Implementation Details of a Computation Model of

TECHNICAL NOTES AND RESEARCH BRIEFS Paul B. Ostergaard 10 GlenwoodWay,WestCaldwell,NJ 07006

Editor's Note.' Original contributions totheTechnical NotesandResearch Briefs section arealways welcome. Manuscripts should bedouble-spaced, andordinarily notlonger thanabout1500words. Therearenopublication charges, and consequently, nofreereprints; however, reprintsmaybepurchased at theusualprices.

ic solutionexistsfortheequations exceptfor periodsof silence. Theseequationsarethereforeevaluatediterativelyusingsmalltimeintervals,dt. The modelis rich in parameters andthefollowingcomments are in order. We continueto exploreimprovements and simplifications to the [43.64.Bt,43.64.Pg,43.64.Nf] modelbut thisnotehasadheredstrictlyto the modelpublishedearlierfor Ray Mealdis,Michael J. Hewitt, and Trevor M. Shackleton reasons ofconsistency. However, threeparameters governing thepremeability function (g, ,•, B) is clearly a luxury. They do allow us to experiment Department of HumanSciences,Un/vers/ty of Technology, Loughborwithdifferent permeability functions butshouldeventually reducetoa pair ough,Le/cestersh/re LE11 3TI./, Eng/and or a singleparameter.Similarly,the firing-ratefactorh is simplya scale factorandthepurpose ofthemaximum transmitter quantityMis togivethe userthechoiceofworkingwithactualnumbers of transmitter packets or, as INTRODUCTION we prefer,to work in termsof proportions. Oncea preference hasbeen thesetwoquantities canbecombined intoa singleparameter. A simpleand computationally efficientmodelof auditory-neural declared, II. COMPUTER PROGRAM transduction at the innerhair cell hasrecentlybeendescribed, (Meddis,

Implementation details of a computation model of the inner hair-cell/auditory-nervesynapse

1986aand1988).Thispaperbrieflypresents a shortcomputer program to implement themodel,anexploration oftheeffects of modifying theparametersofthemodel, a newsetofparameters forsimulating anauditory nerve fibershowing a mediumrateofspontaneous activitywithextended dynamic range,andsomemethodsof quicklyestimatingsomeof the characteristics.It is intendedas advicefor researchers who wishto implementthe modelaspartof a speech recognition deviceor asinputto anothermodelof morecentrallylocatedneurophysiological functions.

Theshortcomputer programinFig.2 isacomplete n^SlCimplementationof themodelsuitable for useonanydesktop micro.In itspresent form the programcanbe usedto explorethe modelandbecomeacquainted with its propertiesprior to incorporationinto a finalapplicationprogram. The samplingrate,dr, can be specified by the userbut valuesgreater than0.1 msare notadvised.With certainsetsof parameters, muchshorter samplingintervalsare requiredto avoidnegativequantitiesappearingin reservoirs.

I. THE MODEL

Theinputto themodelisthepatternof vibrationat a particularpoint alongthecochlear partitionanditsoutputisan excitation functionrepresenting thefluctuating instantaneous probability of a spikeeventin a postsynapticauditorynervefiber.The modelassumes that threereservoirs of transmitter substanceexist within the hair cell and that the rate of transmit-

ter releasefromthecellintothepre-synaptic cleftisa functionof theinstantaneousdisplacement of the neighboring cochlearpartition.The physical basisof themodelisundoubtedly controversial but,in operation, themodel provides a fastandusefulsimulation ofmanyimportantfeatures ofauditory

nerveactivity.It generates realisticpost-stimulus timehistograms for silenceandpulsedpuretonesandshowsrapidandshort-termadaptation. Phaselockingtorepetitive stimulialsooccursforlow-frequency stimulibut is restricted,naturalistically, at higherfrequencies. A particularfeatureof

figure 1

I factory I

•

• y[m-q]

free

par

tranamitter

A=5 B = 300

pool

g = 2000 = 5.05

q

lY=2500

themodelisitssuitability for usewitharbitrarystimulisuchasspeech and

x = 66.3 r = 6580 m =1.0

noisesignals.

