Abstract

We present a numerical image-formation model for investigating the influence of partial coherence, sample thickness and depth-of-focus on the accuracy of tomographic reconstructions in transmission x-ray microscopes. The model combines wave propagation through the object by finite difference techniques with Fourier methods. We include a ray-tracing model to analyse the origin of detrimental stray light in zone plate-based x-ray microscopes. These models allow optimization of x-ray microscopy systems for quantitative tomographic imaging of thick objects. Results show that both the depth-of-focus and the reconstructed local absorption coefficient are highly dependent on the degree of coherence of the optical system.

© 2011 OSA

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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2010 (3)

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

H. N. Chapman and K. A. Nugent, “Coherent lens-less X-ray imaging,” Nat. Photonics 4(12), 833–839 (2010).
[CrossRef]

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]

2009 (1)

M. Uchida, G. McDermott, M. Wetzler, M. A. Le Gros, M. Myllys, C. Knoechel, A. E. Barron, and C. A. Larabell, “Soft X-ray tomography of phenotypic switching and the cellular response to antifungal peptoids in Candida albicans,” Proc. Natl. Acad. Sci. U.S.A. 106(46), 19375–19380 (2009).
[CrossRef] [PubMed]

2007 (3)

P. A. C. Takman, H. Stollberg, G. A. Johansson, A. Holmberg, M. Lindblom, and H. M. Hertz, “High-resolution compact X-ray microscopy,” J. Microsc. 226(2), 175–181 (2007).
[CrossRef] [PubMed]

O. von Hofsten, P. A. C. Takman, and U. Vogt, “Simulation of partially coherent image formation in a compact soft X-ray microscope,” Ultramicroscopy 107(8), 604–609 (2007).
[CrossRef] [PubMed]

C. MessaoudiI, T. Boudier, C. Sorzano, and S. Marco, “TomoJ: tomography software for three-dimensional reconstruction in transmission electron microscopy,” BMC Bioinf. 8(1), 288 (2007).
[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(7046), 1210–1213 (2005).
[CrossRef] [PubMed]

2002 (1)

2000 (2)

Y. Wang, C. Jacobsen, J. Maser, and A. Osanna, “Soft X-ray microscopy with a cryo scanning transmission X-ray microscope: II. Tomography,” J. Microsc. 197(1), 80–93 (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(3-4), 185–197 (2000).
[CrossRef] [PubMed]

1997 (1)

J. Zhenle, F. Junmei, and F. Enxin, “A simple wide-angle beam-propagation method for integrated optics,” Microw. Opt. Technol. Lett. 14(6), 345–347 (1997).
[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,” At. Data Nucl. Data Tables 54(2), 181–342 (1993).
[CrossRef]

1991 (1)

1985 (1)

N. Streibl, “Three-dimensional imaging by a microscope,” J. Opt. Soc. Am. 2(2), 121–127 (1985).
[CrossRef]

1967 (1)

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(7046), 1210–1213 (2005).
[CrossRef] [PubMed]

Attwood, D.

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

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(7046), 1210–1213 (2005).
[CrossRef] [PubMed]

Barron, A. E.

M. Uchida, G. McDermott, M. Wetzler, M. A. Le Gros, M. Myllys, C. Knoechel, A. E. Barron, and C. A. Larabell, “Soft X-ray tomography of phenotypic switching and the cellular response to antifungal peptoids in Candida albicans,” Proc. Natl. Acad. Sci. U.S.A. 106(46), 19375–19380 (2009).
[CrossRef] [PubMed]

Boudier, T.

C. MessaoudiI, T. Boudier, C. Sorzano, and S. Marco, “TomoJ: tomography software for three-dimensional reconstruction in transmission electron microscopy,” BMC Bioinf. 8(1), 288 (2007).
[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(7046), 1210–1213 (2005).
[CrossRef] [PubMed]

Chapman, H. N.

H. N. Chapman and K. A. Nugent, “Coherent lens-less X-ray imaging,” Nat. Photonics 4(12), 833–839 (2010).
[CrossRef]

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,” At. Data Nucl. Data Tables 54(2), 181–342 (1993).
[CrossRef]

Enxin, F.

J. Zhenle, F. Junmei, and F. Enxin, “A simple wide-angle beam-propagation method for integrated optics,” Microw. Opt. Technol. Lett. 14(6), 345–347 (1997).
[CrossRef]

Frieden, B. R.

Gullikson, E. M.

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,” At. Data Nucl. Data Tables 54(2), 181–342 (1993).
[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]

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(3-4), 185–197 (2000).
[CrossRef] [PubMed]

Hadley, G. R.

Harteneck, B. D.

