OSA's Digital Library

Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 8, Iss. 4 — May. 22, 2013
« Show journal navigation

Inner-focusing reconstruction method for grating-based phase-contrast CT

Yan Xi and Jun Zhao  »View Author Affiliations


Optics Express, Vol. 21, Issue 5, pp. 6224-6232 (2013)
http://dx.doi.org/10.1364/OE.21.006224


View Full Text Article

Acrobat PDF (1916 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Grating-based phase-contrast imaging has been a hot topic for several years due to its excellent imaging capability for low-density materials and easy implementation with a laboratory x-ray source. Compared with traditional x-ray computed tomography (CT) systems, the standard data collection procedure, “phase-stepping” (PS), in the grating-based phase-contrast CT (GPC-CT) is time consuming. The imaging time of a GPC-CT scan is usually up to hours. It is unacceptable in clinical CT examinations, and will cause serious motion artifacts in the reconstructed images. Additionally, the radiation dose delivered to the object with the PS-based GPC-CT is several times larger than that by a conventional CT scan. To address these problems, in this paper, we followed the interlaced PS method and proposed a novel image reconstruction method, namely the inner-focusing (IF) reconstruction method. With the interlaced PS method, the sample rotation and the grating stepping in GPC-CT occur at the same time. Thus, the interlaced GPC-CT scan can have a comparable temporal resolution with existing CT systems. Without any additional requirements, the proposed IF reconstruction method can prevent the artifacts existing in the conventional interlaced PS method. Both numerical simulations and real experiments were carried out to verify the proposed IF reconstruction method. And the results demonstrated it was effective in archiving a fast and low-dose GPC-CT.

© 2013 OSA

1. Introduction

X-ray computed tomography (CT) technique has played an important role in clinical diagnoses for its nondestructive investigation of patients. However, since conventional x-ray imaging is based on the absorption properties of materials, it is difficult for current CT systems to distinguish low-density materials, such as soft tissues. Compared with traditional absorption-based x-ray imaging, x-ray phase-contrast imaging (PCI) technique has gained special attention in recent years for its superior soft-tissue imaging capability [1

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]

4

4. 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]

]. Among the various proposed methods for PCI, grating-based PCI technique has been extensively developed and successfully extended to use with a laboratory x-ray tube, which indicates its promise further in clinical imaging applications [5

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

7

7. A. Tapfer, M. Bech, B. Pauwels, X. Liu, P. Bruyndonckx, A. Sasov, J. Kenntner, J. Mohr, M. Walter, J. Schulz, and F. Pfeiffer, “Development of a prototype gantry system for preclinical x-ray phase-contrast computed tomography,” Med. Phys. 38(11), 5910–5915 (2011). [CrossRef] [PubMed]

].

Compared with the traditional absorption-based x-ray CT, grating-based phase-contrast CT (GPC-CT) is much more effective in imaging low-density materials [8

8. Y. Xi, B. Kou, H. Sun, J. Qi, J. Sun, J. Mohr, M. Börner, J. Zhao, L. X. Xu, T. Xiao, and Y. Wang, “X-ray grating interferometer for biomedical imaging applications at Shanghai Synchrotron Radiation Facility,” J. Synchrotron Radiat. 19(5), 821–826 (2012). [CrossRef] [PubMed]

10

10. A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase tomography by X-ray Talbot interferometry for biological imaging,” Jpn. J. Appl. Phys. 45(6A), 5254–5262 (2006). [CrossRef]

], but more complicated. During a general GPC-CT scan, phase-stepping (PS) method is used to capture projections with different grating transverse positions at each projection angle. Thus, the total radiation dose delivered to the scanned object is several times higher than that within a traditional CT scan. What’s worse, the stop-and-go motion in PS-based GPC-CT makes it much slower than the traditional CT scanning. These limitations restrict the standard GPC-CT system adopted in clinical imaging applications. To achieve a practical GPC-CT scanning for clinical diagnosis, fast data collection procedure and acceptable radiation dose are critical.

