Cylindrical geometry: a further step in active microwave tomography

836 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 39, NO. 5, MAY 1991 Cylind ical Geome y: A Fu he S ep in Ac i e Mic owa e Tomog aphy An oni B oque as, Membe , IEEE, Jo di Romeu, S uden Membe , IEEE, Juan M. Rius, S uden Membe , IEEE, An onio R. Elias-Fus e, Membe , IEEE, Angel Ca dama, Membe , IEEE, and Luis Jo e, Membe , IEEE Abs ac -A p o o ype imaging sys em o ac i e mic owa e omog aphy using cylind ical geome y has been de eloped, making is possible o ob ain images o he dielec ic p ope ies o biological a ge s a 2.45 GHz. The sys em equi es no me- chanical mo emen s o illumina e he body om mul iple di ec- ions ( iews) and measu e he sca e ed ields. In his way a comple e da a se consis ing in 64 iews is acqui ed in 3 s using low-powe illumina ion. The sys em is desc ibed, including im- ages ob ained wi h biological phan oms and ac ual bodies. I. INTRODUCTION URRENT esea ch in medical imaging is de o ed C bo h o imp o ing exis ing sys ems based on X ays, nuclea magne ic esonance, ul asound, e c., and o in- es iga ing o he eme ging echniques such as applied po en ial imaging [l] and mic owa e imaging [2]. The in e es in de eloping new imaging me hods when e y good ones al eady exis lies basically in he di e en physical pa ame e s isualized, which depend s ongly on he ype o adia ion used and i s in e ac ion wi h biologi- cal ma e ials. The objec i e o ac i e mic owa e omog aphy is o econs uc he dielec ic p ope ies o a body illumina ed wi h mic owa es om a measu emen o he sca e ed ields. Biological issues p esen la ge a ia ions in hei elec ical cha ac e is ics depending on composi ion, em- pe a u e, i iga ion, e c.; he e o e hei in e nal s uc u e and physiological changes can in p inciple be imaged [3], [41. Unlike ionizing adia ion, low-powe mic owa e adia- ion allows a i ually sa e explo a ion o li ing issues; hus e en con inuous moni o ing can be en isaged. Mo e- o e he echnology in ol ed is common o ada and communica ion sys ems; hus i is well de eloped and inexpensi e. Some d awbacks o his echnique a e i s low esolu ion (o he o de o a wa eleng h o he adia ion in issue), Manusc ip ecei ed July 23, 1990; e ised Decembe 17, 1990. This wo k was suppo ed by he Spanish Commi ee o Scien i ic and Tech- nical Resea ch (CAICYT) unde G an 1165-84, by he Spanish Na- ional Ins i u e o Heal h (FISS) unde G an 84/2112, by he Spanish-F ench Coope a ion P og am unde G an 30/135, and by he Spanish-B i ish Coope a ion P og am unde G an 17/173. The au ho s a e wi h he TSC Dep ., G oup AMR, Uni e si a Poli cnica de Ca alunya, P.O. Box 30002, 08080 Ba celona, Spain. IEEE Log Numbe 9143002. he high a enua ion ha biological ma e ials p esen a mic owa es, which place s ingen equi emen s on he equipmen design, and he di icul y in de eloping imag- ing algo i hms adap ed o he high dielec ic con as o biological bodies. The i s expe imen s on ac i e mic owa e biological imaging we e ca ied ou by La sen and Jacobi in he la e 1970’s [5]. The images, which showed he in e nal ea u es o an isola ed canine kidney, we e ob ained by mechani- cally scanning he body wi h a pai o an ennas and measu ing he ansmission coe icien s be ween hem. Since hen, an impo an e o has been conduc ed o design sys ems o measu e he sca e ed ields p oduced by biological bodies and imaging algo i hms adap ed o he measu emen geome y o econs uc he pe mi i i y da a [61-[14]. Con en ional mic owa e omog aphy sys ems a e based on illumina ing he body wi h a plane wa e and measu ing he sca e ing wi h a linea a ay o p obes, in a way simila o ha p oposed by Muelle in acous ic di ac ion omog aphy [ 151. Wi h plane wa e illumina ion and he assump ion o weak sca e ing bodies, he plane wa e spec um o he sca e ed ield con ains he in o ma ion on a ci cula a c o he bidimensional Fou ie spec al domain o he dielec ic p ope ies o he body [13]. Repea ing he measu emen o di e en di ec ions o incidence o iews, he spec al domain can be illed and in e ed, ob aining an image o a cu o he body. A p ac ical p oblem wi h his me hod is he need o me- chanical o a ion o ei he he body o he an enna in o de o ob ain measu emen s in di e en iews. Al- hough linea syn he ic app oaches ha e been p oposed o a oid his p oblem [9], [16], hey a e unable o p oduce comple e u n mul i iew da a wi hou o a ion. An al e - na i e p oposed by Bolomey consis s in using a wo- dimensional a ay o measu e he sca e ed ields [SI, wi h acquisi ion