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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 EI 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}}</ref>). Although the set-up perhaps superficially resembles that of a grating interferometer, the underpinning physical mechanism is different. In contrast to other PCI techniques, EI 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 }}</ref> For example, 100μm 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 EI set-up results in phase sensitivity at least comparable with other PCI 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|url=https://link.aps.org/doi/10.1103/PhysRevApplied.7.044029|journal=Physical Review Applied|volume=7|issue=4|pages=044029|doi=10.1103/PhysRevApplied.7.044029|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 }}</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|url=https://iopscience.iop.org/article/10.1088/1361-6560/ab4912|journal=Physics in Medicine & Biology|volume=64|issue=23|pages=235005|doi=10.1088/1361-6560/ab4912|pmid=31569079|pmc=7655119|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|issn=1539-4794}}</ref> systems can be built. So far, the method has been successfully demonstrated in areas such as security scanning,<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 = A new generation of x-ray baggage scanners based on a different physical principle | journal = Materials | volume = 4 | issue = 10| pages = 1846–1860 | doi = 10.3390/ma4101846 | pmid = 28824112 | pmc = 5448871 |bibcode = 2011Mate....4.1846I }}</ref> biological imaging,<ref name=":2" /><ref name=":10" /> material science,<ref>{{cite journal | 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. | editor1-first = Robert M | editor1-last = Nishikawa | editor2-first = Bruce R | editor2-last = Whiting | display-authors = etal | year = 2013 | title = Edge illumination and coded-aperture x-ray phase-contrast imaging: increased sensitivity at synchrotrons and lab-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 }}</ref> Alongside simple translation for use with conventional x-ray sources, there are substantial benefits in the implementation of EI 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>
== Phase-contrast x-ray imaging in medicine ==
Four potential benefits of phase contrast have been identified in a medical imaging context:<ref name="Lewis2004" />
# Phase contrast bears promise to increase the signal-to-noise ratio because the phase shift in soft tissue is in many cases substantially larger than the absorption.
# Phase contrast has a different energy dependence than absorption contrast, which changes the conventional dose-contrast trade-off and higher photon energies may be optimal with a resulting lower dose (because of lower tissue absorption) and higher output from the x-ray tube (because of the option to use a higher acceleration voltage)
# Phase contrast is a different contrast mechanism that enhances other target properties than absorption contrast, which may be beneficial in some cases
# The dark-field signal provided by some phase-contrast realizations offers additional information on the small-angle scattering properties of the target.
[[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|last=Fredenberg|first=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=http://doi.wiley.com/10.1118/1.4739195|journal=Medical Physics|language=en|volume=39|issue=9|pages=5317–5335|doi=10.1118/1.4739195|pmc=PMC3427340|pmid=22957600}}</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" /> The main effects were found to be:
# The optimal imaging energy for phase contrast is higher than for absorption contrast and independent of target.
# Grating-based imaging (and other phase-contrast realizations) intrinsically detects 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.
# Talbot interferometry is relatively insensitive to spectrum bandwidth, but the source size must be kept small. The higher optimal energy in phase-contrast imaging compensates for some of the loss of flux when going to s smaller source size (because a higher acceleration voltage can be used for the x-ray tube), but photon economy remains to be an issue.
Some of the tradeoffs are illustrated in the right-hand figure, which shows the benefit of phase contrast over absorption contrast for detection of different targets of relevance in mammography as a function of target size.<ref name=":11" /> Note that these results do not include potential benefits from the dark-field signal.
==References==
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