Abstract

Performance of two types of differential interference contrast objectives, i.e., the XOR pattern and the zone-plate doublet, is quantitatively characterized and compared using modulation transfer function. Effects of partial coherence, finite absorption and phase in a complex object, as well as bias retardation are also examined.

© 2011 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Sakdinawat and D. Attwood, “Nanoscale X-ray imaging,” Nat. Photonics 4, 840–848 (2010).
    [CrossRef]
  2. W. Chao, J. Kim, S. Rekawa, P. Fischer, and E. H. Anderson, “Demonstration of 12 nm resolution Fresnel zone plate lens based soft X-ray microscopy,” Opt. Express 17, 17669–17677 (2009).
    [CrossRef] [PubMed]
  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]
  4. C. Chang, A. Sakdinawat, P. Fischer, E. Anderson, and D. Attwood, “Single-element objective lens for soft X-ray differential interference contrast microscopy,” Opt. Lett. 31, 1564–1566 (2006).
    [CrossRef] [PubMed]
  5. 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]
  6. 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]
  7. A. Sakdinawat and Y. Liu, “Phase contrast soft X-ray microscopy using Zernike zone plates,” Opt. Express 16, 1559–1564 (2008).
    [CrossRef] [PubMed]
  8. O. von Hofsten, M. Bertilson, M. Lindblom, A. Holmberg, and U. Vogt, “Compact Zernike phase contrast X-ray microscopy using a single-element optic,” Opt. Lett. 33, 932–934 (2008).
    [CrossRef] [PubMed]
  9. C. Holzner, M. Feser, S. Vogt, B. Hornberger, S. B. Baines, and C. Jacobsen, “Zernike phase contrast in scanning microscopy with X-rays,” Nat. Phys. 6, 883–887 (2010).
    [CrossRef]
  10. M. Dierolf, A. Menzel, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature (London) 467, 436–439 (2010).
    [CrossRef]
  11. K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. M. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic X-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107, 529–534 (2010).
    [CrossRef]
  12. F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys. 2, 258–261 (2006).
    [CrossRef]
  13. A. Momose, W. Yashiro, H. Maikusa, and Y. Takeda, “High-speed X-ray phase imaging and X-ray phase tomography with talbot interferometer and white synchrotron radiation,” Opt. Express 17, 12540–12545 (2009).
    [CrossRef] [PubMed]
  14. P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based X-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. U.S.A. 107, 13576–13581 (2010).
    [CrossRef] [PubMed]
  15. 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]
  16. M. C. Bertilson, O. von Hofsten, M. Lindblom, T. Wilhein, H. M. Hertz, and U. Vogt, “Compact high-resolution differential interference contrast soft X-ray microscopy,” Appl. Phys. Lett. 92, 064104 (2008).
    [CrossRef]
  17. C. Chang, P. Naulleau, E. Anderson, K. Rosfjord, and D. Attwood, “Diffractive optical elements based on Fourier optical techniques: a new class of optics for extreme ultraviolet and soft X-ray wavelengths,” Appl. Opt. 41, 7384–7389 (2002).
    [CrossRef] [PubMed]
  18. 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]
  19. T. Nakamura and C. Chang, “Quantitative X-ray differential interference contrast microscopy with independently adjustable bias and shear,” Phys. Rev. A 83, 043808 (2011).
    [CrossRef]
  20. R. J. Becherer and G. B. Parrent, “Nonlinearity in optical imaging systems,” J. Opt. Soc. Am. 57, 1479–1482 (1967).
    [CrossRef]
  21. 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 15nm,” Nature (London) 435, 1210–1213 (2005).
    [CrossRef]
  22. O. von Hofsten, M. Bertilson, and U. Vogt, “Theoretical development of a high-resolution differential-interference-contrast optic for X-ray microscopy,” Opt. Express 16, 1132–1141 (2008).
    [CrossRef] [PubMed]
  23. A. Noguchi, H. Ishiwata, M. Itoh, and T. Yatagai, “Optical sectioning in differential interference contrast microscopy,” Opt. Commun. 282, 3223–3230 (2009).
    [CrossRef]
  24. Y. Ichioka, K. Yamamoto, and T. Suzuki, “Image of a sinusoidal complex object in a partially coherent optical system,” J. Opt. Soc. Am. 65, 892–902 (1975).
    [CrossRef]
  25. Y. Ichioka and T. Suzuki, “Image of a periodic complex object in an optical system under partially coherent illumination,” J. Opt. Soc. Am. 66, 921–932 (1976).
    [CrossRef]
  26. S. Inoué and K. R. Spring, Video Microscopy: The Fundamentals , 2nd ed. (Plenum Press, 1997).
    [CrossRef]
  27. J. W. Goodman, Statistical Optics (Wiley, 1985).
  28. T. Nakamura and C. Chang, “Exact space invariant illumination for partially coherent imaging systems,” J. Opt. Soc. Am. A 27, 1953–1961 (2010).
    [CrossRef]
  29. J. W. Goodman, Introduction to Fourier Optics , 3rd ed. (Roberts & Company Publishers, 2005).
  30. D. Attwood, Soft X-rays and Extreme Ultraviolet Radiation: Principles and Applications (Cambridge University Press, 1999).
  31. C. Chang, E. Anderson, P. Naulleau, E. Gullikson, K. Goldberg, and D. Attwood, “Direct measurement of index of refraction in the extreme-ultraviolet wavelength region with a novel interferometer,” Opt. Lett. 27, 1028–1030 (2002).
    [CrossRef]
  32. C. Preza, D. L. Snyder, and J. A. Conchello, “Theoretical development and experimental evaluation of imaging models for differential-interference-contrast microscopy,” J. Opt. Soc. Am. A 16, 2185–2199 (1999).
    [CrossRef]
  33. C. Chang and T. Nakamura, “Partially coherent image formation theory for X-ray microscopy,” in Microscopy: Science, Technology, Applications and Education , 4th ed., A. Méndez-Vilas and J. Díaz, eds. (Formatex Research Center, 2010), Vol. 3, pp. 1897–1904.
  34. M. Born and E. Wolf, Principles of Optics , 6th ed. (Cambridge University Press, 1997).