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(7046), 1210–1213 (2005).
[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]

Henke, B. L.

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,” At. Data Nucl. Data Tables 54(2), 181–342 (1993).
[CrossRef]

Hertz, H. M.

P. A. C. Takman, H. Stollberg, G. A. Johansson, A. Holmberg, M. Lindblom, and H. M. Hertz, “High-resolution compact X-ray microscopy,” J. Microsc. 226(2), 175–181 (2007).
[CrossRef] [PubMed]

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]

Holmberg, A.

P. A. C. Takman, H. Stollberg, G. A. Johansson, A. Holmberg, M. Lindblom, and H. M. Hertz, “High-resolution compact X-ray microscopy,” J. Microsc. 226(2), 175–181 (2007).
[CrossRef] [PubMed]

Jacobsen, C.

Y. Wang, C. Jacobsen, J. Maser, and A. Osanna, “Soft X-ray microscopy with a cryo scanning transmission X-ray microscope: II. Tomography,” J. Microsc. 197(1), 80–93 (2000).
[CrossRef] [PubMed]

Johansson, G. A.

P. A. C. Takman, H. Stollberg, G. A. Johansson, A. Holmberg, M. Lindblom, and H. M. Hertz, “High-resolution compact X-ray microscopy,” J. Microsc. 226(2), 175–181 (2007).
[CrossRef] [PubMed]

Junmei, F.

J. Zhenle, F. Junmei, and F. Enxin, “A simple wide-angle beam-propagation method for integrated optics,” Microw. Opt. Technol. Lett. 14(6), 345–347 (1997).
[CrossRef]

Knoechel, C.

M. Uchida, G. McDermott, M. Wetzler, M. A. Le Gros, M. Myllys, C. Knoechel, A. E. Barron, and C. A. Larabell, “Soft X-ray tomography of phenotypic switching and the cellular response to antifungal peptoids in Candida albicans,” Proc. Natl. Acad. Sci. U.S.A. 106(46), 19375–19380 (2009).
[CrossRef] [PubMed]

Kurokhtin, A. N.

Larabell, C. A.

M. Uchida, G. McDermott, M. Wetzler, M. A. Le Gros, M. Myllys, C. Knoechel, A. E. Barron, and C. A. Larabell, “Soft X-ray tomography of phenotypic switching and the cellular response to antifungal peptoids in Candida albicans,” Proc. Natl. Acad. Sci. U.S.A. 106(46), 19375–19380 (2009).
[CrossRef] [PubMed]

Le Gros, M. A.

M. Uchida, G. McDermott, M. Wetzler, M. A. Le Gros, M. Myllys, C. Knoechel, A. E. Barron, and C. A. Larabell, “Soft X-ray tomography of phenotypic switching and the cellular response to antifungal peptoids in Candida albicans,” Proc. Natl. Acad. Sci. U.S.A. 106(46), 19375–19380 (2009).
[CrossRef] [PubMed]

Liddle, J. A.

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(7046), 1210–1213 (2005).
[CrossRef] [PubMed]

Lindblom, M.

P. A. C. Takman, H. Stollberg, G. A. Johansson, A. Holmberg, M. Lindblom, and H. M. Hertz, “High-resolution compact X-ray microscopy,” J. Microsc. 226(2), 175–181 (2007).
[CrossRef] [PubMed]

Marco, S.

C. MessaoudiI, T. Boudier, C. Sorzano, and S. Marco, “TomoJ: tomography software for three-dimensional reconstruction in transmission electron microscopy,” BMC Bioinf. 8(1), 288 (2007).
[CrossRef]

Maser, J.

Y. Wang, C. Jacobsen, J. Maser, and A. Osanna, “Soft X-ray microscopy with a cryo scanning transmission X-ray microscope: II. Tomography,” J. Microsc. 197(1), 80–93 (2000).
[CrossRef] [PubMed]

McDermott, G.

M. Uchida, G. McDermott, M. Wetzler, M. A. Le Gros, M. Myllys, C. Knoechel, A. E. Barron, and C. A. Larabell, “Soft X-ray tomography of phenotypic switching and the cellular response to antifungal peptoids in Candida albicans,” Proc. Natl. Acad. Sci. U.S.A. 106(46), 19375–19380 (2009).
[CrossRef] [PubMed]

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]

MessaoudiI, C.

C. MessaoudiI, T. Boudier, C. Sorzano, and S. Marco, “TomoJ: tomography software for three-dimensional reconstruction in transmission electron microscopy,” BMC Bioinf. 8(1), 288 (2007).
[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]

Myllys, M.

