Abstract

In this paper, the theoretical background and development of a differential-interference contrast (DIC) x-ray optic is presented. The single-element optic is capable of high-resolution phase contrast imaging and is compatible with compact sources. It is shown that an understanding of the coherence requirements in this type of imaging is imperative and is explained in detail. The optic is capable of a wavefront separation equal to the resolution of the optic which places only minor constraints on the object illumination.

© 2008 Optical Society of America

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Theoretical development and experimental evaluation of imaging models for differential-interference-contrast microscopy

Chrysanthe Preza, Donald L. Snyder, and José-Angel Conchello
J. Opt. Soc. Am. A 16(9) 2185-2199 (1999)

Diffractive optical elements for differential interference contrast x-ray microscopy

Enzo Di Fabrizio, Dan Cojoc, Stefano Cabrini, Burkhard Kaulich, Jean Susini, Paolo Facci, and Thomas Wilhein
Opt. Express 11(19) 2278-2288 (2003)

References

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  1. S. Aoki, Y Kagoshima, and Y. Suzuki, eds., X-ray microscopy, (The Institute of Pure and Applied Physics, Tokyo, Japan2006).
  2. D. T. Attwood, Soft X-Rays and Extreme Ultraviolet Radiation,(Cambridge University Press, Cambridge1999).
  3. 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]
  4. C. A. Larabell and M. A. Le Gros, “X-ray Tomography Generates 3-D Reconstructions of the Yeast, Saccharomyces cerevisiae, at 60-nm Resolution,” Mol. Biol. Cell 15, 957–962 (2004).
    [Crossref]
  5. G. Schmahl, D. Rudolph, P. Guttmann, G. Schneider, J. Thieme, and B. Niemann, “Phase contrast studies of biological specimens with the X-ray microscope at BESSY,” Rev. Sci. Instrum. 66, 1282–1286 (1995).
    [Crossref]
  6. G. Schmahl, D. Rudolph, G. Schneider, P. Guttmann, and B. Niemann, “Phase contrast X-ray microscopy studies,” Optik 97, 181–182 (1994).
  7. T. Wilhein, B. Kaulich, and J. Susini, “Two zone plate interference contrast microscopy at 4 keV photon energy,” Opt. Commun. 193, 19–26 (2001).
    [Crossref]
  8. T. Wilhein, B. Kaulich, E. Di Fabrizio, F. Romanato, S. Cabrini, and J. Susini, “Differential interference contrast X-ray microscopy with submicron resolution,” Appl. Phys. Lett. 78, 2082–2084 (2001).
    [Crossref]
  9. B. Kaulich, T. Wilhein, E. Di Fabrizio, F. Romanato, M. Altissimo, S. Cabrini, B. Fayard, and J. Susini, “Differential interference contrast X-ray microscopy with twin zone plates,” J. Opt. Soc. Am. A 19, 797–806 (2002).
    [Crossref]
  10. E. Di Fabrizio, D. Cojoc, S. Cabrini, B. Kaulich, J. Susini, P. Facci, and T. Wilhein, “Diffractive optical elements for differential interference contrast x-ray microscopy,” Opt. Express 11, 2278–2288 (2003).
    [Crossref] [PubMed]
  11. U. Vogt, M. Lindblom, P. A. C. Jansson, T. T. Tuohimaa, A. Holmberg, H. M. Hertz, M. Wieland, and T. Wilhein, “Single-optical-element soft-x-ray interferometry with a laser-plasma x-ray source,” Opt. Lett. 30, 2167–2169 (2005).
    [Crossref] [PubMed]
  12. C. Chang, A. Sakdinawat, P. Fischer, E. H. Anderson, and D. T. Attwood, “Single-element objective lens for soft x-ray differential interference contrast microscopy,” Optics. Letters. 31, 1564–1566 (2006).
    [Crossref] [PubMed]
  13. P. Fischer, G. Denbeaux, T. Ono, T. Okuno, T. Eimuller, D. Goll, and G. Schutz, “Study of magnetic domains by magnetic soft x-ray transmission microscopy,” J. Phys. D-Appl. Phys. 35, 2391–2397 (2002).
    [Crossref]
  14. P. A. C. Takman, H. Stollberg, G. A. Johansson, A. Holmberg, M. Lindblom, and H. M. Hertz, “Highresolution compact x-ray microscopy,” J. Microsc. 226, 175–181 (2007).
    [Crossref] [PubMed]
  15. M. Bertilson, O. von Hofsten, and U. Vogt, “Compact high-resolution differential interference contrast soft x-ray microscopy,” Submitted to Appl. Phys. Lett. (2007).
  16. R. D. Allen, G. B. David, and G. Nomarski, “The Zeiss-Nomarski differential interference equipment for transmitted-light microscopy,” Zeitschrift fur Wissenschaftliche Mikroskopie und Mikroskopische Technik 69, 193–222 (1969).
    [PubMed]
  17. J. W. Goodman, Statistical Optics,(Wiley, New York1985).
  18. C. Preza, D. L. Snyder, and J. Conchello, “Theoretical development and experimental evaluation of imaging models for differential-interference-contrast microscopy,” J. Opt. Soc. Am. A 16, 2185–2199 (1999).
    [Crossref]
  19. 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, 604–609 (2007).
    [Crossref] [PubMed]
  20. M. Born and E. Wolf, Principles of optics: electromagnetic theory of propagation, interference and diffraction of light, (Cambridge University Press, 1999).
    [PubMed]
  21. A. G. Michette, Optical Systems for Soft X Rays, (Plenum Press, New York1986).
    [Crossref]

