref] [PubMed]

2003 (2)

F. M. Kahnert, “Numerical methods in electromagnetic scattering theory,” J. Quant. Spectrosc. Radiat. Transf. 79–80(1), 775–824 (2003).
[Crossref]

X. Wu and H. Liu, “A general theoretical formalism for X-ray phase contrast imaging,” J. XRay Sci. Technol. 11(1), 33–42 (2003).
[PubMed]

2002 (2)

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206(Pt 1), 33–40 (2002).
[Crossref] [PubMed]

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative X-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207(Pt 2), 79–96 (2002).
[Crossref] [PubMed]

2001 (1)

2000 (1)

G. A. Tsihrintzis and A. J. Devaney, “Higher order (nonlinear) diffraction tomography: inversion of the Rytov series,” IEEE Trans. Inf. Theory 46(5), 1748–1761 (2000).
[Crossref]

1999 (1)

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75(19), 2912–2914 (1999).
[Crossref]

1996 (2)

M. I. Mishchenko, L. D. Travis, and D. W. Mackowski, “T-matrix computations of light scattering nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transf. 55(5), 535–575 (1996).
[Crossref]

T. E. Gureyev and K. A. Nugent, “Phase retrieval with the transport-of-intensity equation. II. Orthogonal series solution for nonuniform illumination,” J. Opt. Soc. Am. A 13(8), 1670–1682 (1996).
[Crossref]

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(2), 181–342 (1993).
[Crossref]

1991 (1)

1990 (1)

S.-C. Lee, “Dependent scattering of an obliquely incident plane wave by a collection of parallel cylinders,” J. Appl. Phys. 68(10), 4952–4957 (1990).
[Crossref]

1983 (1)

1982 (1)

W. G. Tam, “Split-step Fourier-transform analysis for laser-pulse propagation in particulate media,” J. Opt. Soc. Am. A 72(10), 1311–1316 (1982).
[Crossref]

1981 (1)

1976 (1)

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. (Berl.) 10(2), 129–160 (1976).
[Crossref]

1965 (1)

P. C. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53(8), 805–812 (1965).
[Crossref]

1957 (1)

J. M. Cowley and A. F. Moodie, “The scattering of electrons by atoms and crystals. I. A new theoretical approach,” Acta Crystallogr. 10(10), 609–619 (1957).
[Crossref]

Abbey, B.

Adam-Neumair, S.

T. Geith, E. Brun, A. Mittone, S. Gasilov, L. Weber, S. Adam-Neumair, A. Bravin, M. Reiser, P. Coan, and A. Horng, “Quantitative Assessment of Degenerative Cartilage and Subchondral Bony Lesions in a Preserved Cadaveric Knee: Propagation-Based Phase-Contrast CT Versus Conventional MRI and CT,” AJR Am. J. Roentgenol. 210(6), 1317–1322 (2018).
[Crossref] [PubMed]

A. Horng, E. Brun, A. Mittone, S. Gasilov, L. Weber, T. Geith, S. Adam-Neumair, S. D. Auweter, A. Bravin, M. F. Reiser, and P. Coan, “Cartilage and soft tissue imaging using X-rays: propagation-based phase-contrast computed tomography of the human knee in comparison with clinical imaging techniques and histology,” Invest. Radiol. 49(9), 627–634 (2014).
[Crossref] [PubMed]

Alakhras, M.

S. T. Taba, T. E. Gureyev, M. Alakhras, S. Lewis, D. Lockie, and P. C. Brennan, “X-ray phase-contrast technology in breast imaging: principles, options, and clinical application,” AJR Am. J. Roentgenol. 211(1), 133–145 (2018).
[Crossref] [PubMed]

Alonso, M. A.

Alves, F.

M. Krenkel, M. Töpperwien, C. Dullin, F. Alves, and T. Salditt, “Propagation-based phase-contrast tomography for high-resolution lung imaging with laboratory sources,” AIP Adv. 6(3), 035007 (2016).
[Crossref]

M. Krenkel, A. Markus, M. Bartels, C. Dullin, F. Alves, and T. Salditt, “Phase-contrast zoom tomography reveals precise locations of macrophages in mouse lungs,” Sci. Rep. 5(1), 9973 (2015).
[Crossref] [PubMed]

Ando, M.

Y. Sung, W. P. Segars, A. Pan, M. Ando, C. J. R. Sheppard, and R. Gupta, “Realistic wave-optics simulation of X-ray phase-contrast imaging at a human scale,” Sci. Rep. 5(1), 12011 (2015).
[Crossref] [PubMed]

Y. Sung, C. J. R. Sheppard, G. Barbastathis, M. Ando, and R. Gupta, “Full-wave approach for x-ray phase imaging,” Opt. Express 21(15), 17547–17557 (2013).
[Crossref] [PubMed]

Auweter, S. D.

A. Horng, E. Brun, A. Mittone, S. Gasilov, L. Weber, T. Geith, S. Adam-Neumair, S. D. Auweter, A. Bravin, M. F. Reiser, and P. Coan, “Cartilage and soft tissue imaging using X-rays: propagation-based phase-contrast computed tomography of the human knee in comparison with clinical imaging techniques and histology,” Invest. Radiol. 49(9), 627–634 (2014).
[Crossref] [PubMed]

Barbastathis, G.

Bartels, M.

M. Krenkel, A. Markus, M. Bartels, C. Dullin, F. Alves, and T. Salditt, “Phase-contrast zoom tomography reveals precise locations of macrophages in mouse lungs,” Sci. Rep. 5(1), 9973 (2015).
[Crossref] [PubMed]

M. Bartels, M. Krenkel, P. Cloetens, W. Möbius, and T. Salditt, “Myelinated mouse nerves studied by X-ray phase contrast zoom tomography,” J. Struct. Biol. 192(3), 561–568 (2015).
[Crossref] [PubMed]

C. Olendrowitz, M. Bartels, M. Krenkel, A. Beerlink, R. Mokso, M. Sprung, and T. Salditt, “Phase-contrast x-ray imaging and tomography of the nematode Caenorhabditis elegans,” Phys. Med. Biol. 57(16), 5309–5323 (2012).
[Crossref] [PubMed]

A. Beerlink, S. Thutupalli, M. Mell, M. Bartels, P. Cloetens, S. Herminghaus, and T. Salditt, “X-ray propagation imaging of a lipid bilayer in solution,” Soft Matter 8(17), 4595–4601 (2012).
[Crossref]

Baruchel, J.

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75(19), 2912–2914 (1999).
[Crossref]

Bech, M.

F. Pfeiffer, O. Bunk, C. David, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “High-resolution brain tumor visualization using three-dimensional x-ray phase contrast tomography,” Phys. Med. Biol. 52(23), 6923–6930 (2007).
[Crossref] [PubMed]

Beerlink, A.

A. Beerlink, S. Thutupalli, M. Mell, M. Bartels, P. Cloetens, S. Herminghaus, and T. Salditt, “X-ray propagation imaging of a lipid bilayer in solution,” Soft Matter 8(17), 4595–4601 (2012).
[Crossref]

C. Olendrowitz, M. Bartels, M. Krenkel, A. Beerlink, R. Mokso, M. Sprung, and T. Salditt, “Phase-contrast x-ray imaging and tomography of the nematode Caenorhabditis elegans,” Phys. Med. Biol. 57(16), 5309–5323 (2012).
[Crossref] [PubMed]

Beister, M.

M. Beister, D. Kolditz, and W. A. Kalender, “Iterative reconstruction methods in X-ray CT,” Phys. Med. 28(2), 94–108 (2012).
[Crossref] [PubMed]

Bessuille, J.

W. S. Graves, J. Bessuille, P. Brown, S. Carbajo, V. Dolgashev, K.-H. Hong, E. Ihloff, B. Khaykovich, H. Lin, K. Murari, E. A. Nanni, G. Resta, S. Tantawi, L. E. Zapata, F. X. Kärtner, and D. E. Moncton, “Compact x-ray source based on burst-mode inverse Compton scattering at 100 kHz,” Phys. Rev. Spec. Top. Accel. Beams 17(12), 120701 (2014).
[Crossref]

Bikis, C.

A. Khimchenko, C. Bikis, A. Pacureanu, S. E. Hieber, P. Thalmann, H. Deyhle, G. Schweighauser, J. Hench, S. Frank, M. Müller-Gerbl, G. Schulz, P. Cloetens, and B. Müller, “Hard x-ray nanoholotomography: large-scale, label-free, 3D neuroimaging beyond optical limit,” Adv. Sci. (Weinh.) 5(6), 1700694 (2018).
[Crossref] [PubMed]

Boistel, R.

Boon, J. J.

Boone, J. M.

C. M. Li, W. P. Segars, G. D. Tourassi, J. M. Boone, and J. T. Dobbins, “Methodology for generating a 3D computerized breast phantom from empirical data,” Med. Phys. 36(7), 3122–3131 (2009).
[Crossref] [PubMed]

Bravin, A.

T. Geith, E. Brun, A. Mittone, S. Gasilov, L. Weber, S. Adam-Neumair, A. Bravin, M. Reiser, P. Coan, and A. Horng, “Quantitative Assessment of Degenerative Cartilage and Subchondral Bony Lesions in a Preserved Cadaveric Knee: Propagation-Based Phase-Contrast CT Versus Conventional MRI and CT,” AJR Am. J. Roentgenol. 210(6), 1317–1322 (2018).
[Crossref] [PubMed]

A. Horng, E. Brun, A. Mittone, S. Gasilov, L. Weber, T. Geith, S. Adam-Neumair, S. D. Auweter, A. Bravin, M. F. Reiser, and P. Coan, “Cartilage and soft tissue imaging using X-rays: propagation-based phase-contrast computed tomography of the human knee in comparison with clinical imaging techniques and histology,” Invest. Radiol. 49(9), 627–634 (2014).
[Crossref] [PubMed]

A. Bravin, P. Coan, and P. Suortti, “X-ray phase-contrast imaging: from pre-clinical applications towards clinics,” Phys. Med. Biol. 58(1), R1–R35 (2013).
[Crossref] [PubMed]

F. Pfeiffer, O. Bunk, C. David, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “High-resolution brain tumor visualization using three-dimensional x-ray phase contrast tomography,” Phys. Med. Biol. 52(23), 6923–6930 (2007).
[Crossref] [PubMed]

Brennan, P. C.

S. T. Taba, T. E. Gureyev, M. Alakhras, S. Lewis, D. Lockie, and P. C. Brennan, “X-ray phase-contrast technology in breast imaging: principles, options, and clinical application,” AJR Am. J. Roentgenol. 211(1), 133–145 (2018).
[Crossref] [PubMed]

Brown, P.

W. S. Graves, J. Bessuille, P. Brown, S. Carbajo, V. Dolgashev, K.-H. Hong, E. Ihloff, B. Khaykovich, H. Lin, K. Murari, E. A. Nanni, G. Resta, S. Tantawi, L. E. Zapata, F. X. Kärtner, and D. E. Moncton, “Compact x-ray source based on burst-mode inverse Compton scattering at 100 kHz,” Phys. Rev. Spec. Top. Accel. Beams 17(12), 120701 (2014).
[Crossref]

Brun, E.

T. Geith, E. Brun, A. Mittone, S. Gasilov, L. Weber, S. Adam-Neumair, A. Bravin, M. Reiser, P. Coan, and A. Horng, “Quantitative Assessment of Degenerative Cartilage and Subchondral Bony Lesions in a Preserved Cadaveric Knee: Propagation-Based Phase-Contrast CT Versus Conventional MRI and CT,” AJR Am. J. Roentgenol. 210(6), 1317–1322 (2018).
[Crossref] [PubMed]

A. Horng, E. Brun, A. Mittone, S. Gasilov, L. Weber, T. Geith, S. Adam-Neumair, S. D. Auweter, A. Bravin, M. F. Reiser, and P. Coan, “Cartilage and soft tissue imaging using X-rays: propagation-based phase-contrast computed tomography of the human knee in comparison with clinical imaging techniques and histology,” Invest. Radiol. 49(9), 627–634 (2014).
[Crossref] [PubMed]

Buffière, J. Y.

R. Mokso, P. Cloetens, E. Maire, W. Ludwig, and J. Y. Buffière, “Nanoscale zoom tomography with hard x rays using Kirkpatrick-Baez optics,” Appl. Phys. Lett. 90(14), 144104 (2007).
[Crossref]

Bunk, O.

M. Guizar-Sicairos, J. J. Boon, K. Mader, A. Diaz, A. Menzel, and O. Bunk, “Quantitative interior x-ray nanotomography by a hybrid imaging technique,” Optica 2(3), 259–266 (2015).
[Crossref]

F. Pfeiffer, O. Bunk, C. David, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “High-resolution brain tumor visualization using three-dimensional x-ray phase contrast tomography,” Phys. Med. Biol. 52(23), 6923–6930 (2007).
[Crossref] [PubMed]

Carbajo, S.

W. S. Graves, J. Bessuille, P. Brown, S. Carbajo, V. Dolgashev, K.-H. Hong, E. Ihloff, B. Khaykovich, H. Lin, K. Murari, E. A. Nanni, G. Resta, S. Tantawi, L. E. Zapata, F. X. Kärtner, and D. E. Moncton, “Compact x-ray source based on burst-mode inverse Compton scattering at 100 kHz,” Phys. Rev. Spec. Top. Accel. Beams 17(12), 120701 (2014).
[Crossref]

Chen, M.

