Measurement of thickness of dielectric materials from microwave reflection data

Transcription

1 st Intenatonal Confeence on Sensng Technology Novembe -, 5 Palmeston Noth, New Zealan Measuement of thckness of electc mateals fom mcowave eflecton ata Abstact Kalash Thaku an Wayne Holmes Electomagnetc Sensng Competency Imagng an Detectng Platfom Inustal eseach Lmte Balfou oa, Panell, Aucklan e-mal: kthaku@lcnz Subhas Chana Mukhopahyay Insttute of Infomaton Scences an Technology Massey Unvesty (Tutea) Palmeston Noth Ths pape pesents a technque fo the measuement of thckness of electc mateal usng mcowave The measuements ae cae out fo the electc backe by metal eflecto The eflecton coeffcents at X-ban fequences ae measue usng a focusse mcowave system so that a plane wave appoxmaton can be apple The esults ae pesente fo seven ffeent samples of acylc sheets backe by metal eflecto It s foun that the mcowave measuement one at a sngle fequency geneates a numbe of solutons fo the thckness Hence measuements must be cae out at moe than one fequency to get the coect answe fo the thckness of the electc Keywos: plane electc, thckness, mcowave, pemttvty, plane wave, focusng antenna Intoucton Ths pape pesents a smple technque to estmate the thckness of electc mateals usng mcowave We have been nvolve n the evelopment of thckness measuement system fo electcs usng mcowave fo past few yeas [-] A mathematcal soluton fo such measuements s usually an nvese technque In the past, we have use nonlnea least squaes egesson [-], whch geneates an oveall aveage value of thckness fom a numbe of measuements Ths pape escbes a technque whch s useful fo a quck estmaton of the thckness fo low loss o loss fee electcs It oes not nee a lage numbe of ata as eque n the nonlnea least squaes egesson [-] Moeove, ths technque coul be mplemente n a low cost system The system can be potable an hence qute useful fo fel measuements Measuement Pncple The electc sheet of thckness, an pemttvty, s place on the metal suface as shown n Fg The plane mcowave ncent upon the sheet s eflecte back an obeys the Fesnel s equatons The Fesnel s equatons fo the eflecton coeffcent of a plane wave ncent on the taget meum backe by a hghly eflectve plane can be wtten as µ cosθ tan[ k µ cosθ tan[ k θ Metal ( µ sn θ ) ] ( µ sn θ ) ( µ sn θ) ] ( µ sn θ) () Fgue : Expemental setup fo the measuement of thckness 57

2 st Intenatonal Confeence on Sensng Technology Novembe -, 5 Palmeston Noth, New Zealan If the angle of ncence, θ s set to zeo, we have the eflecton coeffcent fo µ, ( k ) tan k ) Equaton () can be solve to fn the thckness of electc n tems of eflecton coeffcent,, pemttvty an wave vecto n fee space, k o k tan () nπ () calculate usng equaton () euce the magnay pat of by a small facto, (say) mag () mag ()/ calculate usng k ) 5 Go back to untl the ffeence between ntal an fnal values of eal component of s less than a peefne toleance value whee n s an ntege an can pove a peoc soluton fo thckness, The poblem wth the soluton of equaton () s that the magnay component of thckness, s not always zeo an hence oes not pove a goo soluton Anothe poblem s that thee ae seveal solutons fo thckness, because of the peoc natue of the functon Ths poblem can be esolve by usng measuements at seveal fequences usng the moe genealse an sophstcate algothm [] Howeve, fo many commecal applcatons a quck an ough estmate mght be neee usng a low cost two o thee fequency senso Fo ths pupose, we have evelope an algothm, to solve fo the thckness an pemttvty of the electc backe by metal plate, usng an teatve poceue The stct equement s that the senso must be calbate fo the measuement of eflecton coeffcents on the plane of measuement 5 n 5 n 5 n 5 n Fequency (GHz) Fgue : Plot of smulate values of thckness, of a cm thck acylc sheet measue usng equaton () fo ffeent values of n Only the esults fo n ae acceptable n ths case Expement an esults In ths measuement, we have use a focussng hon antenna connecte to a sx pot etecton system to measue the eflecton coeffcents The calbaton was cae out on the focal plane of the antenna These measuements wee cae out at 6 ffeent fequences angng fom 85 GHz to GHz The followng algothm s use fo the computaton of thckness, fom the measue eflecton coeffcents: stat wth an ntal value of pemttvty, The esults of the measuements fo seven samples of ffeent thcknesses of acylc sheet ae shown n Table The smulate esults fo thckness, fo fou samples of acylc sheet usng the above algothm ae shown n Fgues to 5 fo ffeent values of n The measue thckness of the sample vaes fom cm to cm an hence only one patcula value of n s acceptable n each case fo a coect esult It s nteestng to note n Fgue that fo n, the value of thckness, s almost constant aoun cm Howeve, fo n >, the evaton n the value of nceases an also the unnng aveage value of eceases wth nceasng fequency Smla esults 57

3 st Intenatonal Confeence on Sensng Technology Novembe -, 5 Palmeston Noth, New Zealan ae seen n Fgue In Fgue, the slope of the cuve coesponng to n s the mnmal wheeas the slope s postve fo n an negatve fo n > In Fgue 5, the slope of the cuve coesponng to n s the mnmal wheeas the slope s postve fo n an n an negatve fo n n 5 5 n 5 n 5 n Fequency (GHz) Fgue : Plot of smulate values of thckness, of a cm thck acylc sheet measue usng equaton () fo ffeent values of n Only the esults fo n ae acceptable n ths case These obsevatons fom the bass fo scmnaton between the acceptable an not acceptable solutons of the peoc functon (), e, the value of thckness, measue at moe than one fequency shoul be the same Moeove, the value of electc constant geneate by ths algothm s constant fo the acceptable value of n an vaes conseably fo othe values of n Ths foms anothe possble way fo the scmnaton of acceptable an unacceptable solutons of equaton () 5 n 5 n 5 n 5 n Fequency (GHz) Fgue : Plot of smulate values of thckness, of a 6 cm thck acylc sheet measue usng equaton () fo ffeent values of n Only the esults fo n ae acceptable n ths case 5 n 5 n 5 n 5 n Fequency (GHz) Fgue 5: Plot of smulate values of thckness, of a cm thck acylc sheet measue usng equaton () fo ffeent values of n Only the esults fo n ae acceptable n ths case Table : Measue values of thckness an pemeablty of acylc sheet n the X-ban /cm eq eal /cm eq magnay ' " /cm n (meas) Calculate thckness (mm) 6 5 st set n Set 5 6 Measue thckness (mm) Fgue 6: Measue an calculate thckness of vaous acylc sheets 575

4 st Intenatonal Confeence on Sensng Technology Novembe -, 5 Palmeston Noth, New Zealan We have also epeate two measuements fo vaous acylc samples The esults ae pesente n Fgue 6 fo the thckness of the acylc samples Only the acceptable soluton fo n has been chosen The plot of the measue an estmate values of thckness n fgue 6 shows the valty of the pesent technque Howeve, thee ae a few outles also n the esults whch mght be ue to the wong choce of n A wong choce fo n can be easly mae n such stues, whch s ue the nhete natue of the nvese poblem We have foun a smple way to estmate the pemttvty of the plana sample wthout takng the nvese Conse two plana electcs of same mateal an of thcknesses, an so that the sum of the thckness s If both electcs ae place on the metal suface an the eflecton coeffcent s measue, we get k ) () The eflecton coeffcents, an ae also measue fo nvual electcs of thckness, an, e k ) (5) an k ) (6) snce (7) Fom equatons () an (7) we get ( k ( ) ) tan (8) o ( k ) k ) ) k ) k ) (9) Fom eq () we get () We have cae out seveal measuements fo seveal samples of acylc of ffeent thcknesses an the pas The esults fo electc constant an loss facto of acylc sheet ae shown n Fgues 7 an 8 These esults ae close to the expemental values shown as a lne The scepancy between the compute an expemental values may be attbute to the expemental eo Moeove, the samples taken fom ffeent supple may not have the same electc constant Delectc Constant Fequency (GHz) Fgue 7: Compute values of electc constant fom eq () fo samples fo seveal pas of acylc sheets Loss Facto Fequency (GHz) Fgue 8: Compute values of loss facto fom eq () fo samples fo seveal pas of acylc sheets o () Summay A mcowave measuement cae out at a sngle fequency wll geneate a numbe of solutons fo the thckness Ths makes t ffcult to select the coect 576

5 st Intenatonal Confeence on Sensng Technology Novembe -, 5 Palmeston Noth, New Zealan soluton Hence the measuement must be cae out at moe than one fequency to get the coect answe fo the thckness of the electc If thee s a stong speson n the electc, the technque wll fal because thee wll be ffeent answes fo pemttvty at ffeent fequences whch may not be able to geneate a sngle value fo thckness, at all fequences Measuement of thckness usng mcowaves n the pesence of stong speson n the mateal can be cae out usng the non-lnea least squaes egesson technque escbe n [] The pesent algothm teste hee can be apple to the measuement of the thckness of electc layes backe by stong eflecto eg, laye of ce on wate, epth of metallc obects bue n sol Ths pape pesents esults of ou pelmnay stuy an moe nvestgaton s neee to mpove the calbaton poceue of the focussng system to mpove the technque 5 Acknowlegements The authos thank Inustal eseach Lmte fo fnancal suppot though the eseach an Development Funnel poects Fnancal help fom the Founaton fo eseach Scence an Technology, New Zealan s also acknowlege 6 efeences [] Thaku K P, Holmes, W S Non-contact measuement of mostue n layee electcs fom mcowave eflecton spectoscopy usng an nvese technque, IEEE Tansactons on Mcowave Theoy an Technques, 5(), pp 76-8, Januay () [] Thaku K P Mostue measuement n Mult- Layee system, Book Chapte n Electomagnetc Aquamety, E K Kupfe, publshe by Spnge-Velag, Gemany, pp - (5) [] Thaku K, Chan K L, Holmes W S, Thckness an pemttvty of nhomogeneous electcs fom mcowave eflecton spectoscopy usng an nvese technque, Ffth Intenatonal Confeence on Electomagnetc Wave Inteacton wth wate an Most Substances, Intenatonal Socety fo Electomagnetc Aquamety (ISEMA), otoua, New Zealan, pp 8-8, Mach () 577