Phase-contrast X-ray imaging: Difference between revisions

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>

The first to discover [[X-rays]] was [[Wilhelm Conrad Röntgen]] in 1895, whichwhere is the reason why they are even today sometimes referred to as "Röntgen rays". Hehe found out that the "new kind of rays"they had the ability to penetrate materials opaque formaterials. [[light|visible light]], and he thusHe recorded the first X-ray image, displaying the hand of his wife.<ref name=Roentgen1895>{{Cite journal | doi = 10.1038/053274b0 | last1 = Roentgen | first1 = W. C.| title = On a New Kind of Rays | journal = Nature | volume = 53 | issue = 1369 | pages = 274–276 | year = 1896 |bibcode = 1896Natur..53R.274. | doi-access = free }}</ref> He was awarded the first [[Nobel Prize in Physics]] in 1901 "in recognition of the extraordinary services he has rendered by the discovery of the remarkable rays subsequently named after him".<ref name=Nobel>{{cite web|title=The Nobel Prize in Physics 1901|url=https://www.nobelprize.org/nobel_prizes/physics/laureates/1901/|publisher=Nobelprize.org|access-date=11 January 2013}}</ref> Since then, X-rays werehave been used as an invaluablea tool to non-destructivelysafely determine the inner structurestructures of different objects, although the information was for a long time obtained by measuring the transmitted intensity of the waves only, and the phase information was not accessible.

The principle of [[phase-contrast imaging]] inwas general wasfirst developed by [[Frits Zernike]] during his work with [[diffraction grating]]s and visible light.<ref name="zernike1942">{{Cite journal | last1 = Zernike | first1 = F. | title = Phase contrast, a new method for the microscopic observation of transparent objects | doi = 10.1016/S0031-8914(42)80035-X | journal = Physica | volume = 9 | issue = 7 | pages = 686–698 | year = 1942 | bibcode=1942Phy.....9..686Z}}</ref><ref name="Zernike1955">{{Cite journal | last1 = Zernike | first1 = F. | title = How I Discovered Phase Contrast | doi = 10.1126/science.121.3141.345 | journal = Science | volume = 121 | issue = 3141 | pages = 345–349 | year = 1955 | pmid = 13237991|bibcode = 1955Sci...121..345Z }}</ref> The application of his knowledge to microscopy won him the [[Nobel Prize]] in Physics in 1953. Ever since, [[phase-contrast microscopy]] has been an important field of [[optical microscopy]].

The transfer of phase-contrast imaging from visible light to X-rays took a long time, due to the slow progress in improving the quality of X-ray beams and the non-availabilityinaccessibility of X-ray optics (lenses). In the 1970s, it was realized that the [[synchrotron radiation]], emitted from charged particles circulating in storage rings constructed for high-energy nuclear physics experiments, wasmay potentiallyhave abeen mucha more intense and versatile source of X-rays than [[X-ray tube]]s.;<ref name=Als-Nielsen2011>{{cite book|last=Als-Nielsen|first=J.; McMorrow, D.|title=Elements of Modern X-ray Physics|date=2011|publisher=Wiley-VCH|isbn=978-0-470-97395-0}}</ref> The construction of [[synchrotron]]s and [[storage ring]]sthis, explicitlycombined aimed at the production of X-rays, and thewith progress in the development of optical elements for X-rays wereoptics, was fundamental for the further advancement of X-ray physics.

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'' ~ 10⁻⁴). 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"/>

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 | s2cid = 202632490 }}</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 | s2cid = 4287341 }}</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 | s2cid = 250885098 }}</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 | doi-access = free }}</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 | s2cid = 119658671 }}</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|last1=Wen|first1=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 | s2cid = 206011618 }}</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| s2cid = 30763084 }}</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>

where {{math|<var>&lambda;</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>&delta;(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.

where 0.02 is a constant given in [[Barn (unit)|barn]], the typical unit of particle interaction cross section area, {{math|<var>k</var>}} the length of the [[wave vector]], {{math|<var>k</var>₀}} the length of a wave vector with wavelength of 1 [[Angstrom]] and {{math|<var>Z</var>}} the [[atomic number]].<ref name=Bechthesis2009>{{cite web|last=Bech|first=M|title=X-ray imaging with a grating interferometer, Ph.D. Thesis, 2009|url=http://www.nbi.ku.dk/english/research/phd_theses/phd_theses_2009/martin_bech/ |archive-url=https://web.archive.org/web/20140717033239/http://www.nbi.ku.dk/english/research/phd_theses/phd_theses_2009/martin_bech/ |archive-date=2014-07-17 |publisher=Niels Bohr Institute, University of Copenhagen|access-date=11 January 2013}}</ref> The valid formula under these conditions for the phase shift cross section is:

where {{math|<var>Z</var>}} is the [[atomic number]], {{math|<var>k</var>}} the length of the [[wave vector]], and {{math|<var>r</var>₀}} the [[classical electron radius]].

