Abstract

An alternative method for quantitative phase retrieval in a transmission X-ray microscope system at sub-50-nm resolution is presented. As an alternative to moving the sample in the beam direction in order to analyze the propagation-introduced phase effect, we have illuminated the TXM using X-rays of different energy without any motor movement in the TXM system. Both theoretical analysis and experimental studies have confirmed the feasibility and the advantage of our method, because energy tuning can be performed with very high energy resolution using a double crystal monochromator at a synchrotron beam line, and there is zero motor error in TXM system in our approach. High-spatial-resolution phase retrieval is accomplished using the proposed method.

© 2011 Optical Society of America

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    [CrossRef]
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  4. W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, "Soft X-ray microscopy at a spatial resolution better than 15 nm," Nature 435, 1210-1213 (2005).
    [CrossRef] [PubMed]
  5. G. C. Yin, M. T. Tang, Y. F. Song, F. R. Chen, K. S. Liang, F. W. Duewer, W. Yun, C. H. Ko, and H. P. D. Shieh, "Energy-tunable transmission x-ray microscope for differential contrast imaging with near 60 nm resolution tomography," Appl. Phys. Lett. 88, 241115 (2006).
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  10. J. Chen, C. Wu, J. Tian, W. Li, S. Yu, and Y. Tian, "Three-dimensional imaging of a complex concaved cuboctahedron copper sulfide crystal by x-ray nanotomography," Appl. Phys. Lett. 92, 233104 (2008).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  24. Ya. I. Nesterets, and S. W. Wilkins, "Phase-contrast imaging using a scanning-double-grating configuration," Opt. Express 16(8), 5849-5867 (2008).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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2010 (1)

J. Andrews, E. Almeida, M. C. H. 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, 327-336 (2010).
[CrossRef] [PubMed]

2009 (3)

S. Rehbein, S. Heim, P. Guttmann, S. Werner, and G. Schneider, "Ultrahigh Resolution Soft-X-Ray Microscopy with Zone Plates in High Orders of Diffraction," Phys. Rev. Lett. 103, 110801 (2009).
[CrossRef] [PubMed]

W. Li, N. Wang, J. Chen, G. Liu, Z. Pan, Y. Guan, Y. Yang, W. Wu, J. Tian, S. Wei, Z. Wu, and Y. Tian, "Quantitative study of interior nanostructure in hollow zinc oxide particles on the basis of nondestructive x-ray nanotomography," Appl. Phys. Lett. 95, 053108 (2009).
[CrossRef]

C. Patty, B. Barnett, B. Mooney, A. Kahn, S. Levy, Y. Liu, P. Pianetta, and J. C. Andrews, "Using X-ray microscopy and Hg L3 XANES to study Hg binding in the rhizosphere of Spartina cordgrass," Environ. Sci. Technol. 43, 7397-7402 (2009).
[CrossRef] [PubMed]

2008 (6)

Y. S. Chu, J. M. Yi, F. De Carlo, Q. Shen, W. K. Lee, H. J. Wu, C. L. Wang, J. Y. Wang, C. J. Liu, C. H. Wang, S. R. Wu, C. C. Chien, Y. Hwu, A. Tkachuk, W. Yun, M. Feser, K. S. Liang, C. S. Yang, J. H. Je, and G. Margaritondo, "Hard-x-ray microscopy with Fresnel zone plates reaches 40 nm Rayleigh resolution," Appl. Phys. Lett. 92, 103119 (2008).
[CrossRef]

M. D. de Jonge, B. Hornberger, C. Holzner, D. Legnini, D. Paterson, I. McNulty, C. Jacobsen, and S. Vogt, "Quantitative Phase Imaging with a Scanning Transmission X-Ray Microscope," Phys. Rev. Lett. 100, 163902 (2008).
[CrossRef] [PubMed]

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]

J. Chen, C. Wu, J. Tian, W. Li, S. Yu, and Y. Tian, "Three-dimensional imaging of a complex concaved cuboctahedron copper sulfide crystal by x-ray nanotomography," Appl. Phys. Lett. 92, 233104 (2008).
[CrossRef]

Y. Liu, B. Chen, E. Li, J. Wang, A. Marcelli, S. W. Wilkins, H. Ming, Y. Tian, K. A. Nugent, P. Zhu, and Z. Wu, "Phase retrieval in x-ray imaging based on using structured illumination," Phys. Rev. A 78, 023817 (2008).
[CrossRef]

Ya. I. Nesterets, and S. W. Wilkins, "Phase-contrast imaging using a scanning-double-grating configuration," Opt. Express 16(8), 5849-5867 (2008).
[CrossRef] [PubMed]

2007 (4)

G. Yin, F. Chen, Y. Hwu, H. D. Shieh, and K. S. Liang, "Quantitative phase retrieval in transmission hard x-ray microscope," Appl. Phys. Lett. 90, 181118 (2007).

