Abstract

we demonstrate a non-absorption grating approach for X-ray phase contrast imaging based-on grating interferometry. This technique overcomes the limitations imposed by absorption gratings, provides another choice for X-ray phase contrast imaging and potentially improves the image quality for higher X-ray photon energies. We constructed the key devices, established the system and obtained phase contrast images with a field of view larger than 5 centimeters, which is the limitation imposed by the size of our current CCD detector. This method has no need for absorption gratings, which represents a significant development for future promising applications in medicine and industry.

© 2011 OSA

1. Introduction

Conventional hard X-ray imaging is based on attenuation as contrast mechanism and has been widely applied in medical diagnostics and non-destructive inspections. For soft tissues and other materials made of low-Z elements (such as H and C), however, it is impossible to obtain high-contrast absorption images. The phase factors for these materials are usually three orders of magnitude larger than their absorption factors [1]. Therefore, phase contrast imaging significantly improves the image contrast of these types of objects.

Several types of X-ray phase contrast imaging have been developed recently. They can be categorized into interferometric methods [2,3], free-space propagation techniques [47], diffraction enhanced imaging [810] and grating interferometry [1118]. The method using a grating interferometer has many advantages over the others and was first used in applications with synchrotron radiation sources [1115]. Introducing an absorption grating near the conventional low-brilliance X-ray tube [1618] enables the grating-based differential phase contrast imaging method, which has potential applications in ordinary laboratories.

The aforementioned grating-based methods use absorption gratings as key optical elements. However, higher X-ray photon energies are required for most clinical and industrial applications, thus, it is essential to manufacture large-area absorption gratings with higher aspect ratios to provide sufficient image contrast for this energy range. The fabricating process for this kind of absorption grating is currently a great challenge, and even state-of-the-art absorption materials used for absorption gratings rely on Au [19,20]. In addition, the transmission properties of absorption gratings lead to deterioration in the image quality. To address these issues, we have proposed a non-absorption grating approach for X-ray phase contrast imaging [21]. To this end, A laboratory-based multi-line X-ray source has been developed to replace the source grating [2224], which essentially overcomes the limitation of un-ideal transmission from the source grating especially for the case using higher X-ray photon energies (Au can’t absorb X-rays completely), and a structured scintillator has been proposed and developed to replace the combination of absorption analyzer grating and X-ray scintillator and overcome its main drawback: the reduction of the fringe visibility for higher X-ray photon energies [25,26]. In this letter, we give the details of our non-absorption grating approach and demonstrate its primary results for X-ray phase contrast imaging.

2. Experimental setup

The arrangement is shown in Fig. 1 . It consists of a multi-line X-ray source with a spatial period of p0, a phase grating G1 of period p1 with π phase shift and an analyzer structured scintillator G2 of period p2. A ladder-shaped structure is fabricated on a tungsten fixed anode by Micro-fabrication techniques. The oil cooling method is used to solve the heat problem. Each step’s length at axial direction is 100μm, and the altitude difference between the adjacent two steps is 31.5μm. The angle between the optical axis and each step’s top surface of the ladder-shaped anode is 6, thus the apparent pitch of the multi-line source is 42μm, and each apparent X-ray emission line width is 10.5μm. Our ladder-shaped structure can reduce the length of multi-line source along the optical axis, which has a maximized emission area and minimal axial length. Corresponding to the functions of both the conventional X-ray source and source grating, the ladder-shaped multi-line X-ray source generates individually spatial coherent but mutually incoherent line source. Its advantages are obvious: it integrates the source grating into the conventional X-ray tube, improves the mechanical stabilization, increases the fringe contrast especially for higher X-ray photon energies, and provides a cheap and commercially available source with uniform radiation for the entire field of view. For the phase contrast image formation process, the spatial coherence length lc should satisfy the condition [16]

lc=z0λγ0p0p1,
where z0 is the distance between the source and the phase grating, γ0 is the duty cycle and λ is the central wavelength of the multi-line X-ray source. According to the Talbot-Lau theory, the first fractional Talbot distance under a spherical wave illumination [27] can be expressed by
z1=Mp128λ,
and
M=(z0+z1)z0,
where M is the geometric magnification projected from the source. To ensure that the fringes of self-image produced by the every line of multi-line source are well overlapped in the detector plane, the geometry of the setup must satisfy the condition

 

Fig. 1 (Color online) The principles of the non-absorption grating X-ray phase-contrast imaging. The system consists of a ladder-shaped multi-line X-ray source, a phase grating and a structured scintillator.

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p2=p0z1z0,

The phase grating has a phase shift of π. It acts as a beam splitter, diffracts the incoming X-rays into the ± 1st orders and attenuates the zero and higher order components. Over 80% of the X-ray energy is carried by the ± 1st order [11]. A linear phase diffraction grating with a high aspect ratio was successfully produced on a 5 inch n-type 100 silicon wafer by the photo-assisted electrochemical etching technique [28]. Because of the Talbot effect, the fringes of self-image of the phase grating can be generated at the detector plane.

Unfortunately, the period of the fringes is too small to be resolved by a CCD detector directly. Accordingly, in the general setup, an absorption grating corresponding to the periodicity and orientation of the fringe pattern of the phase grating is placed immediately in front of the scintillator as an analyzer device to form a detectable Moiré pattern. In the absorption analyzer grating setup, when using the higher X-ray photon energies, the depth of absorption grating should be increased. The high-Z materials such as Au is used to absorb the X-rays, but it cannot absorb the X-ray passing it completely especially for higher X-ray photon energy, which reduces the fringe visibility and therefore deteriorates the image quality. The structured scintillator, which integrates the analyzer grating into the scintillator, functions as both the common scintillator and the analyzer grating. It is fabricated by filling silicon pore arrays with X-ray sensitive materials such as Tl-doped cesium iodide(CsI:Tl). To allow it to function as an analyzer grating, a half period of the structured scintillator is filled with CsI:Tl, which converts X-rays into visible light. Another half period of the structured scintillator is completely made of silicon. To enable total light reflection at the silicon pore inner wall of the structured scintillator, enhancing its conversion efficiency from X-ray to visible light, silicon oxide is formed on the inner wall surface [25,29]. When X-rays penetrate through a structured scintillator, only the half pitch of filling with X-ray sensitive materials converts X-rays into the visible light that can be directly detected by a visible light CCD detector. Therefore the contrast between two half pitches in one spatial period of the structured scintillator is nearly 100% for the visible light CCD detector. Compared with an absorption grating made from Au, the structured scintillator is more suitable for broadband X-rays, especially for higher photon energy X-ray phase contrast imaging. Therefore, it can potentially provide high image quality for harder X-ray with large fields of view.