Inserting typical values of human tissue in the formulas given above shows that {{math|<var>&delta;</var>}} is generally three orders of magnitude larger than {{math|<var>&beta;</var>}} within the diagnostic X-ray range. This implies that the phase-shift of an X-ray beam propagating through tissue may be much larger than the loss in intensity thus making phase contrast X-ray imaging more sensitive to density variations in the tissue than absorption imaging.<ref name=Lewis2004>{{cite journal|doi=10.1088/0031-9155/49/16/005|pmid = 15446788|title = Medical phase contrast x-ray imaging: Current status and future prospects|journal = Physics in Medicine and Biology|volume = 49|issue = 16|pages = 3573–83|year = 2004|last1 = Lewis|first1 = R A|bibcode = 2004PMB....49.3573L | s2cid=250758887 }}</ref>

A general limitation to the spatial resolution of this method is given by the blurring in the analyzer crystal which arises from dynamical refraction, i.e. the angular deviation of the beam due to the refraction in the sample is amplified about ten thousand times in the crystal, because the beam path within the crystal depends strongly on its incident angle. This effect can be reduced by thinning down the analyzer crystal, e.g. with an analyzer thickness of 40 {{math|&mu;}}m a resolution of about 6 {{math|&mu;}}m was calculated. Alternatively the [[Dynamical theory of diffraction|Laue crystals]] can be replaced by [[Dynamical theory of diffraction|Bragg crystals]], so the beam doesn´'t pass through the crystal but is reflected on the surface.<ref name=Koyama2003>{{Cite journal | last1 = Koyama | first1 = I. | last2 = Yoshikawa | first2 = H. | last3 = Momose | first3 = A. | title = Simulation study of phase-contrast X-ray imaging with a triple Laue-case and a triple Bragg-case interferometers | doi = 10.1051/jp4:20030144 | journal = Journal de Physique IV (Proceedings)| volume = 104 | issue = 2 | pages = 563–566 | year = 2003 |bibcode = 2003JPhy4.104..557H | url = http://jp4.journaldephysique.org/10.1051/jp4:20030144/pdf }}</ref>

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 | s2cid = 121354543 }}</ref>

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&nbsp;kVp will have a limiting resolution of 60&nbsp;µmμm.<ref name="Wen 2013"/> Another constraint is that the x-ray beam is slitted down to only tens of micrometers wide. A potential solution has been proposed in the form of parallel imaging with multiple slits.<ref name="Wen 2013"/>

'''Analyzer-based imaging (ABI)''' is also known as '''diffraction-enhanced imaging''', '''phase-dispersion Introscopy''' and '''multiple-image radiography'''<ref name=Wernick2003>{{Cite journal | last1 = Wernick | first1 = M. N. | last2 = Wirjadi | first2 = O. | last3 = Chapman | first3 = D. | last4 = Zhong | first4 = Z. | last5 = Galatsanos | first5 = N. P. | last6 = Yang | first6 = Y. | last7 = Brankov | first7 = J. G. | last8 = Oltulu | first8 = O. | last9 = Anastasio | first9 = M. A. | doi = 10.1088/0031-9155/48/23/006 | last10 = Muehleman | first10 = C. | title = Multiple-image radiography | journal = Physics in Medicine and Biology | volume = 48 | issue = 23 | pages = 3875–3895 | year = 2003 | pmid = 14703164|bibcode = 2003PMB....48.3875W | s2cid = 250749206 }}</ref> Its setup consists of a monochromator (usually a single or double crystal that also collimates the beam) in front of the sample and an analyzer crystal positioned in [[Dynamical theory of diffraction|Bragg geometry]] between the sample and the detector. (See figure to the right)

This analyzer crystal acts as an angular filter for the radiation coming from the sample. When these X-rays hit the analyzer crystal the condition of [[Bragg diffraction]] is satisfied only for a very narrow range of incident angles. When the scattered or refracted X-rays have incident angles outside this range they will not be reflected at all and don´'t contribute to the signal. Refracted X-rays within this range will be reflected depending on the incident angle. The dependency of the reflected intensity on the incident angle is called a rocking curve and is an intrinsic property of the imaging system, i.e. it represents the intensity measured at each pixel of the detector when the analyzer crystal is "rocked" (slightly rotated in angle θ) with no object present and thus can be easily measured.<ref name=Wernick2003/> The typical angular acceptance is from a few microradians to tens of microradians and is related to the [[FWHM|full width at half maximum (FWHM)]] of the rocking curve of the crystal.