2011

T. Nakamura and C. Chang, “Quantitative X-ray differential interference contrast microscopy with independently adjustable bias and shear,” Phys. Rev. A 83, 043808 (2011).
[CrossRef]

2010

T. Nakamura and C. Chang, “Exact space invariant illumination for partially coherent imaging systems,” J. Opt. Soc. Am. A 27, 1953–1961 (2010).
[CrossRef]

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

C. Holzner, M. Feser, S. Vogt, B. Hornberger, S. B. Baines, and C. Jacobsen, “Zernike phase contrast in scanning microscopy with X-rays,” Nat. Phys. 6, 883–887 (2010).
[CrossRef]

M. Dierolf, A. Menzel, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature (London) 467, 436–439 (2010).
[CrossRef]

K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. M. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic X-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107, 529–534 (2010).
[CrossRef]

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based X-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. U.S.A. 107, 13576–13581 (2010).
[CrossRef] [PubMed]

2009

A. Momose, W. Yashiro, H. Maikusa, and Y. Takeda, “High-speed X-ray phase imaging and X-ray phase tomography with talbot interferometer and white synchrotron radiation,” Opt. Express 17, 12540–12545 (2009).
[CrossRef] [PubMed]

W. Chao, J. Kim, S. Rekawa, P. Fischer, and E. H. Anderson, “Demonstration of 12 nm resolution Fresnel zone plate lens based soft X-ray microscopy,” Opt. Express 17, 17669–17677 (2009).
[CrossRef] [PubMed]

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]

A. Noguchi, H. Ishiwata, M. Itoh, and T. Yatagai, “Optical sectioning in differential interference contrast microscopy,” Opt. Commun. 282, 3223–3230 (2009).
[CrossRef]

2008

2006

C. Chang, A. Sakdinawat, P. Fischer, E. Anderson, and D. Attwood, “Single-element objective lens for soft X-ray differential interference contrast microscopy,” Opt. Lett. 31, 1564–1566 (2006).
[CrossRef] [PubMed]

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys. 2, 258–261 (2006).
[CrossRef]

2005

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]

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 15nm,” Nature (London) 435, 1210–1213 (2005).
[CrossRef]

2003

2002

2001

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

1976

1975

1967

Altissimo, M.

Anderson, E.

Anderson, E. H.

