Abstract

The detection, localisation and characterisation of stationary and singular points in the phase of an X-ray wavefield is a challenge, particularly given a time-evolving field. In this paper, the associated difficulties are met by the single-grid, single-exposure X-ray phase contrast imaging technique, enabling direct measurement of phase maxima, minima, saddle points and vortices, in both slowly varying fields and as a means to visualise weakly-attenuating samples that introduce detailed phase variations to the X-ray wavefield. We examine how these high-resolution vector measurements can be visualised, using branch cuts in the phase gradient angle to characterise phase features. The phase gradient angle is proposed as a useful modality for the localisation and tracking of sample features and the magnitude of the phase gradient for improved visualization of samples in projection, capturing edges and bulk structure while avoiding a directional bias. In addition, we describe an advanced two-stage approach to single-grid phase retrieval.

© 2016 Optical Society of America

Full Article  |  PDF Article
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References

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2016 (1)

2014 (6)

O. V. Angelsky, M. P. Gorsky, S. G. Hanson, V. P. Lukin, I. I. Mokhun, P. V. Polyanskii, and P. A. Ryabiy, “Optical correlation algorithm for reconstructing phase skeleton of complex optical fields for solving the phase problem,” Opt. Express 22, 6186–6193 (2014).
[Crossref] [PubMed]

S. Berujon, H. Wang, S. Alcock, and K. Sawhney, “At-wavelength metrology of hard X-ray mirror using near field speckle,” Opt. Express 22, 6438–6446 (2014).
[Crossref] [PubMed]

F. Rothschild, A. I. Bishop, M. J. Kitchen, and D. M. Paganin, “Argand-plane vorticity singularities in complex scalar optical fields: An experimental study using optical speckle,” Opt. Express 22, 6495–6510 (2014).
[Crossref] [PubMed]

S. W. Wilkins, Y. I. Nesterets, T. E. Gureyev, S. C. Mayo, A. Pogany, and A. W. Stevenson, “On the evolution and relative merits of hard x-ray phase contrast imaging methods,” Phil. Trans. R. Soc. 372, 20130021 (2014).
[Crossref]

K. S. Morgan, M. Donnelley, N. Farrow, A. Fouras, N. Yagi, Y. Suzuki, A. Takeuchi, K. Uesugi, R. Boucher, K. K. W. Siu, and D. W. Parsons, “In vivo x-ray imaging reveals improved airway surface hydration after Cystic Fibrosis airway therapy,” Am. J. Respir. Critical Care Med. 190, 469–472 (2014).
[Crossref]

J. Vila-Comamala, A. Sakdinawat, and M. Guizar-Sicairos, “Characterization of x-ray phase vortices by ptychographic coherent diffractive imaging,” Opt. Lett. 18, 5281–5284 (2014).
[Crossref]

2013 (6)

S. Berujon, H. Wang, and K. Sawhney, “At-wavelength metrology using the X-ray speckle tracking technique: case study of a X-ray compound refractive lens,” J. Phys.: Conf. Ser. 425, 052020 (2013).

T. C. Petersen, M. Weyland, D. M. Paganin, T. P. Simula, S. A. Eastwood, and M. J. Morgan, “Electron vortex production and control using aberration induced diffraction catastrophes,” Phys. Rev. Lett. 110, 33901 (2013).
[Crossref]

J. Bahrdt, K. Holldack, P. Kuske, R. Müller, M. Scheer, and P. Schmid, “First observation of photons carrying orbital angular momentum in undulator radiation,” Phys. Rev. Lett. 111, 034801 (2013).
[Crossref] [PubMed]

E. Hemsing, A. Knyazik, M. Dunning, D. Xiang, A. Marinelli, C. Hast, and J. B. Rosenzweig, “Coherent optical vortices from relativistic electron beams,” Nat. Phys. 9, 549–553 (2013).
[Crossref]

