Abstract

Transmission X-ray microscopy (TXM) is a powerful, nondestructive and three-dimensional imaging tool that has been applied in many fields. However, the ability to image large size samples using high-resolution TXM is restricted due to a limited depth of focus (DOF). In this study, a method based on multiple reconstructed slice stacks of an extended sample at different focal positions is developed to extend the DOF of TXM. The simulation and experimental results demonstrate that this novel method effectively and reliably extend the DOF of high-resolution TXM.

© 2017 Optical Society of America

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Corrections

28 March 2017: A correction was made to the body text.


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References

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2013 (2)

J. Frikel and E. T. Quinto, “Characterization and reduction of artifacts in limited angle tomography,” Inverse Probl. 29(12), 125007 (2013).
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[Crossref]

2012 (1)

2011 (1)

Y. Guan, W. Li, Y. Gong, G. Liu, X. Zhang, J. Chen, J. Gelb, W. Yun, Y. Xiong, Y. Tian, and H. Wang, “Analysis of the three-dimensional microstructure of a solid-oxide fuel cell anode using nano X-ray tomography,” J. Power Sources 196(4), 1915–1919 (2011).
[Crossref]

2010 (3)

A. Sakdinawat and D. Attwood, “Nanoscale X-ray imaging,” Nat. Photonics 4(12), 840–848 (2010).
[Crossref]

J. C. Andrews, E. Almeida, M. C. van der Meulen, J. S. Alwood, C. Lee, Y. Liu, J. Chen, F. Meirer, M. Feser, J. Gelb, J. Rudati, A. Tkachuk, W. Yun, and P. Pianetta, “Nanoscale X-ray microscopic imaging of mammalian mineralized tissue,” Microsc. Microanal. 16(3), 327–336 (2010).
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[Crossref] [PubMed]

2008 (1)

G. B. Kim, Y. J. Yoon, T. J. Shin, H. S. Youn, Y. S. Gho, and S. J. Lee, “X-ray imaging of various biological samples using a phase-contrast hard X-ray microscope,” Microsc. Res. Tech. 71(9), 639–643 (2008).
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2004 (3)

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[Crossref]

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[Crossref] [PubMed]

2001 (1)

M. Peuker, “High-efficiency nickel phase zone plates with 20 nm minimum outermost zone width,” Appl. Phys. Lett. 78(15), 2208–2210 (2001).
[Crossref]

2000 (1)

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[Crossref] [PubMed]

1999 (1)

C. Jacobsen, “Soft x-ray microscopy,” Trends Cell Biol. 9(2), 44–47 (1999).
[Crossref] [PubMed]

1995 (1)

H. Li, B. Manjunath, and S. K. Mitra, “Multisensor image fusion using the wavelet transform,” Graph. Models Image Proc. 57(3), 235–245 (1995).
[Crossref]

1992 (1)

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[Crossref]

1991 (1)

C. Jacobsen, S. Williams, E. Anderson, M. T. Browne, C. J. Buckley, D. Kern, J. Kirz, M. Rivers, and X. Zhang, “Diffraction-limited imaging in a scanning transmission x-ray microscope,” Opt. Commun. 86(3-4), 351–364 (1991).
[Crossref]

Almeida, E.

J. C. Andrews, E. Almeida, M. C. van der Meulen, J. S. Alwood, C. Lee, Y. Liu, J. Chen, F. Meirer, M. Feser, J. Gelb, J. Rudati, A. Tkachuk, W. Yun, and P. Pianetta, “Nanoscale X-ray microscopic imaging of mammalian mineralized tissue,” Microsc. Microanal. 16(3), 327–336 (2010).
[Crossref] [PubMed]

Alwood, J. S.

J. C. Andrews, E. Almeida, M. C. van der Meulen, J. S. Alwood, C. Lee, Y. Liu, J. Chen, F. Meirer, M. Feser, J. Gelb, J. Rudati, A. Tkachuk, W. Yun, and P. Pianetta, “Nanoscale X-ray microscopic imaging of mammalian mineralized tissue,” Microsc. Microanal. 16(3), 327–336 (2010).
[Crossref] [PubMed]

Anderson, E.

C. Jacobsen, S. Williams, E. Anderson, M. T. Browne, C. J. Buckley, D. Kern, J. Kirz, M. Rivers, and X. Zhang, “Diffraction-limited imaging in a scanning transmission x-ray microscope,” Opt. Commun. 86(3-4), 351–364 (1991).
[Crossref]

Andrews, J. C.

Y. Liu, J. Wang, Y. Hong, Z. Wang, K. Zhang, P. A. Williams, P. Zhu, J. C. Andrews, P. Pianetta, and Z. Wu, “Extended depth of focus for transmission x-ray microscope,” Opt. Lett. 37(17), 3708–3710 (2012).
[Crossref] [PubMed]

J. C. Andrews, E. Almeida, M. C. van der Meulen, J. S. Alwood, C. Lee, Y. Liu, J. Chen, F. Meirer, M. Feser, J. Gelb, J. Rudati, A. Tkachuk, W. Yun, and P. Pianetta, “Nanoscale X-ray microscopic imaging of mammalian mineralized tissue,” Microsc. Microanal. 16(3), 327–336 (2010).
[Crossref] [PubMed]

Attwood, D.

A. Sakdinawat and D. Attwood, “Nanoscale X-ray imaging,” Nat. Photonics 4(12), 840–848 (2010).
[Crossref]

Bian, R.

Z. Liang, Y. Guan, G. Liu, R. Bian, X. Zhang, Y. Xiong, and Y. Tian, “Reconstruction of limited-angle and few-view nano-CT image via total variation iterative reconstruction,” Proc. SPIE 8851, 885113 (2013).
[Crossref]

Browne, M. T.