W. Chao, J. Kim, S. Rekawa, P. Fischer, and E. H. Anderson, “Demonstration of 12 nm resolution Fresnel zone plate lens based soft X-ray microscopy,” Opt. Express 17, 17669–17677 (2009).
[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 15nm,” Nature (London) 435, 1210–1213 (2005).
[CrossRef]

Attwood, D.

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 15nm,” Nature (London) 435, 1210–1213 (2005).
[CrossRef]

Baines, S. B.

C. Holzner, M. Feser, S. Vogt, B. Hornberger, S. B. Baines, and C. Jacobsen, “Zernike phase contrast in scanning microscopy with X-rays,” Nat. Phys. 6, 883–887 (2010).
[CrossRef]

Becherer, R. J.

Beerlink, A.

K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. M. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic X-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107, 529–534 (2010).
[CrossRef]

Bertilson, M.

Bertilson, M. C.

M. C. Bertilson, O. von Hofsten, M. Lindblom, T. Wilhein, H. M. Hertz, and U. Vogt, “Compact high-resolution differential interference contrast soft X-ray microscopy,” Appl. Phys. Lett. 92, 064104 (2008).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics , 6th ed. (Cambridge University Press, 1997).

Bunk, O.

M. Dierolf, A. Menzel, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature (London) 467, 436–439 (2010).
[CrossRef]

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys. 2, 258–261 (2006).
[CrossRef]

Cabrini, S.

Chang, C.

Chao, W.

W. Chao, J. Kim, S. Rekawa, P. Fischer, and E. H. Anderson, “Demonstration of 12 nm resolution Fresnel zone plate lens based soft X-ray microscopy,” Opt. Express 17, 17669–17677 (2009).
[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 15nm,” Nature (London) 435, 1210–1213 (2005).
[CrossRef]

Cojoc, D.

Conchello, J. A.

David, C.

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys. 2, 258–261 (2006).
[CrossRef]

Di Fabrizio, E.

Dierolf, M.

K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. M. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic X-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107, 529–534 (2010).
[CrossRef]

M. Dierolf, A. Menzel, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature (London) 467, 436–439 (2010).
[CrossRef]

Facci, P.

Fayard, B.

Feser, M.

C. Holzner, M. Feser, S. Vogt, B. Hornberger, S. B. Baines, and C. Jacobsen, “Zernike phase contrast in scanning microscopy with X-rays,” Nat. Phys. 6, 883–887 (2010).
[CrossRef]

Fischer, P.

Giewekemeyer, K.

K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. M. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic X-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107, 529–534 (2010).
[CrossRef]

Goldberg, K.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics , 3rd ed. (Roberts & Company Publishers, 2005).

J. W. Goodman, Statistical Optics (Wiley, 1985).

Gullikson, E.

Guttmann, P.

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]

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 15nm,” Nature (London) 435, 1210–1213 (2005).
[CrossRef]

Heim, S.

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]

Hertz, H. M.

M. C. Bertilson, O. von Hofsten, M. Lindblom, T. Wilhein, H. M. Hertz, and U. Vogt, “Compact high-resolution differential interference contrast soft X-ray microscopy,” Appl. Phys. Lett. 92, 064104 (2008).
[CrossRef]

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]

Holmberg, A.

Holzner, C.

C. Holzner, M. Feser, S. Vogt, B. Hornberger, S. B. Baines, and C. Jacobsen, “Zernike phase contrast in scanning microscopy with X-rays,” Nat. Phys. 6, 883–887 (2010).
[CrossRef]

Hornberger, B.

C. Holzner, M. Feser, S. Vogt, B. Hornberger, S. B. Baines, and C. Jacobsen, “Zernike phase contrast in scanning microscopy with X-rays,” Nat. Phys. 6, 883–887 (2010).
[CrossRef]

Ichioka, Y.

Inoué, S.

S. Inoué and K. R. Spring, Video Microscopy: The Fundamentals , 2nd ed. (Plenum Press, 1997).
[CrossRef]

Ishiwata, H.

A. Noguchi, H. Ishiwata, M. Itoh, and T. Yatagai, “Optical sectioning in differential interference contrast microscopy,” Opt. Commun. 282, 3223–3230 (2009).
[CrossRef]

Itoh, M.

A. Noguchi, H. Ishiwata, M. Itoh, and T. Yatagai, “Optical sectioning in differential interference contrast microscopy,” Opt. Commun. 282, 3223–3230 (2009).
[CrossRef]

Jacobsen, C.

C. Holzner, M. Feser, S. Vogt, B. Hornberger, S. B. Baines, and C. Jacobsen, “Zernike phase contrast in scanning microscopy with X-rays,” Nat. Phys. 6, 883–887 (2010).
[CrossRef]

Jansson, P. A. C.

Kalbfleisch, S.

K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. M. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic X-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107, 529–534 (2010).
[CrossRef]

Kaulich, B.

Kewish, C. M.

K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. M. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic X-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107, 529–534 (2010).
[CrossRef]

M. Dierolf, A. Menzel, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature (London) 467, 436–439 (2010).
[CrossRef]

Kim, J.

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 15nm,” Nature (London) 435, 1210–1213 (2005).
[CrossRef]

Lindblom, M.

Liu, X.

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based X-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. U.S.A. 107, 13576–13581 (2010).
[CrossRef] [PubMed]

Liu, Y.

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based X-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. U.S.A. 107, 13576–13581 (2010).
[CrossRef] [PubMed]

A. Sakdinawat and Y. Liu, “Phase contrast soft X-ray microscopy using Zernike zone plates,” Opt. Express 16, 1559–1564 (2008).
[CrossRef] [PubMed]

Maikusa, H.

Marone, F.

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based X-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. U.S.A. 107, 13576–13581 (2010).
[CrossRef] [PubMed]

McDonald, S. A.

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based X-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. U.S.A. 107, 13576–13581 (2010).
[CrossRef] [PubMed]

Menzel, A.

M. Dierolf, A. Menzel, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature (London) 467, 436–439 (2010).
[CrossRef]

Momose, A.

Nakamura, T.

T. Nakamura and C. Chang, “Quantitative X-ray differential interference contrast microscopy with independently adjustable bias and shear,” Phys. Rev. A 83, 043808 (2011).
[CrossRef]

T. Nakamura and C. Chang, “Exact space invariant illumination for partially coherent imaging systems,” J. Opt. Soc. Am. A 27, 1953–1961 (2010).
[CrossRef]

C. Chang and T. Nakamura, “Partially coherent image formation theory for X-ray microscopy,” in Microscopy: Science, Technology, Applications and Education , 4th ed., A. Méndez-Vilas and J. Díaz, eds. (Formatex Research Center, 2010), Vol. 3, pp. 1897–1904.

Naulleau, P.

Noguchi, A.

A. Noguchi, H. Ishiwata, M. Itoh, and T. Yatagai, “Optical sectioning in differential interference contrast microscopy,” Opt. Commun. 282, 3223–3230 (2009).
[CrossRef]

Parrent, G. B.

Pfeiffer, F.

K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. M. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic X-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107, 529–534 (2010).
[CrossRef]

M. Dierolf, A. Menzel, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature (London) 467, 436–439 (2010).
[CrossRef]

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys. 2, 258–261 (2006).
[CrossRef]

Preza, C.

Rehbein, S.

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]

Rekawa, S.

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]

Rosfjord, K.

Sakdinawat, A.

Salditt, T.

K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. M. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic X-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107, 529–534 (2010).
[CrossRef]

Schneider, G.

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]

Schneider, P.

M. Dierolf, A. Menzel, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature (London) 467, 436–439 (2010).
[CrossRef]

Snyder, D. L.

Spring, K. R.

S. Inoué and K. R. Spring, Video Microscopy: The Fundamentals , 2nd ed. (Plenum Press, 1997).
[CrossRef]

Stampanoni, M.

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based X-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. U.S.A. 107, 13576–13581 (2010).
[CrossRef] [PubMed]

Susini, J.

Suzuki, T.

Takeda, Y.

Thibault, P.

K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. M. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic X-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107, 529–534 (2010).
[CrossRef]

Tuohimaa, T. T.

Vogt, S.

C. Holzner, M. Feser, S. Vogt, B. Hornberger, S. B. Baines, and C. Jacobsen, “Zernike phase contrast in scanning microscopy with X-rays,” Nat. Phys. 6, 883–887 (2010).
[CrossRef]

Vogt, U.

von Hofsten, O.

Wang, Z.

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based X-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. U.S.A. 107, 13576–13581 (2010).
[CrossRef] [PubMed]

Weitkamp, T.

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys. 2, 258–261 (2006).
[CrossRef]

Wepf, R.

M. Dierolf, A. Menzel, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature (London) 467, 436–439 (2010).
[CrossRef]

Werner, S.

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]

Wieland, M.

Wilhein, T.

Wolf, E.

M. Born and E. Wolf, Principles of Optics , 6th ed. (Cambridge University Press, 1997).

Wu, Z.

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based X-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. U.S.A. 107, 13576–13581 (2010).
[CrossRef] [PubMed]

Yamamoto, K.

Yashiro, W.

Yatagai, T.

A. Noguchi, H. Ishiwata, M. Itoh, and T. Yatagai, “Optical sectioning in differential interference contrast microscopy,” Opt. Commun. 282, 3223–3230 (2009).
[CrossRef]

Zhang, K.

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based X-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. U.S.A. 107, 13576–13581 (2010).
[CrossRef] [PubMed]

Zhu, P.

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based X-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. U.S.A. 107, 13576–13581 (2010).
[CrossRef] [PubMed]

Appl. Opt.

Appl. Phys. Lett.

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]

M. C. Bertilson, O. von Hofsten, M. Lindblom, T. Wilhein, H. M. Hertz, and U. Vogt, “Compact high-resolution differential interference contrast soft X-ray microscopy,” Appl. Phys. Lett. 92, 064104 (2008).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Nat. Photonics

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

Nat. Phys.

C. Holzner, M. Feser, S. Vogt, B. Hornberger, S. B. Baines, and C. Jacobsen, “Zernike phase contrast in scanning microscopy with X-rays,” Nat. Phys. 6, 883–887 (2010).
[CrossRef]

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys. 2, 258–261 (2006).
[CrossRef]

Nature (London)

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 15nm,” Nature (London) 435, 1210–1213 (2005).
[CrossRef]

M. Dierolf, A. Menzel, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature (London) 467, 436–439 (2010).
[CrossRef]

Opt. Commun.

A. Noguchi, H. Ishiwata, M. Itoh, and T. Yatagai, “Optical sectioning in differential interference contrast microscopy,” Opt. Commun. 282, 3223–3230 (2009).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

T. Nakamura and C. Chang, “Quantitative X-ray differential interference contrast microscopy with independently adjustable bias and shear,” Phys. Rev. A 83, 043808 (2011).
[CrossRef]

Phys. Rev. Lett.

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]

Proc. Natl. Acad. Sci. U.S.A.

K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. M. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic X-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107, 529–534 (2010).
[CrossRef]

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based X-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. U.S.A. 107, 13576–13581 (2010).
[CrossRef] [PubMed]

Other

C. Chang and T. Nakamura, “Partially coherent image formation theory for X-ray microscopy,” in Microscopy: Science, Technology, Applications and Education , 4th ed., A. Méndez-Vilas and J. Díaz, eds. (Formatex Research Center, 2010), Vol. 3, pp. 1897–1904.

M. Born and E. Wolf, Principles of Optics , 6th ed. (Cambridge University Press, 1997).

J. W. Goodman, Introduction to Fourier Optics , 3rd ed. (Roberts & Company Publishers, 2005).

D. Attwood, Soft X-rays and Extreme Ultraviolet Radiation: Principles and Applications (Cambridge University Press, 1999).

S. Inoué and K. R. Spring, Video Microscopy: The Fundamentals , 2nd ed. (Plenum Press, 1997).
[CrossRef]

J. W. Goodman, Statistical Optics (Wiley, 1985).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (14)

Fig. 1
Fig. 1

Performance comparison between FZP (conventional), XOR, and ZPD based x-ray microscopes. The complex object (left column) is illuminated coherently and imaged by FZP, XOR, and ZPD objectives, respectively (center column). Note that the object’s intensity is defined as the absolute square of the object transmittance function. The resultant image intensity (right column) shows that XOR and ZPD objectives generate higher image contrast for the complex object. It is clearly seen that image visibility produced by the two DIC objectives exceeds the object’s visibility while the image visibility produced by FZP is at best equal to that of the object. The value of MTF for DIC objectives can therefore exceed 1 (see text for details). The same bias retardation value 2Δθ = π/2 is used for the XOR and ZPD objectives in this figure.

Fig. 2
Fig. 2

Schematic diagram of a partially coherent imaging system.

