Abstract

Grating-based x-ray differential phase contrast imaging (DPCI) often uses a phase stepping procedure to acquire data that enables the extraction of phase information. This method prolongs the time needed for data acquisition by several times compared with conventional x-ray absorption image acquisitions. A novel analyzer grating design was developed in this work to eliminate the additional data acquisition time needed to perform phase stepping in DPCI. The new analyzer grating was fabricated such that the linear grating structures are shifted from one detector row to the next; the amount of the lateral shift was equal to a fraction of the x-ray diffraction fringe pattern. The x-ray data from several neighboring detector rows were then combined to extract differential phase information. Initial experimental results have demonstrated that the new analyzer grating enables accurate DPCI signal acquisition from a single x-ray exposure like conventional x-ray absorption imaging.

© 2014 Optical Society of America

1. Introduction

Grating-based x-ray differential phase contrast imaging (DPCI) has shown great promise for potential use in medical and biological imaging. One potential limitation in the current DPCI implementation method is an overhead cost in the total data acquisition time: the so-called phase stepping procedure [1, 2] which has been used as the standard signal extraction approach for the DPCI. In this method, the acquisition of each differential phase contrast (DPC) projection at a given projection angle is divided into several sub-acquisitions (phase-steps), each of which requires one of the gratings to be translated by a fraction of the period of the x-ray diffraction fringe pattern before an x-ray intensity measurement is performed. Typically, 4 to 8 phase steps are needed at each projection angle. Between each phase step, the DPCI acquisitions must wait for the grating to be translated into the designated position and stabilized. The stepping and multiple x-ray measurements prolong the process of acquiring data for DPCI. When DPC tomographic modalities such as differential phase contrast computed tomography (DPC-CT) or tomosynthesis (DPC-Tomosynthesis) [3] are used, the phase stepping procedure may potentially introduce the additional problem of mechanical instability, especially if the gratings are mounted on a rotating CT gantry [4].

To shorten the data acquisition time of DPCI, several interesting methods have been developed, including an interleaved phase stepping method [5], conjugate-ray analysis [6], a moiré pattern analysis method [7], and an electromagnetic phase-stepping method [8]. Although potentially faster than traditional phase stepping methods, the interleaved phase stepping method requires mechanical translation of the analyzer grating (commonly referred to as G2) at different projection views, and the object has to be imaged twice (180° apart) in the conjugate-ray method in order to acquire a single projection. Therefore, although both methods are applicable to DPC-CT, neither supports a true single-shot DPCI projection acquisition [9]. In addition, the conjugate-ray method is not able to provide a dark field image. Although moiré analysis is able to provide a single-shot DPCI acquisition without stepping the grating, doing so requires a trade-off between spatial resolution and fringe visibility, depending on the relative tilting angle between the G1 and G2 gratings [9]. The electromagnetic phase-stepping method eliminates mechanical phase stepping but still requires multiple x-ray measurements at each projection view [8].

This work presents a potential solution to enable single-shot phase stepping DPCI acquisitions with a single x-ray exposure. This is achieved with a novel G2 grating design, which incorporates different phase stepping positions by modifying the conventional parallel 1D structure into a shifted row microstructure. Using this new G2, the temporal overhead introduced in the data acquisition process by the phase stepping method is elegantly addressed to enable a continuous and motionless single-shot DPCI data acquisition. Initial experimental studies have been performed to validate this idea.

2. New grating design

In DPCI, the x-ray phase information is encoded into the phase factor of a Talbot diffraction fringe pattern. It is difficult for most digital x-ray detectors (especially those used in medical imaging) to directly resolve this pattern since its period is usually only a few microns. The phase stepping technique addresses this problem by introducing a half-transmissive, half-absorbing (50% duty cycle) analyzer G2 grating in front of the detector as shown in Fig. 1(a). The pitch of G2 (p2) matches the period of the fringe pattern. During the phase stepping procedure, G2 is translated laterally to different positions to modulate the x-ray intensity incident on each detector pixel, which can be described mathematically as [1, 2]

