Abstract

Using a signal-to-noise ratio estimation based on correlations between multiple simulated images, we compare the dose efficiency of two soft x-ray imaging systems: incoherent brightfield imaging using zone plate optics in a transmission x-ray microscope (TXM), and x-ray diffraction microscopy (XDM) where an image is reconstructed from the far-field coherent diffraction pattern. In XDM one must computationally phase weak diffraction signals; in TXM one suffers signal losses due to the finite numerical aperture and efficiency of the optics. In simulations with objects representing isolated cells such as yeast, we find that XDM has the potential for delivering equivalent resolution images using fewer photons. This can be an important advantage for studying radiation-sensitive biological and soft matter specimens.

© 2009 Optical Society of America

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    [CrossRef]
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2009 (1)

M. Howells, T. Beetz, H. Chapman, C. Cui, J. Holton, C. Jacobsen, J. Kirz, E. Lima, S. Marchesini, H. Miao, D. Sayre, D. Shapiro, J. Spence, and D. Starodub, "An assessment of the resolution limitation due to radiationdamage in x-ray diffraction microscopy," J. Electron. Spectrosc. Relat. Phenom. 170, 4-12 (2009).
[CrossRef]

2008 (1)

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, "High-resolution scanning x-ray diffraction microscopy," Science 321, 379-382 (2008).
[CrossRef] [PubMed]

2007 (2)

G. Williams, H. Quiney, A. Peele, and K. Nugent, "Coherent diffractive imaging and partial coherence," Phys. Rev. B 75, 104,102 (2007).
[CrossRef]

A. Tkachuk, F. Duewer, H. Cui, M. Feser, S. Wang, and W. Yun, "X-ray computed tomography in Zernike phase contrast mode at 8 keV with 50-nm resolution using Cu rotating anode x-ray source," Zeitschrift Kristallographie 222, 650-655 (2007).
[CrossRef]

2006 (3)

G.-C. Yin, M.-T. Tang, Y.-F. Song, F.-R. Chen, K. Liang, F. Duewer,W. Yun, C.-H. Ko, and H.-P. Shieh, "Energytunable transmission x-ray microscope for differential contrast imaging with near 60 nm resolution tomography," Appl. Phys. Lett. 88, 241,115 (2006).
[CrossRef]

P. Thibault, V. Elser, C. Jacobsen, D. Shapiro, and D. Sayre, "Reconstruction of a yeast cell from x-ray diffraction data," Acta Crystallographica A 62, 248-261 (2006).

H. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. Howells, R. Rosen, H. He, J. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, "High resolution ab initio three-dimensional x-ray diffraction microscopy," J. Opt. Soc. Am. A 23, 1179-1200 (2006).
[CrossRef]

2005 (1)

D. Shapiro, P. Thibault, T. Beetz, V. Elser,M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, "Biological imaging by soft x-ray diffraction microscopy," Proc. Natl. Acad. Sci. USA 102, 15,343-15,346 (2005).
[CrossRef]

2004 (2)

Q. Shen, I. Bazarov, and P. Thibault, "Diffractive imaging of nonperiodic materials with future coherent x-ray sources," J. Synchrotron. Radiat. 11, 432-438 (2004).
[CrossRef] [PubMed]

C. Larabell and M. Le Gros, "X-ray tomography generates 3-D reconstructions of the yeast, Saccharomyces cerevisiae, at 60-nm resolution," Molecular Biology of the Cell 15, 957-962 (2004).
[CrossRef]

2003 (2)

A. Kilcoyne, T. Tyliszczak, W. Steele, S. Fakra, P. Hitchcock, K. Franck, E. Anderson, B. Harteneck, E. Rightor, G. Mitchell, A. Hitchcock, L. Yang, T. Warwick, and H. Ade, "Interferometer-controlled scanning transmission X-ray microscopes at the Advanced Light Source," J. Synchrotron. Radiat. 10, 125-136 (2003).
[CrossRef] [PubMed]

V. Elser, "Phase retrieval by iterated projections," J. Opt. Soc. Am. A 20, 40-55 (2003).
[CrossRef]

2002 (1)

G. Schneider, E. Anderson, S. Vogt, C. Kn¨ochel, D. Weiss, M. Legros, and C. Larabell, "Computed tomography of cryogenic cells," Surf. Rev. Lett. 9, 177-183 (2002).
[CrossRef]

2000 (2)

J. Maser, A. Osanna, Y. Wang, C. Jacobsen, J. Kirz, S. Spector, B. Winn, and D. Tennant, "Soft x-ray microscopy with a cryo STXM: I. Instrumentation, imaging, and spectroscopy," J. Microsc. 197, 68-79 (2000).
[CrossRef] [PubMed]

D. Weiß, G. Schneider, B. Niemann, P. Guttmann, D. Rudolph, and G. Schmahl, "Computed tomography of cryogenic biological specimens based on x-ray microscopic images," Ultramicroscopy 84, 185-197 (2000).
[CrossRef] [PubMed]

1999 (1)

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, "An extension of the methods of x-ray crystallography to allow imaging of micron-size non-crystalline specimens," Nature 400, 342-344 (1999).
[CrossRef]

1998 (1)

G. Schneider, "Cryo x-ray microscopy with high spatial resolution in amplitude and phase contrast," Ultramicroscopy 75, 85-104 (1998).
[CrossRef] [PubMed]

1995 (1)

J. Kirz, C. Jacobsen, and M. Howells, "Soft x-ray microscopes and their biological applications," Quart. Rev. Biophys. 28, 33-130 (1995).
[CrossRef]

1993 (1)

B. L. Henke, E. M. Gullikson, and J. C. Davis, "X-ray Interactions: Photoabsorption, Scattering, Transmission, and Reflection at E=50-30,000 eV, Z=1-92," Atomic Data Nuclear Data Tables 54, 181-342 (1993).
[CrossRef]

1989 (1)

1980 (1)

G. Schmahl, D. Rudolph, B. Niemann, and O. Christ, "Zone-plate X-ray microscopy," Quart. Rev. Biophys. 13, 297-315 (1980).
[CrossRef]

1978 (1)

1977 (2)

D. Sayre, J. Kirz, R. Feder, D. M. Kim, and E. Spiller, "Potential operating region for ultrasoft x-ray microscopy of biological specimens," Science 196, 1339-1340 (1977).
[CrossRef] [PubMed]