Cloetens, P.

A. Khimchenko, C. Bikis, A. Pacureanu, S. E. Hieber, P. Thalmann, H. Deyhle, G. Schweighauser, J. Hench, S. Frank, M. Müller-Gerbl, G. Schulz, P. Cloetens, and B. Müller, “Hard x-ray nanoholotomography: large-scale, label-free, 3D neuroimaging beyond optical limit,” Adv. Sci. (Weinh.) 5(6), 1700694 (2018).
[Crossref] [PubMed]

M. Bartels, M. Krenkel, P. Cloetens, W. Möbius, and T. Salditt, “Myelinated mouse nerves studied by X-ray phase contrast zoom tomography,” J. Struct. Biol. 192(3), 561–568 (2015).
[Crossref] [PubMed]

M. Langer, A. Pacureanu, H. Suhonen, Q. Grimal, P. Cloetens, and F. Peyrin, “X-ray phase nanotomography resolves the 3D human bone ultrastructure,” PLoS One 7(8), e35691 (2012).
[Crossref] [PubMed]

A. Beerlink, S. Thutupalli, M. Mell, M. Bartels, P. Cloetens, S. Herminghaus, and T. Salditt, “X-ray propagation imaging of a lipid bilayer in solution,” Soft Matter 8(17), 4595–4601 (2012).
[Crossref]

R. Mokso, P. Cloetens, E. Maire, W. Ludwig, and J. Y. Buffière, “Nanoscale zoom tomography with hard x rays using Kirkpatrick-Baez optics,” Appl. Phys. Lett. 90(14), 144104 (2007).
[Crossref]

F. Pfeiffer, O. Bunk, C. David, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “High-resolution brain tumor visualization using three-dimensional x-ray phase contrast tomography,” Phys. Med. Biol. 52(23), 6923–6930 (2007).
[Crossref] [PubMed]

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

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75(19), 2912–2914 (1999).
[Crossref]

Coan, P.

T. Geith, E. Brun, A. Mittone, S. Gasilov, L. Weber, S. Adam-Neumair, A. Bravin, M. Reiser, P. Coan, and A. Horng, “Quantitative Assessment of Degenerative Cartilage and Subchondral Bony Lesions in a Preserved Cadaveric Knee: Propagation-Based Phase-Contrast CT Versus Conventional MRI and CT,” AJR Am. J. Roentgenol. 210(6), 1317–1322 (2018).
[Crossref] [PubMed]

A. Horng, E. Brun, A. Mittone, S. Gasilov, L. Weber, T. Geith, S. Adam-Neumair, S. D. Auweter, A. Bravin, M. F. Reiser, and P. Coan, “Cartilage and soft tissue imaging using X-rays: propagation-based phase-contrast computed tomography of the human knee in comparison with clinical imaging techniques and histology,” Invest. Radiol. 49(9), 627–634 (2014).
[Crossref] [PubMed]

A. Bravin, P. Coan, and P. Suortti, “X-ray phase-contrast imaging: from pre-clinical applications towards clinics,” Phys. Med. Biol. 58(1), R1–R35 (2013).
[Crossref] [PubMed]

Cowley, J. M.

J. M. Cowley and A. F. Moodie, “The scattering of electrons by atoms and crystals. I. A new theoretical approach,” Acta Crystallogr. 10(10), 609–619 (1957).
[Crossref]

Crossley, K. J.

L. C. P. Croton, K. S. Morgan, D. M. Paganin, L. T. Kerr, M. J. Wallace, K. J. Crossley, S. L. Miller, N. Yagi, K. Uesugi, S. B. Hooper, and M. J. Kitchen, “In situ phase contrast X-ray brain CT,” Sci. Rep. 8(1), 11412 (2018).
[Crossref] [PubMed]

Croton, L. C. P.

L. C. P. Croton, K. S. Morgan, D. M. Paganin, L. T. Kerr, M. J. Wallace, K. J. Crossley, S. L. Miller, N. Yagi, K. Uesugi, S. B. Hooper, and M. J. Kitchen, “In situ phase contrast X-ray brain CT,” Sci. Rep. 8(1), 11412 (2018).
[Crossref] [PubMed]

David, C.

F. Pfeiffer, O. Bunk, C. David, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “High-resolution brain tumor visualization using three-dimensional x-ray phase contrast tomography,” Phys. Med. Biol. 52(23), 6923–6930 (2007).
[Crossref] [PubMed]

Davis, J. C.

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(2), 181–342 (1993).
[Crossref]

Davis, T. J.

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative X-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207(Pt 2), 79–96 (2002).
[Crossref] [PubMed]

Devaney, A. J.

G. A. Tsihrintzis and A. J. Devaney, “Higher order (nonlinear) diffraction tomography: inversion of the Rytov series,” IEEE Trans. Inf. Theory 46(5), 1748–1761 (2000).
[Crossref]

A. J. Devaney, “Inverse-scattering theory within the Rytov approximation,” Opt. Lett. 6(8), 374–376 (1981).
[Crossref] [PubMed]

Deyhle, H.

A. Khimchenko, C. Bikis, A. Pacureanu, S. E. Hieber, P. Thalmann, H. Deyhle, G. Schweighauser, J. Hench, S. Frank, M. Müller-Gerbl, G. Schulz, P. Cloetens, and B. Müller, “Hard x-ray nanoholotomography: large-scale, label-free, 3D neuroimaging beyond optical limit,” Adv. Sci. (Weinh.) 5(6), 1700694 (2018).
[Crossref] [PubMed]

Diaz, A.

Dobbins, J. T.

D. W. Erickson, J. R. Wells, G. M. Sturgeon, E. Samei, J. T. Dobbins, W. P. Segars, and J. Y. Lo, “Population of 224 realistic human subject-based computational breast phantoms,” Med. Phys. 43(1), 23–32 (2016).
[Crossref] [PubMed]

C. M. Li, W. P. Segars, G. D. Tourassi, J. M. Boone, and J. T. Dobbins, “Methodology for generating a 3D computerized breast phantom from empirical data,” Med. Phys. 36(7), 3122–3131 (2009).
[Crossref] [PubMed]

Dolgashev, V.

W. S. Graves, J. Bessuille, P. Brown, S. Carbajo, V. Dolgashev, K.-H. Hong, E. Ihloff, B. Khaykovich, H. Lin, K. Murari, E. A. Nanni, G. Resta, S. Tantawi, L. E. Zapata, F. X. Kärtner, and D. E. Moncton, “Compact x-ray source based on burst-mode inverse Compton scattering at 100 kHz,” Phys. Rev. Spec. Top. Accel. Beams 17(12), 120701 (2014).
[Crossref]

Dullin, C.

M. Krenkel, M. Töpperwien, C. Dullin, F. Alves, and T. Salditt, “Propagation-based phase-contrast tomography for high-resolution lung imaging with laboratory sources,” AIP Adv. 6(3), 035007 (2016).
[Crossref]

M. Krenkel, A. Markus, M. Bartels, C. Dullin, F. Alves, and T. Salditt, “Phase-contrast zoom tomography reveals precise locations of macrophages in mouse lungs,” Sci. Rep. 5(1), 9973 (2015).
[Crossref] [PubMed]

Endrizzi, M.

M. Endrizzi, “X-ray phase-contrast imaging,” Nucl. Instrum. Methods Phys. Res. A 878, 88–98 (2018).
[Crossref]

Erickson, D. W.

D. W. Erickson, J. R. Wells, G. M. Sturgeon, E. Samei, J. T. Dobbins, W. P. Segars, and J. Y. Lo, “Population of 224 realistic human subject-based computational breast phantoms,” Med. Phys. 43(1), 23–32 (2016).
[Crossref] [PubMed]

Feit, M. D.

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. (Berl.) 10(2), 129–160 (1976).
[Crossref]

Fleck, J. A.

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. (Berl.) 10(2), 129–160 (1976).
[Crossref]

Frank, S.

A. Khimchenko, C. Bikis, A. Pacureanu, S. E. Hieber, P. Thalmann, H. Deyhle, G. Schweighauser, J. Hench, S. Frank, M. Müller-Gerbl, G. Schulz, P. Cloetens, and B. Müller, “Hard x-ray nanoholotomography: large-scale, label-free, 3D neuroimaging beyond optical limit,” Adv. Sci. (Weinh.) 5(6), 1700694 (2018).
[Crossref] [PubMed]

Gao, D.

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative X-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207(Pt 2), 79–96 (2002).
[Crossref] [PubMed]

Gasilov, S.

T. Geith, E. Brun, A. Mittone, S. Gasilov, L. Weber, S. Adam-Neumair, A. Bravin, M. Reiser, P. Coan, and A. Horng, “Quantitative Assessment of Degenerative Cartilage and Subchondral Bony Lesions in a Preserved Cadaveric Knee: Propagation-Based Phase-Contrast CT Versus Conventional MRI and CT,” AJR Am. J. Roentgenol. 210(6), 1317–1322 (2018).
[Crossref] [PubMed]

A. Horng, E. Brun, A. Mittone, S. Gasilov, L. Weber, T. Geith, S. Adam-Neumair, S. D. Auweter, A. Bravin, M. F. Reiser, and P. Coan, “Cartilage and soft tissue imaging using X-rays: propagation-based phase-contrast computed tomography of the human knee in comparison with clinical imaging techniques and histology,” Invest. Radiol. 49(9), 627–634 (2014).
[Crossref] [PubMed]

Gbur, G.

Geith, T.

T. Geith, E. Brun, A. Mittone, S. Gasilov, L. Weber, S. Adam-Neumair, A. Bravin, M. Reiser, P. Coan, and A. Horng, “Quantitative Assessment of Degenerative Cartilage and Subchondral Bony Lesions in a Preserved Cadaveric Knee: Propagation-Based Phase-Contrast CT Versus Conventional MRI and CT,” AJR Am. J. Roentgenol. 210(6), 1317–1322 (2018).
[Crossref] [PubMed]

A. Horng, E. Brun, A. Mittone, S. Gasilov, L. Weber, T. Geith, S. Adam-Neumair, S. D. Auweter, A. Bravin, M. F. Reiser, and P. Coan, “Cartilage and soft tissue imaging using X-rays: propagation-based phase-contrast computed tomography of the human knee in comparison with clinical imaging techniques and histology,” Invest. Radiol. 49(9), 627–634 (2014).
[Crossref] [PubMed]

Godden, T. M.

Gouesbet, G.

G. Gouesbet, J. A. Lock, and G. Grehan, “Generalized Lorenz–Mie theories and description of electromagnetic arbitrary shaped beams: localized approximations and localized beam models, a review,” J. Quant. Spectrosc. Radiat. Transf. 112(1), 1–27 (2011).
[Crossref]

J. A. Lock and G. Gouesbet, “Generalized Lorenz–Mie theory and applications,” J. Quant. Spectrosc. Radiat. Transf. 110(11), 800–807 (2009).
[Crossref]

Goy, A.

J. Lim, A. Goy, M. H. Shoreh, M. Unser, and D. Psaltis, “Learning tomography assessed using Mie theory,” Phys. Rev. Appl. 9(3), 34027 (2018).
[Crossref]

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical tomographic image reconstruction based on beam propagation and sparse regularization,” IEEE Trans. Comput. Imaging 2(1), 59–70 (2016).
[Crossref]

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “A learning approach to optical tomography,” Optica 2(6), 517–522 (2015).
[Crossref]

Graves, W. S.

Y. Sung, R. Gupta, B. Nelson, S. Leng, C. H. McCollough, and W. S. Graves, “Phase-contrast imaging with a compact x-ray light source: system design,” J. Med. Imaging (Bellingham) 4(4), 043503 (2017).
[Crossref] [PubMed]

W. S. Graves, J. Bessuille, P. Brown, S. Carbajo, V. Dolgashev, K.-H. Hong, E. Ihloff, B. Khaykovich, H. Lin, K. Murari, E. A. Nanni, G. Resta, S. Tantawi, L. E. Zapata, F. X. Kärtner, and D. E. Moncton, “Compact x-ray source based on burst-mode inverse Compton scattering at 100 kHz,” Phys. Rev. Spec. Top. Accel. Beams 17(12), 120701 (2014).
[Crossref]

Grehan, G.

G. Gouesbet, J. A. Lock, and G. Grehan, “Generalized Lorenz–Mie theories and description of electromagnetic arbitrary shaped beams: localized approximations and localized beam models, a review,” J. Quant. Spectrosc. Radiat. Transf. 112(1), 1–27 (2011).
[Crossref]

Griffith, R. V.

D. R. White, R. V. Griffith, and I. J. Wilson, “ICRU Report 46: photon, electron, proton, and neutron interaction data for body tissues,” J. ICRUos24(1), (1992).

Grimal, Q.

M. Langer, A. Pacureanu, H. Suhonen, Q. Grimal, P. Cloetens, and F. Peyrin, “X-ray phase nanotomography resolves the 3D human bone ultrastructure,” PLoS One 7(8), e35691 (2012).
[Crossref] [PubMed]

Guigay, J. P.

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

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75(19), 2912–2914 (1999).
[Crossref]

Guizar-Sicairos, M.

Gullikson, E. M.

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(2), 181–342 (1993).
[Crossref]

Gupta, R.