The phase stepping technique is used to retrieve the phase information [13,16]. For theπshift of the phase grating, the oscillation intensity of the specimen for each detector pixel(m,n)can be expressed as the Fourier series [30]

I(m,n,yg)=iai(m,n)cos(i2πp2yg+φi(m,n)),
where ai is the amplitude coefficients, yg is the normalized phase stepping position and φi is the phase coefficients. By scanning the phase grating along the longitudinal direction yg with five steps in one period [23], the differential phase contrast images can be extracted from the shift of the intensity modulation.

3. Experimental results

The experiment was performed using the ladder-shaped structured multi-line X-ray source and the structured scintillator. It was operated at 60 KV and a 2 mA tube current. Because of the inclination of the target, the axial length of anode was 2 mm and the total effective X-ray source size was 0.6×0.9mm2. It had an equivalent period of p0=42μm and a line width of w0=10.5μm. The phase grating had a period of 5.6μm, a duty ratio of 0.5 and a depth of 40μm, which corresponded to a π phase shift for 31 keV, the most probable photon energy generated by the multi-line X-ray source. The thickness of the structured scintillator was up to 150μm, and its period was 3μm with a duty ratio of 0.5 (equal to the pitch of the phase grating's self-image at the first fractional Talbot distance). The distance between the multi-line X-ray source and the phase grating was z0=1.47m, and the distance between the phase grating and the structured scintillator was z1=105mm. The scintillator was directly coupled with an ANDOR 2048×2048 pixels (13.5μm/pixel) CCD camera through a fiber optical tape with a demagnification of 2. Thus, the effective scintillator pixel size is 27μm, and the field of view is about 55×55mm2.

Figure 2 shows the experimental results of a weakly absorbing specimen, a piece of a violet leaf. The exposure time is 10 s for each original image, and the field of view is 55×45mm2. Figure 2(a) shows the chromo-photograph of the specimen, where a part of the footstalk and leaf apex is dried. The X-ray transmission image and the differential phase contrast image, which clearly show the contour of the leaf, are shown in Fig. 2(b) and Fig. 2(c), respectively. In the section of the dried leaves shown in Fig. 2(d) and Fig. 2(g), the small difference in the intensity of the tissues is barely discernible in the absorption images in Fig. 2(e) and Fig. 2(h), while the differential phase contrast images shown in Fig. 2(f) and Fig. 2(i) show them clearly.

 

Fig. 2 (Color online) The image of a piece of a violet leaf. (a) is the conventional digital chromo-photograph. (b) is the X-ray transmission image. (c) is the differential phase contrast image. (d), (e) and (f) are magnified sections of the chromatic, transmission and differential phase contrast images, respectively, of the dried footstalk. (g), (h) and (i) are the magnified sections of the chromatic, transmission and differential phase contrast images, respectively, of the dried leaf apex. (j) and (k) are the profile values of the transmission and differential phase contrast images, respectively, of the dried footstalk.

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Figure 3 shows the results obtained by our method with a biological sample containing soft and hard tissues (a chicken claw). The exposure time is 10 s for each original image, and the field of view is 55×55mm2. The absorption and differential phase contrast images are shown in Fig. 3(a) and Fig. 3(b), respectively. As expected, the differential phase contrast image reveals much more detail of the sample, especially for the soft tissues and cartilages, while only some highly absorbing tissues are clearly visible in transmission image. Smaller structures with higher spatial frequencies (the structures of imbricate skins, for example) are also better visualized in the phase contrast images. Finally, in the magnified images corresponding to the rectangular area shown in Fig. 3(c) and Fig. 3(d), we can also see that the phase contrast image provides more information about the nail.

 

Fig. 3 The chicken claw image. (a) is the X-ray transmission image. (b) is the differential phase contrast image. (c) and (d) are magnified sections of the transmission and differential phase contrast images, respectively, of the chicken toes.

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4. Conclusion

On the basis of the key improvements described here, the non-absorption grating X-ray phase contrast imaging technique presented in this work represents an important progress towards applying X-ray phase contrast imaging. As a powerful inspection tool for materials composed of low-Z elements, this technique may play important roles in soft tissue pathologies, biology, paleontology and materials science. Due to the characteristics of the ladder-shaped multi-line X-ray source and the structured scintillator, the approach creates a great number of preponderant applications for higher X-ray photon energies. We believe that our method significantly advances this technique toward future practical applications.

Grating-based X-ray phase contrast imaging has long been restricted by the use of absorption gratings. Unlike absorption gratings, the ladder-shaped multi-line X-ray source and large-area structured scintillator are inexpensively fabricated in ordinary laboratory, which provides another choice for X-ray phase contrast imaging and potentially promote the use of this technique for higher X-ray photon energies. Furthermore, like other techniques, implementing X-ray dark field imaging [30] and X-ray phase contrast tomography [18], is also possible by this approach.

5. Acknowledgments

This work was supported by the Major Program of the National Natural Science Foundation of China (Grant No. 60532090).

References and links

1. A. Momose and J. Fukuda, “Phase-contrast radiographs of nonstained rat cerebellar specimen,” Med. Phys. 22(4), 375–379 (1995). [CrossRef]   [PubMed]  

2. U. Bonse and M. Hart, “An x-ray interferometer with long separated interfering beam paths,” Appl. Phys. Lett. 6(8), 155 (1965). [CrossRef]  

3. A. Momose, T. Takeda, Y. Itai, and K. Hirano, “Phase-contrast X-ray computed tomography for observing biological soft tissues,” Nat. Med. 2(4), 473–475 (1996). [CrossRef]   [PubMed]  

4. A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486 (1995). [CrossRef]  

5. S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature 384(6607), 335–338 (1996). [CrossRef]  

6. K. A. Nugent, T. E. Gureyev, D. J. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard X-rays,” Phys. Rev. Lett. 77(14), 2961–2964 (1996). [CrossRef]   [PubMed]  

7. Y. Hwu, W. Tsai, A. Groso, G. Margaritondo, and J. H. Je, “Coherence-enhanced synchrotron radiology: Simple theory and practical applications,” J. Phys. D Appl. Phys. 35(13), R105 (2002). [CrossRef]  

8. V. N. Ingal and E. A. Beliaevskaya, “X-ray plane-wave topography observation of the phase contrast from a non-crystalline object,” J. Phys. D Appl. Phys. 28(11), 2314–2317 (1995). [CrossRef]  

9. T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373(6515), 595–598 (1995). [CrossRef]  

10. D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997). [CrossRef]   [PubMed]  

11. C. David, B. Nöhammer, H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81(17), 3287 (2002). [CrossRef]  

12. A. Momose, “Phase-sensitive imaging and phase tomography using X-ray interferometers,” Opt. Express 11(19), 2303–2314 (2003). [CrossRef]   [PubMed]  

13. T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13(16), 6296–6304 (2005). [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(31), 13576–13581 (2010). [CrossRef]   [PubMed]  

15. I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, “Two-dimensional x-ray grating interferometer,” Phys. Rev. Lett. 105(24), 248102 (2010). [CrossRef]   [PubMed]  

16. F. Pfeiffer, T. Weikamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys. 2(4), 258–261 (2006). [CrossRef]  

17. C. Kottler, F. Pfeiffer, O. Bunk, C. Grünzweig, J. Bruder, and R. Kaufmann, “Phase contrast X-ray imaging of large samples using an incoherent laboratory source,” Phys. Status Solidi 204(8), 2728–2733 (2007) (a).

