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'''Phase-contrast X-ray imaging''' ('''PCI''') or '''phase-sensitive X-ray imaging''' is a general term for different technical methods that use information concerning changes in the [[phase (waves)|phase]] of an [[X-ray]] beam that passes through an object in order to create its images. Standard X-ray imaging techniques like [[radiography]] or [[computed tomography|computed tomography (CT)]] rely on a decrease of the X-ray beam's intensity ([[attenuation]]) when traversing the [[sample (material)|sample]], which can be measured directly with the assistance of an [[X-ray detector]]. In PCI however, the beam's [[phase shift]] caused by the sample is not measured directly, but is transformed into variations in intensity, which then can be recorded by the detector.<ref name=Keyrilainen2010>{{Cite journal | last1 = Keyriläinen | first1 = J. | last2 = Bravin | first2 = A. | last3 = Fernández | first3 = M. | last4 = Tenhunen | first4 = M. | last5 = Virkkunen | first5 = P. | last6 = Suortti | first6 = P. | doi = 10.3109/02841851.2010.504742 | title = Phase-contrast X-ray imaging of breast | journal = Acta Radiologica | volume = 51 | issue = 8 | pages = 866–884 | year = 2010 | pmid = 20799921}}</ref>
In addition to producing [[Projectional radiography|projection images]], PCI, like conventional transmission, can be combined with [[tomography|tomographic techniques]] to obtain the 3D distribution of the real part of the [[Refractive index#Complex index of refraction and absorption|refractive index]] of the sample. When applied to samples that consist of atoms with low [[atomic number]] ''Z'', PCI is more sensitive to density variations in the sample than [[Radiography|conventional transmission-based X-ray imaging]]. This leads to images with improved [[soft tissue]] contrast.<ref name=diemoz2012>{{Cite journal | last1 = Diemoz | first1 = P. C. | last2 = Bravin | first2 = A. | last3 = Coan | first3 = P. | doi = 10.1364/OE.20.002789 | title = Theoretical comparison of three X-ray phase-contrast imaging techniques: Propagation-based imaging, analyzer-based imaging and grating interferometry | journal = Optics Express | volume = 20 | issue = 3 | pages = 2789–2805 | year = 2012 | pmid = 22330515| bibcode = 2012OExpr..20.2789D | url = http://discovery.ucl.ac.uk/1345033/ | doi-access = free }}</ref>
In the last several years, a variety of phase-contrast X-ray imaging techniques have been developed, all of which are based on the observation of [[Interference (wave propagation)|interference patterns]] between diffracted and undiffracted waves.<ref name=Weon2006>{{cite journal|last=Weon|first=B. M.|author2=Je, J. H. |author3=Margaritondo, G. |title=Phase contrast X-ray imaging|journal=International Journal of Nanotechnology|date=2006|volume=3|issue=2–3|pages=280–297|url=http://inderscience.metapress.com/content/50744rtclhukb8xw/|access-date=11 January 2013|bibcode = 2006IJNT....3..280W |doi = 10.1504/IJNT.2006.009584 |citeseerx=10.1.1.568.1669}}</ref> The most common techniques are crystal interferometry, propagation-based imaging, analyzer-based imaging, edge-illumination and grating-based imaging (see below).
