SYNCHROTRON X-RAY QUASI-FAR-FIELD IMAGING ON LUMINESCENT LITHIUM FLUORIDE DETECTORS

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1 ENRI CO NI CHELATTI D pa r t ment ofus oneet e nol og eperl as ur ez z anu l ea r e D v s onet e nol og ef s heperl as ur ez z ael asal ut e Labor at or om r oenanos t r ut t ur eperl afot on a Cent r or er hecas a a,roma F.BONFI GLI,M. A.VI NCENTI,R. M.MONTEREALI D pa r t ment ofus oneet e nol og eperl as ur ez z anu l ea r e D v s onet e nol og ef s heperl as ur ez z ael asal ut e Labor at or om r oenanos t r ut t ur eperl afot on a Cent r or er hefr as at,roma FABRI ZI A SOMMA D par t ment ods enz e Un v er s t àromat r e,roma ANGELI CA CECI LI A,TI LO BAUMBACH Sy n hr ot r onrad at onfa l t yanka Kar l s r uhei ns t t ut eoft e hnol ogy( KI T),Ger many SYNCHROTRON XRAYQUASI FARFI ELD I MAGI NG ON LUMI NESCENTLI THI UM FLUORI DEDETECTORS RT/ 216/ 8/ ENEA I T ALI AN NATI ONALAGENCYFORNEW TECHNOLOGI ES, ENERGYANDSUST AI NABLEECONOMI CDEVELOPMENT

2 ENRICO NICHELATTI Dpartmento Fusone e Tenologe per la Surezza Nuleare Dvsone Tenologe Fshe per la Surezza e la Salute Laboratoro Mro e Nanostrutture per la Fotona Centro Rerhe Casaa, Roma F. BONFIGLI, M.A. VINCENTI, R.M. MONTEREALI Dpartmento Fusone e Tenologe per la Surezza Nuleare Dvsone Tenologe Fshe per la Surezza e la Salute Laboratoro Mro e Nanostrutture per la Fotona Centro Rerhe Frasat, Roma FABRIZIA SOMMA Dpartmento d Senze Unverstà Roma Tre, Roma ANGELICA CECILIA, TILO BAUMBACH Synhrotron Radaton Falty ANKA Karlsruhe Insttute of Tehnology (KIT), Germany SYNCHROTRON X-RAY QUASI-FAR-FIELD IMAGING ON LUMINESCENT LITHIUM FLUORIDE DETECTORS RT/216/8/ENEA ITALIAN NATIONAL AGENCY FOR NEW TECHNOLOGIES, ENERGY AND SUSTAINABLE ECONOMIC DEVELOPMENT

3 I rapport ten sono sarabl n formato pdf dal sto web ENEA alla pagna I ontenut teno-sentf de rapport ten dell ENEA rspehano l opnone degl autor e non neessaramente quella dell Agenza The tehnal and sentf ontents of these reports express the opnon of the authors but not neessarly the opnon of ENEA.

4 SYNCHROTRON X-RAY QUASI-FAR-FIELD IMAGING ON LUMINESCENT LITHIUM FLUORIDE DETECTORS Enro Nhelatt, F. Bonfgl, M.A. Vnent, R.M. Montereal, F. Somma, A. Cela, T. Baumbah Abstrat Radaton magng detetors based on lumnesent olour entres (CC s) n lthum fluorde (LF) have been reently demonstrated to be relable, effent, and wth hgh spatal resoluton aross a large area. In ths tehnal report, LF rystals and flms are tested as detetors for poly-energet X-ray quas-far-feld magng. The ntensty and phase detals of a test pattern are stored as a spatal dstrbuton of CC s n a LF detetor plate; ths nformaton an be later reovered by extng the plate wth blue lght and reordng the obtaned photolumnesene (PL) mage at an optal mrosope. A theoretal model s put forward for the nteraton between X-rays and test pattern, and for the formaton of CC s n LF under X-rradaton. Detals of alulated PL ntensty maps are fnally ompared wth expermentally obtaned ones. Keywords: X-ray magng, olour entres, photolumnesene, lthum fluorde, radaton detetors Rassunto Reentemente è stato dmostrato quanto rvelator per magng a radazone basat su entr d olore (CC) lumnesent nel fluoruro d lto (LF) sano affdabl, effent, e on alta rsoluzone spazale su grande area. In questo rapporto teno, s verfa la bontà d rstall e flm d LF ome rvelator per l magng n ampo quas lontano d ragg X polenerget. Le nformazon d ntenstà e d fase d un test pattern vengono regstrate, sotto forma d dstrbuzone spazale d CC, n un rvelatore a lastra d LF; tal nformazon sono n seguto reuperabl etando la lastra on lue blu e fotografando l mmagne d fotolumnesenza (FL) n un mrosopo otto. S è svluppato un modello teoro per desrvere l nterazone de ragg X ol test pattern e la formazone nel LF d CC a ausa d rraggamento X. Infne, sono mess a onfronto alun dettagl delle mappe d FL alolate e spermental. Parole have: Imagng a ragg x, entr d olore, fotolumnesenza, fluoruro d lto, rvelator d radazone

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6 INDEX 1. Introduton 2. Colour-entre formaton by X-rradaton 2.1 Spetral absorpton profle 2.2. Total absorpton profle 2.3 Rate of deposted-energy densty Absorbed dose 2.4 Colour-entre densty and photolumnesene 3. X-ray quas-far-feld magng: model and experment 3.1 Interaton wth the test pattern and propagaton to the LF detetor 3.2 Soure-sze orreton 3.3 Best ft of the photolumnesene profle 3.4 Dsusson 4. Conluson Referenes