18. F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett. 98(10), 108105 (2007). [CrossRef]   [PubMed]  

19. C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard X-ray phase contrast imaging,” Microelectron. Eng. 84(5-8), 1172–1177 (2007). [CrossRef]  

20. D. Noda, H. Tsujii, N. Takahashi, and T. Hattori, “Fabrication of high precision X-ray mask for X-ray grating of X-ray Talbot interferometer,” Microsyst. Technol. 16(8-9), 1309–1313 (2010). [CrossRef]  

21. H. Niu, J. Guo, and X. Liu, C.N. Patent No. 200810216469.3 (2008).

22. H. Niu, J. Guo, K. Wang, and Q. Yang, C.N. Patent No. 200610062487.1 (2006).

23. A. Momose, W. Yashiro, H. Huwahara, and K. Kawabata, “Grating-Based X-ray Phase Imaging Using Multiline X-ray Source,” Jpn. J. Appl. Phys. 48(7), 076512 (2009). [CrossRef]  

24. Y. Lei, X. Liu, J. Guo, Z. Zhao, and H. Niu, “Development of x-ray scintillator functioning also as an analyzer grating used in grating-based x-ray differential phase contrast imaging,” Chin. Phys. B 20(4), 042901 (2011). [CrossRef]  

25. S. Rutishauser, I. Zanette, T. Donath, A. Sahlholm, J. Linnros, and C. David, “Structured scintillator for hard x-ray grating interferometry,” Appl. Phys. Lett. 98(17), 171107 (2011). [CrossRef]  

26. T. Weitkamp, C. David, C. Kottler, O. Bunk, and F. Pfeiffer, “Tomography with grating interferometers at low-brilliance sources,” Proc. SPIE 6318, 63180S, 63180S-10 (2006). [CrossRef]  

27. X. Liu, Y. Lei, Z. Zhao, J. Guo, and H. Niu, “Design and fabrication of hard x-ray phase grating,” Acta. Phys. Sin. 59, 6927 (2010).

28. M. Simon, K. J. Engel, B. Menser, X. Badel, and J. Linnros, “X-ray imaging performance of scintillator-filled silicon pore arrays,” Med. Phys. 35(3), 968–981 (2008). [CrossRef]   [PubMed]  

29. X. Liu, J. Guo, and H. Niu, “A new method of detecting interferogram in differential phase-contrast imaging system based on special structured x-ray scintillator screen,” Chin. Phys. B 19(7), 070701 (2010). [CrossRef]  

30. F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008). [CrossRef]   [PubMed]  

References

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  1. A. Momose and J. Fukuda, “Phase-contrast radiographs of nonstained rat cerebellar specimen,” Med. Phys. 22(4), 375–379 (1995).
    [CrossRef] [PubMed]
  2. U. Bonse and M. Hart, “An x-ray interferometer with long separated interfering beam paths,” Appl. Phys. Lett. 6(8), 155 (1965).
    [CrossRef]
  3. A. Momose, T. Takeda, Y. Itai, and K. Hirano, “Phase-contrast X-ray computed tomography for observing biological soft tissues,” Nat. Med. 2(4), 473–475 (1996).
    [CrossRef] [PubMed]
  4. A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486 (1995).
    [CrossRef]
  5. S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature 384(6607), 335–338 (1996).
    [CrossRef]
  6. K. A. Nugent, T. E. Gureyev, D. J. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard X-rays,” Phys. Rev. Lett. 77(14), 2961–2964 (1996).
    [CrossRef] [PubMed]
  7. Y. Hwu, W. Tsai, A. Groso, G. Margaritondo, and J. H. Je, “Coherence-enhanced synchrotron radiology: Simple theory and practical applications,” J. Phys. D Appl. Phys. 35(13), R105 (2002).
    [CrossRef]
  8. V. N. Ingal and E. A. Beliaevskaya, “X-ray plane-wave topography observation of the phase contrast from a non-crystalline object,” J. Phys. D Appl. Phys. 28(11), 2314–2317 (1995).
    [CrossRef]
  9. T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373(6515), 595–598 (1995).
    [CrossRef]
  10. D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
    [CrossRef] [PubMed]
  11. C. David, B. Nöhammer, H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81(17), 3287 (2002).
    [CrossRef]
  12. A. Momose, “Phase-sensitive imaging and phase tomography using X-ray interferometers,” Opt. Express 11(19), 2303–2314 (2003).
    [CrossRef] [PubMed]
  13. T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13(16), 6296–6304 (2005).
    [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(31), 13576–13581 (2010).
    [CrossRef] [PubMed]
  15. I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, “Two-dimensional x-ray grating interferometer,” Phys. Rev. Lett. 105(24), 248102 (2010).
    [CrossRef] [PubMed]
  16. F. Pfeiffer, T. Weikamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys. 2(4), 258–261 (2006).
    [CrossRef]
  17. C. Kottler, F. Pfeiffer, O. Bunk, C. Grünzweig, J. Bruder, and R. Kaufmann, “Phase contrast X-ray imaging of large samples using an incoherent laboratory source,” Phys. Status Solidi 204(8), 2728–2733 (2007) (a).
  18. F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett. 98(10), 108105 (2007).
    [CrossRef] [PubMed]
  19. C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard X-ray phase contrast imaging,” Microelectron. Eng. 84(5-8), 1172–1177 (2007).
    [CrossRef]
  20. D. Noda, H. Tsujii, N. Takahashi, and T. Hattori, “Fabrication of high precision X-ray mask for X-ray grating of X-ray Talbot interferometer,” Microsyst. Technol. 16(8-9), 1309–1313 (2010).
    [CrossRef]
  21. H. Niu, J. Guo, and X. Liu, C.N. Patent No. 200810216469.3 (2008).
  22. H. Niu, J. Guo, K. Wang, and Q. Yang, C.N. Patent No. 200610062487.1 (2006).
  23. A. Momose, W. Yashiro, H. Huwahara, and K. Kawabata, “Grating-Based X-ray Phase Imaging Using Multiline X-ray Source,” Jpn. J. Appl. Phys. 48(7), 076512 (2009).
    [CrossRef]
  24. Y. Lei, X. Liu, J. Guo, Z. Zhao, and H. Niu, “Development of x-ray scintillator functioning also as an analyzer grating used in grating-based x-ray differential phase contrast imaging,” Chin. Phys. B 20(4), 042901 (2011).
    [CrossRef]
  25. S. Rutishauser, I. Zanette, T. Donath, A. Sahlholm, J. Linnros, and C. David, “Structured scintillator for hard x-ray grating interferometry,” Appl. Phys. Lett. 98(17), 171107 (2011).
    [CrossRef]
  26. T. Weitkamp, C. David, C. Kottler, O. Bunk, and F. Pfeiffer, “Tomography with grating interferometers at low-brilliance sources,” Proc. SPIE 6318, 63180S, 63180S-10 (2006).
    [CrossRef]
  27. X. Liu, Y. Lei, Z. Zhao, J. Guo, and H. Niu, “Design and fabrication of hard x-ray phase grating,” Acta. Phys. Sin. 59, 6927 (2010).
  28. M. Simon, K. J. Engel, B. Menser, X. Badel, and J. Linnros, “X-ray imaging performance of scintillator-filled silicon pore arrays,” Med. Phys. 35(3), 968–981 (2008).
    [CrossRef] [PubMed]
  29. X. Liu, J. Guo, and H. Niu, “A new method of detecting interferogram in differential phase-contrast imaging system based on special structured x-ray scintillator screen,” Chin. Phys. B 19(7), 070701 (2010).
    [CrossRef]
  30. F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
    [CrossRef] [PubMed]