According to data collection procedures, the imaging method of GPC-CT can be classified into four categories: the PS method [11

11. 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]

], Moiré analysis method [12

12. N. Bevins, J. Zambelli, K. Li, Z. Qi, and G. H. Chen, “Multicontrast x-ray computed tomography imaging using Talbot-Lau interferometry without phase stepping,” Med. Phys. 39(1), 424–428 (2012). [CrossRef] [PubMed]

, 13

13. A. Momose, W. Yashiro, H. Maikusa, and Y. Takeda, “High-speed X-ray phase imaging and X-ray phase tomography with Talbot interferometer and white synchrotron radiation,” Opt. Express 17(15), 12540–12545 (2009). [CrossRef] [PubMed]

], interlaced PS method [14

14. I. Zanette, M. Bech, A. Rack, G. Le Duc, P. Tafforeau, C. David, J. Mohr, F. Pfeiffer, and T. Weitkamp, “Trimodal low-dose X-ray tomography,” Proc. Natl. Acad. Sci. U.S.A. 109(26), 10199–10204 (2012). [CrossRef] [PubMed]

, 15

15. I. Zanette, M. Bech, F. Pfeiffer, and T. Weitkamp, “Interlaced phase stepping in phase-contrast x-ray tomography,” Appl. Phys. Lett. 98(9), 094101 (2011). [CrossRef]

] and reverse projection method [16

16. 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]

]. Among them, the PS method is commonly used in experiments as the gold standard. Though the others can improve the shortcomings of the PS method in some respects, they are all imperfect, and sacrifice other performances as compensation. In this paper, we follow the imaging scheme of the interlaced PS method and propose a novel reconstruction method for it, named the inner-focusing (IF) reconstruction method. The proposed method can well address the limited field-of-view (FOV) problem of the interlaced GPC-CT without any additional requirements by having a more uniform noise texture [17

17. Y. Xi and J. Zhao, “Fast imaging method for grating-based x-ray computed tomography,” Proc. SPIE 8506, 85061P, 85061P-6 (2012). [CrossRef]

]. Both numerical simulations and real experiments were carried out to investigate its effectiveness in achieving a fast and low-dose GPC-CT.

2. Materials and method

2.1 PS and interlaced PS

Data collection schemes of GPC-CT with PS and interlaced PS methods are plotted in Fig. 1(b). Each of them can be implemented with parallel-beam x-rays (using synchrotron radiation, Fig. 1(a)) or fan-beam x-rays (using laboratory x-ray tube). The PS method is the gold standard for data acquisition of GPC-CT which is based on Talbot effect [18

18. A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-ray Talbot interferometry,” Jpn. J. Appl. Phys. 42(Part 2, No. 7B), L866–L868 (2003). [CrossRef]

]. Through the Talbot effect, the phase modulation generated by the phase grating G1 and the scanned object is transformed into intensity modulation downstream and analyzed by the absorption grating G2, which is placed at a distance from G1. When the PS method is adopted, G1 (or G2) is stepped along the transverse direction perpendicular to grating lines at each projection angle and a series of projections of the sample is recorded. The intensity signal in each detector cell (indexed by t) oscillates as a function of the grating transverse position x and can be approximated by only the zeroth and the first Fourier components as
Px(t)=kak(t)cos(2πg2x+φk)a0(t)+a1(t)cos(2πg2x+φ1),
(1)
where g2 denotes the period of grating G2, a0 represents the transmittance of the sample and gratings, and φ1 is the phase shift signal of the incident x-rays. The analysis of the intensity oscillation at each pixel with and without the sample can yield information about the absorption, x-ray phase change and scattering properties of the sample [11

11. 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]

]. To collect a complete data set for GPC-CT reconstruction, the grating stepping procedure will be repeated at every projection angle. Thus, the total number of projections of the scanned object with the standard PS method is several times larger than that in a traditional CT scan. It makes the radiation dose of standard GPC-CT extremely large. Besides, the scanning time of a standard GPC-CT is up to hours, much longer than that with a conventional absorption-based CT system.

2.1 IF reconstruction

According to the analysis above, the interlaced GPC-CT can be implemented in a continuous rotation mode, and the radiation doses delivered to the scanned object is only a fraction of that with the PS method. However, there are obvious artifacts in the reconstructed images as the signal extraction process at each projection angle is approximate. In this paper, we consider the interlaced GPC-CT method, and propose a novel reconstruction method to improve its performance, making it practical in clinical applications. To address the limited-FOV problem of the interlaced GPC-CT, an alternative reconstruction method is proposed, named the IF method.

