OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 4 — Feb. 24, 2014
  • pp: 4316–4328

A phase demodulation method with high spatial resolution for two-dimensional single-shot X-ray Talbot interferometry

Kentaro Nagai, Genta Sato, Takashi Date, Soichiro Handa, Kimiaki Yamaguchi, Takeshi Kondoh, and Takashi Nakamura  »View Author Affiliations

Optics Express, Vol. 22, Issue 4, pp. 4316-4328 (2014)

View Full Text Article

Enhanced HTML    Acrobat PDF (1825 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A new phase demodulation approach is proposed that uses windowed Fourier transforms to achieve high spatial resolution in fringe pattern analysis with a high signal-to-noise ratio for single-shot X-ray grating-based interferometry. Conventionally, Fourier transforms have been used to demodulate single-fringe patterns, but this requires a fringe pattern with a long period to obtain an acceptable signal-to-noise ratio among the demodulated parameters. However, by controlling the signal-to-noise ratio, the spatial resolution of demodulated parameters is degraded below that obtained from the phase-stepping method, which requires several images to obtain these parameters. In this paper, we introduce the use of a windowed Fourier transform with a process for analyzing the objective spectrum in isolation from other spectra on the Fourier space to overcome the limitations of the Fourier transform method. It is proved that with suitable assumptions the objective spectrum is isolated theoretically, and the spatial resolution is improved by practically accepting the limitations from the assumptions. We demonstrate the validity of the proposed method by comparing the modulation transfer function of a synthetic phantom with the conventional FT method. The proposed method is also valid on practical data obtained by an experimental setup, by which it is demonstrated that a high spatial resolution with high signal-to-noise ratio can be achieved by our proposed method.

© 2014 Optical Society of America

OCIS Codes
(100.2650) Image processing : Fringe analysis
(100.5070) Image processing : Phase retrieval
(110.6760) Imaging systems : Talbot and self-imaging effects
(340.7450) X-ray optics : X-ray interferometry

ToC Category:
X-ray Optics

Original Manuscript: December 12, 2013
Revised Manuscript: January 17, 2014
Manuscript Accepted: January 17, 2014
Published: February 18, 2014

Virtual Issues
Vol. 9, Iss. 4 Virtual Journal for Biomedical Optics

Kentaro Nagai, Genta Sato, Takashi Date, Soichiro Handa, Kimiaki Yamaguchi, Takeshi Kondoh, and Takashi Nakamura, "A phase demodulation method with high spatial resolution for two-dimensional single-shot X-ray Talbot interferometry," Opt. Express 22, 4316-4328 (2014)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, A. W. Stevenson, “Phase-contrast imaging using polychromatic hard x-rays,” Nature 384, 335–338 (1996). [CrossRef]
  2. A. Momose, W. Yashiro, M. Moritake, Y. Takeda, K. Uesugi, A. Takeuchi, Y. Suzuki, M. Tanaka, T. Hattori, “Biomedical imaging by Talbot-type x-ray phase tomography,” Proc. SPIE 6318, 63180T (2006). [CrossRef]
  3. F. Pfeiffer, T. Weitkamp, O. Bunk, C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance x-ray sources,” Nat. Phys. 2, 258–261 (2006). [CrossRef]
  4. A. Olivo, R. Speller, “A coded-aperture technique allowing x-ray phase contrast imaging with conventional sources,” Appl. Phys. Lett. 91, 074106 (2007). [CrossRef]
  5. K. S. Morgan, D. M. Paganin, K. K. W. Siu, “Quantitative single-exposure x-ray phase contrast imaging using a single attenuation grid,” Opt. Express 19, 169–174 (2011). [CrossRef]
  6. A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, Y. Suzuki, “Demonstration of x-ray Talbot interferometry,” Jpn. J. Appl. Phys. 42, L866–L868 (2003). [CrossRef]
  7. T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13, 2912–2914 (2005). [CrossRef]
  8. C. Kottler, C. David, F. Pfeiffer, 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]
  9. I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, C. David, “Two-dimensional x-ray grating interferometer,” Phys. Rev. Lett. 105, 248102 (2010). [CrossRef]
  10. I. Zanette, C. David, S. Rutishauser, T. Weitkamp, “2D grating simulation for x-ray phase-contrast and dark-field imaging with a Talbot interferometer,” AIP Conf. Proc. 1221, 73–79 (2010). [CrossRef]
  11. H. Itoh, K. Nagai, G. Sato, K. Yamaguchi, T. Nakamura, T. Kondoh, C. Ouchi, T. Teshima, Y. Setomoto, T. Den, “Two-dimensional grating-based x-ray phase-contrast imaging using fourier transform phase retrieval,” Opt. Express 19, 3339–3346 (2011). [CrossRef] [PubMed]
  12. G. Sato, T. Kondoh, H. Itoh, S. Handa, K. Yamaguchi, T. Nakamura, K. Nagai, C. Ouchi, T. Teshima, Y. Setomoto, T. Den, “Two-dimensional gratings-based phase-contrast imaging using a conventional x-ray tube,” Opt. Lett. 36, 3551–3553 (2011). [CrossRef] [PubMed]
  13. G. Sato, H. Itoh, K. Nagai, T. Nakamura, K. Yamaguchi, T. Kondoh, S. Handa, C. Ouchi, T. Teshima, Y. Setomoto, “Single-shot x-ray phase-contrast imaging using two-dimensional gratings,” in AIP Conf. Proc.1466, 29–34 (2012). [CrossRef]
  14. M. Takeda, H. Ina, S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982). [CrossRef]
  15. K. Nagai, H. Itoh, G. Sato, T. Nakamura, K. Yamaguchi, T. Kondoh, S. Handa, T. Den, “New phase retrieval method for single-shot x-ray Talbot imaging using windowed Fourier transform,” Proc. SPIE 8127, 812706 (2011). [CrossRef]
  16. Q. Kemao, “Windowed Fourier transform for fringe pattern analysis,” Appl. Opt. 43, 2695–2702 (2004). [CrossRef] [PubMed]

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