imes o he o de o a second. The images ob ained show de ails o he in e nal dielec ic s uc u e o dielec ic changes in eal and phan om biological bod- ies [6]-[8]. Using an enci cling geome y o measu emen would make i possible o ob ain mul i iew da a wi hou me- chanical mo emen . This pape p esen s a i s p o o ype 0018-9480/91/0500-0836$01 .00 0 1991 IEEE BROQUETAS e al.: CYLINDRICAL GEOMETRY x37 based on a cylind ical a ay, whose elemen s can be add essed independen ly as emi e s o ecei e s. This con igu a ion allows a as explo a ion o body’s cu placed along he a ay axis, in a way simila o ha o p esen X- ay scanne s. The elec omagne ic compa ibili y (EMC) o his app oach is c i ical because he s ongly a enua ed ecei ed ields a e measu ed on he same a ay which is being used o emi a high-le el illumina ing signal. The e- o e, ca e ully designed high- equency a chi ec u es and de ec ion echniques a e necessa y. The nex sec ion o he pape shows he equency choice as a comp omise be ween esolu ion o he image and ole able a enua ion, in ou p o o ype a wo king equency o 2.45 GHz has been adop ed. Sec ion 111 desc ibes he main pa s o he p o o ype, an e icien imaging algo i hm o cylind ical geome y and he main WORKSTATION KQU1SITlOh RECONSTRUCTION I equency is inc eased. The wa eleng h in biological is- sues is subs an ially sho e han alues in ai because o he high wa e con en . Wa e has a ela i e dielec ic cons an o he o de o 70 o 80 a mic owa e equen- cies and oom empe a u es. The wa eleng h is educed in his medium by a ac o o almos 9 in ela ion o ai alues. The e o e a heo e ical esolu ion o se e al mil- lime e s can be achie ed wi h ope a ing equencies o a ew gigahe z. On he o he hand, biological bodies exhibi s ong a enua ion a mic owa e equencies because o he high con en o wa e and conduc ing solu es. The a enua ion inc eases apidly wi h equency, which limi s e ec i ely he wo king equency depending on he size o he body, he illumina ion powe , and he ecei e sensi i i y. Fo sa e y easons, he illumina ion powe densi y mus be kep below he mic owa e adia ion s anda ds o con in- uous exposu e [181. Recei e sensi i i y is linked o he in eg a ion ime o each measu emen and consequen ly is p opo ional o he acquisi ion ime. Imaging usually equi es he measu emen o housands o sca e ed ield complex da a, which means ha in o de o ha e acquisi- ion imes o he o de o seconds he in eg a ion ime mus be a ound 1 ms. F om hese conside a ions he use ul equency ange o mic owa e imaging is ound o be om below 1 GHz o la ge bodies such as he ho ax o pel is o se e al GHz o smalle ones such as limbs. In ou case a equency o 2.45 GHz has been chosen, which is assigned o indus ial-scien i ic-medical applica ions. Fig. 1. Block diag am and pho og aph o he p o o ype sys em. 111. A CYLINDRICAL PROTOTYPE SYSTEM A p o o ype cylind ical sys em has been de eloped o e alua e he pe o mance and limi a ions o his app oach and o in es iga e possible clinical applica ions. The sys- em is based on a cylind ical a ay o 64 an ennas equis- paced on a ci cle 25 cm in diame e . Al hough he a ay is in ac ci cula , he name cylind ical is used because each an enna is assumed o p oduce an almos cylind ical wa e on he illumina ed egion. In his way a bidimensional econs uc ion algo i hm has been o mula ed in cylind i- cal coo dina es. The basic measu emen o iew consis s in using an an enna o he a ay as emi e and ecei ing he sca e ed ields wi h he emaining elemen s. This p ocedu e is epea ed, sequen ially emi ing wi h each o he an ennas o comple e one u n. Thus, as many iews as a ay elemen s a e ob ained wi h no mo emen s, using a measu emen me hod e y simila o ha used in he mode n an-beam X- ay scanne s. Howe e , using ele- men s o a common a ay as emi e s and ecei e s e- qui es a complica ed add essing ne wo k wi h se e e iso- la ion speci ica ions. The main pa s o he p o o ype a e he cylind ical a ay o 64 an ennas imme sed in wa e using a plas ic cylind ical con aine ; a mic owa e dis ibu ion ne wo k ha di ec s he ansmi ed and ecei ed signals o a pai I 838 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 39, NO. 5, MAY 1991 0 1 2 N1 Fig. 2. Measu emen p ocedu e in a cylind ical sys em; qe and q a e he angula coo dina es o he emi e and ecei e an ennas in ope a- ion. The objec is illumina ed sequen ially wi h he elemen s o he a ay ( iews); o each iew he sca e ed ields a e measu ed. o an ennas o he a ay; a cohe en mic owa e emi e - ecei e ; some low equency ci cui y (Fig. 