2007 (2)

P. A. C. Takman, H. Stollberg, G. A. Johansson, A. Holmberg, M. Lindblom, and H. M. Hertz, “Highresolution compact x-ray microscopy,” J. Microsc. 226, 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, 604–609 (2007).
[Crossref] [PubMed]

2006 (1)

C. Chang, A. Sakdinawat, P. Fischer, E. H. Anderson, and D. T. Attwood, “Single-element objective lens for soft x-ray differential interference contrast microscopy,” Optics. Letters. 31, 1564–1566 (2006).
[Crossref] [PubMed]

2005 (2)

2004 (1)

C. A. Larabell and M. A. Le Gros, “X-ray Tomography Generates 3-D Reconstructions of the Yeast, Saccharomyces cerevisiae, at 60-nm Resolution,” Mol. Biol. Cell 15, 957–962 (2004).
[Crossref]

2003 (1)

2002 (2)

B. Kaulich, T. Wilhein, E. Di Fabrizio, F. Romanato, M. Altissimo, S. Cabrini, B. Fayard, and J. Susini, “Differential interference contrast X-ray microscopy with twin zone plates,” J. Opt. Soc. Am. A 19, 797–806 (2002).
[Crossref]

P. Fischer, G. Denbeaux, T. Ono, T. Okuno, T. Eimuller, D. Goll, and G. Schutz, “Study of magnetic domains by magnetic soft x-ray transmission microscopy,” J. Phys. D-Appl. Phys. 35, 2391–2397 (2002).
[Crossref]

2001 (2)

T. Wilhein, B. Kaulich, and J. Susini, “Two zone plate interference contrast microscopy at 4 keV photon energy,” Opt. Commun. 193, 19–26 (2001).
[Crossref]

T. Wilhein, B. Kaulich, E. Di Fabrizio, F. Romanato, S. Cabrini, and J. Susini, “Differential interference contrast X-ray microscopy with submicron resolution,” Appl. Phys. Lett. 78, 2082–2084 (2001).
[Crossref]

1999 (1)

1995 (1)

G. Schmahl, D. Rudolph, P. Guttmann, G. Schneider, J. Thieme, and B. Niemann, “Phase contrast studies of biological specimens with the X-ray microscope at BESSY,” Rev. Sci. Instrum. 66, 1282–1286 (1995).
[Crossref]

1994 (1)

G. Schmahl, D. Rudolph, G. Schneider, P. Guttmann, and B. Niemann, “Phase contrast X-ray microscopy studies,” Optik 97, 181–182 (1994).