F. Zhang, G. Pedrini, and W. Osten, "Phase retrieval of arbitrary complex-valued fields through aperture-plane modulation," Phys. Rev. A 75, 043805 (2007).
[CrossRef]

Y. Liu, P. Zhu, B. Chen, J. Wang, Q. Yuan, W. Huang, H. Shu, E. Li, X. Liu, K. Zhang, H. Ming, and Z. Wu, "A new iterative algorithm to reconstruct the refractive index," Phys. Med. Biol. 52, L5-L13 (2007).
[CrossRef] [PubMed]

A. Sakdinawat and Y. Liu, "Soft-x-ray microscopy using spiral zone plates," Opt. Lett. 32(18), 2635-2637 (2007).
[CrossRef] [PubMed]

2006 (2)

G. C. Yin, M. T. Tang, Y. F. Song, F. R. Chen, K. S. Liang, F. W. Duewer, W. Yun, C. H. Ko, and H. P. D. Shieh, "Energy-tunable transmission x-ray microscope for differential contrast imaging with near 60 nm resolution tomography," Appl. Phys. Lett. 88, 241115 (2006).
[CrossRef]

P. Franz, T. Weitkamp, O. Bunk, and C. David, "Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray source," Nat. Phys. 2, 258-261 (2006).
[CrossRef]

2005 (1)

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, "Soft X-ray microscopy at a spatial resolution better than 15 nm," Nature 435, 1210-1213 (2005).
[CrossRef] [PubMed]

2003 (2)

Y. Wang, W. Yun, and C. Jacobsen, "Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging," Nature 424, 50-53 (2003).
[CrossRef] [PubMed]

A. Momose, "Phase-sensitive imaging and phase tomography using X-ray interferometers," Opt. Express 11, 2303-2314 (2003).
[CrossRef] [PubMed]

2002 (1)

Y. Hwu, W. Tsai, A. Groso, G. Margaritondo, and J. Ho Je, "Coherence-enhanced synchrotron radiology: simple theory and practical applications," J. Phys. D Appl. Phys. 35, R105 (2002).
[CrossRef]

1999 (1)

E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, "High-efficiency multilevel zone plates for keV X-rays," Nature 401, 895-898 (1999).
[CrossRef]

1997 (1)

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, "Diffraction enhanced x-ray imaging," Phys. Med. Biol. 42, 2015-2025 (1997).
[CrossRef] [PubMed]

1996 (1)

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, "Phase-contrast imaging using polychromatic hard X-rays," Nature 384, 335-338 (1996).
[CrossRef]

1992 (2)

K. A. Nugent, "Wave field determination using three-dimensional intensity information," Phys. Rev. Lett. 68, 2261-2264 (1992).
[CrossRef] [PubMed]

W. B. Yun, P. J. Viccaro, B. Lai, and J. Chrzas, "Coherent hard x-ray focusing optics and applications," Rev. Sci. Instrum. 63(1), 582-585 (1992).
[CrossRef]

1982 (1)

J. R. Fienup, "Phase retrieval algorithms: a comparison," Appl. Opt. 21, 2758 (1982).
[CrossRef] [PubMed]

1972 (1)

R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of the phase from image and diffraction plane pictures," Optik 35, 237 (1972).

Almeida, E.

J. Andrews, E. Almeida, M. C. H. 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, 327-336 (2010).
[CrossRef] [PubMed]

Alwood, J. S.

J. Andrews, E. Almeida, M. C. H. 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, 327-336 (2010).
[CrossRef] [PubMed]

Anderson, E. H.

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, "Soft X-ray microscopy at a spatial resolution better than 15 nm," Nature 435, 1210-1213 (2005).
[CrossRef] [PubMed]

Andrews, J.

J. Andrews, E. Almeida, M. C. H. 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, 327-336 (2010).
[CrossRef] [PubMed]

Andrews, J. C.