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8 1 Introduton Insulatng materals ontanng pont defets [1] an be suessfully utlsed as radaton detetors [2]. Colour entres (CC s) [3] n lthum fluorde (LF) are known for ther applaton n dosmeters [4], mnatursed lght-emttng deves [5], and tuneable sold-state lasers [6]. Some of these CC s are optally atve and stable at room temperature, wth broad absorpton and emsson bands n the vsble spetral range [7]. Aggregate F 2 and F + 3 entres, onsstng of two eletrons bound to two and three lose anon vaanes, respetvely, emt n the red (F 2 ) and green (F + 3 ) parts of the spetrum and have almost overlappng absorpton bands (M band) peaked at the wavelength of 45 nm [7]. For ths reason, F 2 and F + 3 entres an be smultaneously exted wth a sngle-wavelength optal pump n the blue. Due to ther hgh-penetraton propertes, X-rays are wdely used to analyse the nternal struture of objets and bologal samples. Absorpton ontrast s the most ntutve and ommon tehnque utlsed to reord radographes of samples, when these present detals whose absorpton propertes are learly dstngushable at the operatng X-ray wavelengths. However, for hgh-energy X-rays, the absorpton oeffent of most materals s very small and low-atom-number samples, suh as bologal ones, behave as phase objets. In suh ases, the lak of absorpton ontrast an be ompensated by addng phase nformaton to the reorded mage [8]. A possble approah s n-lne phase-ontrast magng [8, 9]. Hgh-resoluton X-ray magng an be aomplshed wth a varety of methods [1]; all of them are lmted by the resoluton and/or the dynam range of the detetors. However, novel sold-state LF radaton detetors, based on the materal radaton-senstvty and optal readout of photolumnesene (PL) from F 2 and F + 3 CC s, an overome the above-mentoned lmtatons so that they are sutable for the haratersaton of mro and nanostrutures as well as bologal samples. Ther hgh spatal resoluton aross a large feld of vew, wde dynam range, and versatlty make them very attratve and promsng as reordng plates for X-ray absorpton-ontrast [11 14] and phase-ontrast [15] magng. Sutableness of LF, ether n bulk or thn flm form, as magng detetor for poly-energet X- rays was reently tested at the ANKA lght soure of the KIT synhrotron falty n Karlsruhe, Germany [15]. The test onssted of transmttng the poly-energet (6 6 kev) X-ray ollmated beam through a test pattern, and exposng a LF detetor, plaed n the far feld, to the transmtted beam. Optally-atve CC s are reated, n ths way, wthn a superfal layer of LF, whose depth dstrbuton depends on the energet spetrum of the X-rays, and wth a transversal dstrbuton that reprodues the dffrated shadow of the test pattern. Wthout any further treatment or speal handlng, the stored CC dstrbuton an be onvenently deteted and aqured as a b-dmensonal map of vsble PL n a fluoresene mrosope, by llumnatng the exposed LF sample wth blue lght n order to optally pump F 2 and F + 3 CC s. A areful omparson of the obtaned CC lumnesene maps wth those generated by smulatng the rradaton and readout proesses suggests, for the onsdered doses, that an approxmately lnear dependene of the CC volume densty on the deposted energy s not ompletely sutable, and that some sort of saturaton effet has to be taken nto aount. Ths tehnal report s organsed as follows. In se. 2, the theory of photon absorpton n a sold s brefly realled, and s appled to evaluate the energy deposted nto a sold by a beam of poly-energet X-rays. Equatons are ntrodued (se. 2.4) for the estmaton of the volume densty of CC s that are reated n LF as a onsequene of X-rradaton; saturaton effets at 7

9 x X-rays O sold materal z y Fgure 1. Sheme of the Cartesan oordnate system used for the model. The orgn O s plaed on the flat external surfae of the sold materal. The z-axs ponts towards the nteror of the materal. The X-rays mpnge normally onto the materal surfae from the negatve-z half-spae. hgh rradaton doses are taken nto aount n an elementary way. Then, a smple relatonshp s tentatvely assumed for the ntensty of PL radated by optally-pumped CC s. In se. 3, the nteraton of the X-ray wavefront wth a test pattern and ts subsequent free-spae propagaton to a LF detetor are dealt wth; the opportunty to use ether a sngle-step transmsson funton or a beam-propagaton-method algorthm s dsussed. A proper orreton s appled to the beam ntensty mpngng on the detetor plane to aount for the fnte sze of the X-ray soure, wth an estmaton of the atual soure sze; the energy deposted nsde the detetor and the ntensty of PL from CC s theren generated are then alulated. Seton 3.3 s dedated to omparng expermental PL measurements wth orrespondng model expetatons, both for a LF rystal and a flm over glass substrate. 2 Colour-entre formaton by X-rradaton Irradaton of LF wth an X-ray beam generates CC s as a onsequene of the energy that X-rays depost n the materal. In a frst approxmaton, for doses well below saturaton, one an assume the densty of generated CC s to be loally proportonal to the densty of the deposted energy, whh n turn depends on the ntensty of X-rays at the onsdered poston and on the rradaton tme. The loal rate ε of deposted-energy densty an be evaluated by usng the lassal laws of absorpton for photons rossng a materal. Here, the spatal dstrbuton of ε s estmated for a plane-parallel beam of X-rays normally mpngng of the flat surfae of a sold materal. Assumng the materal to be homogeneous, let us dentfy a poston nsde t by the depth oordnate z, whh s set to z = at the materal surfae and nreases nsde the materal see fg. 1 for a sheme of the rradaton setup and the oordnate referene system. The z-axs s perpendular to the surfae and ts postve dreton ponts nsde the materal. The rate of deposted-energy densty vs. the poston (x, y, z) wth z s the quantty beng looked for. 8