Y. Sung, R. Gupta, B. Nelson, S. Leng, C. H. McCollough, and W. S. Graves, “Phase-contrast imaging with a compact x-ray light source: system design,” J. Med. Imaging (Bellingham) 4(4), 043503 (2017).
[Crossref] [PubMed]

Y. Sung, W. P. Segars, A. Pan, M. Ando, C. J. R. Sheppard, and R. Gupta, “Realistic wave-optics simulation of X-ray phase-contrast imaging at a human scale,” Sci. Rep. 5(1), 12011 (2015).
[Crossref] [PubMed]

Y. Sung, C. J. R. Sheppard, G. Barbastathis, M. Ando, and R. Gupta, “Full-wave approach for x-ray phase imaging,” Opt. Express 21(15), 17547–17557 (2013).
[Crossref] [PubMed]

Gureyev, T. E.

S. T. Taba, T. E. Gureyev, M. Alakhras, S. Lewis, D. Lockie, and P. C. Brennan, “X-ray phase-contrast technology in breast imaging: principles, options, and clinical application,” AJR Am. J. Roentgenol. 211(1), 133–145 (2018).
[Crossref] [PubMed]

T. E. Gureyev, S. C. Mayo, D. E. Myers, Y. I. Nesterets, D. M. Paganin, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “Refracting Röntgen’s rays: propagation-based x-ray phase contrast for biomedical imaging,” J. Appl. Phys. 105(10), 102005 (2009).
[Crossref]

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206(Pt 1), 33–40 (2002).
[Crossref] [PubMed]

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative X-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207(Pt 2), 79–96 (2002).
[Crossref] [PubMed]

T. E. Gureyev and K. A. Nugent, “Phase retrieval with the transport-of-intensity equation. II. Orthogonal series solution for nonuniform illumination,” J. Opt. Soc. Am. A 13(8), 1670–1682 (1996).
[Crossref]

Hashimoto, K.

G. Shinohara, K. Morita, M. Hoshino, Y. Ko, T. Tsukube, Y. Kaneko, H. Morishita, Y. Oshima, H. Matsuhisa, R. Iwaki, M. Takahashi, T. Matsuyama, K. Hashimoto, and N. Yagi, “Three dimensional visualization of human cardiac conduction tissue in whole heart specimens by high-resolution phase-contrast CT imaging using synchrotron radiation,” World J. Pediatr. Congenit. Heart Surg. 7(6), 700–705 (2016).
[Crossref] [PubMed]

Hench, J.

A. Khimchenko, C. Bikis, A. Pacureanu, S. E. Hieber, P. Thalmann, H. Deyhle, G. Schweighauser, J. Hench, S. Frank, M. Müller-Gerbl, G. Schulz, P. Cloetens, and B. Müller, “Hard x-ray nanoholotomography: large-scale, label-free, 3D neuroimaging beyond optical limit,” Adv. Sci. (Weinh.) 5(6), 1700694 (2018).
[Crossref] [PubMed]

Henke, B. L.

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(2), 181–342 (1993).
[Crossref]

Herminghaus, S.

A. Beerlink, S. Thutupalli, M. Mell, M. Bartels, P. Cloetens, S. Herminghaus, and T. Salditt, “X-ray propagation imaging of a lipid bilayer in solution,” Soft Matter 8(17), 4595–4601 (2012).
[Crossref]

Hieber, S. E.

A. Khimchenko, C. Bikis, A. Pacureanu, S. E. Hieber, P. Thalmann, H. Deyhle, G. Schweighauser, J. Hench, S. Frank, M. Müller-Gerbl, G. Schulz, P. Cloetens, and B. Müller, “Hard x-ray nanoholotomography: large-scale, label-free, 3D neuroimaging beyond optical limit,” Adv. Sci. (Weinh.) 5(6), 1700694 (2018).
[Crossref] [PubMed]

Hong, K.-H.

W. S. Graves, J. Bessuille, P. Brown, S. Carbajo, V. Dolgashev, K.-H. Hong, E. Ihloff, B. Khaykovich, H. Lin, K. Murari, E. A. Nanni, G. Resta, S. Tantawi, L. E. Zapata, F. X. Kärtner, and D. E. Moncton, “Compact x-ray source based on burst-mode inverse Compton scattering at 100 kHz,” Phys. Rev. Spec. Top. Accel. Beams 17(12), 120701 (2014).
[Crossref]

Hooper, S. B.

L. C. P. Croton, K. S. Morgan, D. M. Paganin, L. T. Kerr, M. J. Wallace, K. J. Crossley, S. L. Miller, N. Yagi, K. Uesugi, S. B. Hooper, and M. J. Kitchen, “In situ phase contrast X-ray brain CT,” Sci. Rep. 8(1), 11412 (2018).
[Crossref] [PubMed]

Horng, A.

T. Geith, E. Brun, A. Mittone, S. Gasilov, L. Weber, S. Adam-Neumair, A. Bravin, M. Reiser, P. Coan, and A. Horng, “Quantitative Assessment of Degenerative Cartilage and Subchondral Bony Lesions in a Preserved Cadaveric Knee: Propagation-Based Phase-Contrast CT Versus Conventional MRI and CT,” AJR Am. J. Roentgenol. 210(6), 1317–1322 (2018).
[Crossref] [PubMed]

A. Horng, E. Brun, A. Mittone, S. Gasilov, L. Weber, T. Geith, S. Adam-Neumair, S. D. Auweter, A. Bravin, M. F. Reiser, and P. Coan, “Cartilage and soft tissue imaging using X-rays: propagation-based phase-contrast computed tomography of the human knee in comparison with clinical imaging techniques and histology,” Invest. Radiol. 49(9), 627–634 (2014).
[Crossref] [PubMed]

Hoshino, M.

G. Shinohara, K. Morita, M. Hoshino, Y. Ko, T. Tsukube, Y. Kaneko, H. Morishita, Y. Oshima, H. Matsuhisa, R. Iwaki, M. Takahashi, T. Matsuyama, K. Hashimoto, and N. Yagi, “Three dimensional visualization of human cardiac conduction tissue in whole heart specimens by high-resolution phase-contrast CT imaging using synchrotron radiation,” World J. Pediatr. Congenit. Heart Surg. 7(6), 700–705 (2016).
[Crossref] [PubMed]

Humphry, M. J.

Ihloff, E.

W. S. Graves, J. Bessuille, P. Brown, S. Carbajo, V. Dolgashev, K.-H. Hong, E. Ihloff, B. Khaykovich, H. Lin, K. Murari, E. A. Nanni, G. Resta, S. Tantawi, L. E. Zapata, F. X. Kärtner, and D. E. Moncton, “Compact x-ray source based on burst-mode inverse Compton scattering at 100 kHz,” Phys. Rev. Spec. Top. Accel. Beams 17(12), 120701 (2014).
[Crossref]

Ishikawa, T.

J. Miao, T. Ishikawa, I. K. Robinson, and M. M. Murnane, “Beyond crystallography: diffractive imaging using coherent x-ray light sources,” Science 348(6234), 530–535 (2015).
[Crossref] [PubMed]

Iwaki, R.

G. Shinohara, K. Morita, M. Hoshino, Y. Ko, T. Tsukube, Y. Kaneko, H. Morishita, Y. Oshima, H. Matsuhisa, R. Iwaki, M. Takahashi, T. Matsuyama, K. Hashimoto, and N. Yagi, “Three dimensional visualization of human cardiac conduction tissue in whole heart specimens by high-resolution phase-contrast CT imaging using synchrotron radiation,” World J. Pediatr. Congenit. Heart Surg. 7(6), 700–705 (2016).
[Crossref] [PubMed]

Jacobsen, C.

Kachelriess, M.

S. Steckmann, M. Knaup, and M. Kachelriess, “Algorithm for hyperfast cone-beam spiral backprojection,” Comput. Methods Programs Biomed. 98(3), 253–260 (2010).
[Crossref] [PubMed]

Kahnert, F. M.

F. M. Kahnert, “Numerical methods in electromagnetic scattering theory,” J. Quant. Spectrosc. Radiat. Transf. 79–80(1), 775–824 (2003).
[Crossref]

Kalender, W. A.

M. Beister, D. Kolditz, and W. A. Kalender, “Iterative reconstruction methods in X-ray CT,” Phys. Med. 28(2), 94–108 (2012).
[Crossref] [PubMed]

Kamilov, U. S.

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical tomographic image reconstruction based on beam propagation and sparse regularization,” IEEE Trans. Comput. Imaging 2(1), 59–70 (2016).
[Crossref]

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “A learning approach to optical tomography,” Optica 2(6), 517–522 (2015).
[Crossref]

Kaneko, Y.

G. Shinohara, K. Morita, M. Hoshino, Y. Ko, T. Tsukube, Y. Kaneko, H. Morishita, Y. Oshima, H. Matsuhisa, R. Iwaki, M. Takahashi, T. Matsuyama, K. Hashimoto, and N. Yagi, “Three dimensional visualization of human cardiac conduction tissue in whole heart specimens by high-resolution phase-contrast CT imaging using synchrotron radiation,” World J. Pediatr. Congenit. Heart Surg. 7(6), 700–705 (2016).
[Crossref] [PubMed]

Kärtner, F. X.

W. S. Graves, J. Bessuille, P. Brown, S. Carbajo, V. Dolgashev, K.-H. Hong, E. Ihloff, B. Khaykovich, H. Lin, K. Murari, E. A. Nanni, G. Resta, S. Tantawi, L. E. Zapata, F. X. Kärtner, and D. E. Moncton, “Compact x-ray source based on burst-mode inverse Compton scattering at 100 kHz,” Phys. Rev. Spec. Top. Accel. Beams 17(12), 120701 (2014).
[Crossref]

Kerr, L. T.

L. C. P. Croton, K. S. Morgan, D. M. Paganin, L. T. Kerr, M. J. Wallace, K. J. Crossley, S. L. Miller, N. Yagi, K. Uesugi, S. B. Hooper, and M. J. Kitchen, “In situ phase contrast X-ray brain CT,” Sci. Rep. 8(1), 11412 (2018).
[Crossref] [PubMed]

Khaykovich, B.

W. S. Graves, J. Bessuille, P. Brown, S. Carbajo, V. Dolgashev, K.-H. Hong, E. Ihloff, B. Khaykovich, H. Lin, K. Murari, E. A. Nanni, G. Resta, S. Tantawi, L. E. Zapata, F. X. Kärtner, and D. E. Moncton, “Compact x-ray source based on burst-mode inverse Compton scattering at 100 kHz,” Phys. Rev. Spec. Top. Accel. Beams 17(12), 120701 (2014).
[Crossref]

Khimchenko, A.

A. Khimchenko, C. Bikis, A. Pacureanu, S. E. Hieber, P. Thalmann, H. Deyhle, G. Schweighauser, J. Hench, S. Frank, M. Müller-Gerbl, G. Schulz, P. Cloetens, and B. Müller, “Hard x-ray nanoholotomography: large-scale, label-free, 3D neuroimaging beyond optical limit,” Adv. Sci. (Weinh.) 5(6), 1700694 (2018).
[Crossref] [PubMed]

Kiarashi, N.

G. M. Sturgeon, N. Kiarashi, J. Y. Lo, E. Samei, and W. P. Segars, “Finite-element modeling of compression and gravity on a population of breast phantoms for multimodality imaging simulation,” Med. Phys. 43(5), 2207–2217 (2016).
[Crossref] [PubMed]

Kienle, A.

J. Schäfer, S. C. Lee, and A. Kienle, “Calculation of the near fields for the scattering of electromagnetic waves by multiple infinite cylinders at perpendicular incidence,” J. Quant. Spectrosc. Radiat. Transf. 113(16), 2113–2123 (2012).
[Crossref]

Kitchen, M. J.

L. C. P. Croton, K. S. Morgan, D. M. Paganin, L. T. Kerr, M. J. Wallace, K. J. Crossley, S. L. Miller, N. Yagi, K. Uesugi, S. B. Hooper, and M. J. Kitchen, “In situ phase contrast X-ray brain CT,” Sci. Rep. 8(1), 11412 (2018).
[Crossref] [PubMed]

Knaup, M.

S. Steckmann, M. Knaup, and M. Kachelriess, “Algorithm for hyperfast cone-beam spiral backprojection,” Comput. Methods Programs Biomed. 98(3), 253–260 (2010).
[Crossref] [PubMed]

Ko, Y.

G. Shinohara, K. Morita, M. Hoshino, Y. Ko, T. Tsukube, Y. Kaneko, H. Morishita, Y. Oshima, H. Matsuhisa, R. Iwaki, M. Takahashi, T. Matsuyama, K. Hashimoto, and N. Yagi, “Three dimensional visualization of human cardiac conduction tissue in whole heart specimens by high-resolution phase-contrast CT imaging using synchrotron radiation,” World J. Pediatr. Congenit. Heart Surg. 7(6), 700–705 (2016).
[Crossref] [PubMed]

Kolditz, D.

M. Beister, D. Kolditz, and W. A. Kalender, “Iterative reconstruction methods in X-ray CT,” Phys. Med. 28(2), 94–108 (2012).
[Crossref] [PubMed]

Krenkel, M.

