IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCYCONTROL,

VOL. 39. NO. 5 , SEPTEMBER 1992

643

Microdefocusing Method for Measuring Acoustic
Properties Using Acoustic Microscope
Hiroshi Kanai, Member, IEEE, Noriyoshi Chubachi, Member, IEEE, and Toshio Sannomiya

phase velocity and the propagation attenuation of the LSAW
Az
componentaredeterminedfromtheinterferenceperiod
andthe slope of the V ( z ) curve,respectively.
For fused-quartz and other samples, the interference period
Az is several times as long as the wave length X, in water. In
order to detect the interference period Az from the V ( z ) curve[S] such as the fast Fourier
based on the periodicity analysis
transform (FFT) and to determine the slope r/ of the lnIV(z)lcurve [7], [9], [lo], it is necessary to measure the V ( z )curve
for a period several times as long as the interference period
L I Z , that is, themaximumwidth
A B of thebeamspot on asample must be several tensof times the wavelength X, ofthelongitudinalwave
in thewater.Therefore,
it isdifficult
to measuretheacousticpropertiesof asamplewithhighresolution by these present acoustic microscope systems. Whenof asample is largeand/orthe
thepropagationattenuation
velocity value of the LSAW is large, sufficient defocus distancefor the periodicity analysis is not available and then it is also
I. INTRODUCTION
difficult to measure the acoustic properties.
HIS PAPERpresentsanewmethodtoobtainacoustic
Therefore, we have proposed anew method to determine theV(.) valuesmeapropertiesofasamplebyanalyzing
acoustic properties of a sample from theV ( z )values measured
an in themicrodefocusingregionnearafocalpoint
sured in the microdefocusing region near a focal point in[ll]. We
acoustic microscope. Since the mechanically scanning acoustic havealsoproposedanew-typeof ultrasonictransducer,themicroscope (SAM) was first developed by C. F. Quate et al. butterfly transducer, in whichtheelectrodeis dividedinto[l], many papershave beenpublished on acousticmeasuretwo parts. The principle of the microdefocusing method was[ 2 ] . Angular preliminarily described in [ll].This paper describes the prinmentandimagingusingacousticmicroscopy
spectrum approaches were developed to derive an expression ciple in detail and develops a new signal processing method
forthecontrastmechanismin theimaging of thereflection
to analyze the two outputs of the electrodes in thebutterfly[3]. The transducer.Byanalyzingthetwooutputcomponents,bothacousticmicroscopeusingthereflectionfunction
V ( z ) curve, which is the transducer output recorded against
components \ ' ~ ( z ) and VI(^) areobtainedseparately.Froma distance z from thefocal point, has many peaks and dips
the resultant components, the acoustic propertiesof a sample
generated due to the interference of a leaky surface acoustic are determined without any periodicity analysis and without
wave (LSAW) component VI(.) and a wave component I f ~ ( z ) measuring the temperature that is generally difficult to obtainreflectedperpendicularly to thesurface.Theperiodicityof accurately.
the dips appearing in the V ( z ) curves was analyzed by R.D.
Weglein [4]. The models describing the relationship betweenAz) and Rayleigh wave
the dip interval (interference period
11. CURRENT v ( z ) ANALYSISAND ITS PROBLEMS
velocity were presented by Parmon et al. [ 5 ] using a ray modelLet
usconsiderthesimplest
caseof oneLSAW mode.
and by A. Atalar [6] using the angular spectrum approach [3].
a
When
the
sampleisbrought
close
to
the
acoustic
lens byBased on these pioneering works, many acoustic microscopic
distancez(z<U) from the focal plane, the transducer output
methods and systems for analyzing the V ( z )curves have beenof V ( z ) detected at the ultrasonic transducer is dominated bydeveloped in the fields of acoustical imaging and quantitativein Fig. 1; onecomponent V L ( ~ )[7]. In aconventionalmethod,
the twocomponentsasshown
measurementssuchas
is the transducer output due to the acoustic wave propagating
ManuscriptreceivedOctober 15, 1991; revised and acceptedJanuary 27, along path (#O) normallyreflectedfromthesurfaceof the1992.
sample, and the other component V I ( Z ) is the transducer output
Theauthorsarewith
the Department of ElectricalEngineering, Tohoku(#l)due toassociated with the waves propagating along path
University, Aramaki-aza-Aoba. Sendai, 980 Japan.
IEEE Log Number 9200693.
the LSAW component propagating on the boundary. Thus, theAbstract-Many papers have been reporting on measurementof acoustic properties of materials by acoustic microscopy. In a
conventional method of l.( :) curve analysis, the phase velocity
and the propagation attenuation of a leaky surface acoustic wave
(LSAW) are determined from the interference period 1: andthe slope of the 1 -(L ) curve, respectively. For this method it
is necessary to measure the I-(: ) curve fora period several
times as long as the interference period 1 2 . Therefore, it isdifficult to measure the acoustic properties of a sample with highresolution bythe method.In order to overcome these problems,
a new method called the microdefocusingmethod is proposed,
to determine the acoustic properties of a sample by analyzing
l * c( ) values measured inthe
microdefocusing region within
an interference period 11near a focal plane. A new-typeof
ultrasonic transducer called the buttefiy transducer is proposed
to be applied to this microdefocusing method and a digital
signal processing procedure is developed to analyze the outputof the ultrasonic transducer. Basic experiments are performed toconfirm the principles of the new method.