1); and a 32 bi mic ocompu e ha con ols he acquisi ion and e- cons uc s and p esen s he image on a high- esolu ion colo sc een. These pa s will now be desc ibed. A. Cylind ical A ay The a ay is o med by 64 wa eguides wo king in he usual TE,, mode opened on a cylind ical E-plane expo- nen ial ape . The ape shape was op imized in o de o concen a e he ields h ough he cu o he body ex- plo ed. The elec ic ield pola iza ion is pa allel o he axis o he a ay. The diame e o he a ay is 25 cm bu owing o he ape he use ul diame e is educed o 20 cm. The a ay is ully imme sed in dis illed wa e ha ing a complex pe mi i i y o E = 77- j9 a 2.45 GHz and oom empe a u e; his medium is used o ma ch he high pe mi i i y alues o biological ma e ials. The wa e- leng h a his equency in wa e is a ound 14 mm; in his way he wa eguides dimensions a e compa able o hose used a K band in ai . Wi h he E plane designed, he ield dis ibu ion along he axis o he a ay p oduced by an emi ing elemen has a wid h o 6 cm measu ed be ween -3 dB poin s, which co esponds o he hickness o he slice o he body which is ac ually explo ed. B. Dis ibu ion Ne wo k An an enna can be used as an emi e o a ecei e , making i possible o use a unique a ay as emi e and ecei e . A comple e sca e ing measu emen would in- ol e add essing sequen ially e e y an enna o he a ay as emi e and hen measu ing he sca e ed ields on all he emaining elemen s o he a ay, as depic ed in Fig. 2. When he body o be imaged is placed in he cen e o he a ay, he ield ecei ed can be conside ed he supe posi- ion o he inciden ield which would be measu ed wi h- ou he body, plus he sca e ed ield. The sca e ed ield is p oduced by he equi alen o induced cu en s in he body and o ms he usual inpu da a o he econs uc ion algo i hms. The sca e ed ield mus be ob ained by sub- ac ing he inciden ield measu ed wi hou he body om he o al ield measu ed once he body has been placed in he measu emen egion. Because o he high a enua ion o mic owa es when p opaga ing h ough wa- e and biological ma e ials (a enua ions in excess o 100 dB a e usual), one soon ealizes he di icul y o pe o m- ing a comple e measu emen . Fi s , he sca e ed ield ecei ed by he elemen s close o he ansmi ing an- enna would be so weak compa ed wi h he inciden ield ha he o al and inciden ields will be almos equal, equi ing an imp ac ical dynamic ange o ob ain use ul da a. Ano he p oblem a ises in conside ing he isola ion o he a ay mul iplexe necessa y o a oid in e e ence be ween he high-le el ansmi ing and weak ecei ing signal pa hs. These p oblems ha e been sol ed by di iding he a ay in o se e al highly isola ed sec ions ha a e add essed globally as ansmi e o ecei e . In ou case he a ay has been di ided in o ou sec ions o 16 ele- men s each. In o de o use he same con igu a ion o ecei ing elemen s pe iew, independen ly o which posi- ion akes he emi e elemen in each sec ion, only he hal a ay opposed o he emi e is used as he ecei e . Nume ical simula ions ha e shown ha usually he sca - e ed ield is mainly di ec ed in ansmission; mo eo e he e lec ed sca e ed ields a e e y di icul o measu e by sub ac ion be ween he s ong o al and inciden ields. The 1 o 16 mul iplexe o each sec ion consis s o a bina y ee o SPDT diode swi ches. The connec ion be ween he a ay sec ion po s and he ansmi e and ecei e is made by means o a swi ching ma ix, howe e , he leakage be ween ansmi ing and ecei ing sec ions equi es nonp ac ical isola ions o he swi ches in ol ed. Thus, addi ional ways o inc easing he isola ion mus be adop ed. In his case he p oblem has been sol ed using low- equency modula ion o dis inguish he use ul signals om in e e ence. A double low- equency ampli ude modula ion is used nea he ansmi e and ecei e an ennas. The de ec ion o he ecei ed signal is syn- ch onous wi h a clock unning a he sum equency o he ansmi e and ecei e modula o s; in his way only he signals modula ed in ansmission and ecep ion a e co - ela ed wi h he de ec o clock and gi e a nonze o ou pu . This p ocedu e a oids, o example, di ec in e e ence be ween he emi e and ecei e . A low-noise ampli ie has been included in he ecei ing pa h in o de o ob ain a noise igu e a he ecei e o 3 dB. C. Mic owa e Emi e - Recei e The emi e consis s o an oscilla o phase-locked o a subha monic s able e e ence, ollowed by a powe ampli- ie deli e ing 1 W o CW signal a 2.45 GHz. The I BROUUETAS e 01.: CYLINDRICAL GEOMETRY 839 maximum inciden powe densi y in he measu emen egion o he a ay is less han 0.1 mW/cm2, which is