M. Uchida, G. McDermott, M. Wetzler, M. A. Le Gros, M. Myllys, C. Knoechel, A. E. Barron, and C. A. Larabell, “Soft X-ray tomography of phenotypic switching and the cellular response to antifungal peptoids in Candida albicans,” Proc. Natl. Acad. Sci. U.S.A. 106(46), 19375–19380 (2009).
[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]

Niemann, B.

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(3-4), 185–197 (2000).
[CrossRef] [PubMed]

Nugent, K. A.

H. N. Chapman and K. A. Nugent, “Coherent lens-less X-ray imaging,” Nat. Photonics 4(12), 833–839 (2010).
[CrossRef]

Osanna, A.

Y. Wang, C. Jacobsen, J. Maser, and A. Osanna, “Soft X-ray microscopy with a cryo scanning transmission X-ray microscope: II. Tomography,” J. Microsc. 197(1), 80–93 (2000).
[CrossRef] [PubMed]

Popov, A. V.

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]

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(3-4), 185–197 (2000).
[CrossRef] [PubMed]

Sakdinawat, A.

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

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(3-4), 185–197 (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]

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(3-4), 185–197 (2000).
[CrossRef] [PubMed]

Sorzano, C.

C. MessaoudiI, T. Boudier, C. Sorzano, and S. Marco, “TomoJ: tomography software for three-dimensional reconstruction in transmission electron microscopy,” BMC Bioinf. 8(1), 288 (2007).
[CrossRef]

Stollberg, H.

P. A. C. Takman, H. Stollberg, G. A. Johansson, A. Holmberg, M. Lindblom, and H. M. Hertz, “High-resolution compact X-ray microscopy,” J. Microsc. 226(2), 175–181 (2007).
[CrossRef] [PubMed]

Streibl, N.

N. Streibl, “Three-dimensional imaging by a microscope,” J. Opt. Soc. Am. 2(2), 121–127 (1985).
[CrossRef]

Takman, P. A. C.

O. von Hofsten, P. A. C. Takman, and U. Vogt, “Simulation of partially coherent image formation in a compact soft X-ray microscope,” Ultramicroscopy 107(8), 604–609 (2007).
[CrossRef] [PubMed]

P. A. C. Takman, H. Stollberg, G. A. Johansson, A. Holmberg, M. Lindblom, and H. M. Hertz, “High-resolution compact X-ray microscopy,” J. Microsc. 226(2), 175–181 (2007).
[CrossRef] [PubMed]

Uchida, M.

M. Uchida, G. McDermott, M. Wetzler, M. A. Le Gros, M. Myllys, C. Knoechel, A. E. Barron, and C. A. Larabell, “Soft X-ray tomography of phenotypic switching and the cellular response to antifungal peptoids in Candida albicans,” Proc. Natl. Acad. Sci. U.S.A. 106(46), 19375–19380 (2009).
[CrossRef] [PubMed]

Vogt, U.

O. von Hofsten, P. A. C. Takman, and U. Vogt, “Simulation of partially coherent image formation in a compact soft X-ray microscope,” Ultramicroscopy 107(8), 604–609 (2007).
[CrossRef] [PubMed]

von Hofsten, O.

O. von Hofsten, P. A. C. Takman, and U. Vogt, “Simulation of partially coherent image formation in a compact soft X-ray microscope,” Ultramicroscopy 107(8), 604–609 (2007).
[CrossRef] [PubMed]

Wang, Y.

Y. Wang, C. Jacobsen, J. Maser, and A. Osanna, “Soft X-ray microscopy with a cryo scanning transmission X-ray microscope: II. Tomography,” J. Microsc. 197(1), 80–93 (2000).
[CrossRef] [PubMed]

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(3-4), 185–197 (2000).
[CrossRef] [PubMed]

Wetzler, M.

M. Uchida, G. McDermott, M. Wetzler, M. A. Le Gros, M. Myllys, C. Knoechel, A. E. Barron, and C. A. Larabell, “Soft X-ray tomography of phenotypic switching and the cellular response to antifungal peptoids in Candida albicans,” Proc. Natl. Acad. Sci. U.S.A. 106(46), 19375–19380 (2009).
[CrossRef] [PubMed]

Zhenle, J.