T

088.5-3010/92$03.00 0 1992IEEE

h34

IEEE TRANSAWIONS ON ULTRASONICS, FERROELEaRICS. ANDFREQVENCYCONTROL,VOL.
VL(.)- - -39, NO. 5, SEPTEMBER 1992

- -- --(a)Fig. 1.

Cross-sectionalgeometry of acousticpoint-focus-beam lens, which
2 ) curves.
explains the construction mechanism of l.(

DEFOCUS DISTANCE(c)transducer output V ( z ) is represented byV(z) = VI(2)+VL(Z).

(1)

Let us assume that V ( z ) be
sampledat theintervaljOz((6z < O), that is, z = 7 1 . 6 2 ( z < O), where n is the sample
number ( 7 1 = 0.1: 2 , . .). Based on references [S],[lo], which
use raytheoryalongpaths#O and #l in waterorontheboundary,each of thesetwocomponentsisre-expressedas
a damped complex sinusoidal:

L?(n .Dz) = CJ . p ;(2)

Fig. 2. (a) Real component of the complex I j ( z ) of (2). (h) Real component
ofthecomplex~~~~(t)of(3).(c)Amplitudecurve)1~(~)~=~~j,(~)+I

in the measured defocusing range as illustrated
in Fig. 2. By
letting the phase difference between f I/L(z) = 2 k , .S,. 71 andi V 1 ( z ) = 2ku, cos. 6z n equal 2n, theinterference
period Az isdescribedby

Az =

7r

(1- cosI9LsA\v)kw.

By re-arranging the equation using Snell’s law as written(g), the phase velocity ‘L’Ls.&\v of the LSAW is obtained as

andV L ( 7 L . 62)=

cr,.p?

(9)
in

(3)

where CL and C1 aretheassumed
complexconstantsdescribing the amplitude and phase characteristics of T/L(z) andV / ( z ) respectively,,
at the focal plane ( z = 0). The complex
quantities p 1 and T I L , which are called “poles” in the research
field of digitalspectrumestimation,aredescribedbythe
product of the amplitude term and the phase term as

v u , in waterisdetermined
where thelongitudinalvelocity
beforehandfromtherelationship[l21between ,uu, andthe
measured temperature of water.
In the present system [g], [lo], the phase velocity T I L S , ~ ~ ~of the LSAW is determined from the interference period 4 2 ,which is obtained by applying the FFT on the IV(z)l curve ofFig. 2(c). The attenuation y of the LSAW is determined fromthe slope 7) of the interference amplitude lV(z)l [7], [9], [lo],. cxp(j2k., cos HLS.A\V 6z),(4)
which is shown by a dotted line in Fig. 2(c).
p L = exp( -2a, . 6 2 ) exp(j2ku Oz).
(5)
For fused-quartz and other samples, the interference periodAz
is usuallymorethan
severalwavelengths
in water.
Thequantitiesa u , and y are
thenormalizedattenuationc ~ s . 4z~ 3400mis, 1 1 , = 1494mis,andf = 200
When
factors for the longitudinal wave in water and for the LSAW,
MHz
for
example,theinterference
period4z=36.7 pm.
4 ~therespectively. Thequantities ku,, ICLS.~IV,and 1 9 ~ s . areFromtheresultsoftheoreticalanalysis
[13].
there
is
a
large
wave number in water, the wave number of the LSAW on theamount in the estimation of the dominant frequency especiallyboundary, and the critical angle for the LSAW, respectively.
when
the FFT isappliedonthewavethathasonlyabout
Let quantity v, bethelongitudinalvelocity
in waterandin order to detecttheinterferenceone
signalperiod.Thus,‘ t l ~ s be
~ the
\ ~ phase velocity of the LSAW. Thentoperiod AZ for the lV(z)l curve using the FFT as well as
2r.f
lnlV(z)I
curve,
itisnecessarydetermine
the
slope
of
the
k.ut (6)21’U,
to measurethe JV(z)l curveatadefocusrangeof several
Az.As a result, the maximum
times the interference period
width A B ofthebeam-spotcoversameasurementarea
morethanseveraltens
of timesthewavelength
in waterandto degrade the resolution. Thus,
it is difficult to measure theby theacoustic properties of a sample with a high resolution
conventional acoustic microscope system.
It is, therefore, necessary to develop an alternative method
where f is the ultrasonic frequency.
not depending on the periodicity analysisto determine acoustic
V’t(2) and L’1(2), theDue to theinterferencebetweenV ( z ) curvesmeasured inproperties of theLSAWfromthe
l afewdips
amplitudecurve J V ( z ) J= JLk(z) V ~ ( z )has’’+

KANA1 el Q[.: MICRODEFOCUSING METHOD FOR MEASURING ACOUSTIC PROPERTIES USING ACOUSTIC MICROSCOPE

the microdefocusing range. Such amethod
Section 111.

64.5

is described in

111. PRINCIPLE OF MICRODEFOCUSING METHOD

iV~(z)
From(2)and (3), each of thephasecomponents) the natural-logarithmic amplitude components
and i V ~ ( zandlnlVI(z)l and ln(VL(z)l varieson the straight line as illustrated
in Fig. 3. Let their gradients be defined as
def
€1 =

a

- L VI(.)

dz= Zk, cos OLS.&\V(11)

DEFOCUS DISTANCE
z = n.62
( b)

rlL

def

a

= -lnlVL(z)l8z= -20,.

