IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. iM-24, NO. 4, DECEMBER 1975

WALSH EXPANSION OF A SINUSOIDThe Walsh expansion of cos (f27rf) is written as the

following:

(11)EAsf cal (s,0)s

where A5f is the Walsh coefficient of sequency s, i.e.,

As = cos (f2irO) cal (s,) dO = 1a (12)

from (4). Substitution of f = 1, s = 1,2,3, -- , in (8) yieldsthe required coefficients. To illustrate, for s = 7 (cal) ina set of 16 Walsh functions, k = 14 = 1001 in Gray code,so a = 2. A term within the product in (8) is a cosine ora sine, depending on whether gx is 0 or 1. Hence

1

A71= a,7 (sinc 1/16) (sin r/2)(cos 7r/4) (cos ir/S) (sin ir/16) ~0.1266.

The sal coefficients may be evaluated in the same way.

ACKNOWLEDGMENTThe author wishes to thank A. S. Gladwin for his

helpful comments.REFERENCES

[1] G. R. Cooper and C. D. McGillem, Methods of Signal and SystemAnalysis. New York: Holt, Rinehart, 1967, pp. 33-38.

[2] H. Schreiber and G. F. Sandy, Eds., Applications of Walsh Func-tions and Sequency Theory. New York: IEEE, 1974, Cat. no.74CH0861-5EMC, ch. 15.

[3] K. H. Siemens and R. Kitai, "A nonrecursive equation for theFourier transform of a Walsh function," IEEE Trans. Electrom-agn. Compat., vol. EMC-15, pp. 81-83, May 1973.

A Calibrated Ultrasonic Field Measuring System forGeneral Use

ALAN J. COUSIN, MEMBER, IEEE, KENNETH C. SMITH, MEMBER, IEEE, AND IAN H. ROWE,MEMBER, IEEE

Abstract-An instrumentation scheme is presented whichprovides a calibrated field intensity equivalent plot using com-mon laboratory equipment. The parameter that is measuredgives a direct indication of the merit of an ultrasonic transducerfor a given application in terms of its beam shape. The compositeoutput of the system yields a three-dimensional representationof the intensity equivalent parameter as a function of a two-di-mensional spatial field. Several applications of the resulting in-strumentation are given including the effects of crystal windowflatness and acoustic lensing.

I. INTRODUCTIONTN THE APPLICATION of ultrasound, there are sev-leral identifiable areas where improvements could bemade provided a straightforward means for characteriz-ing the electroacoustic efficiency of the transducer wereavailable. Two industrial environments whe're ultra-sound is commonly employed are flow metering and vi-sualization of internal structures (e.g., flaw detection,medical visualization, depth finding, etc.). It is apparenthere that a controlled narrow beamshape is required forhigh spatial resolution. For example, in the flowmetercase, a narrow beam is required to resolve the ambigui-ties that could result from turbulence. In broad beam-

Manuscript received May 15, 1975; revised July 16, 1975.The authors are with the Department of Electrical Engineering,

University of Toronto, Toronto, Ont. M5S 1A4, Canada.

width applications, it is also desirable to obtain a pic-ture of the acoustic pattern being generated by thetransducer(s).A combination of a visualization capability with a

knowledge of the properties of the environment inwhich the ultrasound will be employed permits thechoice of a specific beam shape to optimize some crite-ria. Subsequently, by mechanically building and/or ad-justing the parameters of the crystals appropriately, thedesired beamshape can be approximated. This ap-proach increases the signal-to-noise ratio (SNR) at theinput of the processing circuitry by having realized es-sentially a spatial filter that reduces irradiation of un-desired structures. The instrumentation scheme pre-sented here is generally useful for ultrasonic applica-tions that employ both an ultrasonic transmitter and re-ceiver.'

II. BASIS OF INTENSITY EQUIVALENTMEASUREMENT

The basic aim of this instrument is to allow a rapidassessment of ultrasonic transducers by displayingequivalent field intensity. The calibrated parameterthat is used as a measure of goodness G is the ratio of

1 That is, the scheme presented is not intended for use with ultra-sonic crystals used for heating and cleaning purposes.

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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, DECEMBER 1975

receiving transducer voltage output and transmittingtransducer electrical power input.2

Although acoustic effects are of obvious concern,most common applications of ultrasonic transducersutilize eltctrical signal generation and detection. Thusit is sensible to obtain a characterizing parameter thatrepresents the twice transduced signal in electricalterms rather than a singly transduced signal in acousti-cal terms. In addition, for applications where the trans-mitting and receiving crystals are physically different,but exist in the same package, more information is ob-tained from the doubly transduced G parameter. To ob-tain an equivalent characterization using a singly trans-duced method, one would require the acoustic field dis-tribution of each ultrasonic crystal which must then becombined with appropriate shifts to reflect the spatialorientation of the transmitting and receiving crystals.