D. Sayre, J. Kirz, R. Feder, D. M. Kim, and E. Spiller, "Transmission Microscopy of Unmodified Biological Materials: Comparative Radiation Dosages with Electrons and Ultrasoft X-ray Photons," Ultramicroscopy 2, 337-341 (1977).
[CrossRef] [PubMed]

1976 (1)

1975 (1)

J. Frank and L. Al-Ali, "Signal-to-noise ratio of electron micrographs obtained by cross correlation," Nature 256, 376-379 (1975).
[CrossRef] [PubMed]

1974 (2)

N. Bershad and A. Rockmore, "On estimating signal-to-noise ratio using the sample correlation coefficient," IEEE Trans. Inf. Theory 20, 112-113 (1974).
[CrossRef]

J. Kirz, "Phase zone plates for X rays and the extreme UV," J. Opt. Soc. Am. 64, 301-309 (1974).
[CrossRef]

1952 (1)

H. Wolter, "Spiegelsysteme streifenden Einfalls als abbildende Optiken f¨ur R¨ontgenstrahlen," Ann. Phys. 10, 94-114, 286 (1952).
[CrossRef]

1946 (1)

A. Rose, "Unified approach to performance of photographic film, television pickup tubes, and human eye," J. Soc. Motion Pict. Eng. 47, 273-294 (1946).

Ade, H.

A. Kilcoyne, T. Tyliszczak, W. Steele, S. Fakra, P. Hitchcock, K. Franck, E. Anderson, B. Harteneck, E. Rightor, G. Mitchell, A. Hitchcock, L. Yang, T. Warwick, and H. Ade, "Interferometer-controlled scanning transmission X-ray microscopes at the Advanced Light Source," J. Synchrotron. Radiat. 10, 125-136 (2003).
[CrossRef] [PubMed]

Al-Ali, L.

J. Frank and L. Al-Ali, "Signal-to-noise ratio of electron micrographs obtained by cross correlation," Nature 256, 376-379 (1975).
[CrossRef] [PubMed]

Anderson, E.

A. Kilcoyne, T. Tyliszczak, W. Steele, S. Fakra, P. Hitchcock, K. Franck, E. Anderson, B. Harteneck, E. Rightor, G. Mitchell, A. Hitchcock, L. Yang, T. Warwick, and H. Ade, "Interferometer-controlled scanning transmission X-ray microscopes at the Advanced Light Source," J. Synchrotron. Radiat. 10, 125-136 (2003).
[CrossRef] [PubMed]

G. Schneider, E. Anderson, S. Vogt, C. Kn¨ochel, D. Weiss, M. Legros, and C. Larabell, "Computed tomography of cryogenic cells," Surf. Rev. Lett. 9, 177-183 (2002).
[CrossRef]

Barty, A.

Bazarov, I.

Q. Shen, I. Bazarov, and P. Thibault, "Diffractive imaging of nonperiodic materials with future coherent x-ray sources," J. Synchrotron. Radiat. 11, 432-438 (2004).
[CrossRef] [PubMed]

Beetz, T.

M. Howells, T. Beetz, H. Chapman, C. Cui, J. Holton, C. Jacobsen, J. Kirz, E. Lima, S. Marchesini, H. Miao, D. Sayre, D. Shapiro, J. Spence, and D. Starodub, "An assessment of the resolution limitation due to radiationdamage in x-ray diffraction microscopy," J. Electron. Spectrosc. Relat. Phenom. 170, 4-12 (2009).
[CrossRef]

H. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. Howells, R. Rosen, H. He, J. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, "High resolution ab initio three-dimensional x-ray diffraction microscopy," J. Opt. Soc. Am. A 23, 1179-1200 (2006).
[CrossRef]

D. Shapiro, P. Thibault, T. Beetz, V. Elser,M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, "Biological imaging by soft x-ray diffraction microscopy," Proc. Natl. Acad. Sci. USA 102, 15,343-15,346 (2005).
[CrossRef]

Bershad, N.

N. Bershad and A. Rockmore, "On estimating signal-to-noise ratio using the sample correlation coefficient," IEEE Trans. Inf. Theory 20, 112-113 (1974).
[CrossRef]

Bunk, O.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, "High-resolution scanning x-ray diffraction microscopy," Science 321, 379-382 (2008).
[CrossRef] [PubMed]

Chapman, H.

M. Howells, T. Beetz, H. Chapman, C. Cui, J. Holton, C. Jacobsen, J. Kirz, E. Lima, S. Marchesini, H. Miao, D. Sayre, D. Shapiro, J. Spence, and D. Starodub, "An assessment of the resolution limitation due to radiationdamage in x-ray diffraction microscopy," J. Electron. Spectrosc. Relat. Phenom. 170, 4-12 (2009).
[CrossRef]

H. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. Howells, R. Rosen, H. He, J. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, "High resolution ab initio three-dimensional x-ray diffraction microscopy," J. Opt. Soc. Am. A 23, 1179-1200 (2006).
[CrossRef]

Charalambous, P.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, "An extension of the methods of x-ray crystallography to allow imaging of micron-size non-crystalline specimens," Nature 400, 342-344 (1999).
[CrossRef]

Chen, F.-R.

G.-C. Yin, M.-T. Tang, Y.-F. Song, F.-R. Chen, K. Liang, F. Duewer,W. Yun, C.-H. Ko, and H.-P. Shieh, "Energytunable transmission x-ray microscope for differential contrast imaging with near 60 nm resolution tomography," Appl. Phys. Lett. 88, 241,115 (2006).
[CrossRef]

Christ, O.

G. Schmahl, D. Rudolph, B. Niemann, and O. Christ, "Zone-plate X-ray microscopy," Quart. Rev. Biophys. 13, 297-315 (1980).
[CrossRef]

Cui, C.

M. Howells, T. Beetz, H. Chapman, C. Cui, J. Holton, C. Jacobsen, J. Kirz, E. Lima, S. Marchesini, H. Miao, D. Sayre, D. Shapiro, J. Spence, and D. Starodub, "An assessment of the resolution limitation due to radiationdamage in x-ray diffraction microscopy," J. Electron. Spectrosc. Relat. Phenom. 170, 4-12 (2009).
[CrossRef]

H. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. Howells, R. Rosen, H. He, J. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, "High resolution ab initio three-dimensional x-ray diffraction microscopy," J. Opt. Soc. Am. A 23, 1179-1200 (2006).
[CrossRef]

Cui, H.