10 2.1 Spetral absorpton profle For the majorty of materals, refleton of a beam of X-rays that mpnges normally onto ther surfae s extremely low and an be safely negleted. 1 Therefore, the ntensty transmttane of a photon of energy E through a spae nterval of thkness z s gven by the well known Lambert- Beer s law [17], T (E, z) = exp [ α(e)z], (2.1) where α(e) s the materal absorpton oeffent at the photon energy. The ntensty absorbane of the same spae nterval of thkness z s A(E, z) = 1 T (E, z) = 1 exp [ α(e)z]. (2.2) An mpngng photon s absorbed wthn the nfntesmal spatal range [z, z + dz], after rossng the fnte spatal range [, z], wth probablty p(e, z) dz = T (E, z)a(e, dz). (2.3) The prevous equatons allow alulatng the lnear densty of probablty that a photon of energy E s absorbed exatly at the depth z, that s, only after t has rossed the above-standng [, z] layer of materal. The lnear densty of probablty s p(e, z) = α(e) exp [ α(e)z]. (2.4) Ths quantty s also defned as the spetral absorpton profle of mono-energet photons n the materal. One an easly verfy that, exludng the trval ase α(e) =, + p(e, z) dz = 1 (2.5) holds true, suggestng that an mpngng photon s gong to be ertanly absorbed wthn a materal of nfnte extenson. 2.2 Total absorpton profle Now, let us onsder an mpngng poly-energet X-ray beam. In order to ount all the photons that get absorbed at the depth z, one should ntegrate eq. (2.4) over E, provded a sutable weght fator, orrespondng to the spetral energy dstrbuton of the beam, s appled. The result, let us name t P (z), an be defned as the total absorpton profle of photons and wll depend on z only. Let us assume that the spetral flux Φ X (E) of the mpngng beam s known, where Φ X (E) de s the number of photons of energy between E and E +de that ross the unt surfae per unt tme. For the moment, the flux s assumed to be homogeneous over the plane (x, y). The total flux s the energy ntegral of Φ X (E), that s Φ XTOT = Φ X (E) de. (2.6) 1 For nstane, n ase the materal s LF, normally mpngng X-rays of energes larger than 6 kev (see se. 3) have a refleton oeffent R < 1 11 [16]. 9

11 As one mght expet, Φ(E)/Φ XTOT represents the weght needed to alulate P (z). It ensues P (z) = 1 Φ XTOT p(e, z)φ X (E) de. (2.7) P (z) dz s the fraton of photons of whatever energy that are absorbed between z and z + dz after rossng the spatal range [, z]. The total absorpton probablty s + P (z) dz = 1, (2.8) whh s the normalsaton ondton that any probablty densty dstrbuton must obey; ts meanng s that photons are gong to be sooner or later absorbed whle propagatng nsde an nfntely extended materal. In ase the X-rays are mono-energet, the above eq. (2.7) holds stll good, provded the normalsed flux Φ X (E)/Φ XTOT s replaed by a Dra-delta dstrbuton entred around the photon energy. 2.3 Rate of deposted-energy densty The spetral ntensty of the X-ray beam an be defned as I X (E) = Φ X (E)E. (2.9) The quantty I X (E) de represents the energy fraton, per unt tme and rossed surfae, arred by photons havng energes between E and E +de. Here, ths quantty s evaluated at the materal surfae z =, that s, just before rossng t (see fg. 1). It follows that the total ntensty of the mpngng beam s I XTOT = I X (E) de. (2.1) As one an verfy from the prevous results, p(e, z) Φ X (E) de dx dy dz s the number of photons of energes between E and E + de that, per unt tme, are absorbed wthn an nfntesmal ube dx dy dz at the depth z wthn the materal, after rossng the above-standng materal layer [, z]. Therefore, p(e, z) I X (E) de dx dy dz s the energy deposted per unt tme n the nfntesmal ube by those photons whose energes are n the range [E, E + de]. It follows that the energy densty that s deposted per unt tme (rate of deposted-energy densty), ε, at the depth z s the above quantty dvded by the ube volume dx dy dz and ntegrated along E, that s ε(z) = p(e, z)i X (E) de = α(e) exp [ α(e)z] I X (E) de. (2.11) For the sake of smplty and n vew of the applatons n the followng of the present work, the ntensty I X (E) s assumed to be tme-nvarant therefore, also ε(z) s tme-nvarant. For mono-energet X-rays of energy E and ntensty I X, 2 the prevous equaton smplfes to ε(z) = α exp ( αz) I X. (2.12) 2 Rgorously speakng, suh a mono-energet beam possesses a Dra-delta dstrbuted spetral ntensty equal to I X δ(e E), therefore the total ntensty s I XTOT = I X δ(e E) de = I X. However, for smplty, the word ntensty wll be used n ths ase wthout the adjetve spetral or total, unless t s neessary to expltly make suh a dstnton. 1

12 spetral ntensty (1 19 m 2 s 1 ) ANKA synhrotron TOPO TOMO beamlne photon energy (kev) Fgure 2. Spetral ntensty of the TOPO-TOMO beamlne at the ANKA lght soure (Insttute for Synhrotron Radaton, Karlsruhe Insttute of Tehnology KIT, Germany), as transmtted through a 5 µm thk Be-wndow, normalsed aordng to ref. [15]. Note that the ordnate unts nlude no energy unts, beause the spetral ntensty I X (E) s defned n suh a way that atually I X (E) de s the amount of energy, per unt tme and rossed surfae, arred by photons of energy between E and E + de see eqs. (2.9) and (2.1). It an be verfed that + ε(z) dz = I XTOT, (2.13) n agreement wth energy onservaton, both for the poly-energet and the mono-energet ase. 3 Fnally, f t s the rradaton tme, the deposted-energy densty profle at z s smply ε(z) = ε(z) t. (2.14) Absorbed dose Reallng that the absorbed dose, D, s the energy absorbed per unt mass [18], one easly reognses that D must be proportonal to ε. Indeed, aordng to ts defnton, D an be alulated by dvdng ε by the mass densty ρ whh an be a poston-dependent quantty, n ase the materal s non-homogeneous 4 of the rradated materal, D(z) = ε(z) ρ(z). (2.15) 3 See note 2. 4 However, n suh a ase, also the absorpton oeffent of the materal s lkely to be spatally dependent, so that the expresson of ε n eq. (2.11) should be orreted aordngly. 11

13 Let us onsder the whte that s, poly-energet X-ray beam of the TOPO-TOMO beamlne at the ANKA lght soure (Insttute for Synhrotron Radaton, Karlsruhe Insttute of Tehnology KIT, Germany), on whh our attenton wll be foused agan later n ths work. The nomnal beam-flux value at sample poston s 1 16 ph/s aross an area of 1 m 2 [19]. For the setup that s onsdered n se. 3, whh nludes photon propagaton n ar and transmsson through a 5 µm thk Be wndow, the beam-flux s lowered to ph s 1 m 2 [15]. Usng the spetral dstrbuton of the transmtted beam at sample poston [15], shown n fg. 2, and the optal onstants of LF [16], one an estmate the absorbed dose n LF (ρ = g/m 3 ) per unt tme along z by means of eqs. (2.11), (2.14) and (2.15). The theoretal absorbed dose of a LF sample plaed at the sample poston of the beam s shown n fg. 3. It features a quasexponental-deay behavour along z an atual exponental-deay urve 5 s shown n the same fgure for omparson and an be useful to estmate not only the z-dependene of the absorbed dose, but also ts amount (normalsed to the flux), whh s proportonal to the rradaton tme. 1.8 absorbed dose rate (1 4 Gy/s) LF TOPO TOMO (ANKA) whte beam exponental deay penetraton depth z (mm) Fgure 3. Estmated absorbed dose per unt tme n LF vs. penetraton depth (z axs, see fg. 1). The evaluaton has been made by usng the flux value ph/s, aross an area of 1 m 2 [15], of the whtebeam TOPO-TOMO lne of the ANKA lght soure (Insttute for Synhrotron Radaton, Karlsruhe Insttute of Tehnology KIT, Germany), and the spetral ntensty dstrbuton shown n fg. 2. An exponental-deay urve see note 5 s also shown for omparson. It should be ponted out that tabulated data of LF optal onstants we have aess to are avalable only up to 3 kev [16], a value lower than the upper lmt ( 6 kev) of the beam energy dstrbuton shown n fg. 2, so that the numeral ntegraton needed to alulate ε(z), see eq. (2.11), had to be trunated at that value. For ths reason, one s legtmated to wonder whether the absorbed dose plotted n fg. 3 s underestmated. Ths s atually true, but the underestmaton s lkely to be almost neglgble for depth values up to z 2 µm. Let us see why. The attenuaton 5 The exponental funton, whose parameters are hosen to make t follow as muh as possble the absorbed dose rate urve wthn the absssa range, s exp( z/.5). 12

14 LF attenuaton length (mm) photon energy (kev) Fgure 4. Attenuaton length of X-rays n LF aordng to the tabulated optal onstants avalable n [16]. length n LF nreases about lnearly wth photon energy for E 2 kev, see fg. 4, and ts trend suggests that t ould keep nreasng also at energes greater than 3 kev. If that s true, the probablty 2 µm p(e, z) dz for a photon of energy E > 3 kev to be absorbed and hene depost ts energy wthn the frst 2 µm of materal s rather small, less than.17, as one an verfy. Consderng also that the porton E > 3 kev of the spetrum n fg. 2 represents just a tal of the whole dstrbuton, we are qute onfdent to assume the dose plot n fg. 3 to be aurate enough for our purposes, at least wthn the depth nterval z 2 µm. 2.4 Colour-entre densty and photolumnesene In a tentatve lnear-model approah, the volume densty of CC s generated by onsng radaton ould be thought to be proportonal to the amount of deposted-energy densty ε. Ths ould be approxmately true, ndeed, for doses that are not too hgh. However, our frst attempts to replate the expermental data of se. 3 wth suh a lnear model gave results that were not ompletely satsfyng, thus suggestng the need for a more refned model to relate deposted-energy and CC densty. Obvously, the densty of CC s annot grow ndefntely, therefore saturaton should our above a ertan dose threshold. If a sutable saturaton mehansm s nluded n the model so that the expermental data of se. 3 are satsfatorly reprodued, t s hghly probable that those data orrespond to doses lose or above the threshold separatng lnearty from saturaton. The smplest upgrade from the lnear-model approah onssts of negletng partular reombnaton mehansms n the defet formaton proess that are responsble for nonlneartes [2 22] and adoptng the elementary dfferental equaton, ntrodued by Soshea and o-workers to desrbe the formaton of CC s n MgO [23], where the possblty s nluded that onsng radaton 13

15 an medate, besdes reaton, also annhlaton of CC s, dn dt = β ε γ εn. (2.16) Here, N s the volume densty of CC s of a ertan knd, whle β and γ are two parameters of sutable dmensons, assumed to be both tme-nvarant and energy-nvarant, whh regulate defet reaton and annhlaton, respetvely. Assumng null zero-tme entre densty, N() =, and reallng that ε εt, the soluton to ths dfferental equaton gves the smplest, yet saturatonwse, relatonshp between CC densty and deposted-energy densty, N = N max [1 exp ( γ εt)] N max [1 exp ( γε)], (2.17) wth N max β/γ. Note how, as expeted, an elementary lnear dependene N βε s reovered for values of the deposted-energy densty so small that γε 1. Beause, as explaned n se. 2.3, the deposted-energy densty ε s a funton of depth z nsde LF, also the denstes of F 2 and F + 3 CC s should depend on z. Assumng the ntensty of the optal pump, utlsed to exte the CC s, to be well below saturaton, the PL amount that an be extrated from X-rradated LF should be proportonal to the total number of entres wthn the optally pumped volume. 6 Consderng the PL emtted by aggregate CC s that are loated wthn a ertan surfae layer z Z of LF, one an expet the PL ntensty due to eah knd of them to be I PL = Z q(z)n(z) dz, (2.18) where q(z) s a sutably dmensoned funton that aounts for the pump haratersts and the quantum effeny of the proess, plus other possble nhomogenetes along z. Under the smplfyng ondton that q(z) an be approxmated wth ts average n z Z, q(z) q, and by substtutng eq. (2.17) nto eq. (2.18), one fnds I PL = qn max {Z Z } exp [ γ ε(z)t] dz. (2.19) Ths s the expresson for the PL ntensty we are gong to use n se. 3 to ompare expermental results wth theory, wth ε(z) gven by eq. (2.11). 3 X-ray quas-far-feld magng: model and experment As an applaton of the theoretal model ntrodued n se. 2, the reproduton of two expermental PL profles s here addressed. These profles were measured at a onfoal mrosope operated n fluoresene mode by llumnatng wth blue lght the dffraton mages of a test pattern reorded, respetvely, on a LF rystal and a flm as loal dstrbutons of CC s. The rystal thkness was 1 mm, whle the flm was grown on a glass substrate by thermal evaporaton (1 4 Pa vauum pressure) at the ENEA laboratores of Frasat [15, 24] ts thkness amounted to 1 µm. 6 In ase the pump ntensty s not onstant along z, a sutable weghtng funton has to be ntrodued. 14

16 x X-ray soure test pattern z mpngng beam Be-wndow dffrated beam y LF detetor 29 m 17.5 m Fgure 5. Smplfed sheme of the rradaton setup n the quas-far-feld X-ray magng experment on LF detetor at the TOPO-TOMO beamlne of the ANKA lght soure (Insttute for Synhrotron Radaton, Karlsruhe Insttute of Tehnology KIT, Germany). Fgure 6. Features of the Xrada X5-2-3 (Xrada, Pleasanton, CA, USA) test pattern that was utlsed n the quas-far-feld X-ray magng experment on LF at the TOPO-TOMO beamlne of the ANKA lght soure (Insttute for Synhrotron Radaton, Karlsruhe Insttute of Tehnology KIT, Germany). 15

17 1 m Fgure 7. Partular of the PL map read from the X-ray-exposed LF flm [15]. The whte lne ndates the path along whh the PL profle Anka3 was sanned for further analyss. The LF rystal and flm were used as detetors for a quas-far-feld magng experment performed at the TOPO-TOMO beamlne of the ANKA lght soure (Insttute for Synhrotron Radaton, Karlsruhe Insttute of Tehnology KIT, Germany) [15]. An Xrada X5-2-3 (Xrada, Pleasanton, CA, USA) test pattern was plaed aross the poly-energet X-ray beam after ths latter had been transmtted through a 5 µm thk polshed Be-wndow (6 kev to about 6 kev, see fg. 2) and then through the test pattern, see fgs. 5 and 6. The presene of the Be-wndow between the lght soure and the test pattern was properly taken nto aount; t exerted an attenuaton of beam so that the photon flux that mpnged onto the test pattern was estmated to be ph s 1 m 2. The LF rystal and flm were exposed for t = 3 s, under dental ondtons, to the dffrated X-ray beam at a dstane of 17.5 m from the test pattern. In ths way they were exposed to the X-ray dffrated mage of the test pattern, n whh the ntensty and phase pees of nformaton of the latter were embedded [25]. Two PL ntensty profles were measured wth a onfoal mrosope (Nkon Elpse 8-C1) operatng n fluoresene mode: one profle was measured on the exposed LF rystal (sample name: Anka2), the other one on the exposed LF flm on glass substrate (sample name: Anka3). The onfoal mrosope utlses a blue-lght (457.9 nm ontnuous-wave argon laser) optal pump to exte the optally atve CC s n the examned sample, and detets the spetrally-ntegrated radated PL as a b-dmensonal mage that s reorded by a CCD amera [15]. If needed, optal flters an provde a separaton of the red and green parts of the spetrum n the deteton proess. Later, the dgtsed mage s sanned along the desred dreton to get a mono-dmensonal ntensty profle. The examned PL profles are sans of the test-pattern dffrated mages that were reorded as loal onentratons of CC s on the LF detetors. The path of one of the profles the one orrespondng to the LF flm sanned perpendularly to a detal of the test pattern onsstng of a tny ral formng the larger pattern grd, s shown n fg. 7. In ths way, expermental PL ntensty profles were aqured along a ommon sannng dreton (the x-axs, to fx deas). They are beng ompared n the followng to ther theoretally estmated ounterparts. 16

18 X-rays 2.5 m Au 3 m 33 nm S N 3 4 Fgure 8. Cross-seton of the test-pattern detal that was onsdered for the smulatons: a mrosop gold ral plaed over a S 3 N 4 plate. See the text for further detals. 3.1 Interaton wth the test pattern and propagaton to the LF detetor The detal of the test pattern that s overed n the sanned profles onssts of a mrosop gold ral, h Au = 3 µm hgh and 2w Au = 2.5 µm wde, plaed over a S 3 N 4 plate of thkness 33 nm, see fg. 8. To avod the unrealst perfetly sharp orners of a retangle that ould spol the X-ray dffraton numeral evaluaton, the transverse seton of the ral (plane Oxz) was smulated wth a super-gaussan urve, h Au exp [ ( x /w Au ) n SG ], wth super-gaussanty order n SG = 1 4. As shown n fg. 5, the X-rays mpnge along the z-axs onto the struture, are transmtted through t, then propagate for 17.5 m untl they reah the LF detetor, whh les over the Oxy plane. The followng smulatons assume, for the sake of smplty, dffraton along the x-axs only (twodmensonal approxmaton), and nfnte extenson of the ral along the y-dreton. The mpngng radaton s supposed to be a poly-energet plane-wave wth wavevetor parallel to z, and energy dstrbuton as spefed n ref. [15] and shown n fg. 2. The optal onstants of the materals at the X-ray energes are those reported n the webpage of the Centre for X-ray Opts of the Berkeley Laboratores [16]. At the onsdered energes, the gold ral thkness orresponds to a large number of X-ray wavelengths, whh span the range Å. 7 For ths reason, transmsson of the X-ray wavefront through the gold ral and the S 3 N 4 plate along z was alulated n two ways: (a) by smply multplyng the mpngng wavefunton by a global ampltude-transmttane funton, and (b) by utlsng the mproved beam propagaton method (IBPM) [27] to more rgorously address the wavefront transmsson problem. The results of the two methods were later ompared: the former approah, 7 Use of the term quas-far-feld s due to the dmensons nvolved n the experment. Far-feld nomnally orresponds to a dstane that an be onsdered muh larger than the Fraunhofer dstane. Beause the Fraunhofer dstane s defned as d F a 2 /λ [26], where a s the lateral sze of the detal beng dffrated (lassally, a slt wdth), one an verfy that, for the onsdered sample (a 2w Au = 2.5 µm) and poly-energet beam (.4 Å λ 12.4 Å), the Fraunhofer dstane spans the range.5 m d F 15.5 m aordng to the onsdered wavelength. Therefore, the free-spae propagaton dstane of 17.5 m an mean far-feld for some wavelengths of the beam, near-feld for some others. It s, however, not fully far-feld for the 12 kev spetral-ntensty peak (see fg. 2), to whh the Fraunhofer dstane d F 6.1 m orresponds. 17

19 smpler and less lengthy, resulted to be aurate enough to alulate the wavefront transmtted by the struture. Fnally, free-spae propagaton of the X-ray wavefront from the test pattern ext plane to the LF detetor surfae was evaluated n the Fourer spae [28, 29] by usng the Fast Fourer Transform (FFT) lbrares of MATLAB [3], n whose envronment all the smulatons reported n ths work were performed. 3.2 Soure-sze orreton The Xrada X5-2-3 (Xrada, Pleasanton, CA, USA) test pattern was dstant z 1 = 29 m from the soure of the TOPO-TOMO beamlne (see fg. 5). After passng through the test pattern, the X-ray beam propagated for other z 2 = 17.5 m before reahng the LF detetor. Beause the sze of the soure s non-zero, the transversal oherene of the beam s not nfnte [31, 32]. For ths reason, the ntensty I X of the X-ray beam at the LF surfae (z = ), needed to alulate the rate of deposted-energy densty nsde the detetor materal see eqs. (2.9) and (2.11) has to be sutably orreted. A way to aheve the orreted ntensty onssts of a two-step proess: frst, X-ray propagaton from the soure up to the LF detetor, passng through the test pattern, s alulated by temporarly assumng full transversal oherene; then, the resultng fully-oherent ntensty on the LF surfae s onvoluted wth a properly saled verson of the soure dstrbuton funton (SDF) [9, 33]. Assumng, for smplty, a Gaussan SDF, the saled SDF s ) S (x) exp ( x2, (3.2) 2σ 2 ( ) z1 S(x) S x. (3.21) z 2 The full-wdth at half-maxmum (FWHM) of a Gaussan urve lke S (x) s approxmately 2.35 σ. Ths value has to math the lateral extenson of the soure, whh s nomnally a 8 µm 2 µm retangle 8 [19]. Therefore, 2.35 σ an be expeted to be valued between 2 µm and 8 µm, dependng on the orentaton of the sanned segment (fg. 7) wth respet to the soure, plus other fators. After the X-ray ntensty I X (x) normalsed as n fg. 2 mpngng on the LF surfae has been orreted for the fnte sze of the soure by onvolutng t wth S(x), t an be nserted n eq. (2.11) to alulate the rate of deposted-energy densty ε n a more orret way. 3.3 Best ft of the photolumnesene profle The theoretal model of se. 2 was utlsed to best ft expermental PL profles obtaned by sannng at the optal mrosope CC maps reorded wth the above desrbed quas-far-feld magng setup. 8 Those lengths orrespond to the FWHMs of the soure ntensty along the horzontal and vertal dreton, respetvely. 18

20 mert funton (arb. unts) Z = 1 m (thn flm) Z = 1 m (rystal) Z = 2 m (rystal) average (1 m,1 m) soure sze ( m) Fgure 9. Mert-funton values vs. soure sze (2.35 σ ) for the ases of rystal and thn flm. For the rystal, the plots orrespondng to two dfferent values of the optally-pumped thkness Z are shown. See the text for further detals. Beause we are dealng wth PL profles along the x-axs, let us rewrte eq. (2.17) by makng explt the dependene on x of the nvolved parameters. Moreover, let us ntrodue three onvenent ft parameters p 1, p 2 and p 3. The resultng expresson for the PL ntensty s Z } I PL (x) = p 1 {Z exp [ p 2 ε(x p 3, z)] dz. (3.22) The frst two parameters, p 1 qn max and p 2 γt, are assumed to be sample-dependent beause of the peular struture that eah LF flm or rystal an have; therefore, they are not fored to assume dental values for dstnt samples. The same holds true for the thrd parameter, p 3, whh ats as a shft operator along x and s used to algn eah theoretal PL profle to ts expermental ounterpart. It s worth mentonng that p 1 also nludes a sale fator, non expltly wrtten to keep notaton smple, used to properly sale theoretal ntensty data to the arbtrary unts used for measured data. Data elaboraton started by estmatng an optmal soure sze 2.35 σ that should be ommon to eah measurement. To that purpose, a MATLAB [3] best-ft program was developed, whose output s a theoretal PL ntensty profle made as lose as possble to the nput expermental one by varyng the three ft parameters. The dstane between the expermental and theoretal ntensty profles s quantfed by means of a lassal root-mean-square mert funton, whh assumes a mnmum value when the expermental and theoretal ponts are as lose as possble. For the rystal only, several values Z of the optally-pumped thkness were tested, showng that the best results, n terms of mert funton, are obtaned for Z 1 µm the fat that Z s smaller than the rystal thkness s very lkely asrbable to the lmted z-range of the foused optal pump. For the flm, the value of Z was set to exatly onde wth the flm thkness, Z = 1 µm. Fgure 9 dsplays the obtaned optmal mert-funton fgures vs. soure-sze values only the best two among several tested Z values for the rystal are shown. As antpated, Z = 1 µm represents the best optally-pumped depth for the rystal. The plots demonstrate that whle 2.35 σ = 2 µm s the optmal soure sze for the LF flm, the mert funton orrespondng to the LF rystal (wth Z = 1 µm) has a mnmum at about 2.35 σ = 34 µm. A trade- 19

