OSA's Digital Library

Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editor: Gregory W. Faris
  • Vol. 3, Iss. 9 — Sep. 8, 2008

Efficiency of capturing a phase image using cone-beam x-ray Talbot interferometry

Wataru Yashiro, Yoshihiro Takeda, and Atsushi Momose  »View Author Affiliations


JOSA A, Vol. 25, Issue 8, pp. 2025-2039 (2008)
http://dx.doi.org/10.1364/JOSAA.25.002025


View Full Text Article

Enhanced HTML    Acrobat PDF (569 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We assesses the efficiency of x-ray Talbot interferometry (XTI), a technique based on the Talbot effect for measuring a wavefront gradient, in terms of how quickly it can capture a high-quality phase image with a large signal-to-noise ratio for a given incident photon number. Photon statistics cause errors in the phase of the moiré fringes and impose a detection limit on the wavefront gradient. The relation between the incident photon number and the detection limit is determined, and a figure of merit of XTI for a monochromatic cone beam is then defined. The dependence of the figure of merit on optical system parameters, such as grating pitch and position, is then discussed. The effects of varying the pattern height and linewidth of the second grating are shown for rectangular and trapezoidal teeth. Finally, we show how to design a practical cone-beam Talbot interferometer for certain boundary conditions.

© 2008 Optical Society of America

OCIS Codes
(110.6760) Imaging systems : Talbot and self-imaging effects
(170.0170) Medical optics and biotechnology : Medical optics and biotechnology
(340.7450) X-ray optics : X-ray interferometry

ToC Category:
Imaging Systems

History
Original Manuscript: January 24, 2008
Revised Manuscript: May 12, 2008
Manuscript Accepted: May 15, 2008
Published: July 14, 2008

Virtual Issues
Vol. 3, Iss. 9 Virtual Journal for Biomedical Optics

Citation
Wataru Yashiro, Yoshihiro Takeda, and Atsushi Momose, "Efficiency of capturing a phase image using cone-beam x-ray Talbot interferometry," J. Opt. Soc. Am. A 25, 2025-2039 (2008)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=josaa-25-8-2025


