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X-ray phase contrast imaging at the Mainz microtron MAMI [Elektronische Ressource] / vorgelegt von Mahmoud el Ghazaly

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X-RAY PHASE CONTRAST IMAGINGAT THEMAINZ MICROTRON MAMIDissertationzur Erlangung des Grades"Doktor der Naturwissenschaften"am Fachbereich Physikder Johannes Gutenberg{Universit˜atMainzVorgelegt vonMahmoud El Ghazaly˜geboren in AgyptenMainz, im Oktober 2005Tag der Mundlic˜ hen Prufung:˜ Mittwoch 7-12-2005AbstractExperiments have been performed to explore the potential of the low emittance 855MeV electron beam of the Mainz Microtron MAMI for imaging with coherent X-rays.Transition radiation from a micro-focused electron beam traversing a foil stack servedas X-ray source with good transverse coherence.In a flrst series of experiments a polychromatic transition radiation X-ray source withtypical photon energies in the range of 8-30 keV and a spot size of standard deviation? = (8:6§0:1) „m in horizontal and ? = (7:5§0:1) „m in vertical direction wash vused to record refraction contrast radiographs of low absorbing materials, in particularpolymer strings with diameters between 30 and 450 „m. As detectors X-ray fllmswere used. The source-to-detector distance amounted to 13 m. The edge enhancementcontrast C = (I ¡ I )=(I + I ) was investigated as a function of theref max min max mindistance between the object and the X-ray fllm which was varied between 0.5 and 5.5m. The measured contrast C of up to 20% can well be explained in the frameworkrefof a geometrical and a wave optical model.Inasecondseriesofexperimentshologramsofstringsweretakenwithabeamspotsize?

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Published 01 January 2005
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YX-RA

CONTRASTPHASE

THETA

GINGIMA

MAINZMAMIONOTRMICR

DissertationGradesdesErlangungzurhaften”Naturwissenscder”DoktoramFachbereichPhysik
derJohannesGutenberg–Universit¨at
Mainz

der

onvorgelegtVMahmoudGhazalyEl¨Agypteninorengeb

Mainz,

im

erOktob

2005

agT

der

undlic¨Mhen

ufung:¨Pr

owMitt

hc

7-12-2005

Abstract

Experimentshavebeenperformedtoexplorethepotentialofthelowemittance855
MeVelectronbeamoftheMainzMicrotronMAMIforimagingwithcoherentX-rays.
Transitionradiationfromamicro-focusedelectronbeamtraversingafoilstackserved
asX-raysourcewithgoodtransversecoherence.
InafirstseriesofexperimentsapolychromatictransitionradiationX-raysourcewith
typicalphotonenergiesintherangeof8-30keVandaspotsizeofstandarddeviation
σh=(8.6±0.1)µminhorizontalandσv=(7.5±0.1)µminverticaldirectionwas
usedtorecordrefractioncontrastradiographsoflowabsorbingmaterials,inparticular
polymerstringswithdiametersbetween30and450µm.AsdetectorsX-rayfilms
wereused.Thesource-to-detectordistanceamountedto13m.Theedgeenhancement
contrastCref=(Imax−Imin)/(Imax+Imin)wasinvestigatedasafunctionofthe
distancebetweentheobjectandtheX-rayfilmwhichwasvariedbetween0.5and5.5
m.ThemeasuredcontrastCrefofupto20%canwellbeexplainedintheframework
ofageometricalandawaveopticalmodel.
Inasecondseriesofexperimentshologramsofstringsweretakenwithabeamspotsize
σv=(0.50±0.05)µmandamonochromaticX-raybeamof6keVenergy.Thegood
longitudinalcoherencehasbeenobtainedbythe(111)reflectionofaflatsiliconsingle
crystalinBragggeometry.IthasbeendemonstratedthatadirectexposureCCDchip
withapixelsizeof13×13µm2providesahighlyefficienton-linedetector.Contrast
imagescaneasilybegeneratedwithacompleteeliminationofallparasiticbackground.
Theon-linecapabilityallowsaminimizationofthebeamspotsizebyobservingthe
smallestvisibleinterferencefringespacingsorthenumberofvisiblefringes.
InathirdseriesofexperimentsitwasdemonstratedthatX-rayfilmsareveryuseful
detectorsforthemicro-focusedandmonochromizedtransitionradiationX-raysource
atMAMI.ThemainadvantageincomparisonwiththedirectexposureCCDchipis
theresolution.FortheX-rayfilmStructurixD3(Agfa)thestandarddeviationof
theresolutionwasmeasuredtobeσf=(1.2±0.4)µm,whichisaboutafactorof6
betterasforthedirectexposureCCDchip.WiththesmalleffectiveX-rayspotsizein
verticaldirectionofσv=(1.4±0.5)µmandageometricalmagnificationofupto7.24
highqualityhologramsoftinytransparentandopaquestringsweretakeninwhichthe
holographicinformationiscontainedinupto18interferencefringes.
X-rayradiographyusingcoherentX-raysenhancesalsothevisibilityofhighlyabsorbing
materialsviadiffractionatedges.Thiswasdemonstratedwithtungstenwiresofvarious
thicknessesbetween4and40µmdiameter.Incombinationwithahighgeometrical
magnificationthiseffectallowstheobservationofsmallhighlyabsorbingfeatureswith
micrometersizeintheinvestigatedobject.

ZusammenfassungAmMainzerMikrotronMAMIwurdenExperimentedurchgef¨uhrt,umdasPotentialdes
855MeVElektronenstrahlesniedrigerEmittanzf¨urdieBildgebungmitkoh¨arenterR¨ont-
genstrahlungzuuntersuchen.AlsStrahlungsquellemitgutertransversalerKoh¨arenzdiente
¨Ubergangsstrahlung,dievoneinemmikro-fokussiertenElektronenstrahlineinemFolienstapel
wurde.erzeugtIneinererstenExperimentseriewurdenmitpolychromatischer¨Ubergangsstrahlungeiner
PhotonenenergieimBereichzwischen8-30keVPhasenkontrastradiographienvonschwach
absorbierendenMaterialien-insbesonderePolymerf¨adenmitDurchmessernzwischen30und
450µm-aufgenommen.DieStrahlfleckgr¨oßeninhorizontalerundvertikalerRichtungbetru-
genσh=(8.6±0.1)µmbzw.σv=(7.5±0.1)µm(Standardabweichungen).AlsDetektoren
wurdenR¨ontgenfilmeverwendet.DerAbstandzwischenQuelleundDetektorbetrug13m.
DerPhasenkontrastanKantenvonPolymerf¨adenCref=(Imax−Imin)/(Imax+Imin)wurde
alsFunktiondesAbstandszumDetektoruntersucht,derzwischen0.05und5.5mvariierte.
DergemessenKontrastCrefvonbiszu20%kannsowohlimRahmeneineswellenoptischen
ModellsalsaucheinesModellsaufderBasisdergeometrischenOptikgutbeschriebenwerden.
IneinerzweitenExperimentseriewurdenHologrammevonPolymerf¨adenbeieinerPho-
tonenenergievon6keVaufgenommen,wobeidieStrahlfleckgr¨oßeσv=(0.50±0.05)µmbe-
trug.DienotwendigelongitudinaleKoh¨arenzwurdemitHilfedes(111)-Bragg-Reflexeseines
ebenenSilizium-Einkristallserreicht.Eskonntegezeigtwerden,dasseinoffenerCCD-Chip
miteinerPixelgr¨oßevon13×13µm2alsortsaufl¨osenderR¨ontgendetektorgutgeeignetist.
Mitihmk¨onnenrelativeinfachKontrastbildererzeugtwerden,beidenenjeglicherparasit¨arer
UntergrunddurchSubtraktioneinesBildesohneObjekteliminiertwird.DerEchtzeiteinsatz
diesesDetektorserlaubt¨uberdieBeurteilungderholographischenInterferenzstrukturendie
MinimierungderStrahlfleckgr¨oßederR¨ontgenquelle.
IneinerdrittenExperimentseriekonntegezeigtwerden,dassR¨ontgenfilmegutgeeignete
ortsaufl¨osendeDetektorenf¨urdieAufnahmevonHologrammenmitdermikrofokussierten,
monochromatisierten¨UbergangsstrahlungsquelleanMAMIsind.DerHauptvorteilimVer-
gleichzumoffenenCCD-ChipliegtinseinerdeutlichbesserenAufl¨osung.F¨urdenR¨ontgenfilm
StructurixD3(Agfa)wurdeeineAufl¨osungσf=(1.2±0.4)µm(Standardabweichung)
gemessen,wasimVergleichzumCCD-ChipumeinenFaktor6besserist.Mitderkleinen
effektivenStrahlfleckgr¨oßedesR¨ontgenstrahlesinvertikalerRichtungvonσv=(1.4±0.5)µm
undeinergeometrischenVergr¨oßerungvon7.24konntenqualitativhochwertigeHologramme
vonsehrkleinentransparentensowievollst¨andigabsorbierendenF¨adenaufgenommenwerden.
DieholographischeInformationistdabeiinbiszu18Interferenzringenenthalten.
Schließlichkonntegezeigtwerden,dassdieRadiographiemitkoh¨arentenR¨ontgenstrahlen
auchdieSichtbarkeitvonstarkabsorbierendenMaterialieninfolgederBeugungandenBe-
grenzungenerh¨oht.DieswurdeanhandvonWolframdr¨ahtenmitDurchmessernzwischen4
und40µmdemonstriert.BeihohergeometrischerVergr¨oßerungk¨onnen¨uberdiesenEffekt
starkabsorbierendeStrukturenmitGr¨oßenimMikrometerbereichineinemzuuntersuchen-
denObjektsichtbargemachtwerden.

Contents

1

2

3

4

5

ductionIntro

PrinciplesofX-rayphasecontrastimaging
2.1Complexrefractionindex..........................
2.2Refractioncontrastradiography......................
2.2.1Principles..............................
2.2.2Principleoftheexperimentalsetup................
2.3ImagingwithacoherentX-raybeam...................
2.3.1Coherence..............................
2.3.2Coherenceandvisibility......................

ThetransitionradiationX-raysource
3.1TheMainzMicrotronfacility(MAMI)..................
3.2Transitionradiation.............................
3.3Bremsstrahlung...............................

radiographycontrastRefraction4.1Basicbackground..............................
4.1.1Contactregion...........................
4.1.2Smalldistancebetweenobjectanddetector-phasecontrast..
4.1.3Refractioncontrastinthepictureofgeometricaloptics.....
4.2Experimental................................
4.2.1Set-up................................
4.2.2X-rayfilm..............................
4.3Measurements................................
4.4Determinationofthenormalizedcontrast.................
4.5Results....................................
4.6Discussion..................................
4.7Furtherexamples..............................
4.8Concludingremarks.............................

TowardshardX-rayin-lineholography
5.1BasicBackground..............................
5.2Experimentalset-upandtestmeasurements...............
5.2.1Principleoftheexperimentandoverview.............

1

446789911

14141619

2424242627292930323538404648

51515252

I

tstenCon5.2.2Theelectronbeamline.......................54
5.2.3Targetsetup.............................55
5.2.3.1Electronbeamdiagnostics................56
5.2.3.2Transitionradiationfoilstacks.............58
5.2.4Singlecrystalmonochromator...................60
5.2.5Detectorcarriage..........................60
5.3Charge-coupleddevice(CCD)asX-raydetector.............61
5.3.1Descriptionoftheback-illuminatedCCDchip..........61
5.3.2Electronicsanddataacquisition..................63
5.3.3Thedirectexposuremode.....................64
5.3.4X-rayimagingwithaluminescentscreen.............67
5.4Investigationofthefeaturesofthemonochromizedphotonbeam....70
5.4.1Energywidthandlongitudinalcoherencelength.........70
5.4.2Higherorderreflexes........................72
5.4.3Transversecoherencelengthsinhorizontalandverticaldirection74
5.4.4Streaks................................77
5.5HardX-rayin-lineholographywiththedirectexposureCCDchip...81
5.5.1Optimizationofthebeamspotsizeandmeasurements.....81
5.5.2Analysis...............................84
5.5.3Resultsanddiscussion.......................88
5.5.3.1Hologramsofhighlyabsorbingobjects.........88
5.5.3.2Hologramsoftransparentobjects............93
5.5.4Applications............................96
5.6HardX-rayin-lineholographywithhighresolutionX-rayfilms.....98
5.6.1CharacterizationoftheX-rayfilm.................99
5.6.1.1Photographicdensity...................99
5.6.1.2Spatialresolution.....................100
5.6.2X-raysourcesizedeterminationfromX-rayholograms.....105
5.6.3Resultsanddiscussions.......................106
5.6.3.1Hologramsfortransparentobjects...........106
5.6.3.2Hologramsforopaqueobjects..............111
5.7Concludingremarks.............................115
119okOutlo6ARefractionanddiffractionofX-raysbyacylindricalstring121
A.1Refractionintheapproximationofgeometricaloptics..........121
A.2DiffractionintheFresnelapproximationofwaveoptics.........124
BFurtherresultsofrefractioncontrastradiography129
CX-rayimagingwithaGdOS:Tbluminescencescreen134
22C.1Experimentalset-up............................134
C.2TestoftheX-rayimagingsystemandmeasurements..........135
C.2.1Off-linetests.............................135
C.2.2On-linemeasurementswithpolychromaticX-rays........136
II

D

withtsmeasuremenOn-lineC.2.3C.3Conclusions............

Derivation

of

Eq.

(5.11)

hromaticcmono.........

ysX-ra....

.

..

..

..

..

tstenCon

..

..

..

140141

142

III

Contsten

IV

ductionIntro1

X-rayimaginghasbeenbegunover100yearsago,whenWilhelmKonradR¨ontgen
discoveredX-raysintheyear1895[R¨o96].Someoftheintrinsicadvantagesovercon-
ventionalimagingtechniques,suchaslightandelectronmicroscopy,isthepenetration
depthofX-rayphotons.Amongothersthispropertyallows,withtheso-callednon-
destructivetesting,theobservationofthickspecimensinitsnaturalenvironment.X-
rayimagingbecamerapidlyanimportantdiagnostictoolinmedicine,materialscience,
biologyandenvironmentalresearch[Ari94,Mon04].
ThecontrastinconventionalabsorptionX-rayimagingisbasedonthedifferencein
theabsorptionofdifferentmaterialsconstitutingthesample.Thinsamplesoflight
elements(Z<16),suchassofttissuesandorganicmaterials,showaweakabsorption
contrastevenatlowX-rayenergies,i.e.,thebigdeficiencyisthattheconventional
absorptionradiographycannotdistinguishbetweenmaterialswithsimilarattenuation
coefficients[Lui05].Inaddition,itmustbenotedthatthehighabsorbeddosewithin
anobjecttobeimagedmayleadtoradiationhazards.ForlowZmaterials,however,a
highcontrastcouldbeobtainedifthephaseshiftoftheX-raysintroducedbytheobject
couldbemeasuredinsteadoftheintensityofthetransmittedwave.Theenhancement
ofthecontrastisattributedtothefactthatinparticularforlow-Zmaterialsthe
phaseshiftforX-raysishigherthantheabsorptionofincidentX-rays.Also,forthe
radiographybasedonthephaseshiftmechanism,theabsorbeddoseisconsiderably
lowerincomparisontotheconventionalabsorptionradiography[Arf98,Kot99,Tur04].
X-rayphasecontrastimagingcanbecarriedoutwithaverysimpleexperimentalsetup
withpolychromaticX-rayswhichareemittedfromasmallmicro-focusedsourcespot
withasizeintheorderofsomemicrometers.Thisfacthasbeenpointedoutin[Wil96].
Informationcanbesuppliedonthesamplemorphology,i.e.,itsboundaries,interfaces
andlocationofsmallfeatures[Xiz03,Tak98,Lew04]canbeobtained.
PhasecontrastmicroscopyinthehardX-rayregionhasbeendonewithdifferenttech-
niqueswiththecommonfeaturethatallincludecrystalopticstorenderthephase
visible.Two-beamBonse-Hartinterferometry[Bon65,Mom95,Mom02]anddiffrac-
tioncontrastimagingutilizeananalyzercrystal[Cha97,Ing95].Suchtechniquesusing
severalcrystalsleadtolossesofX-raysphotons.Alsotheexperimentalsetupisrather
sophisticated.PhaseinformationcouldbealsoobtainedwithanexperimentalsetupsimilartoGabor
in-lineholography[Gab49].Inprinciplesuchasetupisverysimplebutasevere
restrictioncomesfromthedemandofahighlycoherentX-raysourceandalsohigh
spatialresolutiondetectors.Thelackofcoherent(transversalandlongitudinal)X-
raysourcespreventedthedevelopmentofX-rayholographyformanyyears.With

1

ductiontroIn1

theadventofsynchrotronradiationsourcessoftX-rayholographyhasbeenachieved
[Mcn92]withsub-micrometerresolution.Withthirdgenerationsynchrotronradiation
sourceslikeESRF,APSandSPRING8,hardX-rayphasecontrastimaging,in-line
holographyandmicrotomographyhavebeenaccomplished[Spa99,Col96,Hu01].
Fromthethreerequirementsforphasecontrastradiography,abrilliantX-raysource,
anX-raymonochromatorandatwodimensionalhighresolutiondetector,theX-ray
sourceisofaparticularimportance.Withtheadventofelectronaccelerators,somenew
coherentX-raysourceshavebeendevelopedwhicharebasedonsynchrotronradiation,
wiggler-orundulatorradiation[Ste03].Theworkpresentedhereexploitsthepotential
ofthelowemittance855MeVelectronbeamoftheracetrackmicrotronMAMIto
producecoherentX-rays.Ourapproachisbasedontransitionradiationproductionin
theX-rayregion.Transitionradiationisproducedwhentheelectronbeampenetrates
athinfoiloraperiodicstructureofthinfoils.Itfeaturesabroadbandcharacteristics
withacutoffenergyofabout40keV[Bac96],andishighlydirectionalwithanapex
angleintheorderof0.6mrad.Averygoodtransversecoherencecanbeachieved
bymicro-focusingthelowemittanceelectronbeamofMAMI[Kph93].Therequired
longitudinalcoherenceisobtainedbymonochromizingthepolychromatictransition
radiationX-raybeamwiththeaidofaflatsiliconsinglecrystal.Theradiographsare
capturedwithhighresolutionX-rayfilmsandadirectexposureCCDcamerawitha
pixelresolutionof13×13µm2.Justtheinvestigationofthenovelon-linecapabilities
ofthelatterwasanessentialmotivationoftheinvestigationsofthiswork.
Thetreatiseisorganizedasfollows.Inchapter2anintroductiontotheprinciplesof
X-rayimagingwillbepresented.Acomparisonbetweentheconventionalradiography
(basedonX-rayattenuation)andphaseradiographywillbegiven.SincetheX-ray
beamcoherenceisaprerequisiteforX-rayphaseradiography,abriefreviewonthe
coherencewillbegivenaswell.
Chapter3dealswiththetransitionradiationproductionfromfoilstackswhichare
usedasahighbrillianceX-raysources.Theoptimizationandconstructionofafoil
stackwhichproducesX-rayphotonswithahighfluxat6keVwillbepresented.The
accompanyingbremsstrahlungwhichrepresentsaseriousbackgroundproblemwillbe
ell.wasdiscussedInChapter4theresultsofrefractionorphasecontrastimagingwithapolymonochro-
maticX-raybeamfromatransitionradiationfoilstackwithgoodtransversecoherence
willbepresented.TheradiographswererecordedwithanX-rayfilm.Theimagedob-
jectswerelowabsorbingmaterialslikepolymerstringsandgreenleaveswhichdonot
producecontrastincaseoftraditionalabsorptionradiography.
Chapter5dealswiththeX-rayphasecontrastimagingandhardX-rayin-linehologra-
phyusingmonochromaticX-rays.Thelongitudinalcoherenceisachievedwiththeaid
ofasiliconcrystalmonochromatorwhilethetransversalcoherencebymicrofocusing
theelectronbeamatthetransitionradiationfoilstacktovaluesinthemicrometer
region.AdvantagesanddisadvantagesofX-raydetectorsasadirectexposureCCD
camera,andaluminescencescreenwhichconvertstheX-raysintovisiblelightina
combinationwithalensandaCCDcamera,willbediscussed.

2

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X-ray

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3

2PrinciplesofX-rayphasecontrast
imaging

InX-raytransmissionimaging,abeamofhardX-raysintheenergyrangebetween
approximately6-60keVtraversesasample.Theintensitydistributioninaplaneper-
pendiculartothepropagationdirectionsomewheredownstreamthesampleisregistered
withciselyathetwintensito-dimensionalydistribution,detectorofdephighendsspatialstronglyonresolution.thetypeTheofinimage,teractionorbmoreetwpre-een
theX-rayswiththesamplematerial.Ingeneral,thecontrastgenerationmechanism
Incanthisbecdescribhapter,edabybrieftheinreviewtroonductiontheofthecomplexcomplexrefractiverefractivindexeandindextheoftheprincipleX-rays.of
refractioncontrastradiographywillbepresented.

indexrefractionComplex2.1

WhenaparallelbeamofX-rayspenetratesmatter,itsuffersanattenuationanda
phaseshift.Suchmacroscopicinteractionsaredescribedbythecomplexrefraction
[Jam65]ysX-raofindexn(ω)=1−δ(ω)+iβ(ω).(2.1)
Therealpart[n(ω)]=1−δ(ω)describestherefractionofthewaveofangular
frequencyωinamaterial,thequantityδ(ω)givesthedeviationoftherefractiveindex
ofamaterialfromunity(refractionindexofvacuum).Therefore,itisalsoknownas
thedecrementoftherefractiveindex.Inthecurrentworkitwillbecalleddispersion
index.Theimaginarypart[n(ω)]=β(ω)specifiestheattenuationoftheX-raysin
matter[Com35].Itisknownastheabsorptionindex.
Thetransmissionofanelectromagneticwavethroughapieceofmatterofthicknessdis
illustratedschematicallyinFig.2.1.Theundisturbedwavepropagationinx-direction
isdescribedbythefollowingexpression
Av=A0ei[ωt−kvd];kv=ω.(2.2)
cTheamplitudeoftheoutgoingwavebehindtheobjectiswrittenas
Am=A0ei[ωt−kmd]=A0ei[ωt−kvd]eicωδde−cωβd(2.3)

4

Complex2.1indexrefraction

Figure2.1:Transmissionofanelectromagneticwavethroughapieceofmatterofthickness
dandcomplexrefractionindexn=1−δ+iβ.TheamplitudeAmisattenuatedbythefactor
e−cωβ(ω)dandhasaphaseshiftcωδ(ω)drelativetotheundisturbedwaveAv.

wherekm=ωn/cisthewavenumberinthemedium.ComparingEq.(2.2)and
Eq.(2.3),thetransmittedwavesuffersaphaseshift
Δφ=cωδ(ω)d(2.4)
relativetotheundisturbedwave,andanattenuation
|Am|=e−cωβ(ω)d.(2.5)
Av||Thedispersionindexδ(ω)andabsorptionindexβ(ω)areexpressedas[Aga91,Len94]
22δ(ω)=2πre2cnaf1(ω)andβ(ω)=2πre2cnaf2(ω).(2.6)
ωωHere,re=2.818∙10−15mistheclassicalelectronradiusandna=NAρ/Mmisthe
atomicdensity,NA=6.022∙1023mol−1theAvogadro’snumber,ρthedensityofthe
f2(ωmaterial)areandMtabulatedmtheformolaralargemass.rangeTheofvaluesenergiesofthe[Hen93,atomicAga91].scatteringForafactorsgivenf1(ω)materialand
theabsorptionindexβ(ω)fallsoffverysteeplywithincreasingX-rayenergywhilethe
dispersionindexδ(ω)∼1/ω2decreasesmoresmoothly.Forenergieshigherthan6keV
thedispersionindexofrefractionδ(ω)ismorethanthreeordersofmagnitudelarger
thanβ(ω)∼1/ω4.Fig.2.2showstheratioδ/βasafunctionoftheX-rayenergy.The
mostimportantfeatureisthedrasticdifferenceofthisratioforthehigh-Zmaterial
Niinexample,atcomparison¯hω=to30ktheeV,loδw-Z/βformaterialpolycarbpolycarbonateisonateapproathigherximatelyphoton40timesenergies.largerFasor
fornickel.Thisclearlydemonstratesthatforlow-absorbingmaterialsthephaseshift
isthedominatingeffectincomparisontotheattenuation.Asanumericalexample,for
apolycarbonateplateofthickness10µmandaphotonenergy¯hω=12keVforwhich

5

2PrinciplesofX-rayphasecontrastimaging

pFigureolycarb2.2:onatemTheuchδ/βlargerratio.asforThishigh-Zratioismaterialsforlowasnickatomiceln[Hen93].umber(Z)materialssuchas

thecomplexrefractionindexparametersareδ=1.826∙10−6andβ=1.573∙10−9the
phaseshiftisalmost11.35∙πwhiletheattenuationisonly1.3∙π∙10−4.
Theseconsiderationsleadtotheimportantconclusionthatahighcontrastcombined
withalow-absorbeddosecouldbeachievedbyusingthephaseshiftmechanismto
producearadiograph[Wil96].Radiographybasedonphaseshiftisreferredtoasre-
fractioncontrast,edge-enhancedcontrast,refraction-enhancedorphasecontrast.In
thecurrentworkitwillbecalledrefraction-contrastradiographyforimagingwithpoly-
chromaticX-ray,andphase-contrastorholographyforimagingwithmonochromatic
.yX-ra

Refraction2.2radiographycontrast

Inrefractionthefolloasawingmecsectionhanismatonovproelducekindaofhighconradiographtrastyofislodescribw-absorbingedwhichismaterialsbasedusingon
X-raysfromatransitionradiationsource.Theprinciplesofrefraction-contrastradiog-
raphywillbeexplainedaswellastheinterpretationaccordingtogeometricalandwave
optics.Theenhancedvisualizationoflow-absorbingmaterialsanditsmostimportant
advantagethatdifferentobjectsofsimilardensitiescaneasilybedistinguishedwillalso
ted.preseneb

6

Principles2.2.1

2.2Refractioncontrastradiography

X-raysaselectromagneticwavesaresubjectedtoreflection,diffraction,andrefraction.
TheX-raywavefrontisdeformedwhenpassingthroughasampleofinhomogeneous
thicknessorrefractiveindex.Accordingtothegeometricalapproximationthephase
differenceΔφforaraypaththroughanobjectwithrefractionindexn(λ;x,y,z)=
1−δ(λ;x,y,z)+iβ(λ;x,y,z)relativetoanundisturbedwave,assumingthatthe
opticalaxisisparalleltothex-axis,isgivenaccordingtoEq.(2.4)by
Δφ(λ;x,y,z)=2λπδ(λ;x,y,z)dx=reλρe(λ;x,y,z)dx.(2.7)
Hereρe(z,y,x)istheelectrondensityatthepoint(x,y,z),retheclassicalelectron
radius,andλistheX-raywavelength.Theintegrationiscarriedoutoverthepathof
theX-raybeam[Wil96,Suz02].

Figure2.3:Formationofarefractioncontrastradiographaccordingtogeometricaloptics.
RefractedX-raysslightlydeviatefromrectilinearpropagationattheinterfacesinaccordance
withSnell’slawofrefraction.SincetherefractionindexforX-raysisslightlysmallerthan
unity(about10−6),X-raysarerefractedinoppositemannertovisiblelight,i.e.theyare
focusedbyaconcaveanddefocusedbyaconvexobject.FortangentiallyincidentX-rays
onaninterface,X-raysencountermaximumdeviationwhichresultsintheformationofa
black/whitecontrastwhichenhancesthevisibilityoftheinterfaces.

ForsimplicityinFig.2.3aonedimensionalobjectsuchasastringofradiusRand
amediumrefractionofindexrefractionn2(ω)index=n1(−ω)δ2(=ω1)−+δiβ(2ω()ω)+isiβ(ω)considered,andwhicwhichishisemilluminatedbeddedwithinaa
parallelX-raybeam.Thephase1shiftof1theoutgoing1waverelativetowaveinvacuum
isgivenby
φ=4π(δ2−δ1)R1−(zo)2.(2.8)

7

2PrinciplesofX-rayphasecontrastimaging

Figure2.4:Schematicexperimentalsetupfortherefractioncontrastradiography.

TheangulardeviationΔαofthenormaltothewavefrontis[Wil96]

Δα=2λπ|zφ|=4π(δ2R−δ1)[1−(zzoo)2]−23.(2.9)
RThephasegradientdivergesatz=R,theraysdeviatebyalargeanglefromthe
originalpropagationdirectioneventhough(δ2−δ1)isverysmallasinthecaseof
ThisX-rays.explainsThiswhleadsytothealossradiographofintensitlooksyatlikbeaoundariesdirectorimageaofblackcon/whitetoursofedgethecondetailstrast.
whichconstitutethesample.Moregenerally,anyrapidvariationoftherefraction
blacindexk/orwhitetheconthictrastknesswhicofhtheappearssampleatmatheybecorrespimagedondingaspanoinintstensitinythedisturbanceradiographevorena
whenapolychromaticX-raybeamisused.
Theblack/whiteedgecontrastisexpressedas[Hec89]
Cref=IImaxmax+−IIminmin(2.10)
withImaxandIminasshowninFig.2.3.

2.2.2Principleoftheexperimentalsetup

(2.10)

Thetypicalexperimentalsetupforrefractioncontrastradiographyisillustratedin
Fig.2.4.ApolychromaticX-raysourceilluminatesasamplewhichismountedata
distancexsofromthesource.Thedetectorismountedatadistancexodfromthe
object.ThisconfigurationfeaturesageometricalmagnificationMandageometrical
.Sunsharpness

8

2.3ImagingwithacoherentX-raybeam

Thegeometricalmagnificationisexpressedas
M=xso+xod=1+xod.(2.11)
xxsosoInthecurrentworktheimagecanbemagnifiedupto7timesbyincreasingxod2to
overcomethelimitedspatialresolutionoftheX-rayimagedetectorof13×13µm.A
hugemagnificationofupto65timeshasbeenusedtogetultraspatialresolutionup
tothesub-micrometerrangeaspointedoutin[May02].
ThegeometricalunsharpnessS,arisingfromthefinitesizeofthefocalspotprojection
onthedetectorplane,isgivenby
S=S∙xxod=S(M−1).(2.12)
so1,HerehowSeviser,theatfoancal-spobotsize.ject-to-detectorThegeometricaldistancexod=unsharpness0theisphasenegligiblecontrastsmallvforanishesMas=
willbepointedoutbelowinsection4.1.1.

2.3ImagingwithacoherentX-raybeam

Theholographrecordsinterferencepatternsbetweenthedisturbedwavesbythesample
andtheundisturbedwavefromthesource.Fig.2.5showsthearrangementofin-
lineholography.Apointsourceemanatesamonochromaticwave(solidlines)and
illuminatesthesampleofsmallsize.Thewavescatteredbythesample(dashedlines)
interferewiththeundisturbedwave.Thescatteredwaveandtheunscatteredwave
formaninterferencepatternatthedetector.Theresultinghologramisrecordedbyan
imagedetectorofhighspatialresolution.Theamplitudeatthedetectorplane
E(r)=Eo(r)+Escat(r)(2.13)
consistsoftwodifferentterms[Har96]Eo(r)andEscat(r)whicharetheunscattered
andscatteredwave,respectively.Therecordedintensityisexpressedas
I(r)=|Eo(r)|2+Eo∗(r)Escat(r)+Eo(r)E∗scat(r)+|Escat(r)|2.(2.14)
Thefirsttermontherighthandsideistheintensityoftheundisturbedwave.The
secondandthirdtermdescribetheinterferencebetweenscatteredandunscattered
waves.Thisistheholographicdiffractionpattern.Thelasttermisthepurediffraction
patternofthescatteredwaveonly.Thediffractionpatterndependsonthesizeofthe
objectanditspositionrelativetothesourceandthedetector.

Coherence2.3.1

ForallX-raybeamsproducedbyavailableX-raysources,suchasstandardX-raytubes,
third-generationsynchrotroninsertiondevicesandtransitionradiation,thespectral

9

2PrinciplesofX-rayphasecontrastimaging

Figure2.5:Schematicdemonstrationofin-lineholography.ApointX-raysourceemanatesa
sphericalwaveofwavelengthλwhichilluminatesasmallobject.Theobjectismountedclose
toasourceandfarfromtheimagingdetector(CCDcameraorhighresolutionX-rayfilm).
Theinterferencebetweenthescatteredwavebytheobject(dashedlines)andunscattered
waveemanatingfromthesource(solidlines)formsahologramontheimagedetector.

bandwidthandfinitespatialdimensionofthesourcehavetobetakenintoaccount.
Finitespectralbandwidthandfinitespatialdimensionresultinincoherentproperties
ofthebandwidthX-rayonbtheeam.Acoherencequanproptitativeertiesofmeasurementhebteamofisthetheeffecttransvofaersesourceandspotlongitudinalanda
abilitcoherenceyofthelengthwavesortotheprodegreeduceofinterference.coherenceofThisthebmeanseam.thatCoherenceforimagingiswithconnectedcoherentothet
wavmerelyes,thesummingamplitudeupandindividualphaseinofalltensities.individualThewinavesterferencearesuperimppatternosed,isratherqualitativthanely
describedbythevisibilityVofthefringes.
V=IImax−+IImin(2.15)
minmaxinwheretheIinmaxterferenceandIminarepattern.themaximalandminimalintensitiesoftwoneighboringfringes
Thecoherencepropertiesofasourcearedividedconvenientlyintotwocategories,
thesearethetransverse(spatial)coherencewhichisrelatedtothefiniteextentof
themonocX-rayhromaticitsourceyofandthetheX-rayblongitudinaleam.(temporal)coherencewhichisrelatedtothe

10

2.3ImagingwithacoherentX-raybeam

pTheointstransvemiterseradiationcoherenceindependenoriginatestlyfromfromeacthehfactother.that,Tasransitionarule,theradiationindividualX-raysourcessource
areizedinthiswquasihomogeneousorkitcanbe[Car77].consideredButitincangoobdeshoapprownthatximationforastheabsourceeamspforotsizeincoherenreal-t
radiation.InthislimiteachelectronpassingtheradiatorfoilstackemitsX-raysin-
dependently.Therefore,everysourcepointproducesinterferencepatternsshiftedby
(xod/xso)ΔS,withΔSbeingthetransversedisplacementinthespot.Thissmearsout
antion.yinInorderterferencetoavpatternoidthiswhichdeterioration,resultsinatheX-radeteriorationysourceofsizethemustbholographicekeptasinforma-small
asthepossible.distanceTxoodbimproevereduced.thetransvHoweverseer,thecoherencelatterthedistancedistancecanxsonotcanbebemadeincreasedtosmalland
ThesincetransvrestrictionserseimpcoherenceosedbylengththeLfiniteisdefineddetectorastheresolutiondistancemustbbetewtakeenenpinointotsonaccounthet.
Tobservationplaneforwhichtherelativephasesofthewavefrontsfromoutermostpoints
inthesourcedifferby1/2π.Itisgivenby
LT=2λπ∙∙xSsd.(2.16)
aThespectrallongitudinaldistributioncoherenceofwidthlengthΔLλldescribretainsesitstherelativdistanceephasesalongawithinraythepathovlimitserofwhicπh.
ItlengthisindifferenceparticularthatcriticalcanforbeX-rayacceptedholographbetwyeenbraecauseysitpassingrestrictsfromthethemaximsourceumtopaththe
detectorlongitudinalandrayscoherencewhichlengthpLenetrateisgivtheenobbyject[Bor75]andthengoingtothedetector.The
l2Ll=2Δλλ.(2.17)
IndentlycaseoffromantheothersincoherenantinX-rayterferencesourceevpatterneryresultingfrequencyinacompblurringonentofprotheducesinindepterferenceen-
pattern.

yvisibilitandCoherence2.3.2Inthissection,theeffectofafinitesourcesizeandafinitewidthofthespectral
intensitydistributionontheinterferencepatternwillbedemonstratedforapolymer
thestringyofaxis.radiusForRtheanddefinitioncomplexoftherefractioncoordinateparameterssystemδandseeβ,Fig.whic2.6.hisThestretchednormalizedalong
oelectricwavefieldE(zd)/E(z0)atthedetectorplanecanbecalculatedbymeansofthe
Fresnel-Kirchhoffintegral.AsshownintheappendixA.2theresultis
R+E(zd,λ)=1+xsdexp[−4π(iδ+β)R2−zo2]−1∙
E0(zd,λ)iλxsoxod−Rλ
xxπsosd∙exp[iλxsoxod(zo−zdxsd)2]dzo.(2.18)

11

2PrinciplesofX-rayphasecontrastimaging

inFigurethesource,2.6:OisStandardapointingeometrytheofobjectrefractionplaneandconPtrastistheandpoinin-linetintheholographdetectory.Sisplane.apoint

ThenormalizedintensitydistributionIn(λ)(zd,λ)=|E(zd,λ)|2/|E0(zd,λ|2isshownin
Fig.2.7(a).Theeffectofapartialcoherence,originatingfromthespectraldistribution
andfringesaasfiniteshobwneaminspFig.otsize2.7of(b)theandX-ra(c).ys,Sourcedeterioratesspotsizetheandspvisibilitectralyofthedistributioninterferencehave
gb(zeens)oftaktheenbintoeamspaccounottandasf(conλ)vforolutionsthespwithectralthedistributionnormalizedinaccordingtensitytodistributions
In(zd)=In(λ)(zd−xodzs,λ)∙g(zs)∙f(λ)∙dzsdλ.(2.19)
xso

Inconclusion,radiographybasedonphasecontrastisausefultechniquetoincreasethe
contrastforlow-Zmaterialswithasmallabsorbeddose[Arf98].ForX-rayrefraction
contrastradiography,ontheonehand,agoodtransversecoherenceoftheX-raybeam
isrequiredwhilethelongitudinalcoherenceisnotofmajorimportance.Thelatter
hasbeendemonstratedwithFig.2.7(b).ForX-rayin-lineholography,ontheother
hand,both,averygoodtransversecoherenceandagoodlongitudinalcoherenceof
theX-raybeamarenecessarysincetheholographicinformationisimprintedinthe
interferencepattern.InthefollowingchaptersexperimentsattheMainzMicrotron
facility(MAMI)willbepresentedinwhichthecapabilitiesofatransitionradiation
X-raysourceincombinationwithamicro-focusedbeamspotwillbedemonstratedfor
both,X-rayrefractionradiographywithbroadbandX-raysaswellasin-lineholography
withmonochromaticX-rays.

