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'''Phase-contrast X-ray imaging''' 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]]. However, in phase contrast X-ray imaging, 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| s2cid = 19137685 }}</ref>
In addition to producing [[Projectional radiography|projection images]], phase contrast X-ray imaging, 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'', phase contrast X-ray imaging 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 | hdl = 10281/345410 | hdl-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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==History==
The first to discover [[X-rays]] was [[Wilhelm Conrad Röntgen]] in 1895,
The principle of [[phase-contrast imaging]]
The transfer of phase-contrast imaging from visible light to X-rays took a long time, due to
The pioneer work to the implementation of the phase-contrast method to X-ray physics was presented in 1965 by Ulrich Bonse and Michael Hart, Department of Materials Science and Engineering of Cornell University, New York. They presented a crystal [[Interferometry|interferometer]], made from a large and highly perfect [[single crystal]].<ref name=Bonse>{{Cite journal | last1 = Bonse | first1 = U. | last2 = Hart | first2 = M. | doi = 10.1063/1.1754212 | title = An X-Ray Interferometer | journal = Applied Physics Letters | volume = 6 | issue = 8 | pages = 155–156 | year = 1965 |bibcode = 1965ApPhL...6..155B }}</ref> Not less than 30 years later the Japanese scientists [[Atsushi Momose]], Tohoru Takeda and co-workers adopted this idea and refined it for application in biological imaging, for instance by increasing the field of view with the assistance of new setup configurations and [[phase retrieval]] techniques.<ref name="Momose1995a">{{Cite journal | last1 = Momose | first1 = A. | last2 = Fukuda | first2 = J. | title = Phase-contrast radiographs of nonstained rat cerebellar specimen | doi = 10.1118/1.597472 | journal = Medical Physics | volume = 22 | issue = 4 | pages = 375–379 | year = 1995 | pmid = 7609717|bibcode = 1995MedPh..22..375M }}</ref><ref name="Momose1996">{{Cite journal | last1 = Momose | first1 = A. | last2 = Takeda | first2 = T. | last3 = Itai | first3 = Y. | last4 = Hirano | first4 = K. | title = Phase–contrast X–ray computed tomography for observing biological soft tissues | doi = 10.1038/nm0496-473 | journal = Nature Medicine | volume = 2 | issue = 4 | pages = 473–475 | year = 1996 | pmid = 8597962| s2cid = 23523144 }}</ref> The Bonse–Hart interferometer provides several orders of magnitude higher sensitivity in biological samples than other phase-contrast techniques, but it cannot use conventional X-ray tubes because the crystals only accept a very narrow energy band of X-rays (Δ''E''/''E'' ~ 10<sup>−4</sup>). In 2012, Han Wen and co-workers took a step forward by replacing the crystals with nanometric phase gratings.<ref name="Wen 2013">{{cite journal|last=Wen|first=Han|display-authors=4|author2=Andrew G. Gomella |author3=Ajay Patel |author4=Susanna K. Lynch |author5=Nicole Y. Morgan |author6=Stasia A. Anderson |author7=Eric E. Bennett |author8=Xianghui Xiao |author9=Chian Liu |author10=Douglas E. Wolfe |title=Subnanoradian X-ray phase-contrast imaging using a far-field interferometer of nanometric phase gratings|journal=Nat. Commun.|date=2013|volume=4|pages=2659|doi=10.1038/ncomms3659|pmid=24189696|pmc=3831282|bibcode = 2013NatCo...4.2659W }}</ref> The gratings split and direct X-rays over a broad spectrum, thus lifting the restriction on the bandwidth of the X-ray source. They detected sub nano[[radian]] refractive bending of X-rays in biological samples with a grating Bonse–Hart interferometer.<ref name="Wen 2013"/>
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:<math>\Phi (z)=\frac {2\pi}{\lambda} \int_0^z \! \delta (z') \, \mathrm{d} z'</math>,
where {{math|<var>λ</var>}} is the [[wavelength]] of the incident X-ray beam. This formula means that the phase shift is the projection of the decrement of the real part of the refractive index in imaging direction. This fulfills the requirement of the [[Tomographic reconstruction|tomographic principle]], which states that "the input data to the reconstruction algorithm should be a projection of a quantity ''f'' that conveys structural information inside a sample. Then, one can obtain a tomogram which maps the value ''f''."<ref name=Momose1998>{{cite journal|doi=10.1107/S0909049597014271|pmid = 15263497|title = Phase-Contrast Tomographic Imaging Using an X-ray Interferometer|journal = Journal of Synchrotron Radiation|volume = 5|issue = 3|pages = 309–314|year = 1998|last1 = Momose|first1 = Atsushi|last2 = Takeda|first2 = Tohoru|last3 = Itai|first3 = Yuji|last4 = Yoneyama|first4 = Akio|last5 = Hirano|first5 = Keiichi|doi-access = free| bibcode=1998JSynR...5..309M }}</ref> In other words, in phase-contrast imaging a map of the real part of the refraction index {{math|<var>δ(x,y,z)</var>}} can be reconstructed with standard techniques like [[filtered back projection]] which is analog to conventional [[X-ray computed tomography]] where a map of the imaginary part of the refraction index can be retrieved.