C. Jacobsen, S. Williams, E. Anderson, M. T. Browne, C. J. Buckley, D. Kern, J. Kirz, M. Rivers, and X. Zhang, “Diffraction-limited imaging in a scanning transmission x-ray microscope,” Opt. Commun. 86(3-4), 351–364 (1991).
[Crossref]

Buckley, C. J.

C. Jacobsen, S. Williams, E. Anderson, M. T. Browne, C. J. Buckley, D. Kern, J. Kirz, M. Rivers, and X. Zhang, “Diffraction-limited imaging in a scanning transmission x-ray microscope,” Opt. Commun. 86(3-4), 351–364 (1991).
[Crossref]

Carazo, J. M.

Chen, J.

Y. Guan, W. Li, Y. Gong, G. Liu, X. Zhang, J. Chen, J. Gelb, W. Yun, Y. Xiong, Y. Tian, and H. Wang, “Analysis of the three-dimensional microstructure of a solid-oxide fuel cell anode using nano X-ray tomography,” J. Power Sources 196(4), 1915–1919 (2011).
[Crossref]

J. C. Andrews, E. Almeida, M. C. van der Meulen, J. S. Alwood, C. Lee, Y. Liu, J. Chen, F. Meirer, M. Feser, J. Gelb, J. Rudati, A. Tkachuk, W. Yun, and P. Pianetta, “Nanoscale X-ray microscopic imaging of mammalian mineralized tissue,” Microsc. Microanal. 16(3), 327–336 (2010).
[Crossref] [PubMed]

Feser, M.

J. C. Andrews, E. Almeida, M. C. van der Meulen, J. S. Alwood, C. Lee, Y. Liu, J. Chen, F. Meirer, M. Feser, J. Gelb, J. Rudati, A. Tkachuk, W. Yun, and P. Pianetta, “Nanoscale X-ray microscopic imaging of mammalian mineralized tissue,” Microsc. Microanal. 16(3), 327–336 (2010).
[Crossref] [PubMed]

Fogelqvist, E.

Frikel, J.

J. Frikel and E. T. Quinto, “Characterization and reduction of artifacts in limited angle tomography,” Inverse Probl. 29(12), 125007 (2013).
[Crossref]

Gelb, J.

Y. Guan, W. Li, Y. Gong, G. Liu, X. Zhang, J. Chen, J. Gelb, W. Yun, Y. Xiong, Y. Tian, and H. Wang, “Analysis of the three-dimensional microstructure of a solid-oxide fuel cell anode using nano X-ray tomography,” J. Power Sources 196(4), 1915–1919 (2011).
[Crossref]

J. C. Andrews, E. Almeida, M. C. van der Meulen, J. S. Alwood, C. Lee, Y. Liu, J. Chen, F. Meirer, M. Feser, J. Gelb, J. Rudati, A. Tkachuk, W. Yun, and P. Pianetta, “Nanoscale X-ray microscopic imaging of mammalian mineralized tissue,” Microsc. Microanal. 16(3), 327–336 (2010).
[Crossref] [PubMed]

Gho, Y. S.

G. B. Kim, Y. J. Yoon, T. J. Shin, H. S. Youn, Y. S. Gho, and S. J. Lee, “X-ray imaging of various biological samples using a phase-contrast hard X-ray microscope,” Microsc. Res. Tech. 71(9), 639–643 (2008).
[Crossref] [PubMed]

Gong, Y.

Y. Guan, W. Li, Y. Gong, G. Liu, X. Zhang, J. Chen, J. Gelb, W. Yun, Y. Xiong, Y. Tian, and H. Wang, “Analysis of the three-dimensional microstructure of a solid-oxide fuel cell anode using nano X-ray tomography,” J. Power Sources 196(4), 1915–1919 (2011).
[Crossref]

Guan, Y.

P. F. Guo, Y. Guan, G. Liu, Z. T. Liang, J. H. Liu, X. B. Zhang, Y. Xiong, and Y. C. Tian, “Modeling of gas transport with electrochemical reaction in nickel-yttria-stabilized zirconia anode during thermal cycling by Lattice Boltzmann method,” J. Power Sources 327, 127–134 (2016).
[Crossref]

Z. Liang, Y. Guan, G. Liu, R. Bian, X. Zhang, Y. Xiong, and Y. Tian, “Reconstruction of limited-angle and few-view nano-CT image via total variation iterative reconstruction,” Proc. SPIE 8851, 885113 (2013).
[Crossref]

Y. Guan, W. Li, Y. Gong, G. Liu, X. Zhang, J. Chen, J. Gelb, W. Yun, Y. Xiong, Y. Tian, and H. Wang, “Analysis of the three-dimensional microstructure of a solid-oxide fuel cell anode using nano X-ray tomography,” J. Power Sources 196(4), 1915–1919 (2011).
[Crossref]

Guo, P. F.

P. F. Guo, Y. Guan, G. Liu, Z. T. Liang, J. H. Liu, X. B. Zhang, Y. Xiong, and Y. C. Tian, “Modeling of gas transport with electrochemical reaction in nickel-yttria-stabilized zirconia anode during thermal cycling by Lattice Boltzmann method,” J. Power Sources 327, 127–134 (2016).
[Crossref]

Guttmann, P.

G. Schneider, P. Guttmann, S. Heim, S. Rehbein, F. Mueller, K. Nagashima, J. B. Heymann, W. G. Müller, and J. G. McNally, “Three-dimensional cellular ultrastructure resolved by X-ray microscopy,” Nat. Methods 7(12), 985–987 (2010).
[Crossref] [PubMed]

Heim, S.