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An alternative approach called analyzer-based imaging was first explored in 1995 by Viktor Ingal and Elena Beliaevskaya at the X-ray laboratory in Saint Petersburg, Russia,<ref name= Ingal1995>{{Cite journal | last1 = Ingal | first1 = V. N. | last2 = Beliaevskaya | first2 = E. A. | doi = 10.1088/0022-3727/28/11/012 | title = X-ray plane-wave topography observation of the phase contrast from a non-crystalline object | journal = Journal of Physics D: Applied Physics | volume = 28 | issue = 11 | pages = 2314–2317 | year = 1995 |bibcode = 1995JPhD...28.2314I }}</ref> and by Tim Davis and colleagues at the [[CSIRO]] (Commonwealth Scientific and Industrial Research Organisation) Division of Material Science and Technology in Clayton, Australia.<ref name=Davis1995>{{Cite journal | last1 = Davis | first1 = T. J. | last2 = Gao | first2 = D. | last3 = Gureyev | first3 = T. E. | last4 = Stevenson | first4 = A. W. | last5 = Wilkins | first5 = S. W. | title = Phase-contrast imaging of weakly absorbing materials using hard X-rays | doi = 10.1038/373595a0 | journal = Nature | volume = 373 | issue = 6515 | pages = 595–598 | year = 1995 |bibcode = 1995Natur.373..595D }}</ref> This method uses a Bragg crystal as angular filter to reflect only a small part of the beam fulfilling the [[Bragg condition]] onto a detector. Important contributions to the progress of this method have been made by a US collaboration of the research teams of Dean Chapman, Zhong Zhong and William Thomlinson, for example the extracting of an additional signal caused by [[biological small-angle scattering|ultra-small angle scattering]]<ref name= Zhong2000>{{Cite journal | last1 = Zhong | first1 = Z. | last2 = Thomlinson | first2 = W. | last3 = Chapman | first3 = D. | last4 = Sayers | first4 = D. | title = Implementation of diffraction-enhanced imaging experiments: At the NSLS and APS | doi = 10.1016/S0168-9002(00)00308-9 | journal = Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment | volume = 450 | issue = 2–3 | pages = 556–567 | year = 2000 |bibcode = 2000NIMPA.450..556Z }}</ref> and the first CT image made with analyzer-based imaging.<ref name=Dilamanian2000>{{Cite journal | last1 = Dilmanian | first1 = F. A. | last2 = Zhong | first2 = Z. | last3 = Ren | first3 = B. | last4 = Wu | first4 = X. Y. | last5 = Chapman | first5 = L. D. | last6 = Orion | first6 = I. | last7 = Thomlinson | first7 = W. C. | doi = 10.1088/0031-9155/45/4/309 | title = Computed tomography of x-ray index of refraction using the diffraction enhanced imaging method | journal = Physics in Medicine and Biology | volume = 45 | issue = 4 | pages = 933–946 | year = 2000 | pmid = 10795982|bibcode = 2000PMB....45..933D }}</ref> An alternative to analyzer-based imaging, which provides equivalent results without requiring the use of a crystal, was developed by Alessandro Olivo and co-workers at the Elettra synchrotron in Trieste, Italy.<ref name=":0" /> This method, called “edge-illumination”, operates a fine selection on the X-ray direction by using the physical edge of the detector pixels themselves, hence the name. Later on Olivo, in collaboration with Robert Speller at University College London, adapted the method for use with conventional X-ray sources,<ref name=":6" /> opening the way to translation into clinical and other applications. Peter Munro (also from UCL) substantially contributed to the development of the lab-based approach, by demonstrating that it imposes practically no coherence requirements<ref>{{cite journal | last1 = Munro | first1 = P. R. T. | last2 = Ignatyev | first2 = K. | last3 = Speller | first3 = R.D. | last4 = Olivo | first4 = A. | year = 2010 | title = Source size and temporal coherence requirements of coded aperture type x-ray phase contrast imaging systems | journal = Optics Express | volume = 18 | issue = 19| pages = 19681–19692 | doi = 10.1364/OE.18.019681 | pmid = 20940863 | pmc = 3000604 | bibcode = 2010OExpr..1819681M }}</ref> and that, this notwithstanding, it still is fully quantitative.<ref name=":1" />