1969 (1)

R. D. Allen, G. B. David, and G. Nomarski, “The Zeiss-Nomarski differential interference equipment for transmitted-light microscopy,” Zeitschrift fur Wissenschaftliche Mikroskopie und Mikroskopische Technik 69, 193–222 (1969).
[PubMed]

Allen, R. D.

R. D. Allen, G. B. David, and G. Nomarski, “The Zeiss-Nomarski differential interference equipment for transmitted-light microscopy,” Zeitschrift fur Wissenschaftliche Mikroskopie und Mikroskopische Technik 69, 193–222 (1969).
[PubMed]

Altissimo, M.

Anderson, E. H.

C. Chang, A. Sakdinawat, P. Fischer, E. H. Anderson, and D. T. Attwood, “Single-element objective lens for soft x-ray differential interference contrast microscopy,” Optics. Letters. 31, 1564–1566 (2006).
[Crossref] [PubMed]

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]

Attwood, D. T.

C. Chang, A. Sakdinawat, P. Fischer, E. H. Anderson, and D. T. Attwood, “Single-element objective lens for soft x-ray differential interference contrast microscopy,” Optics. Letters. 31, 1564–1566 (2006).
[Crossref] [PubMed]

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]

D. T. Attwood, Soft X-Rays and Extreme Ultraviolet Radiation,(Cambridge University Press, Cambridge1999).

Bertilson, M.

M. Bertilson, O. von Hofsten, and U. Vogt, “Compact high-resolution differential interference contrast soft x-ray microscopy,” Submitted to Appl. Phys. Lett. (2007).

Born, M.

M. Born and E. Wolf, Principles of optics: electromagnetic theory of propagation, interference and diffraction of light, (Cambridge University Press, 1999).
[PubMed]

Cabrini, S.

Chang, C.

C. Chang, A. Sakdinawat, P. Fischer, E. H. Anderson, and D. T. Attwood, “Single-element objective lens for soft x-ray differential interference contrast microscopy,” Optics. Letters. 31, 1564–1566 (2006).
[Crossref] [PubMed]

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]

Cojoc, D.

Conchello, J.

David, G. B.

R. D. Allen, G. B. David, and G. Nomarski, “The Zeiss-Nomarski differential interference equipment for transmitted-light microscopy,” Zeitschrift fur Wissenschaftliche Mikroskopie und Mikroskopische Technik 69, 193–222 (1969).
[PubMed]

Denbeaux, G.

P. Fischer, G. Denbeaux, T. Ono, T. Okuno, T. Eimuller, D. Goll, and G. Schutz, “Study of magnetic domains by magnetic soft x-ray transmission microscopy,” J. Phys. D-Appl. Phys. 35, 2391–2397 (2002).
[Crossref]

Di Fabrizio, E.

Eimuller, T.

P. Fischer, G. Denbeaux, T. Ono, T. Okuno, T. Eimuller, D. Goll, and G. Schutz, “Study of magnetic domains by magnetic soft x-ray transmission microscopy,” J. Phys. D-Appl. Phys. 35, 2391–2397 (2002).
[Crossref]

Facci, P.

Fayard, B.

Fischer, P.

C. Chang, A. Sakdinawat, P. Fischer, E. H. Anderson, and D. T. Attwood, “Single-element objective lens for soft x-ray differential interference contrast microscopy,” Optics. Letters. 31, 1564–1566 (2006).
[Crossref] [PubMed]

P. Fischer, G. Denbeaux, T. Ono, T. Okuno, T. Eimuller, D. Goll, and G. Schutz, “Study of magnetic domains by magnetic soft x-ray transmission microscopy,” J. Phys. D-Appl. Phys. 35, 2391–2397 (2002).
[Crossref]

Goll, D.

P. Fischer, G. Denbeaux, T. Ono, T. Okuno, T. Eimuller, D. Goll, and G. Schutz, “Study of magnetic domains by magnetic soft x-ray transmission microscopy,” J. Phys. D-Appl. Phys. 35, 2391–2397 (2002).
[Crossref]

Goodman, J. W.

J. W. Goodman, Statistical Optics,(Wiley, New York1985).

Guttmann, P.

G. Schmahl, D. Rudolph, P. Guttmann, G. Schneider, J. Thieme, and B. Niemann, “Phase contrast studies of biological specimens with the X-ray microscope at BESSY,” Rev. Sci. Instrum. 66, 1282–1286 (1995).
[Crossref]

G. Schmahl, D. Rudolph, G. Schneider, P. Guttmann, and B. Niemann, “Phase contrast X-ray microscopy studies,” Optik 97, 181–182 (1994).

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, 1210–1213 (2005).
[Crossref] [PubMed]

Hertz, H. M.

Holmberg, A.

Jansson, P. A. C.

Johansson, G. A.

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

Kaulich, B.

E. Di Fabrizio, D. Cojoc, S. Cabrini, B. Kaulich, J. Susini, P. Facci, and T. Wilhein, “Diffractive optical elements for differential interference contrast x-ray microscopy,” Opt. Express 11, 2278–2288 (2003).
[Crossref] [PubMed]

B. Kaulich, T. Wilhein, E. Di Fabrizio, F. Romanato, M. Altissimo, S. Cabrini, B. Fayard, and J. Susini, “Differential interference contrast X-ray microscopy with twin zone plates,” J. Opt. Soc. Am. A 19, 797–806 (2002).
[Crossref]

T. Wilhein, B. Kaulich, and J. Susini, “Two zone plate interference contrast microscopy at 4 keV photon energy,” Opt. Commun. 193, 19–26 (2001).
[Crossref]

T. Wilhein, B. Kaulich, E. Di Fabrizio, F. Romanato, S. Cabrini, and J. Susini, “Differential interference contrast X-ray microscopy with submicron resolution,” Appl. Phys. Lett. 78, 2082–2084 (2001).
[Crossref]

Larabell, C. A.

C. A. Larabell and M. A. Le Gros, “X-ray Tomography Generates 3-D Reconstructions of the Yeast, Saccharomyces cerevisiae, at 60-nm Resolution,” Mol. Biol. Cell 15, 957–962 (2004).
[Crossref]

Le Gros, M. A.

C. A. Larabell and M. A. Le Gros, “X-ray Tomography Generates 3-D Reconstructions of the Yeast, Saccharomyces cerevisiae, at 60-nm Resolution,” Mol. Biol. Cell 15, 957–962 (2004).
[Crossref]

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, 1210–1213 (2005).
[Crossref] [PubMed]

Lindblom, M.

Michette, A. G.

A. G. Michette, Optical Systems for Soft X Rays, (Plenum Press, New York1986).
[Crossref]

Niemann, B.

G. Schmahl, D. Rudolph, P. Guttmann, G. Schneider, J. Thieme, and B. Niemann, “Phase contrast studies of biological specimens with the X-ray microscope at BESSY,” Rev. Sci. Instrum. 66, 1282–1286 (1995).
[Crossref]

G. Schmahl, D. Rudolph, G. Schneider, P. Guttmann, and B. Niemann, “Phase contrast X-ray microscopy studies,” Optik 97, 181–182 (1994).

Nomarski, G.

R. D. Allen, G. B. David, and G. Nomarski, “The Zeiss-Nomarski differential interference equipment for transmitted-light microscopy,” Zeitschrift fur Wissenschaftliche Mikroskopie und Mikroskopische Technik 69, 193–222 (1969).
[PubMed]

Okuno, T.

P. Fischer, G. Denbeaux, T. Ono, T. Okuno, T. Eimuller, D. Goll, and G. Schutz, “Study of magnetic domains by magnetic soft x-ray transmission microscopy,” J. Phys. D-Appl. Phys. 35, 2391–2397 (2002).
[Crossref]

Ono, T.

P. Fischer, G. Denbeaux, T. Ono, T. Okuno, T. Eimuller, D. Goll, and G. Schutz, “Study of magnetic domains by magnetic soft x-ray transmission microscopy,” J. Phys. D-Appl. Phys. 35, 2391–2397 (2002).
[Crossref]

Preza, C.

Romanato, F.

B. Kaulich, T. Wilhein, E. Di Fabrizio, F. Romanato, M. Altissimo, S. Cabrini, B. Fayard, and J. Susini, “Differential interference contrast X-ray microscopy with twin zone plates,” J. Opt. Soc. Am. A 19, 797–806 (2002).
[Crossref]

T. Wilhein, B. Kaulich, E. Di Fabrizio, F. Romanato, S. Cabrini, and J. Susini, “Differential interference contrast X-ray microscopy with submicron resolution,” Appl. Phys. Lett. 78, 2082–2084 (2001).
[Crossref]

Rudolph, D.

G. Schmahl, D. Rudolph, P. Guttmann, G. Schneider, J. Thieme, and B. Niemann, “Phase contrast studies of biological specimens with the X-ray microscope at BESSY,” Rev. Sci. Instrum. 66, 1282–1286 (1995).
[Crossref]

G. Schmahl, D. Rudolph, G. Schneider, P. Guttmann, and B. Niemann, “Phase contrast X-ray microscopy studies,” Optik 97, 181–182 (1994).

Sakdinawat, A.

C. Chang, A. Sakdinawat, P. Fischer, E. H. Anderson, and D. T. Attwood, “Single-element objective lens for soft x-ray differential interference contrast microscopy,” Optics. Letters. 31, 1564–1566 (2006).
[Crossref] [PubMed]

Schmahl, G.

G. Schmahl, D. Rudolph, P. Guttmann, G. Schneider, J. Thieme, and B. Niemann, “Phase contrast studies of biological specimens with the X-ray microscope at BESSY,” Rev. Sci. Instrum. 66, 1282–1286 (1995).
[Crossref]

G. Schmahl, D. Rudolph, G. Schneider, P. Guttmann, and B. Niemann, “Phase contrast X-ray microscopy studies,” Optik 97, 181–182 (1994).

Schneider, G.

G. Schmahl, D. Rudolph, P. Guttmann, G. Schneider, J. Thieme, and B. Niemann, “Phase contrast studies of biological specimens with the X-ray microscope at BESSY,” Rev. Sci. Instrum. 66, 1282–1286 (1995).
[Crossref]

G. Schmahl, D. Rudolph, G. Schneider, P. Guttmann, and B. Niemann, “Phase contrast X-ray microscopy studies,” Optik 97, 181–182 (1994).

Schutz, G.

P. Fischer, G. Denbeaux, T. Ono, T. Okuno, T. Eimuller, D. Goll, and G. Schutz, “Study of magnetic domains by magnetic soft x-ray transmission microscopy,” J. Phys. D-Appl. Phys. 35, 2391–2397 (2002).
[Crossref]

Snyder, D. L.

Stollberg, H.

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

Susini, J.

E. Di Fabrizio, D. Cojoc, S. Cabrini, B. Kaulich, J. Susini, P. Facci, and T. Wilhein, “Diffractive optical elements for differential interference contrast x-ray microscopy,” Opt. Express 11, 2278–2288 (2003).
[Crossref] [PubMed]

B. Kaulich, T. Wilhein, E. Di Fabrizio, F. Romanato, M. Altissimo, S. Cabrini, B. Fayard, and J. Susini, “Differential interference contrast X-ray microscopy with twin zone plates,” J. Opt. Soc. Am. A 19, 797–806 (2002).
[Crossref]

T. Wilhein, B. Kaulich, and J. Susini, “Two zone plate interference contrast microscopy at 4 keV photon energy,” Opt. Commun. 193, 19–26 (2001).
[Crossref]

T. Wilhein, B. Kaulich, E. Di Fabrizio, F. Romanato, S. Cabrini, and J. Susini, “Differential interference contrast X-ray microscopy with submicron resolution,” Appl. Phys. Lett. 78, 2082–2084 (2001).
[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, 604–609 (2007).
[Crossref] [PubMed]

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

Thieme, J.