2011 (2)

Y. Lei, X. Liu, J. Guo, Z. Zhao, and H. Niu, “Development of x-ray scintillator functioning also as an analyzer grating used in grating-based x-ray differential phase contrast imaging,” Chin. Phys. B 20(4), 042901 (2011).
[CrossRef]

S. Rutishauser, I. Zanette, T. Donath, A. Sahlholm, J. Linnros, and C. David, “Structured scintillator for hard x-ray grating interferometry,” Appl. Phys. Lett. 98(17), 171107 (2011).
[CrossRef]

2010 (5)

X. Liu, Y. Lei, Z. Zhao, J. Guo, and H. Niu, “Design and fabrication of hard x-ray phase grating,” Acta. Phys. Sin. 59, 6927 (2010).

X. Liu, J. Guo, and H. Niu, “A new method of detecting interferogram in differential phase-contrast imaging system based on special structured x-ray scintillator screen,” Chin. Phys. B 19(7), 070701 (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(31), 13576–13581 (2010).
[CrossRef] [PubMed]

I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, “Two-dimensional x-ray grating interferometer,” Phys. Rev. Lett. 105(24), 248102 (2010).
[CrossRef] [PubMed]

D. Noda, H. Tsujii, N. Takahashi, and T. Hattori, “Fabrication of high precision X-ray mask for X-ray grating of X-ray Talbot interferometer,” Microsyst. Technol. 16(8-9), 1309–1313 (2010).
[CrossRef]

2009 (1)

A. Momose, W. Yashiro, H. Huwahara, and K. Kawabata, “Grating-Based X-ray Phase Imaging Using Multiline X-ray Source,” Jpn. J. Appl. Phys. 48(7), 076512 (2009).
[CrossRef]

2008 (2)

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[CrossRef] [PubMed]

M. Simon, K. J. Engel, B. Menser, X. Badel, and J. Linnros, “X-ray imaging performance of scintillator-filled silicon pore arrays,” Med. Phys. 35(3), 968–981 (2008).
[CrossRef] [PubMed]

2007 (3)

C. Kottler, F. Pfeiffer, O. Bunk, C. Grünzweig, J. Bruder, and R. Kaufmann, “Phase contrast X-ray imaging of large samples using an incoherent laboratory source,” Phys. Status Solidi 204(8), 2728–2733 (2007) (a).

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett. 98(10), 108105 (2007).
[CrossRef] [PubMed]

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard X-ray phase contrast imaging,” Microelectron. Eng. 84(5-8), 1172–1177 (2007).
[CrossRef]

2006 (2)

F. Pfeiffer, T. Weikamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys. 2(4), 258–261 (2006).
[CrossRef]

T. Weitkamp, C. David, C. Kottler, O. Bunk, and F. Pfeiffer, “Tomography with grating interferometers at low-brilliance sources,” Proc. SPIE 6318, 63180S, 63180S-10 (2006).
[CrossRef]

2005 (1)

2003 (1)

2002 (2)

C. David, B. Nöhammer, H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81(17), 3287 (2002).
[CrossRef]

Y. Hwu, W. Tsai, A. Groso, G. Margaritondo, and J. H. Je, “Coherence-enhanced synchrotron radiology: Simple theory and practical applications,” J. Phys. D Appl. Phys. 35(13), R105 (2002).
[CrossRef]

1997 (1)

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

1996 (3)

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature 384(6607), 335–338 (1996).
[CrossRef]

K. A. Nugent, T. E. Gureyev, D. J. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard X-rays,” Phys. Rev. Lett. 77(14), 2961–2964 (1996).
[CrossRef] [PubMed]

A. Momose, T. Takeda, Y. Itai, and K. Hirano, “Phase-contrast X-ray computed tomography for observing biological soft tissues,” Nat. Med. 2(4), 473–475 (1996).
[CrossRef] [PubMed]

1995 (4)

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486 (1995).
[CrossRef]

A. Momose and J. Fukuda, “Phase-contrast radiographs of nonstained rat cerebellar specimen,” Med. Phys. 22(4), 375–379 (1995).
[CrossRef] [PubMed]

V. N. Ingal and E. A. Beliaevskaya, “X-ray plane-wave topography observation of the phase contrast from a non-crystalline object,” J. Phys. D Appl. Phys. 28(11), 2314–2317 (1995).
[CrossRef]

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373(6515), 595–598 (1995).
[CrossRef]

1965 (1)

U. Bonse and M. Hart, “An x-ray interferometer with long separated interfering beam paths,” Appl. Phys. Lett. 6(8), 155 (1965).
[CrossRef]

Arfelli, F.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

Badel, X.

M. Simon, K. J. Engel, B. Menser, X. Badel, and J. Linnros, “X-ray imaging performance of scintillator-filled silicon pore arrays,” Med. Phys. 35(3), 968–981 (2008).
[CrossRef] [PubMed]

Barnea, Z.

K. A. Nugent, T. E. Gureyev, D. J. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard X-rays,” Phys. Rev. Lett. 77(14), 2961–2964 (1996).
[CrossRef] [PubMed]

Bech, M.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[CrossRef] [PubMed]

Beliaevskaya, E. A.

V. N. Ingal and E. A. Beliaevskaya, “X-ray plane-wave topography observation of the phase contrast from a non-crystalline object,” J. Phys. D Appl. Phys. 28(11), 2314–2317 (1995).
[CrossRef]

Bonse, U.

U. Bonse and M. Hart, “An x-ray interferometer with long separated interfering beam paths,” Appl. Phys. Lett. 6(8), 155 (1965).
[CrossRef]

Brönnimann, Ch.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[CrossRef] [PubMed]

Bruder, J.