G. Schneider, P. Guttmann, S. Heim, S. Rehbein, F. Mueller, K. Nagashima, J. B. Heymann, W. G. Müller, and J. G. McNally, “Three-dimensional cellular ultrastructure resolved by X-ray microscopy,” Nat. Methods 7(12), 985–987 (2010).
[Crossref] [PubMed]

Hertz, H. M.

Heymann, J. B.

G. Schneider, P. Guttmann, S. Heim, S. Rehbein, F. Mueller, K. Nagashima, J. B. Heymann, W. G. Müller, and J. G. McNally, “Three-dimensional cellular ultrastructure resolved by X-ray microscopy,” Nat. Methods 7(12), 985–987 (2010).
[Crossref] [PubMed]

Hong, Y.

Jacobsen, C.

C. Jacobsen, “Soft x-ray microscopy,” Trends Cell Biol. 9(2), 44–47 (1999).
[Crossref] [PubMed]

C. Jacobsen, J. Kirz, and S. Williams, “Resolution in soft x-ray microscopes,” Ultramicroscopy 47(1-3), 55–79 (1992).
[Crossref]

C. Jacobsen, S. Williams, E. Anderson, M. T. Browne, C. J. Buckley, D. Kern, J. Kirz, M. Rivers, and X. Zhang, “Diffraction-limited imaging in a scanning transmission x-ray microscope,” Opt. Commun. 86(3-4), 351–364 (1991).
[Crossref]

Kern, D.

C. Jacobsen, S. Williams, E. Anderson, M. T. Browne, C. J. Buckley, D. Kern, J. Kirz, M. Rivers, and X. Zhang, “Diffraction-limited imaging in a scanning transmission x-ray microscope,” Opt. Commun. 86(3-4), 351–364 (1991).
[Crossref]

Kim, G. B.

G. B. Kim, Y. J. Yoon, T. J. Shin, H. S. Youn, Y. S. Gho, and S. J. Lee, “X-ray imaging of various biological samples using a phase-contrast hard X-ray microscope,” Microsc. Res. Tech. 71(9), 639–643 (2008).
[Crossref] [PubMed]

Kirz, J.

C. Jacobsen, J. Kirz, and S. Williams, “Resolution in soft x-ray microscopes,” Ultramicroscopy 47(1-3), 55–79 (1992).
[Crossref]

C. Jacobsen, S. Williams, E. Anderson, M. T. Browne, C. J. Buckley, D. Kern, J. Kirz, M. Rivers, and X. Zhang, “Diffraction-limited imaging in a scanning transmission x-ray microscope,” Opt. Commun. 86(3-4), 351–364 (1991).
[Crossref]

Lee, C.

J. C. Andrews, E. Almeida, M. C. van der Meulen, J. S. Alwood, C. Lee, Y. Liu, J. Chen, F. Meirer, M. Feser, J. Gelb, J. Rudati, A. Tkachuk, W. Yun, and P. Pianetta, “Nanoscale X-ray microscopic imaging of mammalian mineralized tissue,” Microsc. Microanal. 16(3), 327–336 (2010).
[Crossref] [PubMed]

Lee, S. J.

G. B. Kim, Y. J. Yoon, T. J. Shin, H. S. Youn, Y. S. Gho, and S. J. Lee, “X-ray imaging of various biological samples using a phase-contrast hard X-ray microscope,” Microsc. Res. Tech. 71(9), 639–643 (2008).
[Crossref] [PubMed]

Li, H.

H. Li, B. Manjunath, and S. K. Mitra, “Multisensor image fusion using the wavelet transform,” Graph. Models Image Proc. 57(3), 235–245 (1995).
[Crossref]

Li, W.

Y. Guan, W. Li, Y. Gong, G. Liu, X. Zhang, J. Chen, J. Gelb, W. Yun, Y. Xiong, Y. Tian, and H. Wang, “Analysis of the three-dimensional microstructure of a solid-oxide fuel cell anode using nano X-ray tomography,” J. Power Sources 196(4), 1915–1919 (2011).
[Crossref]

Liang, Z.

Z. Liang, Y. Guan, G. Liu, R. Bian, X. Zhang, Y. Xiong, and Y. Tian, “Reconstruction of limited-angle and few-view nano-CT image via total variation iterative reconstruction,” Proc. SPIE 8851, 885113 (2013).
[Crossref]

Liang, Z. T.

P. F. Guo, Y. Guan, G. Liu, Z. T. Liang, J. H. Liu, X. B. Zhang, Y. Xiong, and Y. C. Tian, “Modeling of gas transport with electrochemical reaction in nickel-yttria-stabilized zirconia anode during thermal cycling by Lattice Boltzmann method,” J. Power Sources 327, 127–134 (2016).
[Crossref]

Liu, G.

P. F. Guo, Y. Guan, G. Liu, Z. T. Liang, J. H. Liu, X. B. Zhang, Y. Xiong, and Y. C. Tian, “Modeling of gas transport with electrochemical reaction in nickel-yttria-stabilized zirconia anode during thermal cycling by Lattice Boltzmann method,” J. Power Sources 327, 127–134 (2016).
[Crossref]

Z. Liang, Y. Guan, G. Liu, R. Bian, X. Zhang, Y. Xiong, and Y. Tian, “Reconstruction of limited-angle and few-view nano-CT image via total variation iterative reconstruction,” Proc. SPIE 8851, 885113 (2013).
[Crossref]

Y. Guan, W. Li, Y. Gong, G. Liu, X. Zhang, J. Chen, J. Gelb, W. Yun, Y. Xiong, Y. Tian, and H. Wang, “Analysis of the three-dimensional microstructure of a solid-oxide fuel cell anode using nano X-ray tomography,” J. Power Sources 196(4), 1915–1919 (2011).
[Crossref]

Liu, J. H.