C. Patty, B. Barnett, B. Mooney, A. Kahn, S. Levy, Y. Liu, P. Pianetta, and J. C. Andrews, "Using X-ray microscopy and Hg L3 XANES to study Hg binding in the rhizosphere of Spartina cordgrass," Environ. Sci. Technol. 43, 7397-7402 (2009).
[CrossRef] [PubMed]

Arfelli, F.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, "Diffraction enhanced x-ray imaging," Phys. Med. Biol. 42, 2015-2025 (1997).
[CrossRef] [PubMed]

Attwood, D. T.

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, "Soft X-ray microscopy at a spatial resolution better than 15 nm," Nature 435, 1210-1213 (2005).
[CrossRef] [PubMed]

Barnett, B.

C. Patty, B. Barnett, B. Mooney, A. Kahn, S. Levy, Y. Liu, P. Pianetta, and J. C. Andrews, "Using X-ray microscopy and Hg L3 XANES to study Hg binding in the rhizosphere of Spartina cordgrass," Environ. Sci. Technol. 43, 7397-7402 (2009).
[CrossRef] [PubMed]

Barrett, R.

E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, "High-efficiency multilevel zone plates for keV X-rays," Nature 401, 895-898 (1999).
[CrossRef]

Bunk, O.

P. Franz, T. Weitkamp, O. Bunk, and C. David, "Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray source," Nat. Phys. 2, 258-261 (2006).
[CrossRef]

Cabrini, S.

E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, "High-efficiency multilevel zone plates for keV X-rays," Nature 401, 895-898 (1999).
[CrossRef]

Chao, W.

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, "Soft X-ray microscopy at a spatial resolution better than 15 nm," Nature 435, 1210-1213 (2005).
[CrossRef] [PubMed]

Chapman, D.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, "Diffraction enhanced x-ray imaging," Phys. Med. Biol. 42, 2015-2025 (1997).
[CrossRef] [PubMed]

Chen, B.

Y. Liu, B. Chen, E. Li, J. Wang, A. Marcelli, S. W. Wilkins, H. Ming, Y. Tian, K. A. Nugent, P. Zhu, and Z. Wu, "Phase retrieval in x-ray imaging based on using structured illumination," Phys. Rev. A 78, 023817 (2008).
[CrossRef]

Y. Liu, P. Zhu, B. Chen, J. Wang, Q. Yuan, W. Huang, H. Shu, E. Li, X. Liu, K. Zhang, H. Ming, and Z. Wu, "A new iterative algorithm to reconstruct the refractive index," Phys. Med. Biol. 52, L5-L13 (2007).
[CrossRef] [PubMed]

Chen, F.

G. Yin, F. Chen, Y. Hwu, H. D. Shieh, and K. S. Liang, "Quantitative phase retrieval in transmission hard x-ray microscope," Appl. Phys. Lett. 90, 181118 (2007).

Chen, F. R.

G. C. Yin, M. T. Tang, Y. F. Song, F. R. Chen, K. S. Liang, F. W. Duewer, W. Yun, C. H. Ko, and H. P. D. Shieh, "Energy-tunable transmission x-ray microscope for differential contrast imaging with near 60 nm resolution tomography," Appl. Phys. Lett. 88, 241115 (2006).
[CrossRef]

Chen, J.

J. Andrews, E. Almeida, M. C. H. 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, 327-336 (2010).
[CrossRef] [PubMed]

W. Li, N. Wang, J. Chen, G. Liu, Z. Pan, Y. Guan, Y. Yang, W. Wu, J. Tian, S. Wei, Z. Wu, and Y. Tian, "Quantitative study of interior nanostructure in hollow zinc oxide particles on the basis of nondestructive x-ray nanotomography," Appl. Phys. Lett. 95, 053108 (2009).
[CrossRef]

J. Chen, C. Wu, J. Tian, W. Li, S. Yu, and Y. Tian, "Three-dimensional imaging of a complex concaved cuboctahedron copper sulfide crystal by x-ray nanotomography," Appl. Phys. Lett. 92, 233104 (2008).
[CrossRef]

Chien, C. C.