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard X-ray phase contrast imaging,” Microelectron. Eng. 84(5-8), 1172–1177 (2007).
[CrossRef]

C. Kottler, F. Pfeiffer, O. Bunk, C. Grünzweig, J. Bruder, and R. Kaufmann, “Phase contrast X-ray imaging of large samples using an incoherent laboratory source,” Phys. Status Solidi 204(8), 2728–2733 (2007) (a).

Bunk, O.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[CrossRef] [PubMed]

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard X-ray phase contrast imaging,” Microelectron. Eng. 84(5-8), 1172–1177 (2007).
[CrossRef]

C. Kottler, F. Pfeiffer, O. Bunk, C. Grünzweig, J. Bruder, and R. Kaufmann, “Phase contrast X-ray imaging of large samples using an incoherent laboratory source,” Phys. Status Solidi 204(8), 2728–2733 (2007) (a).

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett. 98(10), 108105 (2007).
[CrossRef] [PubMed]

T. Weitkamp, C. David, C. Kottler, O. Bunk, and F. Pfeiffer, “Tomography with grating interferometers at low-brilliance sources,” Proc. SPIE 6318, 63180S, 63180S-10 (2006).
[CrossRef]

F. Pfeiffer, T. Weikamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys. 2(4), 258–261 (2006).
[CrossRef]

Chapman, D.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

Cloetens, P.

Cookson, D. J.

K. A. Nugent, T. E. Gureyev, D. J. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard X-rays,” Phys. Rev. Lett. 77(14), 2961–2964 (1996).
[CrossRef] [PubMed]

David, C.

S. Rutishauser, I. Zanette, T. Donath, A. Sahlholm, J. Linnros, and C. David, “Structured scintillator for hard x-ray grating interferometry,” Appl. Phys. Lett. 98(17), 171107 (2011).
[CrossRef]

I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, “Two-dimensional x-ray grating interferometer,” Phys. Rev. Lett. 105(24), 248102 (2010).
[CrossRef] [PubMed]

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[CrossRef] [PubMed]

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard X-ray phase contrast imaging,” Microelectron. Eng. 84(5-8), 1172–1177 (2007).
[CrossRef]

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett. 98(10), 108105 (2007).
[CrossRef] [PubMed]

T. Weitkamp, C. David, C. Kottler, O. Bunk, and F. Pfeiffer, “Tomography with grating interferometers at low-brilliance sources,” Proc. SPIE 6318, 63180S, 63180S-10 (2006).
[CrossRef]

F. Pfeiffer, T. Weikamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys. 2(4), 258–261 (2006).
[CrossRef]

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13(16), 6296–6304 (2005).
[CrossRef] [PubMed]

C. David, B. Nöhammer, H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81(17), 3287 (2002).
[CrossRef]

Davis, T. J.

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373(6515), 595–598 (1995).
[CrossRef]

Diaz, A.

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard X-ray phase contrast imaging,” Microelectron. Eng. 84(5-8), 1172–1177 (2007).
[CrossRef]

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13(16), 6296–6304 (2005).
[CrossRef] [PubMed]

Donath, T.

S. Rutishauser, I. Zanette, T. Donath, A. Sahlholm, J. Linnros, and C. David, “Structured scintillator for hard x-ray grating interferometry,” Appl. Phys. Lett. 98(17), 171107 (2011).
[CrossRef]

I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, “Two-dimensional x-ray grating interferometer,” Phys. Rev. Lett. 105(24), 248102 (2010).
[CrossRef] [PubMed]

Eikenberry, E. F.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[CrossRef] [PubMed]

Engel, K. J.

M. Simon, K. J. Engel, B. Menser, X. Badel, and J. Linnros, “X-ray imaging performance of scintillator-filled silicon pore arrays,” Med. Phys. 35(3), 968–981 (2008).
[CrossRef] [PubMed]

Fukuda, J.

A. Momose and J. Fukuda, “Phase-contrast radiographs of nonstained rat cerebellar specimen,” Med. Phys. 22(4), 375–379 (1995).
[CrossRef] [PubMed]

Gao, D.

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature 384(6607), 335–338 (1996).
[CrossRef]

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373(6515), 595–598 (1995).
[CrossRef]

Gmür, N.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

Groso, A.

Y. Hwu, W. Tsai, A. Groso, G. Margaritondo, and J. H. Je, “Coherence-enhanced synchrotron radiology: Simple theory and practical applications,” J. Phys. D Appl. Phys. 35(13), R105 (2002).
[CrossRef]

Grünzweig, C.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[CrossRef] [PubMed]

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard X-ray phase contrast imaging,” Microelectron. Eng. 84(5-8), 1172–1177 (2007).
[CrossRef]

C. Kottler, F. Pfeiffer, O. Bunk, C. Grünzweig, J. Bruder, and R. Kaufmann, “Phase contrast X-ray imaging of large samples using an incoherent laboratory source,” Phys. Status Solidi 204(8), 2728–2733 (2007) (a).

Guo, J.

Y. Lei, X. Liu, J. Guo, Z. Zhao, and H. Niu, “Development of x-ray scintillator functioning also as an analyzer grating used in grating-based x-ray differential phase contrast imaging,” Chin. Phys. B 20(4), 042901 (2011).
[CrossRef]

X. Liu, J. Guo, and H. Niu, “A new method of detecting interferogram in differential phase-contrast imaging system based on special structured x-ray scintillator screen,” Chin. Phys. B 19(7), 070701 (2010).
[CrossRef]

X. Liu, Y. Lei, Z. Zhao, J. Guo, and H. Niu, “Design and fabrication of hard x-ray phase grating,” Acta. Phys. Sin. 59, 6927 (2010).

Gureyev, T. E.

K. A. Nugent, T. E. Gureyev, D. J. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard X-rays,” Phys. Rev. Lett. 77(14), 2961–2964 (1996).
[CrossRef] [PubMed]

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature 384(6607), 335–338 (1996).
[CrossRef]

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373(6515), 595–598 (1995).
[CrossRef]

Hart, M.

U. Bonse and M. Hart, “An x-ray interferometer with long separated interfering beam paths,” Appl. Phys. Lett. 6(8), 155 (1965).
[CrossRef]

Hattori, T.

D. Noda, H. Tsujii, N. Takahashi, and T. Hattori, “Fabrication of high precision X-ray mask for X-ray grating of X-ray Talbot interferometer,” Microsyst. Technol. 16(8-9), 1309–1313 (2010).
[CrossRef]

Hirano, K.

A. Momose, T. Takeda, Y. Itai, and K. Hirano, “Phase-contrast X-ray computed tomography for observing biological soft tissues,” Nat. Med. 2(4), 473–475 (1996).
[CrossRef] [PubMed]

Huwahara, H.

A. Momose, W. Yashiro, H. Huwahara, and K. Kawabata, “Grating-Based X-ray Phase Imaging Using Multiline X-ray Source,” Jpn. J. Appl. Phys. 48(7), 076512 (2009).
[CrossRef]

Hwu, Y.

Y. Hwu, W. Tsai, A. Groso, G. Margaritondo, and J. H. Je, “Coherence-enhanced synchrotron radiology: Simple theory and practical applications,” J. Phys. D Appl. Phys. 35(13), R105 (2002).
[CrossRef]

Ingal, V. N.

V. N. Ingal and E. A. Beliaevskaya, “X-ray plane-wave topography observation of the phase contrast from a non-crystalline object,” J. Phys. D Appl. Phys. 28(11), 2314–2317 (1995).
[CrossRef]

Itai, Y.

A. Momose, T. Takeda, Y. Itai, and K. Hirano, “Phase-contrast X-ray computed tomography for observing biological soft tissues,” Nat. Med. 2(4), 473–475 (1996).
[CrossRef] [PubMed]

Je, J. H.

Y. Hwu, W. Tsai, A. Groso, G. Margaritondo, and J. H. Je, “Coherence-enhanced synchrotron radiology: Simple theory and practical applications,” J. Phys. D Appl. Phys. 35(13), R105 (2002).
[CrossRef]

Johnston, R. E.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

Kaufmann, R.

C. Kottler, F. Pfeiffer, O. Bunk, C. Grünzweig, J. Bruder, and R. Kaufmann, “Phase contrast X-ray imaging of large samples using an incoherent laboratory source,” Phys. Status Solidi 204(8), 2728–2733 (2007) (a).

Kawabata, K.

A. Momose, W. Yashiro, H. Huwahara, and K. Kawabata, “Grating-Based X-ray Phase Imaging Using Multiline X-ray Source,” Jpn. J. Appl. Phys. 48(7), 076512 (2009).
[CrossRef]

Kohn, V.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486 (1995).
[CrossRef]

Kottler, C.

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard X-ray phase contrast imaging,” Microelectron. Eng. 84(5-8), 1172–1177 (2007).
[CrossRef]

C. Kottler, F. Pfeiffer, O. Bunk, C. Grünzweig, J. Bruder, and R. Kaufmann, “Phase contrast X-ray imaging of large samples using an incoherent laboratory source,” Phys. Status Solidi 204(8), 2728–2733 (2007) (a).

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett. 98(10), 108105 (2007).
[CrossRef] [PubMed]

T. Weitkamp, C. David, C. Kottler, O. Bunk, and F. Pfeiffer, “Tomography with grating interferometers at low-brilliance sources,” Proc. SPIE 6318, 63180S, 63180S-10 (2006).
[CrossRef]

Kraft, P.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[CrossRef] [PubMed]

Kuznetsov, S.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486 (1995).
[CrossRef]

Lei, Y.

Y. Lei, X. Liu, J. Guo, Z. Zhao, and H. Niu, “Development of x-ray scintillator functioning also as an analyzer grating used in grating-based x-ray differential phase contrast imaging,” Chin. Phys. B 20(4), 042901 (2011).
[CrossRef]

X. Liu, Y. Lei, Z. Zhao, J. Guo, and H. Niu, “Design and fabrication of hard x-ray phase grating,” Acta. Phys. Sin. 59, 6927 (2010).

Linnros, J.

S. Rutishauser, I. Zanette, T. Donath, A. Sahlholm, J. Linnros, and C. David, “Structured scintillator for hard x-ray grating interferometry,” Appl. Phys. Lett. 98(17), 171107 (2011).
[CrossRef]

M. Simon, K. J. Engel, B. Menser, X. Badel, and J. Linnros, “X-ray imaging performance of scintillator-filled silicon pore arrays,” Med. Phys. 35(3), 968–981 (2008).
[CrossRef] [PubMed]

Liu, X.

Y. Lei, X. Liu, J. Guo, Z. Zhao, and H. Niu, “Development of x-ray scintillator functioning also as an analyzer grating used in grating-based x-ray differential phase contrast imaging,” Chin. Phys. B 20(4), 042901 (2011).
[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(31), 13576–13581 (2010).
[CrossRef] [PubMed]

X. Liu, J. Guo, and H. Niu, “A new method of detecting interferogram in differential phase-contrast imaging system based on special structured x-ray scintillator screen,” Chin. Phys. B 19(7), 070701 (2010).
[CrossRef]

X. Liu, Y. Lei, Z. Zhao, J. Guo, and H. Niu, “Design and fabrication of hard x-ray phase grating,” Acta. Phys. Sin. 59, 6927 (2010).

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(31), 13576–13581 (2010).
[CrossRef] [PubMed]

Margaritondo, G.

Y. Hwu, W. Tsai, A. Groso, G. Margaritondo, and J. H. Je, “Coherence-enhanced synchrotron radiology: Simple theory and practical applications,” J. Phys. D Appl. Phys. 35(13), R105 (2002).
[CrossRef]

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(31), 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(31), 13576–13581 (2010).
[CrossRef] [PubMed]

Menk, R.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

Menser, B.

M. Simon, K. J. Engel, B. Menser, X. Badel, and J. Linnros, “X-ray imaging performance of scintillator-filled silicon pore arrays,” Med. Phys. 35(3), 968–981 (2008).
[CrossRef] [PubMed]

Momose, A.

A. Momose, W. Yashiro, H. Huwahara, and K. Kawabata, “Grating-Based X-ray Phase Imaging Using Multiline X-ray Source,” Jpn. J. Appl. Phys. 48(7), 076512 (2009).
[CrossRef]

A. Momose, “Phase-sensitive imaging and phase tomography using X-ray interferometers,” Opt. Express 11(19), 2303–2314 (2003).
[CrossRef] [PubMed]

A. Momose, T. Takeda, Y. Itai, and K. Hirano, “Phase-contrast X-ray computed tomography for observing biological soft tissues,” Nat. Med. 2(4), 473–475 (1996).
[CrossRef] [PubMed]

A. Momose and J. Fukuda, “Phase-contrast radiographs of nonstained rat cerebellar specimen,” Med. Phys. 22(4), 375–379 (1995).
[CrossRef] [PubMed]

Niu, H.

Y. Lei, X. Liu, J. Guo, Z. Zhao, and H. Niu, “Development of x-ray scintillator functioning also as an analyzer grating used in grating-based x-ray differential phase contrast imaging,” Chin. Phys. B 20(4), 042901 (2011).
[CrossRef]

X. Liu, Y. Lei, Z. Zhao, J. Guo, and H. Niu, “Design and fabrication of hard x-ray phase grating,” Acta. Phys. Sin. 59, 6927 (2010).

X. Liu, J. Guo, and H. Niu, “A new method of detecting interferogram in differential phase-contrast imaging system based on special structured x-ray scintillator screen,” Chin. Phys. B 19(7), 070701 (2010).
[CrossRef]

Noda, D.