P. F. Guo, Y. Guan, G. Liu, Z. T. Liang, J. H. Liu, X. B. Zhang, Y. Xiong, and Y. C. Tian, “Modeling of gas transport with electrochemical reaction in nickel-yttria-stabilized zirconia anode during thermal cycling by Lattice Boltzmann method,” J. Power Sources 327, 127–134 (2016).
[Crossref]

Liu, S. P.

Y. Liu, S. P. Liu, and Z. F. Wang, “A general framework for image fusion based on multi-scale transform and sparse representation,” Inf. Fusion 24, 147–164 (2015).
[Crossref]

Liu, Y.

Y. Liu, S. P. Liu, and Z. F. Wang, “A general framework for image fusion based on multi-scale transform and sparse representation,” Inf. Fusion 24, 147–164 (2015).
[Crossref]

Y. Liu, J. Wang, Y. Hong, Z. Wang, K. Zhang, P. A. Williams, P. Zhu, J. C. Andrews, P. Pianetta, and Z. Wu, “Extended depth of focus for transmission x-ray microscope,” Opt. Lett. 37(17), 3708–3710 (2012).
[Crossref] [PubMed]

J. C. Andrews, E. Almeida, M. C. van der Meulen, J. S. Alwood, C. Lee, Y. Liu, J. Chen, F. Meirer, M. Feser, J. Gelb, J. Rudati, A. Tkachuk, W. Yun, and P. Pianetta, “Nanoscale X-ray microscopic imaging of mammalian mineralized tissue,” Microsc. Microanal. 16(3), 327–336 (2010).
[Crossref] [PubMed]

Lucchesi, J.

S. Vogt, G. Schneider, A. Steuernagel, J. Lucchesi, E. Schulze, D. Rudolph, and G. Schmahl, “X-ray microscopic studies of the Drosophila dosage compensation complex,” J. Struct. Biol. 132(2), 123–132 (2000).
[Crossref] [PubMed]

Manjunath, B.

H. Li, B. Manjunath, and S. K. Mitra, “Multisensor image fusion using the wavelet transform,” Graph. Models Image Proc. 57(3), 235–245 (1995).
[Crossref]

Manuel de la Cruz, J.

G. Pajares and J. Manuel de la Cruz, “A wavelet-based image fusion tutorial,” Pattern Recognit. 37(9), 1855–1872 (2004).
[Crossref]

Marabini, R.

McNally, J. G.

G. Schneider, P. Guttmann, S. Heim, S. Rehbein, F. Mueller, K. Nagashima, J. B. Heymann, W. G. Müller, and J. G. McNally, “Three-dimensional cellular ultrastructure resolved by X-ray microscopy,” Nat. Methods 7(12), 985–987 (2010).
[Crossref] [PubMed]

Meirer, F.

J. C. Andrews, E. Almeida, M. C. van der Meulen, J. S. Alwood, C. Lee, Y. Liu, J. Chen, F. Meirer, M. Feser, J. Gelb, J. Rudati, A. Tkachuk, W. Yun, and P. Pianetta, “Nanoscale X-ray microscopic imaging of mammalian mineralized tissue,” Microsc. Microanal. 16(3), 327–336 (2010).
[Crossref] [PubMed]

Mitra, S. K.

H. Li, B. Manjunath, and S. K. Mitra, “Multisensor image fusion using the wavelet transform,” Graph. Models Image Proc. 57(3), 235–245 (1995).
[Crossref]

Mueller, F.

G. Schneider, P. Guttmann, S. Heim, S. Rehbein, F. Mueller, K. Nagashima, J. B. Heymann, W. G. Müller, and J. G. McNally, “Three-dimensional cellular ultrastructure resolved by X-ray microscopy,” Nat. Methods 7(12), 985–987 (2010).
[Crossref] [PubMed]

Müller, W. G.

G. Schneider, P. Guttmann, S. Heim, S. Rehbein, F. Mueller, K. Nagashima, J. B. Heymann, W. G. Müller, and J. G. McNally, “Three-dimensional cellular ultrastructure resolved by X-ray microscopy,” Nat. Methods 7(12), 985–987 (2010).
[Crossref] [PubMed]

Nagashima, K.

G. Schneider, P. Guttmann, S. Heim, S. Rehbein, F. Mueller, K. Nagashima, J. B. Heymann, W. G. Müller, and J. G. McNally, “Three-dimensional cellular ultrastructure resolved by X-ray microscopy,” Nat. Methods 7(12), 985–987 (2010).
[Crossref] [PubMed]

Otón, J.

Pajares, G.

G. Pajares and J. Manuel de la Cruz, “A wavelet-based image fusion tutorial,” Pattern Recognit. 37(9), 1855–1872 (2004).
[Crossref]

Pereiro, E.

Petrovic, V. S.

V. S. Petrović and C. S. Xydeas, “Gradient-based multiresolution image fusion,” IEEE Trans. Image Process. 13(2), 228–237 (2004).
[Crossref] [PubMed]

V. S. Petrović and C. S. Xydeas, “Gradient-based multiresolution image fusion,” IEEE Trans. Image Process. 13(2), 228–237 (2004).
[Crossref] [PubMed]

Peuker, M.