Furthermore, equivalent acoustic transmitted powercan be measured from electrical power input to thetransducer, while acoustic received power can be deter-mined from electrical voltage output of a transducerinto a high input impedance amplifier. Therefore, the Gparameter is appropriate for measuring the electroac-oustoelectric transfer function of an ultrasonic system.

III. REALIZATION OF A PRACTICALVISUALIZATION TOOL

To make the instrument a useful research tool forother ultrasonic investigations and other investigators,the following instrumentation criteria were established.

1) The crystals should be tested in the same mannerin which they will ultimately be used. This allows thecombined field characteristics of the transmitter and re-ceiver to be obtained.

2) The instrument must provide equal electricalpower drive to all transducers at various frequencies.This permits comparisons in intensity and conversionefficiencies between transducers and transducer config-urations.

3) All parameters must be calibrated or calibratableand, therefore, repeatable. This is a somewhat difficultproblem as a result of the cumbersome nature of themultivariable spatial and amplitude requirements.

4) The display must be readily interpretable andprovide a permanent record in a graphic hardcopy for-mat.

5) The entire instrument should satisfy the two nec-essary requirements of a properly designed instrumentintended for wide general use: it must be easy to use andinexpensive to build.What has been realized is an instrument composed of

common laboratory components which satisfies all ofthe above criteria.To begin with, a photograph of the complete instru-

mentation system is shown in Fig. 1. On the left is the

2 G A receiving transducer voltage outputtransmitting transducer power input'

ultrasonic field portion which consists of a water tank,the transducer fixture and the device for controlling thereflecting target's position. The- latter device uses an in-verted X-Y plotter (in this case a Hewlett-Packardmodel 7005B) to obtain precise mechanical movementsof the reflecting target with this target fastened in placeof the usual felt pen.The transducer is mounted in a watertight fixture

with its radiating face directed along the horizontal andunder the water surface. The fixture is physically at-tached to the X-Y plotter to obviate the inconvenienceof mechanically referencing the transducer to the targetfor each experiment. Without a reference of this type,alignment becomes a problem in the three dimensionalcase since it requires that the plane in which the reflect-ing target travels be aligned with a perpendicular lineemanating from the transducer face and that this align-ment be repeatable. The entire assembly has the advan-tage of not requiring alignment to insure that the trans-ducer and reflector are in the same transverse planesuch that the locus of all lines perpendicular to the faceof the transducer will be parallel to the plane in whichthe target moves. In addition, the transducer fixture it-self can be raised and lowered to facilitate off-centermeasurements and the transducer can be rotated in thefixture to observe field asymmetry. Fig. 2 shows a clo-seup of this fixture.A stainless-steel ball of about one-half inch in diame-

ter is used to provide a self-aligning target. By choosingthe diameter to be much greater than a wavelength, therange of relative maxima and minima in the near field isaveraged [11 with the averaging "space constant" pro-portional to the ball diameter to a first order. Thechoice of the spherical ball as a reflecting target is notideal, however, and although it possesses a self-aligningproperty it does bring three disadvantages.

Firstly, the reflected energy at any fixed position is afunction of the reflector size. In particular, the energyreceived back at the transducer is proportional to thereflector's cross-sectional area. Secondly, the reflectormaterial has a certain acoustic impedance and thisimplies a particular reflection and transmission coeffi-cient. These two disadvantages are not serious draw-backs as the amount of error produced can be calculateda priori [2], [3].The third problem is the most noteworthy of the

three. Presume for the moment that all of the soundrays leave the transducer face in parallel. Then as thereflector is moved away from the transducer, the netsurface that will reflect an acoustic ray at such an angleso as to impinge back upon the transducer varies as thesquare of the target distance. A similar effect exists asthe ball moves transversely. However, the entire situa-tion is complicated by the fact that the acoustic rays donot really emanate in a parallel fashion. If the directionin which all the rays were pointing was known, then acalculation could be made to correct for this r2 type dis-crepancy. Although this effect might appear to consti-

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COUSIN et al.: ULTRASONIC FIELD MEASURING SYSTEM

tute a strong disadvantage, it should be rememberedthat the intention is not to measure field intensity di-rectly, but rather the transfer function of the totalacoustic system. In this sense then, the steel ball is serv-ing as a standardized reflector of a particular size andwill, in this sense, give an indication of the response tobe expected in the actual ultrasonic reflection system.