To get information about the compounding of a sample, basically the density distribution of the sample, one has to relate the measured values for the refractive index to intrinsic parameters of the sample, such a relation is given by the following formulas:
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The imaged object is placed near the central grating. Absolute phase images are obtained if the object intersects one of a pair of coherent paths. If the two paths both pass through the object at two locations which are separated by a lateral distance d, then a phase difference image of Φ(r) - Φ(r-d) is detected. Phase stepping one of the gratings is performed to retrieve the phase images. The phase difference image Φ(r) - Φ(r-d) can be integrated to obtain a phase shift image of the object.
This technique achieved substantially higher sensitivity than other techniques with the exception of the crystal interferometer.<ref name="Wen 2013"/><ref name=Yoneyama2004>{{cite journal|last=Yoneyama|first=Akio|display-authors=4|author2=Tohoru Takeda|author3=Yoshinori Tsuchiya|author4=Jin Wu|author5=Thet-Thet-Lwin|author6=Aritaka Koizumi|author7=Kazuyuki Hyodo|author8=Yuji Itai|title=A phase-contrast X-ray imaging system—with a 60×30 mm field of view—based on a skew-symmetric two-crystal X-ray interferometer|journal=Nucl. Instrum. Methods A|date=2004|volume=523|issue=1–2 |pages=217–222|doi=10.1016/j.nima.2003.12.008|bibcode = 2004NIMPA.523..217Y }}</ref> A basic limitation of the technique is the chromatic dispersion of grating diffraction, which limits its spatial resolution. A tabletop system with a tungsten-target x-ray tube running at 60 kVp will have a limiting resolution of 60
===Analyzer-based imaging===
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While the method in principle requires monochromatic, highly collimated radiation and hence is limited to a synchrotron radiation source, it was shown recently that the method remains feasible using a laboratory source with a polychromatic spectrum when the rocking curve is adapted to the K {{math|<var>α</var>}} spectral line radiation of the target material.<ref name=Muehleman2010>{{Cite journal | last1 = Muehleman | first1 = C. | last2 = Fogarty | first2 = D. | last3 = Reinhart | first3 = B. | last4 = Tzvetkov | first4 = T. | last5 = Li | first5 = J. | last6 = Nesch | first6 = I. | doi = 10.1002/ca.20993 | title = In-laboratory diffraction-enhanced X-ray imaging for articular cartilage | journal = Clinical Anatomy | volume = 23 | issue = 5 | pages = 530–538 | year = 2010 | pmid = 20544949| s2cid = 37556894 }}</ref>
Due to its high sensitivity to small changes in the refraction index this method is well suited to image soft tissue samples and is already implemented to medical imaging, especially in Mammography for a better detection of microcalcifications<ref name=Keyrilainen2010/> and in bone cartilage studies.<ref name=Mollenhauer2002>{{Cite journal | last1 = Mollenhauer | first1 = J. | last2 = Aurich | first2 = M. E. | last3 = Zhong | first3 = Z. | last4 = Muehleman | first4 = C. | last5 = Cole | first5 = A. A. | last6 = Hasnah | first6 = M. | last7 = Oltulu | first7 = O. | last8 = Kuettner | first8 = K. E. | last9 = Margulis | first9 = A. | last10 = Chapman | first10 = L. D. | title = Diffraction-enhanced X-ray imaging of articular cartilage | doi = 10.1053/joca.2001.0496 | journal = Osteoarthritis and Cartilage | volume = 10 | issue = 3 | pages = 163–171 | year = 2002 | pmid = 11869076| url = http://www.lib.ncsu.edu/resolver/1840.2/1943 | doi-access = free }}</ref>
===Propagation-based imaging===