D. Noda, H. Tsujii, N. Takahashi, and T. Hattori, “Fabrication of high precision X-ray mask for X-ray grating of X-ray Talbot interferometer,” Microsyst. Technol. 16(8-9), 1309–1313 (2010).
[CrossRef]

Nöhammer, B.

C. David, B. Nöhammer, H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81(17), 3287 (2002).
[CrossRef]

Nugent, K. A.

K. A. Nugent, T. E. Gureyev, D. J. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard X-rays,” Phys. Rev. Lett. 77(14), 2961–2964 (1996).
[CrossRef] [PubMed]

Paganin, D.

K. A. Nugent, T. E. Gureyev, D. J. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard X-rays,” Phys. Rev. Lett. 77(14), 2961–2964 (1996).
[CrossRef] [PubMed]

Pfeiffer, F.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[CrossRef] [PubMed]

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard X-ray phase contrast imaging,” Microelectron. Eng. 84(5-8), 1172–1177 (2007).
[CrossRef]

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett. 98(10), 108105 (2007).
[CrossRef] [PubMed]

C. Kottler, F. Pfeiffer, O. Bunk, C. Grünzweig, J. Bruder, and R. Kaufmann, “Phase contrast X-ray imaging of large samples using an incoherent laboratory source,” Phys. Status Solidi 204(8), 2728–2733 (2007) (a).

T. Weitkamp, C. David, C. Kottler, O. Bunk, and F. Pfeiffer, “Tomography with grating interferometers at low-brilliance sources,” Proc. SPIE 6318, 63180S, 63180S-10 (2006).
[CrossRef]

F. Pfeiffer, T. Weikamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys. 2(4), 258–261 (2006).
[CrossRef]

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13(16), 6296–6304 (2005).
[CrossRef] [PubMed]

Pisano, E.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

Pogany, A.

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature 384(6607), 335–338 (1996).
[CrossRef]

Rohbeck, T.

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard X-ray phase contrast imaging,” Microelectron. Eng. 84(5-8), 1172–1177 (2007).
[CrossRef]

Rutishauser, S.

S. Rutishauser, I. Zanette, T. Donath, A. Sahlholm, J. Linnros, and C. David, “Structured scintillator for hard x-ray grating interferometry,” Appl. Phys. Lett. 98(17), 171107 (2011).
[CrossRef]

I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, “Two-dimensional x-ray grating interferometer,” Phys. Rev. Lett. 105(24), 248102 (2010).
[CrossRef] [PubMed]

Sahlholm, A.

S. Rutishauser, I. Zanette, T. Donath, A. Sahlholm, J. Linnros, and C. David, “Structured scintillator for hard x-ray grating interferometry,” Appl. Phys. Lett. 98(17), 171107 (2011).
[CrossRef]

Sayers, D.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

Schelokov, I.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486 (1995).
[CrossRef]

Simon, M.

M. Simon, K. J. Engel, B. Menser, X. Badel, and J. Linnros, “X-ray imaging performance of scintillator-filled silicon pore arrays,” Med. Phys. 35(3), 968–981 (2008).
[CrossRef] [PubMed]

Snigirev, A.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486 (1995).
[CrossRef]

Snigireva, I.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486 (1995).
[CrossRef]

Solak, H.

C. David, B. Nöhammer, H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81(17), 3287 (2002).
[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(31), 13576–13581 (2010).
[CrossRef] [PubMed]

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13(16), 6296–6304 (2005).
[CrossRef] [PubMed]

Stevenson, A. W.

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373(6515), 595–598 (1995).
[CrossRef]

Stevenson, W.

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature 384(6607), 335–338 (1996).
[CrossRef]

Takahashi, N.

D. Noda, H. Tsujii, N. Takahashi, and T. Hattori, “Fabrication of high precision X-ray mask for X-ray grating of X-ray Talbot interferometer,” Microsyst. Technol. 16(8-9), 1309–1313 (2010).
[CrossRef]

Takeda, T.

A. Momose, T. Takeda, Y. Itai, and K. Hirano, “Phase-contrast X-ray computed tomography for observing biological soft tissues,” Nat. Med. 2(4), 473–475 (1996).
[CrossRef] [PubMed]

Thomlinson, W.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

Tsai, W.

Y. Hwu, W. Tsai, A. Groso, G. Margaritondo, and J. H. Je, “Coherence-enhanced synchrotron radiology: Simple theory and practical applications,” J. Phys. D Appl. Phys. 35(13), R105 (2002).
[CrossRef]

Tsujii, H.

D. Noda, H. Tsujii, N. Takahashi, and T. Hattori, “Fabrication of high precision X-ray mask for X-ray grating of X-ray Talbot interferometer,” Microsyst. Technol. 16(8-9), 1309–1313 (2010).
[CrossRef]

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(31), 13576–13581 (2010).
[CrossRef] [PubMed]

Washburn, D.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

Weikamp, T.

F. Pfeiffer, T. Weikamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys. 2(4), 258–261 (2006).
[CrossRef]

Weitkamp, T.

I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, “Two-dimensional x-ray grating interferometer,” Phys. Rev. Lett. 105(24), 248102 (2010).
[CrossRef] [PubMed]

T. Weitkamp, C. David, C. Kottler, O. Bunk, and F. Pfeiffer, “Tomography with grating interferometers at low-brilliance sources,” Proc. SPIE 6318, 63180S, 63180S-10 (2006).
[CrossRef]

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13(16), 6296–6304 (2005).
[CrossRef] [PubMed]

Wilkins, S. W.

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature 384(6607), 335–338 (1996).
[CrossRef]

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373(6515), 595–598 (1995).
[CrossRef]

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(31), 13576–13581 (2010).
[CrossRef] [PubMed]

Yashiro, W.

A. Momose, W. Yashiro, H. Huwahara, and K. Kawabata, “Grating-Based X-ray Phase Imaging Using Multiline X-ray Source,” Jpn. J. Appl. Phys. 48(7), 076512 (2009).
[CrossRef]

Zanette, I.

S. Rutishauser, I. Zanette, T. Donath, A. Sahlholm, J. Linnros, and C. David, “Structured scintillator for hard x-ray grating interferometry,” Appl. Phys. Lett. 98(17), 171107 (2011).
[CrossRef]

I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, “Two-dimensional x-ray grating interferometer,” Phys. Rev. Lett. 105(24), 248102 (2010).
[CrossRef] [PubMed]

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(31), 13576–13581 (2010).
[CrossRef] [PubMed]

Zhao, Z.

Y. Lei, X. Liu, J. Guo, Z. Zhao, and H. Niu, “Development of x-ray scintillator functioning also as an analyzer grating used in grating-based x-ray differential phase contrast imaging,” Chin. Phys. B 20(4), 042901 (2011).
[CrossRef]

X. Liu, Y. Lei, Z. Zhao, J. Guo, and H. Niu, “Design and fabrication of hard x-ray phase grating,” Acta. Phys. Sin. 59, 6927 (2010).