A. Tkachuk, F. Duewer, H. Cui, M. Feser, S. Wang, and W. Yun, "X-ray computed tomography in Zernike phase contrast mode at 8 keV with 50-nm resolution using Cu rotating anode x-ray source," Zeitschrift Kristallographie 222, 650-655 (2007).
[CrossRef]

David, C.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, "High-resolution scanning x-ray diffraction microscopy," Science 321, 379-382 (2008).
[CrossRef] [PubMed]

Davis, J. C.

B. L. Henke, E. M. Gullikson, and J. C. Davis, "X-ray Interactions: Photoabsorption, Scattering, Transmission, and Reflection at E=50-30,000 eV, Z=1-92," Atomic Data Nuclear Data Tables 54, 181-342 (1993).
[CrossRef]

Dierolf, M.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, "High-resolution scanning x-ray diffraction microscopy," Science 321, 379-382 (2008).
[CrossRef] [PubMed]

Duewer, F.

A. Tkachuk, F. Duewer, H. Cui, M. Feser, S. Wang, and W. Yun, "X-ray computed tomography in Zernike phase contrast mode at 8 keV with 50-nm resolution using Cu rotating anode x-ray source," Zeitschrift Kristallographie 222, 650-655 (2007).
[CrossRef]

G.-C. Yin, M.-T. Tang, Y.-F. Song, F.-R. Chen, K. Liang, F. Duewer,W. Yun, C.-H. Ko, and H.-P. Shieh, "Energytunable transmission x-ray microscope for differential contrast imaging with near 60 nm resolution tomography," Appl. Phys. Lett. 88, 241,115 (2006).
[CrossRef]

Elser, V.

P. Thibault, V. Elser, C. Jacobsen, D. Shapiro, and D. Sayre, "Reconstruction of a yeast cell from x-ray diffraction data," Acta Crystallographica A 62, 248-261 (2006).

D. Shapiro, P. Thibault, T. Beetz, V. Elser,M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, "Biological imaging by soft x-ray diffraction microscopy," Proc. Natl. Acad. Sci. USA 102, 15,343-15,346 (2005).
[CrossRef]

V. Elser, "Phase retrieval by iterated projections," J. Opt. Soc. Am. A 20, 40-55 (2003).
[CrossRef]

Fakra, S.

A. Kilcoyne, T. Tyliszczak, W. Steele, S. Fakra, P. Hitchcock, K. Franck, E. Anderson, B. Harteneck, E. Rightor, G. Mitchell, A. Hitchcock, L. Yang, T. Warwick, and H. Ade, "Interferometer-controlled scanning transmission X-ray microscopes at the Advanced Light Source," J. Synchrotron. Radiat. 10, 125-136 (2003).
[CrossRef] [PubMed]

Feder, R.

D. Sayre, J. Kirz, R. Feder, D. M. Kim, and E. Spiller, "Potential operating region for ultrasoft x-ray microscopy of biological specimens," Science 196, 1339-1340 (1977).
[CrossRef] [PubMed]

D. Sayre, J. Kirz, R. Feder, D. M. Kim, and E. Spiller, "Transmission Microscopy of Unmodified Biological Materials: Comparative Radiation Dosages with Electrons and Ultrasoft X-ray Photons," Ultramicroscopy 2, 337-341 (1977).
[CrossRef] [PubMed]

Feser, M.

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M. Howells, T. Beetz, H. Chapman, C. Cui, J. Holton, C. Jacobsen, J. Kirz, E. Lima, S. Marchesini, H. Miao, D. Sayre, D. Shapiro, J. Spence, and D. Starodub, "An assessment of the resolution limitation due to radiationdamage in x-ray diffraction microscopy," J. Electron. Spectrosc. Relat. Phenom. 170, 4-12 (2009).
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H. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. Howells, R. Rosen, H. He, J. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, "High resolution ab initio three-dimensional x-ray diffraction microscopy," J. Opt. Soc. Am. A 23, 1179-1200 (2006).
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M. Howells, T. Beetz, H. Chapman, C. Cui, J. Holton, C. Jacobsen, J. Kirz, E. Lima, S. Marchesini, H. Miao, D. Sayre, D. Shapiro, J. Spence, and D. Starodub, "An assessment of the resolution limitation due to radiationdamage in x-ray diffraction microscopy," J. Electron. Spectrosc. Relat. Phenom. 170, 4-12 (2009).
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D. Shapiro, P. Thibault, T. Beetz, V. Elser,M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, "Biological imaging by soft x-ray diffraction microscopy," Proc. Natl. Acad. Sci. USA 102, 15,343-15,346 (2005).
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J. Maser, A. Osanna, Y. Wang, C. Jacobsen, J. Kirz, S. Spector, B. Winn, and D. Tennant, "Soft x-ray microscopy with a cryo STXM: I. Instrumentation, imaging, and spectroscopy," J. Microsc. 197, 68-79 (2000).
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D. Sayre, J. Kirz, R. Feder, D. M. Kim, and E. Spiller, "Transmission Microscopy of Unmodified Biological Materials: Comparative Radiation Dosages with Electrons and Ultrasoft X-ray Photons," Ultramicroscopy 2, 337-341 (1977).
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G.-C. Yin, M.-T. Tang, Y.-F. Song, F.-R. Chen, K. Liang, F. Duewer,W. Yun, C.-H. Ko, and H.-P. Shieh, "Energytunable transmission x-ray microscope for differential contrast imaging with near 60 nm resolution tomography," Appl. Phys. Lett. 88, 241,115 (2006).
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G. Schneider, E. Anderson, S. Vogt, C. Kn¨ochel, D. Weiss, M. Legros, and C. Larabell, "Computed tomography of cryogenic cells," Surf. Rev. Lett. 9, 177-183 (2002).
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G.-C. Yin, M.-T. Tang, Y.-F. Song, F.-R. Chen, K. Liang, F. Duewer,W. Yun, C.-H. Ko, and H.-P. Shieh, "Energytunable transmission x-ray microscope for differential contrast imaging with near 60 nm resolution tomography," Appl. Phys. Lett. 88, 241,115 (2006).
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M. Howells, T. Beetz, H. Chapman, C. Cui, J. Holton, C. Jacobsen, J. Kirz, E. Lima, S. Marchesini, H. Miao, D. Sayre, D. Shapiro, J. Spence, and D. Starodub, "An assessment of the resolution limitation due to radiationdamage in x-ray diffraction microscopy," J. Electron. Spectrosc. Relat. Phenom. 170, 4-12 (2009).
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D. Shapiro, P. Thibault, T. Beetz, V. Elser,M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, "Biological imaging by soft x-ray diffraction microscopy," Proc. Natl. Acad. Sci. USA 102, 15,343-15,346 (2005).
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Marchesini, S.

M. Howells, T. Beetz, H. Chapman, C. Cui, J. Holton, C. Jacobsen, J. Kirz, E. Lima, S. Marchesini, H. Miao, D. Sayre, D. Shapiro, J. Spence, and D. Starodub, "An assessment of the resolution limitation due to radiationdamage in x-ray diffraction microscopy," J. Electron. Spectrosc. Relat. Phenom. 170, 4-12 (2009).
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J. Maser, A. Osanna, Y. Wang, C. Jacobsen, J. Kirz, S. Spector, B. Winn, and D. Tennant, "Soft x-ray microscopy with a cryo STXM: I. Instrumentation, imaging, and spectroscopy," J. Microsc. 197, 68-79 (2000).
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M. Howells, T. Beetz, H. Chapman, C. Cui, J. Holton, C. Jacobsen, J. Kirz, E. Lima, S. Marchesini, H. Miao, D. Sayre, D. Shapiro, J. Spence, and D. Starodub, "An assessment of the resolution limitation due to radiationdamage in x-ray diffraction microscopy," J. Electron. Spectrosc. Relat. Phenom. 170, 4-12 (2009).
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D. Shapiro, P. Thibault, T. Beetz, V. Elser,M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, "Biological imaging by soft x-ray diffraction microscopy," Proc. Natl. Acad. Sci. USA 102, 15,343-15,346 (2005).
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J. Miao, P. Charalambous, J. Kirz, and D. Sayre, "An extension of the methods of x-ray crystallography to allow imaging of micron-size non-crystalline specimens," Nature 400, 342-344 (1999).
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A. Kilcoyne, T. Tyliszczak, W. Steele, S. Fakra, P. Hitchcock, K. Franck, E. Anderson, B. Harteneck, E. Rightor, G. Mitchell, A. Hitchcock, L. Yang, T. Warwick, and H. Ade, "Interferometer-controlled scanning transmission X-ray microscopes at the Advanced Light Source," J. Synchrotron. Radiat. 10, 125-136 (2003).
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D. Shapiro, P. Thibault, T. Beetz, V. Elser,M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, "Biological imaging by soft x-ray diffraction microscopy," Proc. Natl. Acad. Sci. USA 102, 15,343-15,346 (2005).
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D. Weiß, G. Schneider, B. Niemann, P. Guttmann, D. Rudolph, and G. Schmahl, "Computed tomography of cryogenic biological specimens based on x-ray microscopic images," Ultramicroscopy 84, 185-197 (2000).
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J. Maser, A. Osanna, Y. Wang, C. Jacobsen, J. Kirz, S. Spector, B. Winn, and D. Tennant, "Soft x-ray microscopy with a cryo STXM: I. Instrumentation, imaging, and spectroscopy," J. Microsc. 197, 68-79 (2000).
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G. Williams, H. Quiney, A. Peele, and K. Nugent, "Coherent diffractive imaging and partial coherence," Phys. Rev. B 75, 104,102 (2007).
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P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, "High-resolution scanning x-ray diffraction microscopy," Science 321, 379-382 (2008).
[CrossRef] [PubMed]

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G. Williams, H. Quiney, A. Peele, and K. Nugent, "Coherent diffractive imaging and partial coherence," Phys. Rev. B 75, 104,102 (2007).
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A. Kilcoyne, T. Tyliszczak, W. Steele, S. Fakra, P. Hitchcock, K. Franck, E. Anderson, B. Harteneck, E. Rightor, G. Mitchell, A. Hitchcock, L. Yang, T. Warwick, and H. Ade, "Interferometer-controlled scanning transmission X-ray microscopes at the Advanced Light Source," J. Synchrotron. Radiat. 10, 125-136 (2003).
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Rudolph, D.

D. Weiß, G. Schneider, B. Niemann, P. Guttmann, D. Rudolph, and G. Schmahl, "Computed tomography of cryogenic biological specimens based on x-ray microscopic images," Ultramicroscopy 84, 185-197 (2000).
[CrossRef] [PubMed]

G. Schmahl, D. Rudolph, B. Niemann, and O. Christ, "Zone-plate X-ray microscopy," Quart. Rev. Biophys. 13, 297-315 (1980).
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B. Niemann, D. Rudolph, and G. Schmahl, "X-ray microscopy with synchrotron radiation," Appl. Opt. 15, 1883-1884 (1976).
[CrossRef] [PubMed]

Sayre, D.

M. Howells, T. Beetz, H. Chapman, C. Cui, J. Holton, C. Jacobsen, J. Kirz, E. Lima, S. Marchesini, H. Miao, D. Sayre, D. Shapiro, J. Spence, and D. Starodub, "An assessment of the resolution limitation due to radiationdamage in x-ray diffraction microscopy," J. Electron. Spectrosc. Relat. Phenom. 170, 4-12 (2009).
[CrossRef]

P. Thibault, V. Elser, C. Jacobsen, D. Shapiro, and D. Sayre, "Reconstruction of a yeast cell from x-ray diffraction data," Acta Crystallographica A 62, 248-261 (2006).

D. Shapiro, P. Thibault, T. Beetz, V. Elser,M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, "Biological imaging by soft x-ray diffraction microscopy," Proc. Natl. Acad. Sci. USA 102, 15,343-15,346 (2005).
[CrossRef]

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, "An extension of the methods of x-ray crystallography to allow imaging of micron-size non-crystalline specimens," Nature 400, 342-344 (1999).
[CrossRef]

D. Sayre, J. Kirz, R. Feder, D. M. Kim, and E. Spiller, "Transmission Microscopy of Unmodified Biological Materials: Comparative Radiation Dosages with Electrons and Ultrasoft X-ray Photons," Ultramicroscopy 2, 337-341 (1977).
[CrossRef] [PubMed]

D. Sayre, J. Kirz, R. Feder, D. M. Kim, and E. Spiller, "Potential operating region for ultrasoft x-ray microscopy of biological specimens," Science 196, 1339-1340 (1977).
[CrossRef] [PubMed]

Schmahl, G.

D. Weiß, G. Schneider, B. Niemann, P. Guttmann, D. Rudolph, and G. Schmahl, "Computed tomography of cryogenic biological specimens based on x-ray microscopic images," Ultramicroscopy 84, 185-197 (2000).
[CrossRef] [PubMed]

G. Schmahl, D. Rudolph, B. Niemann, and O. Christ, "Zone-plate X-ray microscopy," Quart. Rev. Biophys. 13, 297-315 (1980).
[CrossRef]

B. Niemann, D. Rudolph, and G. Schmahl, "X-ray microscopy with synchrotron radiation," Appl. Opt. 15, 1883-1884 (1976).
[CrossRef] [PubMed]

Schneider, G.

G. Schneider, E. Anderson, S. Vogt, C. Kn¨ochel, D. Weiss, M. Legros, and C. Larabell, "Computed tomography of cryogenic cells," Surf. Rev. Lett. 9, 177-183 (2002).
[CrossRef]

D. Weiß, G. Schneider, B. Niemann, P. Guttmann, D. Rudolph, and G. Schmahl, "Computed tomography of cryogenic biological specimens based on x-ray microscopic images," Ultramicroscopy 84, 185-197 (2000).
[CrossRef] [PubMed]

G. Schneider, "Cryo x-ray microscopy with high spatial resolution in amplitude and phase contrast," Ultramicroscopy 75, 85-104 (1998).
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Shapiro, D.

M. Howells, T. Beetz, H. Chapman, C. Cui, J. Holton, C. Jacobsen, J. Kirz, E. Lima, S. Marchesini, H. Miao, D. Sayre, D. Shapiro, J. Spence, and D. Starodub, "An assessment of the resolution limitation due to radiationdamage in x-ray diffraction microscopy," J. Electron. Spectrosc. Relat. Phenom. 170, 4-12 (2009).
[CrossRef]

P. Thibault, V. Elser, C. Jacobsen, D. Shapiro, and D. Sayre, "Reconstruction of a yeast cell from x-ray diffraction data," Acta Crystallographica A 62, 248-261 (2006).

H. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. Howells, R. Rosen, H. He, J. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, "High resolution ab initio three-dimensional x-ray diffraction microscopy," J. Opt. Soc. Am. A 23, 1179-1200 (2006).
[CrossRef]

D. Shapiro, P. Thibault, T. Beetz, V. Elser,M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, "Biological imaging by soft x-ray diffraction microscopy," Proc. Natl. Acad. Sci. USA 102, 15,343-15,346 (2005).
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Shieh, H.-P.

G.-C. Yin, M.-T. Tang, Y.-F. Song, F.-R. Chen, K. Liang, F. Duewer,W. Yun, C.-H. Ko, and H.-P. Shieh, "Energytunable transmission x-ray microscope for differential contrast imaging with near 60 nm resolution tomography," Appl. Phys. Lett. 88, 241,115 (2006).
[CrossRef]

Song, Y.-F.

G.-C. Yin, M.-T. Tang, Y.-F. Song, F.-R. Chen, K. Liang, F. Duewer,W. Yun, C.-H. Ko, and H.-P. Shieh, "Energytunable transmission x-ray microscope for differential contrast imaging with near 60 nm resolution tomography," Appl. Phys. Lett. 88, 241,115 (2006).
[CrossRef]

Spector, S.

J. Maser, A. Osanna, Y. Wang, C. Jacobsen, J. Kirz, S. Spector, B. Winn, and D. Tennant, "Soft x-ray microscopy with a cryo STXM: I. Instrumentation, imaging, and spectroscopy," J. Microsc. 197, 68-79 (2000).
[CrossRef] [PubMed]

Spence, J.

M. Howells, T. Beetz, H. Chapman, C. Cui, J. Holton, C. Jacobsen, J. Kirz, E. Lima, S. Marchesini, H. Miao, D. Sayre, D. Shapiro, J. Spence, and D. Starodub, "An assessment of the resolution limitation due to radiationdamage in x-ray diffraction microscopy," J. Electron. Spectrosc. Relat. Phenom. 170, 4-12 (2009).
[CrossRef]

H. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. Howells, R. Rosen, H. He, J. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, "High resolution ab initio three-dimensional x-ray diffraction microscopy," J. Opt. Soc. Am. A 23, 1179-1200 (2006).
[CrossRef]

Spiller, E.

D. Sayre, J. Kirz, R. Feder, D. M. Kim, and E. Spiller, "Potential operating region for ultrasoft x-ray microscopy of biological specimens," Science 196, 1339-1340 (1977).
[CrossRef] [PubMed]

D. Sayre, J. Kirz, R. Feder, D. M. Kim, and E. Spiller, "Transmission Microscopy of Unmodified Biological Materials: Comparative Radiation Dosages with Electrons and Ultrasoft X-ray Photons," Ultramicroscopy 2, 337-341 (1977).
[CrossRef] [PubMed]

Starodub, D.

M. Howells, T. Beetz, H. Chapman, C. Cui, J. Holton, C. Jacobsen, J. Kirz, E. Lima, S. Marchesini, H. Miao, D. Sayre, D. Shapiro, J. Spence, and D. Starodub, "An assessment of the resolution limitation due to radiationdamage in x-ray diffraction microscopy," J. Electron. Spectrosc. Relat. Phenom. 170, 4-12 (2009).
[CrossRef]

Steele, W.

A. Kilcoyne, T. Tyliszczak, W. Steele, S. Fakra, P. Hitchcock, K. Franck, E. Anderson, B. Harteneck, E. Rightor, G. Mitchell, A. Hitchcock, L. Yang, T. Warwick, and H. Ade, "Interferometer-controlled scanning transmission X-ray microscopes at the Advanced Light Source," J. Synchrotron. Radiat. 10, 125-136 (2003).
[CrossRef] [PubMed]

Tang, M.-T.

G.-C. Yin, M.-T. Tang, Y.-F. Song, F.-R. Chen, K. Liang, F. Duewer,W. Yun, C.-H. Ko, and H.-P. Shieh, "Energytunable transmission x-ray microscope for differential contrast imaging with near 60 nm resolution tomography," Appl. Phys. Lett. 88, 241,115 (2006).
[CrossRef]

Tennant, D.

