Abstract
Purpose:
A major technical obstacle to bringing x-ray multicontrast (i.e., attenuation, phase, and dark-field) imaging methodology to clinical use is the prolonged data acquisition time caused by the phase stepping procedure. The purpose of this work was to introduce a fast acquisition with seamless stage translation (FASST) technique to a prototype multicontrast breast imaging system for reduced image acquisition time that is clinically acceptable.
Methods:
The prototype system was constructed based on a Hologic full-field digital mammography + digital breast tomosynthesis combination system. During each FASST acquisition process, a motorized stage holding a diffraction grating travels continuously with a constant velocity, and a train of 15 short x-ray pulses (35 ms each) was delivered by using the Zero-Degree Tomo mode of the Hologic system. Standard phase retrieval was applied to the 15 subimages without spatial interpolation to avoid spatial resolution loss. The method was evaluated using a physical phantom, a bovine udder specimen, and a freshly resected mastectomy specimen. The FASST technique was experimentally compared with single-shot acquisition methods and the standard phase stepping method.
Results:
The image acquisition time of the proposed method is 3.7 s. In comparison, conventional phase stepping took 105 s using the same prototype imaging system. The mean glandular dose of both methods was matched at 1.3 mGy. No artifacts or spatial resolution loss was observed in images produced by FASST. In contrast, the single-shot methods led to spatial resolution loss and residual moiré artifacts.
Conclusions:
The FASST technique reduces the data acquisition time of the prototype multicontrast x-ray breast imaging system to 3.7 s, such that it is comparable to a clinical digital breast tomosynthesis exam.
Keywords: breast imaging, mammography, phase stepping, Talbot-Lau interferometer, x-ray dark-field imaging, x-ray phase contrast imaging
1. INTRODUCTION
In addition to x-ray attenuation, the interaction of x-rays with matter is accompanied by two other physical mechanisms - x-ray refraction and small angle scattering (SAS).1–3 Due to the infinitesimal (microradian level) refraction and SAS angles, these two mechanisms are generally not observable and utilizable in medical x-ray imaging, despite the rich amount of material information (e.g., the internal distribution and correlation length of electron densities4–8) encoded via the two mechanisms. The introduction of a grating-based Talbot-Lau interferometric device to a conventional x-ray imaging system enables the simultaneous capturing of all three mechanisms that provide mutually complementary information of the image object.9–14 Information associated with the refraction and SAS processes is encoded as phase shifts and fringe visibility reductions of the interference fringe, respectively, and the corresponding images are known as x-ray differential phase contrast (DPC) and dark-field images, respectively.
Shortly after the initial experimental demonstrations of DPC and dark-field imaging using medical-grade tubes and detectors,11,12 the x-ray imaging community initiated a volley of investigations on the method’s potential applications in human breast imaging.12–27 The concept of DPC and dark-field breast imaging is attractive because of the lack of x-ray attenuation contrast between cancerous and normal fibroglandular tissue. The presence of the so-called breast anatomical noise in attenuation-contrast breast images adds another layer of complexity to confound the detection and classification of masses and microcalcifications in breasts, particularly for women with mammographically dense breast tissue.28 In contrast, the physics of DPC and dark-field imaging suggests the potential to improve the visualization of subtle density variations, spiculated masses, and microcalcifications with significantly reduced anatomical noise. Although earlier synchrotron- or benchtop-based studies demonstrated the potential added values of DPC and dark-field images for breast cancer imaging, to what extent these added values can be transferable to clinical breast imaging remains elusive due to the idealized beam characteristics, extended x-ray propagation distances, extensive use of anti-vibration devices, prolonged imaging time, and/or elevated radiation exposure level far exceeding those deemed clinically acceptable.29
Currently, we are experiencing a concerted effort to understanding the true clinical utility of DPC and dark-field breast imaging. Multiple research groups around the world have gone beyond synchrotron- or benchtop-based studies and have undertaken the mission of constructing clinically and human compatible prototype systems. In this publication, we refer these systems that provide attenuation, DPC, and dark-field images as trimodal x-ray breast imaging systems. Koehler et al. and Arboleda et al. have developed trimodal systems based on slit scanning mammography machines with edge-on photon counting detectors.30,31 At the University of Wisconsin-Madison,32,33 we developed two prototype trimodal systems based on the more prevalent full-field digital mammography (FFDM) platforms with energy integration detectors (Fig. 1): System 1.0 was constructed based on a first-generation FFDM (Senography 2000D, GE Healthcare); System 2.0 was developed based on a 2D FFDM + digital breast tomosynthesis (DBT) combo system (Selenia Dimensions, Hologic Inc). With no modification to the tube, detector, and geometry of clinical mammography systems, the majority of physical characteristics of these prototypes meet the requirements for clinical patient imaging, with the image acquisition time being a notable exception: the acquisition time for our System 1.0 is more than 100 s due to the use of a so-called phase stepping procedure that involves the interleaved translation of a grating and multiple exposures.10 The slit scanning prototype systems reported in Refs. 30 and 31 bypassed the need for phase stepping by leveraging the scanning acquisition mode. However, the total acquisition time is still above 10 s due to the use of a narrowly collimated beam required for implementing slit scanning.