The latest approach discussed here is the so-called grating-based imaging, which makes use of the [[Talbot effect]], discovered by [[Henry Fox Talbot]] in 1836.<ref name=Talbot1836>{{Cite journal | last1 = Talbot | first1 = H. F. | title = LXXVI.Facts relating to optical science. No. IV | doi = 10.1080/14786443608649032 | journal = Philosophical Magazine |series=Series 3 | volume = 9 | issue = 56 | pages = 401–407 | year = 1836 | url = https://zenodo.org/record/1431005 }}</ref> This self-imaging effect creates an interference pattern downstream of a [[diffraction grating]]. At a particular distance this pattern resembles exactly the structure of the grating and is recorded by a detector. The position of the interference pattern can be altered by bringing an object in the beam, that induces a phase shift. This displacement of the interference pattern is measured with the help of a second grating, and by certain reconstruction methods, information about the real part of the refractive index is gained. The so-called Talbot–Lau interferometer was initially used in [[Atom interferometer|atom interferometry]], for instance by [[John Clauser|John F. Clauser]] and Shifang Li in 1994.<ref name="Clauser1994">{{Cite journal | last1 = Clauser | first1 = J. | last2 = Li | first2 = S. | doi = 10.1103/PhysRevA.49.R2213 | title = Talbot-vonLau atom interferometry with cold slow potassium | journal = Physical Review A | volume = 49 | issue = 4 | pages = R2213–R2216 | year = 1994 | pmid = 9910609|bibcode = 1994PhRvA..49.2213C }}</ref> The first X-ray grating interferometers using synchrotron sources were developed by Christian David and colleagues from the [[Paul Scherrer Institute]] (PSI) in Villingen, Switzerland<ref name=David2002>{{Cite journal | last1 = David | first1 = C. | last2 = NöHammer | first2 = B. | last3 = Solak | first3 = H. H. | last4 = Ziegler | first4 = E. | title = Differential x-ray phase contrast imaging using a shearing interferometer | doi = 10.1063/1.1516611 | journal = Applied Physics Letters | volume = 81 | issue = 17 | pages = 3287–3289 | year = 2002 |bibcode = 2002ApPhL..81.3287D }}</ref> and the group of Atsushi Momose from the University of Tokyo.<ref name=Momose2003>{{Cite journal | last1 = Momose | first1 = A. | last2 = Kawamoto | first2 = S. | last3 = Koyama | first3 = I. | last4 = Hamaishi | first4 = Y. | last5 = Takai | first5 = K. | last6 = Suzuki | first6 = Y. | doi = 10.1143/JJAP.42.L866 | title = Demonstration of X-Ray Talbot Interferometry | journal = Japanese Journal of Applied Physics | volume = 42 | issue = 7B | pages = L866–L868 | year = 2003 |bibcode = 2003JaJAP..42L.866M }}</ref> In 2005, independently from each other, both David's and Momose's group incorporated computed tomography into grating interferometry, which can be seen as the next milestone in the development of grating-based imaging.<ref name=Weitkamp2005>{{Cite journal | last1 = Weitkamp | first1 = T. | last2 = Diaz | first2 = A. | last3 = David | first3 = C. | last4 = Pfeiffer | first4 = F. | last5 = Stampanoni | first5 = M. | last6 = Cloetens | first6 = P. | last7 = Ziegler | first7 = E. | doi = 10.1364/OPEX.13.006296 | title = X-ray phase imaging with a grating interferometer | journal = Optics Express | volume = 13 | issue = 16 | pages = 6296–6304 | year = 2005 | pmid = 19498642|bibcode = 2005OExpr..13.6296W | url = https://www.dora.lib4ri.ch/psi/islandora/object/psi%3A13289 | doi-access = free }}</ref><ref name=Momose2005JJAP>{{Cite journal | last1 = Momose | first1 = A. | title = Recent Advances in X-ray Phase Imaging | doi = 10.1143/JJAP.44.6355 | journal = Japanese Journal of Applied Physics | volume = 44 | issue = 9A | pages = 6355–6367 | year = 2005 |bibcode = 2005JaJAP..44.6355M | doi-access = free }}</ref>
In 2006, another great advancement was the transfer of the grating-based technique to [[X-ray tube|conventional laboratory X-ray tubes]] by [[Franz Pfeiffer (physicist)|Franz Pfeiffer]] and co-workers,<ref name=Pfeiffer2006>{{Cite journal | last1 = Pfeiffer | first1 = F. | last2 = Weitkamp | first2 = T. | last3 = Bunk | first3 = O. | last4 = David | first4 = C. | title = Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources | doi = 10.1038/nphys265 | journal = Nature Physics | volume = 2 | issue = 4 | pages = 258–261 | year = 2006 |bibcode = 2006NatPh...2..258P | url = https://www.dora.lib4ri.ch/psi/islandora/object/psi%3A16114 | doi-access = free }}</ref> which fairly enlarged the technique's potential for clinical use. About two years later the group of Franz Pfeiffer also accomplished to extract a supplementary signal from their experiments; the so-called "dark-field signal" was caused by scattering due to the porous microstructure of the sample and provided "complementary and otherwise inaccessible structural information about the specimen at the micrometer and submicrometer length scale".