12

2.3

ImagingwithacoherentX-raybeam

Figure2.7:Effectofpartialcoherenceonthevisibilityoffringesforapolymerstringwith
adiameterof30µm,complexrefractionindexδ=7.24∙10−6andβ=2.42∙10−8atan
X-rayenergyof6keV,source-to-objectdistancexso=10.45m,2object-to-detector2distance
xEq.od=(2.18)3.15form.ap(a)ointsourceNormalizedandinmonotensitcyhromaticdistributionX-ra|ysE(zdwith,λ0λ)0|/=|E0(2.067zd,λ˚A,0|correspaccordingondingto
toanenergyof6keV,(b)forapoint˚sourcebutaGaussianspectraldistributionaroundλ0
withstandarddeviationofσλ=0.2A,(c)foraGaussianintensitydistributionoftheX-ray
sourceaccordingspottowithEq.(2.19).standardIdealdeviationdetectorσz=6resolutionµmandassumed.monochromaticX-rays.Convolutions

13

3ThetransitionradiationX-ray
source

X-raX-rayysourcessourcesas,aree.g.,crucialX-rayelementubes,tsinsynchrotronradiographory.Intransitionprinciple,radiationtherearesources.alotThisof
chapterdealswithtransitionradiationasabrilliantX-rayssource.Transitionradiation
isproproductionducedmecwhenhanismawillrelativisticbebrieflyelectrondiscussed.beamMoreocrossesver,aptheolyimidefeaturefoilofthestack.radiationThe
fromusinga600optimizedMeVfoilstacelectronksbtoeam,produceandathigh33kfluxeVwithradiationanat855aMeVphotonelectronenergybofeam6kwilleV,
ted.preseneb

3.1TheMainzMicrotronfacility(MAMI)

TheMainzMicrotron(MAMI)facilityisthreestagerace-trackelectronaccelerator.It
islocatedintheInstituteforNuclearPhysicsonthecampusoftheJohannesGutenberg
UniversityofMainz.Thefirstrace-trackmicrotrondeliversacontinueselectronbeam
withanenergybetween4and15MeV.Itwasmadeavailableintheyear1979for
coincidenceexperiments.Withtwofurtherrace-trackmicrotrons,anelectronbeamof
lowemittance,highenergyresolutionandstabilitywithanenergyupto855MeVcan
bedeliveredwithabeamcurrentrangingupto10−4A.Afourthacceleratorstageis
nowbeingconstructed,whichwillboosttheelectronbeamenergyupto1500MeV.
Thefinaldevicewillbeoperationalintheyear2006.ThefloorplanofMAMItogether
withthedifferentexperimentalareasisshowninFig.3.1.
Forthecurrentwork,thebeamemittanceinhorizontalandverticaldirectionsare
ofparticularinterestinviewofthepreparationofamicro-focusedelectronbeam.
InFig.3.2bothemittancesaredepictedasafunctionoftheelectronbeamenergy.
Theemittanceinhorizonaldirectionisbiggerthantheemittanceinverticaldirection
becausetheelectronsemitsynchrotronradiationinthebendingmagnetsresulting
inagrowthoftheemittance.Theemittancedependsstronglyontheenergyofthe
electronbeamwhileitisnearlyindependentfromthecurrentoftheelectronbeam,see
[Kph93].Theemittanceinverticaldirectiondecreasesasafunctionofthebeamenergy,
whileinhorizontaldirectiontheemittanceincreasesapproximatelyexponentiallyat
energieslargerthan400MeV.Therefore,thechoiceofthebeamenergytopreparea
microfocusedelectronbeamfortheexperimentsdescribedinthisworkwas600MeV.
MeasurementsofthehorizontalandverticalemittancesandalsoTwissparametersat

14

3.1TheMainzMicrotronfacility(MAMI)

Figure3.1:LayoutoftheMAMIacceleratorwiththeracetrackmicrotronsRTM1-3and
thedoublesidedmicrotronHDSM.ShownarealsotheexperimentalareasA1-A4andX1
[KPHXX].

anelectronbeamenergy600wereperformedwiththemethoddescribedin[Hag01].
Theresultsareinhorizontaldirection:

h=A/π=0.0023mmmrad

β=39.03mα=−0.211γ=0.0271/m,

direction:erticalvinand

v=A/π=0.00052mmmrad

β=9.599mα=3.851γ=1.6951/m.

15

3ThetransitionradiationX-raysource

Figure3.2:EmittanceoftheMAMIelectronbeaminverticalandhorizontaldirectionasa
functionofthebeamenergy[Kph93].

Thesedescribvedaluesin5.2.2havetobeengetausedmicrofoforsimcusedulationelectronbcalculationeam[Rowithy84,theShvXX,programWil92].beamoptic

radiationransitionT3.2

Whenanultrarelativisticelectronbeamcrossesaninterfacebetweenpolyimideand
vacuumabroadbandofelectromagneticradiationisemittedwhichisknownastran-
sitionradiation.Theelectroninducesarounditstrajectoryinthemediumatime-
dependentcylindricalsymmetricdipoledistributionthatemitsaconeoftransition
radiationwhichisradiallypolarized,seeFig.3.3.

Themechanismoftransitionradiationofhighrelativisticchargedparticleshasbeen
inInvtheestigatedcurrenintworkextensivehighlytheoreticalrelativisticandexpelectronerimenbeamstalwithstudies[Fenergiesra45,ofRul97,600Fandab75].855
v2ultraMeVhaverelativisticbeenusedelectronswithandforrelativistictheenergyfactorsofγthe=1/emitted1−(cX-ra)ysfar1.fromIntheabsorptioncaseof
edgesofthemedium,thepermittivityεrcanbeexpressedasεr=1−ωp2/ω2[Jac83]
withtheplasmafrequencyωp.ThenumberofemittedX-rayphotonswithanenergy
v¯hω,ector,isemittedgivenfromperaelectron,singleinperterfacerelativatetheenergyangleθbandwidthwithinresptervectalto(d¯hω/electron¯hω),vandelocitpery

16

radiationransitionT3.2

Figure3.3:Transitionradiationproductionataninterfacebetweenmediumandvacuum.
TheelectricfieldEofahighlyrelativisticelectronproducesatime-dependent,predomi-
nantlytransversalpolarizationinthemediumthatleadstoemissionofdipoleradiation.
Justwavesemittedfromaformationzoneinforwarddirectionatthemedium-vacuumin-
terfacecontributesignificantlytothetransitionradiationthatisstronglypeakedatsmall
anglesθ1/γwithrespecttothevelocityvectoroftheelectron.

solidangledΩby[Che74]
d2N0αθ2ω2
(d¯hω/¯hω)dΩ=F1=16π2υ2(Z1−Z2)2.(3.1)
Hereareα=1/137.04thefinestructureconstant,υtheelectronvelocity,h¯thereduced
Planck’sconstant,andZ1,Z2theformationlengthsofbothmedia.Theformation
lengthZisacharacteristicpropertyofthemedium.Itisdefinedasthelengthinside
themediumwheredifferentpointsemitradiationcoherentlyinforwarddirection.It
iswrittenas[Che74]4υ1
Zi(ω,θ)=ωγ1+θ2+(ωωpi)2.(3.2)
Inthisequationareωpi=4πmρeeie2theplasmafrequenciesofthemediai=1,2which
arecalculatedfromtheelectrondensitiesρeiofthemedia,eistheelementarycharge,
andmeisthemassoftheelectron.Theemittedradiationhasitsmaximumintensity
atanglesθ1/γandacutoffenergylimitat¯hωc=γ¯hωp.Abovethisvaluethe
spectrumfallsoffproportionaltoω−4.Forapolyimidefoilwithaplasmafrequency
of24.6eVandanelectronbeamenergyof855MeV,thecriticalenergyis¯hωc=41.2
eV.k

17

3ThetransitionradiationX-raysource

fromFigurethet3.4:wo(a)Tsurfacesransitionmayinradiationterferefromconstructivasingleelyfoilatofathiccertainknesslthic1.Theknessl1.emitted(b)wTaveransitiontrains
radiationfromseveralfoils.Thewavetrainsmayinterferecoherentlyatacertaindistance
l2andatacertainangleθinforwarddirection.

Thenumberoftheemittedphotonscanbeincreasedwhentheparticlespassthrough
severalboundaries,seeFig.3.4.Theemergingwavesfromdifferentinterfacesmay
interfereconstructivelyordestructively.Thedifferentialenergyspectrumfromafoil
stackofMfoilsofthicknessl1separatedbyequalspacingl2isgivenby[Che74,Bac94,
Bac96]2NdM(d¯hω/¯hω)dΩ=F1∙F2∙F3.(3.3)
ThefactorF2=4sin2(l1/Z1)accountsfortheinterferenceoftheradiationemitted
fromtwointerfacesofasinglefoil.ForafoilstackhavinganumberoffoilsM,the
totalamplitudeoftheradiationisgivenbytheone-foilamplitudemultipliedbythe
interferencefactorF3=sin2(MX)/sin2(X),withX=l1/Z1+l2/Z2.Iftheresonance
conditionsl1/Z1=(m−1/2)πandl1/Z1+l2/Z2=nπaresatisfiedsimultaneously
(m,nareintegerswithm,n≥1),thespectralintensityincreasesbyafactor4M2.The
self-absorptionoftransitionradiationwithinthefoilstackresultsinareductionofthe
outgoingphotonintensity.Itisespeciallyrelevantforlower-energyphotons.Therefore,
theradiatormaterial2musthavealowatomicnumber(Z)inordertominimizetheself-
absorption(∼Z)andalsomulti-scatteringofelectronsbytheelectricfieldsofatomic
nuclei.Theeffectsofelectronbeamdivergenceandelectronmultiplescatteringinthe
foilstackresultinandecreaseoftheenhancementfactor4M2.Also,asthebeam
divergenceincreases,theradiationconewithaminimumatthecenterbeginstosmear
outandeventuallytheminimummaydisappear.
TheparametersofthetwofoilstacksusedinthecurrentworkaretabulatedinTab.3.1.
Thefirstfoilstackhasbeenoptimizedforaphotonenergyof33keV[Zah94,Joh95].

18

Bremsstrahlung3.3

Table3.1:Parametersofbothfoil-stacksusedinthiswork.
X-rayenergyoptimization33keV6keV
MaterialPolyimide(C22H10N2O5)Polyimide(C22H10N2O5)
Numberoffoils3025
Thicknessoffoils[µm]2512.5
Distancebetweenfoils[µm]75100
Electronbeamenergy[MeV]855600
TRcriticalenergy[keV]41.628.9
11741673factortzLoren

However,ithasitsmaximumfluxat10keV.Thisfoilstackhasbeenusedinthe
firstsetofexperimentsforrefraction-contrastradiography.Thecalculatedtransition
radiationcharacteristicsareshowninFig.3.5.TheestimatedoptimumX-rayenergyto
performX-rayphasecontrastimagingandin-lineholographywiththedirect-exposure
CCDcamera,describedinsection5.3,is6keV.Thereforeanewfoilstackhasbeen
constructed,whichhasitsmaximumphotonsfluxat6keV.Indoingthis,asimulation
theprogrammultiplewrittenbscatteringyO.ofKettigthe[Ket00]electronshasbwithineentheused.foilsTheandsimalsoulationselfprogrammabsorptiontakinesto
account.Thesimulationsshowedthattheoptimalthicknessofthepolyimidefoils
isin12.5terfereµm,forconstructivwhichely.theThetransitionoptimalspacingsradiationbetfromweenthethetwofoilsinareterfaces100µofmatsinglewhicfoilh
thetransitionradiationfromdifferentfoilsinterfereconstructively.Thenumberof
foilsislimitedto25inordertominimizetheself-absorptionandelectronmultiple
scattering.ThecalculatedtransitionradiationcharacteristicsareshowninFig.3.6.

Bremsstrahlung3.3

Whenmaterialtheyelectronsemitarescatteredbremsstrahlung.inthepTheositivspeectrumelectricextendsfieldsofupthetontheucleimaximintheumradiatorenergy
oftheimpingingelectron.ForbremsstrahlungproducedbyelectronswithenergyEat
freeatomswithatomicnumberZ,thenumberofphotonsd3N0perelectron,relative
approbandwidthximationd¯hω/¯underhω,themassperconditionunitEarea[MeV]d(ρili),100and∙Zsolid−1/3toangled[Jac83,ΩamounAkh98]tsinBorn
d3N0NA321+γ4θ4
(d¯hω/¯hω)dΩd(ili)=Mm2πσoF(¯hω)γ(1+γ2θ2)4,(3.4)
withσo=αZ2re2,NAtheAvogadro-constant,Mmthemolarmass,retheclassical
electronradius,γtheLorentzfactoroftherelativisticelectron,andθtheobservation
anglewithrespecttotheelectronbeamvelocityvector.ThefunctionF(¯hω)isgiven
ybF(¯hω)=4[(1+(E−¯hω)2−2(E−¯hω))ln(183)+(E−¯hω)].(3.5)
E23EZ1/39E

19

3

ThetransitionradiationX-raysource

Figure3.5:Thecalculatedtransitionradiationspectrafor855MeVelectronsimpinging
perpendicularlyonthefoilstackwhichconsistsof30polyimidefoilsof25µmthicknessand
75µmseparation.(a)Energyspectrumwheremultiplescattering,electronbeamdivergence
(0.6mrad)andself-absorptionaretakenintoaccount.Thespectrumpeaksatabout10keV.
(b)Energyspectrumintegratedoverthesolidangle.Dashedline:self-absorptionneglected,
fullline:self-absorptiontakenintoaccount.(c)Angulardistributionoftransitionradiation
atafixedenergyof10keVwithoutbeamdivergence,multiplescatteringandselfabsorption.
(d)Angulardistributionofthetransitionradiationatafixedenergyof10keV.Dashedline:
electronmultiplescatteringistakenintoaccount,fullline:theelectronbeamdivergenceis
[Ket00].additionallyincluded

20

3.3

Bremsstrahlung

Figure3.6:Thecalculatedtransitionradiationspectrafor600MeVelectronsimpinging
perpendicularlyonthefoilstackwhichconsistsof25polyimidefoilsof12.5µmthicknessand
100µmseparation.(a)Energyspectrumwheremultiplescattering,electronbeamdivergence
(0.8mrad)andself-absorptionaretakenintoaccount.Thespectrumpeaksatabout6keV.
(b)Energyspectrumintegratedoverthesolidangle.Dashedline:self-absorptionneglected,
fullline:self-absorptiontakenintoaccount.(c)Angulardistributionoftransitionradiation
atfixedenergyof6keVwithoutbeamdivergence,multiplescatteringandselfabsorption.
(d)Angulardistributionofthetransitionradiationatafixedenergyof6keV.Dashedline:
electronmultiplescatteringistakenintoaccount,solidline:theelectronbeamdivergenceis
[Ket00].additionallyincluded

21

3ThetransitionradiationX-raysource

Figure3.7:Calculatedbremsstrahlungcharacteristicsforthe6keVpolyimidefoilstackat
anelectronbeamenergyof600MeV.(a)Angulardistributionofphotonswithenergiesof
6keV,20keVand100keVaccordingtoEq.(3.6),(b)energyspectrumintegratedoverthe
solidangle.Inthecalculationsthecontributionsofthespectrafromthedifferentelements
comprisingthepolyimideradiatorhavebeenaddedaccordingtotheirrelativemolecular
ts.eighw

Incondensedmaterialstheintensityandangulardistributionofthebremsstrahlungis
changedduetothedensityeffectandisgivenby[Ter72,Bac98]
d3N0NA32γ41+γ4θ4
(d¯hω/¯hω)dΩd(ili)=Mm2πσoF(¯hω)γ(γ)(1+γ2θ2)4(3.6)
withF(¯hω)=4[(1+(E−¯hω)2−2(E−¯hω))ln(183γ)+(E−¯hω)].(3.7)
E23EZ1/3γ9E
andthemodifiedLorentz-factor

γγ=1+(γωp)2.(3.8)
ωForhighenergyX-rays,i.eforlimω→∞γ=γ,Eq.(3.6)reducestoEq.(3.4).
Fig.3.7(a)showstheangulardistributionofbremsstrahlungatsomephotonenergies.
Thedensityeffectmanifestsitselfinasuppressionofbremstrahlungemissionatphoton
theenergiessmaller¯hω<theγ¯hωp.photonInenergyaddition,itgets.canHobweevseener,thethatthetotalangularemittednumdistributionberofbroadensphotons
remainsreduceddespitethisbroadening.Todemonstratethis,Eq.(3.6)hasbeen
integratedoverthesolidangle.Withtheaidoftheintegral
∞1+γ4θ42π
0(1+γ2θ2)42πθdθ=3γ2(3.9)

22

obtainsone

Bremsstrahlung3.3

oneobtainsd2N0NAγ2
(d¯hω/¯hω)d(ili)=Mmσo(γ)F(¯hω).(3.10)
ThecorrespondingspectraldistributionisshowninFig.3.7(b).Comparingthetran-
sitionradiationspectrumFig.3.6withthebremsstrahlungspectrumFig.3.7(b)itcan
beconcludedthatthespectraldistributionoftransitionradiationataphotonenergy
of6keVisaboutafactor50largerasthehighenergybremsstrahlungspectrumin
theregionwherethedensityeffectcanbeneglected.However,theintegratedhigh
energypartofthebremsstrahlungspectrumyields4.3∙10−3photonsperelectronin
thephotonenergyintervalrangingfrom10MeVtothemaximumenergyof600MeV.
Thiscontaminationofthetransitionradiationspectrumrepresentsabackgroundprob-
lemintheexperimentalareasincephotonswhichhitmatterproduceelectromagnetic
showers.WecomebacktothisprobleminappendixC.

23

radiographycontrastRefraction4

ThecounterpartofnormalabsorptioncontrastradiographywithpolychromaticX-
raysforabsorbingobjectsistherefractioncontrastradiographyforlowabsorbing,
nearlytransparentobjects.Thegeometricalarrangementforthiskindofradiography
isverysimilarasthatfortheabsorptioncontrastradiographywiththefinedifference
thatthetransparentobjectmustnotbeindirectcontactwiththedetectorplane
butbepositionedinsomedistancefromit.Thereasonswillbeoutlinedinmore
detailatthebeginningofthischapterontheexampleofpolyamidefibersbeforethe
experimentalsetup,measurementsandtheresultsaredescribedtotakerefraction
contrastradiographsatMAMI.Finally,furtherexamplesofsomegreenleaves(Rumex
crispusandFicusbenjaminus)willbepresentedinordertoshowhowthecontrastis
significantlyimprovedwithalowabsorbeddose.

backgroundBasic4.1

Principally,anykindofimagingalsowithX-raysisawaveopticalphenomenon.How-
ever,indicationsofwaveopticsdependstronglyonthegeometricalarrangementof
source,objectandthedetector.InFig.4.1onecandistinguishinessencefourarrange-
mentsoftheobjectbetweenthesourceanddetectorplane.Thesource-to-detector
distancewillbeassumedtobeaconstant.Inthissectionthecontactregion(I)and
thenearfieldregion(II)willbediscussedinmoredetail.

4.1.1regionContact

Tostartwith,Eq.(2.18)isrewrittenasE(zd,ω)/E0(zd,ω)=1+a(zd,ω)with
∞+ωxωxx
a(zd,ω)=sd[q(zo,ω)−1]exp[isd(zo−zdso)2]dzo.(4.1)
i2πcxsoxod−∞2cxsoxodxsd

Hereareω/c=k=2π/λ,andforastringwithradiusR

q(zo,ω)=exp[−2(ω/c)(iδ+β)R2−zo2]θ(1−|zo|/R)(4.2)
withθ(x)theunitstepfunction,equaltozeroforx<1and1forx≥1.Atsmall
distancesxod→0,forwhichxso→xsd,theexponentialinEq.(4.1)oscillatesrapidly

24

kgroundbacBasic4.1

Figure4.1:Imagingregimesasafunctionofthedistancebetweenobjectanddetectorplane
xod.restrictionsTheofdistancethexsdsetupbetwandeenkeptsourceconstanandt.Fdetectorourisregionsassumedcanbetobegivdistinguishedenbybtheythegeometricalimaging
isofdistancerelevxodance.For(conthevencontionaltactregionradiograph(I),y).i.e.Inxodthe=0,nearonlyfieldtheregionabsorption(II)aconwithintrastthecanobbjecte
generatedevenfromlowabsorbingmaterialsatsharpchangesoftherefractionindex.Inthe
intermediateregion(III)andtheregion(IV)atclosedistancetothesourceamagnification
oftheobjectcanbeachieved.However,theimageloosmoreandmoreresemblancewiththe
diffraction.toduejectob

andareplacementwithaδεfunctioncanbeperformedaccordingto
ωxsdωxsd2
δε(zo−zd)=xodlim→0i2πcxxexp[i2cxx(zo−zd)]dzo.(4.3)
odsoodso

toreduces(4.1)Eq.Then∞+a(zd,ω)=[q(zo,ω)−1]δε(zo−zd)]dzo=q(zd,ω)−1.(4.4)
−∞

tionTheq(zo,amplitudeω)canbratioeatwrittentheasqdetector(zo,ω)isE=(zd,ωexp[)/E−t0o((zzdo,)(ω)iδ(zo=)+q(βz(dz,oω))]).withTheto(zfunc-o)
afunctionwhic2hcharacterizesthethicknessdep2endenceoftheob2ject.Thein2ten-
sitexp[y|−E2(toz(d,zdω))|β(,zdthe))]|E0(zdetectord,ω)|2.measures,Notice,isthat|E(inzd,ωthe)|con=tact|q(zdregion,ω)|zo|E0=(zd,zdω)|holds.=
Thisisthecommonlyacceptedresultthatonlyanabsorptioncontrastoftheobject
canservbableeinobservthisedingeometryX-rayinimaging.whichAntheyobphasejectiscinhangescloseconcausedtactbywiththeobthejectaredetector.unob-

25

4Refractioncontrastradiography

4.1.2Smalldistancebetweenobjectanddetector-phasecontrast

Anobjectwithnegligibleabsorption,i.e.withβ(z)→0anywhere,generatesalmostno
contrast.Thisis,however,onlytrueiftheobjectisbroughtinclosecontactwiththe
detector.Ifanobjectwithstillnegligibleabsorptionbutwitharapidphasevariation
insomesmalldomainispositionedatafinitebutsmalldistancexodxsdwith
respecttothedetectorplaneaphasecontrastmaybeobserved.Thishasalreadybeen
pointedoutinsection2.2.1intermsofgeometricalarguments.Inthepictureofwave
opticstheexponentialinEq.(4.1)hasnowatypicalwidthσo=λxsoxod/(2πxsd)
inwhichitoscillatesforagivenzdasafunctionofzonottoorapidly.Itcanbe
seenfromEq.(4.2)thatatthestringborderalargephasechangeΔφstring=2(ω/c)δ∙
R1−[(R−Δzo)/R]2mayoccurinasmalldistanceΔzoclosetozo=R,andaround
zdRxsd/xsonowinterferencefringesmayshowup,similarasthoseshowninFig.2.7
(a),providedΔzo<σoholds.Ifthisconditionwouldnotbefulfilled,butinsteadif
Δzoσowouldapply,therapidlyoscillatingintegrandwouldgiveanintegralvalue
closetozeroforanyzdaroundRxsd/xso.
ForpolychromaticX-raysthecontrastisgeneratedbyanincoherentsuperposition
oftheinterferencepatternsofthevariousdifferentiallysmallmonochromaticcompo-
nentsofthespectrum.Theinterferencepatternhasbeencalculatedonthebasisof
theFresnel-KirchhoffintegralEq.(2.18)forastringwiththenormalizedintensity
I(n,wω)(zd,ω)=|E(zd,ω)|2/|E0(zd,ω|2as
2In,w(zd)=√1I(¯n,whω)(zd,¯hω)∙exp[−(zd−2zd)]∙f(¯hω)∙dzd∙d¯hω.(4.5)
σ2σπ2ArealisticX-rayenergydistributionfunctionf(¯hω),theX-rayfilmrecords,hasbeen
assumed,thespectrumofwhichisshowninFig.4.6.Howitcomesaboutwillbe
explainedinthesubsection4.2.2below.Tosavecomputertime,onlydiscretevalues
fi,i=8,30instepsof1keVweretakeninthephotonenergyintervalbetween6and
30keV.TheresultsofthesecalculationsaredepictedinFig.4.2(a)foratransparent
object.Justthemaintwofringesarevisiblewhiletheothersmoreorlessarewipedout.
Thereasonisthat,becausethefirstmaximumandminimumfordifferentwavelengths
appearnearlyatthesameposition,allotherfringesoverlapincoherentlyandcancel
eachother.Thefinalradiographcontainsjustonemaximumandoneminimumatthe
geometricalbordersoftheobjectandtheresultingblack/whitecontrastimagesthe
object.Thecontrastattheedgesoftheobjectisalsocalled”edgeenhancement”or
trast”.con”phasesimplyTheprojectedbeamspotsize(xod/xso)σs,thefiniteresolutionofthedetectorσdand
thepixelresolutionσpoftheopticalfilmscanneraretakenintoaccountbytheGaussian
with(4.5)Eq.inσ=(xod/xso)2σs2+σd2+σp2.(4.6)
TheyfurtherreducethecontrastascanbeseenatFig.4.2(b).

26

kgroundbacBasic4.1

Figure4.2:Calculatedintensitypatternforapolyamidestringof30µmdiameterincase
ofpolychromaticX-rays.StandarddeviationoftheX-raysourcespotsizeσh=8.6µm,of
thedetectorresolutionσd=1.96µm,andthefilmscannerresolutionσp=9.77µm.The
source-to-objectdistanceisxso=5.88mandtheobject-to-detectordistancexod=5.5m.
(a)TheweightedintensityprofileproducedbytheX-rayspectrumrecordedbytheX-ray
film,seeFig.4.6(c).(b)AfterconvolutionwithaGaussianwhichtakesintoaccountX-
raysourcesizeprojectiononthedetectorplaneanddetectorresolutionaccordingtoσ=
(xod/xso)2σv2+σd2+σp2=12.8µm.
4.1.3Refractioncontrastinthepictureofgeometricaloptics

Thecalculationoftherefractioncontrastintheframeworkofwaveopticsistheonly
correctdescription.However,theexamplesshowninthelastsubsectiononthisba-
sisrequireconsiderablecomputationaleffortandcannoteasilybeusedforinvolved
simulationsoftheexperimentstobecarriedthrough.Therefore,asimplemodelhas
beendevelopedintheframeworkofgeometricaloptics[Bac05]whichisdescribedin
A.1.endixAppThenormalizedtotalintensitydistributionI(n,gω)ofarefractioncontrastradiographfora
transparentstringofaradiusRandrefractiveindexdecrementδ2,whichissurrounded
byamediumofrefractiveindexdecrementδ1,isexpressedby
(ω)zddNdN0
In,g(zd/R,ω)=θ(R∙(1+xod/xso)−1)+d(zd/R)/d(zd/R)=(4.7)
zd(1+xod/xso)
=θ(R∙(1+xod/xso)−1)+(1+xod/xso)+A(ω)/(1−(zo/R)2)23
withzo/Rasolutionoftheequation
zd=zo(1+xod)+A(ω)zo/R,(4.8)
RRxso1−(zo/R)2

27

4Refractioncontrastradiography

withθ(x)istheunitstepfunction,andA(ω)=2xodδ(ω)/R.Atypicalintensity
distributionI(¯n,ghω)(zd/R,¯hω)asafunctionofthereduceddetectorcoordinatezd/R
isshowninFig.4.3(a),dashedcurve.Thesharpincreaseoftheintensityatthe
geometricalbordersofthestringoriginatesfromthefactthatinthismodelwaveoptical
phenomenaareomitted(λ→0).However,thesecanbeapproximatelytakeninto
accountbyaconvolutionwithaGaussianofstandarddeviationσw=λxsdxod/(2πxso)
whichcanbeestimatedfromtheexponentialinEq.(4.1).Theargumentisthatfora
fixedpointzointheobjectthetypicalspreadinthedetectorplaneisgivenbyaregion
|zoxsd/xso−zd|<σw.For|zoxsd/xso−zd|σwtheexponentialoscillatesrapidly
andthemeanvalueinzdapproacheszero.Again,projectedsourcesizeσs,detector
resolutionσdandpixelresolutionofthefilmscannerσpdeterioratethecontrast.The
totalstandarddeviationoftheGaussianwithwhichtheinitialdistributionmustbe
convolutedisgivenby

λxxxσ=(od)2σs2+σd2+σp2+odsd.(4.9)
xso2πxso

InthefinalintensitydistributionIn,g(zd/R)alsotheenergydistributionoftheprimary
polychromaticX-raybeam,includingtheresponseoftheX-raydetector,hastobe
takenintoaccount.Itisobtainedbyanintegrationwiththenormalizeddistribution
functionf(¯hω)whichistheX-rayspectrumrecordedbytheX-rayfilm,seebelow
isresultThe4.2.2.subsection

2In,g(zd/R)=√1I(¯hω)(z/R,¯hω)∙exp[−(zd−zd)]∙f(¯hω)∙dz∙d¯hω,(4.10)
2πσn,gd2σ2d


withσgivenbyEq.(4.9).

InFig.4.3(b)thecalculatedcontrastisshown.Withabeamspotsizeapproaching
zeroandidealresolutionoftheX-rayfilmthecontrastCrefinthelimitofgeometrical
optics(λ→0)islargerthan55%.Waveopticalphenomenaconsiderablydiminishthe
contrastatsmalldistancesbetweenobjectanddetectorandalargedistancewould
befavorable.However,thefinitesourcespotsizeandthefinitedetectorresolution
diminishthecontrastaswell.Tokeeptheinfluenceofthefinitebeamspotsizeas
smallaspossible,theobject-to-detectordistanceshouldbesmall.Then,alsothe
detectorresolutionmustbeincreased,however,itmustnotbemuchbetterthanthe
waveopticalvalueσw=λxsdxod/(2πxso).Inaddition,itmustalsobetakeninto
accountthat,despiteatlargerobject-to-detectordistancesxodthecontrastincreases,
thequalityoftheedgeenhancementdeterioratesbecauseofabroadeningoftheedge.

Asdiscussedinthelastparagraph,therearemanyconflictingrequirementsfortheop-
timumobject-to-detectordistancexodandanexperimentalinvestigationofthissubject
e.erativimpabsolutelyis

28

talerimenExp4.2

Figure4.3:Calculatednormalizedintensityprofilesofapolyamidestring.Photonenergy
¯hω0=19.6keV,stringdiameter135µm,source-to-objectdistancexso=5.88m,object-to-
detectordistancesxod=5.5m,δ(¯hω0)=6.75∙10−7,β(¯hω0)=2.6∙10−10.(a)Dashed
line:calculationsbasedongeometricalopticsaccordingtoEq.(4.8),fullline:waveoptics
σ=σw=λxsdxod/(2πxso).(b)ContrastCrefasafunctionoftheobject-to-detector
approximatelytakenintoaccountaccordingtoEq.(4.10)withf(¯hω)=δε(¯hω−¯hω0)and
.xdistanceoderimentalExp4.2

Set-up4.2.1

TheMeVprincipleelectronofbeamtheprorefractionducesinconatrasttransitionradiographradiationyisfoildepictedstackinapFig.olyc4.4.hromaticThe855X-
raybeamwhichpropagatesinforwarddirection.Theelectronbeamisdeflectedbya
bfilmendingtheobmagnetjectstoandbeguidedimagedinaretolothecated.beamdump.InadistancexodfromtheX-ray
AnorefractionverviewconoftrasttheexpradiographerimenytalisshosetupwnatinFig.MAMI4.5.withTheallbreleveamanlinetcomphasboneneentsfordesignedthe
isandfocusedconstructedatthebycenF.terHagenofthebucktarget[Hag01].chambTheerbyelectronmeansbofeamtheofanquadrupenergyole855doubletMeV
Q1.Insidethetargetchamberthetransitionradiationfoilstackandbeamdiagnostic
installed.aretselemenThefoilstackconsistsof30polyimidefoilwithathicknessof25µmandspacings
betwelectroneenbtheeamfoilshasisbofeen75µmmeasured(theb33ykaeVfoiltungstenstackwireinofT10ableµm3.1).diameter.ThespotThesizeofelectronthe
isbeamshieldedisbguidedyabehindconcretethewalltargetof1cmhamthicberknesstotheandb3.5eammdump.heightThefrombeamtheexpguideerimensystemtal

29

4Refractioncontrastradiography

Figure4.4:Schematicdiagramshowingtheexperimentalsetupforrefractioncontrastra-
diography.Themaximumsource-to-detectordistanceisxsd=13m,measurementsatobject-
to-detectordistancesxod=13from0to7.12m.

areatoreducethebackgroundproducedbyelectronswhichemittedabremsstrahlung
asphotonwellasinthetheTRbacfoilkgroundstackfromandtheleftbtheeambeamdump.linebTheehindpolycthebhromaticendingX-ramagnetysproBM2,ceed
in120forwµmardthicknessdirectioninaandleadistancevetheofv5.88acuummfromsystemthefoilthroughstack.apTheobolyimidejectsexittobewindoimagedwof
xareod,mounwith5ted.88inmair<atxso<differen13tmanddistances0m<fromxodthe<7.target12xm.soTheandfrommaximtheumaX-ravyailablefilm
source-to-detectordistancexsdisabout13m.

filmyX-ra4.2.2

FortherefractioncontrastradiographyexperimentsaspositionsensitivedetectorsX-
rayfilmshavebeenused.X-rayfilmshaveahighspatialresolutionofupto2µm
(FWHM),alargeworkingareaandahighquantumefficiencyoverawiderangeof
tophotonrecordinenergies.tensityTheseinformationadvantagesdespitearetheofthereasondisadvthatanX-ratageyoffilmstheircontinlimiteduetobedynamicused
rangewhichistypicallyintheorderof1:1000.
TheX-rayfilmusedinthecurrentworkisMamorayMR5IIPQproducedbyAgfa1.
Itisbasedonsilverbromidewithanemulsionthicknessofdf=12µm[Hen86].
theThebX-raenefityoffilmshighhavebspatialeenusedresolutionwithoutofinabouttensifier200screenslp/mm2.(directTheexposure)utilizationtoofkeepan
intensifierscreenwoulddegradethespatialresolutionto(15-2)0lp/mm[Spy02].The
12lpAgfa-GevmeansaertlinepairN.V.,B2640MortselBelgium

30

4.2

talerimenExp

Figure4.5:Overviewoftheexperimentalsetupfortherefractioncontrastradiography
intheexperimentalareasEXH1,EXH2ofMAMI.Therelevantcomponentsareafocusing
quadrupoledoubletQ2inadistanceof0.94mfromthetransitionradiation(TR)foilstack
intubtheewhictargethcconnectshamber,thethetargetbendingchambermagnetwithBM2,anwhicadditionalhdeflectscrystalthespelectronectrometerbeam,chamabveracuumand
theX-rayfilm.AquadrupoledoubletQ2installedinEXH1isusedtopreparetheelectron
beamforanoptimalfocusingbythequadrupoledoubletQ1.

31

4Refractioncontrastradiography

twithypicalµf(¯hω)absorptionthelinearefficiencyattenofuationthecoX-rayefficienfilmt,disfgivtheenthicbyknesstheoffactortheemexp[−ulsion,µf(¯hωand)dfis],
showninFig.4.6(a).Itvariesbetweenabout2-60%forenergiesbetween6and50
keV[Dia74].AsshowninFig.4.6(b)thelowenergyX-rayspectrumattheposition
ofexitthewindoX-rawyfilmmadeofhardenspolyimidesincewithphotonsthicoftheknessdradiator=120foilµmstackandareintheabsorbeddistanceintheof
pd(1a−5.exp[5−mµpthe(¯hω)dpphotons])∙(1tra−velexp[in−µair.a(¯hωThe)da]).hardeningTheiseffectivtakeeninphotontospaccounectrumtbytheimpingingfactor
theX-rayfilmisshowninFig.4.6(c).Thequantitiesµp(¯hω),andµa(¯hω),arethe
linearattenuationcoefficients,ofthepolyimideexitwindow,andofair,respectively.
Theyweretakenfrom[PhyXX,Sto70,Hen93].
TheexposedX-rayfilmswereprocessedman◦ually.TheyweredevelopedwithG135A
andG153Bdeveloperforthreeminutesat20C.ThentheywerefixedwithG354fixer
forfor5threeminutesminandutesatthenthedried.sameThetempX-rayerature.filmswFinallyerethedigitizedfilmswithwereaNikrinsedonfilmwithwscannerater
3aSuppixelerCosizeofolScan(6.354000×6ED.35)whicµmh2orhasbayaspatialNikonfilmresolutionscannerof4000SuperdpiCocorrespolScan2700ondingEDto
withspatialresolution2700dpicorrespondingto(9.4×9.4)µm2pixelsize.
ThespatialresolutionoftheX-rayfilmhasbeendeterminedbymeasuringtheedge
spreadfunctionofarazor-blademountedincontactwiththefilm.Thelightemitted
fromacondenserlenslightsourceof500µmdiameterwasused,mountedatadistance
of70cmfromthefilm.Asmallrazor-blade-to-filmdistance,alonglightsource-
edgeto-razor-bladespreadfunctiondistancebyandtheasourcesmallprolightjectionsourceonsizetheavfilmoidandthealsodeteriorationdiffraction.ofThethe
manX-rayufacturerfilms,asinusual,ordertohavgetebeenmaximdevumeloppederformance.undertheThefilminstructionswasspdigitizedecifiedbwithythean
oftopticalypeF-ViewmicroscopXSeequipp[OlyXX].edAwithproajectionhighofresolutiontheintensitCCDyprofilecameraandparallelanto8bittheADCedge
hasbeenproducedtoimprovethestatistics.Theintensityprofileoftheedgespread
functionwassmoothedanddifferentiatedtogetfinallythespatialresolution(4.6±
0.2)resultsµmarerep(FWHM)ortedofonthethefilmspatialasshownresolutioninFig.ofthis4.7.filminUnfortunatelycaseof,directnootherexposurepublishedsince
itisoriginallydesignedtobeusedincombinationwithintensifierscreens.