M. Krenkel, M. Töpperwien, C. Dullin, F. Alves, and T. Salditt, “Propagation-based phase-contrast tomography for high-resolution lung imaging with laboratory sources,” AIP Adv. 6(3), 035007 (2016).
[Crossref]

M. Bartels, M. Krenkel, P. Cloetens, W. Möbius, and T. Salditt, “Myelinated mouse nerves studied by X-ray phase contrast zoom tomography,” J. Struct. Biol. 192(3), 561–568 (2015).
[Crossref] [PubMed]

M. Krenkel, A. Markus, M. Bartels, C. Dullin, F. Alves, and T. Salditt, “Phase-contrast zoom tomography reveals precise locations of macrophages in mouse lungs,” Sci. Rep. 5(1), 9973 (2015).
[Crossref] [PubMed]

C. Olendrowitz, M. Bartels, M. Krenkel, A. Beerlink, R. Mokso, M. Sprung, and T. Salditt, “Phase-contrast x-ray imaging and tomography of the nematode Caenorhabditis elegans,” Phys. Med. Biol. 57(16), 5309–5323 (2012).
[Crossref] [PubMed]

Langer, M.

M. Langer and F. Peyrin, “3D X-ray ultra-microscopy of bone tissue,” Osteoporos. Int. 27(2), 441–455 (2016).
[Crossref] [PubMed]

M. Langer, A. Pacureanu, H. Suhonen, Q. Grimal, P. Cloetens, and F. Peyrin, “X-ray phase nanotomography resolves the 3D human bone ultrastructure,” PLoS One 7(8), e35691 (2012).
[Crossref] [PubMed]

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

Le Duc, G.

F. Pfeiffer, O. Bunk, C. David, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “High-resolution brain tumor visualization using three-dimensional x-ray phase contrast tomography,” Phys. Med. Biol. 52(23), 6923–6930 (2007).
[Crossref] [PubMed]

Lee, M.

Lee, S. C.

J. Schäfer, S. C. Lee, and A. Kienle, “Calculation of the near fields for the scattering of electromagnetic waves by multiple infinite cylinders at perpendicular incidence,” J. Quant. Spectrosc. Radiat. Transf. 113(16), 2113–2123 (2012).
[Crossref]

Lee, S.-C.

S.-C. Lee, “Dependent scattering of an obliquely incident plane wave by a collection of parallel cylinders,” J. Appl. Phys. 68(10), 4952–4957 (1990).
[Crossref]

Leng, S.

Y. Sung, R. Gupta, B. Nelson, S. Leng, C. H. McCollough, and W. S. Graves, “Phase-contrast imaging with a compact x-ray light source: system design,” J. Med. Imaging (Bellingham) 4(4), 043503 (2017).
[Crossref] [PubMed]

Lewis, S.

S. T. Taba, T. E. Gureyev, M. Alakhras, S. Lewis, D. Lockie, and P. C. Brennan, “X-ray phase-contrast technology in breast imaging: principles, options, and clinical application,” AJR Am. J. Roentgenol. 211(1), 133–145 (2018).
[Crossref] [PubMed]

Li, C. M.

C. M. Li, W. P. Segars, G. D. Tourassi, J. M. Boone, and J. T. Dobbins, “Methodology for generating a 3D computerized breast phantom from empirical data,” Med. Phys. 36(7), 3122–3131 (2009).
[Crossref] [PubMed]

Li, K.

Lim, J.

J. Lim, A. Goy, M. H. Shoreh, M. Unser, and D. Psaltis, “Learning tomography assessed using Mie theory,” Phys. Rev. Appl. 9(3), 34027 (2018).
[Crossref]

Lin, H.

W. S. Graves, J. Bessuille, P. Brown, S. Carbajo, V. Dolgashev, K.-H. Hong, E. Ihloff, B. Khaykovich, H. Lin, K. Murari, E. A. Nanni, G. Resta, S. Tantawi, L. E. Zapata, F. X. Kärtner, and D. E. Moncton, “Compact x-ray source based on burst-mode inverse Compton scattering at 100 kHz,” Phys. Rev. Spec. Top. Accel. Beams 17(12), 120701 (2014).
[Crossref]

Liu, H.

X. Wu and H. Liu, “A general theoretical formalism for X-ray phase contrast imaging,” J. XRay Sci. Technol. 11(1), 33–42 (2003).
[PubMed]

Lo, J. Y.

D. W. Erickson, J. R. Wells, G. M. Sturgeon, E. Samei, J. T. Dobbins, W. P. Segars, and J. Y. Lo, “Population of 224 realistic human subject-based computational breast phantoms,” Med. Phys. 43(1), 23–32 (2016).
[Crossref] [PubMed]

G. M. Sturgeon, N. Kiarashi, J. Y. Lo, E. Samei, and W. P. Segars, “Finite-element modeling of compression and gravity on a population of breast phantoms for multimodality imaging simulation,” Med. Phys. 43(5), 2207–2217 (2016).
[Crossref] [PubMed]

Lock, J. A.

G. Gouesbet, J. A. Lock, and G. Grehan, “Generalized Lorenz–Mie theories and description of electromagnetic arbitrary shaped beams: localized approximations and localized beam models, a review,” J. Quant. Spectrosc. Radiat. Transf. 112(1), 1–27 (2011).
[Crossref]

J. A. Lock and G. Gouesbet, “Generalized Lorenz–Mie theory and applications,” J. Quant. Spectrosc. Radiat. Transf. 110(11), 800–807 (2009).
[Crossref]

Lockie, D.

S. T. Taba, T. E. Gureyev, M. Alakhras, S. Lewis, D. Lockie, and P. C. Brennan, “X-ray phase-contrast technology in breast imaging: principles, options, and clinical application,” AJR Am. J. Roentgenol. 211(1), 133–145 (2018).
[Crossref] [PubMed]

Ludwig, W.

R. Mokso, P. Cloetens, E. Maire, W. Ludwig, and J. Y. Buffière, “Nanoscale zoom tomography with hard x rays using Kirkpatrick-Baez optics,” Appl. Phys. Lett. 90(14), 144104 (2007).
[Crossref]

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75(19), 2912–2914 (1999).
[Crossref]

Ma, X.

Mackowski, D. W.

M. I. Mishchenko, L. D. Travis, and D. W. Mackowski, “T-matrix computations of light scattering nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transf. 55(5), 535–575 (1996).
[Crossref]

Mader, K.

Maiden, A. M.

Maire, E.

E. Maire and P. J. Withers, “Quantitative x-ray tomography,” Int. Mater. Rev. 59(1), 1–43 (2014).
[Crossref]

E. Maire and P. J. Withers, “Quantitative X-ray tomography,” Int. Mater. Rev. 59(1), 1–43 (2014).
[Crossref]

R. Mokso, P. Cloetens, E. Maire, W. Ludwig, and J. Y. Buffière, “Nanoscale zoom tomography with hard x rays using Kirkpatrick-Baez optics,” Appl. Phys. Lett. 90(14), 144104 (2007).
[Crossref]

Markus, A.

M. Krenkel, A. Markus, M. Bartels, C. Dullin, F. Alves, and T. Salditt, “Phase-contrast zoom tomography reveals precise locations of macrophages in mouse lungs,” Sci. Rep. 5(1), 9973 (2015).
[Crossref] [PubMed]

Matsuhisa, H.

G. Shinohara, K. Morita, M. Hoshino, Y. Ko, T. Tsukube, Y. Kaneko, H. Morishita, Y. Oshima, H. Matsuhisa, R. Iwaki, M. Takahashi, T. Matsuyama, K. Hashimoto, and N. Yagi, “Three dimensional visualization of human cardiac conduction tissue in whole heart specimens by high-resolution phase-contrast CT imaging using synchrotron radiation,” World J. Pediatr. Congenit. Heart Surg. 7(6), 700–705 (2016).
[Crossref] [PubMed]

Matsuyama, T.

G. Shinohara, K. Morita, M. Hoshino, Y. Ko, T. Tsukube, Y. Kaneko, H. Morishita, Y. Oshima, H. Matsuhisa, R. Iwaki, M. Takahashi, T. Matsuyama, K. Hashimoto, and N. Yagi, “Three dimensional visualization of human cardiac conduction tissue in whole heart specimens by high-resolution phase-contrast CT imaging using synchrotron radiation,” World J. Pediatr. Congenit. Heart Surg. 7(6), 700–705 (2016).
[Crossref] [PubMed]

Mayo, S. C.

T. E. Gureyev, S. C. Mayo, D. E. Myers, Y. I. Nesterets, D. M. Paganin, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “Refracting Röntgen’s rays: propagation-based x-ray phase contrast for biomedical imaging,” J. Appl. Phys. 105(10), 102005 (2009).
[Crossref]

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206(Pt 1), 33–40 (2002).
[Crossref] [PubMed]

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative X-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207(Pt 2), 79–96 (2002).
[Crossref] [PubMed]

McCollough, C. H.

Y. Sung, R. Gupta, B. Nelson, S. Leng, C. H. McCollough, and W. S. Graves, “Phase-contrast imaging with a compact x-ray light source: system design,” J. Med. Imaging (Bellingham) 4(4), 043503 (2017).
[Crossref] [PubMed]

McNulty, I.

Mell, M.

A. Beerlink, S. Thutupalli, M. Mell, M. Bartels, P. Cloetens, S. Herminghaus, and T. Salditt, “X-ray propagation imaging of a lipid bilayer in solution,” Soft Matter 8(17), 4595–4601 (2012).
[Crossref]

Menzel, A.

Miao, J.

J. Miao, T. Ishikawa, I. K. Robinson, and M. M. Murnane, “Beyond crystallography: diffractive imaging using coherent x-ray light sources,” Science 348(6234), 530–535 (2015).
[Crossref] [PubMed]

Miller, P. R.

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative X-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207(Pt 2), 79–96 (2002).
[Crossref] [PubMed]

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206(Pt 1), 33–40 (2002).
[Crossref] [PubMed]

Miller, S. L.

L. C. P. Croton, K. S. Morgan, D. M. Paganin, L. T. Kerr, M. J. Wallace, K. J. Crossley, S. L. Miller, N. Yagi, K. Uesugi, S. B. Hooper, and M. J. Kitchen, “In situ phase contrast X-ray brain CT,” Sci. Rep. 8(1), 11412 (2018).
[Crossref] [PubMed]

Mishchenko, M. I.

M. I. Mishchenko, L. D. Travis, and D. W. Mackowski, “T-matrix computations of light scattering nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transf. 55(5), 535–575 (1996).
[Crossref]

M. I. Mishchenko, “Light scattering by randomly oriented axially symmetric particles,” J. Opt. Soc. Am. A 8(6), 871–882 (1991).
[Crossref]

Mittone, A.

T. Geith, E. Brun, A. Mittone, S. Gasilov, L. Weber, S. Adam-Neumair, A. Bravin, M. Reiser, P. Coan, and A. Horng, “Quantitative Assessment of Degenerative Cartilage and Subchondral Bony Lesions in a Preserved Cadaveric Knee: Propagation-Based Phase-Contrast CT Versus Conventional MRI and CT,” AJR Am. J. Roentgenol. 210(6), 1317–1322 (2018).
[Crossref] [PubMed]

A. Horng, E. Brun, A. Mittone, S. Gasilov, L. Weber, T. Geith, S. Adam-Neumair, S. D. Auweter, A. Bravin, M. F. Reiser, and P. Coan, “Cartilage and soft tissue imaging using X-rays: propagation-based phase-contrast computed tomography of the human knee in comparison with clinical imaging techniques and histology,” Invest. Radiol. 49(9), 627–634 (2014).
[Crossref] [PubMed]

Möbius, W.

M. Bartels, M. Krenkel, P. Cloetens, W. Möbius, and T. Salditt, “Myelinated mouse nerves studied by X-ray phase contrast zoom tomography,” J. Struct. Biol. 192(3), 561–568 (2015).
[Crossref] [PubMed]

Mokso, R.

C. Olendrowitz, M. Bartels, M. Krenkel, A. Beerlink, R. Mokso, M. Sprung, and T. Salditt, “Phase-contrast x-ray imaging and tomography of the nematode Caenorhabditis elegans,” Phys. Med. Biol. 57(16), 5309–5323 (2012).
[Crossref] [PubMed]

R. Mokso, P. Cloetens, E. Maire, W. Ludwig, and J. Y. Buffière, “Nanoscale zoom tomography with hard x rays using Kirkpatrick-Baez optics,” Appl. Phys. Lett. 90(14), 144104 (2007).
[Crossref]

Moncton, D. E.

W. S. Graves, J. Bessuille, P. Brown, S. Carbajo, V. Dolgashev, K.-H. Hong, E. Ihloff, B. Khaykovich, H. Lin, K. Murari, E. A. Nanni, G. Resta, S. Tantawi, L. E. Zapata, F. X. Kärtner, and D. E. Moncton, “Compact x-ray source based on burst-mode inverse Compton scattering at 100 kHz,” Phys. Rev. Spec. Top. Accel. Beams 17(12), 120701 (2014).
[Crossref]

Moodie, A. F.

J. M. Cowley and A. F. Moodie, “The scattering of electrons by atoms and crystals. I. A new theoretical approach,” Acta Crystallogr. 10(10), 609–619 (1957).
[Crossref]

Moore, N. J.

Morgan, K. S.