well below he ecommended ANSI s anda d [18] limi o con inuous exposu e (5 mW/cm* a 2.45 GHz). The e- cei e uses a cohe en homodyne I/Q de ec o . A di ec- ional couple inse ed in he ansmi e pa h p o ides he LO e e ence signal o he de ec o . The in-phase and quad a u e ou pu s con ain a dc componen , as a consequence o de ec o bias and con inuous wa e in e - e ence, and low- equency modula ed signals. The de- si ed signals a e ex ac ed wi h a pai o synch onous de ec o s, p o iding a high sensi i i y o he sys em. The dc ou pu s o he de ec o s a e sampled by wo 13 bi A/D con e e s wi h an in eg a ion ime o app oxi- ma ely 1 ms. This means ha he basic dynamic ange o he sys em is 78 dB; howe e his igu e can be inc eased by da a a e aging i necessa y. D. Acquisi ion and Calib a ion The sys em is con olled by a 32 bi wo ks a ion (HP9000-320) using a pa allel inpu /ou pu bus and con en ional logic ci cui y. The acquisi ion consis s in add essing all possible pai s o sec o s, one ac ing as ansmi e and he o he as ecei e . Fo each pai he indi idual elemen s a e add essed in such a way ha o each emi ing elemen he o al ield is measu ed wi h he opposi e hal a ay. A ield da a se is a ma ix o 64x64 elemen s whe e he columns a e he ansmi ing ele- men s and he ows he ecei e s; only 2112 poin s con- ain sca e ing da a because he e lec ed ields a e no measu ed. The acquisi ion ime o he sys em is 3 s; da a a e aging makes i possible o inc ease he sys em sensi- i i y a he expense o longe measu emen imes. As poin ed ou be o e, he sca e ed ields a e ob ained by sub ac ion be ween o al and inciden ields, so s abil- i y and epea ibili y a e c ucial in he ope a ion o he sys em. Ano he impo an aspec when conside ing mea- su emen sys ems is p o iding an adequa e means o calib a ion, which has been a key ac o in mic owa e ins umen a ion. To calib a e he sys em, an objec wi h p edic able sca e ing cha ac e is ics is measu ed and hen he necessa y co ec ion coe icien s o each emi e - ecei e couple o elemen s a e ob ained by di iding he heo e ical measu emen by he ac ual one. A 4-cm-diam- e e me allic cylinde is used o his pu pose; he diame- e has been chosen as a comp omise be ween sca e ing ampli ude and ela i e la ness along he ecei ing ele- men s. IV. IMAGING ALGORITHM Unlike X ays, mic owa e adia ion has a wa eleng h compa able o he size o he objec ; hus e ac ion and di ac ion canno be neglec ed and di ac ion imaging algo i hms mus be used. In a cylind ical a ay he ield p oduced by each elemen will be app oxima ely a cylin- d ical wa e eme ging om he an enna i he ield ene gy is assumed o be con ined o he hickness o he a ay. Fo each emi e he'sca e ed ield will be measu ed on o he elemen s o he a ay, yielding a ma ix E,(cp,,cp,), whe e cp, is he angula posi ion o he ecei e elemen and cp, he angula posi ion o he emi e , as shown in Fig. 2. Using an elec ic ield pola ized axially and neglec ing depola iza ion e ec s in he body, we can use an app oxi- ma e scala ep esen a ion o cu en s and elec ic ield [ 161. Con en ional algo i hms a e based on linea geome- ies o measu emen and make use o i s -o de app oxi- ma ions, which means ha he body is assumed o pe u - ba e sligh ly he inciden ield. Illumina ing he body wi h a plane wa e, he plane wa e angula spec um o he sca e ed ield con ains he spec um o he dielec ic con as o he objec along ci cles o adius k, ( he wa enumbe o he ield in he embedding e e ence medium) [16]. The dielec ic con as C(7) is he ela i e di e ence be ween he complex pe mi i i y o each poin o he body 47) and he e e ence pe mi i i y E, co e- sponding o he embedding medium: C(J) = 1 - E(~)/E,. In ou case he geome y o measu emen is cylind ical and a simila algo i hm can be ob ained based on Hankel ans o ms; howe e his algo i hm is di icul o imple- men on a digi al compu e and e y ine icien because o he la ge numbe o Bessel unc ions in ol ed. A much mo e e icien algo i hm can be ob ained by using a syn he ic app oach o o m plane wa es as a combina ion o cylind ical wa es. Fi s , gi en he linea i y o he sca e ing, we can syn- hesize a plane wa e illumina ion in an a bi a y di ec ion by combining he measu emen s o he di e en emi e s weigh ed by he cu en dis ibu ion on he a ay ha would p oduce his plane wa e illumina ion: J 0 whe e J,(cp,; e^,> a e he cu en s on he a ay pcoducing a plane wa e in he di ec ion o he uni ec o 0,. On he o he hand, using he ecip oci y heo em, he Fou ie spec um o he induced cu en s J(7) in he dielec ic can be