21 4 ε (1 2 ev m 3 s 1 ) z = z = 5 µm z = 1 µm x axs (µm) Fgure 1. Theoretal x-profles of the rate ε of deposted-energy densty n LF at the surfae (z = ) and at two depth values (z = 5 µm and z = 1 µm), as due to the quas-far-feld (17.5 m) dffraton of the poly-energet TOPO-TOMO X-ray beam through the Xrada X5-2-3 test pattern. off urve, obtaned as the mathematal average between the flm and the rystal (Z = 1 µm) urves, an be alulated; t s shown n fg. 9 as well, featurng a mnmum at 2.35 σ = 3 µm. Therefore, ths value was hosen as the optmal soure sze for both the rystal and flm ases. The theoretal x-profles of the rate ε of deposted-energy densty n LF at the surfae (z = ) and at two representatve depth values (z = 5 µm and z = 1 µm), as due to the quas-farfeld (17.5 m) dffraton of the poly-energet TOPO-TOMO X-ray beam through the Xrada X5-2-3 test pattern, are plotted n fg. 1. They were alulated by means of eq. (2.11), nto whh the ntensty I X of the dffrated X-ray feld, havng spetral dstrbuton as shown n fg. 2, was nserted. I X was also orreted for the fnte sze of the X-ray soure, 2.35 σ = 3 µm, as explaned n se The measured PL ntensty profles of samples Anka2 and Anka3 and ther orrespondng bestfttng theoretal profles, alulated wth eq. (3.22), are shown n fgs. 11 and 12, respetvely. In both the fgures, one notes a farly good reproduton of the expermental data near the entre, orrespondng to the shadow of the gold ral that s projeted onto the detetor. Outsde ths entral area, the reproduton s slghtly worse, espeally for Anka3, sne the rppled behavour (enhaned edge ontrast) s followed less aurately. An attempt was made to refne the theoretal profles n those external lobes by takng nto aount that other rals, parallel to the examned one and spaed 5 µm apart see fgs. 6 and 7 are present. Wth that n mnd, the alulaton x-doman of the FFT propagaton routne was extended to nlude the losest neghbourng rals, however the results were very lose to the ones obtaned wth the sngle entral ral only and shown n fgs. 11 and 12. Perhaps one ould get better results by onsderng that a three-dmensonal treatment of the propagaton problem should be faed n the Oxyz spae nstead of the smplfed b-dmensonal approah n the Oxz plane, thus nludng also rals that le along the x-axs to form a porton of the mesh whh s vsble n fg. 6. For the flm ase only, a better agreement ould be reahed by takng nto aount nterferene of the nternal mult-refletons both for the optal pump and radated PL. Suh mprovements of the model are beng targeted n future studes 2

22 sample Anka2: LF rystal PL ntensty (arb. unts) measured model x axs (µm) Fgure 11. Expermental and theoretal PL ntensty profles due to olour entres formed by X-ray exposton n a LF rystal of thkness 1 mm (atual optally-atve thkness of 1 µm). Irradaton was performed at the TOPO-TOMO beamlne of the ANKA lght soure (Insttute for Synhrotron Radaton, Karlsruhe Insttute of Tehnology KIT, Germany) n the framework of a quas-far-feld X-ray magng experment usng an Xrada X5-2-3 (Xrada, Pleasanton, CA, USA) test pattern. See the text for more detals. sample Anka3: LF flm 2 PL ntensty (arb. unts) measured model x axs (µm) Fgure 12. Expermental and theoretal PL ntensty profles due to olour entres formed by X-ray exposton n a LF flm of thkness 1 µm. Irradaton was performed at the TOPO-TOMO beamlne of the ANKA lght soure (Insttute for Synhrotron Radaton, Karlsruhe Insttute of Tehnology KIT, Germany) n the framework of a quas-far-feld X-ray magng experment usng an Xrada X5-2-3 (Xrada, Pleasanton, CA, USA) test pattern. See the text for more detals. 21

23 N/Nmax.4.3 Anka2 (rystal).2.1 Anka3 (flm) ε (1 21 ev m 3 ) Fgure 13. Theoretal normalsed volume densty of CC s n the two samples alulated aordng to the results of the best ft. See the text for more detals. together wth the analyss of samples of other shapes and materals. 3.4 Dsusson By omparng fgs. 11 and 12, t s worth notng how dfferent ontrast values of the PL profles are found for the rystal and the flm. As a matter of fat, let us onsder the rato of the PL mnmum loated at the entre of the gold ral shadow to the PL external plateau. As one an verfy, ths rato s 6% for the rystal, and 4% for the flm, thus ndatng a better ontrast for the latter. SAMPLE type p 1 (arb. unts) p 2 (m 3 s/ev) p 3 (µm) Anka2 rystal Anka3 flm Table 1. Best-fttng values of the three parameters. Let us look at the optmal parameter values, lsted n tab. 1, that result from the best fttng. The value of p 2,.e., γt, s one order of magntude larger n the rystal than n the flm. 9 Consderng that the exposton tme to X-rays, t = 3 s, was the same for the rystal and for the flm, one onludes that γ s muh larger n the rystal than n the flm. We partally asrbe the abovementoned dfferent ontrast values of the PL profles to ths relevant dfferene n γ, whh an be nterpreted as a tendeny of CC s n a rystal to be destroyed more qukly than n a flm. Indeed, aordng to eq. (2.16), a larger value of γ means that a smaller value of εn s needed to get the same negatve ontrbuton to dn/dt. In other words, the reaton proess of CC s n the rystal seems to saturate earler than n the flm. 9 Note that the values of p 2 are nfluened by the normalsaton hosen for I X. Here we are usng the normalsaton shown n fg