Y. S. Chu, J. M. Yi, F. De Carlo, Q. Shen, W. K. Lee, H. J. Wu, C. L. Wang, J. Y. Wang, C. J. Liu, C. H. Wang, S. R. Wu, C. C. Chien, Y. Hwu, A. Tkachuk, W. Yun, M. Feser, K. S. Liang, C. S. Yang, J. H. Je, and G. Margaritondo, "Hard-x-ray microscopy with Fresnel zone plates reaches 40 nm Rayleigh resolution," Appl. Phys. Lett. 92, 103119 (2008).
[CrossRef]

Chrzas, J.

W. B. Yun, P. J. Viccaro, B. Lai, and J. Chrzas, "Coherent hard x-ray focusing optics and applications," Rev. Sci. Instrum. 63(1), 582-585 (1992).
[CrossRef]

Chu, Y. S.

Y. S. Chu, J. M. Yi, F. De Carlo, Q. Shen, W. K. Lee, H. J. Wu, C. L. Wang, J. Y. Wang, C. J. Liu, C. H. Wang, S. R. Wu, C. C. Chien, Y. Hwu, A. Tkachuk, W. Yun, M. Feser, K. S. Liang, C. S. Yang, J. H. Je, and G. Margaritondo, "Hard-x-ray microscopy with Fresnel zone plates reaches 40 nm Rayleigh resolution," Appl. Phys. Lett. 92, 103119 (2008).
[CrossRef]

David, C.

P. Franz, T. Weitkamp, O. Bunk, and C. David, "Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray source," Nat. Phys. 2, 258-261 (2006).
[CrossRef]

De Carlo, F.

Y. S. Chu, J. M. Yi, F. De Carlo, Q. Shen, W. K. Lee, H. J. Wu, C. L. Wang, J. Y. Wang, C. J. Liu, C. H. Wang, S. R. Wu, C. C. Chien, Y. Hwu, A. Tkachuk, W. Yun, M. Feser, K. S. Liang, C. S. Yang, J. H. Je, and G. Margaritondo, "Hard-x-ray microscopy with Fresnel zone plates reaches 40 nm Rayleigh resolution," Appl. Phys. Lett. 92, 103119 (2008).
[CrossRef]

de Jonge, M. D.

M. D. de Jonge, B. Hornberger, C. Holzner, D. Legnini, D. Paterson, I. McNulty, C. Jacobsen, and S. Vogt, "Quantitative Phase Imaging with a Scanning Transmission X-Ray Microscope," Phys. Rev. Lett. 100, 163902 (2008).
[CrossRef] [PubMed]

Di Fabrizio, E.

E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, "High-efficiency multilevel zone plates for keV X-rays," Nature 401, 895-898 (1999).
[CrossRef]

Duewer, F. W.

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S. Rehbein, S. Heim, P. Guttmann, S. Werner, and G. Schneider, "Ultrahigh Resolution Soft-X-Ray Microscopy with Zone Plates in High Orders of Diffraction," Phys. Rev. Lett. 103, 110801 (2009).
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S. Rehbein, S. Heim, P. Guttmann, S. Werner, and G. Schneider, "Ultrahigh Resolution Soft-X-Ray Microscopy with Zone Plates in High Orders of Diffraction," Phys. Rev. Lett. 103, 110801 (2009).
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Y. S. Chu, J. M. Yi, F. De Carlo, Q. Shen, W. K. Lee, H. J. Wu, C. L. Wang, J. Y. Wang, C. J. Liu, C. H. Wang, S. R. Wu, C. C. Chien, Y. Hwu, A. Tkachuk, W. Yun, M. Feser, K. S. Liang, C. S. Yang, J. H. Je, and G. Margaritondo, "Hard-x-ray microscopy with Fresnel zone plates reaches 40 nm Rayleigh resolution," Appl. Phys. Lett. 92, 103119 (2008).
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G. Yin, F. Chen, Y. Hwu, H. D. Shieh, and K. S. Liang, "Quantitative phase retrieval in transmission hard x-ray microscope," Appl. Phys. Lett. 90, 181118 (2007).

Shieh, H. P. D.