Measurements4.3

Atthebeginningofeachmeasurementtheelectronbeamspotsizewasoptimized.
ItssizeatthefoilstackdeterminestheX-rayspotsize.Theelectronspotsizewas
measuredbyatungstenwireof(10±1)µmdiameter.Twocrossedtungstenwires
weremountedinthetransitionradiationchamberonagoniometer.Thegoniometer
givesthepossibilitytoadjustthetargetpositionwithrespecttotheelectronbeam
3dotsperinch

32

4.3

tsMeasuremen

Figure4.6:X-rayspectrumrecordedbytheX-rayfilm.Part(a)representstheabsorption
coefficientsµf(¯hω),µp(¯hω)2andµa(¯hω)ofthe2X-rayfilmemulsionofthickness12µmwitha
compositionof3.1mg/cmAgand4.66mg/cmBr,polyimide,andair,respectively.Part
b(b)y855showsMeVasdashedelectrons,lineseethechaptertransition3,andasradiationsolidsplinetheectrumspofectrumthe33afterkeVfoiltransmissionstack,prothroughduced
thepolyimidewindowwiththicknessof120µmandtravelofadistanceof5.5minair.Part
(c)istherecordedspectrumbytheX-rayfilm[PhyXX].

33

4Refractioncontrastradiography

Figure4.7:Edgespreadfunction(a)andspatialresolution(b)oftheX-rayfilmMamoray
MR5IIPQ(Agfa).Pointsaretheexperimentalresults,solidlinesfitswithanerrorfunction
(a)andaGaussian(b).Thespatialresolutionofthefilmamountsto(4.6±0.2)µm(FWHM).

direction.Whenthetungstenwiremovesacrosstheelectronbeam,bremsstrahlungis
emitted.Itsintensityisrecordedbyaphotodiode,positionedinforwarddirectionclose
totheX-rayfilmpositioninFig.4.5,asafunctionofthepositionofthetungstenwire.
ThemeasuredelectronbeamprofilesareshowninFig.4.8.Theelectronbeamspot
sizeafterdeconvolutionwiththewirescannersensitivityprofilefunction(semicircle),
representingapproximatelytheresponsefunctionofthetungstenwire,wasσh=(8.6±
0.1)µminthehorizontaldirectionandσv=(7.5±0.1)µmintheverticaldirection.
InthenextsteptheX-raybeamspotsizeatthepositionoftheX-rayfilmhasbeen
measured.ItisshowninFig.4.9andthecorrespondingintensityprofilesinFig.4.10.
Theilluminatedareaatadistanceof10mfromthesourceamountstoapproximately
(100×30)mm2(FWHM)whichgivestheopportunitytoimageobjectsuptothe
samesize.TheexpectedX-raybeamsizeat10mfromthesourcecanbeestimated
fromFig.3.5tobeabout28mm(FWHM)inbothdirections.However,withthe
measuredelectronbeamspotsizeandthebeamemittancesh=7.4∙10−3mmmrad
andv=6.6∙10−4mmmrad,standarddeviationsofthebeamdivergenceσh≥0.9mrad
andσv≥0.09result,respectiv2ely.Fromthesenumbersanemittance-givenspotsizein
10mdistanceof(90×9)mm(FWHM)canbecalculated.Fromtheseconsiderations
itcanbeconcludedthatthemeasuredwidthinhorizontaldirectionisdetermined
bytheemittanceoftheelectronbeamwhileinverticaldirectionbytheTRemission
haracteristics.caThedensitobyjectsofto1.14beg/cmimaged3,wanderepolycomplexamiderefractionfibreswithindexthecparametershemicalformδ=ula6.C7512∙H1022−N72Oand2,
β=2.6∙10−10ataphotonenergyof19.6keV.Thestringshavedifferentdiametersof
30,170,270,350and450µm.Theseobjectshavenegligibleabsorptionataphoton
energyof19.6keVrangingfrom0.1%to1.26%,whichassuresthattheyareoptimal

34

4.4Determinationofthenormalizedcontrast

Figure4.8:Measuredelectronbeamspotsizeatanelectronbeamenergyof855MeV,(a)
inthehorizontaldirection,and(b)intheverticaldirection.Theelectronbeamcurrentwas
335nA,thestepincrementhorizontally1.6µmandvertically4µmandtherecordingtime
2.5sperpoint.Themeasuredstandarddeviationsofthespotsizeafterdeconvolutionare
σh=(8.6±0.1)µminthehorizontalandσv=(7.5±0.1)µminverticaldirection.Taken
[Hag01].from

phaseobjects.Inaddition,twodimensionalobjectsasgreenleaves,Rumexcrispus
andFicusbenjaminus,wereimaged.
Differentradiographshavebeenrecordedatdifferentobject-to-detectordistancesxod
rangingfrom0to5.5mandalsowithdifferentexposuretimesdependingonthe
ameasuremensource-to-detectortisshowndistanceinxFig.sd,and4.11,alsowhereonthethevisibilitelectronybeamenhancemencurrentt.ofAnlowexampleabsorbingof
materialslikepolyamidestringscanclearlyberecognized.

4.4Determinationofthenormalizedcontrast

TheconversionofthehighresolutioninformationontheX-rayfilmrequiresapointby
pointconversionofthefilmimagesintodigitalform.Thisproceduremayalsolimitthe
dynamicalrangeoftheradiographifthedigitizingdepthsofthescanningdensitometer
isnotsufficient.Sinceourlaboratoryisneitherequippedwithahighperformance
developingstationforX-rayfilms(theexposedX-rayfilmsmustbecarefullyprocessed)
norahighperformancedensitometer,reductionsintheobtainableaccuracycouldnot
beavoided.Inthissectiontheappliedproceduretoobtainquantitativeintensity
informationfromtheradiographsdespitetheseshortcomingsisdescribed.
TheprimaryquantitywhichismeasuredbyanX-rayfilmisthephotographicdensity

35

4Refractioncontrastradiography

theFigureX-ray4.9:film.X-raTheybspeamotsizespotamounsizeintsatoabdistanceout100of10mmminfromhorizonthetalX-raandy30sourcemmasintakvenerticalby
direction.Thisshaperesultsfromtheelectronbeamdivergenceandthetransitionradiation
cone.emission

Figure4.10:IntensityprofileoftheradiographshowninFig.4.9.(a)Horizontallyand(b)
erticallyv

Dlighp.tItinistensitydefinedasimpingingtheonbasisthe10filmandlogarithmitheasinDptensit=ylog(imeasured0/i)bwithythei0thedetectoropticalof
antheunexpdensitometer.osedpartFofromthethisfilmmprimaryustbequantitsubtractedythetosocalledobtainfogtheDfdensit=yDlog(i=0/i0Df)p−of
pDerf=unitlogarea(i0fdE/i)/dAwhichdepmustositedbebyrelatedtheX-ratoytheexpphotonsosureatbaofcertainthefilm,locationi.e.the−r→atenergythe
cfilm.haracteristicsThelatterofisthegivenX-rahereybysource.theTheanglesexpθandosureϕiswhicgivhenbydescribethephotonemission

2dAdE(θ,ϕ)=(Ie/ex)2∙texpd(d¯Nhω(θ/,¯hωϕ,)¯dhωΩ)∙(1−exp[−µp(¯hω)dp])∙
sds∙(1−exp[−µa(¯hω)da])∙(1−exp[−µo(¯hω)do])∙exp[−µf(¯hω)df]∙d¯hω.

36

4.4Determinationofthenormalizedcontrast

Figure4.11:Radiographofasetofpolyamidestringsofdifferentdiametersasgivenatthe
topoftheviewgraph,andtungstenwiresof40µmdiameter.Thesource-to-objectdistance
wasxso=8.11mandtheobject-to-detectordistancexod=3.27m.Theexposuretimewas
40secatanelectronbeamcurrentof6nA.Thevisibilityofthepolyamidestringsisstrongly
enhancedattheinterfaces.Theobjectwiresweremountedvertically.

(4.11)2Here,(dd¯Nhω(/θ¯hω,ϕ,)¯dhωΩ)sistheemittedX-rayphotonspectrumfromthe33keVfoilstack
ethedescribedelemenabovtarye,cseeharge,alsocthapterthe3,expIeisosurethetime,electronandxcurrenttheimpingingdistancebonetwtheeenfoilthestacfoilk,
sdexpstackandtheX-rayfilm.Thequantitiesµp(¯hω),µa(¯hω),µo(¯hω),andµf(¯hω)arethe
linearattenuationcoefficientsofthepolyimideexitwindow(thicknessofdp=120µm),
raofyairfilmem(distanceulsionda(thic5.5knessm),dfthe),obrespjectectivunderely.inThevinestigationtegral(thicextendsknessovdero),theandthecompleteX-
photonemissionspectrum,includingthebremsstrahlungpart.
Inasimpletheoreticalmodel[Geo58]thephotographicdensitycanbedescribedby
D(−r→)=Dsat(1−exp(−b(−r→)/b0))(4.12)
withb(−r→)=dE(−r→)/dAtheexposureattheposition−r→atthefilm.Thesaturation

37

4Refractioncontrastradiography

densityDsatandb0arecharacteristicquantitiesoftheX-rayfilm.
FromEq.(5.13)therelativeexposureisobtainedas
b(−r→)Dsat
b0=lnDsat−D(−r→).(4.13)
Sinceweareinterestedincontrastratios(b(−r→)/b0)/(b/b0)withbameanvalueon
somepositionoutsidethedomainofinterest,theunknownquantityb0cancels.The
stillunknownsaturationdensitymust,inprinciple,bedetermined.However,sincethe
digitizationdevicestoourdisposalhadonlyadepthsof8bitsthemainrestrictionin
thedynamicalrangeisexpectedtooriginatefromthedigitizationprocedureandnot
thedynamicalrangeoftheX-rayfilm.
Theprocedureweadaptedtoobtainthecontrastratioofastringwasthefollowing.At
first,domainsontheX-rayfilmwereselectedinwhichthephotographicdensitywas
assumedtobeinthelinearregion.InthiscaseEq.(5.13)reducestoD(−r→)=Dmax∙
b(−r→)/b0andinthecontrastratioalsothesaturationdensitycancels.Thereafter,we
determinedthecontrastratioatvariouspositionsofthestringforwhichtheexposure
varied,seee.g.Fig.4.12,andselectedthemaximumvalueastheexperimentalcontrast.

4.5Results

Anextensivestudyofthecontrastgenerationasafunctionoftheobject-to-detector
distancexodhasbeenperformedforpolyamidestringsofdifferentdiametersandalsofor
astronglyabsorbingtungstenwire.Thecalculatedabsorptioncontrastforapolyamide
stringwithadiameterof270µmdosnotexceed1%.Therefore,noabsorptioncontrast
canbeobservedwiththetraditionalcontactradiography,i.e.forxod=∼0,inaccord
withourmeasurements.Bymovingtheobjectawayfromthedetector,theimaging
regimeischangedfromabsorptionradiographytophasecontrastradiographyand
phaseshiftisthemechanismtoproducethecontrast.Thecontrastappearsatthe
bordersofthepolyamidestringwherethedensitygradientreachesitsmaximumvalue
andismeasuredbythequantityCref=(Imax−Imin)/(Imax+Imin),seeFig.2.3.
Figs.4.13,4.14,and4.15showasetofradiographsofapolyamidestring4[GooXX]with
adiameterofabout270µmatdifferentobject-to-detectordistances.InFig.4.13(a)the
object-to-detectordistancewasxod=0.5mandacontrastCref=(5.2±3.1)%hasbeen
observed.InFig.4.14theobject-to-detectordistancewasincreasedtoxod=3.27m
andacontrastofCref=(17.8±2.1)%wasdetermined.Forthelongobject-to-detector
distancexod=5.5m,thecontrastCref=(16.7±1.9)%seemstodecreaseagain
slightly,seeFig.4.13.ItcanbeseenfromFigs.4.13,4.14,and4.15thatthebordersof
theblack/whitecontrastbroadenwithincreasingdistancebetweenobjectandfilmxod.
Tothisbroadeningtheprojectedbeamspotsizecontributesatthelargestxod=5.5m
accordingtoEq.(2.12)to19µm(FWHM)whichisalreadyaratherlargefractionin
4suppliedbyGoodfellow

38

4.5

Results

Figure4.12:Radiographofapolyamidestringwithadiameterof270µm.Source-to-
objectdistancexso=7.38,object-to-detectordistancexod=4m,X-raysourcesizeσh=
(8.6±0.1)µm,andσv=(7.5±0.1)µm.Thewhiterectanglesshowthepositionswhere
theintensityprofilesshownattherighthandsideweregenerated,100pixelsaresummed
upvertically.ThechangeinblacknessisduetothechangeoftheX-rayfluxincidentonthe
differentparts.ThecontrastCrefreachesamaximuminpanel(a).

39

4Refractioncontrastradiography

comparisontothedifferencebetweenmaximumandminimumattheborderofabout
m.µ40ThecontrastCrefisdepictedinFig.4.16forallmeasurementsasafunctionof
theobject-to-detectordistancexod.Thecontrastincreaseswithincreasingobject-
to-detectordistancexod,reachesamaximumatabout4m,anddecreasesagainfor
largerxod.Thelatterisaconsequenceoftheincreasingprojectedbeamspotsizeon
thedetectorplane.Furtherresultsforanylonstringof30µmdiameterarepresented
B.endixapptheinFig.4.17(a),(b)and(c)showradiograph,intensityprofileandcalculationofatungsten
wire.Itisinterestingtonotice,thatalsoaweakedgeenhancementisobservedforthis
ject.obabsorbingstrongly

Discussion4.6

isThethatmostaninedgeterestingenhancemenfeaturetorofthephaseconradiographstrastcanshobewninobservFigs.edwith4.13,ap4.14,olycandhromatic4.15
X-raybeam.Thisfacthasbeendiscussedinanumberofpapersalsoinconnection
withtheinterplaybetweenrefractionanddiffraction[Wil96,Hwu99].Thegeneral
featuresofrefractioncontrastimagingwillbediscussedbymeansofFig.4.16,where
allobmeasuremenject-to-detectortsofdistancetheconxod.trastItCcanrefbearestatedshownthatastheerrordistancebarsasbetaweenfunctionobjectofandthe
detectorxodmustbeatleastsolargethatthewaveopticalspreadofthediffracted
X-raysataninterfaceoftheobjectbecomescomparablewiththedetectorresolution.
Otherwisetheinterferencefringesareblurredandthecontrastislow.Withincreasing
prodistancejectedxodX-ratheyspconottrastsizeonincreasestheabdetectoroutplanelinearly.increasesHowever,whatatwtheorsenssamethecontimetrastthe
atlargerdistances.Themaximumofthecontrastisafunctionofbeamspotsizeand
filmresolution.Butcontrastisnottheonlyfigureofmerit.Itmustalsobetaken
intodeteriorates.accountThethatlatterwithmighincreasingtbexodundesirabletheedgeincasespreadthatincreasesresolutionandisoftheimpresolutionortance
andnearbyobjectsmustberesolved.
Next,thequestionwillbeaddressedwhetherthemeasurededgeenhancementstruc-
turesometricalcanbmoedels.understoAsohasdquanalreadytitativbeenelypinointhetedoutframewinorkofsubsectionthewav4.1.2,etheopticalandrefractionge-
contrastisinastrictsenseawaveopticalphenomenon,however,withsomecareit
canalsobeexplainedintheframeworkofgeometricalopticsasshowninsubsection
4.1.3.Bothmodelshavetwofreeparameterswhicharethestandarddeviationofthe
beamstandardspotsizedeviationsandofthethebresolutioneamspotofsizetheandX-raythefilmintrinsicincludingresolutionthefilmofthescanner.X-rayfilmThe
havebeenmeasuredtobeσh=8.6µmandσf=2.0µm,respectively.Thepixelsize
ofthescanneris(9.4×9.4)µm2.Thetotalresolutionofthefilmandthescannerwas
measuredtobeσt=(10.0±0.4)µm.

40

Discussion4.6

Figure4.13:(a)Refractionenhancedradiographofapolyamidestringwithadiameter
of270µmatanobject-to-detectordistancexod=0.5m,andasource-to-detectordistance
xsd=11.38m.ThepolychromaticX-raybeamfromtransitionradiationwithspectral
refractivdistributioneindexshowninparametersFig.3.5arehasδb=7een.2∙10used.−7Atandtheβsp=2.74ectrally10−w10.eighThetedenergyelectronofb19.6eamkeVcurrenthet
was6nA,theexposuretimeamountedto60sec.X-raysourcesizeswereσh=(8.6±0.1)µm
andσv=(7.5±0.1)µminhorizontalandverticaldirection,respectively.Theradiograph(a)
wascapturedbyanX-rayfilm(AgfaMamorayMR5IIPQ).Thedevelopedfilmwasdigitized
byanX-rayscanner(NikonSuperCoolScan2700ED)withapixelsizeof9.4∙9.4µm2.(b)
Intensityprofileforwhich100verticalpixelswereaddedtogethertoimprovethestatistics.
(c)Normalizedintensityprofileaccordingtogeometricalopticsasdescribedinsubsection
thewaveopticalcontributionσw=λxsdxod/(2πxso)=2.3µmwithλ=0.633˚A.(d)
4.1.3withthefollowingparameters:filmandscannerresolutionσd=(10.0±0.4)µm,and
Sameas(c)onthebasisofwaveoptics

41

4Refractioncontrastradiography

Figure4.14:(a)Refractionenhancedradiographofapolyamidestringwithadiameterof
270µmatanobject-to-detectordistancexod=3.27m.Forfurtherexplanationsseecaption
4.13.Fig.of

Figs.4.13(c),4.14(c),4.15(c)showcalculationswiththegeometricalmodelpresented
insection4.1.Figs.4.13(d),4.14(d),4.15(d)showcalculationswiththewaveoptical
modelpresentedinappendixA.2.ForbothcalculationsbeamspotsizeandX-ray
filmresolutionhavebeentakenasexplainedabove.Forthegeometricalmodelthe
X-rayspectrumhasbeenapproximatedbyadelta-functionatthemeanphotonenergy
¯hω=19.6keVsincemodelcalculationsshowedaratherweakenergydependenceof
theedgestructure.Thewaveopticalcalculationswereperformedwiththedetected
X-rayspectrumshowninFig.4.6whichwasapproximatedwith22discretevaluesin
theenergyrangebetween8and30keV.Ascanbeseen,both,thegeometricalandthe
waveopticalmodeldescribethegeneralfeaturesofthemeasurementwell.

TheFigs.rather4.13(c),good4.14results(c),for4.15the(c)conaretrastsomehoratiowCrefsurprisingofthesinceingeometricalthemomodeldelanasshoadditionalwnin

42

Discussion4.6

Figure4.15:(a)Refractionenhancedradiographofapolyamidestringwithadiameterof
270µmatanobject-to-detectordistancexod=5.5m.Forfurtherexplanationsseecaption
4.13.Fig.of

Theparameterrealσwparameter=λxmasoxyod/differ(2πxsd)fromwastheintroassumedducedone.whichHowaccounevertstheforgotheoddiffraction.agreement
maybeaconsequenceoftheratherpoortotalfilmresolutionσt=(10.0±0.4)µm.
TheresultsarecollectedinTab.4.1.

Inadditiontotheedgeenhancementthereisalsoanareacontrastforthestringwhich
increaseswithincreasingobject-to-detectordistances.Thiscanbeexplainedasfollows.
SincetheX-rayrefractionindexissmallerthanunity,thestringwithcylindricalshape
behaveslikeaconcavelens.Thefocallengthfcanbecalculatedwiththelensmaker’s
[Hec89]:ulaform

1=2∙((n)−1)=−2δ.
rfr

(4.14)

43

4Refractioncontrastradiography

Figure4.16:ContrastCrefforapolyamidestringof270µmdiameterasafunctionof
theobject-to-detectordistancexod.Thesource-to-detectordistancexso=11.38mwaskept
constantduringthemeasurements.Errorbarsaremeasurements,crossedcirclescalculations
withthewaveopticalmodelwithabeamspotsizeσh=8.6µmandatotalX-rayfilm
resolutionandthescannerresolutionσt=(10.0±0.4)µm.Starsdesignatecalculations
opticsgeometricaltoaccording

δFor=a7.p2∙oly10−7amideatanstringsX-raywithenergydiametersof19.6ofkeV,270µthemfoandcal30µlengthmisandabaoutdisp93.8ersionandindex10.3
.elyectivrespm,Itisveryinterestingthatfortheradiographofastronglyabsorbingtungstenwirewitha
X-radiameterybeam,of40seeµmFig.alsoa4.17.weakTheedgecalculatedenhancemeninttensitcanybeprofileobservofedthewithapradiographolyconhromaticthe
basiscalculatedoftheagainwavefor22opticaldiscretedescription,energyEq.values(4.5),israngingshownformin8Fig.to304.17keV(c).andItwthenas
convresolutionolutedwithfunctionthewithX-raaystandardsourcespotdeviationsizeσσth==(108..06±µ0m.4)andµm.theItcandetectorbeseenspatialthat
justonemaximumremainswhichbringsabouttheedgeenhancement,andallother
fringeshavedisappeared.
Thecomparisonbetweentheexperimentalresultsandthesimulationsbasedonge-
ometricalopticsandwaveopticsshowsthattheedgeenhancementoflowabsorbing
thematerialsinterplacanybbeetweenexplainedrefractionontheconbasestrastofwandaveopticsdiffractionalone.depInendsotheronthepapersobject[Hwu99],mor-

44

4.6

Discussion

Figure4.17:(a)Radiographofatungstenwirewithadiameter40µmatanobject-to-
detectordistancexod=3.27m,andasource-to-detectordistancexod=8.11m,imaged
withpolychromaticX-raysofameanenergyof19.6keV.Theexposuretimeamountedat
anelectronbeamcurrentof6nAto40s.(b)Intensityprofileand(c)asimulationbasedon
waveopticsassumingapolychromaticX-raybeamwithaspectraldistributionasshownin
4.6.Fig.45

45

4Refractioncontrastradiography

Table4.1:ComparisonofthemeasuredcontrastCrefwithcalculationsonthebasisof
thegeometricalmodelCgandthewaveopticalmodelCwforapolyamidestringof270
µmdiameterforvariousobject-to-detectordistancesxod.Thesource-to-detectordistance
xbsdeam=sp11.ot38sizemσwas=k8.ept6µmconstanandt.atotalTheX-raycalculationsfilmwresolutionerepanderformedtheinbscannerothcasesresolutionwithofa
hσt=(10.0±0.4)µm.ThemagnificationisdenotedbyM.
xso[m]xod[m]MCgCwCref[%]
11.330.0510.350.450
10.880.51.054.17.2(5.2±3.1)
9.382.01.2113.115.8(10±3.8)
8.113.271.416.4820.2(17.8±2.1)
7.384.01.5417.921.65(21.0±3.6)
5.885.51.9418.7622.76(16.7±2.0)
phologyandtheobject-to-detectordistance.
AbigadvantageofX-rayphasecontrastimagingisthereductionoftheabsorbed
dosebythesample.ThisreductioncanbeexplainedintheframeworkoftheX-ray
interactionwithmatter.TheX-rayphasecontrastimagingisbasedontheelastically
scatteredphotonsbytheobject(forwarddirection).Thereforeitisproportionalto2
f(atomicscatteringfactor),whereastheabsorptioncontrastisproportionaltof
[Hen93].Asreportedin[Car98]theabsorbeddoseincaseofthephasecontrastimaging
is10timessmallerthantheabsorbeddoseforabsorptioncontrastimaging.

examplesurtherF4.7

Greenstructure,leavwes,ereobusedjectstooftestthebiologicalpinerformanceterestofwitharefractionratherconcomplextrastthreeradiographydimensionalontwo
dimensionalimagesatMAMIusinghardpolychromaticX-raysfromthetransition
radiationsource.Suchobjectswithathicknesssmallerthan1mm,havenegligible
attencauseuationgreenleaconvestrastconsistforofhardtissuesX-rayswith(19.6similarkeV).densitiesX-rayandexaminationsrathersimilarareattendifficultuationbe-
ts.efficiencoTodemonstrate,howtherefractioncontrastradiographyenhancesthevisualization
ofFig.low-Z4.18shomaterialswstwoandradiographsalsotoofshoawgreentheleafdifferenceofFicustobtheconenjaminusvenattionaldifferentradiographobject-y,
to-detectordistances.Ficusbenjaminusisaveryinterestingobjectbecauseitcontains
calciumcarbonate(CaCO)crystalsofsizesabout50µmwhichhavecomplexrefraction
indexparametersδ=1.373∙10−6andβ=3.46∙10−8at19.6keV.Theseinclusionsare
similartothecalcificationinafemalecancerbreast.
ofInconFig.ven4.18tional(a)theradiographobjecty.isFinorconthistactwithgeometrythethedetectorcontrast(xodis=0)mainlyasinduethetocasethe

46

4.7examplesurtherF

TheFigureradiographs4.18:wRefractionereconrecordedtrastbytheradiographsX-rayoffilmapart(AgfaofagreenMAMORAleafYofMR5FicusIIbPQ).enjaminusThe.
electronbeamcurrentwas6nA,theexposuretime40s.Thesource-to-detectordistance
wasxsd=11.38m.(a)Picturetakenatanobject-to-detectordistancexso=∼0m,(b)
atxod=2.5m.The33keVkaptonfoilstackwasused.Theelectronbeamenergywas
855MeV,theelectronbeamspotsizehadstandarddeviationsofσh=(8.6±0.1)µmand
σv=(7.5±0.1)µminthehorizontalandverticaldirection,respectively.

absorptionofX-rayphotonsbytheobject.Asexpected,nocontrastisobservedin
toaccordxod=with2.5expm.Theectations.InradiographFig.4.18shows(b)antheobexcellentject-to-detectorvisualizationofdistanceallisfineincreaseddetails
includingcalcificationsinthegreenleaf.

TwoimportantfeaturesareobservedforrefractioncontrastradiographofFig.4.19
inwhichtheimageofagreenleafofRumexcrispusisshown.Firstly,inthepart
vlabascularelledwithtissue(a)(veins)wherecouldthebleafeisresolvedthinnerwiththanhigh1conmm,trast.thevisibilitSecondlyy,ofinathebundlemiddleof
partlabelledby(b),theobjectisabout3mmthickandcontainsabundleofvascular
tissue(veins).However,theidentificationofanindividualveinisdifficultsinceimages
fromthedifferentveinsintheradiographareoverlapping.

Fasoreverycomplexandradiographicthickobmethojectsd,athedeficiencyrefractionduecontotrastmulti-refractionradiographyatfaces,differenintprincipledetails
externalcomprisingdiametertheobofject.aboutFig.4504.21µmshowsandaindividualradiographfibofersapwitholymeraboutfiber30µbundlemwithdiameter.an
Afortthethemeanbundleasphotonawholeenergyandofless19.6thankeV0.1the%formaximtheumindividualabsorptionfiberisofless30µthanm1.26diame-%
ter.However,theradiographdemonstratesanexcellentvisualizationoftheindividual
ers.fib

47

4Refractioncontrastradiography

Figure4.19:ArefractioncontrastradiographofapartofgreenleafRumexcrispus.The
radiographwasrecordedbytheX-rayfilmMAMORAYMR5IIPQ(Agfa).Theobject-to-
detectordistancewasxod=5.5matasource-to-objectdistanceofxso=5.88m.Withthese
parametersthemagnificationwasabout2times.Theelectronbeamcurrentwas6nA,the
exposuretime40s.The33keVkaptonfoilstackwasused.Theelectronbeamenergywas
855MeV,theelectronbeamspotsizehadstandarddeviationsofσh=(8.6±0.1)µmand
σv=(7.5±0.1)µminthehorizontalandverticaldirection,respectively.
rksremaConcluding4.8

IthasbeenshowninthischapterthatthehighlydirectionaltransitionradiationX-ray
beamatMAMIiswellsuitedfornormaland,inparticular,refractioncontrastradiog-
raphy.Duetothelowdivergenceangleofthebeamofabout0.8mradtheobjectcanbe
placedatlargedistancesfromtheX-raysourceinastillconsiderablephotonflux.At
closeobject-to-detectordistancesthedeterioratinginfluenceofthefiniteX-raybeam
spotsizeontheresolutionbecomesnegligiblysmall.AssuminganidealX-raydetector
andconsideringthelimitationbytheeffectiveX-raysourcesize,theminimumachiev-
ablespatialresolutionisS=S∙xod/xso.Thespatialresolutioncanbefurtherreduced
bymicro-focusingtheelectronbeam.Ingeneral,thesmallerthedistancebetweenob-
jectanddetectorthehigherthespatialresolutionintheradiographs.Atransition

48

Concluding4.8remarks

Figure4.20:RefractioncontrastradiographofapartofagreenofleafFicusbenjaminus.
TheradiographwasrecordedbyX-rayfilm(AgfaMamorayMR5IIPQ).Theexposuretime
wmasat50asatansource-to-obelectronjectbeamdistancecurrenoftxofso6=nA.5.88Them.obThe33ject-to-detectorkeVkaptondistancefoilwstacaskxwodas=6used..18
Theelectronbeamenergywas855MeV,theelectronbeamspotsizehadstandarddeviations
ofσh=(8.6±0.1)µmandσv=(7.5±0.1)µminthehorizontalandverticaldirection,
.elyectivresp

Figure4.21:Refractioncontrastradiographofapolymerfiberbundlewirewithanouter
wasdiametercapturedofabwithout450theµX-ramyandfilmsingle(AgfafibersMamoraofayMR5diameterIIofPQ).aboutThe30µelectronm.Thebeamradiographcurrent
was6nA,theexposuretime40s.Theobject-to-detectordistancewas3matasource-to-
objectdistanceof7m.The33keVkaptonfoilstackwasused.Theelectronbeamenergy
was855MeV,theelectronbeamspotsizehadstandarddeviationsofσh=(8.6±0.1)µm
andσv=(7.5±0.1)µminthehorizontalandverticaldirection,respectively.

49

4Refractioncontrastradiography

invradiationariousX-rayapplications,sourcewithsuchaasmicro-fomedicalcusedradiographelectrony,beammaterialcouldbscience,eavenaluablevironmensourcetal
betheapplications,conetc.taminationHowofever,theaX-radisadvybaneamtagewithwhichhighlimitsenergythemedicalbremsstrahlungapplicationsphotons.may
Atfinitebutstillclosedistancesbetweenobjectanddetectorrefractioncontrast(phase
contrastoredgeenhancement)occurs.X-rayphasecontrastradiographycanbecarried
theoutobusingjectsavanderyansimpleX-rayexperimendetector.talsetupDemandswhiconhtheconsiststransvoftheersetransitioncoherenceofX-raythesource,X-ray
beamdetectortoplaneobservecanphasebekconepttrastsmallarebynotasevsmalleresincedistancethebetproweenjectedobjectsourceandsizeatdetector.the
Agoodlongitudinalcoherenceisnotatallaprerequisitesincethepositionofthe
firstinterferencemaximumatdiscontinuitiesdoesessentiallynotalterwiththephoton
.energyThereisnoneedforsophisticatedcalculationstorealizethatforrefractioncontrast
arisesradiographfromyathefactsignificanthattonlyhighfewcontrastphotonsisareobtainedabsorbwithedloinwlowabsorbedabsorbingdose.Thematerialslatterto
radiographed.ebItmightbeworthtocomparetherefractioncontrastradiographsobtainedatMAMI
withsimilarmeasurementsatbigsynchrotronradiationfacilitiesasESRF,APSand
[Mor02,Spring8,etc.Koh00]AtwhicthesehisfacilitiesmuchthelargerprimarythantheX-rayspspototsizesizewhicishincanthebeorderofobtained20-35µwithm
thelowemittanceelectronbeamofMAMI.Althoughthetransitionradiationbrilliance
oftheMAMIX-raybeammaybemuchlowerasthatofthementionedsynchrotron
radiationsources,thequalityofrefractioncontrastradiographsiscomparable[Kun01].
InthischapterapolychromaticX-raysourcehasbeenusedtorecordhighquality
therefractionhardX-raconytrastphaseconradiographstrastofimaginglowandabsorbingin-linematerials.holographyInusingtheafollomonowingcchromatichapter,
X-raybeamwillbeinvestigated.

50

5TowardshardX-rayin-line
holography

Intheprecedingsectionsithasbeenshownthatthetransitionradiation(TR)X-
rainyvsourceestigationiswofellthesuitedpossibilitforyofrefractionX-rayconphasetrastconimaging.trastThisimagingchapterandharddealsX-rawithythein-
lineholographywithmonochromaticX-raysatMAMI.ThegoodemittanceofMAMI
allocoherencewstheofthepreparationTRofX-raaymicro-fosource.cusThewhichislongitudinalaprerequisitecoherenceofthecanberequiredachievtransvedbyersea
fosinglecusedcrystalelectronmonobeamcandhromator.theTheresultsexpobtainederimentalsofarsetup,willthebedescribpreparationedinofthisthechapter.micro-

5.1BackgroundBasic

Inchapter2itwasalreadyshownthattheholographicinformationofanobjectis
imprintedintheinterferencepatternatthedetectorplanewhichoriginatesfromthe
interferenceofthewavescatteredbytheobjectandtheoriginalwaveemanatingfrom
theX-raysource.Thissectiondeepenstheseconsiderations.
Awaveemanatingfroma”point”sourcemayilluminateanobjectfromwhichitis
scattered.ThewaveamplitudeE(r)canbesplitintothereferencewaveE0(r)and
ascatteredwaveEscat(r)=a(r)∙E0(r)andtheamplituderatiocanbewrittenas
E(r)/E0(r)=1+a(r),fordetailsseeappendixA.2.Thescatteringamplitudea(r)
containstherequiredinformationontheobject.Onadetectorscreen,asanX-rayfilm
oraCCDdetector,thesquaredabsolutevaluesoftheamplitudes|E(r)|2and|E0(r)|2
aremeasuredfromwhichthenormalizedcontrastratio
22Inorm(r)=|E(r)|−|E20(r)|=2[a(r)]+|a(r)|2.(5.1)
|E0(r)|
canbedetermined.Thenominatoristhecontrastimage,bydivisionthroughthe
referencewave|E0(r)|2thenormalizedcontrastimageisobtained.
Theappearanceof2[a(r)]=a(r)+a∗(r)ontherighthandsideofEq.(5.1)shows
thatthehologramcontainsalsoinformationontherealpartofthescatteringampli-
tuderatherthanonlyitsabsolutevaluesquared|a(r)|2whichmaybereferredtoas
”classicaldiffractionpattern”ofthecomplementarytransmissionfunctionoftheob-
ject,seeappendixA.2.Suchclassicaldiffractionpatternsareobservedindiffraction

51

5TowardshardX-rayin-lineholography

experimentsinwhichthereferencewaveisabsent,e.g.,atdiffractiononaslitwhichis
thecomplementarytoanopaqueobjectas,e.g.,anopaquewire.Whiletheclassical
oscillatesdiffractionrapidlypattern,seeisFig.rather5.1smo(b).oth,TheseseeFig.5.1oscillations(a),thehaveaholographicrathersmalldiffractionamplitudepatternand
canhardlybeseeninameasurementofthehologramwhichisshowninFig.5.1(c).
Mucstrings,hmoreseeFig.pronounced5.1(d),(e)oscillationswhicharearemainobservtainededforinthetransparensumofttheobjectsclassicalaspandolymerthe
holographicdiffractionpattern,seeFig.5.1(f).Theseoscillationscontaininformation
onthedistancebetweentheobjectfromthedetectororthesource,seealsoappendix
onA.2,theandbulkviaofthetherefractivstring.eFinallyindex,thedecremenhologramtδandconthetainsviaabsorptiontheβtransvalsoerseinformationcoherence
lengthalsoinformationonthebeamspotsize.Alltogether,ahologramoftranspar-
entobjectscontainsalotofinformation.Whichinformationcanbeextractedfrom
hologramsoftransparentobjectswillbediscussedinsection5.5.3.
WithreferencetoFig.4.1,ourexperimentswereperformedintheintermediateregion
(III).AshasbeenpointedoutinmoredetailinappendixA.2wedonotapproachin
thisreduceregiontoaaFsimpleourier-transformsituationofinthewhichthecomplemenFtaryresnel-KirctransmissionhhoffintegralfunctionEq.p(z(2.18)o)ofmathey
object,inourcaseastringwithradiusR.ThereasonisthatthetotalFresnelnumber
NF=R2/(λxso)+R2/(λxod)iseveninthemostfavorablecaseofequalsource-to-
obexample,ject,xso,forandR=ob15µm,ject-to-detector,anX-rayxodw,avedistanceslengthλnot=2smallA˚inandacomparisontosource-to-detectorone.For
Fresneldistancenxumsdb=eris13.6NFm,=whic0.33.hisgivenSophisticatedbyourexpreconstructionerimentalbcodesoundarymaybeconditions,requiredtheto
obtainthegeometricalinformationfromthehologramunderthesecircumstances,but
thedevelopmentofsuchcodesisbeyondthescopeoftheexperimentalinvestigations
ofthisworktobedescribedinthefollowing.

5.2Experimentalset-upandtestmeasurements

5.2.1Principleoftheexperimentandoverview

Theobservationofinterferencepatternsasshown,forinstance,inFig.5.1requires
both,agoodtransverseandagoodlongitudinalcoherencewhichcanbeachieved
withamicrofocusedandmonochromaticX-raybeam.Theserequirementsledtoan
experimentalarrangementatMAMIwhichisschematicallydepictedinFig.5.2.As
monochromatoraflatsinglecrystalinBragggeometryisused.Theobjectstobe
imagedcanbeplacedbetweenTRradiatorandmonochromatorcrystalclosetothe
TRsourceresultinginamagnificationoftheobjectuptoafactorof7.4or,alter-
natively,betweenmonochromatorandX-raydetector.Themagnificationmaybeof
importancetocompensateforamoderatedetectorresolutionif,e.g.,CCD-chipsina
directexposuremodeareused.

52

5.2

Experimentalset-upandtestmeasurements

Figure5.1:Analysisofthenormalizedcontrastimageintodistinctpatternsforatotally
opaquetungstenwire,leftcolumn(a),(b)and(c),andforanapproximatelytransparent
polymerstring,rightcolumn(d),(e)and(f).Bothwireshavethesamediameterof25µm.
TheX-rayphotonenergyis6keV(λ=2.067˚A),thecomplexrefractionindexparametersare
δW=8.5∙10−5andβW=1.1∙10−5andδP=7.3∙10−6andβP=2.55∙10−8fortungstenand
polymer,respectively,atthisenergy.Thesource-to-objectdistanceisxso=1.92mandthe
object-to-detectordistancexod=11.68m.Panels(a)and(d)showtheclassicaldiffraction
pattern|a(zd)|2whichisthediffractionpatternofthecomplementaryobject,(b)and(e)the
holographicdiffractionpattern2Re[a(zd)]whichcomeaboutbytheinterferencebetweenthe
disturbedwavefrontbytheobjectandthereferencewaveemanatingfromthesource,(c)
and(f)showthenormalizedcontrastimages.