J. Maser, A. Osanna, Y. Wang, C. Jacobsen, J. Kirz, S. Spector, B. Winn, and D. Tennant, "Soft x-ray microscopy with a cryo STXM: I. Instrumentation, imaging, and spectroscopy," J. Microsc. 197, 68-79 (2000).
[CrossRef] [PubMed]

Thibault, P.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, "High-resolution scanning x-ray diffraction microscopy," Science 321, 379-382 (2008).
[CrossRef] [PubMed]

P. Thibault, V. Elser, C. Jacobsen, D. Shapiro, and D. Sayre, "Reconstruction of a yeast cell from x-ray diffraction data," Acta Crystallographica A 62, 248-261 (2006).

D. Shapiro, P. Thibault, T. Beetz, V. Elser,M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, "Biological imaging by soft x-ray diffraction microscopy," Proc. Natl. Acad. Sci. USA 102, 15,343-15,346 (2005).
[CrossRef]

Q. Shen, I. Bazarov, and P. Thibault, "Diffractive imaging of nonperiodic materials with future coherent x-ray sources," J. Synchrotron. Radiat. 11, 432-438 (2004).
[CrossRef] [PubMed]

Tkachuk, A.

A. Tkachuk, F. Duewer, H. Cui, M. Feser, S. Wang, and W. Yun, "X-ray computed tomography in Zernike phase contrast mode at 8 keV with 50-nm resolution using Cu rotating anode x-ray source," Zeitschrift Kristallographie 222, 650-655 (2007).
[CrossRef]

Trebes, J. E.

Tyliszczak, T.

A. Kilcoyne, T. Tyliszczak, W. Steele, S. Fakra, P. Hitchcock, K. Franck, E. Anderson, B. Harteneck, E. Rightor, G. Mitchell, A. Hitchcock, L. Yang, T. Warwick, and H. Ade, "Interferometer-controlled scanning transmission X-ray microscopes at the Advanced Light Source," J. Synchrotron. Radiat. 10, 125-136 (2003).
[CrossRef] [PubMed]

Vogt, S.

G. Schneider, E. Anderson, S. Vogt, C. Kn¨ochel, D. Weiss, M. Legros, and C. Larabell, "Computed tomography of cryogenic cells," Surf. Rev. Lett. 9, 177-183 (2002).
[CrossRef]

Wang, S.

A. Tkachuk, F. Duewer, H. Cui, M. Feser, S. Wang, and W. Yun, "X-ray computed tomography in Zernike phase contrast mode at 8 keV with 50-nm resolution using Cu rotating anode x-ray source," Zeitschrift Kristallographie 222, 650-655 (2007).
[CrossRef]

Wang, Y.

J. Maser, A. Osanna, Y. Wang, C. Jacobsen, J. Kirz, S. Spector, B. Winn, and D. Tennant, "Soft x-ray microscopy with a cryo STXM: I. Instrumentation, imaging, and spectroscopy," J. Microsc. 197, 68-79 (2000).
[CrossRef] [PubMed]

Warwick, T.

A. Kilcoyne, T. Tyliszczak, W. Steele, S. Fakra, P. Hitchcock, K. Franck, E. Anderson, B. Harteneck, E. Rightor, G. Mitchell, A. Hitchcock, L. Yang, T. Warwick, and H. Ade, "Interferometer-controlled scanning transmission X-ray microscopes at the Advanced Light Source," J. Synchrotron. Radiat. 10, 125-136 (2003).
[CrossRef] [PubMed]

Weierstall, U.

Weiss, D.

G. Schneider, E. Anderson, S. Vogt, C. Kn¨ochel, D. Weiss, M. Legros, and C. Larabell, "Computed tomography of cryogenic cells," Surf. Rev. Lett. 9, 177-183 (2002).
[CrossRef]

Weiß, D.

D. Weiß, G. Schneider, B. Niemann, P. Guttmann, D. Rudolph, and G. Schmahl, "Computed tomography of cryogenic biological specimens based on x-ray microscopic images," Ultramicroscopy 84, 185-197 (2000).
[CrossRef] [PubMed]

Williams, G.

G. Williams, H. Quiney, A. Peele, and K. Nugent, "Coherent diffractive imaging and partial coherence," Phys. Rev. B 75, 104,102 (2007).
[CrossRef]

Winn, B.

J. Maser, A. Osanna, Y. Wang, C. Jacobsen, J. Kirz, S. Spector, B. Winn, and D. Tennant, "Soft x-ray microscopy with a cryo STXM: I. Instrumentation, imaging, and spectroscopy," J. Microsc. 197, 68-79 (2000).
[CrossRef] [PubMed]

Wolter, H.

H. Wolter, "Spiegelsysteme streifenden Einfalls als abbildende Optiken f¨ur R¨ontgenstrahlen," Ann. Phys. 10, 94-114, 286 (1952).
[CrossRef]

Yang, L.

A. Kilcoyne, T. Tyliszczak, W. Steele, S. Fakra, P. Hitchcock, K. Franck, E. Anderson, B. Harteneck, E. Rightor, G. Mitchell, A. Hitchcock, L. Yang, T. Warwick, and H. Ade, "Interferometer-controlled scanning transmission X-ray microscopes at the Advanced Light Source," J. Synchrotron. Radiat. 10, 125-136 (2003).
[CrossRef] [PubMed]

Yin, G.-C.

G.-C. Yin, M.-T. Tang, Y.-F. Song, F.-R. Chen, K. Liang, F. Duewer,W. Yun, C.-H. Ko, and H.-P. Shieh, "Energytunable transmission x-ray microscope for differential contrast imaging with near 60 nm resolution tomography," Appl. Phys. Lett. 88, 241,115 (2006).
[CrossRef]

Yun, W.