G. C. Yin, M. T. Tang, Y. F. Song, F. R. Chen, K. S. Liang, F. W. Duewer, W. Yun, C. H. Ko, and H. P. D. Shieh, "Energy-tunable transmission x-ray microscope for differential contrast imaging with near 60 nm resolution tomography," Appl. Phys. Lett. 88, 241115 (2006).
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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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Y. Liu, P. Zhu, B. Chen, J. Wang, Q. Yuan, W. Huang, H. Shu, E. Li, X. Liu, K. Zhang, H. Ming, and Z. Wu, "A new iterative algorithm to reconstruct the refractive index," Phys. Med. Biol. 52, L5-L13 (2007).
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G. C. Yin, M. T. Tang, Y. F. Song, F. R. Chen, K. S. Liang, F. W. Duewer, W. Yun, C. H. Ko, and H. P. D. Shieh, "Energy-tunable transmission x-ray microscope for differential contrast imaging with near 60 nm resolution tomography," Appl. Phys. Lett. 88, 241115 (2006).
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S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, "Phase-contrast imaging using polychromatic hard X-rays," Nature 384, 335-338 (1996).
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E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, "High-efficiency multilevel zone plates for keV X-rays," Nature 401, 895-898 (1999).
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G. C. Yin, M. T. Tang, Y. F. Song, F. R. Chen, K. S. Liang, F. W. Duewer, W. Yun, C. H. Ko, and H. P. D. Shieh, "Energy-tunable transmission x-ray microscope for differential contrast imaging with near 60 nm resolution tomography," Appl. Phys. Lett. 88, 241115 (2006).
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W. Li, N. Wang, J. Chen, G. Liu, Z. Pan, Y. Guan, Y. Yang, W. Wu, J. Tian, S. Wei, Z. Wu, and Y. Tian, "Quantitative study of interior nanostructure in hollow zinc oxide particles on the basis of nondestructive x-ray nanotomography," Appl. Phys. Lett. 95, 053108 (2009).
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J. Chen, C. Wu, J. Tian, W. Li, S. Yu, and Y. Tian, "Three-dimensional imaging of a complex concaved cuboctahedron copper sulfide crystal by x-ray nanotomography," Appl. Phys. Lett. 92, 233104 (2008).
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Tian, Y.

W. Li, N. Wang, J. Chen, G. Liu, Z. Pan, Y. Guan, Y. Yang, W. Wu, J. Tian, S. Wei, Z. Wu, and Y. Tian, "Quantitative study of interior nanostructure in hollow zinc oxide particles on the basis of nondestructive x-ray nanotomography," Appl. Phys. Lett. 95, 053108 (2009).
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Y. Liu, B. Chen, E. Li, J. Wang, A. Marcelli, S. W. Wilkins, H. Ming, Y. Tian, K. A. Nugent, P. Zhu, and Z. Wu, "Phase retrieval in x-ray imaging based on using structured illumination," Phys. Rev. A 78, 023817 (2008).
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J. Chen, C. Wu, J. Tian, W. Li, S. Yu, and Y. Tian, "Three-dimensional imaging of a complex concaved cuboctahedron copper sulfide crystal by x-ray nanotomography," Appl. Phys. Lett. 92, 233104 (2008).
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J. Andrews, E. Almeida, M. C. H. 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, 327-336 (2010).
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Y. S. Chu, J. M. Yi, F. De Carlo, Q. Shen, W. K. Lee, H. J. Wu, C. L. Wang, J. Y. Wang, C. J. Liu, C. H. Wang, S. R. Wu, C. C. Chien, Y. Hwu, A. Tkachuk, W. Yun, M. Feser, K. S. Liang, C. S. Yang, J. H. Je, and G. Margaritondo, "Hard-x-ray microscopy with Fresnel zone plates reaches 40 nm Rayleigh resolution," Appl. Phys. Lett. 92, 103119 (2008).
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W. B. Yun, P. J. Viccaro, B. Lai, and J. Chrzas, "Coherent hard x-ray focusing optics and applications," Rev. Sci. Instrum. 63(1), 582-585 (1992).
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Wang, C. L.

Y. S. Chu, J. M. Yi, F. De Carlo, Q. Shen, W. K. Lee, H. J. Wu, C. L. Wang, J. Y. Wang, C. J. Liu, C. H. Wang, S. R. Wu, C. C. Chien, Y. Hwu, A. Tkachuk, W. Yun, M. Feser, K. S. Liang, C. S. Yang, J. H. Je, and G. Margaritondo, "Hard-x-ray microscopy with Fresnel zone plates reaches 40 nm Rayleigh resolution," Appl. Phys. Lett. 92, 103119 (2008).
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Wang, J.