53

5TowardshardX-rayin-lineholography

Figure5.2:SchematicexperimentalsetupforX-rayin-lineholographyatMAMI.Shown
arealsothemaincomponentsandthelocationsoftheobjectstobeimagedwhichcanbe
positionedindistancesof1.88,4.3,7.47,10.78,12.71and13.6mfromtheX-raysource.

Afull-scaleoverviewoftheexperimentalsetupisshownFig.5.3.Itconsistsofthe
theelectrontargetbeamsetuplinewithwithTRvfoilariousstacfoks,cusingthesingleelementscrystalformonopreparationchromatoroftheinamicro-fodistancecus,
mof7.8frommthefrommonothectarget,hromator.andaThepCCDositiondetectoroftheorobanjectsX-rabyetwfilmeeninaX-raydistancesourceofand5.8
detectordependsonthedesirablemagnificationwhichisconnectedwiththespatial
resolutionoftheX-raydetector.Allcomponentsarehousedinaconnectedvacuum
insystemthefollotoavwingoidinselfmoreabsorptiondetail.oftheX-rays.Theessentialcomponentsaredescribed

5.2.2Theelectronbeamline

TheelectronbeamlineislocatedinthehallBoftheMAMIacceleratorfacility.The
7.1◦bendingmagnetBM0attheexitofRTM3guidestheelectronbeamwithamax-
imumenergyupto855MeVintotheX1beamline.AftertheX-rayproductionin
thetargetc◦hambertheelectronbeamisdeflectedbythebendingmagnetBM1byan
angleof43.5withrespecttotheoriginaldirectionwhichcoincideswiththeX-ray

54

5.2Experimentalset-upandtestmeasurements

Figure5.3:LayoutoftheexperimentalareaoftheX1collaborationwithMAMIB.Shownis
theX1beamlinewithbendingmagnetsBMandquadrupolesQ.X-raytransitionradiation,
generatedbytheelectronbeamuptoanenergyof855MeVinafoilstacklocatedinthetarget
chamber,ismonochromizedbyasiliconsinglecrystalinthecrystalspectrometerchamber
anddetectedwithX-raydetectorslocatedonthedetectorcarriage

◦coemissionoledbeamconeanddumpwhicthereafterhisbydesignedthedipforoleamagnetmaximumBM2avbyailable7.2bdoeamwnincurrentothetofw100ater
µA.Themicro-focusoftheelectronbeamdemandsalargebeamspotsizejustprior
tothefocusingquadrupoledoubletQ4.Toaccomplishthis,itwasnecessarytoinstall
anadditionalquadrupoledoubletQ2intheextractionbeamlineoftheRTM3accel-
erator.Raytracecalculationswereperformedtooptimizethelocationofthebeam
opticalelementsandcurrentsettingstoachieveaspotsizeassmallaspossibleinthe
targetchamber.Atypicalresultofsuchacalculationobtainedwiththeinteractive
computercodebeamoptic[ShvXX]isshowninFig.5.4.
inThehorizonstandardtalanddeviationverticalofthedirection,beamsprespotectivamounely.tsTtoσhransition=1.76µradiationmandσwithv=an1.20energyµm
of6results,keVcorrespaccordingtoondingthetoawequationavσelength∙θof2.067λ/2A˚πproandθducedb=yLsuc/xha,insmallabtransveamsperseot
sdTcohcohvsourcecoherenceandlengthdetector.LT=Suc373hµamtransv(standardersecoherencedeviation)atlengthaisdistanceaxsdprerequisite=13.6tombcarryetweenout
experimentsonhardX-rayin-lineholographyatMAMI.

setuprgetaT5.2.3

ThetargetsetupisshowninFig.5.5.Itconsistsofbeamdiagnosticelementsandfoil
stacksfortheproductionoftransitionradiationintheX-rayregion.Thesecomponents
aredescribedinthefollowingsubsections.

55

5TowardshardX-rayin-lineholography

Figure5.4:Simulationofthemicro-focusedelectronbeamusingtheprogrambeamoptic.
QuadrupoletripletQ1andquadrupoledoubletQ2wereusedtooptimizedtheelectronbeam
sizeattheentranceofQ3.BendingmagnetsBME0andBME1deflecttheelectronbeam
byanglesof2.85◦and4.38◦,respectively,toextractitfromtheRTM3.Bendingmagnet
BM0deflectstheelectronbeambyanangleof7.1◦intotheX1beamline.Quadrupole
doubletQ3preparestheelectronbeamforthemicrofocusingquadrupoledoubletQ4.The
bendingmagnetBM1deflectstheelectronbeamtothebeamdump.Becausethelateral
sizeofelectronbeambehindthemicrofocusrapidlyincreases,thegapofBM1is80mm.
ThequadrupoletripletQ5focusestheelectronbeamagaintoasmallsizesothatitcanbe
guidedwithoutlossesthroughthefollowinglatticeelementsintothebeamdump.Both,the
horizontalbeamenvelope(grey)andtheverticalenvelope(black)areshownalongthebeam
lineintermsofstandarddeviations(RMS-values)inammscale.

eambElectron5.2.3.1diagnostics

Fwireorthescannerpreparationwereofused.theTheelectronZnSmicro-fofluorescencecusZnSscreenpfluorescenceermitsascreensroughandapreparationtungstenof
thespotsize.Inafirststepthespotsizewasminimizedvisually.Inasecondstepthe
beamwasfocusedononeofthepin-holesintheZnSfluorescencescreenwithdiameters
of150µm,200µmand300µm.Thereafterthespotwasoptimizedbyminimizingthe
fluorescencelightemittedfromelectronswhichimpingeonthefluorescencescreenclose
totheperipheryofthepin-hole.
Tofurtheroptimizeandtomeasurethespotsizequantitativelytheelectronbeamwas
sweptacrosstungstenwires.AsshowninFig.5.6,twosteerermagnetswereusedfor
ofthat0.45purpmosefromwhictheharetarget.locatedThedowireshawnstreamvethictheknessesquadrupofoleeitherdoublet10µmQ4forinaaroughdistanceor
4µmforaprecisemeasurement.Theelectricallyisolatedwireformsaloopwithtwo
straightsectionswhichareperpendicularlytoeachothertomonitorthespotsizein

56

5.2Experimentalset-upandtestmeasurements

Figure5.5:Pictureofthetargetsetup.Theelectronbeamdirectionshowsinwardthe
picture.(1)Wirescannerwithtungstenwiresof10µmdiameter,(2)ZnSfluorescencescreen
withpin-holesof150µm,200µmand300µmdiameter,(3)wirescannerwithtungsten
wiresof10µmdiameter,(4)polyimidefoilstackoptimizedforemissionof6keVphotonsat
abeamenergyof600MeV,(5)polyimidefoilstackoptimizedforemissionof33keVphotons
atabeamenergyof855MeV

horizontalandverticaldirection.Thecurrentsignalisgeneratedbytheemissionof
lowenergysecondaryelectrons[Hag95,Hag01].InthecaptionsofFig.5.6andFig.5.7
theprocedureisexplainedinmoredetail.

Fig.5.8showsameasurementofthehorizontalandverticalbeamspotsizeatabeam
energyof600MeV.Theoriginallymeasuredcurrentsignalisafunctionofthetime.
Itwasconvertedintoafunctionofdistancebymeasuringacalibrationfactorinterms
ofrespµm/s.ectivelyThe.TospotextractsizehastheabeamFMHMspotof5size,.2µthemandmeasured4.9µmhorizondistributionstallymandustbveerticallydecon-,
volutedfromtheresponseofthetungstenwiretotheemissionofsecondaryelectrons.
Forthelatterarectangularfunctionwithawidthofthewirediameterof4µmwas
Bothassumed.distributionsThebeamwerespotconwvasolutedassumedandtofittedbeoftotheGaussianmeasuredshapeinbdistributionothwithdimensions.the

57

5TowardshardX-rayin-lineholography

Figure5.6:Arrangementtomeasuretheelectronbeamspotsize.Thesteerermagnet
currentsof±4Aaredeliveredbypowersupplies(ElectronicMeasurementInc.)supplying
sawtoothpulses.Thehorizontaltrigger(ScientificInstrumentsGmbHmodel9410)isdelayed
by0.5swithrespecttotheverticaloneresultinginacontourasshownintheinsert.The
repetitionratewastypically2Hz.Thecurrentfromthewireisamplifiedwithapreamplifier
(homemadebyInst.ofNuclearPhysics,Mainz)andconvertedinavoltagesignal.Signaland
groundsignalofthepreamplifieraresenttothecontrolroomofMAMIwhereadifference
signalisformedtosuppresselectricalpick-upandnoise.Thefinalsignalsarecorrelatedto
thesignalsfromthefunctiongenerators,anddisplayedandsavedonastorageoscilloscope
(TektronixTDS744A)oronaPCafteranalog-to-digitalconversion(ADC-212,Pico212)
[PicXX]

standarddeviationoftheGaussianasafreeparameter.Thebestfitisshownasfull
(3line.8in±0.Fig.7)µ5.8.m,Therespectivhorizonely.talWithandvtheerticalemittancestandardof0.002deviationsmmaremrad(4.5and±0.8)0.00052µmandmm
mradthebeamdivergenceturnedouttobe0.41mradand0.13mrad,respectively.

ofTheotherelectronworksbeamanditiscurrentsmallerstabilitthanyat3%,seeMainzerforexampleMicrotron[Ket00,MAMIisHag01].measuredinalot

5.2.3.2Transitionradiationfoilstacks

Twopolyimidefoilstackshavebeenusedtoproducetransitionradiation.Asdescribed
ofin600sectionMeV.3.2,Anoneumisberofoptimized25pforolyimideahighfoilsX-raywithfluxaatthic6kknesseVatofan12.5µelectronmarebeamspacedenergyout
byaluminiumfoilsof100µmthickness,thelatterwithcentricholesof2mmdiameter

58

5.2Experimentalset-upandtestmeasurements

Figure5.7:Blockdiagramshowingthecontrolunitsforthemeasurementoftheelectron
beamspotsizeandthepositioningofthetargetcomponents,suchastungstenwiresand
foilstacks,withrespecttotheelectronbeam.Thegoniometerwiththetargetcomponents
inHallBarecontrolledfromthecontrolroomofMAMIwiththecomputerGENIOPC1.
ItcommunicatesbyethernetwiththecomputerGENIOPC2inexperimentalhallBwhich
controlsviathemotor-controllerMMTARalltablesofthegoniometer.Twofunctiongenera-
tors(FUN.GEN)generateasawtoothsignal.Onesignalisdelayedwithrespecttotheother
onebyusinganexternaltriggerTRIGG.Thesignalsfromthefunctiongeneratorscontrol
twobipolaroperationalpowersuppliesBOS/S(Electr.Meas.Inc.)whichareconnectedto
twodipolessteerermagnets.Thecurrentsignalproducedinthewirescannerisamplified
bypreamplifierA1.AdifferenceamplifierDA1isusedtosuppresspick-upandnoise.The
outputsignalofDA1isrecordedwithastorageoscilloscopeOSCI(Tektronix)orbythe
oscilloscopePICO.Thesignalsarerecordedwithapersonalcomputer(EPC)

forthepassageoftheelectronbeam.Foilsandspacersaretightlypressedtogether.
Theotherfoilstackisoptimizedforemissionof33keVphotonsatabeamenergy
of855MeV[Joh95].Itconsistsof30polyimidefoilsof25µmthicknessand75µm
spacing.Inordertofindthecenterofthefoilstack,ZnSscreensaremountedinfront
ofthestackswithholesof2mmdiameter.

Thewholetargetassemblyismountedonafouraxisgoniometer,seeFig.5.9,per-
mittingpreciseadjustmentsintheyandzcoordinatesperpendiculartothebeam
direction.Themovementofthetargetsetupinxdirectionallowsameasurementof
thebeamspotsizeatdifferentpositionsalongthebeamaxis.Suchmeasurements
provideinformationwhetherthefocusislocateddirectlyinthefoilstackratherthan
beforeorbehindit.

59

5TowardshardX-rayin-lineholography

Figure5.8:Electronbeamspotsizeasmeasuredwithatungstenwireof4µmdiameterata
beamenergyof600MeV.Theelectronbeamcurrentwas50nA.Shownare(a)thehorizontal
bandeam(b)spottheofvσertical=(1.9profile.±0.3)Theµmfullandlineσ=represen(1.6±ts0a.3)bestµmfitwithstandarddeviationsofthe
vh

5.2.4Singlecrystalmonochromator

inTheBraggtransitiongeometryradiationwithitsX-rayssurfacearemonoparallelctothehromatized(111)withcrystalaflatplane.siliconAnsingleappropriatecrystal
bemonocrotatedhromaticuptoX-ra80◦ywithenergyrespcanectbtoetheselectedforwbyardthedirectionangleofofthetheX-radetectorybarmeam.thatcan
Thecrystalmonowithchromatordimensionssetupofis160×depicted40×1inmmFig.3are5.10.minimizedResidualbystrainsfixingonthethecrystalrectangularjust
onfromaonestand.sideForwiththeptheaidositioningofoffinalthedimensionmonochromatorplates,whilecrystaltheintheotherX-rasideyisconesittingand
axisaccurategoniometer.orientationTheatBraggtheangleappropriatemustbeBraggadjustedangle,thewithhighcrystalisprecision,mountedthereforeonafourthe
hasrotatableanangulartableROT1resolutionisofequipp0.ed0002◦with.Faurtherhighlydetailsaccurateoftherotationmonocencoderhromator(ENC)setupwhicareh
describedinRef.[Ket00,Lin97].
conThetrolled.goniometerDetailsoftheareshomonowncinhromatorFig.in5.11.thecrystalspectrometerchamberiscomputer

rDetecto5.2.5rriageca

Inadistanceof5.8mfromthemonochromatorcrystalX-raydetectorscanbemounted
onacarriagewhichisshowninFig.5.12.Thevacuumchamberisevacuatedinorderto
avoidselfabsorptionoftheX-rays.AsdetectorseitherX-rayfilmsorcharged-coupled

60

5.3Charge-coupleddevice(CCD)asX-raydetector

Figure5.9:TargetandgoniometersetupintheTR-chamber.Theelectronbeammovesin
xwithandirection.accuracyTheof1goniometerµm,0.1µconsistsm,andof1fourµm,tablesrespthatectivalloely,waswmotionsellasinx,rotationy,andzarounddirectionsthez
axiswithanaccuracyof0.01◦

devices(CCD’s)wereused.ForexperimentswithfilmstheX-rayspassthrougha
polyimidewindowof25µmthicknessandwithadiameter50mm,asshowninFig.5.13.
Thefilmsarelocatedinairclosetotheexitwindowtominimizeselfabsorptioninair.

Asspatialalreadyresolutionpointedofaboutoutin2µsectionmwhic4.2.2,htheactuallyadvcanantagebeacofhievX-raedywithfilmsishardtheX-ragooys.d
ThedisadvantageisthatX-rayfilmsareslow,off-linedetectorswithasmalldynamic
arange.directexpElectronicosuremodedetectorsisliklimitedebCCD’sytheallowpixelfastsize.on-lineHowever,imaging.luminescenThetresolutionscreensinin
islimitedconjunctionbywithdiffractionaCCDofoffer,visibleinlightprinciple,toabouton-line0.5µopm.erationBothwithdetectoraresolutionsystemshathatve
beenimplementedandaredescribedinthenextsection.

5.3Charge-coupleddevice(CCD)asX-raydetector

5.3.1Descriptionoftheback-illuminatedCCDchip

phQuany,titativrequireearadiographdigitizationywithapplications,lownoise,suchlargeasphasedynamiccontrastrangeandandhardlinearX-rayrelationshiphologra-

61

5TowardshardX-rayin-lineholography

Figure5.10:Monochromatorcrystalandgoniometersetupinthespectrometerchamber.
TheX-raybeammovesinxdirection.Thesiliconsinglecrystalisinstalledonagoniometer
whichconsistsoffourtableswhichallowmotionsintheorthogonalyandzdirectionswithan
accuracyof1µm,aswellasrotationaroundtheverticalzaxis(ROT1)andtiltswithrespect
tothepropagationdirectionoftheX-raybeam(ROT2).Withahighprecisionencoder
(ENC)fortableROT1theBragganglecanbeadjustedwithaprecisionof0.0002◦

betweentheincidentradiationintensityandtheresponseofthedetector.Suchcondi-
tionscanbefulfilledbycharge-coupleddevices(CCDs)whichhadbeendevelopedat
AtheT&TCCDbysystemW.SBoyleANDORandG.E.DO-434SimBNthinCCD1970[Bo[AndXX]y77].wasForused.theItcurrenconttainsexpaerimenback-ts
pixelsilluminatedofasizeCCDoflo13w×noise13µmsensor2.ThefromANDORMarconiDOCCD47-10434BNCCD[MirXX]chipwithis1024depicted×1024in
Fig.5.15,themainpropertiesofthesystemaretabulatedinTab.5.3.1.Theintegrated
PeltiercoolingsystemprovidesacoolingtemperatureoftheCCDchipof-65◦Cwith
0.002air-cooling,eles/pixel.secand-80◦orCevaten0.additional00083watereles/pixel.seccooling.at-80The◦Clowallodarkwslongcurrenexptatosure-65◦Ctimesof
andprovidesawidedynamicrange.
AthetbacoppkositeilluminationsideofthetheelectroincidendetsystemphotonsandentermustthepsensitivenetrateelayonlyeraofthinthelaCCDyerwithfrom
athicknessofabout10nmresultinginagoodquantumefficiency.Forvisiblelight
thislayerservesasananti-reflectioncoatingtoreducesurfacereflectionlosses.As
shownefficiencyinoFig.vera5.14,widethespbackectralrange.illuminatedForMarconihardX-raysCCD47-10of6kceVhiphasenergyagoitodamounquantstumto

62

5.3Charge-coupleddevice(CCD)asX-raydetector

tersFigureanddata5.11:BloacquisitionckdiagramoftheshoCCDwingthecamera.conAtrolcomputerunitsforthe(MONOPC1)monochromatorcommunicatesgoniome-via
ethernetMMMONOwithofathecomputergoniometerinthetables.X1hallThedirect(MONOPC2)exposurewhicCCDhconcameratrolstheisconmotiontrolledmasterfrom
theputermeasuringCCDPC2roinomthewithexptheerimencomputertalhallX1.CCDPC1,ByusingwhichexternalcommunicatetriggerbyTRIGGethernetthewithelectroncom-
bcameraeam-onaresignalsyncandhronized.thestartThesignalelectronforbtheeamisdataswitchedacquisitionoffwithduringthethedirectreadout.exposureCCD

stillabout45%.ThesefeaturesoffertheopportunitytousetheCCDchipeitherinthe
directexposuremodeinwhichthesignalisgeneratedbydirectenergydepositionof
hardX-raysinthesensitivelayer,orincombinationwithaluminescentscreenwhich
convertstheX-rayphotonenergypartlyintovisiblelightwhichisdetectedbythe
CCD.

acquisitiondataandElectronics5.3.2

AfterexposurethechargeacquiredinthepixelsoftheCCDisdigitizedpixelbypixelby
meansofa16bitADC.ThereadoutsequenceisdescribedinthecaptionofFig.5.15.
Essentialpartisalownoiseamplifierintegratedonthechip.Toachieveagoodenergy
resolution,thetimeconstantoftheamplifiermustbesufficientlylong,aboutinthe
orderofis1µs.Thedigitizationtimeperpixel1µs.Consequently,theusedCCD
chipisaslowscandevicewithareadouttimeof1.05s.Incontrast,therequirements
onnoiseanddynamicalrangeoffastscanCCDchips,asusedinvideo-orphotographic
cameras,aremuchlessdemanding.
ThesoftwaresuppliedbyANDORallowsintegrationofsuccessiveframes.Inthe
currentwork,typically100frameswereintegratedbeforetheresultantcompositeframe
wasdownloadedtotheharddiskofaPC.Suchmodeisknownasaccumulationmode

63

5TowardshardX-rayin-lineholography

Figure5.12:Sideviewofthedetectorarrangement.ForX-raydetectionwithfilmsthe
vacuumtubehasapolyimidewindowwith25µmthicknessatadistanceof5.8mfromthe
crystal.ThedirectexposureCCDunitisdirectlyconnectedtothevacuumtubewithoutany
window.Amembranebellow(NW200)ismountedbetweenCCDandbeamtubeforthe
purposeofaprecisepositioningoftheCCDunitbymeansoftheXYtablewithanaccuracy
mµ5of

[Mah95]andhastheadvantageofsavingmemoryspaceonthestoragemedium.The
CCDcameramustnotbeexposedtoX-rayphotonsduringthereadouttoavoidimage
deterioration.Therefore,theelectronbeamwasswitchedoffduringthereadoutof
acthehievCCD.edbyTanypicalexternalexposurereferenceandreadsignaloutTRIGG,cyclesareseeshoFig.wn5.11.inFig.The5.16.CCDTheiscontimingtrolledis
fromtheMAMIacceleratorcontrolroomorfromtheX1measuringroomwithaPC
runningonwindowsXP.

5.3.3Thedirectexposuremode

InhardtheX-radirectyexpphotonsosureinthemodesensitivtheesignallayerisofthegeneratedCCD.byThedirectprimaryenergymecdephanismositionisofphotothe
intheabsorption.potentialThewellresultingofthephotopixels.electronscreateelectron-holepairswhicharecollected
Fig.5.12depictstheinstallationofthedirectexposureCCDatthedetectorcarriage.
vToacuumavoidatacondensationpressureofsmallermoisturethan10or−6oilmonbaristhecorequired.oledCCDForcthathipanpurposeoil-freeoil-freehigh

64

5.3Charge-coupleddevice(CCD)asX-raydetector

Figure5.13:SideviewofthecentralpartofthedetectorarrangementforX-rayfilm
exposureandmeasurementswiththeluminescentimagingsystem.X-rayphotonsimpinge
fromtheleftandenterintotheairthroughapolyimidefoilof25µmthickness.Theend
flangeofthevacuumtubehasaclearanceof50mm.TheX-rayfilmispositioneddirectly
behindtheendflange.Theentranceoftheluminescentimagingsystemismadelighttightby
twoaluminizedHostaphanfoilswithd=250µg/cm2coveredwith20µg/cm2aluminum.
TheGd2O2S:Tbluminescentscreenhas12µmthicknessandanareaof(26×20)mm2.A
Canoncameralenswithafocallengthf=50mmandanF-numberof1.4focusesthepicture
ontothecooledCCDchipwhichislocatedinahighvacuumenvironment.Thepicturecan
befocusedremotelybyamechanicaldriveatthelens.

pumpshavebeenusedwithwhichtheCCDcamerachambercanbeevacuatedupto
apressureof10−8mbar.Inordertoavoidabsorptionlossesinwindows,theCCDwas
operatedinthecommonvacuumsystemofthemonochromatorandtargetchamber.
However,theCCDmustbeprotectedagainstvisiblelightwhichmightbegeneratedin
thetransitionradiationfoilstack.Two250µg/cm2thickaluminizedHostaphanfoils,
withanaluminumthicknessof20µg/cm2,aremountedinadistanceof20cmfrom
theCCDchip.Twofoilswereusedtocoverpin-holesinthefoils.
Anumberoftestmeasurementsinthedirectexposuremodewereperformedusingan
55FesourcewhichemitsKαphotonswithanenergyof5.899keVandKβphotonswith
6.49keV.Thesourcewithanactivityof3MBqwaspositionedinvacuumatadistance
of21cmfromtheCCDchip.Thegeometricalarrangementissimilarasthatshownin
Fig.5.13,withtheCCDdecoupledfromthemainvacuumsystem.TheCCDcamera
wascooleddownto-80◦C.Theexposuretimeforoneframeamountedto10sinwhich
about6000eventswerecollectedattheCCD.Thisnumberissmallenoughtoavoid
doublehitsinonepixel(pileup).ThepulsehightdistributionisshowninFig.5.17
(a).TheKαandKβphotonpeaksareclearlyresolved,seealsoFig.5.17(b).However,
asignificantpartoftheintensityappearsinthelowenergytailofthelines.Thereason
forthistailissplit-eventgenerationwhichwillbeexplainedinthefollowing.

65

5TowardshardX-rayin-lineholography

Table5.1:ANDORDO434BNCCDdetectorcharacterization[AndXX].

47-10MarconihipcCCDDepletionlayerthickness[µm]10◦
darkcurrent[eles/pixel.sec]0.00083at-80C
minimumtemperature[◦C]-80
pixelsize[µm2]13×13
effectivearea[mm2]13.312×13.312
R.m.s.readoutnoise[eles/pixel]6.8at1MHz
100000[eles/pixel]ellwfullgain[e−count]@1&2,16,32µs2,1.4,0.7

Whenanincidentphotonwithanenergyof6keVisabsorbedwithinthe10µmthick
depletionlayeritproducesanumberofne=6000eV/3.65eV=1644electron-hole
pairs,sincefortheproductionofoneelectron-holepairanenergyof3.65eVisrequired
[Deb88].Electronsandholesareseparatedintheelectricalfieldofthedepletionlayer
andtheelectronsarecollectedattheelectrodes.ForX-rayphotonswithanenergy
of6keV,the1initial.75diameterDoftheelectroncloudcanbeestimatedtobeD[µm]
=0.017∙[E[keV]]=0.39µm[Bau86].Duringthetransporttotheelectrodesthe
diameterincreasesbecauseoftheelectrostaticrepulsionbetweenthemanyelectrons
anddiffusion.Thismayleadtoadistributionoftheelectroncloudovermorethanone
pixelandspliteventsaregenerated.Onlyfor17%ofalleventsthechargeiscollected
inasinglepixel,ashasbeendeterminedbyanalyzingsingleframes.Itwasfound
thatthechargemaybesplittedinupto7neighboringpixels.Ontheonehand,such
spliteventsdeterioratethespatialresolutionofaradiographbut,ontheotherhand,
theycanbeexploitedtoimprovetheresolutionbythedeterminationofthecenter
ofgravityofthesplitevents.Algorithmshavebeendeveloped[Tsu02]withwhich
sub-pixelresolutionswereobtained.However,preparatoryexperimentsshowedthat
inourcaseatleast23000singleframesarerequiredtoproducejustoneradiograph
withsub-pixelresolutionandgoodstatistics1.Atareadouttimeof1.05sperframe
thisleadstoanunreasonablelongcollectiontimeofnearly7hours.Therefore,this
ideawasnotfurtherpursued,andforallexperimentsdescribedinthefollowingthe
accumulationmodehasbeenapplied.However,itmustbeconcludedfromthetest
experimentsdescribedinthissectionthatonlyaspatialresolutioncanbeachieved
whichisworsethanthepixelsizeof13µm.

1Aswillbeshowninthesection??,aradiographwithgoodstatisticsrequiresasummedpulsehightof
about350,000ADC-counts/pixel,offsetsubtracted.Toreachsuchapulseheight,580photonswith
anenergyof6keVmustbeabsorbedbyasinglepixelsinceone6keVphotongeneratesanADC-
counabsenttnumwhicbherofmeans600,thatseeexpFig.osure5.17.FtimeoraandX-rareconstructionyfluxmustwithbesub-pixelreduced.Thisresolution,requiremenpileuptmleadsustbtoe
anenlargementofthecollectedframesbyaboutafactorof20incomparisontoanormalexposure.
Therefore,therequiredsingleframesare11600.Sinceforanormalizedcontrastradiographthe
imagemustbebackgroundcorrected,weneedadditionally11600singleframesforthecorrected
radiograph.the

66

5.3Charge-coupleddevice(CCD)asX-raydetector

Figure5.14:Quantumefficiencyofabackilluminated(BN)andafrontilluminated(FI)
CCDMarconihashighCCD47-10quanctumhip.Inefficiencycomparisonoveratowidethespfronectraltrangeilluminatedwhichchip,extendsthebacfromkvisibleilluminatedlight
[AndXX].ys.X-rahardto

inTheFig.section5.17(b)willbandeclosed(c),thatwithaaresolutiondiscussionofofthe(127±4)energyeVwasresolution.achievItediswiththedemonstratedCCD
chip.Thetheoreticallimitoftheenergyresolutionisdeterminedbythestatisticsof
theproducedelectrons(Fano-noise-limitedperformance)andthereadoutnoiseσr.Not
allenergyenergyisoftransferredtheabsorbtoSiedlatticephotoninwhicgeneratehphononselectron-holeareexcited.pairsThesinceresultingsomeamounstatisticaltof
fluctuationsaretakenintoaccountbytheFanofactor[Ber68]whichisF=0.115for
silicon,andtheresolution(FWHM)isexpressedas
Δ¯hω[eV]=2.355∙3.65σr+FE3.[eV]65.(5.2)
Atareadoutrateof1MHzthereadoutnoiseisσr=6.5electron(rms)perpixeland
thebestachievableenergyresolutionformonochromatic6keVphotonsisΔ¯hω=120
eV.Theexperimentalresultisratherclosetothisnumber.

5.3.4X-rayimagingwithaluminescentscreen

ThedirectexposuremodeoftheCCDhastheadvantageofagooddetectionefficiency,
however,asdiscussedintheprecedingsectionthespatialresolutionintheaccumulation
modecannotbebetterthanthepixelsize.Inthissectionanotherpossibilitywillbe
discussedtoachieveagoodspatialresolutionwithaCCDdetectorwhichpreservesthe
on-linecapability.Itbasedonthefactthatwiththeaidofaluminescentscreenthe
X-raypicturecanbetransformedintoavisiblelightpicturewhichcanbemagnified

67

5TowardshardX-rayin-lineholography

Figure5.15:Schemetoillustratetheoperationprincipleofachargecoupleddevice(CCD).
Left:Sideviewtoillustratedirectdetectionofphotonsatbackillumination.Right:Front
viewtoillustratetheread-outmechanismoftheback-illuminatedCCDsensorMarconi
CCD47-10.(a)Thestoredchargesinaframeareshiftedbyonerowsothatthebottom
rowmovestotheshiftregister.(b)Thechargeintheshiftregisterismovedhorizontallyby
onepixel.Thiswaythechargeattheendmostpixeloftheshiftregisterismovedintothe
inputnodeoftheamplifier.(c)Thechargeintheoutputnodeoftheamplifierismovedto
theanalog-to-digitalconverterandisdigitized.(d)Steps(b)and(c)arerepeateduntilthe
shiftregisterisworkedout.(d)Theframeisshiftedverticallyagainbyonerow,i.e.thenext
rowofchargemovesdownintotheshiftregister.Steps(b),(c)and(d)arerepeateduntil
thewholeframeisreadout[AndXX]

Figure5.16:ReadoutoftheCCD.After8sexposureoftheCCDtheelectronbeamis
switchedoff,0.1slaterthereadoutstartswhichlasts1.05s,and0.85slateranewcycle
starts.

68

5.3

Charge-coupleddevice(CCD)asX-raydetector

takFigureenwith5.17:an55FPhotonesourceenergyataspectratemperaturerecordedofbythetheCCDCCDchipofdetector−80c◦hip.C,exp(a)osureSpectrumtime
10s.(b)EnlargementoftheK-lineregion.Themeasuredenergyresolutionamountsto
Δ¯anglehω=ofθ0(127=±19.4)25◦eV.whic(c)hSpcorrespectrumondstaktoenaon-linephotonwithenergytheof6siliconkeV.(111)ElectronreflexbateamthecurrenBraggt
1−50nA,◦C.expTheosureenergytimeperresolutionframeΔ¯1hωs.=Pile(129up±4)caneVbeisabcompletelyoutthesameneglected.astheCCDenergytempresolutionerature
obtainedatthelowertemperatureof-80◦C.

69

5TowardshardX-rayin-lineholography

byopticalimagingwithlensesanddetectedbytheCCDchip[Bus94].Inprinciple,a
diffractionlimitedresolutioninthesub-µmregioncanbeobtainedbysuchamethod
[Koc98].However,althoughtheCCDhasahighquantumefficiencyinthevisible
spectralrange,ascanbeseenfromtheFig.5.14,thedetectionefficiencyisreducedin
comparisontothedirectexposuremodeduetoalowconversionefficiencyoftheX-ray
photonsintovisiblelightof15-20%,andalowlightcollectionefficiencyofthelens
systemof0.6%.Aratherfaintopticalpicturemayresultwhichcanbedeteriorated
bybackgroundprocessesoriginatingfromthehardgamma-ray(bremsstrahlung)part
inthetransitionradiationspectrum,seesection3.3.Inthissectiontheresultsof
experimentswithsuchadetectionsystemaresummarized.Detailsarepresentedin
C.endixapptheTheimagingsystemwithaGd2O2S:TbluminescentscreenisdepictedinFig.5.18,and
aradiographtakenwithmonochromaticX-raysof6keVenergyofdifferentpolymer
stringsisshowninFig.5.19.Theessentialfeatureisthattheradiographislittered
withwhitepoints.Theseweregenerallyobservedwiththiskindofimagingsystem,
seeappendixC.Thereasonwasfoundinthehighenergybremsstrahlungbackground
whichisemittedsimultaneouslywiththeX-raysinthetransition2radiationfoilstack.
SincethebremsstrahlungproductioncrosssectionscaleswithZthisbackgroundcould
bediminishedbyemployingfoilswithloweratomicnumbersZas,e.g.,berylliumor
lithium.Inaddition,asophisticatedshieldingoftheCCDchipmayhelptosuppress
thebackground.However,werefrainedfromanoptimizationofthistypeofdetector
systemsinceitwouldhaverequiredagreatdealofdevelopmentsandtests.

5.4Investigationofthefeaturesofthemonochromized
eambphoton

5.4.1Energywidthandlongitudinalcoherencelength
Theflatsiliconsinglemonochromatorcrystal,cutwiththe(111)latticeplaneparallel
tothesurface,actsasamirrorforthetransitionradiationphotonsemittedfromthe
foilstack[Bea74,Har71,Pin84].However,thismirrorisenergydispersiveinthe
horizontaldirection.Thedeviationεofthephotonenergy,definedbytheequation
¯hω=¯hωB(1+),fromthenominalBraggenergy
√¯hωB=2πh2+k2+l2¯hc(5.3)
a02sinθB
isgivenbytheexpression

(χ0)θx
ε=2sin2θB−tanθB(5.4)
whereθx=θ−θBisthedeviationfromthenominalBraggangleθB.Theintegers
h,k,laretheMillerindices,anda0thelatticeconstant.Inourexperimentthe(111)
reflectionwasselected.TheBragganglefor¯hωB=6keVamountstoθB=19.25◦.

70

5.4Investigationofthefeaturesofthemonochromizedphotonbeam

Figure5.18:Imagingsystem(nottoscale).X-rayphotonsimpingefromtherightontothe
Gd2O2S:Tbluminescentscreenof4and12µmthicknessforpolychromaticandmonochro-
maticX-raydetection,respectively[ProXX,SICXX].Anf=50mmCanoncameralens
withF-numberof1.4hasbeenused[CanXX].Theprincipalpointsarelocatedinfrontofthe
lens.Thepictureattheluminescentscreencanbefocusedremotelybyamechanicaldrive
atthelens.ForadetaileddescriptionoftheCCDcameraheadseesection5.3.

Inin-lineholographyascatteredwavefromtheobjectinterfereswithanunscattered
µwaradvefromresultstheinasource.distanceForofa13.6transvm.erseThecoherenceangularlengthspreadsofLTwhic=h250originateµmaθxfrom=18.4the
bangleeamθspxotcorrespsizeandondsthepixelaccordingtoresolutionEq.are(5.4)lesstoathan1relativµeradandenergycanshiftbeof5.3neglected.∙10−5Theor
0.32eV.Thismeansthattwowaveswithslightlydifferentenergiesmustinterferewhat
wiseonlyfirstpossiblecalculateifthethelongitudinallongitudinalcoherencecoherencelengthlengthofLltheislongBraggenough.reflectedToX-rajudgeysitself.this,
ThefiniteenergywidthoftheBraggreflectioncanbecalculatedfromthereflecting
powerratio|RP|2withtheamplituderatiogivenby[Cat89,Eq.(3.2)]
RP(θx,εθ)=−yP(u)+sign[(yP(u))]yP2(u)−1(5.5)
yP(u)=u+i(χ0)(5.6)
χPHu=2sinθB[θxcosθB+εsinθB]+(χ0).(5.7)
Hereanalyzerareχ0crystal,andχandHPthetheFpourierolarizationcomponenfactor,tsofwiththeP=dielectriccos2θBforsusceptibilitiesπpolarizationofthe

71

5TowardshardX-rayin-lineholography

Figure5.19:MagnifiedpartofaradiographtakenwiththesetupshowninFig.5.18.The
imagewastakenwithmonochromaticX-raysof6keVenergy.Thewhitepointsoriginate
fromelectronsorpositrons,producedinashowerbyhighenergybremsstrahlungphotons,
whichpassthroughtheCCDdetector.Inthepartlabelledwith(a)aheavyparticlemoves
throughthedepletionlayernearlyparalleltothesurfaceoftheCCD

withthepolarizationvectorinthereflectionplane,andP=1forσpolarization
withthepolarizationvectorperpendiculartothereflectionplane.Theresultofthe
calculationforapolychromaticX-raybeamimpingingthecrystalatawelldefined
observationdirectionisdepictedinFig.5.20.
ThewidthofthereflectingpowerratioshowninFig.5.20isΔε=1.4∙10−4corre-
spondingto0.84eV.Thisenergyexceedssomewhattherelativeenergydifferenceof
0.32eVofthetwowaveswhichmustinterfere.Theestimationofthelongitudinal
coherencelengthwillbeperformedwiththelargervalueresultinginLl=0.5λ2/Δλ=
0.5λ/Δε=0.74µm.Thisvalueissufficientlylargeforallobjectsinvestigatedinthis
workwhich−6hadthicknessesinthesub-mmrangesinceatarefractiveindexdecrement
ofδ=1∙10theopticalpathdifferenceislessthan0.01µm.

reflexesrderoHigher5.4.2

Besidethe(111)reflectionofthesiliconmonochromatorcrystalalsothehigherorders
as(333),(444),and(555)areallowedtoo.IfacontinuousX-rayspectrumimpinges
onthecrystalthecorrespondinghigherorderphotonsmayperturbameasurement.
TostudytheintensityofthesehigherorderreflexesaCdZnTedetectorwithanactive
volumeof3mm×3mm×2mmwasinstalleddirectlybehindthepolyimideexit
windowwithathickness25µm.AtaBraggangleof19.25◦monochromaticlinesare
expectedatphotonenergiesof6keV,18keV,24keV,and30keV.Themeasured
energyspectrumisshowninFig.5.21.
Thespectrumisdominatedbythe6keVline,however,lineswithsmallerintensities
areobservedaswellwhichcanbeidentifiedtobelongtothehigherorderreflexes.Since

72

5.4Investigationofthefeaturesofthemonochromizedphotonbeam

Figure5.20:Reflectingpowerratioforthe(111)reflectioninBragggeometryofaperfect
siliconsinglecrystalatanobservationanglewhichcoincideswiththeBraggangleof19.25◦.
TheabscissaisatherelativeenergydeviationfromtheexactBraggenergy.Dielectricsuscep-
tibilitiesareχ0=-0.27354∙10−4,χ0=0.10968∙10−5,χH=0.14454∙10−4,χH=0.76250∙10−6
[SerXX].ThewidthfortheπpolarizationcurveisΔε=1.4∙10−4.

theefficiencyoftheCdZnTedetectorintheenergyrangeupto30keVisapproximately
constant,itcanbeseenthatthecontributionsare3.1%,2.0%,and0.8%forthe(333),
(444)and(555)reflexes,respectively.Therefore,thefluxofX-rayphotonswith6
keVisaboutafactorof20higher.Inaddition,forthedirectexposureCCDcamera
thedetectionefficiencyatanenergyof18keVandlargerisverysmall,seeFig.5.14,
consequentlythedetectionofhighenergyphotonscanbeneglected.ForX-rayfilms
basedonsilverbromide(AgBr)[PhyXX]withnominalthickness12µmthedetection
efficiencyat6keVisabout93%whileitdecreasesat18keVto28.6%andat24keVto
14.2%.At30keVthedetectionefficiencyincreasesagainto19.6%duetotheincrease
oftheabsorptioncoefficientattheabsorptionedgeofAgat25.514keV.Fromthis
discussionitcanbeconcludedthatthecontributionofhigherorderreflexesisrather
small,anditwillbeneglectedinthefollowing.

73

5TowardshardX-rayin-lineholography

Figure5.21:Theenergyspectrumasrecordedwitha3mm×3mm◦×2mmcadmium
antellurideenergyofCdZnT6keeVafterforthemonoc(111)hromatization.reflexction.TheElectronBragg’sbeamanglecurrenist119.25nA,expcorresposureondingtimetois
sec.600

5.4.3Transversecoherencelengthsinhorizontalandvertical
direction

Fig.5.22depictstheradiographsoftwopolymerstringsofthesamethicknessof
30µm.Intheradiograph(a)thewireismountedverticallyandin(b)horizontally.
Althoughthebeamsizeinhorizontaldirectionissmallerthanintheverticaldirection,
nointerferencepatternisobservedfortheverticallymountedpolymerstringwhilea
niceinterferencepatternisobservedforthehorizontallymountedstring.Fig.5.23
showsthenormalizedintensityprofilesofthetwostrings.Themaximumcontrast,
Cref=(Imax−Imin)/(Imax+Imin)forthehorizontallymountedstringis63.9%,while
fortheverticallymountedoneonly11%.Thepossibilitythattheobservedeffect
maybecausedbytoolargeabeamspotinhorizontaldirectionhasbeenexcludedin
ts.erimenexpadditionalForabeamspotsizeσh=(1.7±0.1)µmthetransversecoherencelengthis,according
totheequationsσh∙θcohλ/2πandθcoh=LT/xsdforadistancexsd=13.6m,as

74

5.4Investigationofthefeaturesofthemonochromizedphotonbeam

Figure5.22:Tworadiographsofapolymerstringofdiameter30µm.Inradiograph
σ(a)h=the(1.7±string0.1)isµmmounintedhorizonvtalerticallyand,σinv=(b)(3.9±horizon0.4)tallyµm.inTheverticalX-raydirection.sourcespotThesizeelectronwas
bbeeamsurespotthatsizethewascradiographheckedwithdeteriorationthewireinvscannererticalbeforedirectionandwafterasthenotcausedimagingbyintoorderbigtoa
obspotsizeinject-to-detectorthehorizondistancetalxoddirection.=9.61Them.Electronsource-to-obbeamjectcurrendistancet700wasnA,xso=exp4.3osurem,timeandthe1.8
added.frames50s,

canlargebeasLTobserv=ed263forµmthev(standarderticallymoundeviation).tedHostring.wever,Theonlyonlyaweakreasonableedgeenhancemenexplanationt
forrioratedthisbyobservtheationmonoiscthathromatorthetransvcrystal.erseObcoherenceviously,ininthetheenergyhorizontaldispersivdirectioneisdirectiondete-
(horizontally)anadditionalangulardivergenceisintroducedbythecrystal.
Fig.5.24showsthatanangulardivergenceψintrintroducedbythecrystalresultsina
virtualspotsizeinhorizontaldirectionof

Svirt=ψintr∙xsc,(5.8)
withthesource-to-monochromatordistancexsc,andanapparentspatialresolutionof
Sr=ψintr∙xcd.(5.9)
Lettheusreason.firstWithdiscussthewhethercalculatedthefullangularwidthatwidthhalfofthemaximaofDarwin-PrinstheDarwin-Prinscurvemighcurvtbese
ofψintr,σ=46.5µrad(FWHM)andψintr,π=36.4µrad(FWHM)forσandπ
pmonocolarizationhromator-to-detector[SerXX],respectivelydistance,axcd=source-to-mono5.8m,acvirtualhromatorsourcedistancesizexscand=a7.8spatialm,a
resolutionofS≈360µm(FWHM)andS≈270µm(FWHM)wouldresult,
respectively.vSucirthnumberswouldpreventtherobservationofinterferencesatall,in
contradictiontotheexperimentalobservation.Indeed,accordingtoEq.(5.7)the

75

5TowardshardX-rayin-lineholography

Figure5.23:ProjectionintheradiographsshownintheFig.5.22.Anumberof10rows
resp.columnswereaddedtogethertoimprovethestatistics.(a)Projectionofthevertically
mountedstringonthehorizontalaxis,(b)projectionofthehorizontallymountedstringon
theverticalaxis.Correspondingexpectedinterferencepatternaredepictedinviewgraphs
(c)anddashedlinein(d).Solidlinein(d)iscalculatedinterferencepatternforthevirtual
X-raysourcespotsizeσvirt=37.5µm.

reflectedpoweratconstantenergyεθxisstrictlycorrelatedtotheentranceangleθx
andnoangularspreadingshouldoccur.However,thisequationholdsonlyforplane
waveswithsourceanddetectoratinfinity.Itremainstobeinvestigatedwhetherfor
ourexperimentalgeometrywithsourceanddetectoratfinitedistancesanangular
spreadingcouldoccur,ornot.

Thespreadingangleψintrcanbeestimatedbyacomparisonoftheinterferencepattern
observedfortheverticalpolymerstringwithadiameterof30µmandthesimulatedone
accordingtoEq.(2.18)takingintoaccountthespatialresolutionoftheCCDdetector.
Fig.5.23(c)solidlineshowstheresult.FromtheapparentsourcesizeSr=88µm
whichislargeincomparisontothepixelsizeandthehorizontalspotsize,anψintr=
15µradfollowsaccordingtoEq.(5.9),theresultisshowninFig.5.23(c)solidline.

76

5.4Investigationofthefeaturesofthemonochromizedphotonbeam

Figure5.24:FormationofavirtualX-rayspotbyanangulardivergenceinhorizontal
directionimposedbythesiliconsinglecrystal

pWhatevossibleerthespreadingreasonofforthethereflecteddegradationpowerasofthediscussedhorizonabtalovealsocoherencecrystalmightdefectsbe,bmaesideybea
haveconsidered,beenptheverformederticalwithcoherencehorizonistallymainarrangedtainedandstrings.allexperimentsdescribedbelow

Streaks5.4.4

Fig.5.25showsapicturetakenwiththedirectexposureCCDcamerawithoutanob-
jectsThisinthestructurewtransitionasinvradiationestigatedincone.moreClearydetailvforerticaldifferenstreak-liktephotonstructureenergiescanbbeetwseen.een
5whicandhw20erekeV.digitizedFig.5.26asshodescribwsedthebeloresults.winsectionRadiographs5.6,wanderetakhorizonentalwithstripX-raesywithfilmsa
thewidthstreaksof0.063showmmupwasereinprotensityjectedonfluctuations.totheAhorizonremarktalyableaxis.featureInsucishathattherepresenobservtationed
intensityfluctuationsobviouslydependonthephotonenergy.
Theexperimentalobservationspointtosurfaceorintrinsicdeformationsofthemonochro-
tionmatororcrystal.inhomogeneitiesThecrystalwerewasobservinspedectedonitsundersurface.anopticalTherefore,microscopitmeustbutbenoconcludeddeforma-
thatthestreaksresultfromdeformationsormisorientationsofthecrystalplanesin-
thesidegrothewthcrystalofthe(unobservcrystalorableduringundertheanopticalcuttingormicroscopmechanicale),whicphwolishingereofformedthecrystalduring
surface.

77

5TowardshardX-rayin-lineholography

Figure5.25:Radiographtaken◦withtheCCDcamerawithoutanobjectinthetransition
inradiationaccumulationcone.moBraggde,expangleosure19.25time,2photonsec,numenergyber6ofkeV.singleTheimagesCCDwascamera50,waselectronopberatedeam
current160nA.Clearlyobservableareverticalstreaks.

FromtheintensityfluctuationsshowninFig.5.26informationonthebendingradius
andperiodofthecrystaldeformationcanbeextracted[Chi93,Var96,Kuz99].Itwill
bewithassumedcertainbthatendingtheradiicrystalRi,hasseewaFig.vy5.27.structuresIfabwhicendinghformradiusRsmallisatisfiescylindricaltheimagingmirrors
equation[Pod01]1112
a+b=f=Risin(θB).(5.10)
withmirrora=toxsc=detector,5.38mX-ratheysfromdistancethesourcesourcetocanmirrorbeloandcallyb=foxcdcused=5.8andmthisthewaydistancethe
streaksareformed.Therelationbetweenfocallengthfcanbeobtainedfromthege-
inometrytheofcaptionaRoofwlandFig.circle5.26,b[Jam65].endingFradiirombetEq.ween(5.10)14andandthe55mBraggcanbeanglesasestimated,specifiedthe
formernumberbelongingtoalargerBragganglethanthelatter.
Theobservationthatthespatialperiodofthestreaksdecreasesasafunctionofde-
creasingBragganglestronglysuggestsacommonorigininthewavystructureofthe
tocrystal.theobservAscanedboneeatseenthefromdetectorFig.5.26,planetheyd(pθBerio)bdyyctheoftheequationwavy[Bac05]structureisrelated

yc=xcd∙yd(θB).(5.11)
xscsin(θB)
Fig.5.27showsascalingofthestreakstructuresshowninFig.5.26accordingtothis
equationwith1/sin(θB).Afterthisscalingtheperiodsareobviouslythesame.The

78

5.4Investigationofthefeaturesofthemonochromizedphotonbeam

Figure5.26:StreaksasafunctionoftheX-raysenergyrecordedwithX-rayfilms,(a)at
photonenergyof5keV,Braggangle23.31◦,exposuretimetexp=600s,(b)at8.23keV,
Braggangle13.91◦,exposuretimetexp=70s,(c)at11.98keV,Braggangle9.51◦,exposure
timetexp=100s,and(d)at20keV,Braggangle5.86◦,exposuretimetexp=600s.Electron
beamcurrentforallradiographs550nA,X-rayspotsizeσh=34µmandσv=3.4µm,
source-to-objectdistancexsc=5.38m,crystal-to-detectordistancexcd=5.8m.

resultsofaquantitativeanalysisaretabulatedinTab.5.2.Thefactthatthebending
radiusmustchangeasafunctionoftheBragganglecanbeexplainedbyadepth
dependenceofthebendingradius.

Togroundeliminatecorrected.theeffectSuchofabacthepkgrounderturbingcorrectionstreaksinformcasetheofX-raradiographyfilmsitismustdifficultbebacsincek-
caremustbetakenthatbothexposersareexactlypositionedatthesameplaceand
thatalsotheexposuretimeandthefilmprocessingareexactlythesame.Foradi-
rectexposureCCDsuchaprocedureismuchsimplersincepositionandcurrentofthe
electronbeamcaneasilybekeptstableovertheperiodofthetwoexposureswithand
ject.obthewithout

79

5TowardshardX-rayin-lineholography

Figure5.27:Schematicdiagramconnectingtheintrinsicwavystructureinthecrystalwith
theobservedoneatthedetector.

havFigureebeen5.28:scaledTheaccordingplanarto1morphology/sin(θBof)asthecrystal.suggestedThebyEq.streak(5.11).structuresshowninFig.5.26

80

5.5HardX-rayin-lineholographywiththedirectexposureCCDchip

Table5.2:Braggangles,estimatedperiodsatthedetectorplaneyd,periodycofthesurface
fluctuationsonthecrystal,andbendingradiiRiaccordingtoEq.(5.10).
Bragg◦angleyd[mm]yc[mm]Ri[m]
23.3113.91◦1.32.12.62.62314
◦5.869.51◦0.50.82.32.25433

5.5HardX-rayin-lineholographywiththedirect
chipCCDosureexp

InthissectionthemeasurementsofhardX-rayin-linehologramsaredescribed.Holo-
hairsgramswoferevtakariousenwithlineartheobjectsCCDlikineptheolymerdirectexpstringsosureofmodifferendetaswelldiametersaswithorhX-raumany
films.Tofacilitatetheinterpretationofphasecontrastradiographs,stronglyabsorb-
12ingµobmjectswidthlikeandtungstenspacingwires40µofm[GodifferenoXX]thavdiametersebeenandinvanicestigatedkelgridasofw4ell.µmAllthicofkness,these
objectshavebeenimagedwithanopticalmicroscope.Someofthepicturesareshown
5.29.Fig.in

Figure5.29:Opticalmicroscopepicturesof(a)apolymerfiberbundleofaveragediameter
450µmwhichconsistsofmanystringswithasmalldiameterof30µm,(b)apolymerstring
of30µmdiameter,(c)ahumanhairofabout80µmdiameter.

5.5.1Optimizationofthebeamspotsizeandmeasurements
Themostimportantprerequisitefortakinghighqualityhologramsistheoptimization
ofthebeamspotwhichmustbeassmallaspossible.Therefore,thebeamspotsize
mustbecarefullyprepared.Thefirststepincludedaminimizationofthespotsizewith
thecurrenaidtofofthethewirequadrupscanner,oleasdoubletdescribinfronedtinofthesectionwire5.2.3.1.scannerInwasvparticular,ariedunthetiltheelectricalscan

81

5TowardshardX-rayin-lineholography

withthetungstenwireofsmallestdiameter(4.0±0.4)µmyieldedthesmallestspot
size.InthenextstephologramsweretakenwiththeCCDcamera.Asalreadymentioneda
numberoftimes,aCCDcameraallowsfaston-lineimaging.However,theresolution
inthedirectexposuremodeislimitedbythepixelsizeof13µm.Toovercomethis
disadvantagetheobjectcanbeplacedintheX1beamlineofMAMIinaclosedistance
totheX-raysource.InFig.5.2thepossiblepositionsanobjectcanbeplacedare
identified.TheobjectframesaremountedperpendicularlywithrespecttotheX-ray
beamdirectionwiththeexceptionoftheclosestdistancebetweensourceandobject
xso=1.88mforwhichtheanglebetweenthenormaloftheframeandtheX-raybeam
directionwas46◦.Inaclosedistanceoftheobjecttothesourcethehologramwill
bemagnifiedonexpenseofadeteriorationoftheresolutionandthevisibilityofthe
interferencepatternduetothefinitebeamspotsize.However,justthisfactcanbe
employedtofurtheroptimizethebeamspotsize.Thisprocedurewillbeexplainedin
wing.follotheToquantifythespotsizetheperiodofthesmallestdiscerniblespacingandthevisibility
ofthefringescanbeused.InourexperimentstheX-rayspotsizewasestimatedfrom
thesmallestdiscerniblefringespacingrmaxrecordedintheinterferencepatternof
transparentobjects.Withthisquantity,thestandarddeviationofthesourcesizeis
[Car98]ybengivσ=0.31xsormax.(5.12)
xodFig.5.31illustratestheprocedure.InFig.5.31(a)moreorlessonlyanedgeen-
hancementwasobservedfromwhichrmax117µmcanbeestimated.Withthe
source-to-objectdistancexso=1.88mandtheobject-to-detectordistancexod=12.03
moneobtainswithEq.(5.12)σv=6.4µm.InFig.5.31(b)thecurrentinthevertical
focusingquadrupolewaschangedwhilethatofthehorizontallyfocusingonewaskept
constant.Anrmax52µmcanbededucedresulting,accordingtoEq.5.12,inthe
X-raysourcespotsizeofσv=2.52µm,whilewiththewirescannerσh=(5.9±0.1)µm
andσv=(2.6±0.1)µmwasmeasured.
InFig.5.31(c)thehorizontalquadrupolewasoptimizedaswell.Withrmax26µm
aσv=1.26µmresultedwhilewiththewirescannerσh=(19.1±0.7)µmand
σv=(0.50±0.05)µmwasmeasured,seeFig.5.30.Anotherexampleofsuchabeam
spotmeasurementisshowninFig.5.32.Incomparisonwithwirescannermeasurement
σv=(0.50±0.05)µm,themeasuredvaluewiththedirectexposureCCDdeviates
significantly.Thisdeviationcanbeexplainedbythelongitudinalextentofthefoilstack
whichamountsto2.8mm.Themeasuredverticalemittancesatelectronbeamenergyis
εv=0.52µmmrad,foramicro-focusedelectronbeamspotsizeσv=(0.50±0.05)µm,
thecorrespondingdivergenceamountsto1.04mrad.Forthebestcondition,when
thefocusisexactlyinthemiddleofthefoilstack,thebeamspreadwithinthestack
amountstoastandarddeviationof1.5µm,inaccordwiththeobservationwithdirect
exposureCCDchip2.
2Theerrorsofthefringemethodmaybeintheorderof20%

82

5.5HardX-rayin-lineholographywiththedirectexposureCCDchip

Figure5.30:Measuredelectronbeamspotsizeinverticaldirectionwitha(4.0±0.4)µm
thicktungstenwire.Afterdeconvolutionwiththeboxfunctionofthewirescanner,the
electronbeamsizeis(0.50±0.05)µm.

TheexampleofFig.5.32demonstratesthatthefringemethodforthemeasurementof
thespotsizehasitspracticallimitsinthespatialresolutionoftheCCDdetectorwhich
hasapixelsizeof(13×13)µm2.AccordingtoEq.(5.12)theminimummeasurable
sourcessizeis,therefore,intheorderofσv=1.26µm.
Forcomparison,simulationswerecarriedoutwiththecalculationsbytheprogram
beamoptic.ThesimulatedelectronbeamsizeforthemeasurementsshowninFig.5.32
isσh=43.2µmandσv=0.44µmwhichhavetobecomparedwiththewirescanner
resultsσh=(19.1±0.7)µmandσv=(0.50±0.05)µm.Themeasuredsourcespot
sizeinthehorizontaldirectionissomewhatbetterandthatintheverticaldirection
somewhatworsebutabetteragreementwouldnotbeexpected.
Averysimplemethodtooptimizethebeamspotsizeon-lineistosimplycountthe
numberofinterferencefringes.Thisnumberexhibitsaswelltheimprovementofthe
focussingascanbeseenfromFigs.5.31and5.32.Forexample,inFig.5.32(a)5
fringesareobservedwhileinFig.5.32(b)forthesmallerbeamspot9fringes.The
accuracyofthismethodcanbeimprovedifinsteadtheCCDdetectorswithahigh
spatialresolutionareused.ThiswillbedemonstratedforanX-rayfilminsection5.6.
However,theon-linecapabilityislost.
In[Koh00,Koh01]measurementsofthetransversecoherencelengthLThavebeen
reportedwithstandardobject,suchashomogenousstringswithwelldefinedradiiand
goodcylindricalshapeandwellknownrefractiveindexparameterswithintheobject.
Inourcase,thehighuncertaintyofsuchobjectparameterspreventedtheapplication

83

5TowardshardX-rayin-lineholography

Figure5.31:Sourcesizeminimizationwiththeinterferencepatternofahumanhairof
80µmdiameterandapolymerstringof30µmdiameter.Upperpanelsshowradiographs,
lowerpanelstheprojectedintensityforthepolymerstringforwhich5columnswereadded
up.Thesource-to-objectdistancewasxso=1.88mandtheobject-to-detectordistance
xod=12.03mcorrespondtoamagnificationof7.4times.Thenumbersbetweenupperand
lowerpanelarethecurrentsofthehorizontallyandverticallyfocusingquadrupoles.Electron
beamcurrent1.21µA,exposuretime8.1s,10framesaddedup.

h.approacthisofAnumberofmeasurementswithvariousstringsatdifferentsource-objectandobject-
detectordistanceswereperformedwiththeCCDchipandhighresolutionX-rayfilms
asdetectors.TherelevantparametersforallmeasurementsaresummarizedinTable
5.3,themeasurementsarelistedinTable5.4,andtheusedstringsarecollectedin
5.5.ableT

Analysis5.5.2

Asdescribedinthelastsectionhologramsofvariousstringsundervariousexperimental
conditionshavebeentaken.Theanalysisofthehologramsisbasedonasimplemodel
whichdescribesthehologramsofstringswitharbitrarycross-sectionalshapesand
opticalconstants.Particularattentionwaspaidonanthoroughunderstandingof
opaquetungstenwires.Aswillbeshownbelow,hologramsofopaquematerialswith
preciselyknowndiameterscanbecalculatedwithgoodreliabilityand,therefore,may

84

5.5HardX-rayin-lineholographywiththedirectexposureCCDchip

Figure5.32:FringevisibilityasafunctionoftheX-raysourcespotsize.Shownareholo-
gramsofapolymerstringwithadiameterof30µmforanX-raysourcespotsizeasmea-
suredwiththewirescannerof(a)σh=(5.9±0.1)µm,σv=(2.6±0.1)µm,and(b)
σh=(19.1±0.7)µm,σv=(0.50±0.05)µm.ThefringemethodwithEq.(5.12)yields
(a)σv=2.6µm,(b)σv=1.26µm.Thelattervalueisanestimatewhichisbasedon
thepixelsize,sincethesmallestdistanceofresolvablefringesisintheorderofonepixel.
Source-to-objectdistancexso=1.88m,object-to-detectordistance12.03m,corresponding
toageometricalmagnificationof7.4times.Noticethat,theanglebetweenstringandbeam
directionamountsnotto90◦but46◦.Electronbeamcurrent500nA,exposuretime8.1s
perframe,100framesaddedup.

85

5TowardshardX-rayin-lineholography

Table5.3:Experimentalparametersofphasecontrastandin-linehardX-rayholography.

eambElectron

Radiator

Radiator

ectrometerSp

Detector

filmyX-ratimeosureExpdatawRa

86

HorizonElectrontalbeamwidth(1energyσ)(1855.9±MeV0.3)andµm600MeV
Verticalswidth(1σ)(1.6±0.3)µm
Beamcurrentmaxvalue2µA
Fluctuationofthecurrent≤3%
olyimidePMaterialNumberoffoils25
Thicknessoffoils[µm]12.5
DistanceElectronbbeteamweenenergyfoils[µ[MeV]m]600100
NumMaterialberoffoilsP30olyimide
ThicDistanceknessbetofwfoilseen[µfoilsm][µm]7525
Electronbeamenergy[MeV]855
siliconCrystalNetEnergyplaneresolution(FWHM)(2.[111]4±0.2)eV
m5.8detectortoDistancem7.5sourcetoDistanceCCDeypTPixel-Dimension13×13µm2
Numberofpixel1024×1024
Depletionlayer≈5−10µm
EnergyDetectionresolutionefficiency(FWHM)12760%eV@@(2.56keV);eV50%from@55Fe(6.0keV)
TypeResolutionapproStructruixx.2µD3mX-rayfilm,Agfa
min.15timeosureExps/image7.1timeosureExpNumRecordingberoftimeimages1001000s/singleimages/singleradiographradiograph
Sizeofsingleradiograph5MByte

5.5HardX-rayin-lineholographywiththedirectexposureCCDchip

5.9y-2004Ma

Table5.4:Compilationofbeamtimeswithrelevantparameters,suchas,dateofthemea-
surement,X-raysourcespotsizesσh,σv,samplepositionsxso,xod,magnificationM,and
useddetectors.Noticethat,theanglebetweenstringandX-raybeamdirectionisforthe
distancexso=1.88mnot90◦but46◦.
Dateσh[µm]σv[µm]xso[m]xod[m]Mdectector
April-20041.73.91.8812.037.4directexposureCCD
4.39.613.23directexposureCCD
10.783.131.3directexposureCCD
12.711.201.1directexposureCCD
May-20045.92.61.8812.037.4directexposureCCD
4.39.613.23directexposureCCD
10.783.131.3directexposureCCD
12.711.201.1directexposureCCD
June-200419.10.51.8812.037.4directexposureCCD
4.39.613.23directexposureCCD
10.773.131.3directexposureCCD
12.711.201.1directexposureCCD
June-200419.10.51.8811.737.24highresolution
4.39.313.17X-rayfilm
1.262.8310.781.070.9012.71

19.1June-2004

19.1June-2004

serveastestobjectsforvariousexperimentaluncertaintiesasthereare,e.g.,distances
betweensourceandobject,andapossibleresidualbendingofthemonochromator
crystalwhichmayresultinamagnificationordemagnificationoftheobject.Withsuch
uncertaintiesundercontrol,themuchmoreinvolvedhologramsoftransparentstrings
canbeanalyzedfromwhich,assumingagainthepreciseknowledgeofthediameter,
opticalconstantsandradialdistributionsoftheopticalconstantscanbeextracted.

Inthisparagraphthegenerationofthenormalizedcontrastimage,whichcaneasilybe
comparedwithcalculations,isdescribed.Fig.5.33showsthepictureofahumanhair
andapolymerstring.Theoriginalpicture(a)stillcontainsstreaks.Alsodustparticles
locatedonthesurfaceofthemonochromatorortheCCDchipmaybeimagedaswell
andmayperturbtheinterpretationofthepicture.Theseadulterationsofthepicture
canbeeliminatedbysubtractionofapicturetakenunderidenticalconditionsbut
withouttheobjectintheX-raybeam.Thisbackgroundpicturewastakenimmediately
afterthepicturewithobjectunderidenticalconditions.Sincetheobjecthadtobe
removedmanuallyduringthecourseoftheexperiment,theelectronbeamhadto
beturnedoffandtheexperimentalhallBhadtobeentered.Thewholeprocedure
requiredatimeofabout20minutes.Afterturningonthebeamagain,obviouslythe
sameexperimentalconditionsweremetagainsinceintheresultingcontrastimage
[Kre03]allimperfectionsaretotallyremoved.

87

5TowardshardX-rayin-lineholography

Table5.5:Imagedobjectsandtheirdiameters.
objectdiameter[µm]
Polymerstring(30±3)
Polymerstring(150±20)
PPolymerolymerstringstring(350(270±±20)20)
PHumanolymerhairstring(80450±8)
Tungstenwire(4±0.4)
Tungstenwire(10±1)
Tungstenwire(25±2.5)
Tungstenwire(40±4)

If,inaddition,suchacontrastimageisnormalizedtothereferenceimageanormalized
contrastimageisobtained.Theadvantageofthelatteristhatitiscorrectedforthe
intensitydistributionoftheprimaryX-raybeamoverthepictureandcandirectlybe
comparedwithcalculationsonthebasisofEq.(5.1).Twoexamplesofnormalized
contrastimagesareshowninFig.5.34.Itcanbeseenthatbecauseofthelarge
magnificationofM=7.4thepixelresolutionof13µmimposesnosevererestriction.

discussionandResults5.5.35.5.3.1Hologramsofhighlyabsorbingobjects
Fig.5.35andFig.5.36showhologramsoftungstenwiresofdifferentdiameters.The
complexrefractionindexparametersforaphotonenergyof6keVatwhichtheholo-
gramsweretakenareδ=8.5∙10−5andβ=1.11∙10−5[CxrXX].Theimaginarypartβ
impliesforthewirewiththesmallestdiameterD=10µmadampingoftheintensity
toexp((4π/λ)∙β∙D)=exp(−6.75)=1.2∙10−3andinparticularthethickerwirescan
beconsideredascompletelyopaque.Inspectionunderanopticalmicroscoperevealed
agoodcylindricalshape,someimperfectionsintheorderof6µmwereobservedfor
thewirewithadiameterof40µm.Thesepropertiesareimportantforthecalculation
ofthehologramswhichdependbesidethecomplexrefractionindexparametersalsoon
.morphologyjectobtheTheobservedinterferencepatternresultsfromtheinterferencebetweendiffractedwaves
attheedgeofthewireandundisturbedwavesemanatingfromthesource.Asalready
mentioned,fromsuchdiffractionpatterninformationontheX-raysourcesize,the
locationoftheobjectandtheresidualbendingofthemonochromatorcrystalcanbe
extracted,providedthediameterofthewireisknown.
Inthecalculationstogettheintensitypatternwhichcanbecomparedwiththemea-
surement,theinterferencepatternaccordingtoEq.(2.18)forapoint-likesourcehas

88

5.5

Hard

yX-ra

in-line

yholograph

with

the

direct

osureexp

CCD

hipc

inFigurethedirect5.33:exposureGenerationmode.ofaAconhumantrasthairimagewithfromadiameterradiographsof80takµenmwithandathepCCDolymercamerastring
ofspot29.6sizesµmwerediameterσh=w(19ere.1p±0.ositioned7)µminaandσvdistance=(0.x50so±=0.1.8805)mµm,fromelectrontheX-rabyeamsource.currentX-ra500y
nA,exposuretimeperframe8.1s,100frameswereaddedup.(a)Theoriginalradiograph
arewhichclearlyclearlyobservshowsable.streaks(b)Theduetoimagecrystalwithimptheoberfections.jectremovAlsoed,dustand(c)particlesthecononthetrastcrystalimage
asobtainedbyasubtractionofimage(b)fromimage(a).

89

5TowardshardX-rayin-lineholography

Figure5.34:Normalizedcontrastimages(holograms)for(a)atungstenwireof(25±2.5)µm
diameter(anopaqueobjectwithhighabsorption)and(b)anylonwire(anearlytransparent
object)hologramsofw30ereµmrecordeddiameteratanwhichX-rahasyenergynearlyofthe6ksameeV.Thediametersource-to-obasthejecttungstendistancewire.wasxThe
so=M=1.887.4.mandThetheobhologramswject-to-detectoreretakenwithdistancethexodCCD=c12.03hipm,atacorresptempondingeraturetoofa−50◦Cmagnificationandan
electronbeamcurrentof160nA.Panel(c)depictsthecorrespondingintensityprofileofthe
columnshologramsofofthetheCCDtungstenwereaddedwireandup.(d)thatforthepolymerstring.Intheprojections10

beenconvolutedwiththedirectexposureCCDspatialresolutionwhichisassumedto
haveaGaussianshapewithastandarddeviationof8.3µmandtheprojectedX-ray
sourceprofileonthedetectorwhichisassumedtobeaGaussian.Themonochromator
crystalwasassumedtobeplane.Theexcellentagreementbetweenmeasuredinten-
sity(pointsinthegraphs(c)and(d)ofFig.5.35)andcalculationsconfirmsthatthe
crystalhasanegligibleresidualbendingintheverticaldirectionandthatthemea-
sureddistancesbetweenobject-to-sourceandobject-to-detectorarecorrect.Fromthe
fitabeamspotsizeσv=(2.5±0.2)µmresultswhichissignificantlylargerthanthe
beamspotsizeasmeasuredwiththewirescanner.Thereasonmightbeashiftofthe
spotduringthemeasurement.AccordingtoEq.2.16atransversecoherencelength
LT=157µmisdeduced.Becauseofthisrelativelysmallcoherencelengththeinter-
ferencefringesgetratherweakalreadyatadistanceoftwicetheradiusfromthewire

90

5.5HardX-rayin-lineholographywiththedirectexposureCCDchip

Figure5.35:Normalizedcontrastimagesoftwotungstenwiresof(a)(25±2.5)µm,and(b)
(40±4)µmdiameter.Source-to-objectdistancexso=1.88m,object-to-detectordistance
xwithod=the12.03directm,expcorresposureondingCCDtoacameramagnificationcooleddoofwn7.4totimes.-40◦C,Theexphologramsosuretimewere8.1s,captured100
andframesσv=added(0.50up.±0.05)Electronµmasbeammeasuredcurrentwith1.4aµA,wireX-rascanner.yspotsizeDiagramsσh=(c)(19and.1±(d)0.7)areµthem
intensityprofilesoftheholograms,5columnsadded.Pointsaremeasurements,solidlines
calculatedintensitiesaccordingtoEq.A.42.

ter.cen

Averyimportantfeatureofthesehologramsshouldbementioned.Despiteofthefact
thatX-rayphasecontrastimagingorin-lineholographyispreferredforlowabsorbing
materials,itcouldalsobeusedforhighabsorbingmaterialssuchastungsten.Fig.5.35
andFig.5.36bothrevealaclearedgeenhancementduetorefractionwhichincreases
thecontrast.Theadvantageofthegeometricalmagnificationis,however,thathigh
qualityradiographscanbeobtainedwithadetectorofmoderatespatialresolution,as
theCCDcamerawithapixelresolutionof13µm.Foratungstenwirewithadiameter
of(4.0±0.4)µmwhichissmallerthanthenominalpixelsizeofthedirectexposure
CCDcameraFig.5.36(c)showsaclearlyresolvedpattern.Fig.5.37confirmsthisidea
foratungstenwirewithadiameterof4µm.Inaconventionalradiography(contact
radiography)withoutgeometricalmagnificationsuchawirecouldnotbeimagedwith

91

5

ardswoT

hard

yX-ra

in-line

holography

Figure5.36:Normalizedcontrasthologramsoftungstenwireswithdiameters(a)(40±
4)µm,(b)(25.0±2.5)µm,and(c)(10±1)µm.Source-to-objectdistancexso=4.3m,
obThehologramsject-to-detectorweredistancecapturedxsowith=9.the61m,directcorrespexposureondingCCDtoacameramagnificationcooleddoofwn3.23to-40◦times.C,
0w.1)orkingµminandσaccumv=(2ulated.6±0mo.1)de.µm,Photonelectronenergybeam6keV,currentX-ra600ynA,sourceexpspotosuresizetimeσh=8.1(5s,.9100±
framesaddedup.Rightpanelsdepicttheintensityprofilesoftheholograms,5columns
added.

92

5.5HardX-rayin-lineholographywiththedirectexposureCCDchip

Figure5.37:Diffractioncontrastofatungstenwirewith4µmofdiameter.Thesource-to-
ob(a)jectisadistanceradiographwasxandso=(b)10.the78inmtensitandytheprofile.obPoinject-to-detectortsrepresentdistanceexpxerimenod=tal3.13results,m.Ptheart
ulation.simthelinesolid

resolution.thisofdetectoraInconclusion,twoparametersareofimportance.ThesearetheX-raysourcesize
projectiononthedetectorwhichmustbeassmallaspossibletoavoiddegradation
oftheradiographandthemagnificationwhichisimportanttoovercomethelimited
X-raresolutionydetectorofthemustdetector.beselectedThepositioncarefullyoftotheavoidsamplethewithradiographrespecttoX-radeteriorationysourceviaandthe
X-raysourceprojectionontheX-raydetector.

5.5.3.2Hologramsoftransparentobjects

Thecatedinasthatterferenceforopaquepatternsobofjects.Thetransparentcomplexstrings,refractionaspolymerindexwires,parametersareformoreaphotoncompli-
energyof6keV,atwhichthehologramsweretaken,aretypicallyδ=7.31∙10−6and
β=2.45∙10−8[CxrXX].Theimaginarypartβimpliesforthewirewiththelargest
exp(diameter−0.52)D==0.35059.µmTheaabsorbdampingedofinthetensityoftransmitted41%isintensitalreadyytoratherexp((4πlarge./λ)∙βFig.∙D)5.38=
showsanormalizedcontrastradiographofsuchapolymerstringwithadiameterof
350µm.Theabsorptioncontrastinthemiddleamountstoabout60%whichissome-
whatlargerasthecalculatedvalue.Thedifferencemayoriginatefromtherefraction
contrast.Alsosomefringesontheedgesofthestringareclearlyresolved.
Forthethinnestpolymerstringwithadiameterof30µmtheabsorptionamounts
toatmost4.3%.However,asshowninFigs.5.39and5.40acontrastofupto
60%withrichinterferencepatternisobserved.Thefiguresshowhologramstakenat
differentgeometricalmagnificationsinwhichtheobservedstructuresoriginatefrom

93

5TowardshardX-rayin-lineholography

Figure5.38:(a)Radiographofapolymerstringwithadiameterof350µm,(b)theintensity
profileand(c)thecalculatedintensity.Anumberof10columnswereaddedup.Source-
to-objectdistancexso=4.3matasource-to-detectordistancexsd=13.91m.TheX-ray
sourcespotsizewasσh=(5.9±0.1)µmandσv=(2.6±0.1)µm.Theelectronbeamcurrent
was200nA,exposuretime8.1s,50framesaddedup.Thereductionoftheintensityinthe
middleofthestringispredominantlycausedbyconventionalabsorption.

theinterferenceofthescatteredwavebythestringwiththeunperturbedwavefrom
source.the

SomefeaturesbecomeapparentinFig.5.40whichwillbediscussedinthefollowing
inconnectionwithFig.4.1inwhichdifferentobservationgeometrieswereclassified
intoregions.Thecontactregion(I),thenearfieldregion(II)andtheintermediate
region(III)werediscussedinsections4.1.1,4.1.2,and5.1,respectively.Fig.5.40(a)
and(b)belongtothenearfieldregion(II).Althoughtheobject-to-detectordistanceis
ratherlargeonlyanedgeenhancementdevelopssincethedetectorcannotresolvethe
oscillations.Fig.5.40(c)and(d)belongtotheintermediateregion(III)inwhichfringe
patterndevelop.Theirvisibilitydependsagainonthedetectorresolution.Aswillbe
showninsection5.6amuchbettervisibilityisobtainedwithahighresolutionX-ray
film.Thisdiscussiondemonstratesthattheclassificationintofieldregionsintroduced

94

5.5

HardX-rayin-lineholographywiththedirectexposureCCDchip

Figure5.39:Radiographsofapolymerstringwithadiameterof30µmatdifferentobject-to-
detectordistancesxod.Thesource-to-detectordistancewasxsd=13.91m.(a)Atxod=1.20
m,(b)atxod=3.13m,(c)atxod=9.61mand(d)atxod=12.03m.TheX-raysourcesize
wasσh=(5.9±0.1)µmandσv=(2.6±0.1)µmforallradiographs.Radiographs(a)and
(b)arenotbackgroundcorrected.Theelectronbeamcurrentwas500nA,exposuretime2.5
s,20framesaddedup.Radiographs(c)and(d)arebackgroundcorrected.Exposuretime
was8.1sperframe,electronbeamcurrent500nA,100framesaddedup.

95

5TowardshardX-rayin-lineholography

Figure5.40:NormalizedintensityprofilesoftheradiographsshowninFig.5.39.Anumber
of10columnswereaddedup.Notice,inviewgraph(d)thenormaloftheframeinwhich
thepolymerstringwasfixedmadeanangleof46◦withtheX-raybeamdirection.

inFig.4.1dependsnotonlyonthespectraldistributionoftheX-raysbutalsoonthe
resolution.detectorForthesakeofcompletenessitshouldbementionedthatintheregion(IV)ofFig.4.1
wheretheobjectisclosetothesource,theintegrandinEq.(4.1)oscillatesagainrapidly
andapproachesaδ-function.Ameasurementwouldresultinadeterminationofthe
opticalconstantsδandβmultipliedbythethicknessoftheobject.Thismightbenot
situation.terestinginparticularlya

Applications5.5.4

Asthehasvisibilitalreadyyofbloeenwmenabsorbingtionedadetailsnuminberanofobjecttimes,withX-raayslowphaseabsorbconedtrastdose.canThisenhanceway

96

5.5HardX-rayin-lineholographywiththedirectexposureCCDchip

Figure5.41:Abackgroundcorrectedradiograph(contrastimage)ofapolymerstringof
(150±20)µmdiameter,suppliedbyGoodfellow.Source-to-objectdistancexso=1.88m,
source-to-detectordistancexod=13.91m,correspondingtoamagnificationof7.4times,tilt
angleoftheobject46◦,X-raysourcespotsizeσh=(5.9±0.1)µm,andσv=(2.6±0.1)µm,
areelectronclearlybeamseencurrenwhichtma600ybnA,eairexpbubblesosureortime8.1impurits,y50inclusionsframesaddedwithaup.differentInhomogeneitiesdensityas
thestringmaterial.Thebackgroundcorrectionassuresthattheinhomogeneitiesdooriginate
fromthepolymerstringandnotfromdustparticlesonthemonochromatorcrystalorthe
detector.

tinydetailswithinthebulkofasamplecanbevisualized.Inthissectionsomeexamples
willbepresentedwhichsupportthisstatement.Theradiographswereallcapturedwith
directexposureCCDintheaccumulatedmodewhichallowstoproducenormalized
contrastimages.Thephotonenergywasalways6keV.Thestringsweremounted
horizontallytoexploitthebenefitofthesmallersourcesizeinverticaldirection.
Fig.5.41showsaradiographofapolymerstringwithadiameterof(150±20)µm.Ac-
cordingtoinspectionunderanopticalmicroscopethestringhasnearlyidealcylindrical
shape.Nodeformationsorimpuritiescouldbeobserved.However,itsradiographre-
vealsanumberofdetailswhichmustbeattributedtoun-regularitiesandinclusions
whichareclearlyvisiblewithhighcontrast.
Humanhairsareinterestingphaseobjectswithlowabsorption.Hologramsofhuman
hairshavebeentakenatdifferentdistances.InFig.5.42examplesarepresented.Inside
thehairsinterferencefringesareobservedwhichassurethesmallabsorptionofthe6
keVphotonswithinthehairs.
Fig.5.43showsahologramofapolymerstringof450µmdiameterwhichconsistsof
thinnerstringswithadiameterof30µm.Interferencefringesareclearlyobserved,
moreovertheinterferencefringesfromdifferentsinglestringsformingthebigstring
areoverlapping.Therefore,thetotalinterferencepatternlossesresemblancewiththe
originalobject.Suchanobjectwouldbeaninterestingtestcaseforthereconstruction
ofthe3Dimagefromthehologram.

97

5TowardshardX-rayin-lineholography

Figure5.42:Backgroundcorrectedradiographs(contrastimages)oftwodifferenthuman
hairs(a)and(b).Thediametersareabout80µm.Source-to-objectdistancexso=1.88m,
object-to-detectordistancexod=12.03m,X-raysourcespotsizeσh=(19.1±0.7)µm,and
σv=(0.50±0.05)µm,electronbeamcurrent1.4µA,exposuretime8.1sperframe,100
up.addedframes

5.6HardX-rayin-lineholographywithhighresolution
filmsyX-ra

Ashasbeenpointedoutinthelastsection5.5,adirectexposureCCDhasthead-
vantageofagooddetectionefficiencyandcanbeusedon-line.However,thespatial
resolutionintheaccumulationmodecannotbebetterthanthepixelsizeof13×13µm2.
Ahighspatialresolutioncanbeobtainedwithanimagingsystemwithluminescent
screens,suchaswithGd2O2S:Tb,byopticalmagnification.Itpreservestheon-line
capability.Unfortunately,suchadetectionsystemisnotwellsuitedinthetransition
radiationX-raybeamofMAMIashasbeendemonstratedinsection5.3.4andap-
pendixC.Thereasonisthehighenergybremsstrahlungbackgroundwhichisemitted
simultaneouslywiththeX-raysinthetransitionradiationfoilstack.Inthissectionwe
demonstratethepossibilitiesatMAMIwithahighresolutionX-rayfilm.Theexperi-
mentalconditionsarethesameasdescribedinsection5.2,i.e.imagingwithtransition
radiationfromafoilstackwithamicro-focused600MeVelectronbeamemployinga
flatsiliconsinglecrystalmonochromatorinBragggeometrytoprepareamonochro-

98

5.6HardX-rayin-lineholographywithhighresolutionX-rayfilms

Figure5.43:Radiographofapolymerstringwithadiameterof450µmconsistingof
manythinnerstringswithadiameterof30µm.Source-to-objectdistancexso=4.3m,
source-to-detectordistancexod=13.91m,X-raysourcesizeσh=(5.9±0.1)µm,and
σv=(2.6±0.1)µm,electronbeamcurrent600nA,exposuretime1.6sperframe,50frames
up.added

maticphotonbeamwithanenergyof6keV.IntheexperimentalsetuponlytheCCD
camerawasreplacedbytheX-rayfilm.

5.6.1CharacterizationoftheX-rayfilm

TheprinciplesofimagegenerationwithanX-rayfilmhasbeendescribedinsections
4.2.2and4.4andwillnotberepeatedhere.Nevertheless,itisimportanttocharacterize
thelinearityoftheopticaldensityasafunctionofthedepositedenergyoftheused
StructurixD3X-rayfilmfromAgfa,andalsotheopticaldigitizationsystemtoextract
correctquantifiedinformationfromtheholograms.

ydensitPhotographic5.6.1.1

TheprimaryquantitywhichismeasuredbyanX-rayfilmisthephotographicdensity
Dp.Itisdefinedasthebasis10logarithmasDp=log(i0/i)withi0theoptical
lightintensityimpingingonthefilmanditheintensitymeasuredbythedetectorof
adensitometer.FromthisprimaryquantitythesocalledfogDf=log(i0/i0f)ofan
unexposedpartofthefilmmustbesubtractedtoobtainthedensityD=Dp−Df=
logarea(i0fdE/i)/dAwhicdephmositedustbbeytherelatedX-ratoythephotonsexposureatabofcertainthelofilm,cationi.e.−r→theattheenergyfilm.perInunita

99

5TowardshardX-rayin-lineholography

simpletheoreticalmodel[Geo58]thephotographicdensitycanbedescribedby
D(−r→)=Dsat(1−exp(−b(−r→)/b0)).(5.13)
ThesaturationdensityDsatandb0arecharacteristicquantitiesoftheX-rayfilm.
InordertouseanX-rayfilmforaquantitativeanalysisofradiographs,itismost
convenienttooperateitinthelinearrange,inwhichthephotographicdensity(or
blackness)isproportionaltotheexposureb[Dia74].Todeterminethisregion,the
X-rayfilmwasirradiatedwithX-rayphotonsfromaradioactive55Fesourcewithan
activityof1.1MBq.Thesourcewasplacedatadistanceofabout1cmfromthefilm.
TheX-rayfilmwasexposedfordifferentdurationsintheintervalbetweenzeroand
600minutes.Thelongexposuretimesresultfromthelowactivityofthesourceand
alsothelowresponse(detectionefficiency)ofthefilm.TheX-rayfilmswereprocessed
undertheconditionswhichwerespecifiedbythemanufacturer[Agf90],i.e.developed
intheG128developerfor5min,rinsedinrunningwaterfor15min,fixedinaG328
fixersolutionfor5min,rinsedagaininrunningwaterfor30min,andfinallydried
inhotair.Thetemperatureinthedarkroom(wheretheX-rayfilmswereprocessed)
waskeptconstantatabout20◦C.Thedescribedprocedureassuresthatthemaximum
performanceofthedevelopedfilmcanbeexpected.
ThephotographicdensityofthedevelopedX-rayfilmwasmeasuredbyusingahelium
neonlaserbeamwithawavelengthof632nmandadigitalLuxmeterLM1301withan
apertureof3mm2[ElvXX].Thedistancebetweenlaserandfilmwas20cmandbetween
X-rayfilmandphotodiode3cm.Fig.5.44showstheopticaldensityasafunctionof
theexposuretime(characteristiccurve).AgoodlinearityofthefilmStructurixD3is
observedovermorethanthreedecadesinaccordwiththeproductinformation[Agf90].
Withthehelpofthischaracteristiccurvethelinearityofahologramcanbeassessed
visuallybysimplydemandingthatnopartsexhibitablacknesswhichisclosetothe
alue.vsaturationTheX-rayfilmwasdigitizedwithafilmscanner(NikonCoolscanLS4000[FilXX])and
withanopticalmicroscopeequippedwithahighresolution8-bitCCDcamera(F-View
XS[OlyXX]).Fromthissystemlimitationsareexpectedbecausethedynamicalrange
cannotbebetterthanthedigitizationdepthoftheADC(1:256)whiletheX-rayfilm
hasadynamicalrangewhichismorethanafactorof10better(3.5decadescorrespond-
ingto1:3160).Since,inaddition,theilluminationtimewasselectedautomaticallyby
thescannerafterthepartofinterestofthepictureandtheopticalmagnificationwere
selected,thehologramsweredigitizedatvariouspositionsofthestring,similarlyas
describedinsection4.4.Alongtheimagedstringstheexposureischangingandthe
sectorwiththebestcontrastwasselectedforfurtheranalysis.Examplesareshownin
Fig.5.45,and5.46.Generally,thecontrastisbestforalowexposure.

resolutionSpatial5.6.1.2

TheresolutionspatialoftheresolutionX-rayoffilmaandhologramthehasresolutiontwoconofthetributionsopticalwhichmicroscoparee.theinDifferentrinsict

100

5.6HardX-rayin-lineholographywithhighresolutionX-rayfilms

Figure5.44:Photographicdensitylog(i0f/i)as55afunctionoftheexposuretimeoftheX-ray
filmStructurixD3.ThefilmwasexposedtoaFesource.

objectivelenswithmagnifications(4×)and(10×)wereusedsince,forexample,the
objectivewithmagnification(4×)cannotresolvetheinterferencepatternfortheob-
forjectsthesemounteddifferentclosetothemagnifications.X-rayInfilm.afirstTherefore,step,thetheeffectivresolutionepixelhadsizetowbasedetermineddetermined
withtionsa(4×)standardand(10ob×),jectonepixelmicrometercorrespscaleondsto[LinXX].1.27Fµormtheand0ob.52jectivµm,elensrespectivmagnifica-ely.In
aThesecondmeasuredstep,theedgespatialspreadresolutionfunction,wanasexamplemeasuredisshowithwntheinaidFig.ofa5.47,razorwasbladefittededge.with
functionthe

f(y)=c1+c2(1+erf(y√0−y))(5.14)
σ22scwithc1,c2,y0,andσscfitvariablesfromwhichonlythelatter,whichisthestandard
deviationoftheresolution,isofphysicalimportance.Theresultsareσsc,4=(4.1±
0.1)µmandσsc,10=(1.60±0.01)µm.
Accordingto[Koc98],itispossibletoestimatethespatialresolutionforanimaging
systemfromtheinterferencepattern3.Theprocedureissimilartothebeamspot
optimizationproceduredescribedinsection5.5.1.Thepatternoftheholographic
3Inthebeginningitwastriedtomeasurethespatialresolutionwiththeedgespreadfunctionfora
likelighrazor-blade.tsourceTheof500µrazor-blademwdiameter,asmounplacedtedininacondistancetactwithof70thecmfilmfromandthefilm.illuminatedThiswitharrangemenapointt
minimizesthedeteriorationoftheedgebydiffractionorthelightsourcesizeprojectiononthe

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Figure5.45:Differentsectorsofaradiograph(left)andprojections(right)ofastringof
30µmdiametercorrespondingtovariousexposures.Source-to-objectdistancexso=1.88m,
object-to-detectordistancexod=11.73m,correspondinggeometricalmagnificationis7.24
times,electronbeamcurrent500nA,exposuretime15min.100rowsweresummedup.
ThechangeinblacknessfromtoptobottomisduetothechangeoftheX-rayfluxincident
onthedifferentsectors.Thecontrastreachesamaximuminpanels(g),respectively(h),
wheretheexposurewaslowest.Theradiographwasdigitizedwithanopticalmicroscopeof
).(4magnification×102

5.6

Hard

yX-ra

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yholograph

with

high

resolution

yX-ra

films

Figure5.46:Differentsectorsofaradiograph(left)andprojections(right)ofatungstenwire
1of.88(40m,±4)obµmject-to-detectordiametercorrespdistanceondingxto=v11.arious73m,expcorresposures.ondingSource-to-obgeometricaljectdistancemagnificationxso=
odis7.24times,electronbeamcurrent500nA,exposuretime15min.200rowsweresummed
up.ThechangeinblacknessfromtoptobottomisduetothechangeoftheX-rayflux
incidentonthedifferentsectors.Thecontrastreachesamaximuminpanels(e)respectively
(f).Theradiographwasdigitizedwithanopticalmicroscopeofmagnification(4×).

103

5TowardshardX-rayin-lineholography

Figure5.47:Edgespreadfunctiontodeterminethespatialresolutionoftheopticalmi-
croscopewithobjectivelensmagnificationof(10×).Pointsaremeasurements,thesolidline
afitwithEq.(5.14).Themeasuredspatialresolutionamountstoσsc=(1.60±0.01)µm
correspondingto(3.77±0.02)µm(FWHM).TheilluminationandexposuretimeoftheCCD
camerawereadjustedbeforemeasurementstoavoidsaturation.

isimagesshownofinawFig.eakly5.48.absorbingTheexpobject,erimenaptalolyinamideterferencestringwithpattern(150is±20)comparedµmwithdiameter,the
theoreticalcalculationofapointX-rayspotandafterthatisconvolutedwiththe
spatialresolutionofX-rayfilmandtheopticalmicroscopetogether.TheverticalX-ray
sourcesizeprojectiononthedetectorplaneisσv=σv∙xod/xso=0.035µm.Withsuch
asmalleffectivesourcesizethemaindeteriorationinthefringevisibilityarisesfromthe
withspatialmagnificationresolutionof(10the×).film.Fig.The5.48X-ray(b)filmshowwsasthescannedexpundererimentaltheinopticaltensitymicroscopprofileofe
theradiograph(solidline)showthetheoreticalcalculation(dashedline).Thebest
agreementwasobtainedwithσexp=(2.0±0.2)µm.Thespatialresolutionofthedirect
exposureX-rayfilmStructurixD3afterde-convolutionwiththespatialresolutionofthe
opticalmicroscope(σsc,10=1.6±0.01µm)isthenσf=σ2exp−σ2sc,10=(1.2±0.4)µm.
IncomparisonwiththedirectexposureCCDchipthespatialresolutionoftheX-ray
filmisaboutafactorof6better.

Thisfilm.Holeadswevtoer,lightthistecscatteringhniquewwithinastheunsuccessfulfilmwhicbhecauseresultstheinaStructurixspreadofD3thefilmedge.isdoublecoated.

104

5.6HardX-rayin-lineholographywithhighresolutionX-rayfilms

Figure5.48:SpatialresolutionofthedirectexposureD3StructurixD3.(a)Hologramof
xapoly=0.9amidem.stringThewith(150source-to-detector±20)µmmoundistancetedx=horizon12.71tallym.atobTheX-raject-to-detectorysourcesize,distanceas
sdodmeasuredwiththewirescanner,wasσh=(19.1±0.7)µmandσv=(0.50±0.05)µm.The
X-rayphotonenergywas6keV,theexposuretime15min,electronbeamcurrent500nA.
(b)Thenormalizedintensityprofile,100rowsareaddedtogethertoimprovestatistics.The
radiographwasdigitizedwithanopticalmicroscopeofmagnification(10×).

5.6.2X-raysourcesizedeterminationfromX-rayholograms

TheX-raysourcespotsizecanbeestimatedfromthefringevisibilityofapolyamide
stringsourceinandafarhologramawayfrom[Koh00].theX-raTheystringfilm,inshouldorderbetopmakeositionedtheinahologramclosesensitivdistanceetotothethe
proproachjectedofbeam[Koh00]spisotfollosizewonedthesincefilmattherathermostthanfavtoorableitsspatialclosestresolution.distancexsoHere=the1.88ap-m,
withularlyatothegeometricalwirebutundermagnificationanangleof7.24of46◦.times,Inathestrictstringsense,wasnotthemounformalismtedperppresenendic-ted
inappendixA.2tocalculatethediffractionpatternintheFresnelapproximationdoes

105

5TowardshardX-rayin-lineholography

4.applynotTheapproachof[Koh00]isbasedonthemeasuredfringevisibilityV(zd)=(Imax−
Imin)/(Imax+Imin)atapositionatthehologramzd>1.5Rm,withRm=R∙xsd/xso
theprojectedradiusRofthestring.Thevisibilityofafringeiscalculated[Koh00]as
)z(A2V0(zd)=1+A2(dzd),(5.15)

whereA(zd)=g(zd)f1/2(z1d/2)andf(zd)=(2δxod)2Rm3.(5.16)
[1+f(zd)](zd−Rm)
Thefunctiong(zd)isobtainedfromtheenhancedstationaryphasetechnique.Ittakes
valuesbetween1,forfringesnearthefibershadowedge,and0.5forfringesfaraway
fromtheedge.WiththesequantitiesthesourcesizeS(FWHM)canbecalculated
toaccordingS=2λxsdln1/2(|V0(zd)|).(5.17)
π(|zd|−Rm)V(zd)
Themeasurementswithapolyamidestringof30µmdiameterisshowninFig.5.45(g)
and(h).Thecomplexrefractionindexparametersareδ=7.24∙10−6andβ=2.42∙10−8
atanX-rayphotonenergyof6keV.Themeasuredvisibilityatzd=365µmisV(zd)=
0.49andwithg(zd)=0.75fromEq.(5.17)astandarddeviationσv=(1.4±0.5)µm
calculated.isWiththewirescannertheelectronbeamspotsizeamountedtoσv=(0.50±0.05)µm
whilethesimulatedonewiththeaidofprogramBeamopticgaveσv=0.44µm.While
thismeasurementagreeswithintheerrorswiththeexpectation,themeasuredX-ray
beamspotsizeσv=1.4µmissignificantlylarger.Themostprobableexplanation
forthesefindingsisthelongitudinalextentofthefoilstack,inwhichtheX-raysare
produced,whichamountsto2.8mm.Withthemeasuredverticalbeamemittanceεv=
0.52µmmradat600MeVelectronenergy,thebeamhas,withσv=(0.50±0.05)µm,
adivergenceof1.04mrad.Assumingthatthefocusislocatedinthecenterofthefoil
stackthebeamspreadswithinthestacktoastandarddeviationof1.5µm,inaccord
ation.observthewith

discussionsandResults5.6.35.6.3.1Hologramsfortransparentobjects

Hologramsoftransparentobjectslikepolyamidestringswithdifferentdiametersand
humanhairswererecordedatdifferentsource-to-objectandobject-to-detectordis-
tances.TheX-rayphotonenergywas6keVcorrespondingtoawavelengthλ=2.067
4Inaperhapsquitegoodapproximationtheincreasedthicknessoftheellipticalwirecanbetaken
intoaccountbyanappropriatescalingofthethickness.However,possibleeffectsofthevariable
distancexsoalongthestringremaintobeinvestigated.

106

5.6HardX-rayin-lineholographywithhighresolutionX-rayfilms

Figure5.49:(a)Radiographofapolyamidestringofadiameterof(150±20)µm.Source-
to-objectdistancexso=1.88m,object-to-detectordistancexod=11.73m,corresponding
magnification7.24times,X-raysourcesizeσh=(19.1±0.7)µmandσv=(0.50±0.05)µm.
TheX-rayfilmwasdigitizedwithanopticalmicroscopewithamagnification4×inorderto
maintainagoodresolution.Therefore,onlypartofthehologramwasinthefieldofview.
(b)Intensityprofile200rowsaddedup.

˚A.ThislowX-rayenergywasselectedtoincreasethetransversalcoherencelength.
Thecomplexrefractionindexparametersatthisenergyforpolyamideareδ=7.24∙10−6
andβ=2.42∙10−8.Themaximumabsorption(1−exp[−(4πβD)/λ])withinthestring
isabout19.8%forthestringwiththediameterD=150µm,andtheabsorption
contrastisnotofmajorimportance.Fig.5.49(a)showsapartofahologramfora
polyamide(Nylon)stringofadiameter(150±20)µmmountedatthesource-to-object
distancexso=1.88m.Alargenumberofabout18interferencefringescanbeseen,
asdemonstratedinFig.5.49(b).Inthisradiographthemaindeteriorationinthe
fringevisibilityresultsfromtheX-rayspotsize.Therefore,suchhologramsarealso
wellsuitedtomeasurethespotsizeusingEq.(5.12).Forexampletheminimum
discernabledistancebetweentwoadjacentfringesisabout24µmandtheestimated
X-raysourcesizeisσv=1.12µm.
Fig.5.50(a)and(b)showhologramandintensityprofiles,respectively,againforthe
nylonstringwithadiameterof(150±20)µmforwhichthedistancebetweensource
andobjectwasincreasedtoxso=4.3m.ThecalculationonthebasisoftheKirchhoff-
FresnelintegralEq.(2.18)isshowninFig.5.50(c).Bycomparisonofthemeasured
andthecalculatedprofiledeviationsbecomeapparent.Theycouldarisefromdensityor
morphologicalinhomogeneitiesofthepolyamidestring,orinappropriateassumptions
ontheelectronbeamspotsize.
Tothrowlightonthismatter,largerpartsofthehologramforthepolyamidestringwith
adiameterof150µmareshowninFig.5.51.Cleardensityfluctuationscanbeseenin
thegeometricalshadowofthestring.Suchfluctuationscouldnotbeobservedwiththe
aidofanopticalmicroscope.Tofurtherinvestigatetheoriginofsuchfluctuations,two

107

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Figure5.50:(a)Radiographofapolyamidestringofadiameterof(150±20)µm.Source-
to-obgeometricaljectdistancemagnificationxso=4.3.173m,times,obX-rayject-to-detectorsourcesizeσhdistance=(19x.1od±=0.7)9.µ31mm,andσvcorresp=(0.onding50±
0(b).05)Inµm.tensityTheprofile,X-ray200filmrowwsasaddeddigitizedup.with(c)anCalculatedopticalinmicroscoptensityewithprofileaofthemagnificationradiograph.4×.
σfThe=(1.spatial2±0.4)resolutionµm,andofthetheX-raopticalysourceresolutionspotofsize(σofsc,4σv==4.(01.±500.±10µ.m)05)wµm,ereofincorpthefilmoratedof
calculations.thetoin

108

5.6HardX-rayin-lineholographywithhighresolutionX-rayfilms

Figure5.51:Radiographofapolyamidestringof(150±20)µmdiameteratobject-to-
detectordistancexod=11.73m.thesource-to-detectordistancewasxod=13.61m.The
X-rayenergywas6keV,X-raysourcesizeσh=(19.1±0.7)µm,σv=(0.50±0.05)µm,
electronbeamcurrent500nAandexposuretimewas15min.Theradiographwasdigitized
thefilmscanner(NikonCoolscanLS4000).

differentpolyamidestringswereimaged.ThefirststringwassuppliedbyGoodfellow.
Ithasadiameterof270µm.Theotheroneisafishinglinewithadiameterof350
µm.Fig.5.52showsacomparisonoftheholograms.Thepolyamidestringfrom
Go(b),othedfellow,fishingFig.line,5.52much(a),moreshowsairregularitiesrathergooaredpresenhomogeneitt.Toyb.eHosurewevthater,intheFig.intensit5.52y
fluctuationsinthemiddlepartofthestringoriginatefromtheobjectsthemselves,the
objectswereremovedandaradiographtakenwithoutthem.Nointensityfluctuations
werewithinobservtheed.string,Theyi.e.,matheystringoriginatemaynotfrombeadensitpyerfectandfluctuationsorhomogeneousshapecylinder.deformations

Therearetwopossibilitiestoanalyzehologramsofstrings.Inthefirstone,calculations
onthebasisoftheFresnel-Kirchhoffintegralscanbeperformedinwhichassumptions
aboutthedensityandmorphologyofthestringareincorporated.Therightsolution
canbefoundbytrialanderror.Suchcalculationswentbeyondthescopeofthis
experimentalthesiswork.Thesecondoneisbasedonreconstructionalgorithmsto
findthephaseprofileproducedbythetransparentobject.Oneoftheseisthemodified
Gerchberg-Saxtonalgorithm[Ger72]whichisaniterativemethodwithwhichthephase
informationcanbefoundfromtwohologramswhichweretakenatdifferentdistances
betweenobjectanddetector.Therefore,hologramsofapolyamidestringwithadiam-
eterof30µmandofhumanhairsweretakenatdifferentobject-to-detectordistances.
ThehologramsareshowninFig.5.53andand5.54.

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Figure5.52:Radiographsoftwodifferentpolyamidestrings.(a)AstringfromGoodfellow
withadiameterof270µm,(b)afishinglinewithadiameterof350µm.Thesource-to-
objectdistancewasxso=4.3m,object-to-detectordistancexod=9.31m,X-rayspotsize
σh=(19.1±0.7)µm,σv=(0.50±0.05)µm,electronbeamcurrent500nA,andexposure
time15min.Normalizedintensityprofilesoftheradiographs.(c)Fora270µmpolyamide
stringand(d)for350µm,50rowsaresummedup.Thefilmswerescannedwithafilm
scannerof(NikonCoolscanLS4000).

110

5.6HardX-rayin-lineholographywithhighresolutionX-rayfilms

Theselecteddistancescoverdifferentimagingregimes.Forthecontactregimethe
contrastwouldbe(1−exp[−(4πβD)/λ])=4.26%andtheabsorptioncontrastof
thepolyamidestringwithadiameterofD=30µmcanbeneglected.Inthenear
fieldregion,atanobject-to-detectordistancexod=0.9m,Fig.5.53(a)and(b),the
interferencepatternproducedbyboth√edgeshaveonlyverylittleoverlap.Thereason
isthatthesizeofthefirstFresnelzoneλxod=13.6µmissmallerthanthediameter
ofthestring.However,atthelargest√distancexod=11.73m,Fig.5.53(g)and(h),
oneobtainsforthefirstFresnelzoneλxod=49.2µmandtheinterferencepattern
frombothedgesdooverlap.Theresemblancebetweentheoriginalobjectandthe
radiographismoreorlesslost.Bothlimitingcasesmaybeofparticularinterestfor
thereconstructionofthephaseprofile.However,alsothisissuewentbeyondthescope
ofthisexperimentalthesiswork.

5.6.3.2Hologramsforopaqueobjects

fromOpaquetheobjectsdiffractionareinattheterestingobjecttestboboundaries.jectssinceThetheindistributionterferencewithinpatternstheobarisejectonlyis
invisibleandthereconstructionreducestoatwodimensionalproblemwhichcan,in
principle,mucheasierbesolvedasthethreedimensionaloneoftransparentobjects.
Comnificationbiningandtheahardmicro-foX-raycusedimagingX-rayofspotopaquesize,objectsdetailedwithainformationlargeongeometricalobjectsmag-with
micrometerdimensionsshouldbeobtainable.
ofHologramsdifferentofdiametershighlywabsorbingereobrecordedjectsatsuchdifferenasttungstenobwiresject-to-detector(atomicnumdistancesberZfor=the74)
source-to-detectordistancex=13.61m.Ataphotonenergyof6keVthecomplex
refractionindexparameterssdareδ=8.52∙10−5andβ=1.11∙10−5.Themaximum
1-1.9∙absorption10−12,ini.e.,athetungstenobjectwirecanbewitharegardeddiameterinavofery40goµodmisappro(1−ximationexp[−(4asπβD)completely/λ])=
opaque.Forawirewithadiameterof4µmtheabsorptionis(1−exp[−(4πβD)/λ])
=93.3%,meaningthattheobjectisnotcompletelyopaque.
Fig.differen5.55tshodistances.wsThehologramsinofterferenceatungstenpatternswirearewithproaduceddiameterduetoof40diffractionµm,attakenedgesat
andinterferencewiththeunperturbedwave.Fig.5.56showshologramsofatungsten
wirewithadiameterof(4.0±0.4)µmtakenataobject-to-detectordistanceofxod=
2.83m.Thecalculationsshownin5.56(c)onthebasisoftheKirchhoff-Fresnelintegral
wereconvolutedwithaspotsizeof(0.5±0.05)µm,thespatialresolutionoftheX-ray
filmσf=(1.2±0.4)µmandfinallythespatialresolutionoftheopticalmicroscope
σsc,10=(1.60±0.01)µm.IncontrasttoFig.5.37,takenwiththedirectexposureCCD
camera,wherejustanedgeenhancementoccurred,4fringesareobservedherewith
thehighresolutionX-rayfilm.
Fig.5.57showradiographsofanickelgrid(atomicnumberZ=28)whichdemonstrates
theimportanceofthebeamspotsize.Thecomplexrefractionindexparametersare

111

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x(a)odprofiles

hard

5.53:

X-ray

in-line

Radiographs

of

yholograph

the

olypamide

string

=are0.9shom,wn(c)onxodthe=righ2.83tm,side.(d)Thexodin=tensit9.31y

of

30

diameter

at

tdifferen

positions.

mprofilesand(g)arexodsho=wn11.73atthem.righThetinside,tensit200y

rowsaddedup.TheX-rayfilmwasdigitizedwithanopticalmicroscope(a)and(b)witha

magnificationof10times,(c)and(d)withamagnificationof4times.

112

5.6HardX-rayin-lineholographywithhighresolutionX-rayfilms

Figure5.54:Radiographofahumanhairwithadiameterof80µmatdifferentdistances.
TheX-rayspotsizewasσh=(19.1±0.7)µm,andσv=(0.50±0.05)µm.Theobject-
to-detectordistanceswerexod=0.002m(a),xod=2.83m(b),xod=9.31m(c),xod=
11.73m(d).Thesource-to-detectordistancewasalwaysxso=13.61m.TheX-rayfilmwas
digitizedwithanopticalmicroscope(a),(c)and(d)withamagnificationof(4×),(b)with
amagnificationof(10×).

δ=4.7∙10−5andβ=1.56∙10−6.Theabsorptionofthegridis(1−exp[−(4πβtNi)/λ])
31.6%.=

InFig.5.57(c)theverticalintensityprofileofthegriddisappears.Thisfactcan
beexplainedbythelargebeamspotsizeinhorizontaldirection,whichamountsto
σh=(19.1±0.7)µm.ThecorrespondingX-rayspotsizeprojectiononthedetector
planeisσh−proj=(41.35±1.65)µm.Afurthercontributionoriginatefromthevirtual
beamspotsizeof37.5µmofthecrystalmonochromator,seesection5.4.3.

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Figure5.55:Radiographofatungstenwireof(40±4)µmdiameter.X-rayphotonenergyis
6keV,X-raysourcesizewasσh=(19.1±0.7)µm,andσv=(0.50±0.05)µm.Theobject-to-
detectordistance(a)xod=2.83m,(c)xod=9.31mand(e)xod=12.71m.Theradiograph
isrecordedwithanX-rayfilmanddigitizedwithopticalmicroscopeofmagnifications(10×)
(a),and(4×)(c),(e).

114

rksremaConcluding5.7

remarksConcluding5.7

AtthirdgenerationsynchrotronradiationsourcesX-rayphasecontrastimagingand
hardX-rayin-lineholographybecomearoutinetechniqueforbeamqualitymonitoring,
characterizationoftheopticalelements,samplealignmentandanumberofsimilar
Ste03].Gur96,[Grz99,applicationsAtMAMI,abrilliantX-raybeamhasbeenpreparedonthebasisoftransitionradia-
tion.Thehightransversecoherencelengtharisesfromthemicro-focusedelectronbeam
incombinationwitharelativelongsource-to-detectordistance.Thelongitudinalco-
herencehasbeenobtainedbythe(111)reflectionataflatsiliconsinglecrystalinBragg
geometry.Streakshavebeenobservedwhichprobablyoriginatefromdeformationsin
thecrystallatticeplanesofthemonochromatorcrystal(wavystructures).Ithasbeen
demonstratedthatthedirectexposureCCDchipprovidesahighlyefficienton-linede-
tector.Itwasusedtomonitortheelectronbeamsizebyobservingthesmallestvisible
interferencefringespacingsorthenumberoffringes.
DirectexposureCCDcamerachipshave,comparedwithX-rayfilms,thebigadvantage
thattheyhaveagoodlinearityoverawidedynamicalrange,agoodsignal-to-noise
ratio,andthattheyareon-linecapable.Contrastimagescaneasilybegeneratedin
whichallparasiticbackground,whichoriginatesnotfromtheobject,canbeeliminated.
Theon-linecapabilityallowedaminimizationofthebeamspotsize.Thedisadvantage
ofamoderatespatialresolutionincomparisontoanX-rayfilmcouldbealleviated
byageometricalmagnificationwhichresultedinaneffectivepixelsizeof1.86µm.
Unfortunately,thespatialresolutionislargerthanonepixelbecauseofsplitevents.
Densityfluctuationsandshapedeformationoflowabsorbingmaterialshavebeenob-
servedwithphotonsof6keVenergy.Thereconstructionof3-Dimagesfromthe
hologramsisadifficulttask[Ger72,Koh97]andwasoutsidethescopeofthiswork.
X-rayradiographyusingcoherentX-raysenhancesalsothevisibilityofthehighly
absorbingmaterialsviadiffractionatedges.Thiswasdemonstratedwithtungsten
wiresofvariousthicknessesbetween4and40µmdiameter.Incombinationwitha
highgeometricalmagnificationthiseffectwouldallowtheobservationofsmallhighly
absorbingfeatureswithmicrometersizeinanobjecttobeinvestigated.
Ithasbeenshowninthissection5.6thatX-rayfilms,incombinationwiththemicro-
focusedandmonochromizedtransitionradiationX-raysourceatMAMI,areuseful
detectors.ThemainadvantageincomparisonwiththedirectexposureCCDchipis
theresolution.FortheX-rayfilmStructurixD3thestandarddeviationoftheresolution
wasmeasuredtobeσf=(1.2±0.4)µm,whichisaboutafactorof6betterthanfor
thedirectexposureCCDchip.WiththesmalleffectiveX-rayspotsizeinvertical
directionofσv=(1.4±0.5)µmandageometricalmagnificationofupto7.24high
qualityhologramsoftinytransparentandopaqueobjectsweretaken.Theexposure
timesataphotonenergyof6keVwereaboutthesameforthedirectexposureCCD
chipandtheX-rayfilm.

115

5TowardshardX-rayin-lineholography

Theparticular,mainmakdisadvesanthetageprooftheductionX-raofyfilmnormalizedistheconmissingtraston-lineimagesmorecapability,difficult.which,Thisin
problemcanbesolvedinfutureexperimentsbyaprecisepositioningprocedureof
thesuitablefilmwithabsorptionwhichthemarkers.hologramTheandoftenthestatedreferencedisadvanpicturetageareofatakenlimitedwiththedynamicalaidof
range,fortheStructurixD3filmabout1:3000,wasintheexperimentsofthisworknot
thescanninglimitingmicroscopfactoresincewiththewhicfinalhthedevdynamicalelopedrangeX-raofyfilm1:256wwasasdigitized.definedbyThistheproblemoptical
canbesolvedbyusingasetupsimilartothatdescribedinappendixCinwhichthe
cGdhip2Ois2wS:TbellsuitedluminescenasantscreenopticalisdetectorreplacedbwithyatheX-radynamicalyfilm.rangeTheofabMarconiout16CCD47-10bitsor
1:65500.Withamagnificationoftheopticsofaboutafactorof5times,theeffective
pixelresolutionof2.6µm(standarddeviation)oftheCCDwillbeintheorderofthe
resolution.filmyX-ra

116

5.7

Concluding

remarks

Figure5.56:(a)Radiographofatungstenwirewithadiameterof(4.0±0.4)µm.Source-
to-objectdistancexso=10.78m,object-to-detectordistancexod=2.83m,corresponding
geometricalmagnification1.26times,electronbeamcurrent500nA,exposuretime15min.
Theradiographwasdigitizedwithanopticalmicroscopeofmagnification(10×).(b)The
intensityprofile,200rowsweresummedup,(c)thecalculatedintensityprofile.

117

5TowardshardX-rayin-lineholography

Figure5.57:Picturesofanickelgridwith4µmthickness,widthof12µmandspacingof40
µm.(a)Imagetakenwithanopticalmicroscopewith(10×)magnification.(b)Radiograph
atsource-to-objectdistancexso=12.71mwhiletheobject-to-detectordistancexod=0.9m,
geometricalmagnification1.07times.Theradiographwasscannedwithanopticalmicroscope
withmagnification(10×).(c)Radiographatsource-to-objectdistancexso=4.3mwhile
theobject-to-detectordistancexod=9.31m,geometricalmagnification3.17times.The
radiographwasscannedwithanopticalmicroscopewithmagnification(4×).(d)Vertical
intensityprofileofradiograph(c).X-rayphotonenergy6keV,electronbeamcurrent500nA,
exposuretime15min,X-raysourcesizewasσh=(19.1±0.7)µm,andσv=(0.50±0.05)µm.

118

okOutlo6

AnyworkonX-rayholographyatMAMImust,insomesense,bearcomparisonwith
modernsynchrotronradiationsourcessuchasESRF,APSandSpring8.Atthese
X-rafacilitiesywavenanofoguidescusing[Jar05]parabareboliceingrefractivdevelopeedX-Rawithylenseswhich[ScX-rah03],yspandottsizeswointhedimensionalorder
of50nmcanbeprepared.Thequestionariseswhichdimensions,atleastinprinciple,
infuturecanbeachievedwithatransitionradiationsourceatMAMI.
Toachieveatagivenemittanceasmallbeamspotsizethedivergenceoftheelectron
bshouldeammnotustbbeetoolarge.largeItandwillmbeustnotrequiredexceedthatthetheangleangular2/γspread(standardofthedeviation).electronbWitheam
themeasuredemittancesataelectronbeamenergyof600MeVεh=2.3µmmrad
andεv=0.52µmmradinhorizontalandvertical1direction,respectively,beamspot
sizestheseofσhdimensions=1.35µshouldmbandeacσvhiev=0able.31bµymmicro-foresult.cusingAthedecreasebeamofsptheotspsizeotbysizemeansinto
ofminiaturizedquadrupolesofasmallfocallength.Suchdevicesarecurrentlybeing
developedattheLMUM¨unchen[Hab05]andwillbetestedatMAMIinthenext
future.demagnifiedAbfurtheryacrystalimprovemenoptics,tasshouldscbehematicallyobtainableshownifintheFig.X-ra6.1.ybTheeamspotlongitudinalsizeis
dimensionlofthetransitionradiatormustfulfilltheconditionl≤σγ,i.e.must
notexceedltrtr=364µm.Typically,itconsistsonlyofafewfoilstrwithavthicknessof
babeamoutsp12otµmsizesandwaouldspacingbeinoftheaboutorder100σµh,virm.t=Ata270nmanddemagnificationσv,virtof=562×thenm,i.e.virtualin
theorderofwhatisenvisagedatsynchrotronradiationfacilitieswithtwodimensional
X-raywaveguides.
However,itshouldbestressedthatthedegradationofthetransversecoherenceby
btheesolvcrystaled.Ifinthishorizonwouldtalbepdirection,ossible,whicthehhasanglebineenwhicmenhtionedcoherenintX-rasectionysof5.4.3,amphotonust
energyof6keV,orλ=2.067˚A,areemittedwouldbe,accordingtotheequation
vσh,vertical∙θcohdirection,λ/2π,respaboutectivθelycoh,h.A=ta0.12mradsource-to-crystalandθcoh,v=distance0.84ofxmrad=in7.8m,horizonatalcrystal-and
sclengthto-detectorofthedistancedemagnifyingofxcd=crystal5.8ism,fand=xasc/(M−1)demagnification=1.95m.factorAtaM=distance5×btheetwfoeencal
1Thesenumbersarewellabovethetheoreticaldiffractionlimit.Foratransitionradiationsource
onewithanobtainsopateningaphotonangleofenergytheofradiation6keV,oforθλ==2/γ2.067=1˚A,.7mrad,accordingγ=tothe1174forrelation600σMeVspotθ=λ/electrons,(2π)
aspotsizeσspot=19.4nm.

119

6

Outlook

Figure6.1:DemagnifyingcrystalopticstoproduceananofocusatMAMI.Thesource-to-
crystaldistanceisxsc,thecrystaltodetectordistancexcd,andthedemagnificationfactor
M.Then,thefocallengthofthecrystalmustbef=xsc/(M−1)andthevirtualsource-
to-crystaldistanceisxsc,virt=xsc/M.Focallength,bendingradiusRofthecrystaland
BraggangleθBareconnectedbytheequationf=(R/2)sinθB.Theobjectcanbeplaced
betweenX-raysourceandcrystalorcrystalanddetector.

thevirtualsourceanddetectorxsc,virt=xsc/M+xcd=7.36manellipticalareawith
semiaxesof0.9mm×6.2mmcouldbecoherentlyilluminated.

120

AbyaRefractioncylindricalandstringdiffractionofX-rays

A.1Refractionintheapproximationofgeometrical
optics

aInpointhistlikappeendixX-raythesource,intensitwillybeprofilebcalculatedehindinathecylindricalapprostring,ximationwhicofhisgeometricalilluminatedoptics.by
ItwillbeassumedthattheX-raysarerefractedbytheobject.Thisapproachmight
bareeagosmearedodapproout,i.e.,ximationiftheatobexpjecterimenistalilluminatedconditionswithinpwhicolychinhromaticterferenceX-rays,patternsorif
theprojectedsourcesizeorthedetectorresolutionaretoolargeresp.toobad.The
geometricalconfigurationisdepictedinFig.A.1.

FigureA.1:RefractionofX-raysbyacylindricalstringofradiusRandrefractionindex
n2embeddedinamediumwithrefractionindexn1.Theangleα1istheangleofincidence
withrespecttothesurfacenormalofthestring,α2istherefractionangleinthestring.From
theseanglesthedeflectionangleΔα/2oftheincidentraycanbecalculatedwhichisassumed
tobedoubledattheexit.

121

ARefractionanddiffractionofX-raysbyacylindricalstring

(A.1)

wlaSnell’susingByn1sinα1=n2sinα2(A.1)
wheren1=1−δ1+iβ1andn2=1−δ2+iβ2,
neglectingabsorption,i.e.β1=β2=0,andassumingδ1,δ21oneobtains
δ1−sin(α2)=1−δ1sinα1⇒sinα2=(1−δ1+δ2)sinα1.(A.2)
2Withα2=α1+Δα/2andΔα/2asmallquantityforhardX-raystheequation

sinα2=sin(α1+Δα)=sinα1cosΔα+cosα1sinΔα(A.3)
222toreducessinα1+Δ2αcosα1=[1+(δ2−δ1)]sinα1(A.4)
orΔ2αcosα1=(δ2−δ1)sinα1.(A.5)
ThetotaldeflectionangleΔαisassumedtobedoubledattheexitinterfaceofthe
string,whichprobablyisarathergoodapproximation,andisgivenby
αsin1Δα=2(δ2−δ1)cosα1.(A.6)

Thespatialcoordinatezdoftherayatthedetectorplanebecomes
αsin1zd=zo(1+xod/xso)+sign(zo)∙Δα∙xod=zo(1+xod/xso)+sign(zo)∙2∙(δ2−δ1)xodcosα1.
(A.7)withz0thespatialcoordinateoftherayattheobject,infrontofthestring,seeFig.A.1.
Withoutanyrestrictionofgenerality,onlypositivevaluesofz0willbeassumedinthe
following.Forthedistancebetweensourceandobjectxsolargeagainsttheradius
Rofthestring,i.e.β1,ingoodapproximationsin(α1−β)≈sinα1holds.By
eliminatinginthisequationsinα1andcosα1withtheexpressions
zo=Rsinα1⇒sinα1=zRo⇒cosα1=1−(zRo)2(A.8)
anddividingbothsidesbyRoneobtains
zd=zo(1+xod/xso)+2xod(δ2−δ1)zo/R.(A.9)
RRR1−(zo/R)2
Withthesubstitutionszd/R=ξ,zo/R=ξ1,2(δ2−δ1)xod/R=AEq.(A.9)reads
ξ=ξ1(1+xod/xso)+Aξ1.(A.10)
2ξ11−

122

A.1Refractionintheapproximationofgeometricaloptics

ThescatteredintensitydistributiondN/dzdatthedetectorplaneisconnectedwith
theprimaryintensitydistributiondN0/dz0withoutthestringbytheexpression,
dN=dNdzo=dN0∙(1+xod/xso).(A.11)
dzddzodzddzddξ/dξ1
WithdξA1−2ξ1
dξ1=(1+xod/xso)+1−(ξ12)+Aξ1[−2(1−ξ12)23](A.12)
Adξdξ1=(1+xod/xso)+(1−ξ2)23(A.13)
1andsubstitutionofEq.(A.13)intoEq.(A.11)oneobtainsforthescatteredintensity
distributiondNdN0(1+xod/xso)
d(zd/R)=d(zd/R)(1+xod/xso)+A/(1−(zo/R)2)23.(A.14)
ThenormalizedtotalintensitydistributionI(nω)atthedetectorplaneisgivenby
dNdNz0dIn(ω)(zd/R,ω)=θ(R∙(1+xod/xso)−1)+d(zd/R)/d(zd/R)=(A.15)
zd(1+xod/xso)
=θ(R∙(1+xod/xso)−1)+(1+xod/xso)+A(ω)/(1−(zo/R)2)23
withz0/Rasolutionoftheequation
zd=zo(1+xod/xso)+A(ω)zo/R,(A.16)
RR1−(zo/R)2
θ(x)theunitstepfunction,equaltozeroforx<1and1forx≥1,andA=A(ω)=
2(xod/R)(δ2(ω)−δ1(ω)).InthefinalintensitydistributionIn(zd/R)thefrequencyspec-
trumoftheprimarypolychromaticX-raybeamandtheresponseoftheX-raydetector
hastobetakenintoaccount.Itisobtainedbyanintegrationwithanappropriate
normalizeddistributionfunctionf(ω)andreads
In(zd/R)=In(ω)(zd/R,ω)f(ω)dω.(A.17)
Atypicalexampleofsuchanintensitydistribution,assuminganunlimitedspatial
resolutionofthedetectorandapoint-likeX-raysourceisshowninFig.A.2.
Theedgeenhancementcanclearlyberecognized.Thestep-likeincreaseoftheintensity
atzd/R=1originatesfromtheassumptionλ→0and,therefore,isunrealistically
steep.Tounderstandthedecreaseoftheintensityforzd/R<1itisworthwhileto
noticethatthestringactsinsomesenseasade-focusingcylindricallenssinceinthe
X-rayregiontheindexofrefractionislessthanunity.Thefocallengthfinthecenter
ofthestringisgivenbythelensmakersformula[Hec89]
1=−2(δ2−δ1).(A.18)
Rf

123

ARefractionanddiffractionofX-raysbyacylindricalstring

FigureA.2:Calculatedintensityprofileofapolymerwirewithadiameterof30µmillu-
minatedwithapointlikesource.Calculationsarebasedongeometricalopticsasoutlined
inthisappendix.Theobject-to-detectordistanceisxso=1.92mandtheobject-to-detector
distancexod=11.68m,thecorrespondingmagnificationis7.1times.X-rayphotonenergy
19.6keV,thecomplexrefractionindexparametersareδ=6.8∙10−7andβ=2.6∙10−10.

A.2DiffractionintheFresnelapproximationofwave
optics

ThewavefieldemanatingfromthepointsourceinthegeometryofFig.(A.1)isinthe
Fresnelapproximationattheobjectgivenby

22z+yE0(yo,zo)=EAexp(ikoo),
x2so

(A.19)

withEA=(A/xso)exp(ikxso),k=2π/λthewavenumber,andAtheamplitude.Let
usassumethatourobjectconsistsof”flat”elementswhicharepositionedinspaceat
variousdistancesxsofromthesource.Eachoftheseelementsmaybedescribedby
atransmissionfunctionQ(yo,zo)whichisdefinedinthecompleteobjectplane.This
willbediscussedindetailbelow.ByusingKirchhoff’sintegralthewavefieldatthe

124

A.2DiffractionintheFresnelapproximationofwaveoptics

(A.23)

detectorplaneisgivenby
∞∞k
E(yd,zd)=h0E0(yo,zo)Q(yo,zo)expi[(yd−yo)2+(zd−zo)2]dyodzo,
x2od−∞−∞(A.20)withh0=(−i/λxod)exp(ikxod).InsertingEq.(A.19)oneobtains
E(yd,zd)=h0EAexpikyo+zoQ(yo,zo)expik[(yd−yo)2+(zd−zo)2]dyodzo
∞∞22
−∞−∞2xso2xod
o∞∞ky2(yd−yo)2
=h0EAexpi2[x+x]
odso−∞−∞22∙Q(yo,zo)expik[zo+(zd−zo)]dyodzo.(A.21)
xx2odsotitiesidentheWith222yo+(yd−yo)=xsd(yo−ydxso)2+yd(A.22)
xsoxodxsoxodxsdxsd
and222zo+(zd−zo)=xsd(zo−zdxso)2+zd(A.23)
xsoxodxsoxodxsdxsd
obtainsoneAy2+z2−ix
E(yd,zd)=exp(ikxsd)exp(ikdd)∙sd∙(A.24)
xsd2xsdλxsoxod
expikxsd[(yo−ydxso)2+(zo−zdxso)2]Q(yo,zo)dyodzo.
∞∞
−∞−∞2xsoxodxsdxsd
InthefirstlinetheunperturbedwaveE0(yd,zd)=(A/xsd)exp(ikxsd)exp(ik(yd2+
zd2)/(2xsd)atthedetectorpositioninadistancexsdfromthesourcecanberecognized.
Thesecondlinedescribesthemodificationofthiswavebytheobject.Inthefollowing
weassumethattheobjectisanone-dimensionalstringforwhichthetransmission
functioncanbewrittenasQ(yo,zo)=Q(zo).ThenEq.(A.24)separatesinto
∞E(yd,zd)=E0(yd,zd)−ixsdexpikxsd(yo−ydxso)2dyo
λxsoxod−∞2xsoxodxsd
∞∙expikxsd(zo−zdxso)2Q(zo)dzo.(A.25)
−∞2xsoxodxsd
Thecalculationoftheintegral
∞π∙xsdxso
Iy=expi(yo−yd)2dyo(A.26)
−∞λxsoxodxsd

(A.26)

125

ARefractionanddiffractionofX-raysbyacylindricalstring

∞yieldswiththewellknownexpressionexp(−iβt2)dt=−iπ/β,β=−πxsd/(λxsoxod),
−∞t=yo−ydxso/xsd,dt=dyo
Iy=λxsoxod(A.27)
ixsd−andEq.(A.25)canberewrittenas
∞−ixsdxsdxso
E(yd,zd)=E0(yd,zd)Q(zo)expik(zo−zd)2dzo.(A.28)
λxsoxod−∞2xsoxodxsd
LetusassumethatQ(zo)canbesubdividedintothreeregionsaccordingto
1for|zo|>R
Q(zo)=q(zo)for−R<zo<R.(A.29)
Then,Eq.(A.28)canbereshapedinto
−ix∞xx
E(yd,zd)=E0(yd,zd)sdexpiksd(zo−zdso)2dzo+
λxsoxod2xsoxodxsd
−∞Rxx
[q(zo)−1]expiksd(zo−zdso)2dzo.(A.30)
−R2xsoxodxsd
ThefirstintegralcanbecalculatedandgivesthesameresultasEq.(A.27).Then,the
finalresultforthenormalizedwavefieldatthedetectorplanereads
E(yd,zd)=1+a(zd)(A.31)
E0(yd,zd)

with−ix∞xx
a(zd)=−λxsoxsdodp(zo)expik2xsosdxod(zo−zdxsdso)2dzo(A.32)
−∞andp(zo)=[1−q(zo)]∙θ(1−|zo|/R),(A.33)
thecomplementarytransmissionfunctionoftheobject.Withthisfunctiontheobject
|zoplane|≤Rcan.Ifbeilluminatedregardedastheopaqueamplitudefor|az(oz|d)>Rdescribandesakindtransparenoftslitatthediffraction,object,howi.e.ever,for
withthecomplementarytransmissionfunctionoftheobjectplacedintotheslit.Forthe
limitingfunctioniscaseszeroofaandone,transparenresptectivandelyan.Theopaqueformerobjectcorresptheondscomplementoa(zd)tary=0,thetransmissionlatter
toFresneldiffractionforanilluminatedslit.

126

A.2DiffractionintheFresnelapproximationofwaveoptics

TheexponentoftheexponentialinEq.(A.32)canbeexpandedas
xsdxso2xsd2xsoxso2
k2xsoxod(zo−zdxsd)=k2xsoxod(zo−2zozdxsd+(zdxsd)).(A.34)
andEq.(A.32)withEq.(A.34)rewrittenin
xa(zd)=−expik2xsoxzd2
sdod∞∙−ixsd∙p(zo)expikxsdzo2exp−ikzdzodzo.(A.35)
λxsoxod−∞2xsoxodxod
sdThesecondline−ix∞
λxsoxod∙p˜(zo)exp−iz˜dzodzo.(A.36)
−∞containsaFourierintegralofthemodifiedcomplementarytransmissionfunction
xp˜(zo)=p(zo)expik2xsdxzo2(A.37)
odsointhereducedspacecoordinatez˜d=kzd/xod.Theexponentialinthefirstlineof
Eq.(A.35)oscillatesrapidlywithincreasingzdandcontains,inessence,theholographic
informationonthedistanceofthetransparentobjecttothesourcexso,ortheobject
tothedetectorxod=xsd−xso.
LetusdiscussunderwhichconditionstheintegraltransformEq.(A.36)reducestoa
simpleFouriertransformofp(zo).Generally,thisisthecaseifπxsdzo2/(λxsoxod)=
(πzo2/λ)(1/xso+1/xod)≤(πR2/λ)(1/xso+1/xod)πholds.IntermsofFresnel
ersbumnR2R2
NF=λxso,NF=λxod(A.38)
thisconditioncanalsobeformulatedasNF=NF+NF1.Ataconstantsource-to-
detectordistancexsdthetotalFresnelnumberNFislargeforeitherxodxsdorxso
xsd,anditisminimalatxod=xso=xsd/2.ForthelattercaseNF=4R2/(λxsd)
1orRλxsd/4mustbefulfilled.Forxsd=13.6m,λ=2A˚anR26.0µm
results.Thisconditionwasgenerallynotfulfilledinourexperiments.
AremarkmaybeappropriateunderwhichconditionsEq.(A.35)isequivalenttothe
Fraunhoferapproximation.Thisisthecaseif,inaddition,theexponentialinthefirst
lineofEq.(A.35)reducestoonewhichisthecaseiftheobservationregionobeysthe
inequalit√yzdλxsdx0d/(xso).Undertheassumptionsmadeabovethismeansthat
zdλxsd=52.2µm.Thisconditionwasalsonotfulfilledinourexperiments.
Insummary,sinceneitheroftheabovediscussedconditionswerefulfilledingeneral
inourexperiments,Eq.(A.35)cannotbesimplifiedtotheFraunhoferapproximation
andEq.(A.36)nottoaFouriertransformofp(zo).

127

ARefractionanddiffractionofX-raysbyacylindricalstring

imagetrastconnormalizedTheInorm(zd)=|E(yd,zd)/E0(yd,zd)|2−1=2[a(zd)]+|a(zd)|2(A.39)
separatesintoa”holographicdiffractionpattern”2[a(zd)]whichessentially2contains
theinformationonthedistance,anda”classicaldiffractionpattern”|a(zd)|ofthe
complementarytransmissionfunctionp(zo)oftheobject.Thisseparationisillustrated
inFig.5.1forahomogeneousstringwithradiusRforwhichq(zo)isgivenby
q(zo)=exp−4π(iδ+β)R2−z2o.(A.40)
λTheresultsderivedinthisappendixonthebasisofKirchhoff’sintegralEq.(A.20),
whichcanalsobeobtainedinasystemtheoreticalapproachbyanexpansionofthe
wavebehindtheobjectintoparaboloidalelementarywaves(Fresnelapproximation),
see[Sal91,Eq.(4.1-14)],agreeswiththeresultsreportedby[Koh01].
ForastringwiththetransmissionfunctionEq.(A.40)theEq.(A.32)readswiththe
substitutionzo/R=sinθ,dzo=Rcosθdθ
2/πa(zd)=expikxsozd2R−ixsdexp−4π(iδ+β)zsh(cosθ)−1
2xodxsdλxsoxod−π/2λ
∙expikxsdRsinθ(Rsinθ−2zdxso)cosθdθ.(A.41)
2xsoxodxsd
withzsh(cosθ)=Rcosθ.Thisrepresentationhastheadvantagethatitcaneas-
ilybegeneralizedfornon-circularsurfacesofthestring.Forthatpurposeashape
functionzsh(cosθ)=R(acosnθ)+bcosmθ)hasbeenintroducedwithn,manda
arbitraryrealnumbers,andbdeterminedfromthenormalizationconditionπR2=
2/π2R−π/2zsh(cosθ)cosθdθ.Withsuchanansatzalsoradialinhomogeneitiesoftheden-
sityaswellasδorβmaybedescribed.
Intheforegoingcalculationsapointsourcehasbeenassumed.Inreality,onlyfinite
sourceswithaprofiles(zd)areavailableand,therefore,thecalculatedintensityprofile
mustbeconvolutedwiththeX-raysourceprojectionfunctionatthedetectorplane
sproj(zd)=(xod/xso)s(zd).Inaddition,alsothedetectorhasafinitespatialresolution
whichisintheorderofthepixelsizeandtheresultingintensityprofilemustbeonce
moreconvolutedwiththedetectorspatialresponsefunctionr(zd)togetthefinalprofile
whichcanbecomparedwiththemeasuredones.Theconvolutednormalizedcontrast
aswrittenisimageI¯norm(zd)=Inorm(zd)∗(sproj(zd)∗r(zd)).(A.42)
InthecalculationsGaussianprofileswithstandarddeviationsσsandσdwereassumed
forboth,thesourceprofileandthedetectorresponsefunction,respectively.Thishas
theadvantagethatthedoubleconvolutioninEq.(A.42)reducestoasingleonewith
aGaussianofvarianceσ2=((xod/xso)σs)2+σd2.

128

BFurtherresultsofrefraction
radiographycontrast

Figs.diameterB.1,ofB.230µandmatB.3shodifferenwtobrefractionconject-to-detectortrastradiographsdistances.ofIfathenobylonjectstringisinwithclosea
anconobtactwithject-to-detectorthefilm,nodistancecontrastof0.is5mobservtheedconsincetrastthestartstoabsorptionbuildsisuponlybut0.1%.isstillAt
consmall,trastCref=increases(4.1±to2.C9)ref%.=At(15a.7±larger2.6)ob%,andject-to-detectorreachesatxdistanceod=xod5.5=m3.the27mvaluethe
Cref=(20.1±2.9)%.Alsohereabroadeningoftheedgeisobservedwhichisdueto
theincreasingsizeoftheprojectedX-raysourcespotatthedetectorplane.
ThemostinterestingfeatureoftheradiographsshowninFigs.B.1,B.2,B.3isthat
baneamedgealsoforaenhancemenrathertorthinpphaseolymercontrastwirecanwithbaeobservdiameteredofwith30aµpm.olycInthehromaticfollowingX-raay
ingtocomparisonthewillgeometricalbegivenandbetwwaveeentheopticalininterpretationterpretation.oftheFigs.expB.1erimen(c),talB.2results(c)andaccord-B.3
sp(c)otshosizeswandcalculationsX-rayfilmwiththeresolution,geometricalincludingmodelthepresenscannertedinresolution,subsectionhaveb4.1.3.eentakBeamen
basyameasured.delta-functionFortheatsaktheeofmeanconvphotoneniencetheenergyX-ra¯hωysp=19.6kectrumeV.hasFigs.beenB.1(d)appro,B.2ximated(d)
andB.3(d)showcalculationswiththewaveopticalmodelpresentedinsubsectionA.2.
havAgain,ebbeeneamtakspenotassizesmeasured.andX-raTheyfilmcalculationsresolutions,werepincludingerformedthewithanscannerapproresolution,ximation
ofdiscretethevdetectedaluesinX-ratheyspenergyectrumrangeshobetwnweenin8Fig.and4.630kwhiceV.hwTheasappromeasuredximatedcontrastwithCref22
atframewdifferenorktofobgeometricalject-to-detectorandwavdistanceseopticsxodinareFig.shownB.4.togetherwithcalculationsinthe
ItthatcanonebeonseenthefromFig.geometricalB.4thatopticsthecalculationsunderestimatebasedtheonwameasuremenveopticsts.ovButiterestimateshouldbande
momendel,tionedthethat,evcalculationsenwhenarethetoowloavw.eopticalClearly,correctionlimitationsisofomittedtheinthegeometricalgeometricalmodel
btheecomedigitizationapparent.oftheThehighermeasuremenvaluestwithofthethewpaveolymeropticalstringwithcalculationsadiameterindicateof30thatµmin
isworseashasbeenassumed.

129

BFurtherresultsofrefractioncontrastradiography

FigureB.1:(a)Refractionenhancedradiographofapolymerstringwithadiameter30µm
atanobject-to-detectordistancexod=2.0m,andasource-to-detectordistancexsd=11.38
m.ThepolychromaticX-raybeamfromtransitionradiationwithspectraldistributionshown
inFig.parameters3.5hasarebδeen=7.used.2∙10A−t7theandspβ=ectrally2.74w10eigh−10ted.Theenergyofelectron19.6bkeameVthecurrentrefractivwase6indexnA,
theexposuretimeamountedto60sec.X-raysourcesizeswereσh=(8.6±0.1)µmand
σv=(7.5±0.1)µminhorizontalandverticaldirection,respectively.Theradiograph(a)
wascapturedbyanX-rayfilmoftypeMamorayMR5IIPQ(Agfa).Thedevelopedfilm
wsizeasof9.digitized4∙9.4byµman2.(b)X-rayIntensitscanneryofprofiletypeforSupwhicerhCo100olScanvertical2700pixelsEDw(Nikereon)addedwithatogetherpixel
toimprovethestatistics.(c)Normalizedintensityprofileaccordingtogeometricaloptics
asdescribedinsubsection4.1.3withthefollowingparameters:filmandscannerresolution
σd=(10.0±0.4)µm,andthewaveopticalcontributionσw=λxsdxod/(2πxso)=4.94µm
withλ=0.633˚A.(d)Sameas(c)onthebasisofwaveoptics

130

Figure30

of

Fig.

B.2:anat

B.1.

(a)

ob

Refraction

enhanced

ject-to-detector

distance

radiograph

xod

od

=

27.3

of

m.

a

p

olymer

orF

string

further

with

a

explanations

diameter

see

of

caption

131

B

urtherF

results

of

refraction

trastcon

(a)B.3:FigureenhancedRefraction30µmatanobject-to-detectordistance
B.1.Fig.

132

yradiograph

xod=radiograph5.5m.ofFaorpfurtherolymerstringexplanationswith

diameteracaptionsee

ofof

FigureB.4:ContrastCrefforapolymerstringof30µmdiameterasafunctionofthe
object-to-detectordistancexod.Thesource-to-detectordistancexso=11.38mwaskept
constantduringthemeasurements.Errorbarsaremeasurements,crossedcirclescalculations
withthewaveopticalmodelwithabeamspotsizeσh=8.6µmandatotalX-rayfilm
resolutionofσf=1.96µm,andascannerresolutionofσp=9.77µm.Starsdesignate
optics.geometricaltoaccordingcalculations

133

CX-rayimagingwithaGd2O2S:Tb
screenluminescence

Thedirect-exposureCCDcameraasimagedetectorhasaspatialresolutionwhich
islimitedbythepixelsize,inthepresentcase13×13µm2.Consequently,fringes
ofhologramswithspacingssmallerthanthepixelsizewillbeblurredorinvisible.
However,thespatialresolutionevenwithsuchaCCDasdetectorcanbeimprovedif
theX-raysareconvertedbyasuitableluminescentconverterscreenintovisiblelight
andtheresultingpictureisbeingmagnifiedviaanopticalmicroscope.Thefinitepixel
sizeoftheCCDcameraturnsouttobenegligiblysmallifhighenoughamagnification
ischosen.Suchsystemshavebeendescribedindifferentworks[Bus94,Koc98,And96],
andresolutionsintheorderof0.8µm(FWHM)werereported.Inthefollowing,the
experienceswithsuchasystematMAMI,employingatransitionradiationbeamwhich
iscontaminatedwithhighenergybremsstrahlungphotons,willbedescribed.

set-uperimentalExpC.1

proTheducedsetupbyemplothe6yedkeVatfoilMAMIstack,isdescribdepictededinincFig.hapterC.1.3,TheatantransitionelectronbeamradiationenergyX-raofys
600MeVareconvertedbyaGd2O2S:Tbluminescentscreenof4µmor12µm[APSXX]
thicknessintovisiblelightwhichispartlycollectedbyanopticallensandconveyed
toCCDthechipCCDtocamerabremsstrahlung[And96,Gia89,photons,Kan97,withwhicSwha73].theToatransitionvoiddirectradiationexpX-raosureybofeamthe
◦ciship.conThetaminated,CCDcthehipislightisplacedinreflectedanevbehindacuatedthechamlensbberyaata45pressuremirrorofinto10−the8mCCDbar.
Thesystemlighistenshieldedtersthewithchamableaderwallthroughof20a5cmmmthicthickness.kglassThewwindoallw.hasaholeUpstreamwiththeanwholearea
of7.5×8.2cm2throughwhichtheX-raysenterintotheimagingsystem.Thewhole
systemismadelighttightbystainlesssteelbellowswhichallowaneasypreadjustment
oftheluminescentscreenandtheCCDcameraheadwhicharemountedonanoptical
bencHostaphanh.Thefoilsenoftrance250µwindog/cmw2atthictheknessconvcoerterveredscreenwithis20closedµg/cmwith2twaluminoum.aluminizedThe
wholeimageimagingdetectorpsystemositioniswithmounresptedectontoathepX-raositioningybeam.stagewhichallowstoadjustthe

134

C.2TestoftheX-rayimagingsystemandmeasurements

FigureC.1:Imagingsystem(nottoscale).X-rayphotonsimpingefromtherightontothe
Gd2O2S:Tbluminescentscreenof4and12µmthicknessforpolychromaticandmonochro-
maticX-raydetection,respectively.Anf=50mmCanoncameralenswithF-numberof
1.4hasbeenused.Theprincipalpointsarelocatedinfrontofthelens.Thepictureatthe
luminescentscreencanbefocusedremotelybyamechanicaldriveatthelens.Foradetailed
descriptionoftheCCDcameraheadseesection5.3.

C.2TestoftheX-rayimagingsystemand
measurements

testsOff-lineC.2.1

Theopticalaxisofthesystemwasadjustedwiththeaidofalaserbeam.Inthe
geometryofFig.C.1,themagnificationcanbechosenbetween1to6timesresulting
inaneffectivepixelsizebetween13µmand2.62µm.Thespatialresolutionofthe
systemis,inaddition,affectedbythethicknessofthephosphorscreenandthequality
oftheimaginglens.TheopticsandCCDcamerasystemwastestedwithastandard
Siemensstar[LinXX]withminimumspatialresolutionof8.7µmwhichreplacedthe
luminescentscreen.Thereafter,thecompletesystemwithaconverterscreenwastested
withalphaparticlesfroman241Amsource.Thesourcewaslocatedatadistanceof1
cmfromtheluminescentscreeninair.Anoptimumresolutionof7µm(FWHM)was
foundwitha4µmthickconverterscreenatamagnificationof3.5.

135

CX-rayimagingwithaGd2O2S:Tbluminescencescreen

FigureC.2:LayoutoftheexperimentalareaintheX1halltotesttheX-rayimaging
detectorwithluminescentscreenwithpolychromaticX-raysintheforwarddirectionandwith
monochromaticX-rays(6keV)under38.5◦.Forthelattertheimagingsystemismounted
onthedetectorcarriagewhichallowstheselectionoftheBraggangleandconsequentlythe
.energyyX-ra

C.2.2On-linemeasurementswithpolychromaticX-rays

Firston-lineexperimentswithX-rayswereperformedwithapolychromaticX-raybeam
inforwardgeometry,usingthe6keVfoilstackatanelectronbeamenergyof600MeV,
withtheemissionspectrumasshowninFig.3.6.Thegeometricalarrangementisshown
inFig.C.2.ToavoidabsorptionlossesofthelowenergyX-raysinair,anadditional
aluminumvacuumtubeof60mmdiameterand8mlengthwasmountedbetween
crystalspectrometerchamberandX-raydetectionsystem.Theexitwindowwasmade
ofa25µmthickpolyimidefoil.Adistanceof2miskeptfreebetweenexitwindow
anddetectionsysteminordertoeasilypositionthesamplestobeinvestigated.
Atfirst,agreenleafwaspositionedinadistancexod=1.8mfromtheluminescent
screen.TheresultingradiographisshowninFig.C.3.Althoughtheedgeenhancement
isstillvisible,theresolutionapparentlyisratherbad.Inaddition,theintensityseems
tofluctuatestronglybetweenadjacentpixels.Tofindthereasonforthisratherpoor
result,anexperimenttodeterminethespatialresolutionhasbeenperformednext.
Fig.C.4depictsameasurementofthespatialresolutionoftheimagingsystemusing
thesocallededgespreadfunction(ESF)technique.Partoftheluminescentscreenwas
coveredwithanironslitof30mmwidthand400µmthicknessandcomplexrefraction
indexparametersδ=3.958∙10−5andβ=1.0538∙10−6.Thethicknessislargeenough

136

C.2TestoftheX-rayimagingsystemandmeasurements

FigureC.3:AgreenleafradiographasrecordedwiththeimagingsystemshowninFig.C.1.
TheCCDcamerawascooleddownto-40◦C.Object-to-detectordistancexod=1.8m,source-
to-objectdistancexso=14.01m,geometricalmagnification1.13times,opticalmagnification
3.5times,electronbeamenergy600MeV,6keVfoilstack,electronbeamcurrent100nA,
s.125timeosureexp

toabsorbX-rayswithanenergyof6keVcompletely(1−exp[−(2πβR)/λ]=1).A
smalldistancebetweenslitandluminescentscreenof25mmwaschosen.Atadistance
of15.9mbetweensourceanddetectorapossibledeteriorationoftheresolutiondueto
theX-raysourcesize,whichisintheµmrange,cancompletelybeneglected.Witha
magnificationoftheopticsof3.5timestheeffectivepixelsizeis3.8µm2.
Fig.C.4(b)shows,theedgespreadfunctionobtainedwitha4µmthickofGd2O2S:Tb
luminescentscreen.Theintensityprofilewasaveragedover100neighboringrowsto
improvethestatistics.Thedatahavebeenfittedwiththefunction
f(y)=c1+c22∙1+erf(y0√−y).(C.1)
2σHeretheconstantc1correspondstothebackgroundlevelinthenon-illuminateddo-
main,andc2tothedifferenceoftheintensitiesfarfromtheedgeintheilluminated
andnon-illuminateddomain.Thespatialresolutionofthesystemisthestandard
deviationσintheargumentoftheerrorfunction.Thebestfitprocedureresultsto
σ=(19.5±0.5)µmor45.8µm(FWHM)whichisunexpectedlylargeincomparisonto
theestimationofthecontributionsfromtheeffectivepixelsizeof3.8µm2and4µm2
fromtheluminescentscreenof4µmthickness.
Tofurtherexplorethereasonforthisresult,inFig.C.5(a)thehorizontalintensity
profileofjustonehorizontalrowoftheradiographFig.C.4(a)isshown.Stronginten-
sityfluctuationsareseenontopofthesmoothintensitylevelsintheilluminatedand

137

CX-rayimagingwithaGd2O2S:Tbluminescencescreen

FigureC.4:MeasurementofthespatialresolutionoftheX-rayimagingsystemwitha4
µmthickGd2O2S:Tbluminescentscreenatamagnificationoftheopticsof3.5times.An
ironslitof1.4mmwidthwaspositionedinadistanceof25mmfromtheluminescentscreen
.(a)RadiographastakenwiththecooledCCDcamera(-40◦C)atanelectronbeamcurrent
of100nA,anexposuretimetexp=30s,X-rayspotsizeofσh=2.49µmandσv=3.8µm.
(b)Edgespreadfunction(ESF)derivedfromtherightedgeoftheslitbyaveragingover
100neighboringhorizontalrowsoftheCCDdetector.Thepointsareexperimentalresults,
thesolidlinesshowthebestfitwiththefunctionEq.(C.1).Thestandarddeviationofthe
resolutionisσ=(19.5±0.5)µm.

non-illuminateddomains.Itisjustthisnoisewhichissuspectedofhavingdeteriorated
thespatialresolutionofthesystem.Suchlargeintensity1fluctuationsdonotresult
offromthetheADCdarkis(544curren±t15)orthecountsreadwhicouthisnoisemucofhthesmallerCCDthancamera.theoffsetTheofabelectronicout6000offsetin
thenon-illuminateddomainoftheCCDcamera.Therefore,itmustbeconcludedthat
theexcessnoiseisproducedbyanexternalsource.
ItisstrahlunghighlybacprobablekgroundthatwithsucwhichahthenoisetransitionsourcehasitsradiationoriginX-rainybtheeamhighisconenergytaminated.brems-
Ifthebremsstrahlungphotonshitmatter,asthe8mlongadditionalaluminumvac-
uumtubeormaterialsoftheX-raydetectorsystem,electromagneticshowerswillbe
howevgenerated.er,theTobacfurtherkgroundlocalizedecreasedthebaconlykgroundbyafewsource,perthecent.aluminumThereafter,tubewtheasenremovtranceed,
openingintheleadshieldingoftheX-raydetectorsystemwasclosedwithanaddi-
1Theeles/pixel/s,CCDcamerai.e.atwasancoexpoledosuredowntimetotexp-40=◦30C.sThethedarknoiseiscurren3tateles/pixel.thisThetempreaderatureoutistime0.1
was(rms).1.02Thesecondstotalnpumerberframe,of9.8whicheles/pixelcorrespcorrespondstoondsanatapulseadditionalhightreadsensitivitoutynoiseofof0.366.8couneles/pixelts/eles
to3.5ADCchannelswhichareherecalledcounts.