A. Lubk, G. Guzzinati, F. Borrnert, and J. Verbeeck, “Transport of intensity phase retrieval of arbitrary wave fields including vortices,” Phys. Rev. Lett. 17, 173902 (2013).
[Crossref]

K. S. Morgan, P. Modregger, S. C. Irvine, S. Rutishauser, V. A. Guzenko, M. Stampanoni, and C. David, “A sensitive x-ray phase contrast technique for rapid imaging using a single phase grid analyzer,” Opt. Lett. 38, 4605–4608 (2013).
[Crossref] [PubMed]

2012 (4)

S. A. Eastwood, A. I. Bishop, T. C. Petersen, D. M. Paganin, and M. J. Morgan, “Phase measurement using an optical vortex lattice produced with a three-beam interferometer,” Opt. Express 20, 13947–13957 (2012).
[Crossref] [PubMed]

K. S. Morgan, D. M. Paganin, and K. K. W. Siu, “X-ray imaging with a paper analyser,” Appl. Phys. Lett. 100, 124102 (2012).
[Crossref]

S. Berujon, E. Ziegler, R. Cerbino, and L. Peverini, “Two-dimensional x-ray beam phase sensing,” Phys. Rev. Lett. 108, 158102 (2012).
[Crossref] [PubMed]

A. Fouras, B. J. Allison, M. J. Kitchen, S. Dubsky, J. Nguyen, K. Hourigan, K. K. W. Siu, R. A. Lewis, M. J. Wallace, and S. B. Hooper, “Altered lung motion is a sensitive indicator of regional lung disease,” Ann. Biomed. Eng. 40, 1160–1169 (2012).
[Crossref]

2011 (5)

2010 (4)

C. Xie, X. Zhu, L. Shi, and M. Liu, “Spiral photon sieves apodized by digital prolate spheroidal window for the generation of hard-x-ray vortex,” Opt. Lett. 35, 1765–1767 (2010).
[Crossref] [PubMed]

H. H. Wen, E. E. Bennett, R. Kopace, A. F. Stein, and V. Pai, “Single-shot x-ray differential phase-contrast and diffraction imaging using two-dimensional transmission gratings,” Opt. Lett. 35, 1932–1934 (2010).
[Crossref] [PubMed]

I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, “Two-dimensional x-ray grating interferometer,” Phys. Rev. Lett. 105, 248102 (2010).
[Crossref]

M. Donnelley, K. K. W. Siu, K. S. Morgan, W. Skinner, Y. Suzuki, A. Takeuchi, K. Uesugi, N. Yagi, and D. W. Parsons, “A new technique to examine individual pollutant particle and fibre deposition and transit behaviour in live mouse trachea,” J. Synchrotron Radiat. 17, 719–729 (2010).
[Crossref] [PubMed]

2009 (4)

Y. Qiao, W. Wang, N. Minematsu, J. Liu, M. Takeda, and X. Tang, “A theory of phase singularities for image representation and its applications to object tracking and image matching,” IEEE Trans. Image Process. 18, 2153–2166 (2009).
[Crossref] [PubMed]

M. Bech, O. Bunk, C. David, R. Ruth, J. Rifkin, R. Loewen, R. Feidenhans’l, and F. Pfeiffer, “Hard X-ray phase-contrast imaging with the Compact Light Source based on inverse Compton X-rays,” J. Synchrotron. Radiat. 16, 43–47 (2009).
[Crossref]

A. Olivo, S. E. Bohndiek, J. A. Griffiths, A. Konstantinidis, and R. D. Speller, “A non-free-space propagation x-ray phase contrast imaging method sensitive to phase effects in two directions simultaneously,” Appl. Phys. Lett. 94, 044108 (2009).
[Crossref]

Y. Kohmura, K. Sawada, M. Taguchi, T. Ishikawa, T. Ohigashi, and Y. Suzuki, “Formation of x-ray vortex dipoles using a single diffraction pattern and direct phase measurement using interferometry,” Appl. Phys. Lett. 94, 101112 (2009).
[Crossref]