Zhong, Z.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[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(31), 13576–13581 (2010).
[CrossRef] [PubMed]

Ziegler, E.

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13(16), 6296–6304 (2005).
[CrossRef] [PubMed]

C. David, B. Nöhammer, H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81(17), 3287 (2002).
[CrossRef]

Acta. Phys. Sin. (1)

X. Liu, Y. Lei, Z. Zhao, J. Guo, and H. Niu, “Design and fabrication of hard x-ray phase grating,” Acta. Phys. Sin. 59, 6927 (2010).

Appl. Phys. Lett. (3)

S. Rutishauser, I. Zanette, T. Donath, A. Sahlholm, J. Linnros, and C. David, “Structured scintillator for hard x-ray grating interferometry,” Appl. Phys. Lett. 98(17), 171107 (2011).
[CrossRef]

U. Bonse and M. Hart, “An x-ray interferometer with long separated interfering beam paths,” Appl. Phys. Lett. 6(8), 155 (1965).
[CrossRef]

C. David, B. Nöhammer, H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81(17), 3287 (2002).
[CrossRef]

Chin. Phys. B (2)

Y. Lei, X. Liu, J. Guo, Z. Zhao, and H. Niu, “Development of x-ray scintillator functioning also as an analyzer grating used in grating-based x-ray differential phase contrast imaging,” Chin. Phys. B 20(4), 042901 (2011).
[CrossRef]

X. Liu, J. Guo, and H. Niu, “A new method of detecting interferogram in differential phase-contrast imaging system based on special structured x-ray scintillator screen,” Chin. Phys. B 19(7), 070701 (2010).
[CrossRef]

J. Phys. D Appl. Phys. (2)

Y. Hwu, W. Tsai, A. Groso, G. Margaritondo, and J. H. Je, “Coherence-enhanced synchrotron radiology: Simple theory and practical applications,” J. Phys. D Appl. Phys. 35(13), R105 (2002).
[CrossRef]

V. N. Ingal and E. A. Beliaevskaya, “X-ray plane-wave topography observation of the phase contrast from a non-crystalline object,” J. Phys. D Appl. Phys. 28(11), 2314–2317 (1995).
[CrossRef]

Jpn. J. Appl. Phys. (1)

A. Momose, W. Yashiro, H. Huwahara, and K. Kawabata, “Grating-Based X-ray Phase Imaging Using Multiline X-ray Source,” Jpn. J. Appl. Phys. 48(7), 076512 (2009).
[CrossRef]

Med. Phys. (2)

M. Simon, K. J. Engel, B. Menser, X. Badel, and J. Linnros, “X-ray imaging performance of scintillator-filled silicon pore arrays,” Med. Phys. 35(3), 968–981 (2008).
[CrossRef] [PubMed]

A. Momose and J. Fukuda, “Phase-contrast radiographs of nonstained rat cerebellar specimen,” Med. Phys. 22(4), 375–379 (1995).
[CrossRef] [PubMed]

Microelectron. Eng. (1)

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard X-ray phase contrast imaging,” Microelectron. Eng. 84(5-8), 1172–1177 (2007).
[CrossRef]

Microsyst. Technol. (1)

D. Noda, H. Tsujii, N. Takahashi, and T. Hattori, “Fabrication of high precision X-ray mask for X-ray grating of X-ray Talbot interferometer,” Microsyst. Technol. 16(8-9), 1309–1313 (2010).
[CrossRef]

Nat. Mater. (1)

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[CrossRef] [PubMed]

Nat. Med. (1)

A. Momose, T. Takeda, Y. Itai, and K. Hirano, “Phase-contrast X-ray computed tomography for observing biological soft tissues,” Nat. Med. 2(4), 473–475 (1996).
[CrossRef] [PubMed]

Nat. Phys. (1)

F. Pfeiffer, T. Weikamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys. 2(4), 258–261 (2006).
[CrossRef]

Nature (2)

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373(6515), 595–598 (1995).
[CrossRef]

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature 384(6607), 335–338 (1996).
[CrossRef]

Opt. Express (2)

Phys. Med. Biol. (1)

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

Phys. Rev. Lett. (3)

K. A. Nugent, T. E. Gureyev, D. J. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard X-rays,” Phys. Rev. Lett. 77(14), 2961–2964 (1996).
[CrossRef] [PubMed]

I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, “Two-dimensional x-ray grating interferometer,” Phys. Rev. Lett. 105(24), 248102 (2010).
[CrossRef] [PubMed]

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett. 98(10), 108105 (2007).
[CrossRef] [PubMed]

Phys. Status Solidi (1)

C. Kottler, F. Pfeiffer, O. Bunk, C. Grünzweig, J. Bruder, and R. Kaufmann, “Phase contrast X-ray imaging of large samples using an incoherent laboratory source,” Phys. Status Solidi 204(8), 2728–2733 (2007) (a).

Proc. Natl. Acad. Sci. U.S.A. (1)

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(31), 13576–13581 (2010).
[CrossRef] [PubMed]

Proc. SPIE (1)

T. Weitkamp, C. David, C. Kottler, O. Bunk, and F. Pfeiffer, “Tomography with grating interferometers at low-brilliance sources,” Proc. SPIE 6318, 63180S, 63180S-10 (2006).
[CrossRef]

Rev. Sci. Instrum. (1)

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486 (1995).
[CrossRef]

Other (2)

H. Niu, J. Guo, and X. Liu, C.N. Patent No. 200810216469.3 (2008).

H. Niu, J. Guo, K. Wang, and Q. Yang, C.N. Patent No. 200610062487.1 (2006).

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Figures (3)

Fig. 1
Fig. 1

(Color online) The principles of the non-absorption grating X-ray phase-contrast imaging. The system consists of a ladder-shaped multi-line X-ray source, a phase grating and a structured scintillator.

Fig. 2
Fig. 2

(Color online) The image of a piece of a violet leaf. (a) is the conventional digital chromo-photograph. (b) is the X-ray transmission image. (c) is the differential phase contrast image. (d), (e) and (f) are magnified sections of the chromatic, transmission and differential phase contrast images, respectively, of the dried footstalk. (g), (h) and (i) are the magnified sections of the chromatic, transmission and differential phase contrast images, respectively, of the dried leaf apex. (j) and (k) are the profile values of the transmission and differential phase contrast images, respectively, of the dried footstalk.

Fig. 3
Fig. 3

The chicken claw image. (a) is the X-ray transmission image. (b) is the differential phase contrast image. (c) and (d) are magnified sections of the transmission and differential phase contrast images, respectively, of the chicken toes.

Equations (5)

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

l c = z 0 λ γ 0 p 0 p 1,
z 1 =M p 1 2 8λ ,
M= ( z 0 + z 1 ) z 0 ,
p 2 = p 0 z 1 z 0 ,
I( m,n, y g )= i a i ( m,n )cos( i 2π p 2 y g + φ i ( m,n ) ),

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