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. R. Fitzgerald, “Phase-sensitive x-ray imaging,” Phys. Today 53, 23-26 (2000). [CrossRef]
  2. A. Momose, “Recent advances in x-ray phase imaging,” Jpn. J. Appl. Phys., Part 1 44, 6355-6367 (2005). [CrossRef]
  3. A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of x-ray Talbot interferometry,” Jpn. J. Appl. Phys., Part 1 42, L866-L868 (2003). [CrossRef]
  4. T. Weitkamp, B. Nöhammer, A. Diaz, and C. David, “X-ray wavefront analysis and optics characterization with a grating interferometer,” Appl. Phys. Lett. 86, 54101-54103 (2005). [CrossRef]
  5. A. Momose and S. Kawamoto, “X-ray Talbot interferometry with capillary plates,” Jpn. J. Appl. Phys., Part 1 45, 314-316 (2006). [CrossRef]
  6. T. Weitkamp, A. Diaz, B. Nöhammer, F. Pfeiffer, T. Rohbeck, P. Cloetens, M. Stampanoni, and C. David, “Hard x-ray phase imaging and tomography with a grating interferometer,” Proc. SPIE 5535, 137-142 (2004). [CrossRef]
  7. A. Momose, S. Kawamoto, I. Koyama, and Y. Suzuki, “Phase tomography using an x-ray Talbot interferometer,” Proc. SPIE 5535, 352-360 (2004). [CrossRef]
  8. T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “Quantitative x-ray phase imaging with a grating interferometer,” Opt. Express 13, 6296-6304 (2005). [CrossRef] [PubMed]
  9. A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase tomography by x-ray Talbot interferometry for biological imaging,” Jpn. J. Appl. Phys., Part 1 45, 5254-5262 (2006). [CrossRef]
  10. A. Momose, W. Yashiro, M. Moritake, Y. Takeda, K. Uesugi, A. Takeuchi, Y. Suzuki, M. Tanaka, and T. Hattori, “Biomedical imaging by Talbot-type x-ray phase tomography,” Proc. SPIE 6318, 63180T (2006). [CrossRef]
  11. M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk, and C. David, “High-resolution differential phase contrast imaging using a magnifying projection geometry with a microfocus x-ray source,” Appl. Phys. Lett. 90, 224101 (2007). [CrossRef]
  12. C. Kottler, C. David, F. Pfeiffer, and O. Bunk, “'A two-directional approach for grating based differential phase contrast imaging using hard x-rays,” Opt. Express 15, 1175-1181 (2007). [CrossRef] [PubMed]
  13. H. F. Talbot, “Facts relating to optical science,” Philos. Mag. 9, 401-407 (1836). [CrossRef]
  14. K. Patorski, “The self-imaging phenomenon and its applications,” in Progress in Optics XXVII (Elsevier, 1989). [CrossRef]
  15. P. Cloetens, J. P. Guigay, C. De Martino, and J. Baruchel, “Fractional Talbot imaging of phase gratings with hard X rays,” Opt. Lett. 22, 1059-1061 (1997). [CrossRef] [PubMed]
  16. E. W. Becker, W. Ehrfeld, P. Hagmann, A. Maner, and D. Münchmeyer, “Fabrication of microstructures with high aspect ratios and great structural heights by synchrotron radiation lithography, galvanoforming, and plasticmoulding (LIGA process),” Microelectronics 4, 35-56 (1986). [CrossRef]
  17. Y. Utsumi, T. Kishimoto, T. Hattori, and H. Hara, “Large-area x-ray lithography system for LIGA process operating in wide energy range of synchrotron radiation,” Jpn. J. Appl. Phys., Part 1 44, 5500-5504 (2005). [CrossRef]
  18. M. Matsumoto, K. Takiguchi, M. Tanaka, Y. Hunabiki, H. Takeda, A. Momose, Y. Utsumi, and T. Hattori, “Fabrication of diffraction grating for x-ray Talbot interferometer,” in High Aspect Ratio Micro Structure Technology Workshop 2005 (Harmst, 2005), p. 22.
  19. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).
  20. 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]
  21. T. Weitkamp, C. David, C. Kottler, O. Bunk, and F. Pfeiffer, “Tomography with grating interferometers at low-brilliance sources,” Proc. SPIE 6318, 63180S (2006). [CrossRef]
  22. F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett. 98, 108105 (2007). [CrossRef] [PubMed]
  23. J. T. Winthrop and C. R. Worthington, “Theory of Fresnel images. I. Plane periodic objects in monochromatic light,” J. Opt. Soc. Am. 55, 373-381 (1965). [CrossRef]
  24. J. P. Guigay, “On Fresnel diffraction by one-dimensional periodic object, with application to structure determination of phase object,” Opt. Acta 18, 677-682 (1971). [CrossRef]
  25. J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt. 13, 2693-2703 (1974). [CrossRef] [PubMed]
  26. O. Kafri and I. Glatt, The Physics of Moiré Metrology (Wiley-Interscience, 1990).
  27. J. H. Bruning, Optical Shop Testing, D.Malacara, ed. (Wiley-Interscience, 1978).
  28. M. Takeda, “Spatial-carrier fringe-pattern analysis and its applications to precision interferometry and profilometry: An overview,” Ind. Metrology 1, 79-99 (1990). [CrossRef]
  29. The condition M⩾3 is required for Eq. and the condition M⩾4 is required for Eq. . For this reason the result Eq. is correct for M⩾4. If M=3, ΔΨ depends on φxs because the term of q−1 is not negligible in Eq. .
  30. We assumed that the distribution of intensity from each groove is roughly represented as a Gaussian function of a standard deviation of σs. Then the full width at half-maximum (FWHM) of it is approximately given by 2.35σs.
  31. V. Arrizón and E. López-Olazagasti, “Binary phase grating for array generation at 1/16 of Talbot length,” J. Opt. Soc. Am. A 12, 801-804 (1995). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited