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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics


  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 6, Iss. 9 — Oct. 3, 2011

Quantitative characterization of x-ray differential interference contrast microscopy using modulation transfer function

Takashi Nakamura and Chang Chang  »View Author Affiliations

Optics Express, Vol. 19, Issue 16, pp. 15304-15321 (2011)

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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

OCIS Codes
(030.6600) Coherence and statistical optics : Statistical optics
(110.4100) Imaging systems : Modulation transfer function
(110.4980) Imaging systems : Partial coherence in imaging
(180.3170) Microscopy : Interference microscopy
(340.7460) X-ray optics : X-ray microscopy

ToC Category:

Original Manuscript: April 26, 2011
Revised Manuscript: June 28, 2011
Manuscript Accepted: July 11, 2011
Published: July 26, 2011

Virtual Issues
Vol. 6, Iss. 9 Virtual Journal for Biomedical Optics

Takashi Nakamura and Chang Chang, "Quantitative characterization of x-ray differential interference contrast microscopy using modulation transfer function," Opt. Express 19, 15304-15321 (2011)

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  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).

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