[[File:Propagation-based imaging.PNG|thumb|right|Drawing of Propagation-based imaging]]
'''Propagation-based imaging (PBI)''' is the most common name for this technique but it is also called '''in-line holography''', '''refraction-enhanced imaging'''<ref name=Suzuki2002>{{Cite journal | last1 = Suzuki | first1 = Y. | last2 = Yagi | first2 = N. | last3 = Uesugi | first3 = K. | doi = 10.1107/S090904950200554X | title = X-ray refraction-enhanced imaging and a method for phase retrieval for a simple object | journal = Journal of Synchrotron Radiation | volume = 9 | issue = 3 | pages = 160–165 | year = 2002 | pmid = 11972371| doi-access = free }}</ref> or '''phase-contrast radiography'''. The latter denomination derives from the fact that the experimental setup of this method is basically the same as in conventional radiography. It consists of an in-line arrangement of an X-ray source, the sample and an X-ray detector and no other optical elements are required. The only difference is that the detector is not placed immediately behind the sample, but in some distance, so the radiation refracted by the sample can interfere with the unchanged beam.<ref name=Snigirev1995/>
This simple setup and the low stability requirements provides a big advantage of this method over other methods discussed here.
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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
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 | s2cid = 250738185 }}</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 | s2cid = 14254888 }}</ref>
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If the X-ray beam is vertically thin and impinges on the edge of the detector, X-ray refraction can change the status of the individual X-ray from "detected" to "undetected" and vice versa, effectively playing the same role as the crystal rocking curve in ABI. This analogy with ABI, already observed when the method was initially developed,<ref name=":0" /> was more recently formally demonstrated.<ref>{{cite journal | last1 = Munro | first1 = P. R. T. | last2 = Hagen | first2 = C. K. | last3 = Szafraniec | first3 = M. B. | last4 = Olivo | first4 = A. | year = 2013 | title = A simplified approach to quantitative coded aperture X-ray phase imaging | url =http://discovery.ucl.ac.uk/1392311/1/Peter_RC.pdf | journal = Optics Express | volume = 21 | issue = 9| pages = 11187–11201 | doi = 10.1364/OE.21.011187 | pmid = 23669976 | bibcode = 2013OExpr..2111187M | doi-access = free }}</ref> Effectively, the same effect is obtained – a fine angular selection on the photon direction; however, while in analyzer-based imaging the beam needs to be highly collimated and monochromatic, the absence of the crystal means that edge-illumination can be implemented with divergent and polychromatic beams, like those generated by a conventional rotating-anode X-ray tube. This is done by introducing two opportunely designed masks (sometimes referred to as “coded-aperture” masks<ref name=":6">{{cite journal | last1 = Olivo | first1 = A. | last2 = Speller | first2 = R. | year = 2007 | title = A coded-aperture technique allowing x-ray phase contrast imaging with conventional sources | url = http://discovery.ucl.ac.uk/9890/1/9890.pdf| journal = Applied Physics Letters | volume = 91 | issue = 7| page = 074106 | doi = 10.1063/1.2772193 |bibcode = 2007ApPhL..91g4106O }}</ref>), one immediately before the sample, and one in contact with the detector (see figure).[[File:Fig2forWikip.svg|thumb|right|Drawing of laboratory-based edge-illumination, obtained through (“coded”) aperture x-ray masks.]]