For analyzer-based imaging , the stability requirements of the crystals is less strict than for crystal interferometry but the setup still requires a perfect analyzer crystal that needs to be very precisely controlled in angle and the size of the analyzer crystal and the constraint that the beam needs to be parallel also limits the field of view. Additionally as in crystal interferometry a general limitation for the spatial resolution of this method is given by the blurring in the analyzer crystal due to [[Dynamical theory of diffraction|dynamic diffraction effects]], but can be improved by using [[grazing incidence diffraction]] for the crystal.<ref name=Nesterets2008/>

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 (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/>

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 tubestube|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 | 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>

By performing measurements with and without sample the change in position of the interference pattern caused by the sample can be retrieved. The period of the interference pattern is usually in the range of a few [[micrometers]], which can only be conveniently resolved by a very high resolution detector in combination with a very intense illumination ( a source providing a very high flux) and hence limits the field of view significantly .<ref name=Takeda2007>{{Cite journal | last1 = Takeda | first1 = Y. | last2 = Yashiro | first2 = W. | last3 = Suzuki | first3 = Y. | last4 = Aoki | first4 = S. | last5 = Hattori | first5 = T. | last6 = Momose | first6 = A. | doi = 10.1143/JJAP.46.L89 | title = X-Ray Phase Imaging with Single Phase Grating | journal = Japanese Journal of Applied Physics | volume = 46 | issue = 3 | pages = L89–L91 | year = 2007 |bibcode = 2007JaJAP..46L..89T | s2cid = 119404810 }}</ref> This is the reason why a second grating, typically an absorption grating, is placed at a fractional Talbot length to analyze the interference pattern.<ref name=Momose2003/>

A technique to eliminate mechanical scanning of the grating and still retain the maximum spatial resolution is electronic phase stepping.<ref name="Miao2013">{{cite journal|last=Miao|first=Houxun|display-authors=4|author2=Lei Chen |author3=Eric E. Bennett |author4=Nick M. Adamo |author5=Andrew A. Gomella |author6=Alexa M. DeLuca |author7=Ajay Patel |author8=Nicole Y. Morgan |author9=Han Wen |title=Motionless phase stepping in X-ray phase contrast imaging with a compact source|journal=PNAS|date=2013|volume=110|issue=48|pages=19268–19272|doi=10.1073/pnas.1311053110|pmid=24218599|arxiv = 1307.2126 |bibcode = 2013PNAS..11019268M |pmc=3845166|doi-access=free}}</ref> It scans the source spot of the x-ray tube with an electro-magnetic field. This causes the projection of the object to move in the opposite direction, and also causes a relative movement between the projection and the Moiré fringes. The images are digitally shifted to realign the projections. The end result is that the projection of the object is stationary, while the Moiré fringes move over it. This technique effectively synthesizes the phase stepping process, but without the costs and delays associated with mechanical movements.

It has also been demonstrated that dark-field imaging with the grating interferometer can be used to extract orientational information of structural details in the sub-micrometer regime beyond the spatial resolution of the detection system. While the scattering of X-rays in a direction perpendicular to the grating lines provides the dark-field contrast, the scattering in a direction parallel to the grating lines only lead to blurring in the image, which is not visible at the low resolution of the detector.<ref name="Wen2008" /> This intrinsic physical property of the setup is utilized to extract orientational information about the angular variation of the local scattering power of the sample by rotating the sample around the optical axis of the set-up and collecting a set of several dark-field images, each measuring the component of the scattering perpendicular to the grating lines for that particular orientation. This can be used to determine the local angle and degree of orientation of bone and could yield valuable information for improving research and diagnostics of [[bone disease]]s like [[osteoporosis]] or [[osteoarthritis]].<ref name=Jensen2010>{{Cite journal | last1 = Jensen | first1 = T. H. | last2 = Bech | first2 = M. | last3 = Bunk | first3 = O. | last4 = Donath | first4 = T. | last5 = David | first5 = C. | last6 = Feidenhans'l | first6 = R. | last7 = Pfeiffer | first7 = F. | doi = 10.1088/0031-9155/55/12/004 | title = Directional x-ray dark-field imaging | journal = Physics in Medicine and Biology | volume = 55 | issue = 12 | pages = 3317–3323 | year = 2010 | pmid = 20484780|bibcode = 2010PMB....55.3317J | s2cid = 327836 }}</ref><ref name=Potdevin2012>{{Cite journal | last1 = Potdevin | first1 = G. | last2 = Malecki | first2 = A. | last3 = Biernath | first3 = T. | last4 = Bech | first4 = M. | last5 = Jensen | first5 = T. H. | last6 = Feidenhans'l | first6 = R. | last7 = Zanette | first7 = I. | last8 = Weitkamp | first8 = T. | last9 = Kenntner | first9 = J. | last10 = Mohr | doi = 10.1088/0031-9155/57/11/3451 | first10 = J. R. | last11 = Roschger | first11 = P. | last12 = Kerschnitzki | first12 = M. | last13 = Wagermaier | first13 = W. | last14 = Klaushofer | first14 = K. | last15 = Fratzl | first15 = P. | last16 = Pfeiffer | first16 = F. | title = X-ray vector radiography for bone micro-architecture diagnostics | journal = Physics in Medicine and Biology | volume = 57 | issue = 11 | pages = 3451–3461 | year = 2012 | pmid = 22581131|bibcode = 2012PMB....57.3451P | s2cid = 24346879 }}</ref>