2008 (1)

S. Sasaki and I. McNulty, “Proposal for generating brilliant x-ray beams carrying orbital angular momentum,” Phys. Rev. Lett. 100, 124801 (2008).
[Crossref] [PubMed]

2007 (4)

2006 (1)

D. Cojoc, B. Kaulich, A. Carpentiero, S. Cabrini, L. Businaro, and E. Di Fabrizio, “X-ray vortices with high topological charge,” Microelectron. Eng. 83, 1360–1363 (2006).
[Crossref]

2004 (2)

M. J. Kitchen, D. Paganin, R. A. Lewis, N. Yagi, K. Uesugi, and S. T. Mudie, “On the origin of speckle in x-ray phase contrast images of lung tissue,” Phys. Med. Biol. 49, 4335–4348 (2004).
[Crossref] [PubMed]

A. Peele, K. Nugent, A. Mancuso, D. Paterson, I. McNulty, and J. Hayes, “X-ray phase vortices: theory and experiment,” J. Opt. Soc. Am. A 21, 1575–1584 (2004).
[Crossref]

2002 (3)

A. G. Peele, P. J. McMahon, D. Paterson, C. Q. Tran, A. P. Mancuso, K. A. Nugent, J. P. Hayes, E. Harvey, B. Lai, and I. McNulty, “Observation of an x-ray vortex,” Opt. Lett. 27, 1752–1754 (2002).
[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, 33–40 (2002).
[Crossref] [PubMed]

Y. Suzuki, “Two-beam x-ray interferometer using prism optics,” Jpn. J. Appl. Phys. 41, L1019–L1021 (2002).
[Crossref]

2001 (1)

L. J. Allen, H. M. L. Faulkner, K. A. Nugent, M. P. Oxley, and D. Paganin, “Phase retrieval from images in the presence of first-order vortices,” Phys. Rev. E 63, 037602 (2001).
[Crossref]

1997 (3)

I. Freund, “Saddles, singularities and extrema in random phase fields,” Phys. Rev. E 52, 2348–2360 (1997).
[Crossref]

I. Freund, “Vortex derivatives,” Opt. Commun. 137, 118–126 (1997).
[Crossref]

T. Lindeberg and M-X. Li, “Segmentation and classification of edges using minimum description length approximation and complementary junction cues,” Comput. Vis. Image Und. 67, 88–98 (1997).
[Crossref]

1995 (1)

I. Freund, “Saddles, singularities and extrema in random phase fields,” Phys. Rev. E 52, 2348–2360 (1995).
[Crossref]

1994 (1)

T. Lindeberg, “Scale-space theory: a basic tool for analyzing structures at different scales,” J. Appl. Statist. 21, 225–227 (1994).
[Crossref]

1989 (1)

P. Coullet, L. Gil, and F. Rocca, “Optical vortices,” Opt. Commun. 73, 403–408 (1989).
[Crossref]

1988 (1)

J. F. Nye, J. V. Hajnal, and J. H. Hannay, “Phase saddles and dislocations in two-dimensional waves such as the tides,” Proc. R. Soc. Lond. A 417, 7–20 (1988).
[Crossref]

1986 (1)

J. Canny, “A computational approach to edge detection,” IEEE Trans. Pattern Anal. Mach. Intel. 6, 679–698 (1986).
[Crossref]

1982 (1)

Aksenov, V. P.

Alcock, S.

Allen, L. J.

L. J. Allen, H. M. L. Faulkner, K. A. Nugent, M. P. Oxley, and D. Paganin, “Phase retrieval from images in the presence of first-order vortices,” Phys. Rev. E 63, 037602 (2001).
[Crossref]

Allison, B. J.

A. Fouras, B. J. Allison, M. J. Kitchen, S. Dubsky, J. Nguyen, K. Hourigan, K. K. W. Siu, R. A. Lewis, M. J. Wallace, and S. B. Hooper, “Altered lung motion is a sensitive indicator of regional lung disease,” Ann. Biomed. Eng. 40, 1160–1169 (2012).
[Crossref]

Altissimo, M.