138

C.2TestoftheX-rayimagingsystemandmeasurements

FigureC.5:HorizontalintensityprofilesalongjustonesinglerowoftheCCDcamera,(a)
ofthemarkedrowoftheradiographFig.C.4(a),and(b)ofonerowwiththeentranceholeof
theX-raydetectorsystemblockedwithanadditional10cmthickleadshielding.TheCCD
camerawascooleddownto-40◦Cinbothcases,electronbeamcurrent200nA,exposure
timetexp=30s.

tional10cmthickleadwallwhichcorrespondsto17.86radiationlengths[Tsa74].The
effectofthisshieldingisshowninFig.C.5(b).Thebackgroundleveldecreasedin
comparisontotheopendetectorsystembyaboutafactorof12,butthepulseheights
ofthespikesremainaboutthesame.Thesefeatureswillbediscussedinthefollowing.
Itseemstobereasonabletoassumethattheelectromagneticshowersareproduced
inthematerialoftheX-raydetectorsysteminfrontofandinthelenssystemitself.
ElectronsandpositronsmayproducevisibleCerenkovradiationintheglassbody
ofthelenswhichcouldbedetectedbytheCCDcamerachip.Alsoopticaltransition
radiation,producedbytheshowerelectronsorpositronsattheboundariesofthesingle
lensesofthelenssystemaswellastheflat45◦mirror,mightcontribute.Thislight
couldcontributetotheincreaseofthebackgroundlevelintheopenX-raydetection
systemincomparisontotheshieldedone.
Itremainstoexplainthelargefluctuationorspikesontopofthecontinuousbackground
level.Itseemsreasonabletoassumethattheseareproducedbyelectronsandpositrons
oftheshowerwhicharescatteredintotheCCDchipandp2enetratethe10µmthick
depletionlayer.Atanionizationenergylossof1.8keV/(mg/cm)thedepositedenergy
is4.2keVwhichcreates1150electron-holepairsinapixel,assumingameanenergyof
3.65eVforthegenerationofoneelectron-holepairinsilicon.Withthepulseheight
sensitivityof0.36counts/elesoneobtainsatotalpulseheightof414countsperelectron
passingapixel.Thelargersignalscanbeexplainedundertheassumptionthatseveral
electronspassasinglepixelduringtheexposuretime.Sincesuchdoubleormultiple
eventsremainsmallnumberstheirstatisticalfluctuationsarelarge.

139

CX-rayimagingwithaGd2O2S:Tbluminescencescreen

C.2.3On-linemeasurementswithmonochromaticX-rays

FigureC.6:(a)RadiographofdifferentpolymerstringsimagedwithmonochromaticX-
raysof6keVenergy.(b)Intensityprofilealongthewhitelineintheradiograph(a).For
theoverallgeometricalarrangementseeFig.C.2.TheX-raysourcesizewasσh=(19.1±
0.7)to-detectorµmandσvdistance=(0x.od50=±90..305)mµm,corresptheondingsource-to-obtoajectgeometricaldistancexsomagnification=4.3m,ofthe3.17obtimes.ject-
Themagnificationoftheimagingsystemwas1.8times.Theelectronbeamcurrentwas
1µAandtheexposuretime300s.Thewhitepointsobservedontheradiographresultfrom
inhighteractionsenergyofelectronsbremsstrahlungandpphotonsositronsininthetheexpCCD,erimentalcreatedarea.inelectromagneticshowersfrom

Sincethebremsstrahlungisconcentratedinforwarddirectionatanopeninganglein
theorderof1/γ=0.85mrad(for600MeVelectrons)withrespecttotheelectronbeam
direction,anobservationatmuchlargeranglesmaybefavorable.Largeobservation
anglesphotonmustenergybeofc6khosen,eVantheywayBragg,forangleexpforerimenthets(111)withplanemonocofahromaticsiliconX-rasingleys.Fcrystalora
monochromatoramountsto19.25◦andtheX-raybeamisdeflectedbyangle38.5◦,see
Fig.C.2.ThedisadvantageofthisgeometryisthelowX-rayphotonsflux.Therefore,
electrondecreasebofeamtheX-racurrenytflux.andexposuretimemustbeincreasedtocompensateforthe
Fig.strings.C.6OnshothewsaradiographradiographwhitetakenpoinwithtscanmonobechromaticrecognizedX-rawhicyshofresulteddifferentfrompbacolymerk-
currengroundtinandthetheexpthicerimenknesstalofthehallfoilwhichstaciskThestronglyCCDdepdetectorendentwonasthenotelectronshieldedbeamwith
lead.ComparingFig.C.6andFig.C.5,itcanbeconcludedthattheoffsetlevelincase
ofmonochromaticX-raysissmallerbyaboutafactorof6thantheoffsetlevelincase
inofthecasepofolycmonohromaticchromaticX-raysX-raysalthoughwasthe10exptimesosurelargertimethanandforthepolycelectronhromaticbeamX-racurrenys.t

140

ConclusionsC.3

Theverybigspikescanobviouslynotbeexplainedbyionizationlossesofelectronsand
ositrons.pTheeffectivepixelsizeoftheCCDdetectoratthemagnificationoftheopticalmicro-
scopeof1.8correspondsto7.22µm2.However,thespatialresolutionofthesystemis
obmounviouslytedinratherwrongbad.directionThereasonwithwrespasectfoundtointheanexpnominalerimenlightaltpassmistakine.whicThehitlensiswnotas
erations.abbforcorrected

ConclusionsC.3

TheexperimentsdescribedinthissectionhaveshownthattheX-rayimagingsystem
withaGd2O2S:TbluminescencescreenandaCCDcamerachipaslightsensorisnot
wellsuitedasahighspatialresolutiondetectionsysteminthetransitionradiationX-
raybeamofMAMI.Thereasonisthehighenergybremsstrahlungbackgroundwhich
isemittedsimultaneouslywiththeX-raysinthetransition2radiationfoilstack.Since
thebremsstrahlungproductioncrosssectionscaleswithZthisbackgroundcouldbe
diminishedbyemployingfoilswithloweratomicnumbersZas,e.g.,berylliumor
lithium.Inaddition,asophisticatedshieldingoftheCCDchipmayhelpaswellto
suppressthebackground.However,werefrainedfromanoptimizationofthistypeof
detectorsystemsinceitwouldrequireagreatdealofdevelopmentsandtests.

141

(5.11)Eq.ofDerivationD

ConsiderthegeometryofFig.5.27whichshowstheconnectionbetweenthestreak
bonetwtheeenthesiliconincidencrystaltraandyandtheobservcrystal’sedsurface,fluctuationsα,isonthecalculateddetectorasplane.Theangle
α=2π−2θB+θB,(D.1)
α=2π−θB.(D.2)
NowαcouldbewrittenasafunctionofBragg’sangle
cosα=cos(π−θB)=sinθB.(D.3)
2ξcosα=yc.(D.4)
ThegeometryoftheFig.5.27leadsto
xscy+dxcd=xξsc.(D.5)
BysubstitutionfromEq.(D.4)inEq.(D.5),weget,
xy+dx=ycxsinθB.(D.6)
sccdscFinallythestreak’sseparationsonthecrystalplaneisexpressedas,
yxyc=xsc+scxcd∙sindθB,(D.7)
whichisequivalenttotheEq.(5.11).

142

(D.5)

(D.6)(D.7)

Bibliography

[Aga91]B.K.Agarwal,X-RaySpectroscopy,secondedition,Berlin,Springer,1991.

[Agf90]Agfa-GevaertN.V.,IndustrielleRadiografie,B-2510Mortsil-Belgien(1990).

[Akh98]ofA.I.High-EnerAkhieser,gyN.F.ParticlesShinul’ga,CrystalsCoher,entPhEffeysicsctsinReviewsSc19attering(1998)and1.Radiation

[And96]D.A.MaidmentandM.Yaffe,Analysisofsignalpropagationinoptically
coupleddetectorsfordigitalmammography:II.Lensandfiberoptics,Phys.
475.(1996)41Biol.Med.

[AndXX]http://www.andor-tech.com/germany/products/oem.cfm

[APSXX]http://www.appscintech.com/home/index.html

[Arf98]F.Arfelli,M.Assante,V.Bonvicini,A.Bravin,G.Cantatore,E.Castelli,L.
DallaPalmaz,M.DiMichiel,R.Longox,A.Olivox,S.Panix,D.Pontoni,P.
Poropat,MPrestx,ARashevskyx,GTrombay,A.Vacchix,E.Vallazzaand
F.Zanconati,Low-dosephasecontrastx-raymedicalimaging,Phys.Med.
2845.(1998)43Biol.

[Ari94]V.AristovandA.Erko,X-raymicroscopyIV,BogorodskiiPechatnik,
1994.avkChernogolo

[Bac94]H.heimer,Backe,R.S.Zahn,GampF.ert,R.A.Buskirk,Grendel,H.H.J.Euteneuer,Hartmann,K.H.W.Kaiser,Lauth,G.Ch.WStephan,ein-
Th.emittancWalceher,855RMeVesonantelectrtronbansitioneam,rZ.Phadiationys.Ainthe349X-r(1994)ayre87.gionfromalow

[Bac96]H.Backe,K.H.Brenzinger,F.Buskirk,S.Dambach,Th.Doerk,N.
K.H.Eftekhari,Kaiser,H.O.Euteneuer,Kettig,G.F.G¨Knies,orgen,G.C.KubHerbe,W.erg,F.Lauth,HagenB.Limbuck,burg,K.J.Johann,Lind,
RH.Scadiationh¨ope,inG.theStephan,X-RayRTh.egionWalcfrher,omaTh.lowTonn,EmittancandeR.855Zahn,MeVTrEleansitionctron
BeandaminInner-ShellR.L.Johnson,Processes:H.Sc17thhmidt-B¨ocInternationalking,B.F.ConferSonnenctag,e,AIPeditors,conferenceX-Ray
proceeding389,AIPPress,Woodbury,NewYork,1997.

143

yBibliograph

[Bac98]H.Backe,privatecommunications,Institutf¨urKernphysik,Universit¨at
1998.Mainz,[Bac01]H.Backe,privatecommunications,Institutf¨urKernphysik,Universit¨at
2000.Mainz,[Bac02]H.Backe,privatecommunications,Institutf¨urKernphysik,Universit¨at
2002.Mainz,[Bac05]H.Backe,privatecommunications,Institutf¨urKernphysik,Universit¨at
2005.Mainz,[Bau86]M.W.Bautz,G.E.Berman,J.P.DotyandG.R.Ricker,ACCDX-
RayDetectorPerformanceModel.SPIEVol.688MultilayerStructuresand
LaboratoryX-RayLaserReasearch,1986.
[Bea74]J.H.Beaumont,M.Hart,MultipleBraggreflectionmonochromatorsfor
synchrotronx-radiation,J.Phys.E7(1974)823.
[Ber68]G.BertoliniandA.Coche,SemiconductorDetectors,WileyInterscience,
1986.ork,YNew[Bon65]U.BonseandM.Hart,AnX-rayInterferometer,Appl.Phys.Lett.6,(1965)
155.[Bor75]M.BornandE.Wolf,PrincipleofOptics,5thed.Pergamon,Oxford,1975.
[Boy77]W.BoyleandG.Simth,Chargecoupledsemiconductordevices,BellSystem
Tech.J.49(1970)587.
[Bus94]F.Busch,Aufl¨osungsverm¨ogeneinerMikrotomographiekameraf¨urR¨ontgen-
Synchrotronstrahlung,Ph.D.dissertation,UnverysityofDortmund,Ger-
1994.,ymanttp://www.canon.com.h[CanXX][Car77]W.H.CarterandE.Wolf,Coherenceandradiometrywithquasihomoge-
neousplanarsources,J.Opt.Soc.Am.67,(1977)785.
[Car98]C.Raven,MicroimagingandTomographywithHighEnergyCoherentSyn-
chrotronX-Rays,ShakerVerlag,1998.
[Cat89]A.Caticha,Transition-diffractedradiationandtheCerenkovemissionof
x-rays,Phys.Rev.A40(1989)4322.
[Cha97]D.Chapman,W.Thomlinson,R.E.Johnston,D.Washburn,E.Pisano,N.
Gm¨ur,Z.Zhong,R.Menk,F.ArfelliandD.Sayers,Diffractionenhanced
x-rayimaging,Phys.Med.Biol.42(1997)2015.

144

[Che74][Chi93][Col96][Com35][CxrXX][Deb88][Dia74][ElvXX]ab75][F[FilXX]ra45][F[Hab05][Hag95][Hag01]

[Har71][Har96]

yBibliograph

M.L.Cherry,G.Hartmann,D.M¨uller,T.A.PrinceTransitionradiation
fromrelativisticelectronsinperiodicradiators,Phys.Rev.D10(1974)
3594.Y.ChikauraandY.Suzuki,X-rayreconstructiontopographyforobservation
oftheorientationdistributioninasinglecrystal,J.Appl.Cryst.26(1993)
219.P.Cloetens,R.Barrett,J.Baruchel,J.GuigayandM.Schlenker,Phase
objectsinsynchrotronradiationhardx-rayimaging,J.Phys.D:Appl.Phys.
133.(1996)29A.H.Compton,S.K.Allison,X–raysintheoryandexperiment,second
edition,D.vanNostrandCompanyInc.,Princetown,NewYersey,1935.
http://www.cxro.lbl.gov/opticalconstants
K.DebertinandR.G.Helmer,Gamma-andX-RaySpectrometerywith
SemiconductorDetectors,North-Holland,1988.
J.C.DaintyandR.Shaw,ImageScience,AcademicPress,London,1974.
ttp://www.shop.elv.de.hC.W.Fabjan,W.Struczinkski,Coherentemissionoftransitionradiation
inperiodicradiators,Phys.Lett.B57(1975)483.
http://www.filmscanner.infoNikonSuperCoolscan4000ED.html.
I.M.FrankandV.L.Ginzburg,Radiationofauniformmovingelectron
duetoitstransitionfromonemediumintoanother,J.Phys.USSR9(1945)
107.D.Habs,M.Schrammet,etal.,privatecommunication,LMUM¨unchen,
2005.F.Hagenbuck,EntwurfeinesStrahlf¨uhrungssystemsundstrahloptischeMes-
sungenamElektronenstrahldesMainzerMikrotrons,Diplomarbeit,Institut
f¨urKernphysik,Universit¨atMainz,1995.
F.Hagenbuck,EntwickluneinesneuartigenbildgebendenVerfarenszur
digitalenSubtraktionsradiographiemit¨UbergangsstrahlungamMainzer
MikrotronMAMI,Dissertation,Institutf¨urKernphysik,Universit¨atMainz,
2001.M.Hart,Braggreflectionxrayoptics,Rep.Prog.Phys.,34(1971)435.
P.Hariharan,OpticalHolography,Principles,techniques,andapplication,
SecondEdition,CambridgeUniversityPress,(1996).

145

yBibliograph

[Hec89][Hen86][Hen93][Hu01][Hwu99][Gab49][Geo58][Ger72][Gia89]oXX][Go[Grz99][Gur96][Ing95][Jac83]

146

E.Hecht,Optik,zweiteAuflage,Addison–Wesley,Bonn,Paris,Reading,
1987.usetts,hMassacB.L.Henke,J.Y.Uejio,G.F.Stone,C.H.Dittmore,F.G.Fujiwara,
High-energyx-rayresponseofphotographicfilms:modelsandmeasurement,
J.Opt.Soc.Am.B.11(1986)1540.
B.L.Henke,E.M.Gullikso,J.C.Davis,X-rayinteractions:photoabsorp-
tion,scattering,transimissionandreflectionatE=50-30000eV,Z=1-93,
DataandNucl.DataTabl.54(1993)181.
Z.W.Hu,B.Lai,Y.S.Chu,Z.Cai,D.C.Mancini,B.R.Thomas,and
A.A.Chernov,PhaseSensitiveX-RayDiffractionImagingofDefectsin
BiologicalMacromolecularCrystals,Phys.Rev.Lett.87(2001)148101.
Y.Hwu,H.H.Hsieh,M.J.Lu,W.L.Tsai,H.M.Lin,W.C.Goh,B.
Lai,J.H.Je,C.K.Kim,D.Y.Noh,H.S.Youn,G.TrombaandG.
Margaritondo,Coherence-enhancedsynchrotronradiology:Refractionver-
susdiffractionmechanisms,J.App.Phys.86(8)(1999)4613.
D.Gabor,Anewmicroscopicprinciple,Nature161(1948)777.
GeorgJoos,ErwinSchopper,GrundrissderPhotographieundihrerAnwen-
dungenbesondersinderAtomphysik,AkademischeVerlagsgesellschaftM.
B.H.FrankfurtamMain1958.
R.W.GerchbergandW.O.Saxton,APracticalAlgorithmfortheDetermi-
nationofphasefromImageandDiffractionPlanePictures,Optik35(1972)
237.G.E.Giakoumakis,C.D.NomicosandP.X.Sandilos,Absoluteefficiency
ofGd2O2S:Tbscreensunderfluoroscopicconditions,Phys.Med.Biol.,34
673.(1989)(6)http://www.goodfellow.com/csp/active/gfHome.csp.
GrzegorzKowalski,MoretonMooreandStuartNailer,Applicationofx-ray
phase-contrastimagingtopolycrystallineCVDdiamond,J.Phys.D:Appl.
A166.(1999)32ys.PhT.E.Gureyev,K.A.Nugent,Phaseretrievalwiththetransport-of-intensity
equation.II.Orthogonalseriessolutionfornonuniformillumination,J.
Opt.Soc.Am.A,(1996)1670.
V.N.lngalandE.A.Beliaevskaya,X-rayplane-wavetopographyobservation
ofthephasecontrastfromanon-crystallineobject,J.Phys.DAppl.Phys.
2314.(1995)28J.D.Jackson,KlassischeElektrodynamik,zweiteAuflage,Walterde
Gruyter,Berlin,NewYork,1983.

[Jam65][Jar05][Joh95][Kan97]

yBibliograph

[Jam65]R.W.James,TheopticalPrinciplesoftheDiffractionofX-rays.Cornell
1965.Press,yersitUniv[Jar05]A.Jarre,C.Fuhse,C.Ollinger,J.Seeger,R.TucoulouandT.Salditt,Two-
DimensionalHardX-RayBeamCompressionbyCombinedFocusingand
WaveguideOptics,Phys.Rev.Lett.94,(2005)074801.
[Joh95]K.Johann,AufbaueinesMonochromatorsf¨ur33keVR¨ontgenstrahlungam
855MeVElektronenbeschleunigerMAMI,Diplomarbeit,Institutf¨urKern-
physik,Universit¨atMainz,1995.
[Kan97]I.Kandarakis,D.Cavouras,G.S.Panayiotakis,D.TriantisandC.D.
Nomicos,AnExperimentalmethodfordeterminationofspatial-frequncey-
dependentdetectivequantumefficiency(DQE)ofscintillatorsusedinX-ray
imagingdetectors,Nucl.Inst.andMeth.inPhys.Res.A,399(1997)335.
[Ket00]O.Kettig,EntwicklungundTesteinesR¨ontgeninterferometersaufderBasis
von¨Ubergangsstrahlung,Dissertation,Institutf¨urKernphysik,Universit¨at
2000.Mainz,[Koc98]A.Koch,C.Raven,P.SpanneandA.SnigirevX-rayimagingwithsubmi-
crometerresolutionemployingtransparentluminescentscreens,J.Opt.Soc.
1940.(1998)15(7)Am.[Koh97]V.Kohn,Themethodofphaseretrievalofcomplexwavefieldfromtwointen-
sitymeasurementsapplicabletohardX-ray,PhysicaScripta,56,(1997)14.
[Koh00]V.Kohn,I.SnigirevaandA.Snigirev,DirectMeasurementofTransverse
CoherenceLengthofHardXRaysfromInterferenceFringes,Phys.Rev.
2745.(2000)85Lett.[Koh01]V.Kohn,I.Snigireva,andA.Snigirev,Interferometriccharacterizationof
spatialcoherenceofhighenergysynchrotronX-rays,OpticsCommunications
293.(2001)198[Kot99]C.J.KotreandI.P.Birch,Phasecontrastenhancementofx-raymammog-
raphy:adesignstudy,Phys.Med.Biol.44(1999)2853.
[KPHXX]http://www.kph.uni-mainz.de/information/introduction/prospekt.pdf.
[Kph89]Institutf¨urKernphysik,Jahresbericht1988-1989,Universit¨atMainz,1989.
[Kph93]Institutf¨urKernphysik,Jahresbericht1992-1993,Universit¨atMainz,1993.
[Kre03]H.J.KreuzerandR.A.Pawlitzek,Digitalin-lineholography,Europhysics
(2003).34(2)News[Kun01]C.Kunz,Synchrotronradiation:thirdgenerationsources,J.Phys.:Con-
(2001).749913Matterdens.

147

yBibliograph

[Kuz99]S.Kuznetsov,I.Snigireva,A.SouvorovandA.Snigirev,NewFeaturesof
X-RayBraggDiffractionTopographywithCoherentIllumination,phys.stat.
3.(1999)172(a)sol.[Len94]B.Lengeler,Experimentaldeterminationofthedispersioncorrectionf´(E)
totheatomicscatteringfactor,inG.Materlik,C.J.Sparks,K.Fischer,
editors,Resonantanomalousx–rayscattering,ElsevierScienceB.V.,Ams-
1994.terdam,[Lew04]R.A.Lewis,Medicalphasecontrastx-rayimaging:currentstatusandfuture
prospects,Phys.Med.Biol.49(2004)3573.
[Lin97]J.Lind,AufbaueinesMonochromatorsf¨urR¨ontgenstrahlungmitgebo-
genemSilizium–Einkristall,Diplomarbeit,Institutf¨urKernphysik,Univer-
1997.Mainz,atsit¨atalog.de.ttp://www.linos-kh[LinXX][Lui05]ChenglinLiu,YuanZhang,XinyiZhang,WentaoYang,WeijunPeng,Daren
Shi,PeipingZhu,YulianTian,WanxiaHuang,X-raydiffraction-enhanced
imagingofuterineleiomyomas,MedSciMonit,11(2005)33.
[Mah95]A.Mahendrasingam,C.Martin,W.Fuller,D.J.Blundell,D.Mackerron,
R.J.Rule,R.J.Oldman,J.Liggat,C.RiekelandP.Engstr¨om,Microfocus
X-rayDiffractionofSpherulitesofPoly-3-hydroxybutyrate,J.Synchrotron
308.(1995)2rad.[May02]S.C.Mayo,P.R.Miller,S.W.Wilkins,T.J.Davis,D.Gao,T.E.Gureyev,
D.Paganin,D.J.Parry,A.PoganyandA.W.Stevenson,Quantitative
X-rayprojectionmicroscopy:phase-contrastandmulti-spectralimaging,J.
79.(2002)207:2yMicroscop[May03]S.C.Mayo,T.J.Davis,T.E.Gureyev,P.R.Miller,D.Paganin,A.Pogany,
A.W.Stevenson,S.W.Wilkins,X-rayphase-contrastmicroscopyandmi-
crotomography,Opt.Exp.11(2003)2289.
[Mcn92]I.McNulty,J.Kirz,C.Jacobsen,E.H.Anderson,M.R.HowellsandD.
P.Kern,High-ResolutionImagingbyFourierTransformX-rayhologray,
1009.(1992)256Science,[Mic93]A.G.Michette,X–raysandtheirproperties,inA.G.Michette,C.J.Buck-
ley,editors,X–rayscienceandtechnology,InsituteofPhysicsPublishing,
1993.Philadelphia,Bristol,[MirXX]http://www.data.it/support/datasheets/e2vtech/47-10back.pdf
[Mom95]A.Momose,Demonstrationofphase-contrastx-raycomputedtomography
usinganx-rayinterferometer,Nucl.Inst.andMeth.inPhys.Res.A352
622.(1995)

148

[Mom02][Mon04][Mor02]

[OlyXX]yXX][Ph[PicXX][Pin84][ProXX]d01]o[Po96][R¨y84][Ro[Rul97][Sal91]h03][Sc

[SerXX][ShvXX][SICXX]

yBibliograph

AtsushiMomose,TohoruTakeda,YujiItai,BloodVessels:Depictionat
Phase-ContrastX-rayImagingwithoutContrastAgentsintheMouseand
Rat—FeasibilityStudy,Radiology2172000)593.
D.S.Montgomery,A.Nobile,andP.J.Walsh,CharacterizationofNational
IgnititionFacilitycryogenicberylliumcapsulesusingx-rayphasecontrast
imaging,Rev.Sci.Instrum.75(2004)3986.
K.Mori,N.Sekine,H.Sato,D.Shimao,H.Shiwaku,K.Hyodo,H.
Sugiyama,M.Ando,K.Ohashi,M.KoyamaandY.Nakajima,Application
ofsynchrotronX-rayimagingtophaseobjectsinorthopedics,J.Synchrotron
143.(2002)9Rad.http://www.olympus.pl/pliki/mikroskopy/dokumenty/LMcamerasENG.pdf.
http://physics.nist.gov/PhysRefData/XrayMassCoef/ComTab/kodak.html
http://www.picotech.com/pcoscilloscope.html.
Z.G.Pinsker,Dynamicalscatteringofx-raysincrystals,Springer,Heidel-
1984.erg,bxitronic.de/ttp://www.prohS.G.Podorov1,O.Renner,O.WehrhanandE.F¨orster,Optimizedpoly-
chromaticx-rayimagingwithasymmetricallycutbentcrystals,J.Phys.D
2363.(2001)34W.K.R¨ontgen,Onanewkindofrays,Nature,53(1896)274.
RoyE.Rand,RecirculatingelectronacceleratorsHarwoodAcademicPub-
1984.ork,YNewlishers,P.Rullhusen,X.Artru,P.Dhez,NovelRadiationSourcesUsingRelativistic
Electrons,fromInfraredtoX-Rays:FromInfraredtoX-Rays,Serieson
SynchrotronRadiationTechniquesandApplications,Vol.4,1997.
B.E.A.Saleh,M.C.Teich,Fundamentalsofphotonics,NewYork,(1991).
C.G.Schroer,M.Kuhlmann,U.T.Hunger,T.F.G¨unzler,O.Kurapova,
S.Feste,F.Frehse,B.Lengeler,M.Drakopoulos,A.Somogyi,A.S.
Simionovici,A.Snigirev,I.Snigireva,C.SchugandW.H.Schr¨oder,Nanofo-
cusingparabolicrefractivex-raylenses,Appl.Phys.Letters82(2003)1485.
v/.gmca.aps.anl.gottp://sergeyhI.Shvedunve,INP/MAV,Moskow,privatecommunication,July,(2000).
ttp://www.sico.at/h

149

yBibliograph

[Sin95][Sin96][Spa99]y02][Sp[Ste03]

[Sto70][Suz02]a73][Swak98][Ter72][T[Tsa74][Tsu02]ur04][T

150

A.Snigirev,I.Snigireva,V.Kohn,S.KuznetsovandI.Schelokov,Onthe
possibilitiesofx-rayphasecontrastmicroimagingbycoherenthigh-energy
synchrotronradiation,Rev.Sci.Instrum.66(1995)5486.
A.Snigirev,I.Snigireva,V.Kohn,S.M.Kuznetsov.Ontherequirements
totheinstrumentationforthenewgenerationofthesynchrotronradiation
sources.Berylliumwindows,Nucl.Instr.andMeth.inPhys.Res.A,370
634.(1996)(2-3)P.Spanne,C.Raven,I.SnigirevaandA.Snigirev,In-lineholographyand
phase-contrastmicrotomographywithhighenergyx-rays,Phys.Med.Biol.
741.(1999)44G.Spyrou1,G.Tzanakos,G.Nikiforides1andG.Panayiotakis1,AMonte
Carlosimulationmodelofmammographicimagingwithx-raysourcesoffi-
nitedimensions,Phys.Med.Biol.47(2002)917.
A.W.Stevenson,T.E.Gureyev,D.Paganin,S.W.Wilkins,T.Weitkamp,
A.Snigirev,C.Rau,I.Snigireva,H.S.Youn,I.P.Dolbnya,W.Yun,B.
Lai,R.F.Garrett,D.J.Cookson,K.HyodoandM.Ando,Phase-contrast
X-rayimagingwithsynchrotronradiationformaterialsscienceapplications,
Nucl.Inst.andMeth.inPhys.Res.B,199(2003)427.
E.Storm,H.I.Israel,Photoncrosssectionsfrom1keVto100MeVfor
elementsZ=1toZ=100,Atom.DataandNucl.DataTabl.A7(1970)565.
Y.Suzuki,N.Ysgi,K.Uesugi,X-rayrefraction-enhancedimagingand
methodforphaseretrievalforasimpleobject,J.SynchrotronRad.9(2002)
160.R.K.Swank,Calculationofmodulationtransferfunctionofx-rayfluores-
centscreens,AppliedOptics,12(8)(1973)1865.
T.Takeda,A.Momose,E.UenoandY.Itai,Phase-contrastX-rayCTimage
ofbreasttumor,J.SynchrotronRad.5(1998)1133.
M.L.Ter–Mikaelian,High–energyelectromagneticprocessesincondensed
media,Wiley–Interscience,NewYork,London,Sydney,Toronto,1972.
Y.S.Tsai,Pairproductionandbremsstrahlungofchargedleptons,Rev.
Mod.Phys.46,815(1974).
H.Tsunemia,J.Hiragaa,E.Miyata,Applicationofafinitesizeofthecharge
cloudshapegeneratedbyanX-rayphotoninsidetheCCD,Nucl.Inst.and
Meth.inPhys.Res.A477(2002)155.
L.D.Turner,B.B.Dhal,J.P.Hayes,A.P.Mancuso,K.A.Nugent,D.
Paterson,R.E.Scholten,C.Q.Tran1andA.G.Peele,X-rayphaseimaging:
Demonstrationofextendedconditionswithhomogeneousobjects,OPTICS
2960.(2004)12EXPRESS,

ar96][V

[Wil92]

[Wil96]

[Xiz03]

[Zah94]

yBibliograph

I.A.Vartanyants,J.A.Pitney,J.L.Libbert,andI.K.Robinson,Recon-
structionofsurfacemorphologyfromcoherentx-rayreflectivity,Phys.Rev.
13193.(1997)55B

K.uellen,Wille,B.G.TPhysikeubner,derTStuttgarteilchenb1992.eschleunigerundSynchrotronstrahlungsq-

S.Phase-cW.ontrWilkins,astT.imagingE.Gureyusingpev,D.olychorGao,omaticA.PharogandyX-randays,A.NatureW.Stev(London),enson,
335.(1996)384

XizengWuandHongLiu,Clinicalimplementationofx-rayphase-
contrastimaging:Theoreticalfoundationsanddesignconsiderations,Medi-
calPhysics30,(2003)2169.

R.Zahn,Messungresonanter¨UbergangsstrahlungimR¨ontgenbereichmit
einem855MeVElektronenstrahlgeringerEmittanz,Dissertation,Institut
f¨urKernphysik,Universit¨atMainz,1994.

151

ofListFigures

152

2.1Transmissionofanelectromagneticwavethroughapieceofmatter..
2.2Theδ/βratio.Thisratioisforlowatomicnumber(Z).........
2.3Formationofarefractioncontrastradiographaccording........
2.4Schematicexperimentalsetupfortherefractioncontrastradiography.
2.5Schematicdemonstrationofin-lineholography..............
2.6Standardgeometryofrefractioncontrastandin-lineholography....
2.7Effectofpatrialcoherenceonthevisibilityoffringes...........

3.1LayoutoftheMAMIaccelerator......................
3.2EmittanceoftheMAMIelectronbeaminverticalandhorizontaldirec-
tiononenergy................................
3.3Transitionradiationproductionataninterface..............
3.4(a)Transitionradiationfromasinglefoilofthicknessl,........
13.5Thecalculatedtransitionradiationspectra................
3.6Thecalculatedtransitionradiationspectra................
3.7Calculatedbremsstrahlungcharacteristics.................

5678101213

15161718202122

4.1Coherentimagingregimesasafunctionofthedistance.........25
4.34.2Calculated(a)Calculatedintensitynormalizedpatterninfortensitaypolyprofileamidebasedstringonofthediametergeometrical...op-..27
tics.....................................29
4.44.5ScOvhematicerviewofthediagramexpshoerimenwingtalthesetupexpforerimenthetalrefractionsetupforcontrastrefractionradiographcontrasty3130
4.6X-rayspectrumrecordedbyX-rayfilmrepresent.............33
4.84.7TheSpatialmeasuredresolutionelectronofthebeamX-rayspotfilmsizesMamoraatyelectron...b..eam...energy...855...MeV..3534
4.94.10InX-ratensitybyeamprofilespotofsizetheinaradiographdistanceofsho10wnminfromFig.the4.9..X-ra..y..source...as..tak.en3636
4.11Radiographofasetofpolyamidestringofdifferentdiametersandtung-
4.12stenRadiographwires..of.a.p..oly..amide....string...with..a...diameter...of..270..µ.m.............3937
4.13Refractionenhancedradiographsofapolyamidestring.........41
4.14Refractionenhancedradiographsofapolyamidestring.........42
4.164.15RefractionComparisonbetenhancedweencalculatedradiographsconofatrastpolyamideaccordingstringtothe.w.a.ve...optics....4443

FiguresofList

4.17(a)Radiographofatungstenwirewithadiameter40µm........45
4.18Refractioncontrastradiographsofapartoftheagreenleaf......47
4.19RefractioncontrastradiographofapartofgreenleafRumexcrispus..48
4.20RefractioncontrastradiographofapartofagreenleafFicusbenjaminus49
4.21Refractioncontrastradiographofapolymerfiberbundlewirewithan
outer.....................................49

5.1Analysisofthenormalizedcontrastimage................53
5.2Schematicdiagramshowsthepositionoftheobjects...........54
5.3TheX1beamlinelayoutatMAMI.....................55
5.4Simulationofthemicro-focusedelectronbeamusingprogrambeam-optic.56
5.5Pictureofthetargetsetup..........................57
5.6Arrangementtomeasuretheelectronbeamparameters..........58
5.7Blockdiagramshowingthecontrolunitsforthemeasurement.....59
5.8Electronbeamspotsizeasmeasuredwithatungstenwire.......60
5.9Aschematicdiagramofthetargetandgoniometer............61
5.10Schematicdiagramofthemonochromatorcrystalandgoniometer...62
5.11Blockdiagramwithcontrolunitsforthemonochromatorgoniometers
anddataacquisitionoftheCCDcamera.................63
5.12SideviewofthedirectexposureCCDmountedinthebeamline....64
5.13SchematicdiagramshowingtheX-rayfilmandhighresolutionCCD..65
5.14ThequantumefficiencyforbackilluminatedBNandfrontilluminated
FIforMarconiCCD47-10chip.......................67
5.15Schemetoillustratetheoperationprincipleofachargecoupleddevice.68
5.16TriggerofelectronbeamandCCDreadout................68
5.17TheenergyspectrumrecordedbytheCCD...............69
5.18Imagingsystem...............................71
5.19Magnifiedpartfromaradiographcontainstwopolymerstringsvertically
ofdiameters.................................72
5.20Reflectingpowerratioforthe(111)reflectioninBragggeometry....73
5.21Theenergyspectrumasrecordedbycadmium..............74
5.22Tworadiographsofapolymerstringofdiameter30µm.........75
5.23ProjectionintheradiographsshownintheFig.5.22...........76
5.24FormationofthevirtualX-raysourcebysiliconcrystalinhorizontal
direction...................................77
5.25RadiographtakenwiththeCCDcamerawithoutanobject.......78
5.26StreaksasafunctionoftheX-raysenergies................79
5.27Schematicdiagramfortheintrinsicwavystructure............80
5.28Theplanemorphologyofthecrystal....................80
5.29Opticalmicroscopepictures........................81
5.30Measuredelectronbeamspotsizeinverticaldirectionwitha(4.0±
0.4)µmthicktungsten...........................83
5.31Sourcesizeminimization..........................84
5.32Fringesvisibilityasafunction.......................85
5.33BackgroundcorrectionofaradiographasrecordedbytheCCD....89

153

FiguresofList

154

5.34Normalizedcontrastimages........................90
5.35Normalizedcontrasthologramsoftwotungstenwires...........91
5.36Diffractioncontrastoftungstenwireswithdifferentdiameters......92
5.37Thediffractioncontrastofatungstenwireofdiameter4µm.......93
5.38(a)Radiographofapolymerstringwithadiameterof350µmand(b)94
5.39Radiographsofapolymerstringatdifferentdistances..........95
5.40NormalizedintensityprofilesoftheradiographsshowninFig.5.39...96
5.41Abackgroundcorrectedradiographofapolymerstringof(150±20)µm97
5.42Backgroundcorrectedradiographs(contrastimages)oftwodifferenthu-
manhairs(a)and(b)............................98
5.43Radiographsofpolymerstringofdiameter450µm...........99
5.44CharacteristiccurveofX-rayfilmStructurixD3..............101
5.45Differentsectorsofaradiograph(left)andprojections..........102
5.46Differentsectorsofaradiograph(left)andprojections(right)ofatung-
stenwireof.................................103
5.47Spatialresolutionoftheopticalmicroscope................104
5.48SpatialresolutionofthedirectexposureD3StructurixD3.......105
5.49Radiographofapolyamidestringofdiameter(150±20)µm......107
5.50(a)Radiographofapolyamidestringofadiameterof(150±20)µm..108
5.51Radiographofapolyamidestringof(150±20)µmdiameter......109
5.52Radiographsoftwodifferentpolyamidestrings.............110
5.53Radiographsofthepolyamidestringof30µmdiameteratdifferent
positions...................................112
5.54Radiographofahumanhairofdiameter75µm.............113
5.55Radiographofatungstenwireof(40±4)µmdiameter..........114
5.56(a)Radiographofatungstenwirewithadiameterof(4.0±0.4)µm..117
5.57RadiographsNickelgrid..........................118
6.1DemagnifyingcrystalopticstoproduceananofocusatMAMI.....120
A.1Refractionofx-raysbyacylindricalstringofradiusR.........121
A.2Simulatedintensityprofileofapolymerwirebasedonthegeometricoptic124
B.1(a)Refractionenhancedradiographofapolymerstring.........130
B.2(a)Refractionenhancedradiographofapolymerstring.........131
B.3(a)Refractionenhancedradiographofapolymerstring.........132
B.4Comparisonbetweencalculatedcontrastaccordingtothewaveoptic..133
C.1Imagingsystem...............................135
C.2LayoutoftheexperimentalareaintheX1hall..............136
C.3Greenleafradiograph............................137
C.4Measurementofthespatialtheresolution................138
C.5IntensityprofilealongarowintheCCDcamera.............139
C.6Radiographofpolymerstrings.......................140

ablesTofList

3.1

4.1

5.15.25.35.45.5

Parametersofbothfoil-stacksusedinthiswork..............

ComparisonofthemeasuredcontrastCrefwithcalculationsonthebasis
ofthegeometricalmodelC........................
g

ANDORDO434BNCCDdetectorcharacterization[AndXX]......
Braggangles,estimatedperiodsatthedetectorplane,periodofthe
surfacefluctuationsonthecrystal,andbendingradii..........
Experimentalparametersofphasecontrast................
Beamtimes.................................
Sizesoftheimagedobjects.........................

19

46

6681868788

155