For the Moiré pattern configuration the constraint on the radiation energy is a bit stricter, because a finite bandwidth of energy instead of monochromatic radiation causes a decrease in the visibility of the Moiré fringes and thus the image quality, but a moderate polychromaticity is still allowed.<ref name=Momose2006>{{Cite journal | last1 = Momose | first1 = A. | last2 = Yashiro | first2 = W. | last3 = Takeda | first3 = Y. | last4 = Suzuki | first4 = Y. | last5 = Hattori | first5 = T. | title = Phase Tomography by X-ray Talbot Interferometry for Biological Imaging | doi = 10.1143/JJAP.45.5254 | journal = Japanese Journal of Applied Physics | volume = 45 | issue = 6A | pages = 5254–5262 | year = 2006 |bibcode = 2006JaJAP..45.5254M | s2cid = 43298756 }}</ref> A great advantage of the usage of polychromatic radiation is the shortening of the exposure times and this has recently been exploited by using white synchrotron radiation to realize the first dynamic (time-resolved) Phase contrast tomography.<ref name= Momose2011/>

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, 100μm100&nbsp;μm focal spots are routinely used which are compatible with, for example, diagnostic mammography systems. Quantitative phase retrieval was also demonstrated with (uncollimated) incoherent sources, showing that in some cases results analogous to the synchrotron gold standard can be obtained.<ref name=":1" /> The relatively simple edge-illumination set-up results in phase sensitivity at least comparable with other phase contrast X-ray imaging techniques,<ref name=":2">{{cite journal | last1 = Marenzana | first1 = M. | last2 = Hagen | first2 = C. K. | last3 = Das NevesBorges | first3 = P. | last4 = Endrizzi | first4 = M. | last5 = Szafraniec | first5 = M. B. | last6 = Ignatyev | first6 = K. | last7 = Olivo | first7 = A. | year = 2012 | title = Visualization of small lesions in rat cartilage by means of laboratory-based x-ray phase contrast imaging | journal = Physics in Medicine and Biology | volume = 57 | issue = 24| pages = 8173–8184 | doi = 10.1088/0031-9155/57/24/8173 | pmid = 23174992 |bibcode = 2012PMB....57.8173M | doi-access = free }}</ref> results in a number of advantages, which include reduced exposure time for the same source power, reduced radiation dose, robustness against environmental vibrations, and easier access to high X-ray energy.<ref name=":2" /><ref name=":9">{{Cite journal|last1=Diemoz|first1=P. C.|last2=Hagen|first2=C. K.|last3=Endrizzi|first3=M.|last4=Minuti|first4=M.|last5=Bellazzini|first5=R.|last6=Urbani|first6=L.|last7=De Coppi|first7=P.|last8=Olivo|first8=A.|date=2017-04-28|title=Single-Shot X-Ray Phase-Contrast Computed Tomography with Nonmicrofocal Laboratory Sources|journal=Physical Review Applied|volume=7|issue=4|pages=044029|doi=10.1103/PhysRevApplied.7.044029|bibcode=2017PhRvP...7d4029D|doi-access=free}}</ref><ref>{{cite journal | last1 = Olivo | first1 = A. | last2 = Ignatyev | first2 = K. | last3 = Munro | first3 = P. R. T. | last4 = Speller | first4 = R. D. | year = 2011 | title = Non interferometric phase-contrast images obtained with incoherent x-ray sources | journal = Applied Optics | volume = 50 | issue = 12| pages = 1765–1769 | doi = 10.1364/AO.50.001765 | pmid = 21509069 |bibcode = 2011ApOpt..50.1765O }} (see also: Research Highlights, Nature 472 (2011) p. 382)</ref><ref>{{cite journal | last1 = Ignatyev | first1 = K. | last2 = Munro | first2 = P. R. T. | last3 = Chana | first3 = D. | last4 = Speller | first4 = R. D. | last5 = Olivo | first5 = A. | year = 2011 | title = Coded apertures allow high-energy x-ray phase contrast imaging with laboratory sources | journal = Journal of Applied Physics | volume = 110 | issue = 1| pages = 014906–014906–8 | doi = 10.1063/1.3605514 |bibcode = 2011JAP...110a4906I }}</ref> Moreover, since their aspect ratio is not particularly demanding, masks are cheap, easy to fabricate (e.g.do not require X-ray lithography) and can already be scaled to large areas. The method is easily extended to phase sensitivity in two directions, for example, through the realization of L-shaped apertures for the simultaneous illumination of two orthogonal edges in each detector pixel.