X-ray phase and dark-field computed tomography without optical elements (2310.09496v2)
Abstract: X-ray diffusive dark-field imaging, which allows spatially unresolved microstructure to be mapped across a sample, is an increasingly popular tool in an array of settings. Here, we present a new algorithm for phase and dark-field computed tomography based on the x-ray Fokker-Planck equation. Needing only a coherent x-ray source, sample, and detector, our propagation-based algorithm can map the sample density and dark-field/diffusion properties of the sample in 3D. Importantly, incorporating dark-field information in the density reconstruction process enables a higher spatial resolution reconstruction than possible with previous propagation-based approaches. Two sample exposures at each projection angle are sufficient for the successful reconstruction of both the sample density and dark-field Fokker-Planck diffusion coefficients. We anticipate that the proposed algorithm may be of benefit in biomedical imaging and industrial settings.
- M. Endrizzi, “X-ray phase-contrast imaging,” \JournalTitleNucl. Inst. Meth. Phys. Res. A 878, 88–98 (2018).
- F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, “Hard-x-ray dark-field imaging using a grating interferometer,” \JournalTitleNat. Mater. 7, 134–137 (2008).
- Z. Wang, K. Kang, Z. Huang, and Z. Chen, “Quantitative grating-based x-ray dark-field computed tomography,” \JournalTitleAppl. Phys. Lett. 95, 094105 (2009).
- M. Bech, O. Bunk, T. Donath, R. Feidenhans’l, C. David, and F. Pfeiffer, “Quantitative x-ray dark-field computed tomography,” \JournalTitlePhys. Med. Biol. 55(18), 5529 (2010).
- F. Prade, K. Fischer, P. Meyer, J. Mohr, and F. Pfeiffer, “Time resolved X-ray Dark-Field Tomography Revealing Water Transport in a Fresh Cement Sample,” \JournalTitleSci. Rep. 6, 29108 (2016).
- R. Burkhardt, T. Gora, A. A. Fingerle, A. P. Sauter, F. Meurer, F. T. Gassert, S. Dobiasch, D. Schilling, A. Feuchtinger, A. K. Walch, G. Multhoff, J. Herzen, P. B. Noël, E. J. Rummeny, S. E. Combs, T. E. Schmid, F. Pfeiffer, and J. J. Wilkens, “In-vivo X-ray dark-field computed tomography for the detection of radiation-induced lung damage in mice,” \JournalTitlePhys. Imaging Radiat. Oncol. 20, 11–16 (2021).
- B. K. Blykers, C. Organista, M. N. Boone, M. Kagias, F. Marone, M. Stampanoni, T. Bultreys, V. Cnudde, and J. Aelterman, “Tunable x-ray dark-field imaging for sub-resolution feature size quantification in porous media,” \JournalTitleSci. Rep. 11(1), 18446 (2021).
- K. Willer, A. A. Fingerle, W. Noichl, F. De Marco, M. Frank, T. Urban, R. Schick, A. Gustschin, B. Gleich, J. Herzen, T. Koehler, A. Yaroshenko, T. Pralow, G. S. Zimmermann, B. Renger, A. P. Sauter, D. Pfeiffer, M. R. Makowski, E. J. Rummeny, P. A. Grenier, and F. Pfeiffer, “X-ray dark-field chest imaging for detection and quantification of emphysema in patients with chronic obstructive pulmonary disease: a diagnostic accuracy study,” \JournalTitleLancet Digit 3(111), e733–e744 (2021).
- F. T. Gassert, T. Urban, A. Kufner, M. Frank, G. C. Feuerriegel, T. Baum, M. R. Makowski, C. Braun, D. Pfeiffer, B. J. Schwaiger, F. Pfeiffer, and A. S. Gersing, “Dark-field X-ray imaging for the assessment of osteoporosis in human lumbar spine specimens,” \JournalTitleFront. Physiol. 14, 1217007 (2023).
- M. Viermetz, N. Gustschin, C. Schmid, J. Haeusele, B. Gleich, B. Renger, T. Koehler, and F. Pfeiffer, “Initial characterization of dark-field CT on a clinical gantry,” \JournalTitleIEEE Trans. Med. Imaging 42(4), 1035–1045 (2022).
- E. Pagot, P. Cloetens, S. Fiedler, A. Bravin, P. Coan, J. Baruchel, J. Härtwig, and W. Thomlinson, “A method to extract quantitative information in analyzer-based x-ray phase contrast imaging,” \JournalTitleAppl. Phys. Lett. 82(20), 3421–3423 (2003).
- W. Yashiro, Y. Terui, K. Kawabata, and A. Momose, “On the origin of visibility contrast in x-ray Talbot interferometry,” \JournalTitleOpt. Express 18(16), 16890–16901 (2010).
- F. Schaff, F. Prade, Y. Sharma, M. Bech, and F. Pfeiffer, “Non-iterative Directional Dark-field Tomography,” \JournalTitleSci. Rep. 7, 3307 (2017).
- K. S. Morgan, D. M. Paganin, and K. W. Siu, “X-ray phase imaging with a paper analyzer,” \JournalTitleAppl. Phys. Lett. 100(12), 124102 (2012).
- S. Berujon, H. Wang, and K. Sawhney, “X-ray multimodal imaging using a random-phase object,” \JournalTitlePhys. Rev. A 86, 063813 (2012).
- H. Wang, Y. Kashyap, and K. Sawhney, “Quantitative X-ray dark-field and phase tomography using single directional speckle scanning technique,” \JournalTitleAppl. Phys. Lett. 108(12), 124102 (2016).
- M. C. Zdora, “State of the Art of X-ray Soeckle-Based Phase-Contrast and Dark-Field Imaging,” \JournalTitleJ. Imaging 4(5), 60 (2018).
- M.-C. Zdora, P. Thibault, H. Deyhle, J. Vila-Comamala, C. Rau, and I. Zanette, “Tunable X-ray speckle-based phase-contrast and dark-field imaging using the unified modulated pattern analysis approach,” \JournalTitleJ. Instrum. 13, C05005 (2018).
- S. J. Alloo, D. M. Paganin, K. S. Morgan, M. J. Kitchen, A. W. Stevenson, S. C. Mayo, H. T. Li, B. M. Kennedy, A. Maksimenko, J. C. Bowden, and K. M. Pavlov, “Dark-field tomography of an attenuating object using intrinsic x-ray speckle-tracking,” \JournalTitleJ. Med. Imaging 9(3), 031502 (2022).
- R. Smith, F. De Marco, L. Broche, M.-C. Zdora, N. W. Phillips, R. Boardman, and P. Thibault, “X-ray directional dark-field imaging using Unified Modulated Pattern Analysis,” \JournalTitlePLoS ONE 17(8), e0273315 (2022).
- F. A. Vittoria, M. Endrizzi, P. C. Diemoz, A. Zamir, U. H. Wagner, C. Rau, I. K. Robinson, and A. Olivo, “X-ray absorption, phase and dark-field tomography through a beam tracking approach,” \JournalTitleSci. Rep. 5, 16318 (2015).
- M. Endrizzi, P. C. Diemoz, T. P. Millard, J. Louise Jones, R. D. Speller, I. K. Robinson, and A. Olivo, “Hard X-ray dark-field imaging with incoherent sample illumination,” \JournalTitleAppl. Phys. Lett. 104(2), 024106 (2014).
- A. Doherty, S. Savvidis, C. Navarrete-León, M. F. M. Gerli, A. Olivo, and M. Endrizzi, “Edge-Illumination X-Ray Dark-Field Tomography,” \JournalTitlePhys. Rev. Appl. 19(5), 054042 (2023).
- D. M. Paganin and K. S. Morgan, “X-ray Fokker–Planck equation for paraxial imaging,” \JournalTitleSci. Rep. 9, 17537 (2019).
- T. E. Gureyev, D. M. Paganin, B. Arhatari, S. T. Taba, S. Lewis, P. C. Brennan, and H. M. Quiney, “Dark-field signal extraction in propagation-based phase-contrast imaging,” \JournalTitlePhys. Med. Biol. 65(21), 215029 (2020).
- A. Aminzadeh, B. D. Arhatari, A. Maksimenko, C. J. Hall, D. Hausermann, A. G. Peele, J. Fox, B. Kumar, Z. Prodanovic, M. Dimmock, D. Lockie, K. M. Pavlov, Y. I. Nesterets, D. Thompson, S. C. Mayo, D. Paganin, S. T. Taba, S. Lewis, P. C. Brennan, H. M. Quiney, and T. E. Gureyev, “Imaging breast microcalcifications using dark-field signal in propagation-based phase-contrast tomography,” \JournalTitleIEEE Trans. Med. Imaging 41(11), 2980–2990 (2022).
- T. A. Leatham, D. M. Paganin, and K. S. Morgan, “X-ray dark-field and phase retrieval without optics, via the Fokker-Planck equation,” \JournalTitleIEEE Trans. Med. Imaging 42(6), 1681–1695 (2023).
- J. N. Ahlers, K. M. Pavlov, M. J. Kitchen, and K. S. Morgan, “X-ray dark-field via spectral propagation-based imaging,” \JournalTitlearXiv preprint arXiv:2309.15874 (2023).
- A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” \JournalTitleRev. Sci. Instrum. 66(12), 5486–5492 (1995).