ob ained by weigh ing he measu emen s on he a ay a again by he cu en dis ibu ion ha would p ocuce a plane wa e in he di ec ion o he uni ec o - 0 in he egion s occupied by he body [19]: whe e R is he adius o he a ay. Assuming he sca e - ing o be su icien ly low o app oxima e he o al ield wi hin he body by he inciden ield (Bo n app oxima- ion), we can exp ess he induced cu en s in he dielec- ic as a p oduc o he dielec ic con as and he inci- den ield E,. In a lossless e e epce medium ( eal k,), his p oduc implies a shi o k,,0, be ween he spec al I I 840 IEEE TRANSAnIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 39, NO. 5, MAY 1991 -180’ 180’ Fig. 3. Phase o a syn he ically gene a ed plane wa e om cylind ical wa es eme ging om he elemen s o he a ay. domains o cu en and con as : is he bidimensional Fou ie ans o m o he dielec ic con as C(3. Combining (0, (2), and (3), we ob ain inally he spec al domain o C(<) o? ci cula a cs o adius k, wi h coo dina es = k,(8 - 8”): *J,((Po,; e^,)R2 dcp, &e. (5) A simila exp ession was de i ed p e iously by De aney and Beylkin o a bi a y geome ies using a di e en app oach [20]. Equa ion (5) is o mally a double con olu- ion o he measu ed sca e ed ields E, wi h he cu en s on he a ay J, ha would p oduce a plane wa e illumi- na ion. The con olu ion can be e icien ly calcula ed us- ing FFT echniques as a double p oduc in he spec al domain be ween he Fou ie se ies o E, and J as de- sc ibed in [19]. Fig. 3 shows he supe posi ion o cylind i- cal wa es weigh ed by he coe icien s J,(cp). Only he phase o he esul ing plane wa e in he measu emen egion is shown o simplici y. Because o wa e a enua- ion, he ampli ude decays exponen ially. The image is ob aine: by jn e se bidimensional Fou ie ans o m once C[k,(8-8,)] has been mapped on a ec angula g id by bilinea in e pola ion in a way simila TABLE I S s em Pa ame e s F equency Powe densi y Use ul diame e Da a acquisi ion ime Recons uc ion ime Image - SDa ial esolu ion Con as esolu ion Tempe a u e esolu ion (in wa e ) 2.45 GHz < 0.1 mW/cm 20 cm 3s 31 s on HP320 8 mm 1% 0.YC o ha in linea algo i hms [16]. The econs uc ion ime is 30 s on a HP9000-320 wo ks a ion. Un o una ely he high dielec ic con as o biological bodies o en causes he b eakdown o he Bo n app oxi- ma ion [91, [16]. This depends on bo h he size and he con as o he objec . I has been ound bo h nume ically and expe imen ally ha some biological bodies wi h sec- ions o a ew wa eleng hs can be econs uc ed, e ealing quali a i ely hei in e nal s uc u e. When he size is la ge , i is s ill possible o ge use ul di e en ial econ- s uc ions showing dielec ic changes, as desc ibed in he nex sec ion. Al hough as shown in (2) he spec um o he induced cu en s can be ob ained om he sca e ed ields wi hou app oxima ions, i mus be poin ed ou ha he cu en s a e di e en o each inciden ield and a knowledge o only an a c o a wo-dimensional spec um is no enough o p oduce a ep esen a i e image o he cu en s. Fo his eason i is necessa y o map app oxi- ma ely he cu en s in o he body con as , illing i s 2-D spec um, which is in a ian wi h he inciden ield. Ano he sou ce o e o a ises because o he losses o he e e ence ma e ial (wa e ). The algo i hm desc ibed accoun s o he losses excep in he las s ep, when he image is ob ained by Fou ie in e sion o i s spec al domain using FFT unde he assump ion o a uni o m inciden ield E,. Wi h a lossy medium, E, is a enua ed; consequen ly we ha e access o he Laplace spec um o he dielec ic con as [21]. I has been s a ed by simula- ions ha his low-loss app oxima ion does no cause s ong e o s i he losses in he body a e no signi ican ly di e en om hose in he e e ence medium. Table I summa izes he main cha ac e is ics o he sys em de el- oped and he imaging algo i hm. V. RESULTS One o he ad an ages o he calib a ion me hod p e- sen ed is he possibili y o ob aining an absolu e calib a- ion o he sys em and hus being able o econs uc quan i a i ely he ac ual pe mi i i y dis ibu ion o bod- ies. To es his possibili y, a low-con as gel cylinde was measu ed and econs uc ed. Fig. 4 shows he image o complex pe mi i i y in eal/imagina y pa in a linea g ay scale. Compa ing he image alues wi h he ac ual gel pe mi i i y eg = 68- j16, he imagina y pa is well econs uc ed and he eal pa is co ec ly econs uc ed in he ex e nal laye o he cylinde . Wi h he p esen BROQUETAS e al.: CYLINDRICAL GEOMETRY 84 1 70 78 71 72 73 73 74 75 76 76 77 78 79 79 80 -19 -17 -15 -13 -12 -9.0 % -6.2 REAL I MAG Fig. 4. Quan i