L. C. P. Croton, K. S. Morgan, D. M. Paganin, L. T. Kerr, M. J. Wallace, K. J. Crossley, S. L. Miller, N. Yagi, K. Uesugi, S. B. Hooper, and M. J. Kitchen, “In situ phase contrast X-ray brain CT,” Sci. Rep. 8(1), 11412 (2018).
[Crossref] [PubMed]

K. S. Morgan, K. K. W. Siu, and D. M. Paganin, “The projection approximation and edge contrast for x-ray propagation-based phase contrast imaging of a cylindrical edge,” Opt. Express 18(10), 9865–9878 (2010).
[Crossref] [PubMed]

K. S. Morgan, K. K. W. Siu, and D. M. Paganin, “The projection approximation versus an exact solution for x-ray phase contrast imaging, with a plane wave scattered by a dielectric cylinder,” Opt. Commun. 283(23), 4601–4608 (2010).
[Crossref]

Morishita, H.

G. Shinohara, K. Morita, M. Hoshino, Y. Ko, T. Tsukube, Y. Kaneko, H. Morishita, Y. Oshima, H. Matsuhisa, R. Iwaki, M. Takahashi, T. Matsuyama, K. Hashimoto, and N. Yagi, “Three dimensional visualization of human cardiac conduction tissue in whole heart specimens by high-resolution phase-contrast CT imaging using synchrotron radiation,” World J. Pediatr. Congenit. Heart Surg. 7(6), 700–705 (2016).
[Crossref] [PubMed]

Morita, K.

G. Shinohara, K. Morita, M. Hoshino, Y. Ko, T. Tsukube, Y. Kaneko, H. Morishita, Y. Oshima, H. Matsuhisa, R. Iwaki, M. Takahashi, T. Matsuyama, K. Hashimoto, and N. Yagi, “Three dimensional visualization of human cardiac conduction tissue in whole heart specimens by high-resolution phase-contrast CT imaging using synchrotron radiation,” World J. Pediatr. Congenit. Heart Surg. 7(6), 700–705 (2016).
[Crossref] [PubMed]

Morris, J. R.

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. (Berl.) 10(2), 129–160 (1976).
[Crossref]

Müller, B.

A. Khimchenko, C. Bikis, A. Pacureanu, S. E. Hieber, P. Thalmann, H. Deyhle, G. Schweighauser, J. Hench, S. Frank, M. Müller-Gerbl, G. Schulz, P. Cloetens, and B. Müller, “Hard x-ray nanoholotomography: large-scale, label-free, 3D neuroimaging beyond optical limit,” Adv. Sci. (Weinh.) 5(6), 1700694 (2018).
[Crossref] [PubMed]

Müller-Gerbl, M.

A. Khimchenko, C. Bikis, A. Pacureanu, S. E. Hieber, P. Thalmann, H. Deyhle, G. Schweighauser, J. Hench, S. Frank, M. Müller-Gerbl, G. Schulz, P. Cloetens, and B. Müller, “Hard x-ray nanoholotomography: large-scale, label-free, 3D neuroimaging beyond optical limit,” Adv. Sci. (Weinh.) 5(6), 1700694 (2018).
[Crossref] [PubMed]

Murari, K.

W. S. Graves, J. Bessuille, P. Brown, S. Carbajo, V. Dolgashev, K.-H. Hong, E. Ihloff, B. Khaykovich, H. Lin, K. Murari, E. A. Nanni, G. Resta, S. Tantawi, L. E. Zapata, F. X. Kärtner, and D. E. Moncton, “Compact x-ray source based on burst-mode inverse Compton scattering at 100 kHz,” Phys. Rev. Spec. Top. Accel. Beams 17(12), 120701 (2014).
[Crossref]

Murnane, M. M.

J. Miao, T. Ishikawa, I. K. Robinson, and M. M. Murnane, “Beyond crystallography: diffractive imaging using coherent x-ray light sources,” Science 348(6234), 530–535 (2015).
[Crossref] [PubMed]

Myers, D. E.

T. E. Gureyev, S. C. Mayo, D. E. Myers, Y. I. Nesterets, D. M. Paganin, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “Refracting Röntgen’s rays: propagation-based x-ray phase contrast for biomedical imaging,” J. Appl. Phys. 105(10), 102005 (2009).
[Crossref]

Nanni, E. A.

W. S. Graves, J. Bessuille, P. Brown, S. Carbajo, V. Dolgashev, K.-H. Hong, E. Ihloff, B. Khaykovich, H. Lin, K. Murari, E. A. Nanni, G. Resta, S. Tantawi, L. E. Zapata, F. X. Kärtner, and D. E. Moncton, “Compact x-ray source based on burst-mode inverse Compton scattering at 100 kHz,” Phys. Rev. Spec. Top. Accel. Beams 17(12), 120701 (2014).
[Crossref]

Nelson, B.

Y. Sung, R. Gupta, B. Nelson, S. Leng, C. H. McCollough, and W. S. Graves, “Phase-contrast imaging with a compact x-ray light source: system design,” J. Med. Imaging (Bellingham) 4(4), 043503 (2017).
[Crossref] [PubMed]

Nesterets, Y. I.

T. E. Gureyev, S. C. Mayo, D. E. Myers, Y. I. Nesterets, D. M. Paganin, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “Refracting Röntgen’s rays: propagation-based x-ray phase contrast for biomedical imaging,” J. Appl. Phys. 105(10), 102005 (2009).
[Crossref]

Nilchian, M.

Nugent, K. A.

Olendrowitz, C.

C. Olendrowitz, M. Bartels, M. Krenkel, A. Beerlink, R. Mokso, M. Sprung, and T. Salditt, “Phase-contrast x-ray imaging and tomography of the nematode Caenorhabditis elegans,” Phys. Med. Biol. 57(16), 5309–5323 (2012).
[Crossref] [PubMed]

Oshima, Y.

G. Shinohara, K. Morita, M. Hoshino, Y. Ko, T. Tsukube, Y. Kaneko, H. Morishita, Y. Oshima, H. Matsuhisa, R. Iwaki, M. Takahashi, T. Matsuyama, K. Hashimoto, and N. Yagi, “Three dimensional visualization of human cardiac conduction tissue in whole heart specimens by high-resolution phase-contrast CT imaging using synchrotron radiation,” World J. Pediatr. Congenit. Heart Surg. 7(6), 700–705 (2016).
[Crossref] [PubMed]

Pacureanu, A.

A. Khimchenko, C. Bikis, A. Pacureanu, S. E. Hieber, P. Thalmann, H. Deyhle, G. Schweighauser, J. Hench, S. Frank, M. Müller-Gerbl, G. Schulz, P. Cloetens, and B. Müller, “Hard x-ray nanoholotomography: large-scale, label-free, 3D neuroimaging beyond optical limit,” Adv. Sci. (Weinh.) 5(6), 1700694 (2018).
[Crossref] [PubMed]

M. Langer, A. Pacureanu, H. Suhonen, Q. Grimal, P. Cloetens, and F. Peyrin, “X-ray phase nanotomography resolves the 3D human bone ultrastructure,” PLoS One 7(8), e35691 (2012).
[Crossref] [PubMed]

Paganin, D.

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative X-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207(Pt 2), 79–96 (2002).
[Crossref] [PubMed]

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206(Pt 1), 33–40 (2002).
[Crossref] [PubMed]

Paganin, D. M.

L. C. P. Croton, K. S. Morgan, D. M. Paganin, L. T. Kerr, M. J. Wallace, K. J. Crossley, S. L. Miller, N. Yagi, K. Uesugi, S. B. Hooper, and M. J. Kitchen, “In situ phase contrast X-ray brain CT,” Sci. Rep. 8(1), 11412 (2018).
[Crossref] [PubMed]

K. S. Morgan, K. K. W. Siu, and D. M. Paganin, “The projection approximation and edge contrast for x-ray propagation-based phase contrast imaging of a cylindrical edge,” Opt. Express 18(10), 9865–9878 (2010).
[Crossref] [PubMed]

K. S. Morgan, K. K. W. Siu, and D. M. Paganin, “The projection approximation versus an exact solution for x-ray phase contrast imaging, with a plane wave scattered by a dielectric cylinder,” Opt. Commun. 283(23), 4601–4608 (2010).
[Crossref]

T. E. Gureyev, S. C. Mayo, D. E. Myers, Y. I. Nesterets, D. M. Paganin, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “Refracting Röntgen’s rays: propagation-based x-ray phase contrast for biomedical imaging,” J. Appl. Phys. 105(10), 102005 (2009).
[Crossref]

Pan, A.

Y. Sung, W. P. Segars, A. Pan, M. Ando, C. J. R. Sheppard, and R. Gupta, “Realistic wave-optics simulation of X-ray phase-contrast imaging at a human scale,” Sci. Rep. 5(1), 12011 (2015).
[Crossref] [PubMed]

Pan, F.

Papadopoulos, I. N.

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical tomographic image reconstruction based on beam propagation and sparse regularization,” IEEE Trans. Comput. Imaging 2(1), 59–70 (2016).
[Crossref]

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “A learning approach to optical tomography,” Optica 2(6), 517–522 (2015).
[Crossref]

Park, Y.

Parry, D. J.

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative X-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207(Pt 2), 79–96 (2002).
[Crossref] [PubMed]

Peele, A. G.

Peyrin, F.

M. Langer and F. Peyrin, “3D X-ray ultra-microscopy of bone tissue,” Osteoporos. Int. 27(2), 441–455 (2016).
[Crossref] [PubMed]

M. Langer, A. Pacureanu, H. Suhonen, Q. Grimal, P. Cloetens, and F. Peyrin, “X-ray phase nanotomography resolves the 3D human bone ultrastructure,” PLoS One 7(8), e35691 (2012).
[Crossref] [PubMed]

Pfeifer, M. A.

Pfeiffer, F.

F. Pfeiffer, O. Bunk, C. David, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “High-resolution brain tumor visualization using three-dimensional x-ray phase contrast tomography,” Phys. Med. Biol. 52(23), 6923–6930 (2007).
[Crossref] [PubMed]

Pham, T.-A.

Pogany, A.

T. E. Gureyev, S. C. Mayo, D. E. Myers, Y. I. Nesterets, D. M. Paganin, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “Refracting Röntgen’s rays: propagation-based x-ray phase contrast for biomedical imaging,” J. Appl. Phys. 105(10), 102005 (2009).
[Crossref]

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative X-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207(Pt 2), 79–96 (2002).
[Crossref] [PubMed]

Psaltis, D.

J. Lim, A. Goy, M. H. Shoreh, M. Unser, and D. Psaltis, “Learning tomography assessed using Mie theory,” Phys. Rev. Appl. 9(3), 34027 (2018).
[Crossref]

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical tomographic image reconstruction based on beam propagation and sparse regularization,” IEEE Trans. Comput. Imaging 2(1), 59–70 (2016).
[Crossref]

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “A learning approach to optical tomography,” Optica 2(6), 517–522 (2015).
[Crossref]

Putkunz, C. T.

Quiney, H. M.

Reiser, M.

T. Geith, E. Brun, A. Mittone, S. Gasilov, L. Weber, S. Adam-Neumair, A. Bravin, M. Reiser, P. Coan, and A. Horng, “Quantitative Assessment of Degenerative Cartilage and Subchondral Bony Lesions in a Preserved Cadaveric Knee: Propagation-Based Phase-Contrast CT Versus Conventional MRI and CT,” AJR Am. J. Roentgenol. 210(6), 1317–1322 (2018).
[Crossref] [PubMed]

Reiser, M. F.

A. Horng, E. Brun, A. Mittone, S. Gasilov, L. Weber, T. Geith, S. Adam-Neumair, S. D. Auweter, A. Bravin, M. F. Reiser, and P. Coan, “Cartilage and soft tissue imaging using X-rays: propagation-based phase-contrast computed tomography of the human knee in comparison with clinical imaging techniques and histology,” Invest. Radiol. 49(9), 627–634 (2014).
[Crossref] [PubMed]

Resta, G.

W. S. Graves, J. Bessuille, P. Brown, S. Carbajo, V. Dolgashev, K.-H. Hong, E. Ihloff, B. Khaykovich, H. Lin, K. Murari, E. A. Nanni, G. Resta, S. Tantawi, L. E. Zapata, F. X. Kärtner, and D. E. Moncton, “Compact x-ray source based on burst-mode inverse Compton scattering at 100 kHz,” Phys. Rev. Spec. Top. Accel. Beams 17(12), 120701 (2014).
[Crossref]

Robinson, I. K.

J. Miao, T. Ishikawa, I. K. Robinson, and M. M. Murnane, “Beyond crystallography: diffractive imaging using coherent x-ray light sources,” Science 348(6234), 530–535 (2015).
[Crossref] [PubMed]

Rodenburg, J. M.

Salditt, T.

M. Krenkel, M. Töpperwien, C. Dullin, F. Alves, and T. Salditt, “Propagation-based phase-contrast tomography for high-resolution lung imaging with laboratory sources,” AIP Adv. 6(3), 035007 (2016).
[Crossref]

M. Krenkel, A. Markus, M. Bartels, C. Dullin, F. Alves, and T. Salditt, “Phase-contrast zoom tomography reveals precise locations of macrophages in mouse lungs,” Sci. Rep. 5(1), 9973 (2015).
[Crossref] [PubMed]

M. Bartels, M. Krenkel, P. Cloetens, W. Möbius, and T. Salditt, “Myelinated mouse nerves studied by X-ray phase contrast zoom tomography,” J. Struct. Biol. 192(3), 561–568 (2015).
[Crossref] [PubMed]

C. Olendrowitz, M. Bartels, M. Krenkel, A. Beerlink, R. Mokso, M. Sprung, and T. Salditt, “Phase-contrast x-ray imaging and tomography of the nematode Caenorhabditis elegans,” Phys. Med. Biol. 57(16), 5309–5323 (2012).
[Crossref] [PubMed]

A. Beerlink, S. Thutupalli, M. Mell, M. Bartels, P. Cloetens, S. Herminghaus, and T. Salditt, “X-ray propagation imaging of a lipid bilayer in solution,” Soft Matter 8(17), 4595–4601 (2012).
[Crossref]

Samei, E.