24 Ths fat s more learly llustrated n fg. 13. Here, the volume-densty rato N/N max s alulated by means of eq. (2.17) wthn a range of deposted-energy densty ε that spans the estmated range of ε for the experment, as shown n fg. 1, multpled by the rradaton tme t = 3 s. The two urves have been alulated wth γt set to the values of p 2 found from the best-ft proess and lsted n tab. 1. Note how the volume densty of CC s gets lose to saturaton earler n the rystal than n the flm. Ths fat ould mean that a hgher deposted energy s needed for the flm to reah the same amount of aggregate CC s as n the rystal (as f aggregate CC s n the flm were slower or delayed n formng than n a rystal), and/or that the flm an host more F 2 and F + 3 CC s than the rystal (that s, as f N max was hgher n the flm than n the rystal). Prevous lterature results [34] and some expermental evdene seem to favour the latter hypothess, even though the former one annot be ompletely exluded. Ths top surely deserves further studes. Suh onlusons have, for now, to be regarded as speulatve ones, at least untl further evdene emerges from other analyss, beause they are based on just two examned samples and are the result of qute a smplfed model and assumptons: for nstane, the fat that F 2 and F + 3 entres an be reated wth dstnt rates of densty growth has not been taken nto aount. It s ndeed qute surprsng that suh a smplfed model works deently for suh a omplex experment. Work s n progress to perfet the model and test t for other study ases, n order to better desrbe what atually takes plae. 4 Conlusons The sutablty of LF-based deves as detetors for poly-energet X-rays has been postvely tested. In partular, use of suh detetors n quas-far-feld magng experments n a synhrotron has been demonstrated. They allow for hgh resoluton storage of an mage as a spatal dstrbuton of CC s, whh an be omfortably observed at an optal mrosope provded the aggregate F 2 and F + 3 CC s are optally exted wth sutable blue lght. No development proess s needed, and handlng s possble even n daylght and at room temperature. To analyse the results of the above-mentoned tests, an ad ho theoretal model has been developed and mplemented n MATLAB [3]. The model starts wth evaluatng the rate of depostedenergy densty by a ollmated eletromagnet beam n a sold materal. Then, a smplfed saturaton-wse dfferental equaton s bult: t onnets the volume densty of pont defets beng reated to the deposted-energy densty. By applyng t to CC s n LF, the resultng densty dstrbuton of optally-atve CC s an be evaluated and, onsequently, the ntensty of radated PL estmated. Suh results have been eventually appled to the X-ray dffraton setup of a reent synhrotron experment, where the ollmated poly-energet X-ray beam was transmtted through an Au-S 3 N 4 test pattern and free-propagated tll a LF-based detetor n the quas-far-feld; the dffrated beam mpresses a stable spatal dstrbuton of CC s n the detetor, whose lumnesene an be later read and mapped at hgh defnton wth a sutably equpped optal mrosope. Expermental profles of PL that were read out on suh detetors, both n rystal and flm form, have been ompared to ther orrespondng theoretal ounterparts, obtaned from the abovedesrbed theoretal model. Even though the agreement between experment and theory s far from beng perfet, t s qute satsfyng, espeally n the areas orrespondng to the most absorbed X-ray ntensty. Future experments and studes are beng planned to mprove magng apabltes as far as usablty of LF-based deves and ther theoretal desgn are onerned. 23

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26 Referenes [1] Ashroft N W and Mermn N D 1981 Sold State Physs (Phladelpha: Holt-Saunders Internatonal Edtons) [2] Shonoya S and Yen W M 1998 Phosphor Handbook (Boa Raton: CRC Press) [3] Fowler W B 1968 Physs of Color Centers (New York: Aadem Press) [4] Lakshmanan A R, Madhusoodanan U, Natarajan A and Pangrah B S 1996 phys. stat. sol. (a) [5] Montereal R M 22 Pont defets n thn nsulatng flms of lthum fluorde for optal mrosystems Ferroeletr and Deletr Thn Flms (Handbook of Thn Flm Materals vol 3) ed Nalwa H S (San Dego: Aadem Press) hap 7, pp [6] Basev T T, Mrov S B and Osko V V 1988 IEEE J. Quantum Eletron [7] Nahum J and Wegand D A 1967 Phys. Rev [8] Cowley J M 1995 Dffraton Physs 3rd ed (Amsterdam: North Holland) [9] Pogany A, Gao D and Wlkns S W 1997 Rev. S. Instrum [1] Lagomarsno S and Cedola A 24 X-ray mrosopy and nanodffraton Enylopeda of Nanosene and Nanotehnology vol 1 ed Nalwa H S (USA: Ameran Sentf Publshers) pp [11] Baldahn G, Bonfgl F, Faenov A, Flora F, Montereal R M, Murra D, Nhelatt E and Pkuz T 22 Radat. Eff. Defets Solds [12] Baldahn G, Bonfgl F, Faenov A, Flora F, Montereal R, Pae A, Pkuz T and Reale L 23 J. Nanos. Nanotehnol [13] Baldahn G, Bollant S, Bonfgl F, Flora F, D Lazzaro P, La A, Marolo T, Montereal R M, Murra D, Faenov A, Pkuz T, Nhelatt E, Tomassett G, Reale A, Reale L, Rtu A, Lmong T, Palladno L, Franu M, Martellu S and Petroell G 25 Rev. S. Instrum [14] Almavva S, Bonfgl F, Franzn I, La A, Montereal R M, Pella D, Cedola A and Lagomarsno S 26 Appl. Phys. Lett [15] Bonfgl F, Cela A, Hedar Baten S, Nhelatt E, Pella D, Somma F, Vagov P, Vnent M A, Baumbah T and Montereal R M 213 Radat. Meas [16] URL [17] Platt U and Stutz J 28 Dfferental Optal Absorpton Spetrosopy, Physs of Earth and Spae Envronments (Berln Hedelberg: Sprnger-Verlag) 25

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28 Edto dall ENEA Servzo Promozone e Comunazone Lungotevere Thaon d Revel, Roma Pervenuto l Stampato presso l Laboratoro Tenografo ENEA - C.R. Frasat Fnto d stampare nel mese d marzo 216