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Improved mirror systems for high resolution ultrasonic imaging
TRASONIC IMAGING 7, 107-121
(1985)
IMPROWDMIRRORSYS~
FDRHIGHFESOLUlTIONDLX'PASCNIC
IMAGING
J. J. Nicoll, J. M. Pig-gins', W. N. McDicken and R. Horthwick DepartmentofMedical Physics andMedical Engineering TheRoyal Infinnary Edinburgh Em 9Yw, Scotland
High resolution ultrasonic imaging in a water bath, for example breast demandsatransduceroflargeaperture. Suchanapertureismst imasinsr Previous such mirror systems easily achieved by theuseofmirrors. suffered problems frm reverberations between and within their ccqmnent Changes inthedesignofthesystem, andtheuseof thin metal parts. reduce these reverberationstoanacceptablelevel. There is reflectors, no sacrifice inthe focusitqperformnce, andlosses inthe system are fz 1985 Academic E'ress,Inc. minimized. Key words:
transducers;
Fccusing;imging;mirrors;
ultrasound.
lNTFCXUmON The minimum separation D of two point targets which can be separately distinguishedbyasystemofnumerical apertureNAisgivenby
where x is the wavelength of the radiation. Thecmstant, a, takes the value 0.61 if the Rayleigh criterion is used, or 0.5 for the Sparrow criterion [l]. Because of this relationship, the ability to separate closely spaced targets depends ontheuseof a large ame. For freguencypropagatinginwaterof35Chas a exarrple, ultrasoundof5MHz wavelength X of 0.3 mm. For a resolution D of lmm, if the Rayleigh criterion is used, we require a numerical aperture NA = a&D = 0.18. The normalpractice inultrasonic imaging is toapplythe transducer as close to the region of interest as possible, as this minimizes the size of transducer required for a given numerical aperture. However, we have been developingawater-bathscanner [2] for imaging the breast. In this case, thetransducermuststandscnnedistanceaway frmthe skin, and so theregionof interestmaybeas~~as15Ommfmmthetransducer. Ifwe demand a numerical aperture of 0.18 at this range, then the physical transducermustbeatleast54 nun. diamterofthe Constmction of a highfreguencyultrasonic transducer of such a diameter or larger is fraught with difficulties. Conventional focused probes dependontheuseofbml-shapedpiezoelectrictransducerelements, which are noteasilymanufacturedindiametersmuchabove 25 mm. Flat elements are a little more easy to obtain, but still very fragile, and may befocusedbymeans ofacousticlenses. However,oversuchlargediameters the lenses attain a significant thickness and therefore give rise to problems fmn attenuation in the lens material or reverberations between the surfaces ofthelens. Inparticular, ifaconcavelensisused, the 'Present address: Pantatron Strathclyde, ML1 2AJ, United
Systems Kingdom.
Limited,
Fern
Street,
Motherwell, 0161-7346185
107
All
Copyright 0 198s rrghrs of reproducrron
$3.00
by Academic Press. Inc in any ,form reserved
NICOLL ET AL.
Fig.
1
Conventional mirrorgemetry Fulsestransmitted from PI. T are reflected from the foous Flandfocussedbythe ellipsoidal mirror (surface E) to its internal reference point, n. These echo pulses are then reflezted by the hyperboloidalmimorH, which focussesthemtoitsexternal reference point, F3, where are detected by the they receiver.
additional attenuation in the thicker outer parts effectively apcdizes the trmcer, increasing the size of its main beam. The probe will therefore not achieve the calculated resolution. In consequence of these difficulties, therehaslongbeeninterestin the alternative use of mirrorstoachievethe large apertures [3-61. Essentially, the use ofanappropriatelycmved mirror, or system of mimrs, allcws the beam from a relatively small ultrasonic transducer to Anearlydesign, shorn in besp~dtofilltheregukedlaqeaperture. figure 1, is analcgous totheCassegrain system familiar in optical telescopes. Echoes receivedbytheprknarymirmrare reflected ontothe smaller secondary which inturnconcentratesthenlonto the transducer placed at the apex of the primary. (our terminology follms telescope practice. In figure 1, the ellipsoidal reflector, sarked 'El, is termed the smaller hyperboloid, marked 'HI is the secondary mirror). the primary, Minorvariations inthis designhavebeentried; themirrorsmaybeusedto focus ontransmissionandreceptionusingonetransducer, the transducer and the secondary mirror my be itself may be focused or flat, hyperboloidal [3] or paraboloidal [4]. The primary mirror is generally ellipsoiddl, or to ba more exact, a prolate spheroid. transducer is aimed at one feature comontothesedesignsisthatthe secmdaqmirmr, whichreflectspartofthebeam the bluntcenterofthe transducer amd the relatively flat central area of the straightbacktothe primary mirror (Fig. 1). F&2zverberations between these c5?mpmmts therefore inapulse-e&oimagingsystem, to the well-known occur and give rise, problem of artifactechoes (%tamSngechoes~~ in nondestructive testing In addition, at each parlance)whi&renderpartsoftherangeuuusable. reflection, some of the sonic energy enters the material of the mirror, my be reflected off the rearsurfaceandfiuallymypass back into the Ibis propagatingmediumaftertwo (ormore) transitsthrcughthe n&x-or. causes multiple pulses to be transmitted and nuiltiple echoes are received. Various stepscanbetakentomininðeseeffects. Rearsurfaces ofmirrorscanbeconfiguretisoastoflectorscattertransmittedsaund, and the mirrorsthmselvescanbemadeofhighly attenuating materials. and Olofsson Thestandingechoescausedbygeametryarehardertooverwme, [33resortedtousinghissystemin receptiononly, transmissionbeing from None of these aseparate transducer placedinfmntofthe mirrors. measures is entirely satisfactory.
108
IMPROVED MIRROR SYSTEMS
Fig.
2
Dsvelopnent of improved mirror gemetry. an extreme ray from (4 transdum T, which is dixecbd at its focus, Fl, is reflect4 by two mirror surfacestocmsstheaxisat F3. suchsurfaceswould be (b) ellipses with a common reference point at F2. The secondary mirror, s, has its otherreferencepointat the transducerfm, Fl, while the primary mirror, P, has itsotherreferencepoint at F3. Although Fl and F3 lie onthetransduceraxisF2may be displaced so that the mirror surface crosses the axis at an acute angle. (c) A solid surfaoa my be generated byrotating abcut the transducer axis thus mirrors which are sivins pointed.
NEWMIRlWRCONFIGURATION Reverberationsbetweenthecgnponentpartswouldbegreatlyreducedif the secondary mirrorweretobesharp-pointedrather than blunt. This would meanthatverylittlesonicenergy~dbereflectedstraight back Figure 2 (a) shms a half-section through the to the t?zamducer. hypatheticalsyStem~~~decidedtodevelop. !Ihecenteroftheprimry mirrorwaildnotbe~ill~~~butastheCentral~cannotcontribute tothe focus inanycase,thisisofnoconsequence. suchapointed~~isnotallawedwithintheclassical clearly, whichdemndsreflec&gsurfaceswhose configurations c==slra~ m, Transducer Tis intrinsically focused at point Flon are conicsections. Itsbemisintemeptedbya pointed secondary the axisofthesystem. mirror P. Thebeamreflectedfranpisrequiredtoconvergeatthe final focus F3, alsoontheaxisoftbesystem. Thepmblemistoderivecmms for S and P which will give the system this property, while giving the centralpcintof S the requireddegreeof sharpness. lIhedesired focalprcpertieswillbe&tainedifthesectionsof~ and P are ellipses with gemetric foci Fl and FZ!, F'2 and F3 respectively. Then fmnthewell-knownpmpertiesoftheellipse, thein.itialbeamconvergent towards Fl will be comer&d bythesecom&ymirrortoabeamdiveqmt fmnthe cxxmmnrefererrcepointF2. This in turn Will be reflected by the prinmymirmrtoumveqe to the desired focus at F3. Ifthethreepoints, Fl, F2 ardF3wex-e colinear, thesystemmuld reduce to one case of the classical Gissegrain configuration (i.e. with a blunt secon%ry mirror as in figure 1). However, wemay equally well choose tolccatethecmmonrefereme pintF2 atapointofftheaxis of
109
NICOLL ET AL.
thetransducersystem, as indicated in figure 2 (b). Thisdiagram shms that the section of the secmdaqmirrorS, if drawh inits entirety, is an ellipse whose long axis FlF2 is inclined to the axis of the transdumr system. The curve Sthemforecutstheaxisofthesystemat an angle which is not a right angle. The same is true of curve P, but that is less impomt. Naturally, we wish the completed transducer system to have rotational symmetry about its axis FlF3. Therefore, wetruncatethe ellipses S andP where they cut the axis, andgeneratesolidfigures by rotating the truncatd portions of theseellipsesaboutthe system axis. A cross section of the resultant geometry is shmn in figure 2 (c). It can be seen that because CurveSmeetstheaxisatan angle, the secondary mirror generated in thiswayhasbeenthedesiredpointsothatits surface is never parallel with that of the transducer. Therefore wehaveamirrorsystemwhichhasthe focusirgproperty of the conventional mirror system, but in which the mirrors are not ellipsoids, hyperboloids nor paraboloids. They are insteadsolid figures generatedbyrotatingasegmentofan inclinedellipeeaboutthe principal axisoft.hesysten~.
A design on the principle suggested in the preceding paragraphs is subject toagooddealof freedm. ThedistanceofF1frmtransducer T depends on thefocalpropertiesofthattransducer, whichcanbe chosen accordingly. The position of F2 can be chosen freely. In addition, the sizes of the ellipses S and P, and the outside diameters at which these are terminated (i.e. the diameters of the mimrs) must be specified, as must the diameter of transducer T. The critical considerations inchoosingadesignarerevealedby the The central ray is diverged to central arxdouterraysfmWmsducerT. sewr&zymirmr. It&mild anextentdetemined bythepointangleofthe arrive back at the primary mirror at a radius outside both that of transdlucerT,andthatoftheareaoftheprimarywhoseviewoffocusF3is Asafetymaxginshouldbe left in obstructed by thesecondarymimor. accmmdate geometrical inaccuracies and the effects of order to diffraction. The outennostrayfmn txranduce.rTmuststrikethesewndarymirror near its edge, butagainleavinga rmaonable safetymaxgintopreventany of secondary. Similarly, after reflection frcm thebeamfmnbypassingthe the secondary mirror, the rayshouldxeachtheprimary m%r, but not its edge. Thus,theauterdi~~oftheprimarymirror~t exactly at, be somewhatlargerthantheeffectiveapertureofthesystem. the required gematrical parametere were From these criteria, detenninedbytrial artderror. Theprocesswasaidedbyacoqmterpmgrm which, given positions of Fl, F2 and F3 and Size parameters for the prin-ary and sewndaq ellipses, displayed thecuxvesonavisual display unit attachedto the cmputer. curveswhichlooked reasonable By =P=+=t, were found, andwerethenprintedonahard-capyprintersothatdetailed Paramaters were then modified until a ray tract couldbeperformd. Anexaq~leoftheczxquter out@ is satisfactory designwasachimMi. shcwn in figure 3. which
'IheparametersOfthe~~findllYselectedbythiSProcedure,and wedescribeintherestofthispaper, areasfollmm.
110
Focus Fl,
IMPROVED MIRROR SYSTEMS
Fig.
-80 -40 0 40
80
12Omm
3
mtputof interactive design The vertical axis Program. is through the mmon reference pointof the two ellipses. The axis of symmetry is displaced frcm this by 2.8 mm.
lieS15Om fm T. lies 60 mm from transducer T, andthe finalfoCUsF3 point F2 lies 30 m from T, and 2.8 nm off the The wmon reference Semi-major axes of primary and secondary ellipses P and s principal axis. are respectively 91.7 mn and 19.3 mm. ?heprimarymirroristruncat&at 112mmdiameterandthedesign&apertum, lhnitedasdescxibedabove, to approximately88m. Thisreqiresa transduOe.r of 15 mm active diameter. The configuration, withcentralandoutemcstrays sketched, is shcm in figwx 3. Note that the axis drawn by the com@er is not the principal paralleltotheprincipalaxis. The vertgx axis, but alinethroughF2 half-angle of the secondary mirror S has been calculated to be 71.2 sufficient to spread the reflected beam beyozd the area of the prima& which is occupiedbythe transducer,astheraysdrawninfigum3show.
Gur new gecanetry, with its poinw seamdaqmirmr, doesmch to czmpnents. Thereverberationduetothe reducereverberationsbeixeenthe echo fmn a 2nmsteelballtargetwasfaundtobeless than -60 dB TherelrEmainsthe problem of reducirKJ campared to the echo itself. reverberationwithFneachmirror,whileretainingakighdegreeofacaustic reflectivity. To achievegoodreflectivityatthewater/mimr interface requires a high degree of mimatch of acoustic impedance. Onemethalof achieving thisistomakethereflectorofadensemetal,whoseaccustic impeaanceis mchhigherthanthatofwater. Brass, for exa.uple, was used by !&urstone A disadvantage of metals is that their attenuation is and McKinney [4]. relatively lcrw and therefore reverberations can occur between front and rearsurfaces. An alternativemeansofa~i~ingahi~degreeofmisMtchFR3Uld be to use amaterialwithamuchlmerinpe&methanthatof water. Air serves this plrpose aMU, as there is virtually total reflection at a water/air interface. unforl3.mately, air requires to be contained. an air HOWWCX, if the containing walls are very thin, we have effectively reflector. Ahollcrwprimarymirrorwasthereforeconstruct&. First stage in manufactWeofsu&amirmrwasto tum male aW femalebrassmuldstothe formofthenquiredreflecting surface. This was done by computinglathesettings fmtheparametersof the cwxe. copper sheet, a hole was N=-% frcm a circular piece of 22 mq (0.71m)
111
NICOLL ET AL.
cut frcmthe transducer aperture atthecenterofthemirror. n-ie ccrpper wasthenannealedbyrqxatedheatingandquenching, andpressedto shape between the brassbmlmulds. Thisproducedathin (lessthano.68 mm afterstretching) ccpperbmlwithace.ntralaperture. This was glued at its innerand~~edgestOholl~~copperlinderswhich formedthewalls of the final structure, and finallythebackwas closedbysolderingona flat, annular copper sheet. The same technique couldnotbeusedtomake the small secondary mirror, because it is inpcssibletopress ametalsheettothe sharppoint which is required. A solid brass reflector (as used by 'Ihurstone and McKinney [4]) was found unsatisfactory bemuse of inte.rnal reverberations. A better reflector of reasonably high acoustic iqedame can be made frcnn a cmposite of grains of high densitymetal enbedded in a matrix of attem&ing material. The cxqosite has a high attenuation not only because of the attentuatingmatrixbutalsobecause of the scattering effect of the g-rains. For the sewMarymi?mx, weus&a cxqmsite of Araldite (-inMY 753 +haMenerHY 951, CIIBA- Geigy Ltd) and tungsten powder (1 m in diameter) in a ratio of 1:2.5 by mass. The mixture was thinned by additional hardener so that entrained air bubbles could be remved by evacuation. As sucha ccqmsitedces notmachineeasily, itwas turned frcm lathe cast toshapeinawaxmouldfozmedonabrassmaster, settingscmpulxdasdescribedpreviously. l'herearofthemirrorwasmade conical rather than flat as a further precaution against reverberations. The cxmplete mirror assenblyisshmminfigure facilitate aligmnent, the hollm capper primary methylmethacrylate (Ferspex, trade mark of Implerial
Fig.
4
Coqletedmirmrsystem.
112
4. In order to sits on a WYChemical Industries
IMPROVED MIRROR SYSTEMS
Ltd.) baseplatebetweenthmeequallyspacedadjustingscmaws. Theseallow the~i~~ofthegrimarymirrortobeacc;watelysetsothatitscentrdl in front of it. axis coincideswiththatofthe sew&azymirrormspe&ed The seamWymirrorismountedbywayoftwoslidingmdswhose position iscmtrolledbyaleadscrew, seeninfigure4, sothatthedistance of the seamdaq mirror frwntheprimaryczmbe adjusted. Although this distance has acorrecttheoreticalvalueinaccordance with the design calculations, in practice itwas fou&thatsmallvariationshere varied the position ofthe final focusF!3withcutnoticeabledegradationof the size of the focal zone. As regardsthealigmnentofthesystem, itwasfoundthat this was best done byattachi.ngthemirrortoawater-tankEkscansy.stem [2] and scanned across it. observing the image ofawiretaqetasthemirmr Figure 5 (a) shows the imageobtainsd when the primary mirror was deliberately offset by a fewmillimeters; the asymmetry is apparent, particularly forawirenotatthe focal distance. Eyadjustmentof the screws, ~theprimaqmimxwasmovedsidewaysuntil asymmetrical -ins response pattern as in figure5 (b)was obtained. The whole mirror assenbly was then rotated by 90°, and the pm repeated to obtain Cmrectaligmentinthe0rthcgonaldirection.
The simple point resolutionequation (Eq. 1) assumes Fraunhofer diffraction conditions and applies only approximately in the case of a large numerical aperture. In practice, the aperture of any large transducer will almost inevitably be apadized. Aconcave lens will be thicker txlwadstheouteredge, thereforeattemmtingthebmmmorethere anclinatwo-elemmtm.irmrsystemthe sewmAry will entirely block the center. In that case, transmission and/or reception will be over a broad annulusratherthanacimularaperture. It is possible to predict gualitively that blccking the center of the aperture will reduce the size of the focal spot (Airy disc) and that energy from here will be redistributed to the side lobes [l]. An approach is required which quantifies the effect of apodization arid predicts the relattve performance of such apertures. The mdelusedis adevelopm?ntofonebyArcher-HdllandMi-Bashter They investigatedthe fieldduetoverydeep (scnne hemispherical) concave spheriml bowl transducers over the byintegratingPres== transducer surface. Theuseofcarefullychosengeometrical constraints resultsFnasingleintegral~~andMecaseofamirrorilluminatedby an incidentbmmisdirectlyanalogms [8]toatmnsmitterbutaunifonnly excited surface is assumed and the algorithm nust bs modified to incorpxate apodization. The cqxkerimpkmentaticmofthe model was VerifiedbyreproducingtheresultsofArcher-HdlandAli-Bashter. [71.
This numerical model describes a continuous wave (a) concave, spherical radiator. Thesimplifiedgeomstryandtheuseofcwresults ina model which may beevaluat~easilyandquickly for various numerical apertures and for various sizes of central block. In the pulsed wave (ml) case the focal spot will be ccqarable but the Cw model will have an extensive side lcbe structure and is unable to predict the axial profile of the beam. The CWinterference pattern extends thrwughallspace whereas that of pilsedwaves (Pw) is limitedtophase differences within the pulse Fost1~andHunt[9]fomdgoodagreemen tbetweenCWandPWtiels 1-a in the far field of a plane disc transducer. 'Ike near field of the pw
113
NICOLL ET AL.
Fig.
5
Alignment of mirrorsystemusingB-sznimageofwire a) before adjustment; b) after adjustment. theedgesofthephotogra@sarelOnnnapart.
114
'Ihe bright
targets. marks on
IMPROVED MIRROR SYSTEMS
sticture of the Cw solution although solution lacks the fine interference Fccussing with a spherical bawl will intrcduce minima do exist. This far field CW interference will be interference beyomi thefocus. ameliorated bytheapcdizationbutonlyattheexpenseof increasing the side lobes [lo]. Side lobe mnplitude is an important limitation in an imaging transducer. l'hus, althoughtheaveragepressureshcwnbytheCW solution will indicate the pulsed field, the actual interference structure will not exist more than a pulse length frcm the focal Zone. 'Ihe boundary ccmlitions used are those attributed to Huygens, i.e. a infinite planar baffle. These of Kirchoff (which model a totally rigid, inmmsed trausducer with an ideally rigid back, totally isolated frm the transmitting surface) are a better physical apprmcimation to the hollcw mirrcr but the two models give results which differ only in the size of the peaks in the Fresnel region, and the field close to the aperture is not of interest in the present work. There is no consensus in the literature on which parameters are most apt for describing beam shape. Kossoff [ll] uses the diameter of the first off-axis zeros. Foster andHunt[9] use full width, half maximum. Weyns [lo] refers to both the -3 dB and -10 dB contours. Since apcdization will have most effect on the lcwer part of the zero order focus and on the side lobes, we have investigatedUne radiusofthe -lOdBcontour, the first off-axis zero and the first off-axis maxims. The respmseoftheCWmcdeldescribedprevicuslyto increasir~.~ the size ofthecentralobtructionduetothe secoAaqofamirrcrsystemis shown in figures 6, 7 and 8. !Ihese figures shm calculations for the transmitted field anly. Figure6showsthebehaviourofthethree beam widthpa.mnetersdiecuss&inthelastpa?qra~. Theradiusofthe first off-axis zero (Airy disc) decreases shmingadecreas e in size of the main lobe but the -10 dE! width and the position of the first off-axis peak are unaltexed. 'Ihe peak pressure (Fig. 7) showsadecreaseapproximatelyin pmportiontothereduction insurfaceareaofreflector. Themostnotable effect is in the amplitude of the side lobe maximum relative to the peak value (Fig. 8). Thisimmasessteadily, atldBper6nunincrease in diameterofthecentralstopbetweenloand40mmdiametess. nUIlE?r.icdL ~lWdelwasusedtocalcliiatet.he~tted thedimensionsofthefinaldesign. The resulting
field beam
'IhiS
using
I
IO-
RlTdmdcumlt~=lsonml chLnd=nhn
lo-
l
l
.
.
.
1st
off-am
,'e
10 20 30 40 &
6
Fig. 7
.
lmxm
10 20 30 LO i?L
DAMTER CX=CENTW ST@ m m
Fig.
.
PEAK PRESSURE
RAD(us mm
transverse
0,ANETER OF LWTRE Sl$
Effects cnacalculatedkeamshape size of the center stop of a large Effect on~=alculatedpeakheightof centerstopofaconcavebowl.
I15
parametersofincreasing cmcave bawl. incmxtsingthesize
the of
the
NICOLL ET AL.
RELATIVE PRESSURE
dB /mm) -'
Radus
0
0
10
20
30
of cwvafwe = KOmm chord = loGmm
40
s, mm
OIAMTER OF CENTRE STOP
Fig.
8
Effect on a calculated amplitude of first off axis peak relative to the nmxinnrm of increasw the size of the center stop.
Fig.
9
Transversebeam mcdel.
shape of finaldesigncalculatedbythe
numerical
shape is shcmn infigure9withammothcurvedrawn through the data points usinga piecewisecubic polyncmialn&hod. The CWmodel gives a -12 dB focal depth of field of 9 mm; hmeverasdiscussedearlierthe Pw field will only closely resemble the CM interference pattern close to the gemetrical focus. lbe calculated focal size will be wmpared with obsemedexperimntalperfonnancelater.
ideally
Altlmugh the reflective copper surface is thin (0.68 mm), it thin whem ampared to the wave length in capper (0.95 mm).
is
not
transducerused to drive the The pulse shape fromtheaammrcial mirror system was ewminedusingabilamimr shielded PVDF hydrophone (Marconi F&sear&Laboratories) in the far field, appmximtely1OOm from Theplsewasalso examhedata similarpath its surface (Fig. 10 (a)). length but including a stile reflection by the air backed mimr (Fig. 10 of danping, the (b) 1. Using the transducer manufac%xrer~s specification Hmewr, 2 s afterthestarkof pilselengthis increds%dby0.5cycles. the pulsetherefleckdsignalis still only -27 dBccarparedto its peak while the original pulse is reduced to -35 dEL mchdegradationwouldnot be consider&serious forourpresentpurposes. E&am Shape and Focal Zone Size ~~1ateralpointresponseofthemFrmrsystemwasexaminedbymoving atargetthrcnqhthefocalzone. Tilepcx3itionofthefocuswas&ikntobe the highestp&akpressum The relative fa.lrxI experimentally. positionsofthetwolRimrsandthe tmxdmer~adjustedtoplacethis peakatthegecmtricalfccus. very
~transversebeam~isdifficnilttoexaminebecausethefocusis l'EmXW, the predicteddiameteroftheAirydiscbeing1.1
116
axial
mm.
No
IMPROVED MIRROR SYSTEMS
Fig. 10
(a) (b)
Pulse shape in the far field (range= 100 mm) of I2 le transduoerusedtodrivethemirrorsystem. callmemial The pulse at the samepathlength but after a sing1 .e reflection by an air backed mirror.
117
NICOLL ET AL.
HolfwKfth 034m 034mm 047mm 049mm
0 66mm
011
0
5
w
Fig. 11
Transmitted beam profile observedwithaPVDFhydrophone
Fig.
Fulse-echobeamprofileatthe 2 mmdiameters@ricalsteeltaqet.
12
12 O-
mm
rod/us --mm
at the focus of the mirror (activearealmdiameter). focus ofthemirror
system
systemusinga
target was fomdwhichwassmallcmparedwiththefocus and hence expsrimental beam shape is a convolution of the beam and the target.
any
'Ihe hydrophoneavailablehadanactivediscof1m diameter. Thus when centered on thefirstmininm approximately 42% of its area falls withinthecdlculated zeroorderfccusreceivingabout2O% oftheenergyof the mainlobe. Thetransversebeamshapedetectedbythe hydrophone is directcmparison shown in figure 11. HCWeVX, forthefeasonsstated, with the calculated shape (Fig. 9) is not possible. !Ihe hydrophone is useful examiningpilse shapesbutisunabletodetenninethe shape of such anarrmbeam. As analternativetargeta2mmdiamteXstainless steelballmunted on a 19-gaugehypodermicneedlewasusedtogeneratea pulse-echo plot. This is a standafd target of the type suggested by Lapacewicz and Hill sectionislargecmparedwiththe focalsizeand [=I * Althoughitscross its curved surface pannits finer resolution than the with theh~one, flat 1 nun circle of the hydrophone. Theconvexsurface also makes it difficult to appreciate the effect of the target's size upon the resultixq plot. Smallerreflectivetargetsproved insensitive and unsatisfactory in use. Thinmetalwiretaqets didnotgivereproducible resultsbecausethe echo size was very dependent of the orientation of the wire relative to the beam. This was especially critical with the highly focused and slightly asymetric loams observed frcxn the mirror system. ApiLse-e&oplot, usingthe 2 mqhericaltaxget, is shown in figure 12. This pilse-echo plotmaybecmparedwiththetheoretical plot by approximating theconvolutionoftransmissionandreceptionbythe square 'Ihis has been done in of thetransmitted fieldpredictedbythemodel. 9), pulsetable 1 which shms the widths of the CWnumerical model (Fig. echo (Fig. 12) and hydrcphone (Fig. 11) results at cozpamble levels in the Doththeexperimentalplots areasynetric amI the half-width focal zone. hasbeenobtainedbydividingthe Aill-widthbytwo. Differences between the three beam profiles (Figs. 9, 11, 12) are between the experimental plots of clearly visible. The differences transmitted field (Fig. 11) using the hydrophone amI the pulse-echo field (Fig. 12) using aqhericaltargetcanonlybeunderstoodby considering the influenceofthetaqetupontheexperimental abservations. A=holJm
118
IMPROVED MIRROR SYSTEMS
Table 1.
Performance
of the Mirror
System
cwNLmErica1 rodeI.
Experiment Pulse-Echo Hydrcsphone
-6 dB Half-width
0.22 Rml
0.34 nun
0.44 nml
-10 ds
0.28 mm
0.47 mm
0.56 mm
-12 dE3
0.30 lmn
0.49 nml
0.59 lmn
-20 dB
0.37 mm
0.66 ml
0.74 nml
Relative height of first side lobe
-28 dB
-20 dE3
-18 dE3
Average radius of first side lobe
0.7 mm
1.8 m
1.3 nml
Feature (Transmission
and Reception)
both show a similar as-try the pattern of side lobes and their positions The effects upon presents quitedifferentlywiththedifferenttaqets. beam width, allawing approximately for transmission and reception, are Thepulse~oplotgivesthemoreaccuratedescription ShOWll in table 1. sincethelatqetargetcannot reducethebean~beluwitstruesize; however true beam there is little evidence to suggest that this represen tsthe size. It is hcwever encouraging that one side lobe at least is well defined. The differences betweenthebeamwidthpredictedbythemodelardthat faundbypulse-echoplottingaregenerallyabauttwicetherPagnitudeofthe differences between the~experimentdlplots. Contributions to this difference come fram two sources. Themodelisverysinpleanddces not repment the design exactly. 'Ibe designis ccmplicated and device constructed will not beperfect. An important si.qUfication in the nurkerical model is the use of the Cw approximation [10,13-151. Various workers have reported on the relationship of CWand FW fields although not for suchhighly focusseddevicas. Thequalitativedifferencesbetween CW andFWbeamcouldbeexpe&ed. !lkemainlobewouldbareducedinanplitude andhavea broadershape:thesidesbeingsteepernearthebase. Weyns[lO] found this effectnxxemarked forbowlswithanumericalaperture greater than 0.2. !thereduction inmainlobeamplitudewould increasethe relative size of the first side lobe. Intherealsystemthebeamis spread and then focussed bymirrors~~areatcont~~lyv~~anglesto the directionofpropagation. This will lead to variation in intensity across theannularam. SinCethemodelrepresentsthethreeelen~&nkrror system as one elementtheeffects of this apcdization, which tight be expressedasareduction intheeffectiveuuterdiameter, arenot included in its rf?sults. Differences between the design (Fig. 3) andthemfactured mirror Thedesignassumesthe mm (Fig. 4)cxeneframthreeprincipalsources. sourcetransducerpruduces anaccurate, spherically converging wavefront. The transducerus&inpracticedoesnot. Bothlnirro~~ manufactured fran moulds SIX neither cauldbemadedirectlyand this limits the precisionofthe final surface. Thedesignwithitspointed~r~fa~ isverysensitivetomisali~oftheaxesofthethree elements. Ihe
119
NICOLL ET AL.
asymmetric nature.
beasseenexperimntallysuggests
Using the foundtobe16nnn.
pulse-echo
technigue
a slightmisaligmentof
this
the -12 dB focal depth of
field
was
DISCUSSION me The mirror system perfomswellarrdis a useful imaging device. relatively sinpJle model predicts beam profiles and the effects of the annular aperture well enabling the determination of a suitable annulus for the chosenlengthandfreguehcy. Differences between model at-d observed performance are causednotonlybythe&ange fmncontinuous to pulsed (transducerandti waves but also by the presence of three elements lllirrorS) so increasing the scope for constructional imprecision. In thetransducerisnottheperfectlyfccusseddeviceassumedby partid=, theory,anddLigrrmentofthe~rel~~isnotperfect,asmaybeseen fmn the asymmetry of the txansve.rse plot. Fointedreflectorsweuse are more sensitive tomisaligmentthanaresi~@e conic reflectors. More sophisticatedtechniguesarereqiredtonmasure the beam experimentally. believe that our desigh is a significant inprovement over Firstly, the configuration of previ!Zlyreportedsystemsintwomspects. and secondly, theuseof a the mirrors reduced confus* 3zvedaation6, hollcw reflector maintains acceptablesignalstmangthdespite the four Gursystemgives successivereflections involved inapulse-echoseqence. a 20 dB lateral dynamic Lange. This is achieved withaut sacrifice in its lateral resolution and gives sufficient contrast for the variation of tissue fomd inthelccalisedregionsof interestinmanyapplications.
J. J. Nicoll H8al~.oi~of~Faulty reepectivsly, for financial
thank the Scottish Hme and of Medicine,
support.
FIEFERENCES [l]
Driscoll, WalterG. Hamdbcokofcptics -Optical pp. 6-2, 2-3 (McGraw-Hill, New York, 1978).
[2]
Piggins, J. M., Nicoll, J. J., McDi~, W.N., Kirkpatrick, Muir, B. A. ExperiencewithaVe.rsatileUltrasonicBreastSmmer. Ultzmsmnd Med. Biol. & Supplement 1, 152 (1982).
[33
Olofsson, S. 367 (1963).
[4]
Ihurstone, Ultrasonic Ultrasonic University 1966).
[53
Fry, W. J., Leichnex, G. H., Okuyam, D., Fry, F. J. and Fry, E. K. Ultrasomd visualisation system enplaying new scanning and presentation methods, J. Aamst. Sot. Amar. 4& 1324-1338 (1968).
An ultrasonic
optical
mirmr
Society
of America,
system, Acustica
A. E. and
a
361-
F. L. and McKinney, W. M. Focused TransducerArraysinan Scanning ~mfo;~ological ,Tissue, in Diagnostic - proceeding Inte-matlonal conference, New York, of Pitt&m&, 1965, 191-194 (Plenum Press,
120
IMPROVED MIRROR SYSTEMS
[6]
Patterson, M. S. and Foster, F. S. The Iqmvement and Quantitative AsmsmmtofB-Modemqel3Pmduced by an Annular Array/Cane Hybrid. Ultrasonic linaging -!+ 5 195-213 (1983).
[7]
Archer-Hall, J. A. and Ali-Bashter, A. I. Diffraction patterns of largeaperturebmltransducers, NM' International l3-51-55 (1980).
[8]
Griffirq, reflectcrs,
[9]
Foster, F. S. short pulse ul-
V. and Fox, F. E. Thsoryof intensitygainduetoconcave J. Acoust. Sot. Amer. 2& 348-351 (1949).
[lOI Weyns,
transducers,
A.
Ultrasonice [ll]
and Hunt, J. W. Thedesignandcharacterisationof transducers, Ultrasonics 16, 116-122 (1978). Radiation
part
l&
field calculations of pulsed ultrasonic sphericaldisc-and ring-&a@ transducers, 219-223 (1980). 2:
Kossoff, G., Robimcn, dimensional visualization 44, 1310-1318 (1968).
[12] Lapacewicz,
pulse-echo (1974) .
D. E. and Garrett, for medical diagnosis,
G. and Bill, C. R. equimt evaluation.
W. J. Ultrasonic twoJ. Acoust. See. Amer.
Choice of standard target for medical Ultrasound Med. Biol. L 287-289
[13] Weyns, A. Radiation field calculations of pulsed transducers,part1: Planarcimular,sguareandannulartransducers. Ultrasonics l& 183-188 (1980). [14] Beaver,
Acoust.
w. L. Sonic nearfields of a pulsed piston Sot. Am. 56- 1043-1048 (1974).
J. W., Arditi, M. and Foster, F. S. Ultrasonic pulse-echo medical imaging. IEEE Trans. Bicmed. Erq 481 (1983).
[151 Hunt,
121
ultrasonic
radiator.
J-2
transducers for BNE-30, 453-
(1985)
IMPROWDMIRRORSYS~
FDRHIGHFESOLUlTIONDLX'PASCNIC
IMAGING
J. J. Nicoll, J. M. Pig-gins', W. N. McDicken and R. Horthwick DepartmentofMedical Physics andMedical Engineering TheRoyal Infinnary Edinburgh Em 9Yw, Scotland
High resolution ultrasonic imaging in a water bath, for example breast demandsatransduceroflargeaperture. Suchanapertureismst imasinsr Previous such mirror systems easily achieved by theuseofmirrors. suffered problems frm reverberations between and within their ccqmnent Changes inthedesignofthesystem, andtheuseof thin metal parts. reduce these reverberationstoanacceptablelevel. There is reflectors, no sacrifice inthe focusitqperformnce, andlosses inthe system are fz 1985 Academic E'ress,Inc. minimized. Key words:
transducers;
Fccusing;imging;mirrors;
ultrasound.
lNTFCXUmON The minimum separation D of two point targets which can be separately distinguishedbyasystemofnumerical apertureNAisgivenby
where x is the wavelength of the radiation. Thecmstant, a, takes the value 0.61 if the Rayleigh criterion is used, or 0.5 for the Sparrow criterion [l]. Because of this relationship, the ability to separate closely spaced targets depends ontheuseof a large ame. For freguencypropagatinginwaterof35Chas a exarrple, ultrasoundof5MHz wavelength X of 0.3 mm. For a resolution D of lmm, if the Rayleigh criterion is used, we require a numerical aperture NA = a&D = 0.18. The normalpractice inultrasonic imaging is toapplythe transducer as close to the region of interest as possible, as this minimizes the size of transducer required for a given numerical aperture. However, we have been developingawater-bathscanner [2] for imaging the breast. In this case, thetransducermuststandscnnedistanceaway frmthe skin, and so theregionof interestmaybeas~~as15Ommfmmthetransducer. Ifwe demand a numerical aperture of 0.18 at this range, then the physical transducermustbeatleast54 nun. diamterofthe Constmction of a highfreguencyultrasonic transducer of such a diameter or larger is fraught with difficulties. Conventional focused probes dependontheuseofbml-shapedpiezoelectrictransducerelements, which are noteasilymanufacturedindiametersmuchabove 25 mm. Flat elements are a little more easy to obtain, but still very fragile, and may befocusedbymeans ofacousticlenses. However,oversuchlargediameters the lenses attain a significant thickness and therefore give rise to problems fmn attenuation in the lens material or reverberations between the surfaces ofthelens. Inparticular, ifaconcavelensisused, the 'Present address: Pantatron Strathclyde, ML1 2AJ, United
Systems Kingdom.
Limited,
Fern
Street,
Motherwell, 0161-7346185
107
All
Copyright 0 198s rrghrs of reproducrron
$3.00
by Academic Press. Inc in any ,form reserved
NICOLL ET AL.
Fig.
1
Conventional mirrorgemetry Fulsestransmitted from PI. T are reflected from the foous Flandfocussedbythe ellipsoidal mirror (surface E) to its internal reference point, n. These echo pulses are then reflezted by the hyperboloidalmimorH, which focussesthemtoitsexternal reference point, F3, where are detected by the they receiver.
additional attenuation in the thicker outer parts effectively apcdizes the trmcer, increasing the size of its main beam. The probe will therefore not achieve the calculated resolution. In consequence of these difficulties, therehaslongbeeninterestin the alternative use of mirrorstoachievethe large apertures [3-61. Essentially, the use ofanappropriatelycmved mirror, or system of mimrs, allcws the beam from a relatively small ultrasonic transducer to Anearlydesign, shorn in besp~dtofilltheregukedlaqeaperture. figure 1, is analcgous totheCassegrain system familiar in optical telescopes. Echoes receivedbytheprknarymirmrare reflected ontothe smaller secondary which inturnconcentratesthenlonto the transducer placed at the apex of the primary. (our terminology follms telescope practice. In figure 1, the ellipsoidal reflector, sarked 'El, is termed the smaller hyperboloid, marked 'HI is the secondary mirror). the primary, Minorvariations inthis designhavebeentried; themirrorsmaybeusedto focus ontransmissionandreceptionusingonetransducer, the transducer and the secondary mirror my be itself may be focused or flat, hyperboloidal [3] or paraboloidal [4]. The primary mirror is generally ellipsoiddl, or to ba more exact, a prolate spheroid. transducer is aimed at one feature comontothesedesignsisthatthe secmdaqmirmr, whichreflectspartofthebeam the bluntcenterofthe transducer amd the relatively flat central area of the straightbacktothe primary mirror (Fig. 1). F&2zverberations between these c5?mpmmts therefore inapulse-e&oimagingsystem, to the well-known occur and give rise, problem of artifactechoes (%tamSngechoes~~ in nondestructive testing In addition, at each parlance)whi&renderpartsoftherangeuuusable. reflection, some of the sonic energy enters the material of the mirror, my be reflected off the rearsurfaceandfiuallymypass back into the Ibis propagatingmediumaftertwo (ormore) transitsthrcughthe n&x-or. causes multiple pulses to be transmitted and nuiltiple echoes are received. Various stepscanbetakentomininðeseeffects. Rearsurfaces ofmirrorscanbeconfiguretisoastoflectorscattertransmittedsaund, and the mirrorsthmselvescanbemadeofhighly attenuating materials. and Olofsson Thestandingechoescausedbygeametryarehardertooverwme, [33resortedtousinghissystemin receptiononly, transmissionbeing from None of these aseparate transducer placedinfmntofthe mirrors. measures is entirely satisfactory.
108
IMPROVED MIRROR SYSTEMS
Fig.
2
Dsvelopnent of improved mirror gemetry. an extreme ray from (4 transdum T, which is dixecbd at its focus, Fl, is reflect4 by two mirror surfacestocmsstheaxisat F3. suchsurfaceswould be (b) ellipses with a common reference point at F2. The secondary mirror, s, has its otherreferencepointat the transducerfm, Fl, while the primary mirror, P, has itsotherreferencepoint at F3. Although Fl and F3 lie onthetransduceraxisF2may be displaced so that the mirror surface crosses the axis at an acute angle. (c) A solid surfaoa my be generated byrotating abcut the transducer axis thus mirrors which are sivins pointed.
NEWMIRlWRCONFIGURATION Reverberationsbetweenthecgnponentpartswouldbegreatlyreducedif the secondary mirrorweretobesharp-pointedrather than blunt. This would meanthatverylittlesonicenergy~dbereflectedstraight back Figure 2 (a) shms a half-section through the to the t?zamducer. hypatheticalsyStem~~~decidedtodevelop. !Ihecenteroftheprimry mirrorwaildnotbe~ill~~~butastheCentral~cannotcontribute tothe focus inanycase,thisisofnoconsequence. suchapointed~~isnotallawedwithintheclassical clearly, whichdemndsreflec&gsurfaceswhose configurations c==slra~ m, Transducer Tis intrinsically focused at point Flon are conicsections. Itsbemisintemeptedbya pointed secondary the axisofthesystem. mirror P. Thebeamreflectedfranpisrequiredtoconvergeatthe final focus F3, alsoontheaxisoftbesystem. Thepmblemistoderivecmms for S and P which will give the system this property, while giving the centralpcintof S the requireddegreeof sharpness. lIhedesired focalprcpertieswillbe&tainedifthesectionsof~ and P are ellipses with gemetric foci Fl and FZ!, F'2 and F3 respectively. Then fmnthewell-knownpmpertiesoftheellipse, thein.itialbeamconvergent towards Fl will be comer&d bythesecom&ymirrortoabeamdiveqmt fmnthe cxxmmnrefererrcepointF2. This in turn Will be reflected by the prinmymirmrtoumveqe to the desired focus at F3. Ifthethreepoints, Fl, F2 ardF3wex-e colinear, thesystemmuld reduce to one case of the classical Gissegrain configuration (i.e. with a blunt secon%ry mirror as in figure 1). However, wemay equally well choose tolccatethecmmonrefereme pintF2 atapointofftheaxis of
109
NICOLL ET AL.
thetransducersystem, as indicated in figure 2 (b). Thisdiagram shms that the section of the secmdaqmirrorS, if drawh inits entirety, is an ellipse whose long axis FlF2 is inclined to the axis of the transdumr system. The curve Sthemforecutstheaxisofthesystemat an angle which is not a right angle. The same is true of curve P, but that is less impomt. Naturally, we wish the completed transducer system to have rotational symmetry about its axis FlF3. Therefore, wetruncatethe ellipses S andP where they cut the axis, andgeneratesolidfigures by rotating the truncatd portions of theseellipsesaboutthe system axis. A cross section of the resultant geometry is shmn in figure 2 (c). It can be seen that because CurveSmeetstheaxisatan angle, the secondary mirror generated in thiswayhasbeenthedesiredpointsothatits surface is never parallel with that of the transducer. Therefore wehaveamirrorsystemwhichhasthe focusirgproperty of the conventional mirror system, but in which the mirrors are not ellipsoids, hyperboloids nor paraboloids. They are insteadsolid figures generatedbyrotatingasegmentofan inclinedellipeeaboutthe principal axisoft.hesysten~.
A design on the principle suggested in the preceding paragraphs is subject toagooddealof freedm. ThedistanceofF1frmtransducer T depends on thefocalpropertiesofthattransducer, whichcanbe chosen accordingly. The position of F2 can be chosen freely. In addition, the sizes of the ellipses S and P, and the outside diameters at which these are terminated (i.e. the diameters of the mimrs) must be specified, as must the diameter of transducer T. The critical considerations inchoosingadesignarerevealedby the The central ray is diverged to central arxdouterraysfmWmsducerT. sewr&zymirmr. It&mild anextentdetemined bythepointangleofthe arrive back at the primary mirror at a radius outside both that of transdlucerT,andthatoftheareaoftheprimarywhoseviewoffocusF3is Asafetymaxginshouldbe left in obstructed by thesecondarymimor. accmmdate geometrical inaccuracies and the effects of order to diffraction. The outennostrayfmn txranduce.rTmuststrikethesewndarymirror near its edge, butagainleavinga rmaonable safetymaxgintopreventany of secondary. Similarly, after reflection frcm thebeamfmnbypassingthe the secondary mirror, the rayshouldxeachtheprimary m%r, but not its edge. Thus,theauterdi~~oftheprimarymirror~t exactly at, be somewhatlargerthantheeffectiveapertureofthesystem. the required gematrical parametere were From these criteria, detenninedbytrial artderror. Theprocesswasaidedbyacoqmterpmgrm which, given positions of Fl, F2 and F3 and Size parameters for the prin-ary and sewndaq ellipses, displayed thecuxvesonavisual display unit attachedto the cmputer. curveswhichlooked reasonable By =P=+=t, were found, andwerethenprintedonahard-capyprintersothatdetailed Paramaters were then modified until a ray tract couldbeperformd. Anexaq~leoftheczxquter out@ is satisfactory designwasachimMi. shcwn in figure 3. which
'IheparametersOfthe~~findllYselectedbythiSProcedure,and wedescribeintherestofthispaper, areasfollmm.
110
Focus Fl,
IMPROVED MIRROR SYSTEMS
Fig.
-80 -40 0 40
80
12Omm
3
mtputof interactive design The vertical axis Program. is through the mmon reference pointof the two ellipses. The axis of symmetry is displaced frcm this by 2.8 mm.
lieS15Om fm T. lies 60 mm from transducer T, andthe finalfoCUsF3 point F2 lies 30 m from T, and 2.8 nm off the The wmon reference Semi-major axes of primary and secondary ellipses P and s principal axis. are respectively 91.7 mn and 19.3 mm. ?heprimarymirroristruncat&at 112mmdiameterandthedesign&apertum, lhnitedasdescxibedabove, to approximately88m. Thisreqiresa transduOe.r of 15 mm active diameter. The configuration, withcentralandoutemcstrays sketched, is shcm in figwx 3. Note that the axis drawn by the com@er is not the principal paralleltotheprincipalaxis. The vertgx axis, but alinethroughF2 half-angle of the secondary mirror S has been calculated to be 71.2 sufficient to spread the reflected beam beyozd the area of the prima& which is occupiedbythe transducer,astheraysdrawninfigum3show.