A fulldescription ofthemodelanditsabilitytomatchempirical results aregivenelsewhere (Meddis,1986a,1988).It isillustratedin Fig. I and worksasfollows.A quantityq(t) of packets of transmitter substance isheld ina freetransmitter poolthatliescloseto thecellmembrane. Thesepackets

lost

Ic

-! rc

Ireprocessing • reuptake store

are released acrossthemembraneinto thecleftat a ratedeterminedby the w instantaneous degreeof displacementof the basilarmembraneS(t). The releasefractionk(t) iscomputedusingEq. (4) in Fig. 1.The totalamount of transmitterin thecleftc(t) determines theinstantaneous post-synaptic (1) dq/dt = y(m-q(t)) + xw(t) - k(t)q(t) probabilityof spikeoccurrence.The releasefraction k(t) is intendedto (2) dc/dt = k(t)q(t)- Ic(t) - rc(t) reflectthe permeability of the membraneat the synapse. It is givenas a directfunctionof stimulusintensity,s(t), andtherefore avoidsspeculation (3) dw/dt = rc(t) - xw(t) as to howthe effectis mediated.The actualprobabilitycan be foundby multiplyingby a constanth. k(t) = g.dt[s(t)+A]/[s(t)+A+B] for [s(t)+A] > 0 Transmitterin thecleftiscontinuously subjectto depletionthrough (4) dissipation at a ratelc(t) s •. Transmitter isalsorecovered fromthecleft k(1) = 0 for [s(t)+A] < 0 into the cell at a rate rc(t) s •. Recoveredtransmitter,w(t), is held in a reprocessing pooland is released againinto the freetransmitterpoolat a FIG. 1.Summaryof theoperationof thehaircellmodelwithdifferentialequations and

ratexw(t) s- •. Thefreetransmitter poolisalsosubject to continuous replenishment at a ratey(M-q(t)) s-•. Here,Mspecifies themaximumnumber packetsof transmitterin the freepool.It canbesetarbitrarily to oneso thatall otherquantitiesareviewedasfractionsof thismaximum.No analyt-

1813

J. Acoust.Soc. Am. 87(4), April1990

parameters for a highspontaneous ratefiber.The instantaneous firingrateof thefiber isa linearfunctionof c (the cleftcontents).Here, S(t) is the instantaneous amplitude of the signal.When usingreal arithmetic,the valueof m (maximum transmitter)is convenientlyset to 1.

0001-4966/90/041813-04500.80

@ 1990 AcousticalSocietyof America

1813

III. CHOOSING NixfRae f•e

transmitter

A. Method

Usedle IMemMbillty equation Used In paK•N•lllty 4qMtlon USedi# p•eiblllty equation i•plenlsMmt re•e 80 I-2M0 gO

bt4

•

1•s

h•

of •

f•

•

f•

No simpleway hasbeenfoundto generateindividualparametersthat will producea requiredsetof characteristics of the system;the originally published setof parameters werefoundlargelyby trial and error using guidedrandomwalks.TableI givestheparameters usedin Meddis(1988) alongwith the consequences of changingindividualparameters by 50%. Each set of parametersis evaluatedusing250-ms, 1~kHz tone burstsof increasing amplitude from20to 120dBin 5-dBstepsinterspersed withlong silentintervals.Toneburstshada 2.5-msrisetime.The followingoutput measures are generatedfor eachconfiguration of parameters: (i) thespontaneous rate (rate after500 msusinga -20-dBstimulus); (ii) the saturatedrate (rate after 250 msusinga 120-dBstimulus); (iii) therate-intensity threshold(lowestlevelto showa 5% increasein

cleft

•

cleft

100 x-66.31

120:

I• I•

•t•'dt •t-•dt

IM Idt-l•t I• •t-rødt I•

•.dt

2•

event rate abovespontaneousrate); (iv) the saturation threshold (lowest level to show a rate within 5% of the saturatedrate);

Reprocuss leg stere 2H: 270:

Ites•ttsble onplltucieof slgnol 30 dB is ron-I 0uratfon of Initial

•

sJlonns

TIM of 1ut spike (for re• Countsrobberof spikesso

lastt 1•

PARAMETERS

effect)

Harts the ewnt epoch

sgcQnd.beginsulth s11enMtheft tkllz tom but can be an• signal

(v) rapid and short-termadaptationtime constantsof the rate response to stimuli20 and50 dB aboverate-intensity threshold(seeMeddis, 1986band 1988for methodsfor computingthese); (vi) recoverytime constantafter 120-dBstimulusoffset; (vii) Roseet al.'s (1967) phase-locking synchronization measureat 1 kHz andat 5 kHz (50% signifies noeffective phaselocking). B. Results

•

•x•-

410: 42Q F•

ttm'.'

q','

it','

cleft','

splkus'.'

u'.'

stlonlus'

time - dt TO t STTP dt

430

:P•

C•uts

stimulus amplitude

440..