M. Peuker, “High-efficiency nickel phase zone plates with 20 nm minimum outermost zone width,” Appl. Phys. Lett. 78(15), 2208–2210 (2001).
[Crossref]

Pianetta, P.

Y. Liu, J. Wang, Y. Hong, Z. Wang, K. Zhang, P. A. Williams, P. Zhu, J. C. Andrews, P. Pianetta, and Z. Wu, “Extended depth of focus for transmission x-ray microscope,” Opt. Lett. 37(17), 3708–3710 (2012).
[Crossref] [PubMed]

J. C. Andrews, E. Almeida, M. C. van der Meulen, J. S. Alwood, C. Lee, Y. Liu, J. Chen, F. Meirer, M. Feser, J. Gelb, J. Rudati, A. Tkachuk, W. Yun, and P. Pianetta, “Nanoscale X-ray microscopic imaging of mammalian mineralized tissue,” Microsc. Microanal. 16(3), 327–336 (2010).
[Crossref] [PubMed]

Quinto, E. T.

J. Frikel and E. T. Quinto, “Characterization and reduction of artifacts in limited angle tomography,” Inverse Probl. 29(12), 125007 (2013).
[Crossref]

Rehbein, S.

G. Schneider, P. Guttmann, S. Heim, S. Rehbein, F. Mueller, K. Nagashima, J. B. Heymann, W. G. Müller, and J. G. McNally, “Three-dimensional cellular ultrastructure resolved by X-ray microscopy,” Nat. Methods 7(12), 985–987 (2010).
[Crossref] [PubMed]

Rivers, M.

C. Jacobsen, S. Williams, E. Anderson, M. T. Browne, C. J. Buckley, D. Kern, J. Kirz, M. Rivers, and X. Zhang, “Diffraction-limited imaging in a scanning transmission x-ray microscope,” Opt. Commun. 86(3-4), 351–364 (1991).
[Crossref]

Rudati, J.

J. C. Andrews, E. Almeida, M. C. van der Meulen, J. S. Alwood, C. Lee, Y. Liu, J. Chen, F. Meirer, M. Feser, J. Gelb, J. Rudati, A. Tkachuk, W. Yun, and P. Pianetta, “Nanoscale X-ray microscopic imaging of mammalian mineralized tissue,” Microsc. Microanal. 16(3), 327–336 (2010).
[Crossref] [PubMed]

Rudolph, D.

S. Vogt, G. Schneider, A. Steuernagel, J. Lucchesi, E. Schulze, D. Rudolph, and G. Schmahl, “X-ray microscopic studies of the Drosophila dosage compensation complex,” J. Struct. Biol. 132(2), 123–132 (2000).
[Crossref] [PubMed]

Sakdinawat, A.

A. Sakdinawat and D. Attwood, “Nanoscale X-ray imaging,” Nat. Photonics 4(12), 840–848 (2010).
[Crossref]

Schmahl, G.

S. Vogt, G. Schneider, A. Steuernagel, J. Lucchesi, E. Schulze, D. Rudolph, and G. Schmahl, “X-ray microscopic studies of the Drosophila dosage compensation complex,” J. Struct. Biol. 132(2), 123–132 (2000).
[Crossref] [PubMed]

Schneider, G.

G. Schneider, P. Guttmann, S. Heim, S. Rehbein, F. Mueller, K. Nagashima, J. B. Heymann, W. G. Müller, and J. G. McNally, “Three-dimensional cellular ultrastructure resolved by X-ray microscopy,” Nat. Methods 7(12), 985–987 (2010).
[Crossref] [PubMed]

S. Vogt, G. Schneider, A. Steuernagel, J. Lucchesi, E. Schulze, D. Rudolph, and G. Schmahl, “X-ray microscopic studies of the Drosophila dosage compensation complex,” J. Struct. Biol. 132(2), 123–132 (2000).
[Crossref] [PubMed]

Schulze, E.

S. Vogt, G. Schneider, A. Steuernagel, J. Lucchesi, E. Schulze, D. Rudolph, and G. Schmahl, “X-ray microscopic studies of the Drosophila dosage compensation complex,” J. Struct. Biol. 132(2), 123–132 (2000).
[Crossref] [PubMed]

Selin, M.

Shin, T. J.

G. B. Kim, Y. J. Yoon, T. J. Shin, H. S. Youn, Y. S. Gho, and S. J. Lee, “X-ray imaging of various biological samples using a phase-contrast hard X-ray microscope,” Microsc. Res. Tech. 71(9), 639–643 (2008).
[Crossref] [PubMed]

Sorzano, C. O.

Steuernagel, A.

S. Vogt, G. Schneider, A. Steuernagel, J. Lucchesi, E. Schulze, D. Rudolph, and G. Schmahl, “X-ray microscopic studies of the Drosophila dosage compensation complex,” J. Struct. Biol. 132(2), 123–132 (2000).
[Crossref] [PubMed]

Tian, Y.

Z. Liang, Y. Guan, G. Liu, R. Bian, X. Zhang, Y. Xiong, and Y. Tian, “Reconstruction of limited-angle and few-view nano-CT image via total variation iterative reconstruction,” Proc. SPIE 8851, 885113 (2013).
[Crossref]

Y. Guan, W. Li, Y. Gong, G. Liu, X. Zhang, J. Chen, J. Gelb, W. Yun, Y. Xiong, Y. Tian, and H. Wang, “Analysis of the three-dimensional microstructure of a solid-oxide fuel cell anode using nano X-ray tomography,” J. Power Sources 196(4), 1915–1919 (2011).
[Crossref]

Tian, Y. C.