At each projection angle, the differential phase-contrast projection corresponding to the virtual rotation center f(r) is retrieved from {Pj(t)}. They are calculated by fitting cosine functions (as expressed by Eq. (1)) with the Levenberg–Marquardt algorithm [20

20. G. A. F. Seber and C. J. Wild, Nonlinear Regression (LibreDigital, 2003), pp. 624.

] in Matlab software (MathWorks, Massachusetts, USA). By taking these differential phase-contrast projections around the sample, the refractive index of the local area in the sample can be reconstructed using a FBP algorithm [9

9. 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]

]. This is the so-called inner-focusing process. To reconstruct a complete cross slice of the sample, multiple virtual rotation centers are set, and the final reconstructed complete image is composed with these sub-images around each virtual rotation center. With the IF reconstruction method, phase-contrast, absorption-contrast and scattering-contrast images can be reconstructed simultaneously, same as the interlaced PS method [14

14. I. Zanette, M. Bech, A. Rack, G. Le Duc, P. Tafforeau, C. David, J. Mohr, F. Pfeiffer, and T. Weitkamp, “Trimodal low-dose X-ray tomography,” Proc. Natl. Acad. Sci. U.S.A. 109(26), 10199–10204 (2012). [CrossRef] [PubMed]

]. Since the refractive index is more suitable for representing low-density materials, in this paper, we show the reconstructed phase-contrast images in the following experiments.

3. Results and discussion

To evaluate the proposed IF reconstruction method for GPC-CT, a numerical phantom was designed with four kinds of rods embedded inside as shown in Fig. 4
Fig. 4 Numerical phantom used in simulations. (a) is its absorption coefficient map and (b) the distribution of refractive index.
. The diameter of the phantom was 4 mm. The setup of GPC-CT system is shown in Fig. 1(a) where the phase shift of grating G1 was set at π/2, and the periods of G1 and G2 were 2.4 μm. Projections of the sample were recorded by a detector with an effective pixel size of 5 μm. The visibility of the phase-stepping curve was set at 40%. In numerical experiments, a parallel-beam interlaced GPC-CT scan of the phantom was performed with x-ray energy of 25 keV. The number of projection angles was NP with 180 degrees around the sample. According to the data collection scheme of interlaced GPC-CT plotted in Fig. 1(b), the stepping of grating G1 and the rotation of the sample were simultaneous. 9 steps of grating G1 movement covered a full period of grating G2. The sample was placed exactly on the center of the rotation stage.

According to the reconstruction method of interlaced PS, the center area of the cross slice of the sample can be reconstructed with acceptable quality. Meanwhile, there will be obvious artifacts within regions far from the rotation center as shown in Fig. 5(a)
Fig. 5 Reconstructed phase-contrast images with the interlaced PS method (a–b) and IF reconstruction method (d–e). The display window is the same with Fig. 4(b). The number of projections (NP) in (a), (d) is 360 and (b), (e) 1080. (c) and (f) Plots of the line profile indicated by the red line in (a) with the interlaced PS method and IF reconstruction method respectively. The red triangle in (d) marks the virtual rotation center (–200, 200) in IF reconstruction, and red circles show the reconstruction region. The images are displayed with the same window as in Fig. 4(b).
. Increasing the angular sampling rate around the sample is an effective way to solve this problem. The reconstruction result with 1080 projections is shown in Fig. 5(b). Its image quality is much better than that with 360 projection angles. Linear profiles as marked in Fig. 5(a) are plotted in Fig. 5(c) where the base line is from the image with standard PS method and 1080 projection angles.

Figures 5(d) and 5(e) show reconstructed sub-images with the IF reconstruction method with 360 and 1080 projection angles respectively. The virtual rotation center is marked by the red triangle in Fig. 5(d). Compared with reconstruction results using the interlaced PS method, the proposed IF method can effectively maintain structural boundaries within the sub-image as marked by red dashed circles in Figs. 5(d) and 5(e). The linear profiles demonstrate the edge preserve ability of the proposed IF reconstruction method (Fig. 5(f)). Consistent with the analysis above, regions far from the virtual rotation center are asymmetrically blurred, as indicated by red arrows in Figs. 5(d) and 5(e).

In our real experiment, a phantom consisting of polymethylmethacrylate (PMMA) balls was utilized to investigate the effectiveness of the proposed IF reconstruction method for interlaced GPC-CT. The phantom was scanned by a grating-based interferometer installed into the BL13W beam line at Shanghai Synchrotron Radiation Facility (SSRF) [8

8. Y. Xi, B. Kou, H. Sun, J. Qi, J. Sun, J. Mohr, M. Börner, J. Zhao, L. X. Xu, T. Xiao, and Y. Wang, “X-ray grating interferometer for biomedical imaging applications at Shanghai Synchrotron Radiation Facility,” J. Synchrotron Radiat. 19(5), 821–826 (2012). [CrossRef] [PubMed]

]. G1 was designed to be π/2, and its period is 2.396 µm. The period of G2 is 2.4 µm. The inner distance between G1 and G2 was 46.4 mm. X-ray tomography of the phantom was carried out at 20 keV, in which 720 projection angles were recorded over 180 degrees with an effective pixel size of 9 μm (Photonic Science, East Sussex, UK). The exposure time for each projection image was 10 ms. In each phase-stepping scan, the grating G1 moved along the transverse direction perpendicular to the grating line direction with 9 steps to cover one full period of the grating G2. To simulate the data collection schemes of GPC-CT with PS and interlaced PS methods, as illustrated in Fig. 1(b), we rearranged the complete CT data set into specific data sets according to their data collection protocols. In the interlaced GPC-CT, the sample rotation and the grating stepping occur at the same time, and 9 steps of grating G1 stepping cover one period of G2.

