Focal Spot Size Estimation for a 4 MeV Small-size Betatron Using Digital X-ray Detector

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1 Focal Spot Sze Estmaton for a 4 MeV Small-sze Betatron Usng Dgtal X-ray Detector K V Sukarnkov 1, M M Ryckov, V G Gentselman 2 1 Post-graduate student, Insttute of NDT, TPU, Tomsk, Russa 2 Head of laboratory, Insttute of NDT, TPU, Tomsk, Russa Engneer, Insttute of NDT, TPU, Tomsk, Russa E-mal: k.sukarnkov@gmal.com Abstract. One of te man advantages of small-sze betatrons s small focal spot sze. However tere s no conventonal procedure of focal spot sze measurement for betatrons. Tecnques descrbed n standards are sutable only for low- and md-energy tubes. Te task become more complex f te focal spot sze sould be estmated quckly usng modern dgtal detectors. In ts paper we present prelmnary results of focal spot sze measurement of a 4 MeV small-sze betatron wt two dfferent procedures usng dgtal x-ray detector. 1. Introducton A betatron s a pulsed nducton electron accelerator. Te frst operable betatron was created by Donald W. Kerst n 1940, altoug patents descrbng devces based on smlar prncples ad been publsed decades before [1]. Te development of betatrons untl reacng te energy up to about 00 MeV was of ncreasng nterest. Ten te g energy betatons ave been gradually supplanted by lnacs. Neverteless, low energy macnes reman effectve sources of ard X-rays used n nondestructve testng. One of te most promsng felds of applcaton of te betatrons s g-energy X-ray computed tomograpy (CT). Te man advantage of te betatrons n CT over te oter types of ard X-rays sources s small focal spot sze [2]. Obtanng te focal spot szes wtn te lmts of µm s possble because of te cyclc nature of betatrons tat allows multple nteracton of te accelerated electron beam wt a bremsstralung target mounted nsde te acceleraton camber. In contrast wt lnacs, te sze of te target can be reduced wt mnor effect on te radaton ntensty. Focal spot sze s one of te most sgnfcant parameters of te X-rays source for CT. However tere s no conventonal procedure of focal spot sze measurement for betatrons. Tecnques descrbed n European Standard EN 1254 are applcable for x-ray tubes wt voltage restrcted to 500 kv. As well as Russan Standard GOST s sutable only for low- and md-energy tubes. Te task become more complex f te focal spot sze sould be estmated quckly usng modern dgtal detectors. Te am of ts work s to present prelmnary result of focal spot sze measured of a 4 MeV smallsze betatron wt two dfferent procedures usng dgtal x-ray detector. Te metods to be appled n te researc are slt camera radograpc metod and ndrect metod based on mage unsarpness measurement usng mage qualty ndcator (IQI). Content from ts work may be used under te terms of te Creatve Commons Attrbuton.0 lcence. Any furter dstrbuton of ts work must mantan attrbuton to te autor(s) and te ttle of te work, journal ctaton and DOI. Publsed under lcence by Ltd 1

2 2. Expermental setup Te betatron (fgure 1) used n te experments s a small-sze pulsed betatron MIB-4 wt maxmal bremsstralung energy 4 MeV and clamed focal spot sze 0. mm. Postonng was performed wt a motorzed postonng systems by PI GmbH & Co. KG. Fgure 1. Expermental setup layout: 1 betatron; 2 tungsten target mount nsde acceleraton camber; collmator; 4 postonng system; 5 test object; 6 magng system. A dgtal X-ray detector Perkn Elmer XRD 1622 was used as te magng system (fgure 1). Total pxel number s wt ptc 200 µm. An mportant caracterstc of te X-ray detector tat must be taken nto account and corrected s lne spread functon (LSF). Full wdt at alf maxmum (FWHM) of te X-ray beam FWHM I can be found from te mage obtaned usng te relaton []: FWHM R = FWHM I + FWHM LSF (1) Were FWHM R s FWHM of te obtaned mage and FWHM LSF s FWHM of detector s LSF. Lkewse t was done n [] te LSF of te detector system was found by dfferentaton of te edge spread functon (ESF) obtaned by contact radograpy of te test object wt sarp edge. Gaussan approxmaton of te LSF s sown on fgure LSF, arb.unts x, mm Fgure 2. Gaussan approxmaton of te LSF. FWHM = 0.6 mm. LSF. Slt camera metod Focal spot sze measurement usng pnole and slt cameras s based on te camera obscura prncple. Fgure ndcates te common layout of te expermental setup used for ts metod. 2

3 Fgure. Slt camera experment layout. In te deal case te tckness of te edges s neglgble small tat s practcally unacevable. Takng nto consderaton te fnte slt camera tckness, ntensty dstrbuton sown on fgure 2 can be ntroduced. F 1 and F 2 can be calculated troug geometrcal optcs approac: 1 ( ) 2 L+ F = f d d (2) 2l 2 ( ) 2 L F = f + d + d () 2l+ Were f s focal spot sze, d s slt sze, s slt camera tckness. F1 F2 ndcates te penumbra sze. Influence of te fnte slt camera tckness can be corrected by usng te FWHM of te X-ray beam profle. FWHM I 1 f = d 1 (4) M 1 M L+ l M = (5) l Settng and d equal to 0 (tckness s neglgble small) expressons can be transformed to te deal case (no penumbra s observed): F1 = F2 = f( M 1) (6) Takng nto consderaton (2) and () one can fgure out an expresson for te edge tckness and slt sze lmts by solvng te equaton F1 F2= 0. Te soluton s as follows: 2dl f = max ; dmn f = 2l (7) Usng te expressons (7) as well as te expresson for lnear attenuaton coeffcent for te desred materal of te slt camera one can evaluate boundares for te geometrcal sze of te camera. Fgure 4 ndcates geometry of te steel dapragm used n te experment.

4 Fgure 4. Te camera wt varable slt sze used n te experment. Te focal spot sze (orzontal value) of te 4 MeV betatron s clamed to be f = 0. mm. So assumng te dstance l = 250 mm (fgure 1) and slt sze d = 0.1 mm one can make certan tat te maxmal slt camera tckness does not exceed te maxmal value allowed. Te slt camera s cosen to be made of steel because of smplcty of manufacturng. In artcle [] slt camera made of tungsten was used to measure te focal spot sze of a 5 MeV lnac. In comparson to te lnac te betatron as lower radaton ntensty as well as smaller spot sze. It dmnses te requrements for slt camera materal used n our expermental setup. Also usage of te dgtal X-ray detector n our expermental faclty (fgure 1) allows enancng contrast of te mages obtaned n comparson of an X-ray flm. However an experment wt tungsten-made slt camera s planned. Profle of te mage obtaned wt 100 µm slt s sown on fgure 5. x Intensty, arb.unts X: Y:.002e+04 X: Y: 2.99e x, mm Fgure 5. Slt camera mage profle. Te focal spot sze can be now found usng (1) and (4) wt followng parameters: l = 250 mm, L = 1000 mm, M = 5, d = 0.1 mm. Te evaluated value s f = mm. 4. Indrect measurement usng IQI Te ndrect metod s based on relaton between basc spatal resoluton and focal spot sze. Equaton (8) taken from ASTM E 2698 [4]. It can be used for focal spot sze assessment by measurng te basc spatal resoluton SRb and mage unsarpness U. 4

5 M 2.0 = f U SRb M 1 M One of te most wdely used metod for measurement of SRb and U uses duplex wre type IQI. (8) Fgure 6. Duplex wre type IQI experment layout. Te penumbra areas ndcated on fgure 6 merge wen focal spot sze f matces wre dameter and spacng D. Gray level profles for varous cases are sown on fgure 7. Results of geometrcal optcs modelng provde an ntutve representaton of te tecnque. But te relatons are ardly to apply practcally, by vrtue of te fact tat te wres are penetrable for te ard x-rays. Also probablstc nature of nteracton of radaton wt matter as well as detector noses sould be taken nto account. For ts reason a metod based on spatal resoluton measurement can be appled. Fgure 7. Gray level profle: a) f < D; b) f = D; c) f > D; d) f = 2 D. Profles of radograp captured on te real experment are sown on fgure 8. Te experment s based on te layout presented on fgure 1 wt l = 245 mm, L = 1045 mm, M =

6 12000 D1 D2 D D4 D5 D6 D7 D8 D9 D10 D Intensty, arb.unts x, px Intensty, arb.unts X: 101 Y: 8478 X: 1028 Y: 7876 X: Y: 7719 Fgure 8. Radograp profle of duplex wre IQI. X: 1120 Y: 7778 X: 1116 Y: 8684 X: 1122 Y: 796 X: 1124 Y: x, px Obtaned radograp can be used to assess a spatal resoluton SRb and mage unsarpness U by measurement of modulaton dept (dp) for negborng IQI wres. Te results are sown n table 1. Table 1. Results of dp measurement IQI Element No D8 D9 D10 D11 D12 Measured dp, % Maxmum Unsarpness, mm Maxmum Basc Spatal Resoluton, mm Fnally te focal spot sze can be found from (8) usng SRb and U values for D11. Te evaluated value s f = mm. 5. Concluson Focal spot sze of a 4 MeV betatron was measured usng slt camera and resoluton metods. Te results of te experments are very close and do not exceed clamed focal spot sze 0. mm. However te presented results are course and ave to be verfed. Ways to get more accurate measurements are as follows: Use of te slt camera made of tungsten. Precse measurement of te LSF of te magng system. Reteraton of te experments usng dfferent detectors to collect statstcs. Monte-Carlo smulaton of te experment to obtan extra data. Use of a betatron wt a cangeable bremsstralung target. References [1] Kerst D W (1946) Hstorcal development of te betatron Nature [2] Vaynberg E I, Kasyanov V A, Caklov V L, Sten M M (2004) Experence of Usng Small- Sze Betatron Mb-5 n te Structure of Industral Computed Tomograp Bt-500Xa 16t World Conference on NDT (WCNDT 2004) Proceedngs 1 5 [] Gambaccn M, Cardarell P, Tab a., Franconer a., Domenco G D, Marzan M, Barnà R C, Audtore L, Morgana E, Lora D, Trfrò A. and Trmarc M (2011) Measurement of focal spot sze n a 5.5MeV lnac Nuclear Instruments and Metods n Pyscs Researc, Secton B: Beam Interactons wt Materals and Atoms [4] Bavendek K, Ewert U, Redo A, Heke U and Zscerpel U (2012) New Measurement Metods of Focal Spot Sze and Sape of X-ray Tubes n Dgtal Radologcal Applcatons n Comparson to Current Standards 18t World Conf. Nondestruct. Test