Fig. 1.

(a) Two prototype trimodal x-ray breast imaging systems developed at the University of Wisconsin-Madison. The fast acquisition with seamless stage translation (FASST) technique was implemented in System 2.0. (b) Grating interferometer inside the wood box in System 2.0. (c) Workflow of the standard phase stepping technique. (d) Workflow of the FASST technique.
To address the limitation of phase stepping without using the narrow beam scanning technique, several single-shot acquisition methods have been developed.34–37 These methods make certain assumptions such as the perfect periodicity of the moiré pattern generated by the interferometer and/or the local shift invariance of the refraction index and SAS coefficient of the image object. For human breasts with complex anatomical variations and the severe beam divergence encountered in FFDM systems, these assumptions are often violated in practice, resulting in spatial resolution loss and/or image artifacts that can obscure the visualization and quantitation of masses and microcalcifications.
The purpose of this Letter is to report a fast trimodal image acquisition technique recently developed and implemented in our System 2.0. This technique, referred to as fast acquisition with seamless stage translation (FASST), delivers the total radiation budget via a rapid train of short x-ray pulses, during which a motorized stage that holds a grating is translated seamlessly with a constant velocity. This velocity was determined such that from the first to the last pulse, a complete phase stepping curve is obtained. The whole acquisition procedure takes 3.7 s, which is identical to one mammographic view of a clinical DBT exam.
2. MATERIALS AND METHODS
During a standard phase stepping procedure, one grating in the Talbot-Lau interferometer system is sequentially translated along the lateral direction for M times (M ≥ 3). The travel distance of each translation is set to 1/M of the period of the grating structure. At each grating position, an x-ray exposure is taken and the generated moiré pattern is recorded by the detector. From the M measurements, three sets of unknowns corresponding to attenuation, DPC, and dark-field images can be estimated. Compared with a conventional x-ray imaging process, additional time needs to be spent on the accelerating, decelerating, and stabilizing the grating [Fig. 1(a)]. For trimodal x-ray imaging implemented using a clinical mammography unit, additional time for tube cooling and system reset is required by the imaging system. As an example, for the Hologic system operated at 36 kV and 20 mAs, the minimal system dwelling time between two consecutive exposures is more than 20 s.
To address this limitation of phase stepping, various single-shot trimodal imaging methods were developed in our previous works.35,36 Although these methods enable the extraction of all three contrast mechanisms from a single x-ray exposure without grating motion, they make some strong assumptions that may not be valid in mammographic imaging. Taking the staggered grating method36 as an example: it assumes the image object’s attenuation coefficient, refractive index, and SAS coefficient are locally shift-invariant within a length scale spanning four detector rows. At the boundaries of spiculated lesions or the interface between microcalcification and soft tissue, this assumption can be severely violated and spatial resolution loss can be observed. As another example, a moiré metrology-based single-shot method assumes the object profile is limited within a narrow frequency band along one direction in the Fourier domain.35 For CT imaging, this direction can be chosen to be along the rotation axis so that a violation of the assumption is less noticeable in the axial CT images. For clinical two-dimensional breast imaging, however, this is no direction along which artifacts generated by these methods can be considered tolerable. In addition, single-shot methods often require the interferometer to be adjusted to generate a moiré pattern with a smaller period, which can result in lower fringe visibility and dose efficiency.35 Due to these reasons, when constructing System 2.0, we decided to develop a new trimodal data acquisition method that is not only fast but also preserves image quality.