A. Tkachuk, F. Duewer, H. Cui, M. Feser, S. Wang, and W. Yun, "X-ray computed tomography in Zernike phase contrast mode at 8 keV with 50-nm resolution using Cu rotating anode x-ray source," Zeitschrift Kristallographie 222, 650-655 (2007).
[CrossRef]

G.-C. Yin, M.-T. Tang, Y.-F. Song, F.-R. Chen, K. Liang, F. Duewer,W. Yun, C.-H. Ko, and H.-P. Shieh, "Energytunable transmission x-ray microscope for differential contrast imaging with near 60 nm resolution tomography," Appl. Phys. Lett. 88, 241,115 (2006).
[CrossRef]

Acta Crystallographica A (1)

P. Thibault, V. Elser, C. Jacobsen, D. Shapiro, and D. Sayre, "Reconstruction of a yeast cell from x-ray diffraction data," Acta Crystallographica A 62, 248-261 (2006).

Ann. Phys. (1)

H. Wolter, "Spiegelsysteme streifenden Einfalls als abbildende Optiken f¨ur R¨ontgenstrahlen," Ann. Phys. 10, 94-114, 286 (1952).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

G.-C. Yin, M.-T. Tang, Y.-F. Song, F.-R. Chen, K. Liang, F. Duewer,W. Yun, C.-H. Ko, and H.-P. Shieh, "Energytunable transmission x-ray microscope for differential contrast imaging with near 60 nm resolution tomography," Appl. Phys. Lett. 88, 241,115 (2006).
[CrossRef]

Atomic Data Nuclear Data Tables (1)

B. L. Henke, E. M. Gullikson, and J. C. Davis, "X-ray Interactions: Photoabsorption, Scattering, Transmission, and Reflection at E=50-30,000 eV, Z=1-92," Atomic Data Nuclear Data Tables 54, 181-342 (1993).
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M. Howells, T. Beetz, H. Chapman, C. Cui, J. Holton, C. Jacobsen, J. Kirz, E. Lima, S. Marchesini, H. Miao, D. Sayre, D. Shapiro, J. Spence, and D. Starodub, "An assessment of the resolution limitation due to radiationdamage in x-ray diffraction microscopy," J. Electron. Spectrosc. Relat. Phenom. 170, 4-12 (2009).
[CrossRef]

J. Microsc. (1)

J. Maser, A. Osanna, Y. Wang, C. Jacobsen, J. Kirz, S. Spector, B. Winn, and D. Tennant, "Soft x-ray microscopy with a cryo STXM: I. Instrumentation, imaging, and spectroscopy," J. Microsc. 197, 68-79 (2000).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

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A. Rose, "Unified approach to performance of photographic film, television pickup tubes, and human eye," J. Soc. Motion Pict. Eng. 47, 273-294 (1946).

J. Synchrotron. Radiat. (2)

Q. Shen, I. Bazarov, and P. Thibault, "Diffractive imaging of nonperiodic materials with future coherent x-ray sources," J. Synchrotron. Radiat. 11, 432-438 (2004).
[CrossRef] [PubMed]

A. Kilcoyne, T. Tyliszczak, W. Steele, S. Fakra, P. Hitchcock, K. Franck, E. Anderson, B. Harteneck, E. Rightor, G. Mitchell, A. Hitchcock, L. Yang, T. Warwick, and H. Ade, "Interferometer-controlled scanning transmission X-ray microscopes at the Advanced Light Source," J. Synchrotron. Radiat. 10, 125-136 (2003).
[CrossRef] [PubMed]

Molecular Biology of the Cell (1)

C. Larabell and M. Le Gros, "X-ray tomography generates 3-D reconstructions of the yeast, Saccharomyces cerevisiae, at 60-nm resolution," Molecular Biology of the Cell 15, 957-962 (2004).
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J. Frank and L. Al-Ali, "Signal-to-noise ratio of electron micrographs obtained by cross correlation," Nature 256, 376-379 (1975).
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J. Miao, P. Charalambous, J. Kirz, and D. Sayre, "An extension of the methods of x-ray crystallography to allow imaging of micron-size non-crystalline specimens," Nature 400, 342-344 (1999).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. B (1)

G. Williams, H. Quiney, A. Peele, and K. Nugent, "Coherent diffractive imaging and partial coherence," Phys. Rev. B 75, 104,102 (2007).
[CrossRef]

Proc. Natl. Acad. Sci. USA (1)

D. Shapiro, P. Thibault, T. Beetz, V. Elser,M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, "Biological imaging by soft x-ray diffraction microscopy," Proc. Natl. Acad. Sci. USA 102, 15,343-15,346 (2005).
[CrossRef]

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[CrossRef]

Science (2)

D. Sayre, J. Kirz, R. Feder, D. M. Kim, and E. Spiller, "Potential operating region for ultrasoft x-ray microscopy of biological specimens," Science 196, 1339-1340 (1977).
[CrossRef] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, "High-resolution scanning x-ray diffraction microscopy," Science 321, 379-382 (2008).
[CrossRef] [PubMed]

Surf. Rev. Lett. (1)

G. Schneider, E. Anderson, S. Vogt, C. Kn¨ochel, D. Weiss, M. Legros, and C. Larabell, "Computed tomography of cryogenic cells," Surf. Rev. Lett. 9, 177-183 (2002).
[CrossRef]

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G. Schneider, "Cryo x-ray microscopy with high spatial resolution in amplitude and phase contrast," Ultramicroscopy 75, 85-104 (1998).
[CrossRef] [PubMed]

D. Weiß, G. Schneider, B. Niemann, P. Guttmann, D. Rudolph, and G. Schmahl, "Computed tomography of cryogenic biological specimens based on x-ray microscopic images," Ultramicroscopy 84, 185-197 (2000).
[CrossRef] [PubMed]

D. Sayre, J. Kirz, R. Feder, D. M. Kim, and E. Spiller, "Transmission Microscopy of Unmodified Biological Materials: Comparative Radiation Dosages with Electrons and Ultrasoft X-ray Photons," Ultramicroscopy 2, 337-341 (1977).
[CrossRef] [PubMed]

Zeitschrift Kristallographie (1)

A. Tkachuk, F. Duewer, H. Cui, M. Feser, S. Wang, and W. Yun, "X-ray computed tomography in Zernike phase contrast mode at 8 keV with 50-nm resolution using Cu rotating anode x-ray source," Zeitschrift Kristallographie 222, 650-655 (2007).
[CrossRef]

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D. Sayre, "Prospects for long-wavelength X-ray microscopy and diffraction," in Imaging Processes and Coherence in Physics, M. Schlenker, ed., (Springer-Verlag, Berlin, 198 pp. 229-235 0).