Y. Liu, B. Chen, E. Li, J. Wang, A. Marcelli, S. W. Wilkins, H. Ming, Y. Tian, K. A. Nugent, P. Zhu, and Z. Wu, "Phase retrieval in x-ray imaging based on using structured illumination," Phys. Rev. A 78, 023817 (2008).
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Y. Liu, P. Zhu, B. Chen, J. Wang, Q. Yuan, W. Huang, H. Shu, E. Li, X. Liu, K. Zhang, H. Ming, and Z. Wu, "A new iterative algorithm to reconstruct the refractive index," Phys. Med. Biol. 52, L5-L13 (2007).
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Y. S. Chu, J. M. Yi, F. De Carlo, Q. Shen, W. K. Lee, H. J. Wu, C. L. Wang, J. Y. Wang, C. J. Liu, C. H. Wang, S. R. Wu, C. C. Chien, Y. Hwu, A. Tkachuk, W. Yun, M. Feser, K. S. Liang, C. S. Yang, J. H. Je, and G. Margaritondo, "Hard-x-ray microscopy with Fresnel zone plates reaches 40 nm Rayleigh resolution," Appl. Phys. Lett. 92, 103119 (2008).
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W. Li, N. Wang, J. Chen, G. Liu, Z. Pan, Y. Guan, Y. Yang, W. Wu, J. Tian, S. Wei, Z. Wu, and Y. Tian, "Quantitative study of interior nanostructure in hollow zinc oxide particles on the basis of nondestructive x-ray nanotomography," Appl. Phys. Lett. 95, 053108 (2009).
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Wang, Y.

Y. Wang, W. Yun, and C. Jacobsen, "Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging," Nature 424, 50-53 (2003).
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D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, "Diffraction enhanced x-ray imaging," Phys. Med. Biol. 42, 2015-2025 (1997).
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W. Li, N. Wang, J. Chen, G. Liu, Z. Pan, Y. Guan, Y. Yang, W. Wu, J. Tian, S. Wei, Z. Wu, and Y. Tian, "Quantitative study of interior nanostructure in hollow zinc oxide particles on the basis of nondestructive x-ray nanotomography," Appl. Phys. Lett. 95, 053108 (2009).
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S. Rehbein, S. Heim, P. Guttmann, S. Werner, and G. Schneider, "Ultrahigh Resolution Soft-X-Ray Microscopy with Zone Plates in High Orders of Diffraction," Phys. Rev. Lett. 103, 110801 (2009).
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Y. Liu, B. Chen, E. Li, J. Wang, A. Marcelli, S. W. Wilkins, H. Ming, Y. Tian, K. A. Nugent, P. Zhu, and Z. Wu, "Phase retrieval in x-ray imaging based on using structured illumination," Phys. Rev. A 78, 023817 (2008).
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S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, "Phase-contrast imaging using polychromatic hard X-rays," Nature 384, 335-338 (1996).
[CrossRef]

Wu, C.

J. Chen, C. Wu, J. Tian, W. Li, S. Yu, and Y. Tian, "Three-dimensional imaging of a complex concaved cuboctahedron copper sulfide crystal by x-ray nanotomography," Appl. Phys. Lett. 92, 233104 (2008).
[CrossRef]

Wu, H. J.

Y. S. Chu, J. M. Yi, F. De Carlo, Q. Shen, W. K. Lee, H. J. Wu, C. L. Wang, J. Y. Wang, C. J. Liu, C. H. Wang, S. R. Wu, C. C. Chien, Y. Hwu, A. Tkachuk, W. Yun, M. Feser, K. S. Liang, C. S. Yang, J. H. Je, and G. Margaritondo, "Hard-x-ray microscopy with Fresnel zone plates reaches 40 nm Rayleigh resolution," Appl. Phys. Lett. 92, 103119 (2008).
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Wu, S. R.

Y. S. Chu, J. M. Yi, F. De Carlo, Q. Shen, W. K. Lee, H. J. Wu, C. L. Wang, J. Y. Wang, C. J. Liu, C. H. Wang, S. R. Wu, C. C. Chien, Y. Hwu, A. Tkachuk, W. Yun, M. Feser, K. S. Liang, C. S. Yang, J. H. Je, and G. Margaritondo, "Hard-x-ray microscopy with Fresnel zone plates reaches 40 nm Rayleigh resolution," Appl. Phys. Lett. 92, 103119 (2008).
[CrossRef]

Wu, W.