<ref>{{cite journal | last1 = Olivo | first1 = A. | last2 = Bohndiek | first2 = S. E. | last3 = Griffiths | first3 = J. A. | last4 = Konstantinidis | first4 = K. | last5 = Speller | first5 = R. D. | year = 2009 | title = A non-free-space propagation x-ray phase contrast imaging method sensitive to phase effects in two directions simultaneously | journal = Applied Physics Letters | volume = 94 | issue = 4| page = 044108 | doi = 10.1063/1.3078410 |bibcode = 2009ApPhL..94d4108O }}</ref> More generally, while in its simplest implementation beamlets match individual pixel rows (or pixels), the method is highly flexible, and, for example, sparse detectors and asymmetric masks can be used<ref>{{cite journal | last1 = Olivo | first1 = A. | last2 = Pani | first2 = S. | last3 = Dreossi | first3 = D. | last4 = Montanari | first4 = F. | last5 = Bergamaschi | first5 = A. | last6 = Vallazza | first6 = E. Arfelli | last7 = Longo | display-authors = etal | year = 2003 | title = A Multilayer edge-on single photon counting silicon microstrip detector for innovative imaging techniques in diagnostic radiology | journal = Review of Scientific Instruments | volume = 74 | issue = 7| pages = 3460–3465 | doi = 10.1063/1.1582390 |bibcode = 2003RScI...74.3460O | url = https://www.openaccessrepository.it/record/138881 }}</ref> and compact<ref name=":10">{{Cite journal|last1=Havariyoun|first1=Glafkos|last2=Vittoria|first2=Fabio A|last3=Hagen|first3=Charlotte K|last4=Basta|first4=Dario|last5=Kallon|first5=Gibril K|last6=Endrizzi|first6=Marco|last7=Massimi|first7=Lorenzo|last8=Munro|first8=Peter|last9=Hawker|first9=Sam|last10=Smit|first10=Bennie|last11=Astolfo|first11=Alberto|date=2019-11-26|title=A compact system for intraoperative specimen imaging based on edge illumination x-ray phase contrast|journal=Physics in Medicine & Biology|volume=64|issue=23|pages=235005|doi=10.1088/1361-6560/ab4912|pmid=31569079|pmc=7655119|bibcode=2019PMB....64w5005H|issn=1361-6560|doi-access=free}}</ref> and microscopy<ref>{{Cite journal|last1=Endrizzi|first1=Marco|last2=Vittoria|first2=Fabio A.|last3=Diemoz|first3=Paul C.|last4=Lorenzo|first4=Rodolfo|last5=Speller|first5=Robert D.|last6=Wagner|first6=Ulrich H.|last7=Rau|first7=Christoph|last8=Robinson|first8=Ian K.|last9=Olivo|first9=Alessandro|date=2014-06-01|title=Phase-contrast microscopy at high x-ray energy with a laboratory setup|url=https://www.osapublishing.org/ol/abstract.cfm?uri=ol-39-11-3332|journal=Optics Letters|language=EN|volume=39|issue=11|pages=3332–3335|doi=10.1364/OL.39.003332|pmid=24876046|bibcode=2014OptL...39.3332E|issn=1539-4794}}</ref> systems can be built. So far, the method has been successfully demonstrated in areas such as security scanning,<ref>{{citeCite journal | last1 = IgnatyevPartridge | first1 = KT. | last2 = MunroAstolfo | first2 = P. R. TA. | last3 = ChanaShankar | first3 =S. DS. | last4 = SpellerVittoria | first4 = RF. DA. | last5 = OlivoEndrizzi | first5=M. |last6=Arridge A|first6=S. |last7=Riley-Smith year|first7=T. |last8=Haig 2011|first8=I. G. |last9=Bate title|first9=D. |last10=Olivo |first10=A. new|date=2022-09-09 |title=Enhanced generationdetection of threat materials by dark-field x-ray baggageimaging scannerscombined basedwith ondeep aneural different physical principlenetworks | journal =Nature MaterialsCommunications |language=en |volume = 413 | issue =1 10| pages = 1846–18604651 | doi = 10.33901038/ma4101846s41467-022-32402-0 | pmid issn= 288241122041-1723 | pmc = 54488719463187 |pmid=36085141|bibcode = 2011Mate2022NatCo..13..4.1846I | doi-access = free4651P }}</ref> biological imaging,<ref name=":2" /><ref name=":10" /> material science,<ref>{{cite journalbook | last1 = Endrizzi | first1 = M. | last2 = Diemoz | first2 = P. C. | last3 = Szafraniec | first3 = M. B. | last4 = Hagen | first4 = C. K. | last5 = Millard | first5 = P. T. | last6 = Zapata | first6 = C. E. | last7 = Munro | first7 = P. R. T. | last8 = Ignatyev | first8 = K. | chapter = Edge illumination and coded-aperture X-ray phase-contrast imaging: Increased sensitivity at synchrotrons and lab-based translations into medicine, biology and materials science | editor1-first = Robert M | editor1-last = Nishikawa | editor2-first = Bruce R | editor2-last = Whiting | display-authors = etal | year = 2013 | title = EdgeMedical illuminationImaging and coded-aperture x-ray phase-contrast imaging2013: increasedPhysics sensitivityof atMedical synchrotronsImaging and| labchapter-based translation into medicine, biology and materials science | url = http://discovery.ucl.ac.uk/1392354/| journal = Proceedings of SPIE | volume = 8668 | page = 866812 | doi = 10.1117/12.2007893 | series = Medical Imaging 2013: Physics of Medical Imaging | s2cid = 41898312 }}</ref> paleontology<ref name=":4">{{cite journal | last1 = Diemoz | first1 = P. C. | last2 = Endrizzi | first2 = M. | last3 = Zapata | first3 = C. E. | last4 = Bravin | first4 = A. | last5 = Speller | first5 = R. D. | last6 = Robinson | first6 = I.K. | last7 = Olivo | first7 = A. | year = 2013 | title = Improved sensitivity at synchrotrons using edge illumination x-ray phase contrast imaging | journal = Journal of Instrumentation | volume = 8 | issue = 6| page = C06002 | doi = 10.1088/1748-0221/8/06/C06002 |bibcode = 2013JInst...8C6002D | doi-access = free }}</ref><ref name=":5">{{cite journal | last1 = Olivo | first1 = A. | last2 = Diemoz | first2 = P. C. | last3 = Bravin | first3 = A. | year = 2012 | title = Amplification of the phase contrast signal at very high x-ray energies | journal = Optics Letters | volume = 37 | issue = 5| pages = 915–917 | doi = 10.1364/OL.37.000915 | pmid = 22378437 |bibcode = 2012OptL...37..915O }}</ref> and others; adaptation to 3D (computed tomography) was also demonstrated.<ref name=":4" /><ref>{{cite journal | last1 = Endrizzi | first1 = M. | last2 = Diemoz | first2 = P. C. | last3 = Munro | first3 = P. R. T. | last4 = Hagen | first4 = C. K. | last5 = Szafraniec | first5 = M. B. | last6 = Millard | first6 = P. T. | last7 = Zapata | first7 = C. E. | last8 = Speller | first8 = R. D. | display-authors = etal | year = 2013 | title = Applications of a non-interferometric x-ray phase contrast imaging method with both synchrotron and conventional sources | url =http://discovery.ucl.ac.uk/1395169/1/Endrizzi_JINST3013_revised.pdf | journal = Journal of Instrumentation | volume = 8 | issue = 5| page = C05008 | doi = 10.1088/1748-0221/8/05/C05008 |bibcode = 2013JInst...8C5008E | s2cid = 250674793 }}</ref> Alongside simple translation for use with conventional x-ray sources, there are substantial benefits in the implementation of edge-illumination with coherent synchrotron radiation, among which are high performance at very high X-ray energies<ref name=":5" /> and high angular resolutions.<ref name=":3">{{cite journal | last1 = Diemoz | first1 = P.C. | last2 = Endrizzi | first2 = M. | last3 = Zapata | first3 = C. E. | last4 = Pešić | first4 = Z. D. | last5 = Rau | first5 = C. | last6 = Bravin | first6 = A. | last7 = Robinson | first7 = I.K. | last8 = Olivo | first8 = A. | year = 2013 | title = X-ray phase-contrast imaging with nanoradian angular resolution | url = http://discovery.ucl.ac.uk/1392865/1/PhysRevLett.110.138105.pdf| journal = Physical Review Letters | volume = 110 | issue = 13| page = 138105 | doi = 10.1103/PhysRevLett.110.138105 | bibcode=2013PhRvL.110m8105D | pmid=23581380}}</ref>