(14)

Using (8) and (6), thephasevelocity
ULS.&\~ of theLSAW
component is obtained from the gradient EI of (11) by"LS.4W =-v,

J1 - cos2 I9LS*Tt.

4

A

(15)

DEFOCUSDISTANCEd+

1 - ( ~ ~ ~ 1 4 .r f )Thus, if Vr(z) is obtainedseparatelyfrom
V ( z ) in thedefocusingregion that is sufficient to measure the gradient €1of i V ~ ( z )the, phasevelocity VLSAM; of theLSAWcanbe€1 into (15), where
determined by substitutingthegradient,in water is obtained from either
the longitudinal velocity v
v, [l21 orfromthe
therelationbetweentemperatureandmeasured gradient € L of L V L ( Z ) in (12) by the relationz = n.62(d 1
Fig. 3. The phase components LIT,(z ) and L1 1.( z ) and the amplitude
components hllli( :)I and 1 1 1 ~ 1 ~ ~ . ( ~ ) ~are determined as follows. Let
R denote the distance of thepath (#l) from the z-axis as shownin Figs. 4 and 5(c-2). By(B) in Fig. 5(c-2),
applying Snell's law with respect to point
the following relation is obtained.

4rf'Ux, = €L

In the case where the velocity t i u , in water is determined fromthe measured gradient <L, it is not necessary to measure thetemperature of water, which in general is difficult to determine
precisely.
y fortheLSAW
is
Thenormalizedattenuationfactor
determined from the gradient 71 of lnlVI(z)l by using either~[l41 or the measured
the relation cr,/f2 = 2 5 . 3 10-17s2/cn1= -2a, in (14). Therefore,
both
the
phase
gradient
velocity and the attenuation properties of the LSAW componentcanbe obtained from the V ( z ) curves measured in the
microdefocusing region without relyingon periodicity analysis
FFT, if thetwocomplexcomponents
methodssuchasthe
VI(.) and VL ( 2 ) are obtained separately.

71sForthepurposeof obtaining the two components VL( 2 )and Vl(z)separately,anewtype of transducer,whichwe
called a butterfly transducer, is introduced into a conventional
point-focus-beam(PFB)lenstransducersystemasshown
inFig. 4. The transducer is actually composed of three individualofpartsandisdividedintoacentertransducerandapair
surrounding transducers. The radiusa of the center partand theinner radius b and the outer radius c of the surrounding parts

Piu,

(1 7)

sin(8s - O L S A ~ ~ )where 0s is the angle between the z-axis and 0sat the centerin theof curvature (0) and us is thelongitudinalvelocity
acousticallens.Usingtherelation

tan 0s is described bytan 8s =us sin H L S A ~ ~us cos HLSA\V - U,, .

From Snell's law given in (8):tan 8s =IV. ANEW-TYPEULTRASONIC
TRANSDUCER-

sin 19s

71,.
JW- ,ll.,L,71Ls*\v/71.s(18)

Using the radius T of curvature of the PFB acoustic lens, thedistance R isdescribed by

By takingintoaccountsomemargin,theradiib and c are646

Fig. 4.

IEEETRANSACTIONSONULTRASONICS,FERROELECTRICS.ANDFREQUENCYCONTROL,

VOL. 39, NO. 5 , SEPTEMBER 1992

Cross-sectional and top views of the proposed new-type of butterfly
transducer. The electrodes are divided into two parts.

determined from the range of expected U L S ~ ~values
Vof thesamples to be measured. The radius a is determined so as tomake a ascloseaspossible
to b.
Forthestudyof anisotropicmaterials,severalexcellent
Fin theliterature
directionaltransducershavebeenproposed(d[l51 such as the bow-tie [l61 and the oblong [l71 transducers
Fig. 5. Illustrations explaining various transducers proposed in literature. (a)to obtaindirectionalimageswithhigh
inPFBmicroscopes
Electrode in the Bow-tie type transducer. (b) Electrode in the oblongtype
resolution. In the bow-tie transducer of Fig. 5(a), the effect due transducer. (c) Electrodes in the butterfly transducerandthecorresponding
to beam steering is not taken into account. In the oblong trans- paths of acoustic wave propagating through lens, in water, and on the surface
of a sample.
ducer of Fig. 5(b), the resolution for detecting directionality is
reduced for the materials with high LSAW velocity.
We proposed the butterfly-shaped transducer [l11 as shown
V. SIGNAL
PROCESSINGFOR SEPARATINGr/, (2) AND V I ( z )in Fig.5(c). In thistransducer,thecircularcenterelectrode
Since the acoustical wave propagates through the lens, wais surroundedbyapairof fan-shapedelectrodeswithan
terisample, and back to the lens in sequence, these propagation
angle U; to compose the central and the fan-shaped transducers,
paths are divided into three phases as shownin Figs. 6(a), 6(b),respectively. By considering the effects due to beam steering,and 6(c), respectively. In the first and third phases in Figs. 6(a)the centers ( 0 ' ) of the fan-shaped electrodes do not coincideand 6(c), the diffraction effect should be taken into account.
in Fig. 4, thewiththecenterof thetransducer.Asshown
L e t V o ( z ) and V,( z ) bethecomplexresponsesof theeccentric radius d is determined from the position of the point
to theinput amplitudes
centralandfan-shapedtransducers(A) where the longitudinal wave in water reaches the sample
IO and 11 and also, let the complex coefficients{ H i j ,GJZ},
at the incident angle OLS.A\~ and the LSAW starts to propagate( i = 0,1; j = L , I ) represent the transfer system due to theon the boundary withpowerflowangle@ / 2 . The eccentric
H L ( z ) and H l ( z ) in
diffraction and the complex coefficients
radius d is approximately set to be equal to the distance R in
Fig. 6(b) the transfer system due to the two components l$,(z)(19) in thispaper.
(path #0) and V j ( z )(path #l)in (2) and (3), respectively. Thus,
A RF pulse Iir, excitesboththecentraltransducerandthe output V i ( z ) and Vl(z) are described as
the pair of the fan-shaped transducers simultaneously. Thesetransducersalsoactasreceiversandpickupthe
reflected
K O ( 2 ) = (IOHOLIlHlL)HL(Z)GLO
pulses. The reflectedpulsedetectedbyeachtransducer
is
(
I
O
H
O
I IIHII)HI(~)GIO
V(z)passedthroughacirculator.Then,thetwocomplex
VI(.) = ( I O H O L I I H ~ L ) H L ( ~ ) G L I
curvesaremeasured
byapulsemodemeasurementsystem[18]. In order to apply the microdefocusing method, the two(1oHor I ~ H I I ) H I ( ~ ) G I ~(20).
components VL(Z)and V l ( z )are obtained separately from theIn these equations, H L ( z ) and H [ ( z ) are equivalent represenmeasured V ( z )curves by using the signal processing method
tations of I/L(z) and V r ( z ) ,respectively.
asdescribed in theSection V.

+

+

+

+

+
+

KANA1 et al.: MICRODEFOCUSING METHOD FOR MEASURING ACOUSTIC PROPERTIES USING ACOUSTIC MICROSCOPE

h47

Oncetheresultantcoefficientsaredeterminedfromthetransformed data, V L ( Zand
) V I ( Z of
) (21) are obtained sepaVo(z) and Vl ( 2 ) .
rately from the measured data

where det = C ~ , C i , - C ~ , C ~ ,Although.
theresultant
V; ( z ) and Vi(.) are
dividedbythe factors CL and
C I , respectively,thegradients
EL, €1, V L , and 71 of( l l H 1 4 ) do notdependon thesefactors.
Thus,
using
the gradients of L V L ( z ) , i V f ( z ) , lnlLy(z)l, and lnlVf(z)l,the acoustic properties (velocity and attenuation factor) of the
LSAWcomponentandthelongitudinalwaveinwaterare
determinedfrom(11)-(16).
Let us consider how to determine the complex amplitudes
CL0, C;,,, CLl, and Cil byassuming that f = 200 M H z ,lSzl = 0.1 pm, U L S A ~zz 3400 m / s (for fused quartz), andv, = 1491 m/s (for T = 25°C)forexample.Forthis
purpose,popularparametricspectrumestimationtechnique[19]-[21] should be applied. However, the angles of the poles
p~ and p 1 are -9.64" and -8.66', respectively, in the z-plane
under these conditions as shown in Fig. 7(a). Thus, the angle
difference between these poles in the z-plane is usually verysmall and it is difficult for the popular parametric spectrum
estimation method to accurately separate and determine thesepoles. Therefore, it is necessary to transform the measured data
Vo(z)and V1 ( 2 ) into the appropriate forms before applying the(C)spectrum estimation technique for these conditions.
Fig. 6. Thepropagationpathsofwavesaredividedintothreephases.
Letusdesamplethesemeasureddata
periodaat(a) In thelens. (b) In watedsample. (c) In the lens. Complexcoefficients{ H z j , G j z } ,( i = 0 . 1 ; j = L , I ) , HL(z),and H l ( z ) represent
the[ p . b z l ( p > l), after applying an appropriate low passfiltercorresponding transfer systems.
to V o ( z ) and1'1 ( 2 ) . In order to remove the rapid change due
L (5), let us multiplytheresultant
tothephaseterm L ~ in
VD(.)
and
VI(.)
by the factor exp(-j2k& . p . S z ) ,desampled
Equation (20) is rewritten in matrix form as
where k$ istheassumedwavenumber
in water at theV0( x )
VLk)
temperature. Then, the angles of the resultant poles p! and p:
V,(J =(V&))(21) in the z-plane are describedby e x p ( j 2 p . Sz(lc,, - /c;,)) and
.
S
z
(
k
,
cos
6
'
~
s
~
~IC;,)),v respectively. If the value
exp(j2pby defining the complex constant
Cji asof p is 64, Vo(z) and VI ( 2 ) aredesampled at aperiod of
Cji = (10Hoj l l H 1 j ) G j z . (i = 0 , l ; j
L,I).
6.4 pm and if IC:, = IC, the angles of the poles p~ and p 1
as shown in
The complex amplitudes CLO, CJO,
CL,, and GI1 are deter- are 0" and 62.7", respectively,inthez-plane
p!
is
on
the
real
axis
in the zFig.
7(b).
The
resultantpole
10 and 11,the shape andmined only by the input amplitudes
plane.
Thus,
it
is
still
difficulttoestimatethepositionof suchthe material of the transducer and the acoustical lens, and the
or
on
the
real
axis
becausethedc
component
a
pole
near
frequency. This is because the paths (M and #l) in the lensdo not change for various defocus ranges near the focal plane. is deletedbeforeapplyingthepopularparametricspectrum
Using (2) and (3), the sampled V ( z )curves, namely Vo(n. S z ) estimationmethod.
Therefore, let us multiply the desampled VD(.) and Vl(z)and V,( n . Sz) curves, are modeled bynotbythefactor
exp(-j2kfp . S z ) butbythefactor
0 5 @ 5 1.
exp(-j2IChp. 6 z . p)), where @ isaconstant
It is not necessary to set the assumed wave number
as justequal to the true wave number C
I,
at the temperature because
where C;i= C,, . C,, (i = 0 , l ; j = L , I ) . Thecomplex
the difference can be corrected as described in the following.
amplitudes CLo, CLl, and C;, aredeterminedonlybytheThis processing is equivalent to the demodulation of a complex
shapeandthematerialof thetransducerandtheacousticalsignal. From (4) and ( 9 , the angles of the resultant poles p ilens, and the frequency. This is because the paths (M and # l )and p> in the z-plane are respectively represented byin the lens do not change for various defocus ranges near the
focalplane.
LP; = 2 ( k , - k : p ) p . S2
(24)

( 2 2:)

(

+

IC:,

IEEE TRANSACTIONS ON ULTRASONICS. FERROELECTRICS, AND FREQUENCYCONTROL, VOL. 39, NO. 5, SEPTEMBER 1992

648

TABLE IPARAMETERS
OF THE FABRICATEDBUTTERFLY
TRANSDUCER
TRANSDUCERS:
Material: ZnO Thin-Film ( f = 200 5m).
Radius: n = 0.25 mm. h = 0.35 mm, c = 1.08 mm, tl = 0.60 mm.
Angle: o = 30"
The Point-Focus-Beam Acoustic Lens:
Material: Z-cut sapphire
Rod Length: 7.0 mm.
Radius of curvature: I' = 1.25 mm.
Half-Aperture angle: GO".

P=

P=
acomplexsequenceasalinearcombinationof complex
pi estimatedexponentials. From the angles of the poles andabove, vu, and ULSA\\' arepredeterminedbythefollowing
equations, which are derived from (6), (S), (23), and (24):27rfv, = h
kW

-

P=

2T.f

k:,p

+ LC; / 2 p . s z

where uLt = 2 r ; f / k L is the assumed velocity
temperatureandP=

in water at theOnce thecoefficients CLo, Cia, CLl; and Cil aredetermined in advance using the procedure above, VJz) and c i ( z )are separately obtained from the observed outputs
Vo(z) andV 1 ( z )of theproposedtransducerusing(23), andthenthe
acoustic properties are determined from (11)-(16).

P=

P=

VI. EXPERIMENTS
ANDTHERESULTS

Based on thedesignrulesdescribedin Section IV, theparameters of the butterfly transducer were determinedso as todetect an LSAW component with a phase velocity in the range
Fig. 7. Illustrationsexplainingtheeffectof multiplying w q ( - j 2 k i , , p . b.:of2100 m/s to 5500 m/s. Table I shows the parameters of. , 3 ) when the poles are estimated by popular parametric spectrum estimation
the fabricated butterfly transducer, whichis employed in themethods.(a) .3 = 0. p = 1. (b) = 1. p = 61. (c) 3 = 0.96. p = G 4
following experiments.
RF burstpulseswithawidthof 500 nsareappliedtoandboth transducers through the attenuators and the circulators in
ip; = 2 ( k ,cos /3L.S24\V - k ; , B ) p . Sz.
(25) Fig. 4. The repetition rateof the RF burst pulses is 0.1 ms. The
attenuation level for the inputsof the central transducer andthe surrounding transducers are 10 dB and 0 dB, respectively.
For the conditions described above, these values are -24.7"
Vo(z) and V,(2) areobtainedbymeasuringtheresultant
and 38.1°, respectively,asshownin Fig.7(c)byassuming
voltageaftergatingandamplifyingtheoutputsignalofthek,, = k;, p = 64, and ,# = 0.96.
[l91 simultaneously to the corresponding transducer while the z-stage is moved along theBy applyingProny'smethod
resultant transformed data of Vo(n . p . b z ) and V l ( n. p . S z ) , z-axis by the step 16z)of 0.1 pm. The employed frequency fbothpoles, p i and p i , andtheircomplexamplitudes
CLo, is 200 MHz.
Fig. 8 shows the measured Vo(71 . Sz) and Vl(n . 62) for a
Cia, CLl, andaredeterminedby solvingtwicethelinear
sample of fused quartz in the defocus range fromz = 0 to z =simultaneousequationsderived
byminimizingtheaverage
500 pm. In order to remove the rapid change of the phase, eachpower ofthedifferenceamongtheterms
in theright-handvalue is multiplied by exp(-j2kk, . Sz . p ) , ( p = 0.96), where
and the left-handsides of (22). Prony'smethodcanmodel
(c)

h49

KANA1 er ai.: MICRODEFOCUSINGMETHODFORMEASURINGACOUSTICPROPERTIESUSINGACOUSTICMICROSCOPE

2-00-

W

-20O l - - - - - I

m/
+-Rm/

2+”
S”

G
& U

0

..................................

-7r

t

0

--R

i

W
m

............................

0

250

4

x
a

500

DEFOCUS DISTANCE z ( p m )DEFOCUS DISTANCE z ( p m )
( b)

( b)

Fig. 8. The characteristics of the I b ( 2 ) and 1i ( z ) measured in the defocus
range from 0 p m to 500 pm.

Fig. 9. The characteristics of the measured_ I b ( :) and I i ( 3 ) and theestimated & ( z ) and ll(z).

IC:,is obtainedfromthemeasuredtemperature.

By applying
the nonlinear least square optimization technique [22] using
the parameters obtained by Prony’s method as initial values,
satisfactoryresultsareobtainedbecauseboththemeasured
in phase and amplitude.
and the modeled data coincide wellSz) and theFig. 9 shows the measured Vo(n. S z ) and V ~ (. Restimated Co(n ’62)and Cl(n. h z ) modeled in (22) in the
defocus range from z = 50 pm to z = 200 pm.
In thenonlinearleastsquareoptimizationprocedure,theisminimizedwith
followingnormalizederrorfunction
respect to the poles p i and p > andthecomplexcoefficients
CLo, CLl, Cjo, and Cjl (see(28)atthebottom
ofthepage) where nl and 712 represent the points for the beginning( z = z1 = p . b z ‘ n 1 ) and the end ( z = z2 = p . Sz . n 2 ) of
the defocusing range, respectively.
Fig. 10 shows the minimized error function C obtained from[ X I , 221 of V o ( z ) andthe data of the various defocus ranges
VI(.) in Fig. S(a). When the defocus range[ z l ,221 involvesof the resultant errora region less than 50 pm, the values
Dz =function takes large values for each defocus distance
122 - 211. Thus, it is foundfortheseexperimentsthat thein defocus
models of (2) and (3) do notholdforthedata<c10,.............................................................................................
h.....................

Dz:DEFOCUS RANGE(= J z-~~ 1 1 )g;z.v8o.............................................................................................
;
Y& h I.............................................................................................

w v..........

....

......

.............

100
200 ’ 300
400
51 0
CENTER OF DEFOCUS RANGE [ z I , z ~( p] m )

”0

’

’

‘

Fig. 10. The minimized error function C obtained for the data of the various
defocus range [;,.;L] of l b ( z ) and l i ( z ) i n Fig. 8.

regions near the focal plane( z = 50 pm).
In the experiments, therefore, the defocus region employed
50 pm toto determinethecomplexcoefficientsisfrom
200pm.Fig. l l ( a ) shows thepositions of theresultantes-

IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, 4 N D FREQUENCY COWTROL, VOL. 39, NO. S . SEPTEMBER 1YY2

h50

W

IrnI

DEFOCUS DISTANCE z(P,>
(h)

I

(b)

,-.

-

,..

Fig. 11. (a)Positionsof the estimated poles p', andin the :-plane.
(h) Positions of the obtainedcomplexcoefficients
C;-,,, C;(,, and C';lnormalized by the magnitude I C ' ; , I

1.

h

h

Fig. 12. Two components l j i ( z ) and l ) ' ( z ) obtainedseparatelyfrom
thc
1b ( 2 ) and l .l ( 2 ) measured In the defocus range from SO p m to 125 I'm.

necessary for the reasonable determinationof the velocity to
use the data in the defocus distance greater than 40 pm, whichis almost equal to the interference period h ( = 36.7 / m ) in(9).

timatedpoles
andin thez-plane.
Fig.
l l ( b ) showsthe
positions of the obtained complex coefficients CLo, CLl, Cia,
and Cfl of (22), which are normalized by the magnitude !CLl1.
VII. CONCLUSION
Bysubstitutingtheresultantcomplexcoefficentsi n s theand V;(z)This paper has described a new method
to obtain acoustic
right-hand side of (23), the two components
are obtained near the focal plane separately from the measured properties by analyzingthetransduceroutputs
V ( z ) , which\k(z) and V l ( z )as shown in Figs. 12(a) and (b), respectively. are measured within the microdefocusing region near the focal
Each term is multiplied by exp(-j2k:L. . 6 z . [j), ( p = l).The plane. The proposed method determinesthe acoustic properties
and T/I(z) curves
phase characteristics are represented by almost straight lines,of a sample from the gradients of the VL(Z)V r ( z ) and V, ( z ) are withoutapplying anyperiodicanalysis.
In order to obtainwhichmeansthatbothcomponents
r/o(z) and these components VL(Z)and VI(,Z)
successfully obtained from the transducer outputs
separately, a new-type ofV l ( z ) . The reason why the phase value
L L k ( z ) in Fig. 12(a) transducercalled the"butterflytransducer,"whichhastwo
thedifferencebetween
ku, sets of electrodesisintroduced andasignalprocessingfordoes not equalzeroisdueto
determinedfrom themeasureddataandobtainedfromthe
determining the 1'~( z ) and V ~ ( Z
components)
from the resuland VI (2) of the transducer is developed.
temperature. By determining the average gradient <L and (1 of tant outputs l%(.)
confirmtheprinciple
i c ; i ( z ) and L v ; ( z ) in the defocusing range from 50 p m to Someexperimentshaveperformedto
V L ( Zand
) L'I(z) fromdeveloped in this study for obtaining
125 pm, the longitudinal phase velocity
in water and the
71,:= the outputs 1/o(z) and Vl(z)of the transducer.
phase velocity ~ I L S A I V of fused quartz are obtained as
Whenthepropagationattenuationof asample is large
1497 m/s and V L S A ~ V = 3442 m/s, respectively,whichareof theLSAW islarge,sufficientreasonable values. Thus, the principle of the microdefocusing and/orthevelocityvalue
for current V ( Z ) analysiscannot
defocusdistancenecessary
method is successfully proved by the experiments.
[ z l 221 forbe attained. Though the experimental results
are shown only
It is important to evaluatethedefocusrange
the determination of the gradients and the velocities. Fig.
13 for a fused quartz in this paper, the proposed method willbeapplied to overcome these problems. It is also expected that ashowsthephasevelocity'L!LsA\~of theLSAWandthe
practical acoustic microscope system for quantitative imaging
longitudinal velocity 'vw in water estimated from the various
ranges of theresultant V,( 2 ) and T/l(z) in Fig. 12. It is will be constructed based on the proposed principle and it will

v;(.)

'U,,

KANA1 er ul.: MICRODEFOCUSINGMETHODMEASURINGFOR

ACOUSTIC PROPERTIES USING ACOUSTICMICROSCOPE

3800
3700

..........................
..................................

iI

32001........................

!.:............ ............
~

1
1

J

(a)

6oo .......................................................

1400 .......................................................
l
50
70
90
110 125
UPPER BOUND (pm) OF DEFOCUS

RANGE FOR OBTAINING VELOCITIES(h)(‘1,.,\\\.
of theLSAWandthelongitudinal
Fig. 13. The phasevelocity
velocity r t , , in waterestimatedfrom the variousdefocusranges [:I. : 2 ] of:.lof thethe resultant l , ’ ( :) and l;‘( :) in Fig. 12. where the lower boundrange is 5 0 p m .

-play a significant rolernicrospectroscopy.

65 I[9] J . Kushibiki, Y. Mastumoto,andN.Chubachi,“Attenuationmeasureon Germanium by acousticline-focus-beam,”ment of leakywaves
Electron.Lett., vol. 19, pp. 512-514, July1983.
[IO] J. Kushibiki and N. Chubachi, “Material characterization by line-focusbeam acoustic microscope.” lEEE Trans. Sonics Ultrason., vol. SU-32.
pp.189-212,Mar.1985.
[ 1 l ] N.Chubachi, H . Kanai. T. Sannomiya,and T. Wakahara,“Acousticmicroscopeformeasuringacousticproperties
by microdefocusing-P.Harjes,Eds.
method,” in Acourticai Imaging, H. ErmertandH.
NewYork:Plenum,
1991.(Also presented in 19thSymp.Acoust.
Imaging,Ruhr-UniversiVit Bochum, Germany. Apr. 1991.
[l21 M. Greenspan and C. E. Tschiegg, “Speed of sound in water by a direct
method,” J. Res. Nut. Bur. Srand, vol. 59, pp. 249-254, Oct. 1957.
[l31 H. Kanai, N . Chubachi, and H. Suzuki, “A method to evaluate accurqcy
in low SNR,”of FFT-based periodicity analysis for short length signal
in Proc. IEEE 1992 Int. Con[ Acoust.. SDcech, Sipnal- Processinp.
- Mar.
1992,pp.V45-V48.
J. M. M. Pinkerton. “The absorption of ultrasonic waves in liquids and1141.
>
its relation to molecular constitution,”
Proc. Phys. Soc., vol. B20, Feb.
1949,pp.129-141.
L. K . Lam,“Directionalacousticmicroscopefor[l51 J.A.Hildehrandandobservation of elasticanisotropy,” Appl. Phys. Lett.. vol. 42, No. 5,
pp. 413-415, Mar. 1983.
[ 161 D. A.Davidsand
H. L. Bertoni,“Bow-tietransducersformeasurement of anisotropicmaterials i n acousticmicroscopy,” in Proc. lEEE
Ultrason. Symp., 1986. pp.735-740.
[l71 N. Chubachi, et ai., “Acousticimages observed by directional PFB
microscope,” in Proc. 18th Symp. Acousr. Imaging, 1989.
1181 Y. Sugawara, J . Kushibiki, and N. Chubachi, “Performanceof concave
transducers in acousticmicroscopy,“in Proc.1988IEEEUirrason.
Sympo., 1988,pp.751-756.
[ 191 J. D. Markel and A. H. Gray, Jr., Lineur Predictiorl of Speech. Heidelburg,Germany:Springer,Ch.
2. 1976.
[20] S. L. Marple,Jr., DigitalSpectral Analysis w>ithAppimrtions. EnglewoodCliffs, NJ: PrenticeHall,1987.
[21j S. M. Kay, .Modern SpectralEstimationTllcory and Applicutiun. EnHall, 1988.
glewoodCliffs,Prenticeof nonlinear
1221 D. Marquardt,“Analgorithmforleast-squaresestimation
parameters,” SIAM J . Appl. Math., vol. l l , pp. 431-441. 1963.

-

in fields of the acoustical imaging and

ACKNOWLEDGMENT
The authors wish to thank Mr. Toshihiro Wakahara for his
assistance of the experiments and Mr. Derek Iwamoto of ourlaboratory for his preparation of the manuscript.

REFERENCES
R.A.Lemons and C.F. Quate, “A scanningacousticmicroscope,inProc.1973lEEEUltrason.Symp.,
1973, pp. 18-20,
C F . Quate,A.Atalar,andH.K. Wickramasinghe,“AcousticmicroProc.IEEE, vol.67,
scopewithmechanicalscanning-Areview,”
pp. 1092- 11 14, Aug. 1979.
in reflection
A.Atalar,“Anangular-spectrumapproachtocontrast
acousticmicroscope,” J. Appl. Phys., vol.49, pp. 5130-5139,Oct.
1978.
R. D. Weglein, “A modelforpredictingacousticmaterialsignatures,”
AppL Phys. Lett., vol. 34, pp. 179- 181, Feb. 1979.
W. Parmon and H. L. Bertoni, “Ray interpretation of the material signature in the acoustic microscope.” Electron. Lett.. vol. 15, pp. 684-686.
Oct.1979.
J . Appl. f‘lrys.,
A. Atalar, “A physicalmodelforacousticsignatures,”vol.50,pp.8237-8239,Dec.1979.
R. D. Weglein,“Rayleighwaveabsorptionviaacousticmicro\copy,”
Electron. Leti.. vol. 18, pp. 20-21, Jan.1982.
J . Kushibiki,K.Horii,
and N. Chubachi,“Velocitymeasurementofon Germanium by line-focus-beamacouslicmimultipleleakywaves
croscope using FFT,” Electron. Leu., vol. 19, pp. 404-405, May 1983.

Hiroshi Kanai (A’89-”91)
was born in Matsumoto, Japan on November 29, 1958. He received
the B.E.degree fromTohokuUniversity,Sendai,
Japan, in 1981,andtheM.E.andtheDr.Eng.
i n 1983 anddegrees. also from Tohoku University,
in 1986, both in electrical engineering.
From1986to1988
he waswith the Education
Center for Information Processing. Tohoku University. a5 a Research Associate. From 1990 to 1992, he
was a Lecturer with the Faculty of Engineering, Tohoku University. Since 1992 he has been a Associate
Professor at the Department of Electrical Engineering, Faculty of Engineering,Tohoku University. His present interest is in digital signal processing and its
application on the acoustical, ultrasonic, and electrical measurements.
of Japan,theInstituteDr. Kanai is amember of theAcousticalSocietyof Electronics,Information.andCommunicationEngineeringof Japan,theof Ultrasonics inJapanSociety o f MechanicalEngineers.theJapanSociety
Medicine, Japan Society of Medical Electronics and Biological Engineering,and the Institute of Electrical Engineers of Japan.

h52

IEEETRANSACTIONSONL'LTRASONICS,FERROELECTRICS,

Noriyoshi Chuhachi ("83)
was born i n Kokura.
Japan, on October 5, 1933. He received the B.S., M.
S., and Ph.D degrees in electrical engineering fromin 1956and in
TohokuUniversity,Sendai,Japan.
1962,and1965,respectively.
In 1965, he joined the Research Institute of Electrical Communication. Tohoku University, where he
was an AssociateProfessorfrom1966to1978.
Since 1979 he has been a Professor at the Department of Electrical Engineering, Tohoku University.
From1982to 1983 he was a visiting Professor of
Electrical and Computer Engineering, University of California, Santa Barbara,
CA. He has worked on ultrasonic transducers and delay lines, surface acoustic
devices, acoustoelectronics, piezoelectric materials. accoustic microscopy, andrelatedproblems.
Dr.Chubachi is amember of theInstitute of ElectronicsandCommunicationEngineers of Japan,theSocietyof JapaneseAppliedPhysics.theof Ultrasonics in Medicine,
AcousticalSociety of Japan,theJapanSociety
the Japan Society for Nondestructive Inspection. the Japan Society of Medicalof MechanicalElectronicsandBiologicalEngineering,theJapanSocietyof ElectricalEngineers of Japan.Heservedas
Engineers,andtheInstitutechairman, Tokyo chapter of IEEE UFFC Society, from 1987 to 1988.

AND FREQUENCYCONTROL. VOL. 39, NO. 5. SEPTEMBER I Y Y 2

Toshio Sannomiya was born in Miyagi Prefecture,
Japan, on October 3, 1938.
He graduated from thein 1959.
SendaiRadioHighSchool
From1959to1978,
he was withtheResearchInstitute of Electrical Communication, Tohoku Uniat
vesity,Sendai,Japan.Since1979,hehasbeen
theDepartment of ElectricalEngineering,Facultyof Engineering, Tohoku University. He has engaged
in thestudies of ultrasonictransducers,ultrasonicmeasurements, and acoustic microscopy.
Mr.Sannomiya is a member of the AcousticalSociety of Japan, and the Japan Society of Ultrasonics i n Medicine.