G. M. Sturgeon, N. Kiarashi, J. Y. Lo, E. Samei, and W. P. Segars, “Finite-element modeling of compression and gravity on a population of breast phantoms for multimodality imaging simulation,” Med. Phys. 43(5), 2207–2217 (2016).
[Crossref] [PubMed]

D. W. Erickson, J. R. Wells, G. M. Sturgeon, E. Samei, J. T. Dobbins, W. P. Segars, and J. Y. Lo, “Population of 224 realistic human subject-based computational breast phantoms,” Med. Phys. 43(1), 23–32 (2016).
[Crossref] [PubMed]

Schäfer, J.

J. Schäfer, S. C. Lee, and A. Kienle, “Calculation of the near fields for the scattering of electromagnetic waves by multiple infinite cylinders at perpendicular incidence,” J. Quant. Spectrosc. Radiat. Transf. 113(16), 2113–2123 (2012).
[Crossref]

Schlenker, M.

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75(19), 2912–2914 (1999).
[Crossref]

Schulz, G.

A. Khimchenko, C. Bikis, A. Pacureanu, S. E. Hieber, P. Thalmann, H. Deyhle, G. Schweighauser, J. Hench, S. Frank, M. Müller-Gerbl, G. Schulz, P. Cloetens, and B. Müller, “Hard x-ray nanoholotomography: large-scale, label-free, 3D neuroimaging beyond optical limit,” Adv. Sci. (Weinh.) 5(6), 1700694 (2018).
[Crossref] [PubMed]

Schweighauser, G.

A. Khimchenko, C. Bikis, A. Pacureanu, S. E. Hieber, P. Thalmann, H. Deyhle, G. Schweighauser, J. Hench, S. Frank, M. Müller-Gerbl, G. Schulz, P. Cloetens, and B. Müller, “Hard x-ray nanoholotomography: large-scale, label-free, 3D neuroimaging beyond optical limit,” Adv. Sci. (Weinh.) 5(6), 1700694 (2018).
[Crossref] [PubMed]

Segars, W. P.

D. W. Erickson, J. R. Wells, G. M. Sturgeon, E. Samei, J. T. Dobbins, W. P. Segars, and J. Y. Lo, “Population of 224 realistic human subject-based computational breast phantoms,” Med. Phys. 43(1), 23–32 (2016).
[Crossref] [PubMed]

G. M. Sturgeon, N. Kiarashi, J. Y. Lo, E. Samei, and W. P. Segars, “Finite-element modeling of compression and gravity on a population of breast phantoms for multimodality imaging simulation,” Med. Phys. 43(5), 2207–2217 (2016).
[Crossref] [PubMed]

Y. Sung, W. P. Segars, A. Pan, M. Ando, C. J. R. Sheppard, and R. Gupta, “Realistic wave-optics simulation of X-ray phase-contrast imaging at a human scale,” Sci. Rep. 5(1), 12011 (2015).
[Crossref] [PubMed]

C. M. Li, W. P. Segars, G. D. Tourassi, J. M. Boone, and J. T. Dobbins, “Methodology for generating a 3D computerized breast phantom from empirical data,” Med. Phys. 36(7), 3122–3131 (2009).
[Crossref] [PubMed]

Sheppard, C. J. R.

Y. Sung, W. P. Segars, A. Pan, M. Ando, C. J. R. Sheppard, and R. Gupta, “Realistic wave-optics simulation of X-ray phase-contrast imaging at a human scale,” Sci. Rep. 5(1), 12011 (2015).
[Crossref] [PubMed]

Y. Sung, C. J. R. Sheppard, G. Barbastathis, M. Ando, and R. Gupta, “Full-wave approach for x-ray phase imaging,” Opt. Express 21(15), 17547–17557 (2013).
[Crossref] [PubMed]

Shin, S.

Shinohara, G.

G. Shinohara, K. Morita, M. Hoshino, Y. Ko, T. Tsukube, Y. Kaneko, H. Morishita, Y. Oshima, H. Matsuhisa, R. Iwaki, M. Takahashi, T. Matsuyama, K. Hashimoto, and N. Yagi, “Three dimensional visualization of human cardiac conduction tissue in whole heart specimens by high-resolution phase-contrast CT imaging using synchrotron radiation,” World J. Pediatr. Congenit. Heart Surg. 7(6), 700–705 (2016).
[Crossref] [PubMed]

Shoreh, M. H.

J. Lim, A. Goy, M. H. Shoreh, M. Unser, and D. Psaltis, “Learning tomography assessed using Mie theory,” Phys. Rev. Appl. 9(3), 34027 (2018).
[Crossref]

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical tomographic image reconstruction based on beam propagation and sparse regularization,” IEEE Trans. Comput. Imaging 2(1), 59–70 (2016).
[Crossref]

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “A learning approach to optical tomography,” Optica 2(6), 517–522 (2015).
[Crossref]

Siu, K. K. W.

K. S. Morgan, K. K. W. Siu, and D. M. Paganin, “The projection approximation versus an exact solution for x-ray phase contrast imaging, with a plane wave scattered by a dielectric cylinder,” Opt. Commun. 283(23), 4601–4608 (2010).
[Crossref]

K. S. Morgan, K. K. W. Siu, and D. M. Paganin, “The projection approximation and edge contrast for x-ray propagation-based phase contrast imaging of a cylindrical edge,” Opt. Express 18(10), 9865–9878 (2010).
[Crossref] [PubMed]

Soubies, E.

Sprung, M.

C. Olendrowitz, M. Bartels, M. Krenkel, A. Beerlink, R. Mokso, M. Sprung, and T. Salditt, “Phase-contrast x-ray imaging and tomography of the nematode Caenorhabditis elegans,” Phys. Med. Biol. 57(16), 5309–5323 (2012).
[Crossref] [PubMed]

Stampanoni, M.

Steckmann, S.

S. Steckmann, M. Knaup, and M. Kachelriess, “Algorithm for hyperfast cone-beam spiral backprojection,” Comput. Methods Programs Biomed. 98(3), 253–260 (2010).
[Crossref] [PubMed]

Stevenson, A. W.

T. E. Gureyev, S. C. Mayo, D. E. Myers, Y. I. Nesterets, D. M. Paganin, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “Refracting Röntgen’s rays: propagation-based x-ray phase contrast for biomedical imaging,” J. Appl. Phys. 105(10), 102005 (2009).
[Crossref]

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative X-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207(Pt 2), 79–96 (2002).
[Crossref] [PubMed]

Sturgeon, G. M.

D. W. Erickson, J. R. Wells, G. M. Sturgeon, E. Samei, J. T. Dobbins, W. P. Segars, and J. Y. Lo, “Population of 224 realistic human subject-based computational breast phantoms,” Med. Phys. 43(1), 23–32 (2016).
[Crossref] [PubMed]

G. M. Sturgeon, N. Kiarashi, J. Y. Lo, E. Samei, and W. P. Segars, “Finite-element modeling of compression and gravity on a population of breast phantoms for multimodality imaging simulation,” Med. Phys. 43(5), 2207–2217 (2016).
[Crossref] [PubMed]

Suhonen, H.

M. Langer, A. Pacureanu, H. Suhonen, Q. Grimal, P. Cloetens, and F. Peyrin, “X-ray phase nanotomography resolves the 3D human bone ultrastructure,” PLoS One 7(8), e35691 (2012).
[Crossref] [PubMed]

Suman, R.

Sung, Y.

Y. Sung, R. Gupta, B. Nelson, S. Leng, C. H. McCollough, and W. S. Graves, “Phase-contrast imaging with a compact x-ray light source: system design,” J. Med. Imaging (Bellingham) 4(4), 043503 (2017).
[Crossref] [PubMed]

Y. Sung, W. P. Segars, A. Pan, M. Ando, C. J. R. Sheppard, and R. Gupta, “Realistic wave-optics simulation of X-ray phase-contrast imaging at a human scale,” Sci. Rep. 5(1), 12011 (2015).
[Crossref] [PubMed]

Y. Sung, C. J. R. Sheppard, G. Barbastathis, M. Ando, and R. Gupta, “Full-wave approach for x-ray phase imaging,” Opt. Express 21(15), 17547–17557 (2013).
[Crossref] [PubMed]

Y. Sung and G. Barbastathis, “Rytov approximation for x-ray phase imaging,” Opt. Express 21(3), 2674–2682 (2013).
[Crossref] [PubMed]

Suortti, P.

A. Bravin, P. Coan, and P. Suortti, “X-ray phase-contrast imaging: from pre-clinical applications towards clinics,” Phys. Med. Biol. 58(1), R1–R35 (2013).
[Crossref] [PubMed]

Taba, S. T.

S. T. Taba, T. E. Gureyev, M. Alakhras, S. Lewis, D. Lockie, and P. C. Brennan, “X-ray phase-contrast technology in breast imaging: principles, options, and clinical application,” AJR Am. J. Roentgenol. 211(1), 133–145 (2018).
[Crossref] [PubMed]

Takahashi, M.

G. Shinohara, K. Morita, M. Hoshino, Y. Ko, T. Tsukube, Y. Kaneko, H. Morishita, Y. Oshima, H. Matsuhisa, R. Iwaki, M. Takahashi, T. Matsuyama, K. Hashimoto, and N. Yagi, “Three dimensional visualization of human cardiac conduction tissue in whole heart specimens by high-resolution phase-contrast CT imaging using synchrotron radiation,” World J. Pediatr. Congenit. Heart Surg. 7(6), 700–705 (2016).
[Crossref] [PubMed]

Tam, W. G.

W. G. Tam, “Split-step Fourier-transform analysis for laser-pulse propagation in particulate media,” J. Opt. Soc. Am. A 72(10), 1311–1316 (1982).
[Crossref]

Tantawi, S.

W. S. Graves, J. Bessuille, P. Brown, S. Carbajo, V. Dolgashev, K.-H. Hong, E. Ihloff, B. Khaykovich, H. Lin, K. Murari, E. A. Nanni, G. Resta, S. Tantawi, L. E. Zapata, F. X. Kärtner, and D. E. Moncton, “Compact x-ray source based on burst-mode inverse Compton scattering at 100 kHz,” Phys. Rev. Spec. Top. Accel. Beams 17(12), 120701 (2014).
[Crossref]

Teague, M. R.

Thalmann, P.

A. Khimchenko, C. Bikis, A. Pacureanu, S. E. Hieber, P. Thalmann, H. Deyhle, G. Schweighauser, J. Hench, S. Frank, M. Müller-Gerbl, G. Schulz, P. Cloetens, and B. Müller, “Hard x-ray nanoholotomography: large-scale, label-free, 3D neuroimaging beyond optical limit,” Adv. Sci. (Weinh.) 5(6), 1700694 (2018).
[Crossref] [PubMed]

Thuering, T.

Thutupalli, S.

A. Beerlink, S. Thutupalli, M. Mell, M. Bartels, P. Cloetens, S. Herminghaus, and T. Salditt, “X-ray propagation imaging of a lipid bilayer in solution,” Soft Matter 8(17), 4595–4601 (2012).
[Crossref]

Tian, L.

Töpperwien, M.

M. Krenkel, M. Töpperwien, C. Dullin, F. Alves, and T. Salditt, “Propagation-based phase-contrast tomography for high-resolution lung imaging with laboratory sources,” AIP Adv. 6(3), 035007 (2016).
[Crossref]

Tourassi, G. D.

C. M. Li, W. P. Segars, G. D. Tourassi, J. M. Boone, and J. T. Dobbins, “Methodology for generating a 3D computerized breast phantom from empirical data,” Med. Phys. 36(7), 3122–3131 (2009).
[Crossref] [PubMed]

Travis, L. D.

M. I. Mishchenko, L. D. Travis, and D. W. Mackowski, “T-matrix computations of light scattering nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transf. 55(5), 535–575 (1996).
[Crossref]

Tsihrintzis, G. A.

G. A. Tsihrintzis and A. J. Devaney, “Higher order (nonlinear) diffraction tomography: inversion of the Rytov series,” IEEE Trans. Inf. Theory 46(5), 1748–1761 (2000).
[Crossref]

Tsukube, T.

G. Shinohara, K. Morita, M. Hoshino, Y. Ko, T. Tsukube, Y. Kaneko, H. Morishita, Y. Oshima, H. Matsuhisa, R. Iwaki, M. Takahashi, T. Matsuyama, K. Hashimoto, and N. Yagi, “Three dimensional visualization of human cardiac conduction tissue in whole heart specimens by high-resolution phase-contrast CT imaging using synchrotron radiation,” World J. Pediatr. Congenit. Heart Surg. 7(6), 700–705 (2016).
[Crossref] [PubMed]

Uesugi, K.

L. C. P. Croton, K. S. Morgan, D. M. Paganin, L. T. Kerr, M. J. Wallace, K. J. Crossley, S. L. Miller, N. Yagi, K. Uesugi, S. B. Hooper, and M. J. Kitchen, “In situ phase contrast X-ray brain CT,” Sci. Rep. 8(1), 11412 (2018).
[Crossref] [PubMed]

Unser, M.