K. M. Pavlov, D. M. Paganin, D. J. Vine, J. A. Schmalz, Y. Suzuki, K. Uesugi, A. Takeuchi, N. Yagi, A. Kharchenko, G. Blaj, J. Jakubek, M. Altissimo, and J. N. Clark, “Quantized hard-x-ray phase vortices nucleated by aberrated nanolenses,” Phys. Rev. A 83, 013813 (2011).
[Crossref]

Angelsky, O. V.

Atuchin, V. V.

Bahrdt, J.

J. Bahrdt, K. Holldack, P. Kuske, R. Müller, M. Scheer, and P. Schmid, “First observation of photons carrying orbital angular momentum in undulator radiation,” Phys. Rev. Lett. 111, 034801 (2013).
[Crossref] [PubMed]

Bech, M.

M. Bech, O. Bunk, C. David, R. Ruth, J. Rifkin, R. Loewen, R. Feidenhans’l, and F. Pfeiffer, “Hard X-ray phase-contrast imaging with the Compact Light Source based on inverse Compton X-rays,” J. Synchrotron. Radiat. 16, 43–47 (2009).
[Crossref]

Bennett, E. E.

Berujon, S.

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M. Donnelley, D. W. Parsons, K. S. Morgan, and K. K. W. Siu, “Animals in synchrotrons: Overcoming challenges for high-resolution, live, small-animal imaging,” in AIP Conference Proceedings of the 6th International Conference on Medical Applications of Synchrotron Radiation2010, Vol. 1266, Iss. 1, pp. 30–34.

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Pavlov, K. M.

K. M. Pavlov, D. M. Paganin, D. J. Vine, J. A. Schmalz, Y. Suzuki, K. Uesugi, A. Takeuchi, N. Yagi, A. Kharchenko, G. Blaj, J. Jakubek, M. Altissimo, and J. N. Clark, “Quantized hard-x-ray phase vortices nucleated by aberrated nanolenses,” Phys. Rev. A 83, 013813 (2011).
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G. Ruben and D. M. Paganin, “Phase vortices from a Young’s three-pinhole interferometer,” Phys. Rev. E 75, 066613 (2007).
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K. S. Morgan, M. Donnelley, N. Farrow, A. Fouras, N. Yagi, Y. Suzuki, A. Takeuchi, K. Uesugi, R. Boucher, K. K. W. Siu, and D. W. Parsons, “In vivo x-ray imaging reveals improved airway surface hydration after Cystic Fibrosis airway therapy,” Am. J. Respir. Critical Care Med. 190, 469–472 (2014).
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K. S. Morgan, D. M. Paganin, and K. K. W. Siu, “X-ray imaging with a paper analyser,” Appl. Phys. Lett. 100, 124102 (2012).
[Crossref]

A. Fouras, B. J. Allison, M. J. Kitchen, S. Dubsky, J. Nguyen, K. Hourigan, K. K. W. Siu, R. A. Lewis, M. J. Wallace, and S. B. Hooper, “Altered lung motion is a sensitive indicator of regional lung disease,” Ann. Biomed. Eng. 40, 1160–1169 (2012).
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K. S. Morgan, D. M. Paganin, and K. K. W. Siu, “Quantitative x-ray phase contrast imaging using a single grating of comparable pitch to sample feature size,” Opt. Lett. 36, 55–57 (2011).
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M. Donnelley, D. W. Parsons, K. S. Morgan, and K. K. W. Siu, “Animals in synchrotrons: Overcoming challenges for high-resolution, live, small-animal imaging,” in AIP Conference Proceedings of the 6th International Conference on Medical Applications of Synchrotron Radiation2010, Vol. 1266, Iss. 1, pp. 30–34.