I(k)(x,z)=I0(x,z)+I1(x,z)cos[2πMk+φ(x,z)],
where k = 1, 2,···, M denotes each of the M intensity measurements. The coordinate notation is defined in Fig. 3(a). The DC term, I0, represents the conventional x-ray absorption contrast signal, I1 is related to the dark field or small-angle scatter signal, and φ represents the DPCI signal. The ratio of the I1 and I0 defines the fringe visibility of the interference pattern [10]. As a result, one complete DPCI acquisition simultaneously yields three different x-ray images with different contrast mechanisms: conventional absorption, differential phase, and dark field. This fact by itself represents a major breakthrough in x-ray imaging [10]. Each of these contrast mechanisms may be extracted from the measured data, {I(k)(x, z)}, as follows:
I0(x,z)=1Mk=1MI(k)(x,z),
I1(x,z)=2M[k=1MI(k)(x,z)sin(2πk/M)]2+[k=1MI(k)(x,z)cos(2πk/M)]2,
φ(x,z)=tan1[k=1MI(k)(x,z)sin(2πk/M)k=1MI(k)(x,z)cos(2πk/M)].

 

Fig. 1 (a) Conventional G2 grating design. (b) New G2 grating design.

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Fig. 2 An SEM image of the new G2 grating.

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Fig. 3 A schematic illustration (a) and a photo (b) of the DPCI experimental system equipped with the new G2 grating.

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Rather than mechanically stepping a grating multiple times in order to perform phase stepping, our method uses the new G2 design shown in Fig. 1(b): the original one-dimensional (1D) G2 was divided into separate rows, each with a height h that is equal to the height of a detector pixel. Any two adjacent grating rows have a relative offset of d that is equal to 1/M of the period of the fringe pattern (p2).

With this new G2 grating design, the acquired single-shot projection image has to be processed in order to extract the desired absorption, differential phase, and dark field signals. It uses the data from adjacent detector rows (the grating presented here is designed with M = 4) to replace the needed intensity measurement in Eq. (1) at each detector pixel (x, z):

I(1)(x,z)=I(x,z1),
I(2)(x,z)=I(x,z),
I(3)(x,z)=I(x,z+1),
I(4)(x,z)=I(x,z+2).
Thus, by using Eqs. (2)(4), one can extract the conventional absorption signal I0, DPC signal φ, and dark field-related signal I1 from a single x-ray exposure.

3. Experimental methods and results

A G2 grating based on this new design was fabricated (MicroWorks GmbH, Karlsruhe, Germany). The height h of each grating row is 48 μm to match the pixel size of a CMOS x-ray flat panel detector in our lab (Shad-o-Box™ 2048, Rad-icon Imaging Corp., California, USA). Figure 2 shows a scanning electron microscope (SEM) image of part of the grating. This grating has a pitch of 4.8 μm and a depth of 60 μm (the aspect ratio is 12.5). The total active area of the grating is 5×5 cm2. We performed initial performance testing of this grating using a micro-focus x-ray tube (L10321, Hamamatsu Photonics, Hamamatsu, Japan) and a π-phase Talbot x-ray diffraction grating (commonly known as G1). The G1 grating was designed to operate at a mean x-ray energy of 28 keV and has a pitch of 8 μm. During experimental data acquisition, the x-ray tube was operated at 40 kVp and 175 μA with an exposure time for each acquisition of 60 seconds. Both a schematic illustration and a photo of the experimental setup are shown in Figs. 3(a) and 3(b), respectively. System geometric information can be found in Table. 1.

Tables Icon

Table 1. List of system geometric parameters.

Experimental data acquisitions were performed with both physical phantoms and biological samples, which include a PTFE tube with an inner diameter of 9.2 mm and a wall thickness of 1.9 mm, a grasshopper sample, and an acrylic tube phantom (Fig. 4). The tube has an outer diameter of 9.6 mm and a wall thickness of 1.5 mm. The tube was filled with spheres of different materials (POM, acrylic, and PS) and vegetable oil.

 

Fig. 4 The cylindrical acrylic phantom used during DPC-CT data acquisition. The numbers next to the phantom represent the layers of spheres within the phantom.

