Abstract

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

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  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]

2011

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]

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]

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]

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]

2010

I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, C. David, “Two-dimensional x-ray grating interferometer,” Phys. Rev. Lett. 105, 248102 (2010).
[CrossRef]

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]

2007

A. Olivo, R. Speller, “A coded-aperture technique allowing x-ray phase contrast imaging with conventional sources,” Appl. Phys. Lett. 91, 074106 (2007).
[CrossRef]

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]

2006

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]

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]

2005

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]

2004

2003

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]

1996

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]

1982

Bunk, O.

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]

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]

Cloetens, P.

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]

David, C.

I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, C. David, “Two-dimensional x-ray grating interferometer,” Phys. Rev. Lett. 105, 248102 (2010).
[CrossRef]

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]

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]

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]

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]

Den, T.

Diaz, A.

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]

Donath, T.

I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, C. David, “Two-dimensional x-ray grating interferometer,” Phys. Rev. Lett. 105, 248102 (2010).
[CrossRef]

Gao, D.

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]

Gureyev, T. E.

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]

Hamaishi, Y.

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]

Handa, S.

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]

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]

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]

Hattori, T.

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]

Ina, H.

Itoh, H.

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]

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]

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]

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]

Kawamoto, S.

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]

Kemao, Q.

Kobayashi, S.

Kondoh, T.

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]

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]

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]

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]

Kottler, C.

Koyama, I.

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]

Momose, A.

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]

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]

Morgan, K. S.

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]

Moritake, M.

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]

Nagai, K.

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]

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]

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]

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]

Nakamura, T.

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]

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]

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]

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]

Olivo, A.

A. Olivo, R. Speller, “A coded-aperture technique allowing x-ray phase contrast imaging with conventional sources,” Appl. Phys. Lett. 91, 074106 (2007).
[CrossRef]

Ouchi, C.

Paganin, D. M.

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]

Pfeiffer, F.

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]

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]

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]

Pogany, A.

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]

Rutishauser, S.

I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, C. David, “Two-dimensional x-ray grating interferometer,” Phys. Rev. Lett. 105, 248102 (2010).
[CrossRef]

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]

Sato, G.

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]

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]

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]

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]

Setomoto, Y.

Siu, K. K. W.

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]

Speller, R.

A. Olivo, R. Speller, “A coded-aperture technique allowing x-ray phase contrast imaging with conventional sources,” Appl. Phys. Lett. 91, 074106 (2007).
[CrossRef]

Stampanoni, M.

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]

Stevenson, A. W.

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]

Suzuki, Y.

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]

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]

Takai, K.

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]

Takeda, M.

Takeda, Y.

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]

Takeuchi, A.

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]

Tanaka, M.

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]

Teshima, T.

Uesugi, K.

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]

Weitkamp, T.

I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, C. David, “Two-dimensional x-ray grating interferometer,” Phys. Rev. Lett. 105, 248102 (2010).
[CrossRef]

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]

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]

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]

Wilkins, S. W.

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]

Yamaguchi, K.

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]

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]

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]

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]

Yashiro, W.

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]

Zanette, I.

I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, C. David, “Two-dimensional x-ray grating interferometer,” Phys. Rev. Lett. 105, 248102 (2010).
[CrossRef]

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]

Ziegler, E.

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]

AIP Conf. Proc.

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]

Appl. Opt.

Appl. Phys. Lett.

A. Olivo, R. Speller, “A coded-aperture technique allowing x-ray phase contrast imaging with conventional sources,” Appl. Phys. Lett. 91, 074106 (2007).
[CrossRef]

J. Opt. Soc. Am.

Jpn. J. Appl. Phys.

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]

Nat. Phys.

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]

Nature

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]

Opt. Express

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]

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]

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]

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]

Opt. Lett.

Phys. Rev. Lett.

I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, C. David, “Two-dimensional x-ray grating interferometer,” Phys. Rev. Lett. 105, 248102 (2010).
[CrossRef]

Proc. SPIE

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]

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]

Other

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]

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 (6)

Fig. 1
Fig. 1

(a) A sample synthetic fringe pattern. (b) Fourier spectrum intensity pattern.