G. Schmahl, D. Rudolph, P. Guttmann, G. Schneider, J. Thieme, and B. Niemann, “Phase contrast studies of biological specimens with the X-ray microscope at BESSY,” Rev. Sci. Instrum. 66, 1282–1286 (1995).
[Crossref]

Tuohimaa, T. T.

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, 604–609 (2007).
[Crossref] [PubMed]

U. Vogt, M. Lindblom, P. A. C. Jansson, T. T. Tuohimaa, A. Holmberg, H. M. Hertz, M. Wieland, and T. Wilhein, “Single-optical-element soft-x-ray interferometry with a laser-plasma x-ray source,” Opt. Lett. 30, 2167–2169 (2005).
[Crossref] [PubMed]

M. Bertilson, O. von Hofsten, and U. Vogt, “Compact high-resolution differential interference contrast soft x-ray microscopy,” Submitted to Appl. Phys. Lett. (2007).

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, 604–609 (2007).
[Crossref] [PubMed]

M. Bertilson, O. von Hofsten, and U. Vogt, “Compact high-resolution differential interference contrast soft x-ray microscopy,” Submitted to Appl. Phys. Lett. (2007).

Wieland, M.

Wilhein, T.

Wolf, E.

M. Born and E. Wolf, Principles of optics: electromagnetic theory of propagation, interference and diffraction of light, (Cambridge University Press, 1999).
[PubMed]

Appl. Phys. Lett. (1)

T. Wilhein, B. Kaulich, E. Di Fabrizio, F. Romanato, S. Cabrini, and J. Susini, “Differential interference contrast X-ray microscopy with submicron resolution,” Appl. Phys. Lett. 78, 2082–2084 (2001).
[Crossref]

J. Microsc. (1)

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

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

J. Phys. D-Appl. Phys. (1)

P. Fischer, G. Denbeaux, T. Ono, T. Okuno, T. Eimuller, D. Goll, and G. Schutz, “Study of magnetic domains by magnetic soft x-ray transmission microscopy,” J. Phys. D-Appl. Phys. 35, 2391–2397 (2002).
[Crossref]

Mol. Biol. Cell (1)

C. A. Larabell and M. A. Le Gros, “X-ray Tomography Generates 3-D Reconstructions of the Yeast, Saccharomyces cerevisiae, at 60-nm Resolution,” Mol. Biol. Cell 15, 957–962 (2004).
[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, 1210–1213 (2005).
[Crossref] [PubMed]

Opt. Commun. (1)

T. Wilhein, B. Kaulich, and J. Susini, “Two zone plate interference contrast microscopy at 4 keV photon energy,” Opt. Commun. 193, 19–26 (2001).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Optics. Letters. (1)

C. Chang, A. Sakdinawat, P. Fischer, E. H. Anderson, and D. T. Attwood, “Single-element objective lens for soft x-ray differential interference contrast microscopy,” Optics. Letters. 31, 1564–1566 (2006).
[Crossref] [PubMed]

Optik (1)

G. Schmahl, D. Rudolph, G. Schneider, P. Guttmann, and B. Niemann, “Phase contrast X-ray microscopy studies,” Optik 97, 181–182 (1994).