[[File:Phase contrast benefit ratio.jpg|thumb|The benefit of phase contrast mammography relative to absorption contrast for (1) a tumor structure (“tumor”), (2) a glandular structure (“glandular”), (3) a microcalcification (“MC”), and (4) an air cavity (“air”) as a function of target size at optimal energy and equal dose.<ref name=":11">{{Cite journal|last1=Fredenberg|first1=Erik|last2=Danielsson|first2=Mats|last3=Stayman|first3=J. Webster|last4=Siewerdsen|first4=Jeffrey H.|last5=Åslund|first5=Magnus|date=2012-08-10|title=Ideal-observer detectability in photon-counting differential phase-contrast imaging using a linear-systems approach: Ideal-observer detectability in differential phase-contrast imaging|url= |journal=Medical Physics|language=en|volume=39|issue=9|pages=5317–5335|doi=10.1118/1.4739195|pmc=3427340|pmid=22957600|bibcode=2012MedPh..39.5317F }}</ref>]]

A quantitative comparison of phase- and absorption-contrast mammography that took realistic constraints into account (dose, geometry, and photon economy) concluded that grating-based phase-contrast imaging (Talbot interferometry) does not exhibit a general signal-difference-to-noise improvement relative to absorption contrast, but the performance is highly task dependent.<ref name=":11" /><ref name=":12">{{Cite book|last1=Fredenberg|first1=E.|last2=Roessl|first2=E.|last3=Koehler|first3=T.|last4=van Stevendaal|first4=U.|last5=Schulze-Wenck|first5=I.|last6=Wieberneit|first6=N.|last7=Stampanoni|first7=M.|last8=Wang|first8=Z.|last9=Kubik-Huch|first9=R. A.|last10=Hauser|first10=N.|last11=Lundqvist|first11=M.|title=Medical Imaging 2012: Physics of Medical Imaging|date=2012-02-23|editor-last=Pelc|editor-first=Norbert J.|editor2-last=Nishikawa|editor2-first=Robert M.|editor3-last=Whiting|editor3-first=Bruce R.|chapter=Photon-counting spectral phase-contrast mammography|volume=8313|chapter-url=http://proceedings.spiedigitallibrary.org/proceeding.aspx?doi=10.1117/12.910615|location=San Diego, California, USA|pages=155–166|doi=10.1117/12.910615|arxiv=2101.09660|s2cid=121130207}}</ref> TheSuch maina effectscomparison wereis foundyet to be undertaken for all phase contrast methods, however, the following considerations are central to such a comparison:

# Grating-basedDifferential phase contrast imaging (andmethods othersuch phase-contrastas, e.g., Analyser Based Imaging, Grating Based Imaging and Edge realizations)Illumination intrinsically detectsdetect 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.

# TalbotGrating-based interferometryimaging 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" />

#TalbotGrating-based interferometryimaging 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.