As illustrated in Fig. 1, the basic idea of the proposed FASST technique is to replace the interleaved grating motion by a continuous translation during which a rapid train of 15 ultra-short (35 ms) x-ray pulses are fired over a total time span of 3.7 s. The continuous translation eliminates the time spent on accelerating, decelerating, and stabilizing the grating. The speed of the translation stage is fixed at a value such that between the first and last pulses, the stage travels one grating period. As a result of the ultra short duration of each pulse (35 ms) relative to the pulse-to-pulse time (264 ms), the grating travels only 0.02 μm during each exposure, which makes the grating motion artifact negligible. This short pulse width also reduces the impact of system vibration during each exposure.
The FASST technique was implemented in System 2.0 using the Zero-Degree Tomo mode provided by the Hologic DBT system. This mode was originally designed by the vendor for DBT quality control: its acquisition parameters and time are identical to those of a typical DBT exam, except that the x-ray tube is kept stationary at the zero-degree projection angle. The Hologic system uses a 29 × 24 cm2 amorphous selenium direct-conversion digital detector, a C-arm gantry with 70 cm source-to-detector distance, a rotating tungsten anode tube, and a 7 kW high-frequency generator. Detailed description of this Hologic DBT system can be found in Ref. 38. A source grating was mounted at the exit window of the beam collimator; a π-phase grating and an analyzer grating were installed above the detector and enclosed with a customized box. The top surface of the box is made of acrylic and serves both as the grating protector and as the breast support; the side walls of the box are composed of wood and lead to reject scattered radiation from entering the patient body. The height of the box is 6 cm. As shown in Ref. 33 the gratings were bent to reduce the vignetting effect. The field-of-view (FOV) covered by the current grating system is 4 × 4 cm2. The maximal object thickness supported by this imaging system is 10 cm. Other parameters of the gratings can be found in Refs. 32,33. The phase grating was mounted on a motorized linear translation stage (P-611.1S, Physik Instrumente, Germany) that was programmed to travel at a constant speed of 0.57 μm/s. During each FASST procedure, a zero-degree tomo acquisition is activated once the translation stage goes to a continuous motion. A movie showing a complete FASST process and the acquired 15 images is provided in the Supplemental Material (Video S1).
The FASST technique was evaluated using a custom-built physical phantom and a bovine udder specimen. The physical phantom is made of a 9 × 6 × 2 cm3 acrylic box that contains three layers of 6.3 and 2.9 mm acrylic spheres for evaluating attenuation and DPC images and a cotton swab for evaluating dark-field images. The udder specimen has a thickness of 4 cm. Under IRB approval, the technique was also evaluated using a fresh (within 20 min of surgical resection) human mastectomy specimen with a thickness of 8 cm.
For each object, three acquisitions were performed: standard phase stepping, FASST, and single shot. All acquisitions used the tungsten anode target and 36 kVp, 100 mAs. The original rhodium and aluminum filters of the Hologic system were replaced by the source grating. The air kerma value (6.4 mGy) was measured at the object surface using a Rad-Cal 10×6–6 ionization chamber. To estimate the mean glandular dose (MGD) for the mastectomy specimen, the air kerma and the conversion (g) factors provided in Ref. 39 were used. A 50% glandular-50% adipose breast composition was assumed when estimating MGD. For the 8-cm-thick mastectomy specimen, the value of the g factor39 is 0.195.
3. RESULTS
Figure 2 shows images of a physical phantom acquired from the prototype system using three acquisition methods: standard phase stepping, a single-shot method (moiré metrology), and FASST. Although all three methods were able to produce trimodal images with complementary material information, the single-shot method generated images with blurred edges and residual moiré artifacts. In comparison, the image quality of FASST images matched that of standard phase stepping images. The line profiles shown in Fig. 2 confirmed the absence of spatial resolution loss in the FASST images.
Fig. 2.

Trimodal images of a physical phantom that contains PMMA spheres and a cotton swab. Multi-contrast images shown in the first, second rows were acquired using the standard phase stepping, fast acquisition with seamless stage translation, and moirÉ metrology-based single-shot acquisition method, respectively. The display ranges for the attenuation, differential phase contrast, and dark-field images are [0.15, 0.75], [−0.7, 0.7], and [0, 1.2], respectively. The dashed arrows in the first column indicate locations where the line profiles in the last column were measured.
Trimodal images of the udder specimen are shown in Fig. 3. The spatial resolution and other aspects of the image quality for the FASST results matched those of the conventional phase stepping results. In contrast, the staggered grating method36 resulted in spatial resolution loss along the vertical direction and residual moiré artifacts that obscured the visualization of microcalcifications.
Fig. 3.

Trimodal images of an udder specimen acquired using three methods: the conventional phase stepping, a single-shot method,36 and the fast acquisition with seamless stage translation technique. Close-up images of the region marked by a dash box are provided. The black arrows point to microcalcifications. The display ranges for the attenuation, differential phase contrast, and dark-field images are [0.1, 0.5], [−0.5, 0.5], and [0, 0.65], respectively.
Figure 4 compares images of the human mastectomy specimen acquired using three methods: conventional phase stepping, FASST, and the moiré metrology-based single-shot method. Based on the thickness of the specimen (8 cm), the MGD was calculated to be 1.3 mGy. As a reference, the average MGD per digital mammography view for 8-cm-thick breasts in the multivendor/multisite ACRIN trial is 3.0 ± 1.3 mGy.40 Compared with the conventional phase stepping method, the FASST method preserved the sharpness of the metal clips and interfaces between fibroglandular and adipose tissues. In comparison, the single-shot method not only degraded spatial resolution but also introduced residual moiré artifacts and contrast loss (e.g., for the metal clip in the DPC and dark-field images).
Fig. 4.

Trimodal images of the human mastectomy specimen. Images in the top row were acquired using conventional phase stepping (105 s). Images in the second and third rows were acquired using fast acquisition with seamless stage translation (3.7 s) and the moirÉ metrology-based single-shot method (1 s), respectively. The display ranges for the attenuation, differential phase contrast, and dark-field images are [0.8, 1.5], [−0.5, 0.5], and [0, 1.0], respectively. The arrow in the phase stepping dark field image points to a metal clip in the mastectomy specimen.
4. DISCUSSION
Multicontrast imaging in mammography has been hampered by prolonged image acquisition times. The FASST technique replaces the step-and-shoot scheme used in conventional phase stepping by a continuous grating motion and 15 short x-ray pulses (35 ms each). With an interpulse dwell time of 227 ms, the total acquisition time of FASST is 3.7 s. The continuous motion eliminates times spent on accelerating and decelerating the grating between exposures; the pulsed x-ray mode reduces the system dwell time between exposures. Together, these two strategies reduce the total trimodal image acquisition by 95%. Note that the 227 ms interpulse dwell time not only facilitates tube cooling but also reduces the required speed of the grating translation: without this dwell time, the grating needs to travel 2.15 μm in 525 ms (35 ms × 15). In that case, the grating moves a distance of 0.14 μm per pulse, which is quite significant compared to the grating period and can cause a degradation of fringe visibility. In contrast, the presence of the dwell time in FASST reduces the grating travel distance per exposure to only 0.02 μm, which did not lead to any observable visibility drop or other grating motion artifacts.
Compared with single-shot acquisition methods, the FASST technique does not make assumptions about the local shift-invariance of the multicontrast signals, nor does it require the use of any nonconventional grating designs (e.g., the staggered grating) with higher fabrication costs. Furthermore, it does not require the moiré fringes to follow a specific pattern with a specific period. Therefore, the FASST technique is more robust against beam divergence and grating misalignment.
In addition to FASST and the single-shot methods, there are other fast acquisition techniques available.30,41–45 Some of these techniques such as reverse protection42 and interlaced phase stepping43 were developed for trimodal CT and are not applicable to planar imaging at a single projection angle. Due to similar reasoning, our prototype system does not employ those fast acquisition techniques developed for slit-scanning systems.42 An electromagnetic electron beam steering method developed by Miao et al. enables motionless phase stepping44 and can be potentially combined with FASST, albeit further modification to the tube hardware is required to perform the electromagnetic steering.
This work has the following limitations. First and foremost, the prototype imaging system used in this work has an effective field-of-view (FoV) of only 4 × 4 cm2 at the moment. This FoV is significantly smaller than what is required clinically to cover the whole breast. Although FASST allows the trimodal image acquisition time to meet the clinical standard, this technology alone does not make a trimodal breast imaging system fully compatible with clinical patient imaging. An important future work is to enlarge the FoV by tiling multiple sets of gratings to reach a FoV of 24 × 18 cm2 or similar. As reported in Ref. 33, the analyzer grating used in the current system was bent to reduce the penumbra effect.46 When tiling multiple gratings in the future, not only should individual gratings be bent but also the curvature of the whole grating assembly needs to match the beam divergence. Second, the current implementation of FASST used a fixed kVp of 36 and fixed mAs of 100 for all image acquisitions regardless of the thickness of the sample. In future implementations, these technical factors need to be adjusted based on the thicknesses and compositions of the breasts, otherwise the multicontrast image quality and radiation dose efficient may not be optimized especially for very thick (e.g., >8 cm) breasts. Third, the current version of FASST is based on a special service mode (zero-degree tomo) provided by the Hologic DBT system. To implement FASST on other mammographic imaging platforms, it is required that the x-ray source is capable of running at the pulsed mode and the detector is capable of running at four frames per seconds or faster.
5. CONCLUSIONS
A fast acquisition with seamless stage translation (FASST) technique was developed to enable a prototype trimodal x-ray breast imaging system to accomplish the acquisition of attenuation, DPC, and dark-field images in 3.7 s without spatial resolution loss. This technique enables the imaging time of the trimodal system to be clinically acceptable while matching the image quality of the conventional phase stepping method.
Supplementary Material
ACKNOWLEDGMENTS
This work was supported by the National Institute of Biomedical Imaging and Bioengineering of the National Institutes of Health under Award Number R01EB020521, and by the Office of the Assistant Secretary of Defense for Health Affairs, through the Breast Cancer Research Program, under Award No. W81XWH-16-1-0031. The services of the Translational Science Biocore BioBank (University of Wisconsin Carbone Cancer Center, under the Support of NIH Grant P30CA014520) were utilized for collecting the mastectomy specimens. We also thank the patient volunteers and the research study coordinators Monica Langeland, Jan Yakey, Loran Zwiefelhofer, and Chloe Smith.
Footnotes
CONFLICT OF INTEREST
Lee Wilke, MD is a founder and minority stock owner for Elucent Medical. The Department of Radiology receives in-kind research support from GE Healthcare.
SUPPORTING INFORMATION
Additional supporting information may be found online in the Supporting Information section at the end of the article.
Contributor Information
Ran Zhang, Department of Medical Physics, University of Wisconsin-Madison, 1111 Highland Avenue, Madison, WI 53705, USA.
Amy M. Fowler, Department of Radiology, University of Wisconsin-Madison, 600 Highland Avenue, Madison, WI 53792, USA University of Wisconsin Carbone Cancer Center, 600 Highland Avenue, Madison, WI 53792, USA.
Lee G. Wilke, University of Wisconsin Carbone Cancer Center, 600 Highland Avenue, Madison, WI 53792, USA Department of Surgery, Clinical Science Center, University of Wisconsin School of Medicine and Public Health, Madison, WI 53792, USA.
REFERENCES
- 1.Guinier A Diffraction of x-rays at small angles: application to the study of microscopic phenomena. Ann Phys. 1939;12:161. [Google Scholar]
- 2.Bonse U, Hart M. An x-ray interferometer. Appl Phys Lett. 1965;6:155–156. [Google Scholar]
- 3.Glatter O, Kratky O. Small Angle X-ray Scattering. London: Academic Press; 1982. [Google Scholar]
- 4.Chen G-H, Bevins N, Zambelli J, Qi Z. Small-angle scattering computed tomography (SAS-CT) using a Talbot-Lau interferometerand a rotating anode x-ray tube: theory and experiments. Opt Express. 2010;18:12960–12970. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 5.Bech M, Bunk O, Donath T, Feidenhans’l R, David C, Pfeiffer F. Quantitative x-ray dark-field computed tomography. Phys Med Biol. 2010;55:5529. [DOI] [PubMed] [Google Scholar]
- 6.Qi Z, Zambelli J, Bevins N, Chen G-H. Quantitative imaging of electron density and effective atomic number using phase contrast CT. Phys Med Biol. 2010;55:2669–2677. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 7.Lynch SK, Pai V, Auxier J, et al. Interpretation of dark-field contrast and particle-size selectivity in grating interferometers. Appl Opt. 2011;50:4310–4319. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 8.Strobl M General solution for quantitative dark-field contrast imaging with grating interferometers. Sci Rep. 2014;4:7243. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 9.Momose A, Kawamoto S, Koyama I, Hamaishi Y, Takai H, Suzuki Y. Demonstration of x-ray Talbot interferometry. Jpn J Appl Phys. 2003;42: L866. [Google Scholar]
- 10.Weitkamp T, Diaz A, David C, et al. X-ray phase imaging with a grating interferometer. Opt Express. 2005;13:6296–6304. [DOI] [PubMed] [Google Scholar]
- 11.Weitkamp T, David C, Kottler C, Bunk O, Pfeiffer F. Tomography with grating interferometers at low-brilliance sources. Proc SPIE 2006;6318:63180S. [Google Scholar]
- 12.Pfeiffer F, Weitkamp T, Bunk O, David C. Phase retrieval and differential phasecontrast imaging with low-brilliance x-ray sources. Nat Phys. 2006;2:258–261. [Google Scholar]
- 13.Pfeiffer F, Bech M, Bunk O, et al. Hard-x-ray dark-field imaging using a grating interferometer. Nat Mater. 2008;7:134–137. [DOI] [PubMed] [Google Scholar]
- 14.Miao H, Panna A, Gomella AA, et al. A universal moiré effect and application in x-ray phase-contrast imaging. Nat Phys. 2016;12:830. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 15.Stampanoni M, Wang Z, Thuring T, et al. The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography. Invest Radiol. 2011;46:801. [DOI] [PubMed] [Google Scholar]
- 16.Keyrilainen J, Bravin A, Fernandez M, Tenhunen M, Virkkunen P, Suortti P. Phase-contrast x-ray imaging of breast. Acta Radiol. 2010;51:866–884. [DOI] [PubMed] [Google Scholar]
- 17.Bravin A, Coan P, Suortti P. X-ray phase-contrast imaging: from pre-clinical applications towards clinics. Phys Med Biol. 2012;58:R1–R35. [DOI] [PubMed] [Google Scholar]
- 18.Michel T, Rieger J, Anton G, et al. On a darkfield signal generated by micrometer-sized calcifications in phase-contrast mammography. Phys Med Biol. 2013;58:2713–2732. [DOI] [PubMed] [Google Scholar]
- 19.Grandl S, Willner M, Herzen J, et al. Evaluation of phase-contrast CT of breast tissue at conventional x-ray sources-presentation of selected findings. Z Med Phys. 2013;23:212–221. [DOI] [PubMed] [Google Scholar]
- 20.Hauser N, Wang Z, Kubik-Huch RA, et al. A study on mastectomy samples to evaluate breast imaging quality and potential clinical relevance of differential phase contrast mammography. Invest Radiol. 2014;49:131–137. [DOI] [PubMed] [Google Scholar]
- 21.Scherer K, Birnbacher L, Chabior M, et al. Bi-directional x-ray phase-contrast mammography. PLoS One. 2014;9:1–7. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 22.Wang Z, Hauser N, Singer G, et al. Non-invasive classification of microcalcifications with phase-contrast xray mammography. Nat Commun. 2014;5:3797. [DOI] [PubMed] [Google Scholar]
- 23.Li K, Ge Y, Garrett J, Bevins N, Zambelli J, Chen G-H. Grating-based phase contrast tomosynthesis imaging: proof-of-concept experimental studies. Med Phys. 2014;41:011903. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 24.Garrett J, Ge Y, Li K, Chen G-H. Anatomical background noise power spectrum in differential phase contrast and dark field contrast mammograms. Med Phys. 2014;41:120701. [DOI] [PubMed] [Google Scholar]