4. Summary

Based on the data collection scheme of interlaced GPC-CT, we proposed a novel reconstruction method, namely the IF reconstruction method. This method can effectively enlarge the limited FOV of interlaced GPC-CT by preserving boundary in reconstructed images without any additional requirements. Combined with the proposed IF reconstruction method, GPC-CT scan can be implemented with fast speed and reasonable radiation dose with an acceptable imaging quality. Both numerical simulations and real experiments results have demonstrated that the IF reconstruction method is effective in archiving a low-dose and fast GPC-CT scan. We believe that the proposed IF reconstruction method will be one of critical factors promoting GPC-CT applied in clinical imaging applications.

Acknowledgment

This work was performed at the BL13W beamline of Shanghai Synchrotron Radiation Facility and supported by the National Basic Research Program of China (973 Program; 2010CB834302).

References and links

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]

2.

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

3.

D. Gao, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast radiography,” Radiographics 18(5), 1257–1267 (1998). [PubMed]

4.

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]

5.

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

6.

M. Stampanoni, Z. Wang, T. Thüring, C. David, E. Roessl, M. Trippel, R. A. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Invest. Radiol. 46(12), 801–806 (2011). [CrossRef] [PubMed]

7.

A. Tapfer, M. Bech, B. Pauwels, X. Liu, P. Bruyndonckx, A. Sasov, J. Kenntner, J. Mohr, M. Walter, J. Schulz, and F. Pfeiffer, “Development of a prototype gantry system for preclinical x-ray phase-contrast computed tomography,” Med. Phys. 38(11), 5910–5915 (2011). [CrossRef] [PubMed]

8.

Y. Xi, B. Kou, H. Sun, J. Qi, J. Sun, J. Mohr, M. Börner, J. Zhao, L. X. Xu, T. Xiao, and Y. Wang, “X-ray grating interferometer for biomedical imaging applications at Shanghai Synchrotron Radiation Facility,” J. Synchrotron Radiat. 19(5), 821–826 (2012). [CrossRef] [PubMed]

9.

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]

10.

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase tomography by X-ray Talbot interferometry for biological imaging,” Jpn. J. Appl. Phys. 45(6A), 5254–5262 (2006). [CrossRef]

11.

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]

12.

N. Bevins, J. Zambelli, K. Li, Z. Qi, and G. H. Chen, “Multicontrast x-ray computed tomography imaging using Talbot-Lau interferometry without phase stepping,” Med. Phys. 39(1), 424–428 (2012). [CrossRef] [PubMed]

13.

A. Momose, W. Yashiro, H. Maikusa, and Y. Takeda, “High-speed X-ray phase imaging and X-ray phase tomography with Talbot interferometer and white synchrotron radiation,” Opt. Express 17(15), 12540–12545 (2009). [CrossRef] [PubMed]

14.

I. Zanette, M. Bech, A. Rack, G. Le Duc, P. Tafforeau, C. David, J. Mohr, F. Pfeiffer, and T. Weitkamp, “Trimodal low-dose X-ray tomography,” Proc. Natl. Acad. Sci. U.S.A. 109(26), 10199–10204 (2012). [CrossRef] [PubMed]

15.

I. Zanette, M. Bech, F. Pfeiffer, and T. Weitkamp, “Interlaced phase stepping in phase-contrast x-ray tomography,” Appl. Phys. Lett. 98(9), 094101 (2011). [CrossRef]

16.

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]

17.

Y. Xi and J. Zhao, “Fast imaging method for grating-based x-ray computed tomography,” Proc. SPIE 8506, 85061P, 85061P-6 (2012). [CrossRef]

18.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-ray Talbot interferometry,” Jpn. J. Appl. Phys. 42(Part 2, No. 7B), L866–L868 (2003). [CrossRef]

19.