460 IF tli•ndsllonc• THENst-aN)'S[N(tlm'2*P!'fi•qusncy) ELSEst-0 460 IF st*A;O TI/ENkt-gdtt(st9A)/(st*A,'O) ELSEkt-O 470:

480

:P• Conputl cringe quantities

4gQIF H )- q THINm•lonlsh-2KIt'(H-q) 5OQe,lect-ktOq StO loss-ldt'c

520 reuT)tike-rdt'c S30r•rQcess-xdt ew S40 :AO4 lion updaternsorvolr qusntltles 550 q-el*rapleftI shoe3ect *reprocess 560 c-c.eject - luss*muptake 570 •pu*f•wptske-reOrQcuss 500 :R• If not In refractory phase.ap91¾ SgO :RF. FI St. CrUSttc prQcess GO0ZF ttme-lasttlon).001 NtO IIdt'c•qNO(l) DEN evonts-evonts*t: listtlonotlm;

610 •INT tton,kt.q.c.kS*'

'•ev•nts.v,'

';st:

A•-' ß

62O NEXT 630 STOP

FIG. 2. artsicprogramfor implementing theprocedure shownin Fig. 1 anddescribed in the text.

The effectof changingindividualparametersin a nonlinearsystem dependson the initial configuration.However,for modelersstartingfrom thissetof parameters,someusefulpointsdo emerge. ( 1) Increasing 21(a permeabilityconstant)raisesthespontaneous rate andboththeratethresholdandthesaturation ratethreshold. It alsospeeds adaptationto low amplitudestimuli. (2) IncreasingB (a permeabilityconstant)increasesthe dynamic

rangeof thefiberfrom25 to 35 dB anddepresses thespontaneous rate.It alsospeeds rapidadaptation to low-amplitude stimuli. (3) Reducingg (releaserate) lowersthe spontaneous rate and increases dynamicrange.It slowsadaptationto high-amplitude stimuli. (4) Reducingy (replenishment rate) lowersspontaneous and saturated firing rates.

( 5) Reducing1(cleftlossrate) raisesfiringrates,increases thedynamic range,slowsadaptation to all stimuli,andreduces phaselocking. (6) Reducingr (recoveryrate) increases spontaneous firingrateand selectively speeds short-termadaptationbut,moreimportantly,istheonly parameter thatsubstantially reduces phaselocking. (7) Reducing x (reprocessing rate)slowsshorttermandspeeds rapid adaptationto low-amplitudestimuli. IV. SIMULATING MEDIUM SPONTANEOUS-RATE

FIBERS

Thestateof themodelisdetermined bythethreequantities representingreservoircontents, q, c, w, whichcanbesetto anyinitialpositivevalue lessthanM. In silence, thesequantities willrapidlysettletovalues appropriate to the parametersof the modeland independentof the initial values used.The parameters of themodelareM, .4,B, g,y, 1,r, x, anda firing-rate factorh. Someof theseparametersneedto be adjustedusingdt to obtain workingvaluesfor theequationsandto allowa checkto bemadethat none oftherelease fractions aregreaterthan1.Thus,Mis, roughlyspeaking, the maximumamountof transmitter in thesystem.It isnormallysetto 1andall valuesare understood to be fractions of M. For integerimplementations,

The spontaneous ratesof discharge of populations of auditorynerve fibersoccurina bimodaldistribution (Kiangetal., 1965)andpossibly a tri-

however,Mcan be set to a value suchas 1000 or whateveris believedto be

Thespontaneous rateof discharge hasbeenreduced bychanging the permeability parameters 2t,B, andg, asshownin TableII. Thesechanges resultinaspontaneous discharge rateofonly15events persecond, a slightly

the numberof packetsof transmitterin the system. The incidence of spikesis determinedby a uniformrandomnumber generatorsubjectto two conditions:(a) no spikecanfollowanotherwithin 1 ms(refractoryperiod)and(b) therandomnumbermustbesmallerthan thevaluecorresponding tothecleftcontents multipliedbya ratefactor.The

modal distribution (Liberman, 1978). The fiber simulated in Table I would

becharacterized asa "high" spontaneous-rate fiber.Fiberswith a substan-

tiallylowerrateof discharge typicallyshowa muchwiderdynamicrange and modelersmay wish to include suchfibersin their simulations.Geisler et

al. (1985) haveshown,usingstatistically definedcriteria,that fiberswith mediumratesof spontaneous dischargehave only slightlyraisedrate

thresholds andthatearliercontrary viewsmaybebased uponlessadequate criteria.

raisedrate threshold( + 5 dB) and a greatlyincreaseddynamicrange (50-95 dB). This mediumspontaneous-rate unit showsslowerratesof adaptation, a resultthatisconsistent withthefindingsof RhodeandSmith

ratefactorhismostconveniently setbynotingthecleftcontents aftera long

(1985).

periodof silenceandmatchingthisto a desiredspontaneous rateof firing:

Our modeloffersan explanationof the differencebetweenthe two typesof fibersin termsof the permeabilitycharacteristics of the innerhair cell innervatingthe fiber.The lower permeabilityof the cell causeslower

rate factor = spontrate/cleft contents.

The programillustratesthe reponseof the modelto a brief (0.01-s) periodof silencefollowedby a longer80-dB, 1-kHz,sinusoidal toneburst

(0.99s), Thesevaluesareeasilyaltered.ThedB ratingisarbitrarybut,on thisscale,30dBcorresponds toa signalrmsof 1.The15rogram computes all quantities of transmitter movingfromonereservoir to anotherbeforeupdatingthereservoir contentvalues.All variablequantities areprintedout for inspectionon eachCycle. 1814

J. Acoust. Soc. Am., Vol. 87, No. 4, April 1990

ratesof spontaneous firing,a lessvigorous response to stimulus onset,and slowerdepletion ofavailable transmitter. It doesnotaffectthesteady-state response rate after adaptationbecause thisis mainlydependent upona balancebetweentherateof lossof transmitterfromthesystem(1) andthe rate of replenishment (y), asshownin Table I.

Geisler(1981) hasmodeledthe difference betweenthe two typesof fibersin termsof thereduced sensitivity of thepost-synaptic membrane for Notes and Briefs

1814

TABLE I. Theeffects ofchanging asingle model parameter onvarious measures ofsingle fiber response to250-ms I-kHztone bursts (see text).Allparameter values arereduced except AandBthatareincreased toshow their effect upon dynamic range more clearly. Asterisks indicate achange greater than10%from baseline. Fixed parameters were M = 1, h = 50 000, anddt = 0.05 ms.

Meddis( 1988)

.4

.4

5

10

B

300

B

g

y

/

r

x

Parameter

g release

2000

Y replenish I loss from cleft

2500

ß recovery

6580

x reprocessing

1000

5.05

2.5 1250

3270

66.31

33

Spontaneous rate

64

78*

47*

47*

39*

102'

74*

64

Saturatedrate

99

99

99

97

49*

198

99

100

rate-threshold(dB SL) sat-threshold (dB SL) .

45 70

50* 75

45 80*

45

45

45

45

45

80*

70

80*

65

75

75 57

61' 56

72 57

78

82

97*

51'

99*

72* 7.2

57 7.8

89* 4.5*

36* 8.1

98 5.4*

1.2

1.1

1.2

1.2

Adaptationtimeconstants(ms) T2 ( + 20 dB) short term T2 ( + 50dB) short term

TI ( + 20riB) rapid TI ( + 50dB) rapid

synchronization( I kHz)% synchronization(5kHz)%

7.7 1.2

3.2* 1.3

91 62

91 62

6.8* 1.3

2.2*

91 63

lowspontaneous ratefibers.We havenotexplored thispossibility, butit is unlikelythat post-synaptic sensitivity changes canpredictadaptationrate differences suchasthoseobserved by Rhodeand Smith ( 1985).

91

91

87

83*

91

63

63

61

58*

63

V. QUICK CALCULATION

OF SYSTEM CHARACTERISTICS

For a givensetof parameters, somecharacteristics of thesystemcanbe

directlyspecified. It isan incomplete listbut maybe usefulfor somepurposes.For example,it is usefulto know the valuesof reservoircontents TABLE II. Effectofchanging all permeability parameters toproduce a medium spontaneous -ratefiberwithhigherthreshold andwiderdynamic range.Asterisks indicate changed parameters. Fixedparameters wereM = 1, h = 50000,dt = 0.05ms. Mediumspontaneous Meddis (1988)

rate fiber

duringspontaneous firing.Thisallowsusto setup themodelbeforeintroducinga stimulus in a mannerconsistent witha longpreceding silence. Usinganalytical approximations it ispossible fora givensetofparametersto determine thespontaneous andsaturated firingratesaswellasthe rate-intensityand saturationthresholds.

Thespontaneous firingrateisdetermined fromtheequilibrium stateof thesystem withno input.That is, thereservoir contents donotchangein time so Eqs. ( 1)-(3) of Fig. I canbe rewrittenwith the derivativessetto

Parameter

.4

5

10'

B

300

3000*

g release y replenish

2000 5.05

1000' 5.05

/ loss

2580

2500

r recovery

6580

6580

x reprocessing

66.31

66.31

Spontaneous rate

64

15

Saturated rate

99

97

zero.Uponsolvingthethreesimultaneous equations weobtain c = kym/[y(l q=c(l

+ r) + kl],

+r)/k,

t• = C r/x, where

k=gA/(A

+ B).

Theseequations areexact,thespontaneous firingrateisobtained in the usualway from c. We may obtainan approximationfor the saturatedfiring rateby con-

Rate threshold (dB SL) Sat threshold (dB SL)

45 70

50 95

thereservoirs donotvaryin time.Wemaytherefore usetheaboveequation for thecleftcontents, c,butwitha modified valueofthepermeability functionk. For therangeof parameters considered in thispaper,at saturation

Adaptationtime constants(ms) T2 ( + 20dB) short term

75

99

T2 ( + 50 dB) short term

57

61

TI ( + 20dB) rapid TI ( + 5ORB) rapid

synchronization( 1 kHz) % synchronization(5 kHz)%

1815

sideringthebehaviorof thesystemat a frequencysufficiently highfor phase lockingnottooccur.In thiscase,oncethenervehasadapted,thecontents of

7.7 1.2

91 62

kl• y( l + r)

II.l 3.2

sothecleftcontents aregivenapproximately by

91 63

To determine therate-intensity andsaturation thresholds weagainuse the equationfor cleftcontents, but with the permeability functionk replacedby (k), theaverage of k overa singlecycleof input. Thereis no simpleanalyticalsolutionfor theaverageof k(t) overa

J. Acoust.Soc. Am., Vol. 87, No. 4, April 1990

c•ym/l.

Notes and Briefs

1815

singlecycle,butit isa simplematterto numericallyintegrateto obtain(k) and then usethis in the equationfor cleft contents.The rate-intensityand saturationthresholdsmay then be obtainedby interpolatingbetweenthe calculated values of cleft contents at different stimulus levels.

Although theseapproximationsare formally derived as a high-frequencylimiting case,simulationsshowthat theseresultsare valid overthe entire frequencyrange. ACKNOWLEDGMENTS

tory fibersusingstatisticallydefinedcriteria,"J. Acoust.Soc.Am. 77, 1102-1109. Kiang, N.Y. S, Watanabe,T., Thomas,E. C., andClark, L. F. (1965). Discharge Patterns ofSingleFibersin theCat'sAuditoryNerve(MIT, Cambridge, MA). Liberman,M. C. (1978). "Auditory-nerveresponse from catsraisedin a low-noise chamber," J. Acoust. Sec. Am. 63, 442-455.

Meddis,R. (1986a). "Simulationof mechanical to neuraltransduction in theauditory receptor,"J. Acoust. Soc. Am. 79, 702-711.

Meddis,R. (1986b). "Commentson'Very rapidadaptationin theguineapigauditory nerve'by Yates, G. K. etal., 19857 Hear. Res. 23, 287-290.

We wouldlike to thank Roy Patterson,StrangeRoss,PeterAssman,

andQuentinSummerfield for usefuldiscussions andhelpfulsuggestions. The work is supportedby an SERC grant.

Meddis,R. (1988). "Simulationof auditory-neural transduction: Furtherstudies,"J. Acoust. Soc. Am. 83, 1056-1063.

Rhode,W. S.,andSmith,P. H. (1985)."Characteristics oftone-pip response patterns in relationship to spontaneous ratein catauditorynervefibers,"Hear. Res.18, 159168.

Geisler,C. D. (1981). "A modelfor dischargepatternsof primaryauditory-nerve fibers," Brain Res. 212, 198-201.

Geisler,C. D., Dcng,L., andGreenberg, S.R. (1985). "Thresholds for primaryaudi-

Quality evaluation by acousto-ultrasonic testing of composites [43,35.Cg,43.40.Le] A report preparedby Alex Vary of Lewis ResearchCenter reviews acousto-ultrasonic technologyfor nondestructivetesting.The report dis-

Rose,J. E., Brugge,J. F., Anderson,D. J., and Hind, J. E. (1967). "Phase-locked response to low-frequency tonesin singleauditorynerveFibersof thesquirrelmonkey," J. Neurophysiol.30, 767-793.

fydamage ordegradation ofproperties aftercomposites havebeenexposed to hostile environments.