Fig. 3
Fig. 3

XOR and ZPD based DIC objectives with various bias retardation values. (a) XOR with Δθ = 0, (b) XOR with Δθ = π/4, (c) XOR with Δθ = π/2, (d) ZPD with Δθ = 0, (e) ZPD with Δθ = π/4, and (f) ZPD with Δθ = π/2.

Fig. 4
Fig. 4

Pupil functions corresponding to the objectives in Fig. 3. (a) XOR with Δθ = 0, (b) XOR with Δθ = π/4, (c) XOR with Δθ = π/2, (d) ZPD with Δθ = 0, (e) ZPD with Δθ = π/4, and (f) ZPD with Δθ = π/2.

Fig. 5
Fig. 5

Absorption (top) and phase (bottom) variations of (a) absorption sinusoidal, (b) phase sinusoidal, and (d) complex sinusoidal grating objects. Period of the grating is denoted by T.

Fig. 6
Fig. 6

MTF of the absorption sinusoidal grating object for (a) FZP, (b) XOR with Δθ = 0, (c) XOR Δθ = π/12, (d) XOR Δθ = π/4, (e) XOR Δθ = π/3, and (f) XOR Δθ = π/2. The coherent cases, i.e., σ = 0, are plotted separately and located at the bottom of each panel.

Fig. 7
Fig. 7

MTF of the absorption sinusoidal grating object for (a) FZP, (b) ZPD Δθ = 0, (c) ZPD Δθ = π/12, (d) ZPD Δθ = π/4, (e) ZPD Δθ = π/3, and (f) ZPD Δθ = π/2. The results for Δθ = 0 and Δθ = π/12 are very similar. The coherent cases, i.e., σ = 0, are plotted separately and located at the bottom of each panel.

Fig. 8
Fig. 8

Image visibility Vimage of the phase sinusoidal grating object with φ = 0 ∼ π/3 for various σ values. First column shows the coherent case, i.e., σ = 0. (a) FZP, (b) XOR Δθ = 0, (c) XOR Δθ = π/12, (d) XOR Δθ = π/4, (e) XOR Δθ = π/3, and (f) XOR Δθ = π/2.

Fig. 9
Fig. 9

Image visibility Vimage of the phase sinusoidal grating object with φ = 0 ∼ π/3 for various σ values. First column shows the coherent case, i.e., σ = 0. (a) FZP, (b) ZPD Δθ = 0, (c) ZPD Δθ = π/12, (d) ZPD Δθ = π/4, (e) ZPD Δθ = π/3, and (f) ZPD Δθ = π/2.

Fig. 10
Fig. 10

MTF of the complex sinusoidal object with η = 0.1 and δ/β = 0 ∼ 10 for various σ values. (a) FZP, (b) XOR Δθ = 0, (c) XOR Δθ = π/12, (d) XOR Δθ = π/4, (e) XOR Δθ = π/3, and (f) XOR Δθ = π/2.

Fig. 11
Fig. 11

MTF of the complex sinusoidal object with η = 0.1 and δ/β = 0 ∼ 10 for various σ values. (a) FZP, (b) ZPD Δθ = 0, (c) ZPD Δθ = π/12, (d) ZPD Δθ = π/4, (e) ZPD Δθ = π/3, and (f) ZPD Δθ = π/2.

Fig. 12
Fig. 12

DIC objectives, (a) XOR and (b) ZPD, with rotation angle θr . In both examples, Δθ = π/2 and θr = 40° are used.

Fig. 13
Fig. 13

Effect of XOR’s orientation on MTF for various σ values. A complex sinusoidal object with η = 0.1 and δ/β = 0 ∼ 10 is used. XOR is rotated an angle of θr = 0° ∼ 90° with respect to the grating. The normalized object spatial frequency α is fixed at 0.6. (a) XOR Δθ = 0, (b) XOR Δθ = π/12, (c) XOR Δθ = π/4, (d) XOR Δθ = π/3, and (e) XOR Δθ = π/2.

Fig. 14
Fig. 14

Effect of ZPD’s orientation on MTF for various σ values. A complex sinusoidal object with η = 0.1 and δ/β = 0 ∼ 10 is used. ZPD is rotated an angle of θr = 0° ∼ 90° with respect to the grating. The normalized object spatial frequency α is fixed at 0.6. (a) ZPD Δθ = 0, (b) ZPD Δθ = π/12, (c) ZPD Δθ = π/4, (d) ZPD Δθ = π/3, and (e) ZPD Δθ = π/2.