The purpose of the latter mask is simply to create insensitive regions between adjacent pixels, and its use can be avoided if specialized detector technology is employed. In this way, the edge-illumination configuration is simultaneously realized for all pixel rows of an area detector. This plurality of individual beamlets means that, in contrast to the synchrotron implementation discussed above, no sample scanning is required – the sample is placed downstream of the sample mask and imaged in a single shot (two if phase retrieval is performed<ref name=":1">{{cite journal | last1 = Munro | first1 = P. R. T. | last2 = Ignatyev | first2 = K. | last3 = Speller | first3 = R.D. | last4 = Olivo | first4 = A. | year = 2012 | title = Phase and absorption retrieval using incoherent x-ray sources | journal = Proceedings of the National Academy of Sciences of the United States of America | volume = 109 | issue = 35| pages = 13922–13927 | doi = 10.1073/pnas.1205396109 |bibcode = 2012PNAS..10913922M | pmid=22891301 | pmc=3435200| doi-access = free }}</ref>). Although the set-up perhaps superficially resembles that of a grating interferometer, the underpinning physical mechanism is different. In contrast to other phase contrast X-ray imaging techniques, edge-illumination is an incoherent technique, and was in fact proven to work with both spatially and temporally incoherent sources, without any additional source aperturing or collimation.<ref name=":1" /><ref>{{cite journal | last1 = Olivo | first1 = A. | last2 = Speller | first2 = R. | year = 2007 | title = Modelling of a novel x-ray phase contrast imaging technique based on coded apertures | journal = Physics in Medicine and Biology | volume = 52 | issue = 22| pages = 6555–6573 | doi = 10.1088/0031-9155/52/22/001 | pmid = 17975283 |bibcode = 2007PMB....52.6555O | s2cid = 19911974 }}</ref> For example,
== Phase-contrast x-ray imaging in medicine ==
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# Differential phase contrast imaging methods such as, e.g., Analyser Based Imaging, Grating Based Imaging and Edge Illumination intrinsically detect the phase differential, which causes the noise-power spectrum to decrease rapidly with spatial frequency so that phase contrast is beneficial for small and sharp targets, e.g., tumor spicula rather than solid tumors, and for discrimination tasks rather than for detection tasks.
# Phase contrast favors detection of materials that differ in density compared to the background tissue, rather than materials with differences in atomic number. For instance, the improvement for detection / discrimination of calcified structures is less than the improvement for soft tissue.
# Grating-based imaging is relatively insensitive to spectrum bandwidth. It should also be noted, however, that other techniques such as propagation-based imaging and edge-illumination are even more insensitive, to the extent that they can be considered practically achromatic.<ref>{{Cite journal |last1=Endrizzi |first1=Marco |last2=Vittoria |first2=Fabio A. |last3=Kallon |first3=Gibril |last4=Basta |first4=Dario |last5=Diemoz |first5=Paul C. |last6=Vincenzi |first6=Alessandro |last7=Delogu |first7=Pasquale |last8=Bellazzini |first8=Ronaldo |last9=Olivo |first9=Alessandro |date=2015-06-15 |title=Achromatic approach to phase-based multi-modal imaging with conventional X-ray sources |url=https://opg.optica.org/abstract.cfm?URI=oe-23-12-16473 |journal=Optics Express |language=en |volume=23 |issue=12 |pages=16473–16480 |doi=10.1364/OE.23.016473 |pmid=26193618 |bibcode=2015OExpr..2316473E |issn=1094-4087|doi-access=free }}</ref><ref name="Wilkins1996" /> In addition, if phase-contrast imaging is combined with an energy sensitive photon-counting detector, the detected spectrum can be weighted for optimal detection performance.<ref name=":12" />
#Grating-based imaging is sensitive to the source size, which must be kept small; indeed, a "source" grating must be used to enable its implementation with low-brilliance x-ray sources.<ref name="Pfeiffer2006" /> Similar considerations apply to propagation-based imaging and other approaches. The higher optimal energy in phase-contrast imaging compensates for some of the loss of flux when going to a smaller source size (because a higher acceleration voltage can be used for the x-ray tube), but photon economy remains to be an issue. It should be noted, however, that edge illumination was proven to work with source sizes of up to 100 micron,<ref name=":6" /> compatible with some existing mammography sources, without a source grating.
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