H. Rarback, J. M. Kenney, J. Kirz, M. R. Howells, P. Chang, P. J. Coane, R. Feder, P. J. Houzego, D. P. Kern, and D. Sayre, "Recent results from the Stony Brook scanning microscope," in X-ray Microscopy, G. Schmahl and D. Rudolph, eds., vol. 43 of Springer Series in Optical Sciences, pp. 203-215 (Springer-Verlag, Berlin, 1984).

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Figures (7)

Fig. 1.
Fig. 1.

(a) Images with noise simulated according to different mean photon numbers per pixel n̄. Without noise, each pixel p has a value Ip of between 0 and 1. With illumination of n̄ photons per pixel, each pixel has a starting value of n̄Ip photons which was used on a pixel-by-pixel basis to generate an image using signal-dependent noise calculated using the positive-integer-truncated Gaussian approximation. (b) signal-to-noise ratio (SNR) calculated from the images versus incident photon number per pixel n̄. The signal-to-noise ratio was calculated both by comparison of the noisy image with the noise-free original image described in Eqs. (7) and (8), and by using the two-noisy-image correlation method described in Eqs. (11) and (14). Since a fit of the data on a log-log plot of SNR versus n̄ shows a slope of 0.5 as expected from Eq. (5), both image SNR methods give the expected scaling of SNR versus exposure n̄.

Fig. 2.
Fig. 2.

Defined objects used for image simulations. Shown here are the magnitudes of the simulated exit waves resulting from plane wave illumination of the objects. Cell A has random protein thicknesses within an irregular boundary, while Cell B has a lipid membrane and several protein bars and ellipses inside.

Fig. 3.
Fig. 3.

Diffraction patterns of the exit waves from the two defined objects, cell A and cell B, and their azimuthally averaged, unit-integral-normalized power spectral densities. In both cases the exit wave amplitudes were Fourier transformed and then squared to yield the diffraction intensity. Both defined objects have the signal decline with spatial frequency in a power law relationship with a slope of about 3.3 over most frequencies. For cell A, this trend then levels off at a spatial frequency of about 10 µm-1 where the pixel-by-pixel uncorrelated protein thickness dominate the diffraction pattern; this yields a flat power spectrum corresponding to a delta (δ) function in real space. For cell B, the overall round shape of the object gives rise to Airy rings in the diffraction pattern which show up at spatial frequencies above 10 µm-1.

Fig. 4.
Fig. 4.

Schematic of the two x-ray imaging systems considered in simulations. In the TXM or transmission x-ray microscope at left, incoherent brightfield imaging is assumed where the numerical aperture of the condenser is 1.5 times the numerical aperture of the objective lens; a magnified image is recorded on a detector such as a CCD. The TXM objective is a zone plate with 30 nm outermost zone width and 10% diffraction efficiency. In XDM or x-ray diffraction microscopy at right, the specimen is assumed to be illuminated by a fully coherent beam and the far-field x-ray diffraction pattern is recorded on a detector such as a CCD. A reconstructed image is obtained by computational phasing of the coherent diffraction pattern.

Fig. 5.
Fig. 5.

Images resulting from the simulations. Shown here are both TXM (top row) and XDM (bottom row) images calculated for the two defined objects, cells A and B, with exposures of n̄=1×103 and n̄=1×105 photons per pixel. The lack of “salt and pepper” shot noise in background region outside of the cell in the XDM reconstructions is a result of the imposition of a finite support constraint in the reconstruction process.

Fig. 6.
Fig. 6.

Plots of the signal-to-noise ratio SNR as a function of incident photons per pixel n̄ for our simulation set. The results at left are for the defined object “cell A”, while those at right are for “cell B” (see Fig. 2). The results for both x-ray diffraction microscopy (XDM) and transmission x-ray microscopy (TXM) are shown. In each case a slope of about 1/2 is observed in the log10(SNR) versus log10(n̄) plot (Eq. (5)), and for both objects the SNR for x-ray diffraction microscopy is about 7 times higher than it is for transmission x-ray microscopy. For x-ray diffraction microscopy of cell B, the SNR curve oscillates around the straight line fit. This oscillation corresponds to providing enough signal to phase data in successive Airy rings in the diffraction pattern of the overall spherical shape of cell B, as shown in Fig. 3.

Fig. 7.
Fig. 7.

Investigation of the dose versus resolution trend for x-ray diffraction microscopy of defined object B. (a) The ratio 〈I recon(f)〉/〈I data(f)〉 for the example case of incident photon number n̄=1000. This ratio measures how consistent the reconstructed intensity Irecon averaged over many iterates compared to the recorded intensity Idata . We chose a cutoff value of 0.7 as providing an estimate of the resolution of the reconstructed image. (b) The resulting trend of incident photon number n̄ versus resolution Δmin, along with a straight line fit to determine the dose versus resolution scaling parameter mr . The value of mr =-3.2±0.2 is consistent with the scaling of m=-3.30±0.03 shown in Fig. 3 for the diffracted signal from this object.

Equations (24)

Equations on this page are rendered with MathJax. Learn more.

D=nˉEphotonμΔ2ρ,
SNR=SignalNoise=nˉIfIb(nˉIf)2+(nˉIb)2=nˉIfIbIf+Ib=nˉΘ,
Θ=IfIbIf+Ib
C=IfIbIf+Ib.
log10SNR=log10(nˉΘ)=12log10nˉ+log10Θ.
I1=S+N1andI2=S+N2,
Signal2=(SS)(SS)*=S2S2,
Noise2=(N1,2N1,2)(N1,2N1,2)*=N1,22,
σ1,22=(I1,2I1,2)(I1,2I1,2)*
=S2+N1,22S2,
rσ1σ2=rσ2=(I1I1)(I2I2)*
=S2S2,
r=(I1I1)(I2I2)*(I1I1)2(I2I2)2.
σ2=(S2S2)+N1,22=Signal2+Noise2.
rσ2=S2S2=Signal2.
SNR=Signal2Noise2=r1r,
image=object*intensity_psf.
image=1{{object}·{intensity_psf}}=1 {{object}·MTF},
MTF={2π[cos1(ff0)ff01(ff0)2]ff00f>f0,
P(f)=10bfm
Smin=nˉP(fc).
fc=12Δmin.
Smin=nˉ10b(2Δmin)mr,
log10nˉ=mrlog10(Δmin)+mrlog102+log10Sminb,

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