a i e image o complex pe mi i i y in eal/imagina y pa o a homogeneous gel od wi h pe mi i i y cs = 68- j16. algo i hm, his is possible only wi h weak sca e ing ob- jec s. The expe imen al esolu ion o he sys em has been ob ained by econs uc ing wo close hin me allic ods. The objec s ha e been ound sepa able a a minimum dis ance o 8 mm. This alue is close o he heo e ical hal -wa eleng h di ac ion limi (7 mm). Wi h high-con as biological bodies mul iple sca e ing appea s and he inciden ield is a wo se app oxima ion o he o al ield in he body; howe e he algo i hm desc ibed s ill co ec ly econs uc s small sec ion bodies. Fig. 5 shows a omog aphic image o dielec ic con as ampli ude co esponding o he inge s o a human hand. Fig. 6 is he diag am o a simpli ied a m phan om and i s econs uc ion (imagina y pa o pe mi i i y). Al hough he image is quali a i e, which means ha he econ- s uc ed dielec ic alues a e no co ec , he s uc u e o he objec is success ully isualized. Fig. 7 is he econ- s uc ion o a human o ea m in cico. The imagina y pa o he pe mi i i y shows he ou e skin and a laye s, he bones adius and ulna, and some less well de ined de ails in he muscula egion wi h a much highe dielec ic cons an . This esul shows ha i is possible o isualize high-con as bodies which all ou side he egion o alid- i y o he Bo n app oxima ion. The acquisi ion speed o he sys em makes i possible o moni o unc ional changes in a body. Fo his pu pose di e en ial images a e o med by p ocessing he di e - ence in o al ields p oduced by a e e ence and al e ed bodies. Fig. 8 shows a di e en ial image o dielec ic con as ampli ude co esponding o a blood con en al- e a ion in a human a m when a ou nique is applied [22]. This expe imen shows he po en ial applica ion Fig. 5. Tomog aphic image o he inge s o a human hand. o mic owa e imaging echniques o he moni o ing o changes in ol ing pe mi i i y al e a ions such as i - iga ion. Wa e pe mi i i y exhibi s a high sensi i i y o empe a u e (-0.5%/"C in eal pa and -2%/"C in imagina y pa ), making i possible o o m images o empe a u e changes in bodies. The empe a u e esolu- ion was ound expe imen ally o ming di e en ial images o a hin, 3-cm-diame e plas ic ube illed wi h empe a- u e con olled wa e [22]. The minimum de ec able change was 0.5"C, which co esponds o a con as esolu- ion o app oxima ely 1%. This sensi i i y is expec ed o I 842 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 3Y, NO. 5, MAY 1991 Fig. 6. Diag am o a simpli ied a m phan om and i s econs uc ion. Fig. 8. Di e en ial image co esponding o a blood con en al e a ion in he a m shown in Fig. 7 when a ou nique is applied. Fig. 7. Recons uc ion o a human o ea m in .ic,o. de e io a e in biological media because o hei highe con as and losses. Mo eo e he ac ual he mal sensi i - i y o pe mi i i y is expec ed o depend on he cons i u- i e ma e ials o he issue and possible he mo egula o y mechanisms wi h impac on pe mi i i y, such as blood low a ia ions. Fu he esea ch is needed o e alua e he ac ual he mal sensi i i ies in his applica ion. Di e en ial echniques can be applied o la ge bodies when absolu e images do no show hei in e nal ea u es owing o he b eakdown o i s -o de app oxima ions [23]. Fig. 9 shows he di e en ial econs uc ion o a human head phan om when a whi e ma e equi alen medium wi h pe mi i i y E = 49 - j18.5 (close o da a epo ed in [3]) is eplaced wi h wa e wi h a highe pe mi i i y. The image o he eal pa o he dielec ic con as shows well he change, al hough he absolu e image shows only he con ou o he phan om because o i s size and high con as . A highe sensi i i y would be necessa y o isualize small pe mi i i y changes ha could be ela ed o ce eb al ac i i y. VI. CONCLUSIONS A cylind ical sys em o ac i e mic owa e omog aphy has been cons uc ed and e alua ed. The sys em allows a 64 iew scan in 3 s using mic owa e mul iplexe s. The hickness o he explo ed cu o he objec is 6 cm wide; his alue could be possibly educed using a lens o ocus he ene gy in he a ay plane. The elec omagne ic com- pa ibili y o he sys em is c i ical, and he desi ed signal has been isola ed om he in e e ence by subdi iding he a ay and using a double low- equency synch onous de ec ion. BROQUETAS e al.: CYLINDRICAL GEOMETRY 843 Fig. 9. Di e en ial econs uc ion o a human head phan om when a whi e ma e equi alen medium is subs i u ed by wa e wi h highe pe mi i i y. The imaging algo i hm is based on he syn hesis o plane wa es and can be e icien ly implemen ed on a compu e . The algo i hm is based on a bidimensional scala o mula ion o he ields, weak sca e ing, and low-loss app oxima ions. An absolu e calib a ion p oce- du e has been de eloped which allows quan i a i e imag- ing o weak sca e ing bodies. High con as bodies can be quali a i ely imaged p o iding hei size is below i e o six wa eleng hs. New algo i hms mo e adap ed o he high dielec ic con as o biological bodies would make i possible o o e come his limi a ion. Di e en ial imaging is able o econs uc dielec ic changes in he body, e en i elec ically la ge, by p ocessing he a ia ions measu ed in he o al o sca e ed ields. Some expe imen al esul s wi h phan oms and bodies in uii’o ha e shown he capabil- i y o mic owa e omog aphy o image he dielec ic s uc- u e o unc ional changes o biological bodies. Compa ed wi h o he con en ional imaging me hods, mic owa e omog aphy has se e al ad an ages. Fi s , he adia ion is nonionizing and can be conside ed i ually sa e using low-powe illumina ion. P esen acquisi ion imes o he o de o a ew seconds could be educed in he u u e, making i possible o pe o m dynamic s udies o issue mo emen s as in he hea , join s, blood essels, e c., o o isualize dielec ic changes caused by physiolog- ical and biochemical al e a ions. Finally, he high cos and en i onmen al cons ain s imposed by magne ic eso- nance imaging, X- ay CT, and posi on emission omog a- phy sys ems limi hei clinical a ailabili y. Mic owa e sys ems ha e a lowe cos and can be compa ible wi h o he clinical equipmen . These ad an ages a e expec ed o play an impo an ole in he u u e de elopmen and clinical accep ance o his echnique. Al hough he sys em has been concei ed o biomedical applica ions a 2.45 GHz, i could be easily adap ed o indus ial o nondes uc i e- es ing (NDT) pu poses scal- ing he dimensions and equency, depending on he sizes and dielec ic cha ac e is ics o he objec s. ACKNOWLEDGMENT The au ho s a e g ea ly indeb ed o E. de 10s Reyes, M. Fe ando, M. Baque o, M. Hawley, and H. Almi all o hei con ibu ions and help ul discussions. Special hanks go o A. Cano, J. Gine , and J. M. Ha o o hei suppo in he cons uc i e aspec s o he p o o ype. REFERENCES [l] D. C. Ba be , B. H. B own. and I. L. F ees on, “Imaging spa ial dis ibu ions o esis i i y using applied po en ial omog aphy,” Elec on. Le ., ol. 19, no. 22, pp, 933-934. 1983. [2] L. E. La sen e al., Eds., Medical Applica ions o Mic owa ,e Imag- ing. New Yo k: IEEE P ess, 1986, pp. 148-166. [31 M. A. S uchly and S. S. S uchly. “Dielec ic p ope ies o biological subs ances-Tabula ed,” J. Mic owa ,e Powe , ol. 15, no. 1, pp. 19-25, 1980. [4] H. P. Schwan. “Elec ical p ope ies o issue and cell suspensions,” Ad[.. Biol. and Med. Phps., ol. 5, pp. 147-209, 1957. [51 L. E. La sen and J. H. Jacobi, “Mic owa e sca e ing pa ame e image y o an isola ed canine kidney,” Med. Phys., ol. 6. no. 5, pp. 394-403, Sep ./Oc . 1979. [6] G. Pe onne . Ch. Picho , J. Ch. Bolomey, and L. 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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL 39, NO 5, MAY 1991 X44 ion o biological a ge s," in Medic l App/ p[ cci iom o ' Mic w .e Imzg ig. L. E. La sen and J. H. Jacobi, Eds. New Yo k: IEEE P ess. 1986, pp. 148-166. [I21 L. Jo e e U/.. "A cylind ical sys em o quasi- eal- ime mic owa e omog aphy." in P oc. 16 h Eu opeu z Mic owu e Con . (Dublin). [13] S. X. Pan and A. C. Kak, "A compu a ional s udy o econs uc ion algo i hms o di ac ion omog aphy: In e pola ion e sus il e ed backp opaga ion," IEEE T ans. Acous ics, Speech, Signal P ocess. [14] D. K. Ghodgaonka , 0. P. Ghandhi, and M. J. Hagmann. "Es ima- ions o complex pe mi i i ies o h ee-dimensional inhomogeneous bodies," IEEE T ans. b4ic owu .e Th ow Tech.. ol. MTT-31, PP. Sep . 1986, pp. 599-604. ol. ASSP-31. pp. 1962-1275, Oc . 1983. .. 142-446. June 1983. R. K. Muelle , M. Ka eh, and G. Wade, "Recons uc i e omog a- phy and applica ion o ul asonics." P oc. IEEE, ol. 67. pp. 567-587. Ap . 1979. M. Slaney and A. C. Kak, "Imaging wi h di ac ion omog aphy." Pu due Uni e si y, School o Elec . Eng., Tech. Rep. TR-EE 85-5. 1985. J. W. Goodman, I i duc ion o Fou ie Op ics. New Yo k: Mc- G aw-Hill. 1968. Ame ican Na ional S anda ds Ins i u e ANSI C95.1- 1982 "Sa e y le els wi h espec o human exposu e o adio equency elec o- magne ic ields, 300 kHz o 100 GHz." IEEE. New Yo k, NY. 1001 7. J. M. Rius. M. Fe ando. L. Jo e. and A. B oque as. "Mic owa e omog aphy: An algo i hm o cylind ical geome ies." Elec on. Le .. ol. 23, no. 11. pp. 564-565. 