If it is desired to eliminate this distance effect, onemust procure a target that presents a surface perpendic-ular to the acoustic beam at all points. For a parallelbeam, this perfectly aligned flat surface. In practice,however, it appears difficult to obtain a parallel beamacoustic source and, in any case, cumbersome to align aflat surface perpendicularly to the beam at all points.

omplete instrumentation system.

IV. FUNCTIONAL DESCRIPTION

A block diagram of the instrument is shown in Fig. 3.This diagram can perhaps most easily be digested by di-viding it into three parts. The first part, the transmit-ting section, consists of an oscillator that is gated so as

i; N0 00g 0g to drive the transmitting crystal with a sinusoidal volt-age for a preset time denoted by "transmit burstwtdrvthe ta g cs wh a"The second part, the receiving section, samples the

reflected signal after a controlled delay (range delay)following the transmitted burst. This delay is set to cor-respond to the transit time of the ultrasound over theforward and return path from the transducer to reflec-tor.The signal that exists at the receiving amplifier's

input is the result of a twice transduced signal that hasbeen reflected from the steel ball. This signal is thenpeak detected during the period of the receive window(sample-and-hold gate width) and stored.The third part, the recording section, utilizes two

X-Y plotters. The first moves the reflector and the sec-ond plots the field characteristics. The X-sweep genera-

ig. 2. Transducer fixture. tor controls the arm of both X-Y plotters in parallel.

POWER|GATED 1 PWRITRNMTNGIRECEIVNGI I I(IPEAK DETECTING SML|GULTMA OAND HOLD

TRANSMIT TRANSDCERIPOER|ITIOBURST WIDTHX I. In

_-N v-- t. Ir . ///rXX IRECORDING(D - REELEC I E|]PLOTTER

RANGE v91 I I YIGERTNOTE I~6- REPRESES TE 1 'PLOTTER

(t) < I I I g~~~~~~~~~~L X PENS I ARMSAMPLE AND HOLDI

GATE WIDTH -9XY STE

ITASDUCER POSITION~~~~~~~~~~~~~~~~~~~~CONTROLLING(g) I X SWEEP I I I r oll | ~~~~~~~PLOTTERNOTE:- X' REPRESENTS THE _t.xREL PLOTTER ARM

ABILITY TO CONTROLTHE NAMED QUANTITY

Fig. 3. Field pattern vizualization instrumentation.

Fig. 1. C

F

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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, DECEMBER 1975

AY = .5 cm. AY = .5 cm.0 -1 2 3 40 1 2 3 4 cm. X = .37 cm./cm.

0 1 2 30 1 2 3 4 cm.

C)h

a)

(n-C)

C)

0

.,,cmI)

A Sample Field Intensity Distributionfor a Commercial Ultrasowud Transducer

Fig. 4.

With the completion of each sweep the Y-step generatoris incremented. This motion moves the ball along a lineparallel to the face of the transducer and successivelyincreases the perpendicular distance from the transduc-er to this line.

In the present design, a portion of the Y-step genera-tor is added to the peak detected and held value fromthe receiving section and the sum is supplied to the Yaxis of the recording plotter. In addition, calibrationlines are drawn on alternate sweeps representing con-stant values of the incrementing Y position. These ap-pear as horizontal grid lines on the "caricaturized" ex-ample shown on the X-Y recording plotter in this fig-ure.

Fig. 4 shows a sample plot of G versus the two spatialcoordinates in which the reflecting target moves. The Xdirection (horizontal) is easily calibrated since thelength of a calibration line corresponds directly to thelength of travel of the reflecting target. The Y direction(vertical) is also easily calibrated in a similar fashionand is represented as the spacing between the calibra-tion lines. The third dimension G, representing intensi-ty, should appear to come out of the paper perpendicu-larly (as though a real Z axis existed).One of the several advantages of these calibration

lines is that G can be measured on the basis of the spac-ing of the calibration lines which is known. That is, G isproduced as a level that adds in the summing amplifier(see Fig. 3) and by knowing the gain constants of the re-ceiving section, the correspondence of the spacing tothis third dimension is trivially available. In addition,notice that the signals themselves going to the fieldplotter have an inherent self-calibrating feature. Thismakes it a relatively simple matter to readjust the con-trols of the recording plotter if it is required for otherpurposes. This has, in fact, occurred several times dur-ing the course of experiments with no significant dis-crepancy in the results.

Field Intensity Distribution for a GroundVersion of anl Obstetrical Transducer

Fig. 5.

t:oLOld IlotellSito )iStribUtt oo forthe Lens/ lrantsduce r (omi inati ot

Fig. 6.

V. APPLICATION OF THE INSTRUMENTFig. 4 shows results taken from a commercial Doppler

obstetrical transducer. It consists of two D-shaped disksof lead zirconate titanate with a resonant frequency of 2MHz. These two crystals are mounted in a plastic caseand protected by an epoxy window. The importantpoints of note in this figure are the multiplicity of peaksand the relatively wide field pattern.

Since the protective window was visibly rough andalso slightly domed, the effect of making this surfaceflat was investigated. This was accomplished using agrinding procedure with increasingly finer grades of car-borundum powder placed between the transducer faceand a flat glass slab. The resultant field characteristicsare shown in Fig. 5. Of note here is the spatial narrowing

x

C)

*0U.)

CT)C)4

U)H

320

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r-Cd

F.

L-..

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COUSIN et al.: ULTRASONIC FIELD MEASURING SYSTEM

I-als Perspectivc Lcns/[raisdJuceri-,jLltllltcfisity DlistribUvtion

Fig. 7.

of the beam compared to Fig. 4 and also the two nearfield lobes merging into one in the far field.

Ideally, the beamshape could be made more ideal byincreasing the acoustic power received without increas-ing electrical power drive. This requires narrowing ofthe beam so that most of the energy exists in the desiredarea. Equivalently, this can be considered as taking en-ergy from the sidelobes and moving it to the centralpart of the beam. In addition, it would be useful to havethe resultant high sensitivity of the beam occur at aspecified depth. Conceptually, it can be seen that anacoustic lens which focuses the energy is the device thatis required.

Plexiglas is chosen for the lens material as a goodcompromise among the three important acoustic prop-erties: speed of sound different from that in water, mostfluids and body tissue, low attenuation to ultrasound,and minimum acoustic impedance mismatch betweentransducer, lens, and water, most fluids, or body tissue.In addition, Plexiglas also possesses three very practicalproperties: favorable cost, ready availability, and ease offabrication.A 10-cm focal-length lens was fabricated using a

hardened radius arm on a lathe. The resultant G pat-tern is shown in Fig. 6. A factor of approximately ten inG gain was obtained over the original transducer. Moreimportantly, however, by focusing most of the acousticenergy into a smaller volume, a narrowing of the beam isobtained. The practical consequence of this is reducedspatial interference and subsequently a higher signal tonoise ratio at the input to the receiver.

As it evolved, a high degree of beam narrowing wasobtained with acoustic lenses. In fact, so much so that itbecame difficult to obtain quantitative informationfrom the section of the plot where there are overlappinglines. This difficulty was easily overcome with a slightmodification of the pseudo-three-dimensional plot.A straightforward false perspective method has been

implemented. It maintains the calibratability and sim-ply adds some of the Y-step generator's output to the Xaxis by means of an additional summer. This provides aplot similar to the previous ones shown but with the dis-tinction that with each Y increment, the X axis is shift-ed by a small amount to one side. Fig. 7 illustrates thefalse perspective solution. Notice that the calibratablefeature is maintained in this format and the G lines canbe arranged to appear distinctly.

VI. CONCLUSIONSAn instrumentation scheme which allows the visual-

ization of ultrasound beam patterns has been devel-oped. It is both easy to use and relatively inexpensive.This instrument has played a valuable part in two dis-tinctly different but somewhat related fields. In onecase, it was used to optimize the active field of an indus-trial ultrasonic flow meter. In the other, it is currentlyused to optimize medical instrumentation intended forreliable, dynamic, fetal cardiac monitoring.

REFERENCES[1] C. C. Grossman, C. Jayner, J. H. Holmnes, and E. W Purnell, Eds.,

Diagnostic Ultrasound (Proceedings of the First InternationalConference). New York: Plenum Press, 1966.

[2] W. J. Fry and F. Dunn, "Ultrasound: Analysis and experimentalmethods in biological research," in Physical Techniques in Bio-logical Research, Vol. IV, Ch. 6. London: Academic Press, 1962.

[3] P. N. T. Wells, "The directivities of some ultrasonic Dopplerprobes," Med. Biol. Eng., vol. 8, pp. 241-256, 1970.

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