- P. Cloetens, R. Barrett, J. Baruchel, J. Guigay, and M. Schlenker, “Phase objects in synchrotron radiation hard x-ray imaging,” \JournalTitleJ. Phys. D: Appl. Phys 29(1), 133–146 (1996).
- S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard x-rays,” \JournalTitleNature 384(6607), 335–338 (1996).
- M. R. Teague, “Deterministic phase retrieval: a Green’s function solution,” \JournalTitleJ. Opt. Soc. Am. 73, 1434–1441 (1983).
- 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,” \JournalTitleJ. Microsc. 206, 33–40 (2002).
- T. Weitkamp, D. Hass, D. Wegrzynek, and A. Rack, “ANKAphase: software for single-distance phase retrieval from inline X-ray phase-contrast radiographs,” \JournalTitleJ. Synchrotron Rad. 18(4), 617–629 (2011).
- T. E. Gureyev, Y. Nesterets, D. Ternovski, D. Thompson, S. W. Wilkins, A. W. Stevenson, A. Sakellariou, and J. A. Taylor, “Toolbox for advanced x-ray image processing,” Proc. SPIE 8141, 841410B (2011).
- M. A. Beltran, D. M. Paganin, K. Uesugi, and M. J. Kitchen, “2D and 3D X-ray phase retrieval of multi-material objects using a single defocus distance,” \JournalTitleOpt. Express 18(7), 6423–6436 (2010).
- M. A. Beltran, D. M. Paganin, and D. Pelliccia, “Phase-and-amplitude recovery from a single phase contrast image using partially spatially coherent radiation,” \JournalTitleJ. Opt. 20(5), 055605 (2018).
- K. S. Morgan and D. M. Paganin, “Applying the Fokker–Planck equation to grating-based x-ray phase and dark-field imaging,” \JournalTitleSci. Rep. 9, 17465 (2019).
- D. M. Paganin, D. Pelliccia, and K. S. Morgan, “Paraxial diffusion-field retrieval,” \JournalTitlePhys. Rev. A 108(1), 013517 (2023).
- Ya. I. Nesterets, “On the origins of decoherence and extinction contrast in phase-contrast imaging,” \JournalTitleOpt. Commun. 281, 533–542 (2008).
- D. M. Paganin, M. Sales, P. M. Kadletz, W. Kockelmann, M. A. Beltran, H. F. Poulsen, and S. Schmidt, “Revisiting Neutron Propagation-Based Phase-Contrast Imaging and Tomography: Use of Phase Retrieval to Amplify the Effective Degree of Brilliance,” \JournalTitlePhys. Rev. Appl. 19(3), 034005 (2023).
- D. M. Paganin, V. Favre-Nicolin, A. Mirone, A. Rack, J. Villanova, M. P. Olbinado, V. Fernandez, J. C. da Silva, and D. Pelliccia, “Boosting spatial resolution by incorporating periodic boundary conditions into single-distance hard-x-ray phase retrieval,” \JournalTitleJ. Opt. 22(11), 115607 (2020).
- J. A. Pollock, K. S. Morgan, L. C. P. Croton, M. K. Croughan, G. Ruben, N. Yagi, H. Sekiguchi, and M. J. Kitchen, “Precise phase retrieval for propagation-based images using discrete mathematics,” \JournalTitleSci. Rep. 12, 18469 (2022).
- S. K. Lynch, V. Pai, J. Auxier, A. F. Stein, E. E. Bennett, C. K. Kemble, X. Xiao, W. Lee, N. Y. Morgan, and H. H. Wen, “Interpretation of dark-field contrast and particle size selectivity in grating interferometers,” \JournalTitleAppl. Opt. 50(22), 4310–4319 (2011).
- C. Hall, D. Hausermann, A. Maksimneko, A. Astolfo, K. Siu, J. Pearson, and A. Stevenson, “Detectors for the Imaging and Medical Beam Line at the Australian Synchrotron,” \JournalTitleJ. Instrum. 8, C06011 (2013).
- S. van der Walt, J. L. Schönberger, J. Nunez-Iglesias, F. Boulogne, J. D. Warner, N. Yager, E. Gouillart, T. Yu, and the scikit-image contributors, “scikit-image: image processing in Python,” (2023). https://scikit-image.org/docs/stable/api/skimage.registration.html.
- B. A. Dowd, G. H. Campbell, R. B. Marr, V. V. Nagarkar, S. V. Tipnis, L. Axe, and D. Peter Siddons, “Developments in synchrotron x-ray computed microtomography at the National Synchrotron Light Source,” Proc. SPIE 3772, 224-236 (1999).
- N. Bevins, J. Zambelli, Z. Qi, and G. Chen, “X-ray dark-field computed tomography using a grating interferometer setup,” Proc. SPIE 7622, 76220P (2010).