- 25.Scherer K, Willer K, Gromann L, et al. Toward clinically compatible phase-contrast mammography. PLoS One. 2015;10:1–7. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 26.Scherer KH. Grating-Based X-Ray Phase-Contrast Mammography Ph.D. thesis, Technical University of Munich, Germany; 2016. [Google Scholar]
- 27.Eggl E, Grandl S, Sztrokay-Gaul A, et al. Dose-compatible grating-based phase-contrast mammography on mastectomy specimens using a compact synchrotron source. Sci Rep. 2018;8:15700. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 28.Karellas A, Vedantham S. Breast cancer imaging: a perspective for the next decade. Med Phys. 2008;35:4878–4897. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 29.Auweter SD, Herzen J, Willner M, et al. X-ray phase-contrast imaging of the breast-advances towards clinical implementation. Br J Radiol. 2014;87:20130606. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 30.Koehler T, Daerr H, Martens G, et al. Slit-scanning differential x-ray phase-contrast mammography: proof-of-concept experimental studies. Med Phys. 2015;42:1959–1965. [DOI] [PubMed] [Google Scholar]
- 31.Arboleda C, Wang Z, Jefimovs K, et al. Towards clinical grating-interferometry mammography. Eur Radiol. 2019;30:1419–1425. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 32.Li K, Zhang R, Garrett J, Ge Y, Ji X, Chen G-H. Design, construction, and initial results of a prototype multi-contrast x-ray breast imaging system. Proc SPIE. 2018;10573:234–239. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 33.Zhang R, Li K, Garrett JW, Chen G-H. Human-compatible multi-contrast mammographic prototype system. Proc SPIE. 2019;10948:109480X. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 34.Bennett EE, Kopace R, Stein AF, Wen H. A grating-based single-shot x-ray phase contrast and diffraction method for in vivo imaging. Med Phys. 2010;37:6047–6054. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 35.Bevins N, Zambelli J, Li K, Qi Z, Chen G-H. Multicontrast x-ray computed tomography imaging using Talbot-Lau interferometry without phase stepping. Med Phys. 2012;39:424–428. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 36.Ge Y, Li K, Garrett J, Chen G-H. Grating based x-ray differential phase contrast imaging without mechanical phase stepping. Opt Express. 2014;22:14246–14252. [DOI] [PubMed] [Google Scholar]
- 37.Ge Y, Garrett J, Li K, Chen G-H. New signal extraction method in x-ray differential phase contrast imaging with a tilted collinear analyzer grating. Proc SPIE. 2015;9412:119–124. [Google Scholar]
- 38.Ren B, Ruth C, Stein J, Smith A, Shaw I, Jing Z. Design and performance of the prototype full field breast tomosynthesis system with selenium based flat panel detector. Proc SPIE. 2005;5745:550–561. [Google Scholar]
- 39.Dance D Monte-Carlo calculation of conversion factors for the estimation of mean glandular breast dose. Phys Med Biol. 1990;35:1211. [DOI] [PubMed] [Google Scholar]
- 40.Hendrick RE, Pisano ED, Averbukh A, et al. Comparison of acquisition parameters and breast dose indigital mammography and screen-film mammography in the American College of Radiology imaging network digital mammographic imaging screening trial. Am J Roentgenol. 2010;194:62. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 41.David C, Pfeiffer F. X-ray interferometer for phase contrast imaging; 2007. [DOI] [PubMed]
- 42.Zhu P, Zhang K, Wang Z, et al. Low-dose, simple, and fast grating-based x-ray phase-contrast imaging. Proc Natl Acad Sci. 2010;107:13576–13581. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 43.Zanette I, Bech M, Pfeiffer F, Weitkamp T. Interlaced phase stepping in phasecontrast x-ray tomography. Appl Phys Lett. 2011;98:094101. [Google Scholar]
- 44.Miao H, Chen L, Bennett EE, et al. Motionless phase stepping in x-ray phase contrast imaging with a compact source. PNAS. 2013;110:19268–19272. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 45.Arboleda C, Wang Z, Stampanoni M. Tilted-grating approach for scanning-mode x-ray phase contrast imaging. Opt Express. 2014;22:15447–15458. [DOI] [PubMed] [Google Scholar]
- 46.Revol V, Kottler C, Kaufmann R, et al. X-ray interferometer with bent gratings: towards larger fields of view. Nucl Instrum Methods Phys Res A. 2011;648:S302. [Google Scholar]
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