J. Zhenle, F. Junmei, and F. Enxin, “A simple wide-angle beam-propagation method for integrated optics,” Microw. Opt. Technol. Lett. 14(6), 345–347 (1997).
[CrossRef]

At. Data Nucl. 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,” At. Data Nucl. Data Tables 54(2), 181–342 (1993).
[CrossRef]

BMC Bioinf. (1)

C. MessaoudiI, T. Boudier, C. Sorzano, and S. Marco, “TomoJ: tomography software for three-dimensional reconstruction in transmission electron microscopy,” BMC Bioinf. 8(1), 288 (2007).
[CrossRef]

J. Microsc. (2)

Y. Wang, C. Jacobsen, J. Maser, and A. Osanna, “Soft X-ray microscopy with a cryo scanning transmission X-ray microscope: II. Tomography,” J. Microsc. 197(1), 80–93 (2000).
[CrossRef] [PubMed]

P. A. C. Takman, H. Stollberg, G. A. Johansson, A. Holmberg, M. Lindblom, and H. M. Hertz, “High-resolution compact X-ray microscopy,” J. Microsc. 226(2), 175–181 (2007).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (2)

B. R. Frieden, “Optical transfer of the three-dimensional object,” J. Opt. Soc. Am. 57(1), 56–66 (1967).
[CrossRef]

N. Streibl, “Three-dimensional imaging by a microscope,” J. Opt. Soc. Am. 2(2), 121–127 (1985).
[CrossRef]

J. Opt. Soc. Am. A (1)

Microw. Opt. Technol. Lett. (1)

J. Zhenle, F. Junmei, and F. Enxin, “A simple wide-angle beam-propagation method for integrated optics,” Microw. Opt. Technol. Lett. 14(6), 345–347 (1997).
[CrossRef]

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 (2)

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

H. N. Chapman and K. A. Nugent, “Coherent lens-less X-ray imaging,” Nat. Photonics 4(12), 833–839 (2010).
[CrossRef]

Nature (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(7046), 1210–1213 (2005).
[CrossRef] [PubMed]

Opt. Lett. (1)

Proc. Natl. Acad. Sci. U.S.A. (1)

M. Uchida, G. McDermott, M. Wetzler, M. A. Le Gros, M. Myllys, C. Knoechel, A. E. Barron, and C. A. Larabell, “Soft X-ray tomography of phenotypic switching and the cellular response to antifungal peptoids in Candida albicans,” Proc. Natl. Acad. Sci. U.S.A. 106(46), 19375–19380 (2009).
[CrossRef] [PubMed]

Ultramicroscopy (2)

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(3-4), 185–197 (2000).
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[CrossRef] [PubMed]

Other (3)

M. Nevière and E. Popov, Light Propagation in Periodic Media, (Marcel Dekker, 2003).

https://www.sonoma.edu/users/c/cannon/biomineralTEM.html

National Center for X-Ray Tomography, http://ncxt.lbl.gov/ BESSY II X-ray Microscope, http://www.bessy.de/bit/bit_station_list.php

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Figures (4)

Fig. 1
Fig. 1

Schematic of a transmission x-ray microscope setup with relevant coordinates. The illuminating waves originate from the condenser point p and propagate through the object. The resulting field behind the object is then imaged by the zone plate onto the detector.

Fig. 2
Fig. 2

Simulated focus series through a thick object using the wave-propagation model. (a) The phantom used in the simulations. (b) The aperture-matched condition, m = 1, yields the shortest DOF. (c) Partially coherent illumination, m = 0.3, provides a longer DOF and (d) a fully coherent illumination, m = 0, results in the longest DOF. Note the defocus phase contrast in (c) and (d) and the longer DOF for larger structures.

Fig. 3
Fig. 3

Slices from reconstructed tomograms based on simulated images. (a) The resolution phantom contains Mylar features (15, 30, 50, and 100 nm in size and separated by two diams) in water. The two cases of aperture-matched illumination (b) and partially coherent illumination (c) provide different contrast mechanisms and resolution. Note that the object is not shown in its whole. The grey levels correspond to the LAC and comparisons with the phantom indicate the error in the reconstructions. The realistic cell phantom (d) is simulated in (e-f) with the same coherence parameters as in (b-c), again showing the role of coherence in the illumination on tomographic reconstructions.

Fig. 4
Fig. 4

Results of stray-light simulations under aperture-matched conditions. (a) Illumination light and stray light shown over the field-of-view for the 99 μm diam, 30 nm outermost zone width zone plate. (b) Stray-light ratio as a function of the source size in the object plane. The stray light increases for shorter focal lengths and for larger source sizes.

Equations (3)

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I ( M x , M y ) = λ p S λ | 1 ( A λ ( ν x , ν y ) ( E p ( x , y ) ) ) | 2 ,
A λ ( ν x , ν y ) = { exp ( i k ( ν x 2 + ν y 2 ) f λ 2 Δ f λ 2 ( f + Δ f λ ) ) ν x 2 + ν y 2 NA O / λ 0 ν x 2 + ν y 2 > NA O / λ .
Z = I ± 1 4 i k ( Δ z 1 i k ) ( 1 ( Δ x ) 2 A + k 2 B ) ,

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