- J. G. Brankov, M. N. Wernick, Y. Yang, J. Li, C. Muehleman, Z. Zhong, and M. A. Anastasio, “A computed tomography implementation of multiple-image radiography,” \JournalTitleMed. Phys. 33(2), 278–289 (2006).
- I. Zanette, T. Weitkamp, G. Le Duc, and F. Pfeiffer, “X-ray grating-based phase tomography for 3D histology,” \JournalTitleRSC Adv. 3(43), 19816–19819 (2013).
- R. P. Carnibella, A. Fouras, and M. J. Kitchen, “Single-exposure dual-energy-subtraction X-ray imaging using a synchrotron source,” \JournalTitleJ. Synchrotron Radiat. 19(6), 954–959 (2012).
- F. García-Moreno, P. H. Kamm, T. R. Neu, F. Bülk, R. Mokso, C. M. Schlepütz, M. Stampanoni, and J. Banhart, “Using X-ray tomoscopy to explore the dynamics of foaming metal,” \JournalTitleNat. Commun. 10, 3762 (2019).
- F. García-Moreno, P. H. Kamm, T. R. Neu, F. Bülk, M. A. Noack, M. Wegener, N. von der Eltz, C. M. Schlepütz, M. Stampanoni, and J. Banhart, “Tomoscopy: Time-Resolved Tomography for Dynamic Processes in Materials,” \JournalTitleAdv. Mater. 33(45), 2104659 (2021).
- P. K. Poola and R. John, “Label-free nanoscale characterization of red blood cell structure and dynamics using single-shot transport of intensity equation,” \JournalTitleJ. Biomed. Opt 22(10), 106001 (2017).
- A. C. Y. Liu, D. M. Paganin, L. Bourgeois, and P. N. H. Nakashima, “Projected thickness reconstruction from a single defocussed transmission electron microscope image of an amorphous object,” \JournalTitleUltramicroscopy 111(8), 959–968 (2011).
- T. H. Jensen, M. Bech, O. Bunk, T. Donath, C. David, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging,” \JournalTitlePhys. Med. Biol. 55(12), 3317–3323 (2010).
- T. H. Jensen, M. Bech, I. Zanette, T. Weitkamp, C. David, H. Deyhle, S. Rutishauser, E. Reznikova, J. Mohr, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging of strongly ordered systems,” \JournalTitlePhys. Rev. B 82, 214103 (2010).
- M. L. Siew, A. B. Te Pas, M. J. Wallace, M. J. Kitchen, R. A. Lewis, A. Fouras, C. J. Morley, P. G. Davis, N. Yagi, K. Uesugi, and S. B. Hooper, “Positive end-expiratory pressure enhances development of a functional residual capacity in preterm rabbits ventilated from birth,” \JournalTitleJ. Appl. Physiol. 106(5), 1487–1493 (2009).
- C. S. Stahr, C. R. Samarage, M. Donnelley, N. Farrow, K. S. Morgan, R. C. Zosky, G. Boucher, K. K. W. Siu, M. A. Mall, D. W. Parsons, S. Dubsky, and A. Fouras, “Quantification of heterogeneity in lung disease with image-based pulmonary function testing,” \JournalTitleSci. Rep. 6, 29438 (2016).
- R. Gradl, M. Dierolf, B. Günther, L. Hehn, W. Möller, D. Kutschke, L. Yang, M. Donnelley, R. Murrie, A. Erl, T. Stoeger, B. Gleich, K. Achterhold, O. Schmid, F. Pfeiffer, and K. S. Morgan, “In vivo Dynamic Phase-Contrast X-ray Imaging using a Compact Light Source,” \JournalTitleSci. Rep. 8, 6788 (2018).
- K. S. Morgan, M. Donnelley, N. Farrow, N. Fouras, A. Yagi, Y. Suzuki, A. Takeuchi, K. Uesugi, R. C. Bocuher, K. K. W. Siu, and D. W. Parsons, “In Vivo X-ray Imaging Reveals Improved Airway Surface Hydration after a Therapy Designed for Cystic Fibrosis,” \JournalTitleAm. J. Respir. Crit. Care Med. 190, 469–472 (2014).
- M. Frank, F. T. Gassert, T. Urban, K. Willer, W. Noichl, R. Schick, M. Schultheiss, M. Viermetz, B. Gleich, F. De Marco, J. Herzen, T. Koehler, K. J. Engel, B. Renger, F. G. Gassert, A. Sauter, A. A. Fingerle, B. Haller, M. R. Makowski, D. Pfeiffer, and F. Pfeiffer, “Dark-field chest X-ray imaging for the assessment of COVID-19-pneumonia,” \JournalTitleCommun. Med. 2, 147 (2022).