W. Li, N. Wang, J. Chen, G. Liu, Z. Pan, Y. Guan, Y. Yang, W. Wu, J. Tian, S. Wei, Z. Wu, and Y. Tian, "Quantitative study of interior nanostructure in hollow zinc oxide particles on the basis of nondestructive x-ray nanotomography," Appl. Phys. Lett. 95, 053108 (2009).
[CrossRef]

Wu, Z.

W. Li, N. Wang, J. Chen, G. Liu, Z. Pan, Y. Guan, Y. Yang, W. Wu, J. Tian, S. Wei, Z. Wu, and Y. Tian, "Quantitative study of interior nanostructure in hollow zinc oxide particles on the basis of nondestructive x-ray nanotomography," Appl. Phys. Lett. 95, 053108 (2009).
[CrossRef]

Y. Liu, B. Chen, E. Li, J. Wang, A. Marcelli, S. W. Wilkins, H. Ming, Y. Tian, K. A. Nugent, P. Zhu, and Z. Wu, "Phase retrieval in x-ray imaging based on using structured illumination," Phys. Rev. A 78, 023817 (2008).
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Y. Liu, P. Zhu, B. Chen, J. Wang, Q. Yuan, W. Huang, H. Shu, E. Li, X. Liu, K. Zhang, H. Ming, and Z. Wu, "A new iterative algorithm to reconstruct the refractive index," Phys. Med. Biol. 52, L5-L13 (2007).
[CrossRef] [PubMed]

Yang, C. S.

Y. S. Chu, J. M. Yi, F. De Carlo, Q. Shen, W. K. Lee, H. J. Wu, C. L. Wang, J. Y. Wang, C. J. Liu, C. H. Wang, S. R. Wu, C. C. Chien, Y. Hwu, A. Tkachuk, W. Yun, M. Feser, K. S. Liang, C. S. Yang, J. H. Je, and G. Margaritondo, "Hard-x-ray microscopy with Fresnel zone plates reaches 40 nm Rayleigh resolution," Appl. Phys. Lett. 92, 103119 (2008).
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Yang, Y.

W. Li, N. Wang, J. Chen, G. Liu, Z. Pan, Y. Guan, Y. Yang, W. Wu, J. Tian, S. Wei, Z. Wu, and Y. Tian, "Quantitative study of interior nanostructure in hollow zinc oxide particles on the basis of nondestructive x-ray nanotomography," Appl. Phys. Lett. 95, 053108 (2009).
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Yi, J. M.

Y. S. Chu, J. M. Yi, F. De Carlo, Q. Shen, W. K. Lee, H. J. Wu, C. L. Wang, J. Y. Wang, C. J. Liu, C. H. Wang, S. R. Wu, C. C. Chien, Y. Hwu, A. Tkachuk, W. Yun, M. Feser, K. S. Liang, C. S. Yang, J. H. Je, and G. Margaritondo, "Hard-x-ray microscopy with Fresnel zone plates reaches 40 nm Rayleigh resolution," Appl. Phys. Lett. 92, 103119 (2008).
[CrossRef]

Yin, G.

G. Yin, F. Chen, Y. Hwu, H. D. Shieh, and K. S. Liang, "Quantitative phase retrieval in transmission hard x-ray microscope," Appl. Phys. Lett. 90, 181118 (2007).

Yin, G. C.

G. C. Yin, M. T. Tang, Y. F. Song, F. R. Chen, K. S. Liang, F. W. Duewer, W. Yun, C. H. Ko, and H. P. D. Shieh, "Energy-tunable transmission x-ray microscope for differential contrast imaging with near 60 nm resolution tomography," Appl. Phys. Lett. 88, 241115 (2006).
[CrossRef]

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]

Yu, S.

J. Chen, C. Wu, J. Tian, W. Li, S. Yu, and Y. Tian, "Three-dimensional imaging of a complex concaved cuboctahedron copper sulfide crystal by x-ray nanotomography," Appl. Phys. Lett. 92, 233104 (2008).
[CrossRef]

Yuan, Q.

Y. Liu, P. Zhu, B. Chen, J. Wang, Q. Yuan, W. Huang, H. Shu, E. Li, X. Liu, K. Zhang, H. Ming, and Z. Wu, "A new iterative algorithm to reconstruct the refractive index," Phys. Med. Biol. 52, L5-L13 (2007).
[CrossRef] [PubMed]

Yun, W.