P. F. Guo, Y. Guan, G. Liu, Z. T. Liang, J. H. Liu, X. B. Zhang, Y. Xiong, and Y. C. Tian, “Modeling of gas transport with electrochemical reaction in nickel-yttria-stabilized zirconia anode during thermal cycling by Lattice Boltzmann method,” J. Power Sources 327, 127–134 (2016).
[Crossref]

Tkachuk, A.

J. C. Andrews, E. Almeida, M. C. van der Meulen, J. S. Alwood, C. Lee, Y. Liu, J. Chen, F. Meirer, M. Feser, J. Gelb, J. Rudati, A. Tkachuk, W. Yun, and P. Pianetta, “Nanoscale X-ray microscopic imaging of mammalian mineralized tissue,” Microsc. Microanal. 16(3), 327–336 (2010).
[Crossref] [PubMed]

van der Meulen, M. C.

J. C. Andrews, E. Almeida, M. C. van der Meulen, J. S. Alwood, C. Lee, Y. Liu, J. Chen, F. Meirer, M. Feser, J. Gelb, J. Rudati, A. Tkachuk, W. Yun, and P. Pianetta, “Nanoscale X-ray microscopic imaging of mammalian mineralized tissue,” Microsc. Microanal. 16(3), 327–336 (2010).
[Crossref] [PubMed]

Vogt, S.

S. Vogt, G. Schneider, A. Steuernagel, J. Lucchesi, E. Schulze, D. Rudolph, and G. Schmahl, “X-ray microscopic studies of the Drosophila dosage compensation complex,” J. Struct. Biol. 132(2), 123–132 (2000).
[Crossref] [PubMed]

Wang, H.

Y. Guan, W. Li, Y. Gong, G. Liu, X. Zhang, J. Chen, J. Gelb, W. Yun, Y. Xiong, Y. Tian, and H. Wang, “Analysis of the three-dimensional microstructure of a solid-oxide fuel cell anode using nano X-ray tomography,” J. Power Sources 196(4), 1915–1919 (2011).
[Crossref]

Wang, J.

Wang, Z.

Wang, Z. F.

Y. Liu, S. P. Liu, and Z. F. Wang, “A general framework for image fusion based on multi-scale transform and sparse representation,” Inf. Fusion 24, 147–164 (2015).
[Crossref]

Werner, S.

Williams, P. A.

Williams, S.

C. Jacobsen, J. Kirz, and S. Williams, “Resolution in soft x-ray microscopes,” Ultramicroscopy 47(1-3), 55–79 (1992).
[Crossref]

C. Jacobsen, S. Williams, E. Anderson, M. T. Browne, C. J. Buckley, D. Kern, J. Kirz, M. Rivers, and X. Zhang, “Diffraction-limited imaging in a scanning transmission x-ray microscope,” Opt. Commun. 86(3-4), 351–364 (1991).
[Crossref]

Wu, Z.

Xiong, Y.

P. F. Guo, Y. Guan, G. Liu, Z. T. Liang, J. H. Liu, X. B. Zhang, Y. Xiong, and Y. C. Tian, “Modeling of gas transport with electrochemical reaction in nickel-yttria-stabilized zirconia anode during thermal cycling by Lattice Boltzmann method,” J. Power Sources 327, 127–134 (2016).
[Crossref]

Z. Liang, Y. Guan, G. Liu, R. Bian, X. Zhang, Y. Xiong, and Y. Tian, “Reconstruction of limited-angle and few-view nano-CT image via total variation iterative reconstruction,” Proc. SPIE 8851, 885113 (2013).
[Crossref]

Y. Guan, W. Li, Y. Gong, G. Liu, X. Zhang, J. Chen, J. Gelb, W. Yun, Y. Xiong, Y. Tian, and H. Wang, “Analysis of the three-dimensional microstructure of a solid-oxide fuel cell anode using nano X-ray tomography,” J. Power Sources 196(4), 1915–1919 (2011).
[Crossref]

Xydeas, C. S.

V. S. Petrović and C. S. Xydeas, “Gradient-based multiresolution image fusion,” IEEE Trans. Image Process. 13(2), 228–237 (2004).
[Crossref] [PubMed]

V. S. Petrović and C. S. Xydeas, “Gradient-based multiresolution image fusion,” IEEE Trans. Image Process. 13(2), 228–237 (2004).
[Crossref] [PubMed]

Yoon, Y. J.

G. B. Kim, Y. J. Yoon, T. J. Shin, H. S. Youn, Y. S. Gho, and S. J. Lee, “X-ray imaging of various biological samples using a phase-contrast hard X-ray microscope,” Microsc. Res. Tech. 71(9), 639–643 (2008).
[Crossref] [PubMed]

Youn, H. S.

G. B. Kim, Y. J. Yoon, T. J. Shin, H. S. Youn, Y. S. Gho, and S. J. Lee, “X-ray imaging of various biological samples using a phase-contrast hard X-ray microscope,” Microsc. Res. Tech. 71(9), 639–643 (2008).
[Crossref] [PubMed]

Yun, W.

Y. Guan, W. Li, Y. Gong, G. Liu, X. Zhang, J. Chen, J. Gelb, W. Yun, Y. Xiong, Y. Tian, and H. Wang, “Analysis of the three-dimensional microstructure of a solid-oxide fuel cell anode using nano X-ray tomography,” J. Power Sources 196(4), 1915–1919 (2011).
[Crossref]

J. C. Andrews, E. Almeida, M. C. van der Meulen, J. S. Alwood, C. Lee, Y. Liu, J. Chen, F. Meirer, M. Feser, J. Gelb, J. Rudati, A. Tkachuk, W. Yun, and P. Pianetta, “Nanoscale X-ray microscopic imaging of mammalian mineralized tissue,” Microsc. Microanal. 16(3), 327–336 (2010).
[Crossref] [PubMed]

Zhang, K.

Zhang, X.

Z. Liang, Y. Guan, G. Liu, R. Bian, X. Zhang, Y. Xiong, and Y. Tian, “Reconstruction of limited-angle and few-view nano-CT image via total variation iterative reconstruction,” Proc. SPIE 8851, 885113 (2013).
[Crossref]

Y. Guan, W. Li, Y. Gong, G. Liu, X. Zhang, J. Chen, J. Gelb, W. Yun, Y. Xiong, Y. Tian, and H. Wang, “Analysis of the three-dimensional microstructure of a solid-oxide fuel cell anode using nano X-ray tomography,” J. Power Sources 196(4), 1915–1919 (2011).
[Crossref]

C. Jacobsen, S. Williams, E. Anderson, M. T. Browne, C. J. Buckley, D. Kern, J. Kirz, M. Rivers, and X. Zhang, “Diffraction-limited imaging in a scanning transmission x-ray microscope,” Opt. Commun. 86(3-4), 351–364 (1991).
[Crossref]

Zhang, X. B.

P. F. Guo, Y. Guan, G. Liu, Z. T. Liang, J. H. Liu, X. B. Zhang, Y. Xiong, and Y. C. Tian, “Modeling of gas transport with electrochemical reaction in nickel-yttria-stabilized zirconia anode during thermal cycling by Lattice Boltzmann method,” J. Power Sources 327, 127–134 (2016).
[Crossref]

Zhu, P.

Appl. Phys. Lett. (1)

M. Peuker, “High-efficiency nickel phase zone plates with 20 nm minimum outermost zone width,” Appl. Phys. Lett. 78(15), 2208–2210 (2001).
[Crossref]

Graph. Models Image Proc. (1)

H. Li, B. Manjunath, and S. K. Mitra, “Multisensor image fusion using the wavelet transform,” Graph. Models Image Proc. 57(3), 235–245 (1995).
[Crossref]

IEEE Trans. Image Process. (2)

V. S. Petrović and C. S. Xydeas, “Gradient-based multiresolution image fusion,” IEEE Trans. Image Process. 13(2), 228–237 (2004).
[Crossref] [PubMed]

V. S. Petrović and C. S. Xydeas, “Gradient-based multiresolution image fusion,” IEEE Trans. Image Process. 13(2), 228–237 (2004).
[Crossref] [PubMed]

Inf. Fusion (1)

Y. Liu, S. P. Liu, and Z. F. Wang, “A general framework for image fusion based on multi-scale transform and sparse representation,” Inf. Fusion 24, 147–164 (2015).
[Crossref]

Inverse Probl. (1)

J. Frikel and E. T. Quinto, “Characterization and reduction of artifacts in limited angle tomography,” Inverse Probl. 29(12), 125007 (2013).
[Crossref]

J. Power Sources (2)

P. F. Guo, Y. Guan, G. Liu, Z. T. Liang, J. H. Liu, X. B. Zhang, Y. Xiong, and Y. C. Tian, “Modeling of gas transport with electrochemical reaction in nickel-yttria-stabilized zirconia anode during thermal cycling by Lattice Boltzmann method,” J. Power Sources 327, 127–134 (2016).
[Crossref]

Y. Guan, W. Li, Y. Gong, G. Liu, X. Zhang, J. Chen, J. Gelb, W. Yun, Y. Xiong, Y. Tian, and H. Wang, “Analysis of the three-dimensional microstructure of a solid-oxide fuel cell anode using nano X-ray tomography,” J. Power Sources 196(4), 1915–1919 (2011).
[Crossref]

J. Struct. Biol. (1)

S. Vogt, G. Schneider, A. Steuernagel, J. Lucchesi, E. Schulze, D. Rudolph, and G. Schmahl, “X-ray microscopic studies of the Drosophila dosage compensation complex,” J. Struct. Biol. 132(2), 123–132 (2000).
[Crossref] [PubMed]

Microsc. Microanal. (1)

J. C. Andrews, E. Almeida, M. C. van der Meulen, J. S. Alwood, C. Lee, Y. Liu, J. Chen, F. Meirer, M. Feser, J. Gelb, J. Rudati, A. Tkachuk, W. Yun, and P. Pianetta, “Nanoscale X-ray microscopic imaging of mammalian mineralized tissue,” Microsc. Microanal. 16(3), 327–336 (2010).
[Crossref] [PubMed]

Microsc. Res. Tech. (1)

G. B. Kim, Y. J. Yoon, T. J. Shin, H. S. Youn, Y. S. Gho, and S. J. Lee, “X-ray imaging of various biological samples using a phase-contrast hard X-ray microscope,” Microsc. Res. Tech. 71(9), 639–643 (2008).
[Crossref] [PubMed]

Nat. Methods (1)

G. Schneider, P. Guttmann, S. Heim, S. Rehbein, F. Mueller, K. Nagashima, J. B. Heymann, W. G. Müller, and J. G. McNally, “Three-dimensional cellular ultrastructure resolved by X-ray microscopy,” Nat. Methods 7(12), 985–987 (2010).
[Crossref] [PubMed]

Nat. Photonics (1)

A. Sakdinawat and D. Attwood, “Nanoscale X-ray imaging,” Nat. Photonics 4(12), 840–848 (2010).
[Crossref]

Opt. Commun. (1)

