Abstract

Hollow glass microcapillaries or x-ray waveguides very efficiently confine x-rays to submicron or nanospots, which can be used for point projection imaging. However, x-ray beams exiting from such devices have ultranarrow cones that are limited by the critical angle for the total external reflection to a few milliradians. Narrow cone beams result in small fields of view, and the application of multiple-reflection optics to cone beam tomography is challenging. In this work, we describe a new nonconventional tomographic geometry realized with multiple confocal ultranarrow cone beams. The geometry enables an increase in the effective radiation cone to over 10° without resolution reduction. The proposed tomographic scans can be performed without truncations of the field of view or limitations of the angular range and do not require sample translations, which are inherent to other multibeam x-ray techniques. Volumetric imaging is possible with a simultaneous iterative reconstruction technique or with a fast approximate noniterative two-step approach. A proof-of-principle experiment was performed in the multipoint projection geometry with polycapillary optics and a multi-pinhole mask inserted upstream of the optics. The geometry is suited for phase-contrast tomography with polychromatic laboratory and synchrotron sources.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2020 (6)

M. Eckermann, M. Töpperwien, A.-L. Robisch, F. van der Meer, C. Stadelmann, and T. Salditt, “Phase-contrast x-ray tomography of neuronal tissue at laboratory sources with submicron resolution,” J. Med. Imaging 7(1), 013502 (2020).
[Crossref]

J. Yamada, S. Matsuyama, R. Hirose, Y. Takeda, Y. Kohmura, M. Yabashi, K. Omote, T. Ishikawa, and K. Yamauchi, “Compact full-field hard x-ray microscope based on advanced Kirkpatrick–Baez mirrors,” Optica 7(4), 367–370 (2020).
[Crossref]

K. M. Sowa, M. P. Kujda, and P. Korecki, “Plenoptic x-ray microscopy,” Appl. Phys. Lett. 116(1), 014103 (2020).
[Crossref]

W. Voegeli, K. Kajiwara, H. Kudo, T. Shirasawa, X. Liang, and W. Yashiro, “Multibeam x-ray optical system for high-speed tomography,” Optica 7(5), 514–517 (2020).
[Crossref]

E. S. Dreier, C. Silvestre, J. Kehres, D. Turecek, M. Khalil, J. H. Hemmingsen, O. Hansen, J. Jakubek, R. Feidenhans’l, and U. L. Olsen, “Single-shot, omni-directional x-ray scattering imaging with a laboratory source and single-photon localization,” Opt. Lett. 45(4), 1021–1024 (2020).
[Crossref]

M. Du, Y. S. G. Nashed, S. Kandel, D. Gürsoy, and C. Jacobsen, “Three dimensions, two microscopes, one code: Automatic differentiation for x-ray nanotomography beyond the depth of focus limit,” Sci. Adv. 6(13), eaay3700 (2020).
[Crossref]

2019 (3)

D. A. Thompson, Y. I. Nesterets, K. M. Pavlov, and T. E. Gureyev, “Fast three-dimensional phase retrieval in propagation-based X-ray tomography,” J. Synchrotron Radiat. 26(3), 825–838 (2019).
[Crossref]

L. Brombal, G. Kallon, J. Jiang, S. Savvidis, P. De Coppi, L. Urbani, E. Forty, R. Chambers, R. Longo, A. Olivo, and M. Endrizzi, “Monochromatic propagation-based phase-contrast microscale computed-tomography system with a rotating-anode source,” Phys. Rev. Appl. 11(3), 034004 (2019).
[Crossref]

A. Ruhlandt and T. Salditt, “Time-resolved x-ray phase-contrast tomography of sedimenting micro-spheres,” New J. Phys. 21(4), 043017 (2019).
[Crossref]

2018 (6)

P. Villanueva-Perez, B. Pedrini, R. Mokso, P. Vagovic, V. A. Guzenko, S. J. Leake, P. R. Willmott, P. Oberta, C. David, H. N. Chapman, and M. Stampanoni, “Hard x-ray multi-projection imaging for single-shot approaches,” Optica 5(12), 1521–1524 (2018).
[Crossref]

C. K. Hagen, F. A. Vittoria, M. Endrizzi, and A. Olivo, “Theoretical framework for spatial resolution in edge-illumination x-ray tomography,” Phys. Rev. Appl. 10(5), 054050 (2018).
[Crossref]

K. M. Sowa, B. R. Jany, and P. Korecki, “Multipoint-projection x-ray microscopy,” Optica 5(5), 577–582 (2018).
[Crossref]

L. Bauer, M. Lindqvist, F. Förste, U. Lundström, B. Hansson, M. Thiel, S. Bjeoumikhova, D. Grötzsch, W. Malzer, B. Kanngießer, and I. Mantouvalou, “Confocal micro-x-ray fluorescence spectroscopy with a liquid metal jet source,” J. Anal. At. Spectrom. 33(9), 1552–1558 (2018).
[Crossref]

R. Vescovi, M. Du, V. de Andrade, W. Scullin, D. Gürsoy, and C. Jacobsen, “Tomosaic: efficient acquisition and reconstruction of teravoxel tomography data using limited-size synchrotron X-ray beams,” J. Synchrotron Radiat. 25(5), 1478–1489 (2018).
[Crossref]

D. Kazantsev, V. Pickalov, S. Nagella, E. Pasca, and P. J. Withers, “TomoPhantom, a software package to generate 2D-4D analytical phantoms for ct image reconstruction algorithm benchmarks,” SoftwareX 7, 150–155 (2018).
[Crossref]

2017 (4)

A. Wawrzyniak, A. Marendziak, A. Kisiel, P. Borowiec, R. Nietubyc, J. Wiechecki, K. Karas, K. Szamota-Leandersson, M. Zajac, C. Bocchetta, and M. Stankiewicz, “Solaris a new class of low energy and high brightness light source,” Nucl. Instrum. Methods Phys. Res., Sect. B 411, 4–11 (2017).
[Crossref]

C. A. MacDonald, “Structured X-Ray Optics for Laboratory-Based Materials Analysis,” Annu. Rev. Mater. Res. 47(1), 115–134 (2017).
[Crossref]

M. Müller, I. de Sena Oliveira, S. Allner, S. Ferstl, P. Bidola, K. Mechlem, A. Fehringer, L. Hehn, M. Dierolf, K. Achterhold, B. Gleich, J. U. Hammel, H. Jahn, G. Mayer, and F. Pfeiffer, “Myoanatomy of the velvet worm leg revealed by laboratory-based nanofocus x-ray source tomography,” Proc. Natl. Acad. Sci. 114(47), 12378–12383 (2017).
[Crossref]

S. Matsuyama, S. Yasuda, J. Yamada, H. Okada, Y. Kohmura, M. Yabashi, T. Ishikawa, and K. Yamauchi, “50-nm-resolution full-field x-ray microscope without chromatic aberration using total-reflection imaging mirrors,” Sci. Rep. 7(1), 46358 (2017).
[Crossref]

2016 (2)

2015 (3)

P. Korecki, T. P. Roszczynialski, and K. M. Sowa, “Simulation of image formation in x-ray coded aperture microscopy with polycapillary optics,” Opt. Express 23(7), 8749–8761 (2015).
[Crossref]

W. van Aarle, W. J. Palenstijn, J. D. Beenhouwer, T. Altantzis, S. Bals, K. J. Batenburg, and J. Sijbers, “The ASTRA Toolbox: A platform for advanced algorithm development in electron tomography,” Ultramicroscopy 157, 35–47 (2015).
[Crossref]

C. K. Egan, S. D. M. Jacques, M. D. Wilson, M. C. Veale, P. Seller, A. M. Beale, R. A. D. Pattrick, P. J. Withers, and R. J. Cernik, “3D chemical imaging in the laboratory by hyperspectral x-ray computed tomography,” Sci. Rep. 5(1), 15979 (2015).
[Crossref]

2014 (1)

C. K. Hagen, P. R. T. Munro, M. Endrizzi, P. C. Diemoz, and A. Olivo, “Low-dose phase contrast tomography with conventional x-ray sources,” Med. Phys. 41(7), 070701 (2014).
[Crossref]

2013 (2)

K. M. Dabrowski, D. T. Dul, A. Wrobel, and P. Korecki, “X-ray microlaminography with polycapillary optics,” Appl. Phys. Lett. 102(22), 224104 (2013).
[Crossref]

K. M. Dabrowski, D. T. Dul, and P. Korecki, “X-ray imaging inside the focal spot of polycapillary optics using the coded aperture concept,” Opt. Express 21(3), 2920–2927 (2013).
[Crossref]

2012 (1)

S. P. Krüger, H. Neubauer, M. Bartels, S. Kalbfleisch, K. Giewekemeyer, P. J. Wilbrandt, M. Sprung, and T. Salditt, “Sub-10nm beam confinement by X-ray waveguides: design, fabrication and characterization of optical properties,” J. Synchrotron Radiat. 19(2), 227–236 (2012).
[Crossref]

2009 (5)

T. Sun, M. Zhang, Z. Liu, Z. Zhang, G. Li, Y. Ma, X. Du, Q. Jia, Y. Chen, Q. Yuan, W. Huang, P. Zhu, and X. Ding, “Focusing synchrotron radiation using a polycapillary half-focusing x-ray lens for imaging,” J. Synchrotron Radiat. 16(1), 116–118 (2009).
[Crossref]

G. Requena, P. Cloetens, W. Altendorfer, C. Poletti, D. Tolnai, F. Warchomicka, and H. Degischer, “Sub-micrometer synchrotron tomography of multiphase metals using Kirkpatrick–Baez optics,” Scr. Mater. 61(7), 760–763 (2009).
[Crossref]

J. T. Dobbins, “Tomosynthesis imaging: at a translational crossroads,” Med. Phys. 36(6Part1), 1956–1967 (2009).
[Crossref]

G. Wang, H. Yu, and Y. Ye, “A scheme for multisource interior tomography,” Med. Phys. 36(8), 3575–3581 (2009).
[Crossref]

R. A. Barrea, R. Huang, S. Cornaby, D. H. Bilderback, and T. C. Irving, “High-flux hard X-ray microbeam using a single-bounce capillary with doubly focused undulator beam,” J. Synchrotron Radiat. 16(1), 76–82 (2009).
[Crossref]

2007 (2)

C. Rau, V. Crecea, W. Liu, C.-P. Richter, K. Peterson, P. Jemian, U. Neuhäusler, G. Schneider, X. Yu, P. Braun, T.-C. Chiang, and I. Robinson, “Synchrotron-based imaging and tomography with hard x-rays,” Nucl. Instrum. Methods Phys. Res., Sect. B 261(1-2), 850–854 (2007).
[Crossref]

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

2002 (3)

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(2), 79–96 (2002).
[Crossref]

F. Pfeiffer, C. David, M. Burghammer, C. Riekel, and T. Salditt, “Two-dimensional x-ray waveguides and point sources,” Science 297(5579), 230–234 (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(1), 33–40 (2002).
[Crossref]

2001 (1)

T. E. Gureyev, S. Mayo, S. W. Wilkins, D. Paganin, and A. W. Stevenson, “Quantitative in-line phase-contrast imaging with multienergy x rays,” Phys. Rev. Lett. 86(25), 5827–5830 (2001).
[Crossref]

1999 (1)

S. Gondrom, J. Zhou, M. Maisl, H. Reiter, M. Kröning, and W. Arnold, “X-ray computed laminography: An approach of computed tomography for applications with limited access,” Nucl. Eng. Des. 190(1-2), 141–147 (1999).
[Crossref]

1996 (1)

P. Cloetens, R. Barrett, J. Baruchel, J.-P. Guigay, and M. Schlenker, “Phase objects in synchrotron radiation hard x-ray imaging,” J. Phys. D: Appl. Phys. 29(1), 133–146 (1996).
[Crossref]

1995 (1)

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).
[Crossref]

1994 (2)

D. H. Bilderback, S. A. Hoffman, and D. J. Thiel, “Nanometer spatial resolution achieved in hard x-ray imaging and laue diffraction experiments,” Science 263(5144), 201–203 (1994).
[Crossref]

K. Machin and S. Webb, “Cone-beam x-ray microtomography of small specimens,” Phys. Med. Biol. 39(10), 1639–1657 (1994).
[Crossref]

1993 (1)

I. Lindgren and E. Selin, “A simple model for optimization of conical capillaries in XRF analysis,” X-Ray Spectrom. 22(4), 216–219 (1993).
[Crossref]

1990 (1)

M. Kumakhov and F. Komarov, “Multiple reflection from surface x-ray optics,” Phys. Rep. 191(5), 289–350 (1990).
[Crossref]

1984 (1)

1976 (1)

D. Mosher and S. J. Stephanakis, “X-ray light pipes,” Appl. Phys. Lett. 29(2), 105–107 (1976).
[Crossref]

Achterhold, K.

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Hagen, C. K.

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Supplementary Material (2)

NameDescription
» Visualization 1       Visualization 1 – Full set of ultranarrow cone beam projection recorded for a phantom: borosilicate glass capillary filled with 25 micron SiO2 spheres.
» Visualization 2       Visualization 2 – Conventional cone beam projections reconstructed in the first step of the FATS algorithm for a phantom: borosilicate glass capillary filled with 25 micron SiO2 spheres.

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Figures (8)

Fig. 1.
Fig. 1. Principle of x-ray tomography with multiple ultranarrow cone beams. (a) A phantom and its calculated conventional cone beam projection. (b) Ultranarrow x-ray cone beam projection calculated for a single capillary fiber. The projection is formed relative to the tip of the capillary ($s$). The FOV is truncated. (c) The cone beam projection calculated for the polycapillary optics. The projection is formed relative to the optics focal spot ($S$). The FOV is larger, but the resolution is low. (d) Multipoint projection with ultranarrow beams calculated for the polycapillary optics and a multi-pinhole inserted upstream of the optics. Projection splits into a set of multiple ultranarrow cone beam projections generated by a set of sources $\{s_{i}\}$ and sharpens. The FOV is large, and the spatial resolution is high. The images on the left show the geometry and the images on the right show the calculated x-ray projections.
Fig. 2.
Fig. 2. Definition of the tomographic geometry with multiple ultranarrow cone beams. For clarity, the sample-to-detector distance $D$ and the detector pixel size were downscaled by factors of 20 and 2, respectively. $\{ s_{i} \}$ is a set of sources that generate ultranarrow beams, $\{\delta _i\}$ is a set of subdetectors that detect ultranarrow beams, $\omega _{j}$ is the $j$-th orientation of the sample and $\mathbf {p}_{ij}$ represents ultranarrow projections.
Fig. 3.
Fig. 3. Tomographic reconstruction of noiseless multiple ultranarrow cone beam projections of the phantom from Fig. 1. (a) Axial slice of the phantom. (b) Back-projection (BP). (c) Simultaneous iterative reconstruction technique (SIRT) from $N_s\times N_{\omega }=31320$ ultranarrow (19$\times$19 pixels, $\gamma \approx 0.3^{\circ }$) cone beam projections. (d) Fast approximate two-stage (FATS) reconstruction. Top row: comparison of the axial slices. Bottom: zoomed areas. (e) Comparison of the one-dimensional profiles. BP is scaled and offset.
Fig. 4.
Fig. 4. Experimental details of x-ray tomography with multiple ultranarrow cone beams. (a) Fragment of the experimental setup. The asterisk marks the position of the sample during the tomographic scan at $\Delta z=1.9$ mm. The short dashed line marks the focal plane at $f=2.5$ mm. During experiments, the multi-pinhole mask is moved to an almost in-contact position with the input surface of the optics. (b) Test sample: borosilicate glass capillary filled with SiO$_{2}$ spheres. Scale bar: 100 $\mu$m. (c) Microscope image of the exit surface of the optics. The red-filled area marks the approximate distribution of sources $\{s_{i}\}$ that generate ultranarrow x-ray cone beams, which are captured by the detector. (d) Experimentally determined distribution of sources $\{s_{i}\}$. The number of sources that generate ultranarrow cone beams is $N_{s}=630$.
Fig. 5.
Fig. 5. Experimental data for a phantom: borosilicate glass capillary filled with 25 $\mu$m diameter SiO$_2$ spheres ($\omega =0$). (a) Cone beam projection relative to the focal spot of the polycapillary optics. (b) Image recorded with polycapillary optics with a multi-pinhole mask inserted upstream of the optics. This image splits into $\mathbf {p}_{ij}$ ($N_{s}=630$) ultranarrow cone beam projections. (c) Conventional cone beam projection $\widetilde {\mathbf {p}}_{j}$ reconstructed from image (b). (d) Sample thickness $\mathbf {F}\widetilde {\mathbf {p}}_{j}$ retrieved with a Paganin filter. Insets show zoomed and contrasted fragments marked with rectangles. The second zoom in (b) shows a numerical mask that was used to eliminate the partial overlap of neighboring ultranarrow cone beams to construct a set of $\mathbf {p}_{ij}$ ultranarrow cone beam projections. Scale bars: 25 $\mu$m.
Fig. 6.
Fig. 6. Reconstructions of tomographic scans recorded for a phantom: a borosilicate glass capillary filled with 25 $\mu$m diameter SiO$_2$ spheres. (a) Slices from conventional cone beam tomography with polycapillary optics. (b) Slices reconstructed with FATS from an ultranarrow multiple cone beam dataset. Scale bar : 50 $\mu$m. (c) 3D view of ultranarrow multiple cone beam reconstruction. (d) Zooms of the regions marked with dashed orange rectangles. (e) Line profiles along white lines marked in (d). Spatial arrangements of spheres slightly differ in (a) and (b).
Fig. 7.
Fig. 7. Simulations with noise. (a) Noisy multipoint projection with ultranarrow beams calculated for the phantom ($\omega =0$). (b) Cone beam projection reconstructed in the first step of FATS. (c) Axial slice of the phantom. (d) SIRT. (e) FATS. Bottom images in (c-e) show zoomed areas. (f) Comparison of the one-dimensional profiles.
Fig. 8.
Fig. 8. Determination of the spatial resolution on the JIMA RT RC-02B chart (a) Conventional cone beam tomography - 7 $\mu$m. (b) Reconstruction of multiple ultranarrow cone beam data - 1.5 $\mu$m.

Equations (5)

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p = W v ,
p = [ p 11 ; ; p i j ; ; p N s N ω ]
v k + 1 = v k + C W T R ( p W v k ) ,
p ~ j = W ~ j W j T p j .
v ~ = W ~ T F p ~ .