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M. Donnelley, K. K. W. Siu, K. S. Morgan, W. Skinner, Y. Suzuki, A. Takeuchi, K. Uesugi, N. Yagi, and D. W. Parsons, “A new technique to examine individual pollutant particle and fibre deposition and transit behaviour in live mouse trachea,” J. Synchrotron Radiat. 17, 719–729 (2010).
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M. Donnelley, K. K. W. Siu, K. S. Morgan, W. Skinner, Y. Suzuki, A. Takeuchi, K. Uesugi, N. Yagi, and D. W. Parsons, “A new technique to examine individual pollutant particle and fibre deposition and transit behaviour in live mouse trachea,” J. Synchrotron Radiat. 17, 719–729 (2010).
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K. M. Pavlov, D. M. Paganin, D. J. Vine, J. A. Schmalz, Y. Suzuki, K. Uesugi, A. Takeuchi, N. Yagi, A. Kharchenko, G. Blaj, J. Jakubek, M. Altissimo, and J. N. Clark, “Quantized hard-x-ray phase vortices nucleated by aberrated nanolenses,” Phys. Rev. A 83, 013813 (2011).
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M. Donnelley, K. K. W. Siu, K. S. Morgan, W. Skinner, Y. Suzuki, A. Takeuchi, K. Uesugi, N. Yagi, and D. W. Parsons, “A new technique to examine individual pollutant particle and fibre deposition and transit behaviour in live mouse trachea,” J. Synchrotron Radiat. 17, 719–729 (2010).
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Uesugi, K.

K. S. Morgan, M. Donnelley, N. Farrow, A. Fouras, N. Yagi, Y. Suzuki, A. Takeuchi, K. Uesugi, R. Boucher, K. K. W. Siu, and D. W. Parsons, “In vivo x-ray imaging reveals improved airway surface hydration after Cystic Fibrosis airway therapy,” Am. J. Respir. Critical Care Med. 190, 469–472 (2014).
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K. M. Pavlov, D. M. Paganin, D. J. Vine, J. A. Schmalz, Y. Suzuki, K. Uesugi, A. Takeuchi, N. Yagi, A. Kharchenko, G. Blaj, J. Jakubek, M. Altissimo, and J. N. Clark, “Quantized hard-x-ray phase vortices nucleated by aberrated nanolenses,” Phys. Rev. A 83, 013813 (2011).
[Crossref]

M. Donnelley, K. K. W. Siu, K. S. Morgan, W. Skinner, Y. Suzuki, A. Takeuchi, K. Uesugi, N. Yagi, and D. W. Parsons, “A new technique to examine individual pollutant particle and fibre deposition and transit behaviour in live mouse trachea,” J. Synchrotron Radiat. 17, 719–729 (2010).
[Crossref] [PubMed]

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S. Berujon, H. Wang, S. Alcock, and K. Sawhney, “At-wavelength metrology of hard X-ray mirror using near field speckle,” Opt. Express 22, 6438–6446 (2014).
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S. Berujon, H. Wang, and K. Sawhney, “At-wavelength metrology using the X-ray speckle tracking technique: case study of a X-ray compound refractive lens,” J. Phys.: Conf. Ser. 425, 052020 (2013).

Wang, W.

Y. Qiao, W. Wang, N. Minematsu, J. Liu, M. Takeda, and X. Tang, “A theory of phase singularities for image representation and its applications to object tracking and image matching,” IEEE Trans. Image Process. 18, 2153–2166 (2009).
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T. C. Petersen, M. Weyland, D. M. Paganin, T. P. Simula, S. A. Eastwood, and M. J. Morgan, “Electron vortex production and control using aberration induced diffraction catastrophes,” Phys. Rev. Lett. 110, 33901 (2013).
[Crossref]

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S. W. Wilkins, Y. I. Nesterets, T. E. Gureyev, S. C. Mayo, A. Pogany, and A. W. Stevenson, “On the evolution and relative merits of hard x-ray phase contrast imaging methods,” Phil. Trans. R. Soc. 372, 20130021 (2014).
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[Crossref] [PubMed]

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E. Hemsing, A. Knyazik, M. Dunning, D. Xiang, A. Marinelli, C. Hast, and J. B. Rosenzweig, “Coherent optical vortices from relativistic electron beams,” Nat. Phys. 9, 549–553 (2013).
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Yagi, N.

K. S. Morgan, M. Donnelley, N. Farrow, A. Fouras, N. Yagi, Y. Suzuki, A. Takeuchi, K. Uesugi, R. Boucher, K. K. W. Siu, and D. W. Parsons, “In vivo x-ray imaging reveals improved airway surface hydration after Cystic Fibrosis airway therapy,” Am. J. Respir. Critical Care Med. 190, 469–472 (2014).
[Crossref]

K. M. Pavlov, D. M. Paganin, D. J. Vine, J. A. Schmalz, Y. Suzuki, K. Uesugi, A. Takeuchi, N. Yagi, A. Kharchenko, G. Blaj, J. Jakubek, M. Altissimo, and J. N. Clark, “Quantized hard-x-ray phase vortices nucleated by aberrated nanolenses,” Phys. Rev. A 83, 013813 (2011).
[Crossref]

M. Donnelley, K. K. W. Siu, K. S. Morgan, W. Skinner, Y. Suzuki, A. Takeuchi, K. Uesugi, N. Yagi, and D. W. Parsons, “A new technique to examine individual pollutant particle and fibre deposition and transit behaviour in live mouse trachea,” J. Synchrotron Radiat. 17, 719–729 (2010).
[Crossref] [PubMed]

M. J. Kitchen, D. Paganin, R. A. Lewis, N. Yagi, K. Uesugi, and S. T. Mudie, “On the origin of speckle in x-ray phase contrast images of lung tissue,” Phys. Med. Biol. 49, 4335–4348 (2004).
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I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, “Two-dimensional x-ray grating interferometer,” Phys. Rev. Lett. 105, 248102 (2010).
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Ziegler, E.

S. Berujon, E. Ziegler, R. Cerbino, and L. Peverini, “Two-dimensional x-ray beam phase sensing,” Phys. Rev. Lett. 108, 158102 (2012).
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Am. J. Respir. Critical Care Med. (1)

K. S. Morgan, M. Donnelley, N. Farrow, A. Fouras, N. Yagi, Y. Suzuki, A. Takeuchi, K. Uesugi, R. Boucher, K. K. W. Siu, and D. W. Parsons, “In vivo x-ray imaging reveals improved airway surface hydration after Cystic Fibrosis airway therapy,” Am. J. Respir. Critical Care Med. 190, 469–472 (2014).
[Crossref]

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Supplementary Material (1)

NameDescription
» Visualization 1: MOV (15901 KB)      The lower periphery of a mouse lung during two breaths, using single-grid x-ray phase imaging to extract a) magnitude and b) angle of the phase gradient, and c) vertical and d) horizontal phase gradients.

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Figures (6)