C. Jacobsen, S. Williams, E. Anderson, M. T. Browne, C. J. Buckley, D. Kern, J. Kirz, M. Rivers, and X. Zhang, “Diffraction-limited imaging in a scanning transmission x-ray microscope,” Opt. Commun. 86(3-4), 351–364 (1991).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Pattern Recognit. (1)

G. Pajares and J. Manuel de la Cruz, “A wavelet-based image fusion tutorial,” Pattern Recognit. 37(9), 1855–1872 (2004).
[Crossref]

Proc. SPIE (1)

Z. Liang, Y. Guan, G. Liu, R. Bian, X. Zhang, Y. Xiong, and Y. Tian, “Reconstruction of limited-angle and few-view nano-CT image via total variation iterative reconstruction,” Proc. SPIE 8851, 885113 (2013).
[Crossref]

Trends Cell Biol. (1)

C. Jacobsen, “Soft x-ray microscopy,” Trends Cell Biol. 9(2), 44–47 (1999).
[Crossref] [PubMed]

Ultramicroscopy (1)

C. Jacobsen, J. Kirz, and S. Williams, “Resolution in soft x-ray microscopes,” Ultramicroscopy 47(1-3), 55–79 (1992).
[Crossref]

Other (4)

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

Z. Liang, Y. Guan, S. Chen, and Y. Tian, “Whole cells imaged by hard X-ray transmission microscopy,” in Advanced Microscopy in Mycology (Springer, 2015), pp. 89–107.

A. Mansoor and A. B. Mansoor, “On image compression using digital curvelet transform,” in 2005 Pakistan Section Multitopic Conference (IEEE, 2005), pp. 1–4.

J. W. Goodman, Statistical Optics (Wiley, 2000).

Supplementary Material (1)

NameDescription
» Visualization 1: AVI (23450 KB)      The 3D reconstruction of the diatom frustules that was obtained from the fused slice images

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Figures (8)

Fig. 1
Fig. 1 Schematic of the proposed fusion framework. ( I θ ) Δ z 1 , ( I θ ) Δ z 2 , ( I θ ) Δ z 3 : projection data in different Δ z ; θ 0 , θ 1 ,…, θ n : the rotation angle of sample; Δ z 1 , Δ z 2 , Δ z 3 : the different distance of the sample between the ZP; FBP: filtered back-projection reconstruction algorithm; R 1 , R 2 , R 3 : 3D reconstruction data in different Δ z ; D W T : 2D DWT; I D W T : inverse 2D DWT; R i n f o c u s : fused in-focus 3D reconstruction data.
Fig. 2
Fig. 2 Schematic of X-ray transmission microscope. Condenser: focuses a hollow central cone of X-rays onto the sample through the inner reflecting surface. Rotation axis: Sample rotates around the axis so that projections at different angles can be obtained. Objective ZP: used as an objective lens for TXM. Charge-coupled device (CCD): serves as a detector [12].
Fig. 3
Fig. 3 (a) Cylinder with a length 8 μm, i.e., longer than the DOF, which was used as the sample in the simulation; (b) Projected image at 0°of the sample at 0 μm defocus distance; (c) Projected image at 0°of the sample at 3 μm defocus distance, and (d) Projected image at 0°of the sample at −3 μm defocus distance; (e), (f), and (g) Local, enlarged views of the projected images in (b), (c), and (d), respectively.
Fig. 4
Fig. 4 (a) 3D reconstruction of the cylinder at 0 μm and (b) a slice of (a); (c) 3D reconstruction of the cylinder at 3 μm and (d) a slice of (c); (e) 3D reconstruction of the cylinder at −3 μm and (f) a slice of (e); (h) fully focused 3D reconstruction of the cylinder obtained using the proposed fusion method and (i) a slice of (h). The insets in each sub-figure show a magnified view of one part of reconstructed slice.
Fig. 5
Fig. 5 (a) Sample used to illustrate the problem that occurs if the DOF is shorter than the sample is thick; (b) Projected image at 0°of the sample at 0μm defocus distance; (c) Projected image at 0°of the sample at 2.5 μm defocus distance, and (d) Projected image at 0°of the sample at −2.5 μm defocus distance. The insets in each sub-figure show a magnified view of two parts of projected image.
Fig. 6
Fig. 6 (a) 3D reconstruction of multiple objects at 0 μm and (b) a slice of (a); (c) 3D reconstruction of multiple objects at 2.5 μm and (d) a slice of (c); (e) 3D reconstruction of multiple objects at −2.5 μm and (f) a slice of (e); (h) fused 3D reconstruction of multiple objects and (i) a slice of (h). The insets in each sub-figure show a magnified view of one part of reconstructed slice.
Fig. 7
Fig. 7 Sliced images viewed along the rotation axis that were obtained from the reconstructions of the diatom frustules at (a) −5 μm, (b) 0 μm, and (c) 5 μm. (d) Fused slice image viewed along the rotation axis. The each sub-figure (rigth) show a magnified view of one part of reconstructed slice.
Fig. 8
Fig. 8 The 3D reconstruction of the diatom frustules that was obtained from the fused slice images (see Visualization 1).

Equations (5)

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( c j ( x , y ) ) 1 , 2 , ... , s = D W T ( s l i c e 1 , 2 , ... , s ( x , y ) ) ,
V n ( x , y ) = i = 2 2 j = 2 2 ( I n ( x + i , y + j ) I ¯ ( x , y ) ) 2 ( I ¯ ( x , y ) ) 2 ,
I ¯ ( x , y ) = 1 25 i = 2 2 j = 2 2 I n ( x + i , y + j ) ,
c m j = arg m a x n ( V n ( x , y ) ) .
s l i c e i n f o c ( x , y ) = | I D W T ( j c m j ( x , y ) ) | ,

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