N. B. Bevins, J. N. Zambelli, K. Li, and G. H. Chen, “Comparison of phase contrast signal extraction techniques,” AIP Conf. Proc. 1466, 169–174 (2012). [CrossRef]

20.

G. A. F. Seber and C. J. Wild, Nonlinear Regression (LibreDigital, 2003), pp. 624.

OCIS Codes
(340.0340) X-ray optics : X-ray optics
(340.6720) X-ray optics : Synchrotron radiation
(340.7450) X-ray optics : X-ray interferometry

ToC Category:
X-ray Optics

History
Original Manuscript: January 14, 2013
Revised Manuscript: February 23, 2013
Manuscript Accepted: February 24, 2013
Published: March 5, 2013

Virtual Issues
Vol. 8, Iss. 4 Virtual Journal for Biomedical Optics

Citation
Yan Xi and Jun Zhao, "Inner-focusing reconstruction method for grating-based phase-contrast CT," Opt. Express 21, 6224-6232 (2013)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-21-5-6224


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  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]
  2. A. Momose, “Phase-sensitive imaging and phase tomography using X-ray interferometers,” Opt. Express11(19), 2303–2314 (2003). [CrossRef] [PubMed]
  3. D. Gao, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast radiography,” Radiographics18(5), 1257–1267 (1998). [PubMed]
  4. 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]
  5. F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys.2(4), 258–261 (2006). [CrossRef]
  6. M. Stampanoni, Z. Wang, T. Thüring, C. David, E. Roessl, M. Trippel, R. A. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Invest. Radiol.46(12), 801–806 (2011). [CrossRef] [PubMed]
  7. A. Tapfer, M. Bech, B. Pauwels, X. Liu, P. Bruyndonckx, A. Sasov, J. Kenntner, J. Mohr, M. Walter, J. Schulz, and F. Pfeiffer, “Development of a prototype gantry system for preclinical x-ray phase-contrast computed tomography,” Med. Phys.38(11), 5910–5915 (2011). [CrossRef] [PubMed]
  8. Y. Xi, B. Kou, H. Sun, J. Qi, J. Sun, J. Mohr, M. Börner, J. Zhao, L. X. Xu, T. Xiao, and Y. Wang, “X-ray grating interferometer for biomedical imaging applications at Shanghai Synchrotron Radiation Facility,” J. Synchrotron Radiat.19(5), 821–826 (2012). [CrossRef] [PubMed]
  9. 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]
  10. A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase tomography by X-ray Talbot interferometry for biological imaging,” Jpn. J. Appl. Phys.45(6A), 5254–5262 (2006). [CrossRef]
  11. T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express13(16), 6296–6304 (2005). [CrossRef] [PubMed]
  12. N. Bevins, J. Zambelli, K. Li, Z. Qi, and G. H. Chen, “Multicontrast x-ray computed tomography imaging using Talbot-Lau interferometry without phase stepping,” Med. Phys.39(1), 424–428 (2012). [CrossRef] [PubMed]
  13. A. Momose, W. Yashiro, H. Maikusa, and Y. Takeda, “High-speed X-ray phase imaging and X-ray phase tomography with Talbot interferometer and white synchrotron radiation,” Opt. Express17(15), 12540–12545 (2009). [CrossRef] [PubMed]
  14. I. Zanette, M. Bech, A. Rack, G. Le Duc, P. Tafforeau, C. David, J. Mohr, F. Pfeiffer, and T. Weitkamp, “Trimodal low-dose X-ray tomography,” Proc. Natl. Acad. Sci. U.S.A.109(26), 10199–10204 (2012). [CrossRef] [PubMed]
  15. I. Zanette, M. Bech, F. Pfeiffer, and T. Weitkamp, “Interlaced phase stepping in phase-contrast x-ray tomography,” Appl. Phys. Lett.98(9), 094101 (2011). [CrossRef]
  16. 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]
  17. Y. Xi and J. Zhao, “Fast imaging method for grating-based x-ray computed tomography,” Proc. SPIE8506, 85061P, 85061P-6 (2012). [CrossRef]
  18. A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-ray Talbot interferometry,” Jpn. J. Appl. Phys.42(Part 2, No. 7B), L866–L868 (2003). [CrossRef]
  19. N. B. Bevins, J. N. Zambelli, K. Li, and G. H. Chen, “Comparison of phase contrast signal extraction techniques,” AIP Conf. Proc.1466, 169–174 (2012). [CrossRef]
  20. G. A. F. Seber and C. J. Wild, Nonlinear Regression (LibreDigital, 2003), pp. 624.

Cited By

Alert me when this paper is cited

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


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited