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.
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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.