1987. A. J. De aney and G. Beylkin. "Di ac ion omog aphy using a bi a y emi e and ecei e su aces." Lil uson. Imaging. no. 6. pp. 181-193. 1984. M. Azimi and A. C. Kak. "Mul iple sca e ing and a enua ion phenomena in di ac ion imaging," Pu due Uni .. School o Elec . Eng., Tech. Rep. TR-EE 85-4. 1985. L. Jo e e U/., "Medical imaging wi h a mic owa e omog aphic scanne ," IEEE T am. Bio ned. Eng,. ol. BME-37. pp. 303-312. Ma . 1990. A. B oque as e U/., "Tempe a u e and pe mi i i y measu emen s using a cylind ical mic owa e imaging sys em." in ' oc. 17 h Eu o- pea ? Mic wu .e C 7 ., (Rome). 1987, pp. 892-895. ol ed in p opaga ioi U.P.C.. whe e he is ada . n An oni B oque as (S'81-M'90) was bo n in Ba celona. Spain. in 1959. He ecei ed he Inge- nie o deg ee in elecommunica ion enginee ing om he Uni e si a Poli 6cnica de Ca alunya (U.P.C.) in 1985. and he Doc o Ingenie o de- g ee in 1989 in elecommunica ion enginee ing o his wo k in mic owa e omog aphy. In 1984 he joined he Elec ophysics g oup o he U.P.C. wo king in mic owa e sys ems and digi al adio links. In 1986 he was a esea ch assis an a Po smou h Poly echnic (U.K.) in- s udies. Cu en ly he is Associa e P o esso a :ngaged in esea ch on mic owa e imaging and Jo di Romeu (S'XX) was bo n in Ba celona, Spain. in 1962. He ecei ed he Ingenie o de- g ee in elecommunica ion enginee ing in 1986 om he Uni e si a Poli kcnica de Ca alunya. In 1985 he joined he An enna-Mic owa e- Rada g oup o he Signal Theo y and Commu- nica ions Depa men he e. His esea ch deals wi h mic owa e imaging, an enna nea ield measu emen s. and an enna diagnos ic a eas. Juan M. Rius (S'89) wds bo n in Ba celona. Spain. in 1963 IIe ecei ed he Ingenie o de- g ee in elecommunicd ion enginee ing om he Uni e sidad Poli 6cnica de Ca alunya (U P C ) in 1987 In 1985 he joined he Elec ophysics g oup a U P C wo king on cylind ical geome y algo- i hms o mic owd e omog aphy. Cu en ly he 15 Associa e P o esw d he Telecommunica- ion Enginee ing School o UP C. and is in- ol ed in elec omagne ic xa e ing echniques o ddd c oss sec ion nume icdl p edic ion An onio R. Elias-Fus e (S'81-M'82) wa5 bo n in Ce e a. Spain, in 1954. He ecei ed he Inge- nie o and Doc o Ingenie o deg ees in elecom- munica ion enginee ing, bo h om he Uni e si- a Poli &cnica de Ca alunya (U.P.C.), in 1978 and 1982. espec i ely. In 1976 he joined he An enas-Mic oondas- Rada G oup o he Depa men o Signal The- o y and Communica ions o he Escuela Ticnica Supe io de Ingenie os de Telecomunicaci6n de Ba celona. whe e his wo k deal wi h mic owa e cha ac e iza ion and RF sys ems design. He became Associa e P o esso in 1985 and P o esso in 1990 a U.P.C., engaged in esea ch in he ield o ada . He is au ho and coau ho o se e al epo s o indus y and o pape s published in echnical jou nals and con e ence p oceedings. D . Elias-Fu C is an AOC membe . Cu en ly, he is Chai man o he AES Spanish Chap e . Angel Ca dama (S'67-M'73) was bo n in San i- ago. Spain, on May 13, 1944. He ecei ed he lngenie o de Telecomunicaci6n deg ee om he Uni e sidad Poli Ccnica de Mad id, Mad id, Spain. in 1968. and he Sc.M. and Ph.D. deg ees in elec ical enginee ing om B own Uni e si y, P o idence, RI, in 1970 and 1973, espec i ely. In 1972 he joined he acul y o he E.T.S.I. de Telecomunicacibn a he Poly echnic Uni e - si y o Ca alonia. Ba celona, Spain, whe e he holds he posi ion o P o esso . His esea ch in e es s ange om p opaga ion in op ical ibe s, high equency ape - u e and a ay an ennas, and nea - ield an enna scanning sys ems o he design o mic owa e imaging sys ems and ada an ennas. Luis Jo e (S'79-M'83) was bo n in Ma a 6. Spain. in 1956. He ecei ed he Ingenie o and Doc o lngenie o deg ees in elecommunica ion enginee ing, bo h om he Uni e si a Poli knica de Ca alunya (U.P.C.) in 1978 and 1982. espec i ely. In 1978 he was a Resea ch Assis an in he Elec ophysics g oup a U.P.C., whe e he wo ked on he analysis and nea - ield measu emen o an ennas. In 1981 he joined he Ecole Sup ieu e d'Elec ici 6 in Pa is, whe e he was in ol ed in mic owa e imaging echniques o biomedical applica ions. Du ing he pe iod 1986-1987 he was a Visi ing Fulb igh Schola a he Geo gia Ins i u e o Technology, A lan a, wo king on an enna measu e- men and elec omagne ic imaging. He is cu en ly P o esso and Di ec- o o he Telecommunica ion Enginee ing School a U.P.C., whe e he is engaged in esea ch on an ennas and elec omagne ic sca e ing and imaging, bo h nume ical and expe imen al aspec s.