<ref name=Pfeiffer2008>{{Cite journal | last1 = Pfeiffer | first1 = F. | last2 = Bech | first2 = M. | last3 = Bunk | first3 = O. | last4 = Kraft | first4 = P. | last5 = Eikenberry | first5 = E. F. | last6 = Brönnimann | first6 = C. | last7 = Grünzweig | first7 = C. | last8 = David | first8 = C. | doi = 10.1038/nmat2096 | title = Hard-X-ray dark-field imaging using a grating interferometer | journal = Nature Materials | volume = 7 | issue = 2 | pages = 134–137 | year = 2008 | pmid = 18204454|bibcode = 2008NatMa...7..134P }}</ref> At the same time, Han Wen and co-workers at the US National Institutes of Health arrived at a much simplified grating technique to obtain the scattering (“dark-field”) image. They used a single projection of a grid and a new approach for signal extraction named "single-shot Fourier analysis".<ref name=Wen2008>{{cite journal|last=Wen|first=Han|author2=Eric E. Bennett |author3=Monica M. Hegedus |author4=Stefanie C. Caroll |title=Spatial Harmonic Imaging of X-ray Scattering—Initial Results|journal=IEEE Transactions on Medical Imaging|date=2008|volume=27|issue=8|pages=997–1002|doi=10.1109/TMI.2007.912393|pmid=18672418|pmc=2882966}}</ref> Recently, a lot of research was done to improve the grating-based technique: Han Wen and his team analyzed animal bones and found out that the intensity of the dark-field signal depends on the orientation of the grid and this is due to the anisotropy of the bone structure.<ref>{{Cite journal|last=Wen|first=Han|last2=Bennett|first2=Eric E.|last3=Hegedus|first3=Monica M.|last4=Rapacchi|first4=Stanislas|date=2009-06-01|title=Fourier X-ray Scattering Radiography Yields Bone Structural Information|journal=Radiology|volume=251|issue=3|pages=910–918|doi=10.1148/radiol.2521081903|issn=0033-8419|pmc=2687535|pmid=19403849}}</ref> They made significant progress towards biomedical applications by replacing mechanical scanning of the gratings with electronic scanning of the X-ray source.<ref name="Miao2013"/> The grating-based phase-contrast CT field was extended by tomographic images of the dark-field signal<ref name=Bech2010>{{Cite journal | last1 = Bech | first1 = M. | last2 = Bunk | first2 = O. | last3 = Donath | first3 = T. | last4 = Feidenhans'l | first4 = R. | last5 = David | first5 = C. | last6 = Pfeiffer | first6 = F. | doi = 10.1088/0031-9155/55/18/017 | title = Quantitative x-ray dark-field computed tomography | journal = Physics in Medicine and Biology | volume = 55 | issue = 18 | pages = 5529–5539 | year = 2010 | pmid = 20808030|bibcode = 2010PMB....55.5529B }}</ref> and time-resolved phase-contrast CT.<ref name=Momose2011>{{Cite journal | last1 = Momose | first1 = A. | last2 = Yashiro | first2 = W. | last3 = Harasse | first3 = S. B. | last4 = Kuwabara | first4 = H. | title = Four-dimensional X-ray phase tomography with Talbot interferometry and white synchrotron radiation: Dynamic observation of a living worm | doi = 10.1364/OE.19.008423 | journal = Optics Express | volume = 19 | issue = 9 | pages = 8423–8432 | year = 2011 | pmid = 21643093|bibcode = 2011OExpr..19.8423M | doi-access = free }}</ref> Furthermore, the first pre-clinical studies using grating-based phase-contrast X-ray imaging were published. Marco Stampanoni and his group examined native breast tissue with "differential phase-contrast mammography",<ref name=Stampanoni2011>{{Cite journal | last1 = Stampanoni | first1 = M. | last2 = Wang | first2 = Z. | last3 = Thüring | first3 = T. | last4 = David | first4 = C. | last5 = Roessl | first5 = E. | last6 = Trippel | first6 = M. | last7 = Kubik-Huch | first7 = R. A. | last8 = Singer | first8 = G. | last9 = Hohl | first9 = M. K. | doi = 10.1097/RLI.0b013e31822a585f | last10 = Hauser | first10 = N. | title = The First Analysis and Clinical Evaluation of Native Breast Tissue Using Differential Phase-Contrast Mammography | journal = Investigative Radiology | volume = 46 | issue = 12 | pages = 801–806 | year = 2011 | pmid = 21788904}}</ref> and a team led by Dan Stutman investigated how to use grating-based imaging for the small joints of the hand.<ref name=Stutman2011>{{Cite journal | last1 = Stutman | first1 = D. | last2 = Beck | first2 = T. J. | last3 = Carrino | first3 = J. A. | last4 = Bingham | first4 = C. O. | title = Talbot phase-contrast x-ray imaging for the small joints of the hand | doi = 10.1088/0031-9155/56/17/015 | journal = Physics in Medicine and Biology | volume = 56 | issue = 17 | pages = 5697–5720 | year = 2011 | pmid = 21841214| pmc =3166798 |bibcode = 2011PMB....56.5697S }}</ref>
Most recently, a significant advance in grating-based imaging occurred due to the discovery of a [[Moiré pattern|phase moiré effect]]<ref name=":8" /><ref name=":7" /> by Wen and colleagues. It led to interferometry beyond the Talbot self-imaging range, using only phase gratings and conventional sources and detectors. X-ray phase gratings can be made with very fine periods, thereby allowing imaging at low radiation doses to achieve high sensitivity.
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Recently developed configurations, using two crystals instead of one, enlarge the field of view considerably, but are even more sensitive to mechanical instabilities.<ref name=Momose2001b>{{Cite journal | last1 = Momose | first1 = A. | last2 = Takeda | first2 = T. | last3 = Yoneyama | first3 = A. | last4 = Koyama | first4 = I. | last5 = Itai | first5 = Y. | title = Wide-area phase-contrast X-ray imaging using large X-ray interferometers | doi = 10.1016/S0168-9002(01)00523-X | journal = Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment | volume = 467–468 | issue = 2002 | pages = 917–920 | year = 2001 |bibcode = 2001NIMPA.467..917M }}</ref><ref name=Yoneyama2006>{{Cite journal | last1 = Yoneyama | first1 = A. | last2 = Amino | first2 = N. | last3 = Mori | first3 = M. | last4 = Kudoh | first4 = M. | last5 = Takeda | first5 = T. | last6 = Hyodo | first6 = K. | last7 = Hirai | first7 = Y. | doi = 10.1143/JJAP.45.1864 | title = Non-invasive and Time-Resolved Observation of Tumors Implanted in Living Mice by Using Phase-Contrast X-ray Computed Tomography | journal = Japanese Journal of Applied Physics | volume = 45 | issue = 3A | pages = 1864–1868 | year = 2006 |bibcode = 2006JaJAP..45.1864Y }}</ref>
Another additional difficulty of the crystal interferometer is that the Laue crystals filter most of the incoming radiation, thus requiring a high beam intensity or very long exposure times.<ref name=Momose2003b>{{Cite journal | last1 = Momose | first1 = A. | title = Phase-sensitive imaging and phase tomography using X-ray interferometers | doi = 10.1364/OE.11.002303 | journal = Optics Express | volume = 11 | issue = 19 | pages = 2303–2314 | year = 2003 | pmid = 19471338|bibcode = 2003OExpr..11.2303M | doi-access = free }}</ref> That limits the use of the method to highly brilliant X-ray sources like synchrotrons.
According to the constraints on the setup the crystal interferometer works best for high-resolution imaging of small samples which cause small or smooth [[Gradient|phase gradients]].
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A high resolution detector is required to resolve the interference fringes, which practically limits the field of view of this technique or requires larger propagation distances. The achieved spatial resolution is relatively high in comparison to the other methods and, since there are no optical elements in the beam, is mainly limited by the degree of [[Coherence (physics)#Spatial coherence|spatial coherence]] of the beam.
As mentioned before, for the formation of the Fresnel fringes, the constraint on the [[coherence (physics)#Spatial coherence|spatial coherence]] of the used radiation is very strict, which limits the method to small or very distant sources, but in contrast to crystal interferometry and analyzer-based imaging the constraint on the [[coherence (physics)#Temporal coherence|temporal coherence]], i.e. the polychromaticity is quite relaxed.<ref name=Nesterets2008>{{Cite journal | last1 = Nesterets | first1 = Y. I. | last2 = Wilkins | first2 = S. W. | doi = 10.1364/OE.16.005849 | title = Phase-contrast imaging using a scanning-doublegrating configuration | journal = Optics Express | volume = 16 | issue = 8 | pages = 5849–5867 | year = 2008 | pmid = 18542696|bibcode = 2008OExpr..16.5849N | doi-access = free }}</ref> Consequently, the method cannot only be used with synchrotron sources but also with polycromatic laboratory X-ray sources providing sufficient spatial coherence, such as [[X-ray tube#Microfocus X-ray tubes|microfocus X-ray tubes]].<ref name=Wilkins1996/>
Generally spoken, the image contrast provided by this method is lower than of other methods discussed here, especially if the density variations in the sample are small. Due to its strength in enhancing the contrast at boundaries, it's well suited for imaging fiber or foam samples.<ref name=Cloetens1999b>{{Cite journal | last1 = Cloetens | first1 = P. | last2 = Ludwig | first2 = W. | last3 = Baruchel | first3 = J. | last4 = Guigay | first4 = J. P. | last5 = Pernot-Rejmánková | first5 = P. | last6 = Salomé-Pateyron | first6 = M. | last7 = Schlenker | first7 = M. | last8 = Buffière | first8 = J. Y. | last9 = Maire | first9 = E. | doi = 10.1088/0022-3727/32/10A/330 | last10 = Peix | first10 = G. | title = Hard x-ray phase imaging using simple propagation of a coherent synchrotron radiation beam | journal = Journal of Physics D: Applied Physics | volume = 32 | issue = 10A | pages = A145 | year = 1999 | bibcode = 1999JPhD...32A.145C }}</ref> A very important application of PBI is the examination of [[fossil]]s with synchrotron radiation, which reveals details about the [[Paleontology|paleontological]] specimens which would otherwise be inaccessible without destroying the sample.<ref name=tafforeau2006>{{Cite journal | last1 = Tafforeau | first1 = P. | last2 = Boistel | first2 = R. | last3 = Boller | first3 = E. | last4 = Bravin | first4 = A. | last5 = Brunet | first5 = M. | last6 = Chaimanee | first6 = Y. | last7 = Cloetens | first7 = P. | last8 = Feist | first8 = M. | last9 = Hoszowska | first9 = J. | last10 = Jaeger | doi = 10.1007/s00339-006-3507-2 | first10 = J. -J. | last11 = Kay | first11 = R. F. | last12 = Lazzari | first12 = V. | last13 = Marivaux | first13 = L. | last14 = Nel | first14 = A. | last15 = Nemoz | first15 = C. | last16 = Thibault | first16 = X. | last17 = Vignaud | first17 = P. | last18 = Zabler | first18 = S. | title = Applications of X-ray synchrotron microtomography for non-destructive 3D studies of paleontological specimens | journal = Applied Physics A | volume = 83 | issue = 2 | pages = 195–202 | year = 2006 |bibcode = 2006ApPhA..83..195T }}</ref>
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An alternative approach is the retrieval of the differential phase by using [[Moiré pattern|Moiré fringes]]. These are created as a superposition of the self-image of G1 and the pattern of G2 by using gratings with the same periodicity and inclining G2 against G1 regarding to the optical axis with a very small angle(<<1). This moiré fringes act as carrier fringes because they have a much larger spacing/period (smaller spatial frequency) than the Talbot fringes and thus the phase gradient introduced by the sample can be detected as the displacement of the Moiré fringes.<ref name=Momose2003/> With a Fourier analysis of the Moiré pattern the absorption and dark-field signal can also be extracted.<ref name=Bevins2012>{{Cite journal | last1 = Bevins | first1 = N. | last2 = Zambelli | first2 = J. | last3 = Li | first3 = K. | last4 = Qi | first4 = Z. | last5 = Chen | first5 = G. H. | title = Multicontrast x-ray computed tomography imaging using Talbot-Lau interferometry without phase stepping | doi = 10.1118/1.3672163 | journal = Medical Physics | volume = 39 | issue = 1 | pages = 424–428 | year = 2012 | pmid = 22225312| pmc =3261056 | bibcode = 2012MedPh..39..424B }}</ref>
Using this approach, the spatial resolution is lower than one achieved by the phase-stepping technique, but the total exposure time can be much shorter, because a differential phase image can be retrieved with only one Moiré pattern.<ref name=Momose2009>{{Cite journal | last1 = Momose | first1 = A. | last2 = Yashiro | first2 = W. | last3 = Maikusa | first3 = H. | last4 = Takeda | first4 = Y. | title = High-speed X-ray phase imaging and X-ray phase tomography with Talbot interferometer and white synchrotron radiation | doi = 10.1364/OE.17.012540 | journal = Optics Express | volume = 17 | issue = 15 | pages = 12540–12545 | year = 2009 | pmid = 19654656|bibcode = 2009OExpr..1712540M | doi-access = free }}</ref> Single-shot Fourier analysis technique was used in early grid-based scattering imaging<ref name="Wen2008" /> similar to the [[Shack–Hartmann wavefront sensor|shack-Hartmann wavefront sensor]] in optics, which allowed first live animal studies.<ref>{{Cite journal|last=Bennett|first=Eric E.|last2=Kopace|first2=Rael|last3=Stein|first3=Ashley F.|last4=Wen|first4=Han|date=2010-11-01|title=A grating-based single-shot x-ray phase contrast and diffraction method for in vivo imaging|journal=Medical Physics|volume=37|issue=11|pages=6047–6054|doi=10.1118/1.3501311|issn=0094-2405|pmc=2988836|pmid=21158316|bibcode=2010MedPh..37.6047B}}</ref>
[[File:EPS figure.jpg|thumb|left| Diagram of Electronic Phase Stepping (EPS). The source spot is moved electronically, which leads to movement of the sample image on the detector.]]