Van Dyck, D.

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75(19), 2912–2914 (1999).
[Crossref]

Van Landuyt, J.

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75(19), 2912–2914 (1999).
[Crossref]

Vonesch, C.

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical tomographic image reconstruction based on beam propagation and sparse regularization,” IEEE Trans. Comput. Imaging 2(1), 59–70 (2016).
[Crossref]

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “A learning approach to optical tomography,” Optica 2(6), 517–522 (2015).
[Crossref]

Wallace, M. J.

L. C. P. Croton, K. S. Morgan, D. M. Paganin, L. T. Kerr, M. J. Wallace, K. J. Crossley, S. L. Miller, N. Yagi, K. Uesugi, S. B. Hooper, and M. J. Kitchen, “In situ phase contrast X-ray brain CT,” Sci. Rep. 8(1), 11412 (2018).
[Crossref] [PubMed]

Waller, L.

Wang, Z.

Waterman, P. C.

P. C. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53(8), 805–812 (1965).
[Crossref]

Weber, L.

T. Geith, E. Brun, A. Mittone, S. Gasilov, L. Weber, S. Adam-Neumair, A. Bravin, M. Reiser, P. Coan, and A. Horng, “Quantitative Assessment of Degenerative Cartilage and Subchondral Bony Lesions in a Preserved Cadaveric Knee: Propagation-Based Phase-Contrast CT Versus Conventional MRI and CT,” AJR Am. J. Roentgenol. 210(6), 1317–1322 (2018).
[Crossref] [PubMed]

A. Horng, E. Brun, A. Mittone, S. Gasilov, L. Weber, T. Geith, S. Adam-Neumair, S. D. Auweter, A. Bravin, M. F. Reiser, and P. Coan, “Cartilage and soft tissue imaging using X-rays: propagation-based phase-contrast computed tomography of the human knee in comparison with clinical imaging techniques and histology,” Invest. Radiol. 49(9), 627–634 (2014).
[Crossref] [PubMed]

Wells, J. R.

D. W. Erickson, J. R. Wells, G. M. Sturgeon, E. Samei, J. T. Dobbins, W. P. Segars, and J. Y. Lo, “Population of 224 realistic human subject-based computational breast phantoms,” Med. Phys. 43(1), 23–32 (2016).
[Crossref] [PubMed]

White, D. R.

D. R. White, R. V. Griffith, and I. J. Wilson, “ICRU Report 46: photon, electron, proton, and neutron interaction data for body tissues,” J. ICRUos24(1), (1992).

Wilkins, S. W.

T. E. Gureyev, S. C. Mayo, D. E. Myers, Y. I. Nesterets, D. M. Paganin, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “Refracting Röntgen’s rays: propagation-based x-ray phase contrast for biomedical imaging,” J. Appl. Phys. 105(10), 102005 (2009).
[Crossref]

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206(Pt 1), 33–40 (2002).
[Crossref] [PubMed]

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative X-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207(Pt 2), 79–96 (2002).
[Crossref] [PubMed]

Williams, G. J.

Wilson, I. J.

D. R. White, R. V. Griffith, and I. J. Wilson, “ICRU Report 46: photon, electron, proton, and neutron interaction data for body tissues,” J. ICRUos24(1), (1992).

Withers, P. J.

E. Maire and P. J. Withers, “Quantitative x-ray tomography,” Int. Mater. Rev. 59(1), 1–43 (2014).
[Crossref]

E. Maire and P. J. Withers, “Quantitative X-ray tomography,” Int. Mater. Rev. 59(1), 1–43 (2014).
[Crossref]

Wojcik, M.

Wolf, E.

Wu, X.

X. Wu and H. Liu, “A general theoretical formalism for X-ray phase contrast imaging,” J. XRay Sci. Technol. 11(1), 33–42 (2003).
[PubMed]

Xiao, W.

Yagi, N.

L. C. P. Croton, K. S. Morgan, D. M. Paganin, L. T. Kerr, M. J. Wallace, K. J. Crossley, S. L. Miller, N. Yagi, K. Uesugi, S. B. Hooper, and M. J. Kitchen, “In situ phase contrast X-ray brain CT,” Sci. Rep. 8(1), 11412 (2018).
[Crossref] [PubMed]

G. Shinohara, K. Morita, M. Hoshino, Y. Ko, T. Tsukube, Y. Kaneko, H. Morishita, Y. Oshima, H. Matsuhisa, R. Iwaki, M. Takahashi, T. Matsuyama, K. Hashimoto, and N. Yagi, “Three dimensional visualization of human cardiac conduction tissue in whole heart specimens by high-resolution phase-contrast CT imaging using synchrotron radiation,” World J. Pediatr. Congenit. Heart Surg. 7(6), 700–705 (2016).
[Crossref] [PubMed]

Zapata, L. E.

W. S. Graves, J. Bessuille, P. Brown, S. Carbajo, V. Dolgashev, K.-H. Hong, E. Ihloff, B. Khaykovich, H. Lin, K. Murari, E. A. Nanni, G. Resta, S. Tantawi, L. E. Zapata, F. X. Kärtner, and D. E. Moncton, “Compact x-ray source based on burst-mode inverse Compton scattering at 100 kHz,” Phys. Rev. Spec. Top. Accel. Beams 17(12), 120701 (2014).
[Crossref]

Acta Crystallogr. (1)

J. M. Cowley and A. F. Moodie, “The scattering of electrons by atoms and crystals. I. A new theoretical approach,” Acta Crystallogr. 10(10), 609–619 (1957).
[Crossref]

Adv. Sci. (Weinh.) (1)

A. Khimchenko, C. Bikis, A. Pacureanu, S. E. Hieber, P. Thalmann, H. Deyhle, G. Schweighauser, J. Hench, S. Frank, M. Müller-Gerbl, G. Schulz, P. Cloetens, and B. Müller, “Hard x-ray nanoholotomography: large-scale, label-free, 3D neuroimaging beyond optical limit,” Adv. Sci. (Weinh.) 5(6), 1700694 (2018).
[Crossref] [PubMed]

AIP Adv. (1)

M. Krenkel, M. Töpperwien, C. Dullin, F. Alves, and T. Salditt, “Propagation-based phase-contrast tomography for high-resolution lung imaging with laboratory sources,” AIP Adv. 6(3), 035007 (2016).
[Crossref]

AJR Am. J. Roentgenol. (2)

T. Geith, E. Brun, A. Mittone, S. Gasilov, L. Weber, S. Adam-Neumair, A. Bravin, M. Reiser, P. Coan, and A. Horng, “Quantitative Assessment of Degenerative Cartilage and Subchondral Bony Lesions in a Preserved Cadaveric Knee: Propagation-Based Phase-Contrast CT Versus Conventional MRI and CT,” AJR Am. J. Roentgenol. 210(6), 1317–1322 (2018).
[Crossref] [PubMed]

S. T. Taba, T. E. Gureyev, M. Alakhras, S. Lewis, D. Lockie, and P. C. Brennan, “X-ray phase-contrast technology in breast imaging: principles, options, and clinical application,” AJR Am. J. Roentgenol. 211(1), 133–145 (2018).
[Crossref] [PubMed]

Appl. Phys. (Berl.) (1)

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. (Berl.) 10(2), 129–160 (1976).
[Crossref]

Appl. Phys. Lett. (2)

R. Mokso, P. Cloetens, E. Maire, W. Ludwig, and J. Y. Buffière, “Nanoscale zoom tomography with hard x rays using Kirkpatrick-Baez optics,” Appl. Phys. Lett. 90(14), 144104 (2007).
[Crossref]

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75(19), 2912–2914 (1999).
[Crossref]

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(2), 181–342 (1993).
[Crossref]

Biomed. Opt. Express (1)

Comput. Methods Programs Biomed. (1)

S. Steckmann, M. Knaup, and M. Kachelriess, “Algorithm for hyperfast cone-beam spiral backprojection,” Comput. Methods Programs Biomed. 98(3), 253–260 (2010).
[Crossref] [PubMed]

IEEE Trans. Comput. Imaging (1)

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical tomographic image reconstruction based on beam propagation and sparse regularization,” IEEE Trans. Comput. Imaging 2(1), 59–70 (2016).
[Crossref]

IEEE Trans. Inf. Theory (1)

G. A. Tsihrintzis and A. J. Devaney, “Higher order (nonlinear) diffraction tomography: inversion of the Rytov series,” IEEE Trans. Inf. Theory 46(5), 1748–1761 (2000).
[Crossref]

Int. Mater. Rev. (2)

E. Maire and P. J. Withers, “Quantitative x-ray tomography,” Int. Mater. Rev. 59(1), 1–43 (2014).
[Crossref]

E. Maire and P. J. Withers, “Quantitative X-ray tomography,” Int. Mater. Rev. 59(1), 1–43 (2014).
[Crossref]

Invest. Radiol. (1)

A. Horng, E. Brun, A. Mittone, S. Gasilov, L. Weber, T. Geith, S. Adam-Neumair, S. D. Auweter, A. Bravin, M. F. Reiser, and P. Coan, “Cartilage and soft tissue imaging using X-rays: propagation-based phase-contrast computed tomography of the human knee in comparison with clinical imaging techniques and histology,” Invest. Radiol. 49(9), 627–634 (2014).
[Crossref] [PubMed]

J. Appl. Phys. (2)

T. E. Gureyev, S. C. Mayo, D. E. Myers, Y. I. Nesterets, D. M. Paganin, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “Refracting Röntgen’s rays: propagation-based x-ray phase contrast for biomedical imaging,” J. Appl. Phys. 105(10), 102005 (2009).
[Crossref]

S.-C. Lee, “Dependent scattering of an obliquely incident plane wave by a collection of parallel cylinders,” J. Appl. Phys. 68(10), 4952–4957 (1990).
[Crossref]

J. Med. Imaging (Bellingham) (1)

Y. Sung, R. Gupta, B. Nelson, S. Leng, C. H. McCollough, and W. S. Graves, “Phase-contrast imaging with a compact x-ray light source: system design,” J. Med. Imaging (Bellingham) 4(4), 043503 (2017).
[Crossref] [PubMed]

J. Microsc. (2)

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206(Pt 1), 33–40 (2002).
[Crossref] [PubMed]

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative X-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207(Pt 2), 79–96 (2002).
[Crossref] [PubMed]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (5)

J. Quant. Spectrosc. Radiat. Transf. (5)

M. I. Mishchenko, L. D. Travis, and D. W. Mackowski, “T-matrix computations of light scattering nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transf. 55(5), 535–575 (1996).
[Crossref]

G. Gouesbet, J. A. Lock, and G. Grehan, “Generalized Lorenz–Mie theories and description of electromagnetic arbitrary shaped beams: localized approximations and localized beam models, a review,” J. Quant. Spectrosc. Radiat. Transf. 112(1), 1–27 (2011).
[Crossref]

F. M. Kahnert, “Numerical methods in electromagnetic scattering theory,” J. Quant. Spectrosc. Radiat. Transf. 79–80(1), 775–824 (2003).
[Crossref]

J. Schäfer, S. C. Lee, and A. Kienle, “Calculation of the near fields for the scattering of electromagnetic waves by multiple infinite cylinders at perpendicular incidence,” J. Quant. Spectrosc. Radiat. Transf. 113(16), 2113–2123 (2012).
[Crossref]

J. A. Lock and G. Gouesbet, “Generalized Lorenz–Mie theory and applications,” J. Quant. Spectrosc. Radiat. Transf. 110(11), 800–807 (2009).
[Crossref]

J. Struct. Biol. (1)

M. Bartels, M. Krenkel, P. Cloetens, W. Möbius, and T. Salditt, “Myelinated mouse nerves studied by X-ray phase contrast zoom tomography,” J. Struct. Biol. 192(3), 561–568 (2015).
[Crossref] [PubMed]

J. XRay Sci. Technol. (1)

X. Wu and H. Liu, “A general theoretical formalism for X-ray phase contrast imaging,” J. XRay Sci. Technol. 11(1), 33–42 (2003).
[PubMed]

Med. Phys. (3)

C. M. Li, W. P. Segars, G. D. Tourassi, J. M. Boone, and J. T. Dobbins, “Methodology for generating a 3D computerized breast phantom from empirical data,” Med. Phys. 36(7), 3122–3131 (2009).
[Crossref] [PubMed]

D. W. Erickson, J. R. Wells, G. M. Sturgeon, E. Samei, J. T. Dobbins, W. P. Segars, and J. Y. Lo, “Population of 224 realistic human subject-based computational breast phantoms,” Med. Phys. 43(1), 23–32 (2016).
[Crossref] [PubMed]

G. M. Sturgeon, N. Kiarashi, J. Y. Lo, E. Samei, and W. P. Segars, “Finite-element modeling of compression and gravity on a population of breast phantoms for multimodality imaging simulation,” Med. Phys. 43(5), 2207–2217 (2016).
[Crossref] [PubMed]

Nucl. Instrum. Methods Phys. Res. A (1)

M. Endrizzi, “X-ray phase-contrast imaging,” Nucl. Instrum. Methods Phys. Res. A 878, 88–98 (2018).
[Crossref]

Opt. Commun. (1)

K. S. Morgan, K. K. W. Siu, and D. M. Paganin, “The projection approximation versus an exact solution for x-ray phase contrast imaging, with a plane wave scattered by a dielectric cylinder,” Opt. Commun. 283(23), 4601–4608 (2010).
[Crossref]