J. Andrews, E. Almeida, M. C. H. 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, 327-336 (2010).
[CrossRef] [PubMed]

Y. S. Chu, J. M. Yi, F. De Carlo, Q. Shen, W. K. Lee, H. J. Wu, C. L. Wang, J. Y. Wang, C. J. Liu, C. H. Wang, S. R. Wu, C. C. Chien, Y. Hwu, A. Tkachuk, W. Yun, M. Feser, K. S. Liang, C. S. Yang, J. H. Je, and G. Margaritondo, "Hard-x-ray microscopy with Fresnel zone plates reaches 40 nm Rayleigh resolution," Appl. Phys. Lett. 92, 103119 (2008).
[CrossRef]

G. C. Yin, M. T. Tang, Y. F. Song, F. R. Chen, K. S. Liang, F. W. Duewer, W. Yun, C. H. Ko, and H. P. D. Shieh, "Energy-tunable transmission x-ray microscope for differential contrast imaging with near 60 nm resolution tomography," Appl. Phys. Lett. 88, 241115 (2006).
[CrossRef]

Y. Wang, W. Yun, and C. Jacobsen, "Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging," Nature 424, 50-53 (2003).
[CrossRef] [PubMed]

Yun, W. B.

W. B. Yun, P. J. Viccaro, B. Lai, and J. Chrzas, "Coherent hard x-ray focusing optics and applications," Rev. Sci. Instrum. 63(1), 582-585 (1992).
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Zhang, F.

F. Zhang, G. Pedrini, and W. Osten, "Phase retrieval of arbitrary complex-valued fields through aperture-plane modulation," Phys. Rev. A 75, 043805 (2007).
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Zhang, K.

Y. Liu, P. Zhu, B. Chen, J. Wang, Q. Yuan, W. Huang, H. Shu, E. Li, X. Liu, K. Zhang, H. Ming, and Z. Wu, "A new iterative algorithm to reconstruct the refractive index," Phys. Med. Biol. 52, L5-L13 (2007).
[CrossRef] [PubMed]

Zhong, Z.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, "Diffraction enhanced x-ray imaging," Phys. Med. Biol. 42, 2015-2025 (1997).
[CrossRef] [PubMed]

Zhu, P.

Y. Liu, B. Chen, E. Li, J. Wang, A. Marcelli, S. W. Wilkins, H. Ming, Y. Tian, K. A. Nugent, P. Zhu, and Z. Wu, "Phase retrieval in x-ray imaging based on using structured illumination," Phys. Rev. A 78, 023817 (2008).
[CrossRef]

Y. Liu, P. Zhu, B. Chen, J. Wang, Q. Yuan, W. Huang, H. Shu, E. Li, X. Liu, K. Zhang, H. Ming, and Z. Wu, "A new iterative algorithm to reconstruct the refractive index," Phys. Med. Biol. 52, L5-L13 (2007).
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Figures (4)

Fig. 1
Fig. 1

Schematic experimental setup of the Transmission X-ray Microscopy installed at beamline 6-2c of Stanford Synchrotron Radiation Lightsource.

Fig. 2
Fig. 2

TXM image of a Siemens calibration standard with 30 nm minimum features. Panel (b) is the magnified view of the highlighted area in panel (a). Scale bar in panel (a) is 5 microns.

Fig. 3
Fig. 3

Computer simulation for the proposed experimental scheme and the phase retrieval algorithm. The distribution of the real and imaginary part of the refractive index are presented in panels (a) and (b) respectively. Panels (c) and (d) are the intensity distributions at the detector plane under X-ray illumination at 5390 eV and 5410 eV respectively. The retrieved phase map and amplitude map are shown in panels (e) and (f).

Fig. 4
Fig. 4

TXM imaging results for quantitative phase retrieval. Raw data collected at 5.40 keV, 5.39 keV, and 5.41 keV are presented in panels (a) (b) and (c), respectively. The retrieved amplitude map and phase map are demonstrated in panel (d) and (e). The scale bar in panel (e) is 3 microns.

Equations (3)

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f = 2 R Δ outermost h c / E incident
F = a 2 L λ = a 2 2 R Δ outermost E incident Δ E incident
E i + 1 = I corr λ 0 ( i Fresnel ( I corr λ ( Fresnel ( E i , λ , f λ f λ 0 ) ) , λ , f λ 0 f λ ) )

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