Fig. 2
Fig. 2

Differential phase images demodulated along x direction with changing the filter radius. Demodulation results of the FT method are shown in the top and bottom row with filter radius (a) 3/π, (b) 3 2 / π, and (c) 6/π, respectively. (d)–(f) Each image shows the results of the CI-WFT method with a window radius equivalent to the filter radius of the image directly above it.

Fig. 3
Fig. 3

(a) A schematic diagram of MTF calculation. (b) MTF curves obtained by using the FT method, the simple-WFT method, and the CI-WFT method.

Fig. 4
Fig. 4

(a) Fringe pattern captured by our experimental setup. (b) Relation between visibility and the period of the fringe pattern.

Fig. 5
Fig. 5

Demodulation results obtained by the FT method. (a) Absorption image. Differential phase images along the (b) x and (c) y directions, and (d) integrated phase image. Modulation amplitude along the (e) x and (f) y directions.

Fig. 6
Fig. 6

Demodulation results obtained by the proposed CI-WFT method. (a) Absorption image. Differential phase images along the (b) x and (c) y directions, and (d) integrated phase image. Modulation amplitude along the (e) x and (f) y directions.

Equations (30)

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

I ( x , y ) = a ( x , y ) ( 1 + b x ( x , y ) cos ( P x ( x , y ) ω x x ) ) × ( 1 + b y ( x , y ) cos ( P y ( x , y ) ω y y ) ) ,
A ( x , y ) = 1 { I ˜ ( k x , k y ) G ( k x , k y ) } ,
P ( x , y ) = Arg ( 1 { I ˜ ( k x q x , k y q y ) G ( k x , k y ) } ) ,
S ( x , y ) = Abs ( 1 { I ˜ ( k x q x , k y q y ) G ( k x , k y ) } ) .
𝒮 f ( x , y , k x , k y ) = f ( x , y ) g ( x x , y y ) exp ( i ( k x x + k y y ) ) d x d y ,
A ( x , y ) = 𝒮 { I ( x , y ) } ( x , y , 0 , 0 ) ,
P ( x , y ) = Arg ( 𝒮 { I ( x , y ) } ( x , y , q x , q y ) ) ,
S ( x , y ) = Abs ( 𝒮 { I ( x , y ) } ( x , y , q x , q y ) ) .
a ( x , y ) ~ a ( x , y ) ,
b x ( x , y ) ~ b x ( x , y ) ,
b y ( x , y ) ~ b y ( x , y ) ,
P x ( x , y ) ~ P x ( x , y ) ,
P y ( x , y ) ~ P y ( x , y ) .
𝒮 I ( x , y , k x , k y ) = a ( x , y ) H ˜ ( x , y , k x , k y ) + 1 2 a ( x , y ) B x ( k x , k y ) H ˜ ( x , y , k x ω x , k y ) + 1 2 a ( x , y ) B x * ( k x , k y ) H ˜ ( x , y , k x + ω x , k y ) + 1 2 a ( x , y ) B y ( k x , k y ) H ˜ ( x , y , k x , k y ω y ) + 1 2 a ( x , y ) B y * ( k x , k y ) H ˜ ( x , y , k x , k y + ω y ) + 1 4 a ( x , y ) B x ( k x , k y ) B y ( k x , k y ) H ˜ ( x , y , k x ω x , k y ω y ) + 1 4 a ( x , y ) B x * ( k x , k y ) B y ( k x , k y ) H ˜ ( x , y , k x + ω x , k y ω y ) + 1 4 a ( x , y ) B x ( k x , k y ) B y * ( k x , k y ) H ˜ ( x , y , k x ω x , k y + ω y ) + 1 4 a ( x , y ) B x * ( k x , k y ) B y * ( k x , k y ) H ˜ ( x , y , k x + ω x , k y + ω y ) ,