Fig. 1
Fig. 1 Plots of the phase gradient behaviour observed around vortices, phase maxima/minima and saddle points.
Fig. 2
Fig. 2 Experimental set-up. Images captured at the medium-length beamline facility, BL20XU beamline, SPring-8 synchrotron, 245 m from the undulator source, using 25 keV x-rays, a π-shifting checkerboard phase grating, a PCO.Edge sCMOS camera, 6.5 μm native pixel size, with 50×, 20× or 10× lenses to produce 0.11 μm, 0.27 μm or 0.54 μm effective pixel sizes, 2560 × 2160 pixels, transverse coherent width of around 40 μm at the sample position.
Fig. 3
Fig. 3 a) Intensity image (without the grid present), showing multiple propagation-based fringes from the fibers in the medical tape placed 174 cm upstream of the grid. A PCO.Edge sCMOS detector with a 50× optical lens was placed a further 80.2 cm downstream of the 5.4 μm period checkerboard phase grid. b) A grid is introduced, populating the image with a grid of high intensity points, which are slightly distorted (inset) relative to c) an image of the grid alone, due to the phase distortions induced by the medical tape. These distortions are tracked using a two step process (interrogation window 80 pixels wide, free to move 9 pixels in each direction, followed by a window of 51, free to move 5 pixels) to find d) vertical and e) horizontal components of the phase gradients in the wavefield (both shown here with a linear grayscale from −10 pixels shift to 10 pixels shift, which corresponds to a deflection angle of +/−0.63 μradians). These can be integrated together to retrieve the wavefront phase map, f), here overlaid with contours of constant phase. The phase gradient can also be expressed using g) magnitude and h) angle to better visualize the stationary phase points in the x-ray wavefield. i) The phase gradient vector field, where the length of the vector indicates the number of pixels by which the grid pattern is shifted and the arrow points in the direction of the maximum gradient. Note that the weak 30 μm diameter circular features in c) are produced by dust on a kapton window several meters upstream of the sample.
Fig. 4
Fig. 4 The two-directional differential information can be used to calculate and visualize additional properties of the wavefield in Fig. 3, including a) the zero-gradient contours of the phase, with stationary points found at the crossings and b) the zero-second derivative contours (as per [35]), c) the longitudinal orbital angular momentum density (as per [36]) and d) the lines of minimum longitudinal orbital angular momentum density magnitude (as per [37]).
Fig. 5
Fig. 5 Crystals of raw and powdered sugar are visualized by looking at a–c) magnitude of the grid pattern shift or the absolute value of the phase gradient, d–f) the projected phase depth, g–i) the horizontal phase gradient, j–k) the vertical phase gradient and m–n) the decrease in amplitude of the cross-correlation, highlighting edges and regions with structures smaller than the grid. Powdered sugar is also shown using l) the phase gradient angle and o) propagation-based phase contrast imaging. An offset of 0.1 pixels shift in the y direction was added before calculating the phase gradient angle so that a phase gradient angle was defined in the otherwise zero-phase-gradient region surrounding the sample. The exposure time was 100 ms, captured by a PCO.Edge sCMOS detector with a 20× optical lens, positioned 22cm downstream of the grid and sugar crystals. Linear grayscales are used with limits of a–b) 0 to 4 pixels (4.9 μradians), c) 0 to 2.5 pixels (3.1 μradians), g–h,j–k) −3 to 3 pixels (+/−3.7μradians), and i) −2 to 2 pixels shift (+/−2.5 μradians deflected angle). The same scale-bar is used for all images.
Fig. 6
Fig. 6 Applications of the imaging approach in biomedical research; 20 μm glass beads transiting the airway surface of a mouse (first row); and the lower periphery of the mouse lung at full inhalation (second row), both imaged using a 14.4 μm period checkerboard phase grid. Images show a/e) vertical phase gradients, b/f) horizontal phase gradients, c/g) magnitude of the phase gradient and d/h) angle of the phase gradient. We also show i) the locations of the beads which create local phase maxima, j) a phase gradient vector map of the lung image, and a magnified section of the lung image, labelling local phase minima in k) the magnitude of the phase gradient and l) the angle of the phase gradient. Airway images are extracted from one 50 ms exposure captured on the PCO.Edge sCMOS camera with a 20× lens (image later cropped and magnified for clarity), 5.5 cm grid-to-sample and 75 cm grid-to-detector distances, and lung images are extracted from one 5 ms exposure, with a 10× lens, 12 cm grid-to-sample and 82 cm grid-to-detector distances. The C57BL/6 mouse was anaesthetised and ventilated for the airway surface imaging (a–d) and breathed freely during the lung imaging (e–h) (see [47] for additional detail). A time sequence of the lung imaging is provided in Visualization 1.

Equations (1)

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D c = k L 2 / ( 2 ϕ ) .

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