Furtherinformationiscontainedin NASA ReportTM-89843 [ N8720562], "The Acousto-Ultrasonic Approach" availablefrom NTIS, Springfield,VA 22161.

cusses principles,suggests advancedsignal-analysis schemes for development, and presentspotentialapplications. Acousto-ultrasonics hasbeenappliedprincipallyto assessdefectsin laminatedand filament-woundfiber-reinforced compositematerials.The techniquecanbe usedto determinevariationsin suchpropertiesastensile, shear,and flexuralstrengthsand reductionsin strengthand toughness causedby defects.It canbeusedto evaluatestatesof cure,porosities,orien-

tationof fibers,volumefractionsof fibersand matrices,and qualitiesof interlaminar

bonds.

The term "acousto-ultrasonics"

is a contraction for "acoustic-emis-

sion simulation with ultrasonic sources." Conventional acoustic-emission

Optical measurement of sound pressure [43.35.Sx, 43.25.Zx] An opticaltechniquethat canbe usedto measureacousticpressure withoutdirectcontacthasbeendevelopedby EugeneH. Trinh, Mark Gaspar,andEmilyW. Leungof CalTechfor NASA'sJetPropulsion Labora-

tory.Thetechnique isespecially valuable whereit isnecessary tomeasure in a remote,inaccessible, or hostileenvironment or to avoidperturbation of themeasured region.In theoriginalapplication, thetechnique wasusedto

testingdependson loadinga part to excitespontaneous stresswaveslike those that accompanyplasticdeformationsand the growth of cracks. Acousto-ultrasonics differsmainlyin that the ultrasonicwavesare benign and are generatedexternallyby pulsedsources(usuallypiezotranducers). In a typicalapparatus, a transmitting probeanda receivingprobeare placeda specified distanceaparton thesamesideof thepart undertest.The

measurethe acousticpressure arounda sphereacoustically leviratedin a

sending-and-receiving paircanbe movedaboutasa unitto scanthe part.

the indexof refraction,and the alternations in turn produceoscillatory deflections of thebeam.The deflection isproportional to theacousticpres-

Signal-processing instrumentation analyzesthereceivedsoundto generate a mapof variationsin the propertiesof the material. The sensitivityof theacousto-ultrasonics hasalreadybeendemonstrated experimentally. The technology hasbeenusedto detectand quantify subtlebut significantvariationsin strengthand resistance to fractureof fiber-reinforced composites. This achievement isremarkablebecause it was

accomplished withrelativelyunsophisticated signal-processing andsignal-

furnace.Because themeasurements are almostinstantaneous, a possible applicationof the techniqueis to generatefeedbackcontrolsignalsfor acoustic levitators.

A laserbeamis directedat theregionof highacoustic pressure to be measured.The soundcausesrapidalterationsof densityand, therefore,of

sure.The laserbeamhasa negligibleinfluenceon the acousticfield. After passing throughtheregionof interest,thebeamisfocusedontoa

knifeedge,asin a schlieren system asshownin Fig. 1. The knifeedgeis adjusted to intercept all or partof theundeflected beamsothattheportion that passes theedgeand fallson a photodetector varieswith the deflection. Thus the greaterthe acousticpressureand the deflectionof the beam,the

analysisprocedures. Althoughacousto-ultrasonic technologyhas beenusedon polymermatrix composites, it is applicableto suchother compositematerialsas metalsreinforcedby fibersand ceramic-matrixcomposites. The use of

greatertheintensityof thedeflected beamandtheamplitude of theoutput

acousto-ultrasonics shouldbeconsidered whenever it isnecessary toquanti-

Baltimore/Washington International Airport,MD 21240.

of thephotodetector. A detailedmapof thepressure fieldcanbeobtainedby scanningthe fieldin threeorthogonaldirections.More informationcanbe obtainedfrom Manager,TechnologyTransferDivision,P.O. Box 8757,

Ptløtø•let [ Knife

Sound Field

Edge

•

Output

FIG. 1. Thesoundfielddeflects thelaserbeamproportionally to itsamplitude. A knifeedgeintercepts theundeflected beam,allowing onlythedeflected beamto reacha photodetector. Theapparatus iscalibrated bycomparing theoutputof thephotodetector withthatof a microphone.

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J. Acoust.Soc. Am. 87(4), April 1990;

0001-4966/90/041816-01500.80;

@ 1990 Acoust.Soc. Am.; Notes and Briefs

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