B x ( x , y , k x , k y ) = b x ( x , y ) exp { i P x ( x , y ) }
B y ( x , y , k x , k y ) = b y ( x , y ) exp { i P y ( x , y ) } ,
H ˜ ( k x , k y ) = g ˜ ( k x , k y ) exp { i k x x i k y y } .
𝒮 I ( 0 , 0 ) = a ( H ˜ ( 0 , 0 ) + 1 2 ( B y H ˜ ( 0 , ω y ) + B y * H ˜ ( 0 , + ω y ) ) ) + a B x 2 ( H ˜ ( ω x , 0 ) + 1 2 ( B y H ˜ ( ω x , ω y ) + B y * H ˜ ( ω x , + ω y ) ) ) + a B x * 2 ( H ˜ ( + ω x , 0 ) + 1 2 ( B y H ˜ ( + ω x , ω y ) + B y * H ˜ ( + ω x , + ω y ) ) ) ,
𝒮 I ( ω x , 0 ) = a ( H ˜ ( ω x , 0 ) + 1 2 ( B y H ˜ ( ω x , ω y ) + B y * H ˜ ( ω x , + ω y ) ) ) + a B x 2 ( H ˜ ( 0 , 0 ) + 1 2 ( B y H ˜ ( 0 , ω y ) + B y * H ˜ ( 0 , + ω y ) ) ) + a B x * 2 ( H ˜ ( + 2 ω x , 0 ) + 1 2 ( B y H ˜ ( + 2 ω x , ω y ) + B y * H ˜ ( + 2 ω x , + ω y ) ) ) .
𝒮 I ( 0 , 0 ) = a ( H ˜ ( 0 ) + 1 2 ( B x H ˜ ( ω x ) + B x * H ˜ ( + ω x ) ) ) × ( H ˜ ( 0 ) + 1 2 ( B y H ˜ ( ω y ) + B y * H ˜ ( + ω y ) ) ) ,
𝒮 I ( ω x , 0 ) = a ( H ˜ ( + ω x ) + 1 2 ( B x H ˜ ( 0 ) + B x * H ˜ ( + 2 ω x ) ) ) × ( H ˜ ( 0 ) + 1 2 ( B y H ˜ ( ω y ) + B y * H ˜ ( + ω y ) ) ) .
𝒮 I ( 0 , 0 ) H ˜ ( 0 ) 𝒮 I ( ω x , 0 ) H ˜ ( + ω x ) = a T y 2 ( B x F x 1 ( ω x , 0 ) + B x * F x 2 ( ω x , 0 ) ) = a T y 2 ( F x 1 ( ω x , 0 ) + F x 2 ( ω x , 0 ) ) { B x } + i ( F x 1 ( ω x , 0 ) F x 2 ( ω x , 0 ) { B x } ) ) ,
F x 1 ( ω x , 0 ) H ˜ ( ω x ) H ˜ ( 0 ) H ˜ ( 0 ) H ˜ ( + ω x ) ,
F x 2 ( ω x , 0 ) H ˜ ( + ω x ) H ˜ ( 0 ) H ˜ ( + 2 ω x ) H ˜ ( + ω x ) .
R x a B x T y 2 = { 𝒮 I ( 0 , 0 ) / H ˜ ( 0 ) 𝒮 I ( ω x , 0 ) / H ˜ ( + ω x ) F x 1 ( ω x , 0 ) + F x 2 ( ω x , 0 ) } + { 𝒮 I ( 0 , 0 ) / H ˜ ( 0 ) 𝒮 I ( ω x , 0 ) / H ˜ ( + ω x ) F x 1 ( ω x , 0 ) F x 2 ( ω x , 0 ) } .
𝒮 I ( 0 , 0 ) R x H ˜ ( ω x ) R x * H ˜ ( ω x ) = a H ˜ ( 0 ) T y
R x H ˜ ( 0 ) 𝒮 I ( 0 , 0 ) R x H ˜ ( ω x ) R x * H ˜ ( ω x ) = B x = b x ( x , y ) exp { i P x ( x , y ) } .
g ( x , y ) = 1 2 π σ 2 exp { x 2 + y 2 2 σ 2 } ,
g ˜ ( k x , k y ) = exp { k x 2 + k y 2 2 σ 2 } .
H ˜ ( k x , k y ) = H ˜ ( k x ) H ˜ ( k y ) , H ˜ ( k ) = exp { σ 2 k 2 2 i k x } .

Metrics