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The grating fabrication challenge was eased by the discovery of a [[Moiré pattern|phase moiré effect]]<ref name=":8" /> which provides an all-phase-grating interferometer that works with compact sources, called the '''polychromatic far-field interferometer''' (see figure on the right). Phase gratings are easier to make when compared with the source and analyzer gratings mentioned above, since the grating depth required to cause phase shift is much less than what is needed to absorb x-rays. Phase gratings of 200 - 400 nanometer periods have been used to improve phase sensitivity in table-top PFI imagers.<ref name=":7">{{Cite journal|last=Miao|first=Houxun|last2=Gomella|first2=Andrew A.|last3=Harmon|first3=Katherine J.|last4=Bennett|first4=Eric E.|last5=Chedid|first5=Nicholas|last6=Znati|first6=Sami|last7=Panna|first7=Alireza|last8=Foster|first8=Barbara A.|last9=Bhandarkar|first9=Priya|date=2015-08-28|title=Enhancing Tabletop X-Ray Phase Contrast Imaging with Nano-Fabrication|journal=Scientific Reports|language=en|volume=5|doi=10.1038/srep13581|issn=2045-2322|pmc=4551996|pmid=26315891|page=13581|bibcode=2015NatSR...513581M}}</ref> In PFI a phase grating is used to convert the fine interference fringes into a broad intensity pattern at a distal plane, based on the [[Moiré pattern|phase moiré effect]]. Besides higher sensitivity, another incentive for smaller grating periods is that the lateral coherence of the source needs to be at least one grating period.
A disadvantage of the standard GBI setup is the sensitivity to only one component of the phase gradient, which is the direction parallel to the 1-D gratings. This problem has been solved either by recording differential phase contrast images of the sample in both direction x and y by turning the sample (or the gratings) by 90°<ref name=Kottler2007>{{Cite journal | last1 = Kottler | first1 = C. | last2 = David | first2 = C. | last3 = Pfeiffer | first3 = F. | last4 = Bunk | first4 = O. | title = A two-directional approach for grating based differential phase contrast imaging using hard x-rays | doi = 10.1364/OE.15.001175 | journal = Optics Express | volume = 15 | issue = 3 | pages = 1175–1181 | year = 2007 | pmid = 19532346|bibcode = 2007OExpr..15.1175K | url = https://www.dora.lib4ri.ch/psi/islandora/object/psi%3A18138 | doi-access = free }}</ref> or by the employment of two-dimensional gratings.<ref name=Zanette2010>{{Cite journal | last1 = Zanette | first1 = I. | last2 = Weitkamp | first2 = T. | last3 = Donath | first3 = T. | last4 = Rutishauser | first4 = S. | last5 = David | first5 = C. | title = Two-Dimensional X-Ray Grating Interferometer | doi = 10.1103/PhysRevLett.105.248102 | journal = Physical Review Letters | volume = 105 | issue = 24 | year = 2010 | pages = 248102| pmid = 21231558|bibcode = 2010PhRvL.105x8102Z | url = https://www.dora.lib4ri.ch/psi/islandora/object/psi%3A16031 }}</ref>
Being a differential phase technique, GBI is not as sensitive as crystal interferometry to low spatial frequencies, but because of the high resistance of the method against mechanical instabilities, the possibility of using detectors with large pixels and a large field of view and, of crucial importance, the applicability to conventional laboratory X-ray tubes, grating-based imaging is a very promising technique for medical diagnostics and soft tissue imaging.
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