Rev. Sci. Instrum. (1)

G. Schmahl, D. Rudolph, P. Guttmann, G. Schneider, J. Thieme, and B. Niemann, “Phase contrast studies of biological specimens with the X-ray microscope at BESSY,” Rev. Sci. Instrum. 66, 1282–1286 (1995).
[Crossref]

Ultramicroscopy (1)

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, 604–609 (2007).
[Crossref] [PubMed]

Zeitschrift fur Wissenschaftliche Mikroskopie und Mikroskopische Technik (1)

R. D. Allen, G. B. David, and G. Nomarski, “The Zeiss-Nomarski differential interference equipment for transmitted-light microscopy,” Zeitschrift fur Wissenschaftliche Mikroskopie und Mikroskopische Technik 69, 193–222 (1969).
[PubMed]

Other (6)

J. W. Goodman, Statistical Optics,(Wiley, New York1985).

M. Born and E. Wolf, Principles of optics: electromagnetic theory of propagation, interference and diffraction of light, (Cambridge University Press, 1999).
[PubMed]

A. G. Michette, Optical Systems for Soft X Rays, (Plenum Press, New York1986).
[Crossref]

M. Bertilson, O. von Hofsten, and U. Vogt, “Compact high-resolution differential interference contrast soft x-ray microscopy,” Submitted to Appl. Phys. Lett. (2007).

S. Aoki, Y Kagoshima, and Y. Suzuki, eds., X-ray microscopy, (The Institute of Pure and Applied Physics, Tokyo, Japan2006).

D. T. Attwood, Soft X-Rays and Extreme Ultraviolet Radiation,(Cambridge University Press, Cambridge1999).

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Figures (6)

Fig. 1.
Fig. 1.

(a). A Visible light DIC microscope. (b) An x-ray DIC microscope

Fig. 2.
Fig. 2.

(a). The degree of coherence (left axis, in black) and the contrast increase (right axis, in gray) versus the coherence factor m for two shears. The arrows point to the appropriate y-axis. (b). Edge response for m=0.5 for three different shears and without DIC. The bias retardation and the phase of the object were both set to pi and there was no absorption in the object.

Fig. 3.
Fig. 3.

Bias and shear (expressed in terms of the outermost zone width) measured in the 2D PSF as a function of the position of the phase cut. As seen, the position of the phase cut affects both the shear and the bias.

Fig. 4.
Fig. 4.

(a). The calculated one-dimensional PSF from a DOE pattern (solid) compared with the PSF from the corresponding complex aperture function (dashed). The PSF calculated from the aperture of a conventional zone plate is also shown. (b) The resulting side-cut DOE.

Fig. 5.
Fig. 5.

(a, b). Simulated images using DIC zone plates and (c). using a conventional zone plate. The lower images show the corresponding zone plates. The image simulated using a side-cut DOE, (a), exhibits the best contrast.

Fig. 6.
Fig. 6.

(a). Intensity profiles of the images shown in Fig. 5. The image taken with the side-cut DIC optic where the shear is 50 nm shows the best contrast. Also shown is the phase of the object, varying between zero and pi/3. (b) Image contrast for the same spatial frequency as in (a) but for different object phase shifts. The side-cut DOE objective yields the best contrast for objects where the phase shift is smaller than 2π/3.

Equations (11)

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f = 4 N ( Δ r ) 2 λ
k ( u , v ) = 1 2 PSF ( u + Δ u 2 , v ) exp ( i Δ θ ) + 1 2 PSF ( u Δ u 2 , v ) exp ( i Δ θ )
μ ( x 1 , y 1 ; x 2 , y 2 ) = κ e j ψ ( λ z ) 2 I ( η , ξ ) exp [ j 2 π λ ¯ z ( ( x 2 x 1 ) η + ( y 2 y 1 ) ξ ) ] d η d ξ I ( η , ξ ) d η d ξ
I image ( u , v ) = n = 1 N k ( u , v ) t ( u , v ) e i φ ( η n , ξ n )
I image ( u , v ) = n = 1 N 1 { k ̂ ( f , g ) t ̂ ( f Δ f n , g Δ g n ) } 2
C = I max I min I max + I min
m = NA condenser NA objective
A ( f , g ) = 1 ( k ( u , v ) ) = ( 2 π ) 2 k ̂ ( f , g )
A ( f , g ) = ( 2 π ) 2 cos ( Δ θ 2 π f Δ u 2 ) P S ̂ F ( f , g )
f cut = 2 Δ θ + l π 2 π Δ u
d cut r = Δ r ( 2 Δ θ + l π ) π Δ u

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