Phase-contrastFollowing imagingpreliminary, haslab-based beenstudies appliedin fore.g. computed tomography, <ref>{{Cite journal |lastlast1=Momose |firstfirst1=Atsushi |last2=Takeda |first2=Tohoru |last3=Itai |first3=Yuji |last4=Hirano |first4=Keiichi |date=April 1996 |title=Phase–contrast X–ray computed tomography for observing biological soft tissues |url=https://www.nature.com/articles/nm0496-473 |journal=Nature Medicine |language=en |volume=2 |issue=4 |pages=473–475 |doi=10.1038/nm0496-473 |issn=1546-170X |pmid=8597962 |s2cid=23523144}}</ref> and for mammography.,<ref>{{Cite journal |lastlast1=Arboleda |firstfirst1=Carolina |last2=Wang |first2=Zhentian |last3=Jefimovs |first3=Konstantins |last4=Koehler |first4=Thomas |last5=Van Stevendaal |first5=Udo |last6=Kuhn |first6=Norbert |last7=David |first7=Bernd |last8=Prevrhal |first8=Sven |last9=Lång |first9=Kristina |last10=Forte |first10=Serafino |last11=Kubik-Huch |first11=Rahel Antonia |date=2020-03-01 |title=Towards clinical grating-interferometry mammography |url=https://doi.org/10.1007/s00330-019-06362-x |journal=European Radiology |language=en |volume=30 |issue=3 |pages=1419–1425 |doi=10.1007/s00330-019-06362-x |issn=1432-1084 |pmc=7033145 |pmid=31440834}}</ref> phase contrast imaging is beginning to be applied in real medical applications, such as lung imaging,<ref>{{Cite journal |last1=Willer |first1=Konstantin |last2=Fingerle |first2=Alexander A |last3=Noichl |first3=Wolfgang |last4=De Marco |first4=Fabio |last5=Frank |first5=Manuela |last6=Urban |first6=Theresa |last7=Schick |first7=Rafael |last8=Gustschin |first8=Alex |last9=Gleich |first9=Bernhard |last10=Herzen |first10=Julia |last11=Koehler |first11=Thomas |last12=Yaroshenko |first12=Andre |last13=Pralow |first13=Thomas |last14=Zimmermann |first14=Gregor S |last15=Renger |first15=Bernhard |date=November 2021 |title=X-ray dark-field chest imaging for detection and quantification of emphysema in patients with chronic obstructive pulmonary disease: a diagnostic accuracy study |journal=The Lancet Digital Health |language=en |volume=3 |issue=11 |pages=e733–e744 |doi=10.1016/S2589-7500(21)00146-1 |pmc=8565798 |pmid=34711378}}</ref> imaging of extremities,<ref>{{Cite journal |last1=Yoshioka |first1=Hiroyuki |last2=Kadono |first2=Yuho |last3=Kim |first3=Yoon Taek |last4=Oda |first4=Hiromi |last5=Maruyama |first5=Takashi |last6=Akiyama |first6=Yuji |last7=Mimura |first7=Toshihide |last8=Tanaka |first8=Junji |last9=Niitsu |first9=Mamoru |last10=Hoshino |first10=Yoshihide |last11=Kiyohara |first11=Junko |last12=Nishino |first12=Satoshi |last13=Makifuchi |first13=Chiho |last14=Takahashi |first14=Atsushi |last15=Shinden |first15=Yuko |date=December 2020 |title=Imaging evaluation of the cartilage in rheumatoid arthritis patients with an x-ray phase imaging apparatus based on Talbot-Lau interferometry |journal=Scientific Reports |language=en |volume=10 |issue=1 |pages=6561 |doi=10.1038/s41598-020-63155-9 |issn=2045-2322 |pmc=7162962 |pmid=32300128|bibcode=2020NatSR..10.6561Y }}</ref> intra-operative specimen imaging.<ref>{{Cite journal |last1=Massimi |first1=Lorenzo |last2=Suaris |first2=Tamara |last3=Hagen |first3=Charlotte K. |last4=Endrizzi |first4=Marco |last5=Munro |first5=Peter R. T. |last6=Havariyoun |first6=Glafkos |last7=Hawker |first7=P. M. Sam |last8=Smit |first8=Bennie |last9=Astolfo |first9=Alberto |last10=Larkin |first10=Oliver J. |last11=Waltham |first11=Richard M. |last12=Shah |first12=Zoheb |last13=Duffy |first13=Stephen W. |last14=Nelan |first14=Rachel L. |last15=Peel |first15=Anthony |date=December 2021 |title=Detection of involved margins in breast specimens with X-ray phase-contrast computed tomography |journal=Scientific Reports |language=en |volume=11 |issue=1 |pages=3663 |doi=10.1038/s41598-021-83330-w |issn=2045-2322 |pmc=7878478 |pmid=33574584|bibcode=2021NatSR..11.3663M }}</ref> ''In vivo'' applications of phase contrast imaging have been kick-started by the pioneering mammography study with synchrotron radiation undertaken in Trieste, Italy.<ref>{{Cite journal |last1=Castelli |first1=Edoardo |last2=Tonutti |first2=Maura |last3=Arfelli |first3=Fulvia |last4=Longo |first4=Renata |last5=Quaia |first5=Emilio |last6=Rigon |first6=Luigi |last7=Sanabor |first7=Daniela |last8=Zanconati |first8=Fabrizio |last9=Dreossi |first9=Diego |last10=Abrami |first10=Alessando |last11=Quai |first11=Elisa |last12=Bregant |first12=Paola |last13=Casarin |first13=Katia |last14=Chenda |first14=Valentina |last15=Menk |first15=Ralf Hendrik |date=June 2011 |title=Mammography with Synchrotron Radiation: First Clinical Experience with Phase-Detection Technique |url=http://pubs.rsna.org/doi/10.1148/radiol.11100745 |journal=Radiology |language=en |volume=259 |issue=3 |pages=684–694 |doi=10.1148/radiol.11100745 |pmid=21436089 |issn=0033-8419}}</ref>