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Figure 5 shows results of the PTFE tube phantom acquired using the new G2 grating with a single x-ray exposure. Figures 5(a) and 5(b) demonstrate the visual differences between the two contrast mechanisms, while Figs. 5(c) and 5(d) show the quantitative comparisons between the experimental measurements and the calculated theoretical values of the attenuation and differential phase contrast signals based on the used phantom geometry and material. Figures 6(a) and 6(c) show projection images of the grasshopper. Compared with the conventional absorption image, the DPC image provides additional information about some fine structures inside the object, and the dark field image led to a better visibility of the radio-transparent wings. Figures 7(a) and 7(c) show the reconstructed CT images of the cylindrical acrylic phantom from a DPC-CT data acquisition with 360 view angles and a 1° angular increment using the new G2 grating. These experimental results clearly demonstrate that the new method has successfully generated DPCI images that provide complementary information about the object to the absorption images.

 

Fig. 5 DPCI images of the PTFE tube. (a) is the x-ray absorption image, (b) is the differential phase contrast image, their line profiles are shown in (c) and (d) respectively. In both (c) and (d), the solid lines represent measurements and the dashed lines are theoretical calculations. Note that the pixel values in (c) have been normalized.

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Fig. 6 Projection images of the grasshopper. (a) the x-ray absorption image, (b) the differential phase contrast image, and (c) the dark field image.

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Fig. 7 Coronal planes of volumetric tomographic images of the cylindrical acrylic phantom. (a) the absorption CT image with a display range of [0.04, 0.10] cm−1, (b) the DPC-CT image with a display range of [0.7, 7.0] × 10−7, and (c) the dark field CT image with a display range of [0.10, 0.50].

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4. Conclusion

In summary, this paper reports a new grating design which was developed to simultaneously remove the overhead in data acquisition time and the need for mechanical grating motion in conventional phase-stepping DPCI systems. It completely eliminates the need to perform multiple exposures during phase stepping in DPCI, and thus removes a major hurdle preventing DPCI from achieving the same data acquisition speed as conventional x-ray absorption imaging. It is worth pointing out that the proposed new data acquisition design does have one potential limitation: the spatial resolution in the direction parallel to the linear grating structures will be different from that in the transverse direction. In practice, this is not necessarily a limitation, it only means that the spatial resolution of acquired DPCI images may not be isotropic, and the spatial resolution in a specific application is limited by the worst spatial resolution component. In the future, we hope to perform a rigorous comparison of the spatial resolution and noise characteristics of images generated with conventional phase stepping and our proposed new G2 grating design.

Acknowledgments

The authors would like to thank the three reviewers for their constructive comments. We are especially grateful to the reviewer who brought to our attention a patent by Christian David and Franz Pfeiffer (patent, WO 2008/006470 A1). In this patent, a group of subgratings, combined with a corresponding group of slits in front of the image object, were proposed such that the phase stepping procedure may be achieved through a translation of the object. This could be a potential means to achieve DPCI without mechanical phase stepping. However, it does require both the translation of the image object and the use of slits in front of the image object, whereas the method presented in this paper does not require either to achieve DPCI.

References and links

1. A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, H. Takai, and Y. Suzuki, “Demonstration of x-ray Talbot interferometry,” Jpn. J. Appl. Phys., Part 2 42, 866–868 (2003). [CrossRef]  

2. T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, E. Zeigler, and P. Cloetens, “X-ray phase imaging with a grating interferometer,” Opt. Express 12, 6296–6304 (2005). [CrossRef]  

3. K. Li, Y. Ge, J. Garrett, N. Bevins, J. Zambelli, and G.-H. Chen, “Grating-based phase contrast tomosynthesis imaging: Proof-of-concept experimental studies,” Med. Phys. 41, 011903 (2014). [CrossRef]   [PubMed]  

4. 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, 5910–5915 (2011). [CrossRef]   [PubMed]  

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

6. 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. 107, 13576–13581 (2010). [CrossRef]   [PubMed]  

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

8. H. Miao, L. Chen, E. Bennett, N. Adamo, A. Gomella, A. DeLuca, A. Patel, N. Morgan, and H. Wen, “Motionless phase stepping in x-ray phase contrast imaging with a compact source,” Proc. Natl. Acad. Sci. U. S. A. 110, 19268–19272 (2013). [CrossRef]   [PubMed]  

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

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

References

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  1. A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, H. Takai, and Y. Suzuki, “Demonstration of x-ray Talbot interferometry,” Jpn. J. Appl. Phys., Part 2  42, 866–868 (2003).
    [Crossref]
  2. T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, E. Zeigler, and P. Cloetens, “X-ray phase imaging with a grating interferometer,” Opt. Express 12, 6296–6304 (2005).
    [Crossref]
  3. K. Li, Y. Ge, J. Garrett, N. Bevins, J. Zambelli, and G.-H. Chen, “Grating-based phase contrast tomosynthesis imaging: Proof-of-concept experimental studies,” Med. Phys. 41, 011903 (2014).
    [Crossref] [PubMed]
  4. 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, 5910–5915 (2011).
    [Crossref] [PubMed]
  5. I. Zanette, M. Bech, F. Pfeiffer, and T. Weitkamp, “Interlaced phase stepping in phase-contrast x-ray tomography,” Appl. Phys. Lett. 98, 094101 (2011).
    [Crossref]
  6. 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. 107, 13576–13581 (2010).
    [Crossref] [PubMed]
  7. N. Bevins, J. Zambelli, K. Li, Z. Qi, and G.-H. Chen, “Multi-contrast x-ray computed tomography imaging using Talbot-Lau interferometry without phase stepping,” Med. Phys. 39, 424–428 (2012).
    [Crossref] [PubMed]
  8. H. Miao, L. Chen, E. Bennett, N. Adamo, A. Gomella, A. DeLuca, A. Patel, N. Morgan, and H. Wen, “Motionless phase stepping in x-ray phase contrast imaging with a compact source,” Proc. Natl. Acad. Sci. U. S. A. 110, 19268–19272 (2013).
    [Crossref] [PubMed]
  9. N. Bevins, J. Zambelli, K. Li, and G.-H. Chen, “Comparison of phase contrast signal extraction techniques,” AIP Conf. Proc. 1466, 169–174 (2012).
    [Crossref]
  10. F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, “Hard-x-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7, 134–137 (2008).
    [Crossref] [PubMed]

2014 (1)

K. Li, Y. Ge, J. Garrett, N. Bevins, J. Zambelli, and G.-H. Chen, “Grating-based phase contrast tomosynthesis imaging: Proof-of-concept experimental studies,” Med. Phys. 41, 011903 (2014).
[Crossref] [PubMed]

2013 (1)

H. Miao, L. Chen, E. Bennett, N. Adamo, A. Gomella, A. DeLuca, A. Patel, N. Morgan, and H. Wen, “Motionless phase stepping in x-ray phase contrast imaging with a compact source,” Proc. Natl. Acad. Sci. U. S. A. 110, 19268–19272 (2013).
[Crossref] [PubMed]

2012 (2)

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

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

2011 (2)

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, 5910–5915 (2011).
[Crossref] [PubMed]

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

2010 (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. 107, 13576–13581 (2010).
[Crossref] [PubMed]

2008 (1)

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

2005 (1)

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, E. Zeigler, and P. Cloetens, “X-ray phase imaging with a grating interferometer,” Opt. Express 12, 6296–6304 (2005).
[Crossref]

2003 (1)

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, H. Takai, and Y. Suzuki, “Demonstration of x-ray Talbot interferometry,” Jpn. J. Appl. Phys., Part 2  42, 866–868 (2003).
[Crossref]

Adamo, N.

H. Miao, L. Chen, E. Bennett, N. Adamo, A. Gomella, A. DeLuca, A. Patel, N. Morgan, and H. Wen, “Motionless phase stepping in x-ray phase contrast imaging with a compact source,” Proc. Natl. Acad. Sci. U. S. A. 110, 19268–19272 (2013).
[Crossref] [PubMed]

Bech, M.

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, 5910–5915 (2011).
[Crossref] [PubMed]

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

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

Bennett, E.

H. Miao, L. Chen, E. Bennett, N. Adamo, A. Gomella, A. DeLuca, A. Patel, N. Morgan, and H. Wen, “Motionless phase stepping in x-ray phase contrast imaging with a compact source,” Proc. Natl. Acad. Sci. U. S. A. 110, 19268–19272 (2013).
[Crossref] [PubMed]

Bevins, N.

K. Li, Y. Ge, J. Garrett, N. Bevins, J. Zambelli, and G.-H. Chen, “Grating-based phase contrast tomosynthesis imaging: Proof-of-concept experimental studies,” Med. Phys. 41, 011903 (2014).
[Crossref] [PubMed]

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

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

Brönnimann, C.

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

Bruyndonckx, P.

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, 5910–5915 (2011).
[Crossref] [PubMed]

Bunk, O.

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

Chen, G.-H.

K. Li, Y. Ge, J. Garrett, N. Bevins, J. Zambelli, and G.-H. Chen, “Grating-based phase contrast tomosynthesis imaging: Proof-of-concept experimental studies,” Med. Phys. 41, 011903 (2014).
[Crossref] [PubMed]

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

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

Chen, L.

H. Miao, L. Chen, E. Bennett, N. Adamo, A. Gomella, A. DeLuca, A. Patel, N. Morgan, and H. Wen, “Motionless phase stepping in x-ray phase contrast imaging with a compact source,” Proc. Natl. Acad. Sci. U. S. A. 110, 19268–19272 (2013).
[Crossref] [PubMed]

Cloetens, P.

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, E. Zeigler, and P. Cloetens, “X-ray phase imaging with a grating interferometer,” Opt. Express 12, 6296–6304 (2005).
[Crossref]

David, C.

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

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, E. Zeigler, and P. Cloetens, “X-ray phase imaging with a grating interferometer,” Opt. Express 12, 6296–6304 (2005).
[Crossref]

DeLuca, A.

H. Miao, L. Chen, E. Bennett, N. Adamo, A. Gomella, A. DeLuca, A. Patel, N. Morgan, and H. Wen, “Motionless phase stepping in x-ray phase contrast imaging with a compact source,” Proc. Natl. Acad. Sci. U. S. A. 110, 19268–19272 (2013).
[Crossref] [PubMed]

Diaz, A.

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, E. Zeigler, and P. Cloetens, “X-ray phase imaging with a grating interferometer,” Opt. Express 12, 6296–6304 (2005).
[Crossref]

Eikenberry, E. F.

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

Garrett, J.

K. Li, Y. Ge, J. Garrett, N. Bevins, J. Zambelli, and G.-H. Chen, “Grating-based phase contrast tomosynthesis imaging: Proof-of-concept experimental studies,” Med. Phys. 41, 011903 (2014).
[Crossref] [PubMed]

Ge, Y.

K. Li, Y. Ge, J. Garrett, N. Bevins, J. Zambelli, and G.-H. Chen, “Grating-based phase contrast tomosynthesis imaging: Proof-of-concept experimental studies,” Med. Phys. 41, 011903 (2014).
[Crossref] [PubMed]

Gomella, A.

H. Miao, L. Chen, E. Bennett, N. Adamo, A. Gomella, A. DeLuca, A. Patel, N. Morgan, and H. Wen, “Motionless phase stepping in x-ray phase contrast imaging with a compact source,” Proc. Natl. Acad. Sci. U. S. A. 110, 19268–19272 (2013).
[Crossref] [PubMed]

Grünzweig, C.

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

Hamaishi, Y.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, H. Takai, and Y. Suzuki, “Demonstration of x-ray Talbot interferometry,” Jpn. J. Appl. Phys., Part 2  42, 866–868 (2003).
[Crossref]

Kawamoto, S.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, H. Takai, and Y. Suzuki, “Demonstration of x-ray Talbot interferometry,” Jpn. J. Appl. Phys., Part 2  42, 866–868 (2003).
[Crossref]

Kenntner, J.

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, 5910–5915 (2011).
[Crossref] [PubMed]

Koyama, I.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, H. Takai, and Y. Suzuki, “Demonstration of x-ray Talbot interferometry,” Jpn. J. Appl. Phys., Part 2  42, 866–868 (2003).
[Crossref]

Kraft, P.

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

Li, K.

K. Li, Y. Ge, J. Garrett, N. Bevins, J. Zambelli, and G.-H. Chen, “Grating-based phase contrast tomosynthesis imaging: Proof-of-concept experimental studies,” Med. Phys. 41, 011903 (2014).
[Crossref] [PubMed]

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

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

Liu, X.

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, 5910–5915 (2011).
[Crossref] [PubMed]

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. 107, 13576–13581 (2010).
[Crossref] [PubMed]

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. 107, 13576–13581 (2010).
[Crossref] [PubMed]

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. 107, 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. 107, 13576–13581 (2010).
[Crossref] [PubMed]

Miao, H.

H. Miao, L. Chen, E. Bennett, N. Adamo, A. Gomella, A. DeLuca, A. Patel, N. Morgan, and H. Wen, “Motionless phase stepping in x-ray phase contrast imaging with a compact source,” Proc. Natl. Acad. Sci. U. S. A. 110, 19268–19272 (2013).
[Crossref] [PubMed]

Mohr, J.

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, 5910–5915 (2011).
[Crossref] [PubMed]

Momose, A.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, H. Takai, and Y. Suzuki, “Demonstration of x-ray Talbot interferometry,” Jpn. J. Appl. Phys., Part 2  42, 866–868 (2003).
[Crossref]

Morgan, N.

H. Miao, L. Chen, E. Bennett, N. Adamo, A. Gomella, A. DeLuca, A. Patel, N. Morgan, and H. Wen, “Motionless phase stepping in x-ray phase contrast imaging with a compact source,” Proc. Natl. Acad. Sci. U. S. A. 110, 19268–19272 (2013).
[Crossref] [PubMed]

Patel, A.

H. Miao, L. Chen, E. Bennett, N. Adamo, A. Gomella, A. DeLuca, A. Patel, N. Morgan, and H. Wen, “Motionless phase stepping in x-ray phase contrast imaging with a compact source,” Proc. Natl. Acad. Sci. U. S. A. 110, 19268–19272 (2013).
[Crossref] [PubMed]

Pauwels, B.

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, 5910–5915 (2011).
[Crossref] [PubMed]

Pfeiffer, F.

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

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, 5910–5915 (2011).
[Crossref] [PubMed]

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

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, E. Zeigler, and P. Cloetens, “X-ray phase imaging with a grating interferometer,” Opt. Express 12, 6296–6304 (2005).
[Crossref]

Qi, Z.

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

Sasov, A.

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, 5910–5915 (2011).
[Crossref] [PubMed]

Schulz, J.

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, 5910–5915 (2011).
[Crossref] [PubMed]

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. 107, 13576–13581 (2010).
[Crossref] [PubMed]

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, E. Zeigler, and P. Cloetens, “X-ray phase imaging with a grating interferometer,” Opt. Express 12, 6296–6304 (2005).
[Crossref]

Suzuki, Y.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, H. Takai, and Y. Suzuki, “Demonstration of x-ray Talbot interferometry,” Jpn. J. Appl. Phys., Part 2  42, 866–868 (2003).
[Crossref]

Takai, H.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, H. Takai, and Y. Suzuki, “Demonstration of x-ray Talbot interferometry,” Jpn. J. Appl. Phys., Part 2  42, 866–868 (2003).
[Crossref]

Tapfer, A.

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, 5910–5915 (2011).
[Crossref] [PubMed]

Walter, M.

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, 5910–5915 (2011).
[Crossref] [PubMed]

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. 107, 13576–13581 (2010).
[Crossref] [PubMed]

Weitkamp, T.

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

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, E. Zeigler, and P. Cloetens, “X-ray phase imaging with a grating interferometer,” Opt. Express 12, 6296–6304 (2005).
[Crossref]

Wen, H.

H. Miao, L. Chen, E. Bennett, N. Adamo, A. Gomella, A. DeLuca, A. Patel, N. Morgan, and H. Wen, “Motionless phase stepping in x-ray phase contrast imaging with a compact source,” Proc. Natl. Acad. Sci. U. S. A. 110, 19268–19272 (2013).
[Crossref] [PubMed]

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. 107, 13576–13581 (2010).
[Crossref] [PubMed]

Zambelli, J.

K. Li, Y. Ge, J. Garrett, N. Bevins, J. Zambelli, and G.-H. Chen, “Grating-based phase contrast tomosynthesis imaging: Proof-of-concept experimental studies,” Med. Phys. 41, 011903 (2014).
[Crossref] [PubMed]

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

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

Zanette, I.

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

Zeigler, E.

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, E. Zeigler, and P. Cloetens, “X-ray phase imaging with a grating interferometer,” Opt. Express 12, 6296–6304 (2005).
[Crossref]

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. 107, 13576–13581 (2010).
[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. 107, 13576–13581 (2010).
[Crossref] [PubMed]

AIP Conf. Proc. (1)

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

Appl. Phys. Lett. (1)

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

Jpn. J. Appl. Phys., (1)

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, H. Takai, and Y. Suzuki, “Demonstration of x-ray Talbot interferometry,” Jpn. J. Appl. Phys., Part 2  42, 866–868 (2003).
[Crossref]

Med. Phys. (3)

K. Li, Y. Ge, J. Garrett, N. Bevins, J. Zambelli, and G.-H. Chen, “Grating-based phase contrast tomosynthesis imaging: Proof-of-concept experimental studies,” Med. Phys. 41, 011903 (2014).
[Crossref] [PubMed]

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, 5910–5915 (2011).
[Crossref] [PubMed]

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

Nat. Mater. (1)

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

Opt. Express (1)

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, E. Zeigler, and P. Cloetens, “X-ray phase imaging with a grating interferometer,” Opt. Express 12, 6296–6304 (2005).
[Crossref]

Proc. Natl. Acad. Sci. (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. 107, 13576–13581 (2010).
[Crossref] [PubMed]

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

H. Miao, L. Chen, E. Bennett, N. Adamo, A. Gomella, A. DeLuca, A. Patel, N. Morgan, and H. Wen, “Motionless phase stepping in x-ray phase contrast imaging with a compact source,” Proc. Natl. Acad. Sci. U. S. A. 110, 19268–19272 (2013).
[Crossref] [PubMed]

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Figures (7)

Fig. 1
Fig. 1 (a) Conventional G2 grating design. (b) New G2 grating design.
Fig. 2
Fig. 2 An SEM image of the new G2 grating.
Fig. 3
Fig. 3 A schematic illustration (a) and a photo (b) of the DPCI experimental system equipped with the new G2 grating.
Fig. 4
Fig. 4 The cylindrical acrylic phantom used during DPC-CT data acquisition. The numbers next to the phantom represent the layers of spheres within the phantom.
Fig. 5
Fig. 5 DPCI images of the PTFE tube. (a) is the x-ray absorption image, (b) is the differential phase contrast image, their line profiles are shown in (c) and (d) respectively. In both (c) and (d), the solid lines represent measurements and the dashed lines are theoretical calculations. Note that the pixel values in (c) have been normalized.
Fig. 6
Fig. 6 Projection images of the grasshopper. (a) the x-ray absorption image, (b) the differential phase contrast image, and (c) the dark field image.
Fig. 7
Fig. 7 Coronal planes of volumetric tomographic images of the cylindrical acrylic phantom. (a) the absorption CT image with a display range of [0.04, 0.10] cm−1, (b) the DPC-CT image with a display range of [0.7, 7.0] × 10−7, and (c) the dark field CT image with a display range of [0.10, 0.50].

Tables (1)

Tables Icon

Table 1 List of system geometric parameters.

Equations (8)

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

I ( k ) ( x , z ) = I 0 ( x , z ) + I 1 ( x , z ) cos [ 2 π M k + φ ( x , z ) ] ,
I 0 ( x , z ) = 1 M k = 1 M I ( k ) ( x , z ) ,
I 1 ( x , z ) = 2 M [ k = 1 M I ( k ) ( x , z ) sin ( 2 π k / M ) ] 2 + [ k = 1 M I ( k ) ( x , z ) cos ( 2 π k / M ) ] 2 ,
φ ( x , z ) = tan 1 [ k = 1 M I ( k ) ( x , z ) sin ( 2 π k / M ) k = 1 M I ( k ) ( x , z ) cos ( 2 π k / M ) ] .
I ( 1 ) ( x , z ) = I ( x , z 1 ) ,
I ( 2 ) ( x , z ) = I ( x , z ) ,
I ( 3 ) ( x , z ) = I ( x , z + 1 ) ,
I ( 4 ) ( x , z ) = I ( x , z + 2 ) .

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