Opt. Express (11)

K. S. Morgan, K. K. W. Siu, and D. M. Paganin, “The projection approximation and edge contrast for x-ray propagation-based phase contrast imaging of a cylindrical edge,” Opt. Express 18(10), 9865–9878 (2010).
[Crossref] [PubMed]

M. Nilchian, Z. Wang, T. Thuering, M. Unser, and M. Stampanoni, “Spline based iterative phase retrieval algorithm for X-ray differential phase contrast radiography,” Opt. Express 23(8), 10631–10642 (2015).
[Crossref] [PubMed]

N. J. Moore and M. A. Alonso, “Closed form formula for Mie scattering of nonparaxial analogues of Gaussian beams,” Opt. Express 16(8), 5926–5933 (2008).
[Crossref] [PubMed]

E. Soubies, T.-A. Pham, and M. Unser, “Efficient inversion of multiple-scattering model for optical diffraction tomography,” Opt. Express 25(18), 21786–21800 (2017).
[Crossref] [PubMed]

M. Lee, S. Shin, and Y. Park, “Reconstructions of refractive index tomograms via a discrete algebraic reconstruction technique,” Opt. Express 25(22), 27415–27430 (2017).
[Crossref] [PubMed]

C. T. Putkunz, M. A. Pfeifer, A. G. Peele, G. J. Williams, H. M. Quiney, B. Abbey, K. A. Nugent, and I. McNulty, “Fresnel coherent diffraction tomography,” Opt. Express 18(11), 11746–11753 (2010).
[Crossref] [PubMed]

Y. Sung and G. Barbastathis, “Rytov approximation for x-ray phase imaging,” Opt. Express 21(3), 2674–2682 (2013).
[Crossref] [PubMed]

Y. Sung, C. J. R. Sheppard, G. Barbastathis, M. Ando, and R. Gupta, “Full-wave approach for x-ray phase imaging,” Opt. Express 21(15), 17547–17557 (2013).
[Crossref] [PubMed]

X. Ma, W. Xiao, and F. Pan, “Optical tomographic reconstruction based on multi-slice wave propagation method,” Opt. Express 25(19), 22595–22607 (2017).
[Crossref] [PubMed]

T. M. Godden, R. Suman, M. J. Humphry, J. M. Rodenburg, and A. M. Maiden, “Ptychographic microscope for three-dimensional imaging,” Opt. Express 22(10), 12513–12523 (2014).
[Crossref] [PubMed]

K. Li, M. Wojcik, and C. Jacobsen, “Multislice does it all-calculating the performance of nanofocusing X-ray optics,” Opt. Express 25(3), 1831–1846 (2017).
[Crossref] [PubMed]

Opt. Lett. (2)

Optica (2)

Osteoporos. Int. (1)

M. Langer and F. Peyrin, “3D X-ray ultra-microscopy of bone tissue,” Osteoporos. Int. 27(2), 441–455 (2016).
[Crossref] [PubMed]

Phys. Med. (1)

M. Beister, D. Kolditz, and W. A. Kalender, “Iterative reconstruction methods in X-ray CT,” Phys. Med. 28(2), 94–108 (2012).
[Crossref] [PubMed]

Phys. Med. Biol. (3)

C. Olendrowitz, M. Bartels, M. Krenkel, A. Beerlink, R. Mokso, M. Sprung, and T. Salditt, “Phase-contrast x-ray imaging and tomography of the nematode Caenorhabditis elegans,” Phys. Med. Biol. 57(16), 5309–5323 (2012).
[Crossref] [PubMed]

A. Bravin, P. Coan, and P. Suortti, “X-ray phase-contrast imaging: from pre-clinical applications towards clinics,” Phys. Med. Biol. 58(1), R1–R35 (2013).
[Crossref] [PubMed]

F. Pfeiffer, O. Bunk, C. David, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “High-resolution brain tumor visualization using three-dimensional x-ray phase contrast tomography,” Phys. Med. Biol. 52(23), 6923–6930 (2007).
[Crossref] [PubMed]

Phys. Rev. Appl. (1)

J. Lim, A. Goy, M. H. Shoreh, M. Unser, and D. Psaltis, “Learning tomography assessed using Mie theory,” Phys. Rev. Appl. 9(3), 34027 (2018).
[Crossref]

Phys. Rev. Spec. Top. Accel. Beams (1)

W. S. Graves, J. Bessuille, P. Brown, S. Carbajo, V. Dolgashev, K.-H. Hong, E. Ihloff, B. Khaykovich, H. Lin, K. Murari, E. A. Nanni, G. Resta, S. Tantawi, L. E. Zapata, F. X. Kärtner, and D. E. Moncton, “Compact x-ray source based on burst-mode inverse Compton scattering at 100 kHz,” Phys. Rev. Spec. Top. Accel. Beams 17(12), 120701 (2014).
[Crossref]

PLoS One (1)

M. Langer, A. Pacureanu, H. Suhonen, Q. Grimal, P. Cloetens, and F. Peyrin, “X-ray phase nanotomography resolves the 3D human bone ultrastructure,” PLoS One 7(8), e35691 (2012).
[Crossref] [PubMed]

Proc. IEEE (1)

P. C. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53(8), 805–812 (1965).
[Crossref]

Sci. Rep. (3)

M. Krenkel, A. Markus, M. Bartels, C. Dullin, F. Alves, and T. Salditt, “Phase-contrast zoom tomography reveals precise locations of macrophages in mouse lungs,” Sci. Rep. 5(1), 9973 (2015).
[Crossref] [PubMed]

L. C. P. Croton, K. S. Morgan, D. M. Paganin, L. T. Kerr, M. J. Wallace, K. J. Crossley, S. L. Miller, N. Yagi, K. Uesugi, S. B. Hooper, and M. J. Kitchen, “In situ phase contrast X-ray brain CT,” Sci. Rep. 8(1), 11412 (2018).
[Crossref] [PubMed]

Y. Sung, W. P. Segars, A. Pan, M. Ando, C. J. R. Sheppard, and R. Gupta, “Realistic wave-optics simulation of X-ray phase-contrast imaging at a human scale,” Sci. Rep. 5(1), 12011 (2015).
[Crossref] [PubMed]

Science (1)

J. Miao, T. Ishikawa, I. K. Robinson, and M. M. Murnane, “Beyond crystallography: diffractive imaging using coherent x-ray light sources,” Science 348(6234), 530–535 (2015).
[Crossref] [PubMed]

Soft Matter (1)

A. Beerlink, S. Thutupalli, M. Mell, M. Bartels, P. Cloetens, S. Herminghaus, and T. Salditt, “X-ray propagation imaging of a lipid bilayer in solution,” Soft Matter 8(17), 4595–4601 (2012).
[Crossref]

World J. Pediatr. Congenit. Heart Surg. (1)

G. Shinohara, K. Morita, M. Hoshino, Y. Ko, T. Tsukube, Y. Kaneko, H. Morishita, Y. Oshima, H. Matsuhisa, R. Iwaki, M. Takahashi, T. Matsuyama, K. Hashimoto, and N. Yagi, “Three dimensional visualization of human cardiac conduction tissue in whole heart specimens by high-resolution phase-contrast CT imaging using synchrotron radiation,” World J. Pediatr. Congenit. Heart Surg. 7(6), 700–705 (2016).
[Crossref] [PubMed]

Other (5)

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

D. M. Paganin, Coherent X-Ray Optics (Oxford University, 2006).

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company Publishers, 2005).

D. R. White, R. V. Griffith, and I. J. Wilson, “ICRU Report 46: photon, electron, proton, and neutron interaction data for body tissues,” J. ICRUos24(1), (1992).

J. Hsieh, Computed Tomography Principles, Design, Artifacts, and Recent Advances, 3rd ed. (SPIE Press, 2015).

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Figures (7)

Fig. 1
Fig. 1 Scattering geometries in propagation-based X-ray phase contrast imaging. (a) Parallel-beam single-scattering geometry, often used in the Mie solution. (b) Parallel-beam beam propagation method (PB-BPM), which does not account for cone beam effects but does allow multiple scattering. (c) Cone-beam model that only allows a single scattering event, as the object is treated under the projected-object approximation. (d) The model proposed here, CB-BPM, uses cone-beam geometry and allows for a thick, multi-scattering object to be considered.
Fig. 2
Fig. 2 Results of different forward models for a homogeneous sphere of water. Example images from (a) beam propagation method, (b) full-wave Rytov, and (c) Mie solution for a 0.5 mm sphere of water propagated a distance of 2 m. The scale bar shown is shared among (a)-(c). (d) Comparisons of relative error between the three methods as a function of propagation distance. (e) Example lineout from the intensities shown in (a)-(c). All simulations used a 0.5 mm diameter sphere. The photon energy was reduced to 3 keV due to computation limitations of the Mie solution. The object for PB-BPM was set to be equal to the scattering potential used for the FWR method in order to ensure comparison of nearly-identical objects. The intensities were radially averaged.
Fig. 3
Fig. 3 Results of PB-BPM and Mie solution for an infinite cylinder. (a) Comparison of relative difference versus the cylinder diameter between PB-BPM and the Mie solution. (b) Lineout of scattering from a single cylinder. In this case, the diameter of the cylinder was 0.2 mm and the propagation distance was 0.256 mm, as set by the Schäfer implementation’s geometry. Here, the illuminating photon energy was 3 keV. The cylinder object treated with PB-BPM shown in (b) was Gaussian filtered to avoid ringing artifacts due to discretization.
Fig. 4
Fig. 4 Simulation of three axially aligned cylinders. (a) Illustration of cylinder geometry and propagation direction. (b) Lineout of the scattered intensity. Here, the pixel size was 0.25μm, the cylinder diameters were 2 μm, and the photon energy was 0.3 keV. The cylinders were displaced −8 μm, 0 μm, and 12 μm from the center, respectively. Here, the mean difference was <10−5.
Fig. 5
Fig. 5 Simulation of three cylinders offset in two dimensions. (a) Schematic of the three cylinders and propagation direction. (b) Lineout of the intensity for the Mie solution compared to PB-BPM. In this simulation, the pixel size was 0.125 μm, the diameter was 2 μm, and the photon energy was 0.3 keV. The cylinders displaced in the (transverse, axial) coordinates from the center by (−2, −4), (0, 0), and (3, 6) μm, respectively. The mean difference between the intensities was <10−5.
Fig. 6
Fig. 6 Comparison of intensity between the projected-object approximation and multiple scattering events. (a) Schematic of the simulation geometry. (b) Mean difference caused by the projected-object approximation for two axially separated spheres as a function of separation distance. Errors are shown for calcium and water spheres, and for cone beam and parallel beam propagation. (c) Example of two Ca spheres separated by 10 cm treated with CB-BPM and (d) treated under the projected-object approximation followed by the Fresnel scaling theorem. These simulations used 0.5 mm diameter spheres, and propagation distance of 1.5 m. In the cone beam simulation, the distance between the source and the object was 3.5 m. The illumination was 30 keV. The images were radially averaged to smooth propagation artifacts. The color scale is shared between (c) and (d).
Fig. 7
Fig. 7 Simulation with XCAT breast phantom, showing results from PB-BPM (top row), CB-BPM (middle row), and projected-object approximation followed by parallel beam propagation (bottom row). (a)-(c) PB-BPM for propagation distances of 0.1, 5, and 8 m, respectively. (d)-(f) show CB-BPM with a source-object (z1) distance of 3.5 m, and object-detector distances (z2) of 0.1, 1.5, and 4.5 m, respectively. (g)-(i) show the projected-object approximation, followed by parallel beam propagation of the wave over the remaining distance to the detector. Color scales are shared among all images. The photon energy used was 30 keV.

Tables (1)

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Table 1 Parameters used in simulations

Equations (14)

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Δφ( x,y )= 2π λ 0 T δ ( x,y,z )dz
a(x,y)/ a 0 (x,y)=exp[ 2π λ 0 T β(x,y,z)dz ]
|λ f x |1 |λ f y |1
I CB (x,y, z 2 )= 1 M 2 I PB ( x M , y M ; z eff ).
U 1 (x,y)= U 0 (x,y) T 1 (x,y) U 2 (x,y)= P Δz { U 1 (x,y)} T 2 (x,y) U 3 (x,y)= P Δz { U 2 (x,y)} T 3 (x,y) ... U k+1 (x,y)= P Δz { U k (x,y)} T k+1 (x,y)}
P Δz = F 1 exp( iΔz k 2 f x 2 f y 2 )F
Δ z k+1 =Δz M k M k+1 .
U P,k+1 ( x,y )= P Δ z k+1 [ U k (x,y) ]
I kk+1 [ U P,k+1 ( x M k , y M k ) ] U P,k+1 ( x M k y M k+1 , y M k y M k+1 )
U 1 ( x M 1 , y M 1 )= I 1 M 1 [ U 0 (x,y) T 1 (x,y) ].
U P,2 ( x M 1 , y M 1 )= P Δ z 2 [ U 1 ( x M 1 , y M 1 ) ]
U 2 ( x M 2 , y M 2 )= I M 2 M 1 [ U P,2 ( x M 1 , y M 1 ) ] T 2 ( x M 2 , y M 2 ).
U k+1 ( x M k+1 , y M k+1 )= I M k M k+1 [ U P,k ( x M k , y M k ) ] T k+1 ( x M k+1 , y M k+1 ).
F N = a 2 λz

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