Tables (2)

Tables Icon

Table 1 Pupil Functions P(x,y) of FZP, XOR, and ZPD Objectives

Tables Icon

Table 2 Transmittance Functions and Fourier Coefficients of the Gratings Used in the Text *

Equations (32)

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

I i ( u , v ) = + d p d q 𝕁 o ( p , q ) × + d w 1 d w 2 𝕋 o ( w 1 , w 2 ) 𝕂 ( w 1 p , w 2 q ) × + d ν U d ν V exp { j 2 π ( u ν U + v ν V ) } × 𝕋 o * ( w 1 ν U , w 2 ν V ) 𝕂 * ( w 1 p ν U , w 2 q ν V ) ,
I s ( α , β ) = { I o , α 2 + β 2 < R s 0 , otherwise ,
𝕁 o ( p , q ) = κ M 2 I s ( λ f c M p , λ f c M q ) ,
𝕂 ( p , q ) = M P ( λ z o M p , λ z o M q ) ,
t o ( ξ , η ) = n = + a n exp ( j 2 π n ν o ξ ) ,
𝕋 o ( z 1 , z 2 ) = n = + a n δ ( z 1 n ν o , z 2 ) ,
I i ( u , v ) = m = + n = + a n a m * exp { j 2 π [ ( n m ) ν o u ] } × + d p d q 𝕁 o ( p , q ) 𝕂 ( p + n ν o , q ) 𝕂 * ( p + m ν o , q ) .
I i ( u , v ) = m = + n = + a n a m * exp { j 2 π [ ( n m ) ν o u ] } × κ M 2 + I s ( λ f c M p , λ f c M q ) P ( λ z o ( M p + M n ν o ) , λ z o M q ) × P * ( λ z o ( M p + M m ν o ) , λ z o M q ) d ( M p ) d ( M q ) ,
ν c R o λ z o
ν s R s λ f c ,
σ ν s ν c .
α M ν o ν c ,
M T F ( α ) V image ( α ) V object ( α ) ,
t o ( ξ , η ) = 1 + cos ( 2 π ν o ξ ) .
a n = { 1 , n = 0 1 / 2 , n = ± 1 0 , otherwise .
t o ( ξ , η ) = exp [ j ϕ sin ( 2 π ν o ξ ) ] ,
exp ( ± j z sin θ ) = n = + ( ± 1 ) n J n ( z ) e j n θ ,
t o ( ξ , η ) = n = + J n ( ϕ ) exp ( j 2 π n ν o ξ ) .
𝕋 o ( z 1 , z 2 ) = n = + J n ( ϕ ) δ ( z 1 n ν o , z 2 ) ,
a n = J n ( ϕ ) .
t o ( ξ , η ) = exp [ j k ( n n o ) t ( ξ , η ) ] ,
t ( ξ , η ) = t o [ 1 + sin ( 2 π ν o ξ ) ] .
t o ( ξ , η ) = exp [ j k ( δ + j β ) η t a sin ( 2 π ν o ξ ) ] = exp [ j ( δ β + j ) η 2 sin ( 2 π ν o ξ ) ] .
z = ( δ β + j ) η 2 ,
t o ( ξ , η ) = n = + J n ( z ) exp ( j 2 π n ν o ξ ) .
𝕋 o ( z 1 , z 2 ) = n = + J n ( z ) δ ( z 1 n ν o , z 2 ) ,
a n = J n ( z ) ,
V I m a x I m i n I m a x + I m i n ,
| t o ( ξ , η ) | 2 = | 1 + cos ( 2 π ν o ξ ) | 2 = 3 2 + 2 cos ( 2 π ν o ξ ) + 1 2 cos ( 4 π ν o ξ ) .
| t o ( ξ , η ) | 2 = | exp [ j ϕ sin ( 2 π ν o ξ ) ] | 2 = 1 ,
| t o ( ξ , η ) | 2 = | exp [ j ( δ β + j ) η 2 sin ( 2 π ν o ξ ) ] | 2 = exp [ η sin ( 2 π ν o ξ ) ] .
V object = e η e η e η + e η = tanh η .

Metrics