Gur new gecanetry, with its poinw seamdaqmirmr, doesmch to czmpnents. Thereverberationduetothe reducereverberationsbeixeenthe echo fmn a 2nmsteelballtargetwasfaundtobeless than -60 dB TherelrEmainsthe problem of reducirKJ campared to the echo itself. reverberationwithFneachmirror,whileretainingakighdegreeofacaustic reflectivity. To achievegoodreflectivityatthewater/mimr interface requires a high degree of mimatch of acoustic impedance. Onemethalof achieving thisistomakethereflectorofadensemetal,whoseaccustic impeaanceis mchhigherthanthatofwater. Brass, for exa.uple, was used by !&urstone A disadvantage of metals is that their attenuation is and McKinney [4]. relatively lcrw and therefore reverberations can occur between front and rearsurfaces. An alternativemeansofa~i~ingahi~degreeofmisMtchFR3Uld be to use amaterialwithamuchlmerinpe&methanthatof water. Air serves this plrpose aMU, as there is virtually total reflection at a water/air interface. unforl3.mately, air requires to be contained. an air HOWWCX, if the containing walls are very thin, we have effectively reflector. Ahollcrwprimarymirrorwasthereforeconstruct&. First stage in manufactWeofsu&amirmrwasto tum male aW femalebrassmuldstothe formofthenquiredreflecting surface. This was done by computinglathesettings fmtheparametersof the cwxe. copper sheet, a hole was N=-% frcm a circular piece of 22 mq (0.71m)
111
NICOLL ET AL.
cut frcmthe transducer aperture atthecenterofthemirror. n-ie ccrpper wasthenannealedbyrqxatedheatingandquenching, andpressedto shape between the brassbmlmulds. Thisproducedathin (lessthano.68 mm afterstretching) ccpperbmlwithace.ntralaperture. This was glued at its innerand~~edgestOholl~~copperlinderswhich formedthewalls of the final structure, and finallythebackwas closedbysolderingona flat, annular copper sheet. The same technique couldnotbeusedtomake the small secondary mirror, because it is inpcssibletopress ametalsheettothe sharppoint which is required. A solid brass reflector (as used by 'Ihurstone and McKinney [4]) was found unsatisfactory bemuse of inte.rnal reverberations. A better reflector of reasonably high acoustic iqedame can be made frcnn a cmposite of grains of high densitymetal enbedded in a matrix of attem&ing material. The cxqosite has a high attenuation not only because of the attentuatingmatrixbutalsobecause of the scattering effect of the g-rains. For the sewMarymi?mx, weus&a cxqmsite of Araldite (-inMY 753 +haMenerHY 951, CIIBA- Geigy Ltd) and tungsten powder (1 m in diameter) in a ratio of 1:2.5 by mass. The mixture was thinned by additional hardener so that entrained air bubbles could be remved by evacuation. As sucha ccqmsitedces notmachineeasily, itwas turned frcm lathe cast toshapeinawaxmouldfozmedonabrassmaster, settingscmpulxdasdescribedpreviously. l'herearofthemirrorwasmade conical rather than flat as a further precaution against reverberations. The cxmplete mirror assenblyisshmminfigure facilitate aligmnent, the hollm capper primary methylmethacrylate (Ferspex, trade mark of Implerial
Fig.
4
Coqletedmirmrsystem.
112
4. In order to sits on a WYChemical Industries
IMPROVED MIRROR SYSTEMS
Ltd.) baseplatebetweenthmeequallyspacedadjustingscmaws. Theseallow the~i~~ofthegrimarymirrortobeacc;watelysetsothatitscentrdl in front of it. axis coincideswiththatofthe sew&azymirrormspe&ed The seamWymirrorismountedbywayoftwoslidingmdswhose position iscmtrolledbyaleadscrew, seeninfigure4, sothatthedistance of the seamdaq mirror frwntheprimaryczmbe adjusted. Although this distance has acorrecttheoreticalvalueinaccordance with the design calculations, in practice itwas fou&thatsmallvariationshere varied the position ofthe final focusF!3withcutnoticeabledegradationof the size of the focal zone. As regardsthealigmnentofthesystem, itwasfoundthat this was best done byattachi.ngthemirrortoawater-tankEkscansy.stem [2] and scanned across it. observing the image ofawiretaqetasthemirmr Figure 5 (a) shows the imageobtainsd when the primary mirror was deliberately offset by a fewmillimeters; the asymmetry is apparent, particularly forawirenotatthe focal distance. Eyadjustmentof the screws, ~theprimaqmimxwasmovedsidewaysuntil asymmetrical -ins response pattern as in figure5 (b)was obtained. The whole mirror assenbly was then rotated by 90°, and the pm repeated to obtain Cmrectaligmentinthe0rthcgonaldirection.
The simple point resolutionequation (Eq. 1) assumes Fraunhofer diffraction conditions and applies only approximately in the case of a large numerical aperture. In practice, the aperture of any large transducer will almost inevitably be apadized. Aconcave lens will be thicker txlwadstheouteredge, thereforeattemmtingthebmmmorethere anclinatwo-elemmtm.irmrsystemthe sewmAry will entirely block the center. In that case, transmission and/or reception will be over a broad annulusratherthanacimularaperture. It is possible to predict gualitively that blccking the center of the aperture will reduce the size of the focal spot (Airy disc) and that energy from here will be redistributed to the side lobes [l]. An approach is required which quantifies the effect of apodization arid predicts the relattve performance of such apertures. The mdelusedis adevelopm?ntofonebyArcher-HdllandMi-Bashter They investigatedthe fieldduetoverydeep (scnne hemispherical) concave spheriml bowl transducers over the byintegratingPres== transducer surface. Theuseofcarefullychosengeometrical constraints resultsFnasingleintegral~~andMecaseofamirrorilluminatedby an incidentbmmisdirectlyanalogms [8]toatmnsmitterbutaunifonnly excited surface is assumed and the algorithm nust bs modified to incorpxate apodization. The cqxkerimpkmentaticmofthe model was VerifiedbyreproducingtheresultsofArcher-HdlandAli-Bashter. [71.
This numerical model describes a continuous wave (a) concave, spherical radiator. Thesimplifiedgeomstryandtheuseofcwresults ina model which may beevaluat~easilyandquickly for various numerical apertures and for various sizes of central block. In the pulsed wave (ml) case the focal spot will be ccqarable but the Cw model will have an extensive side lcbe structure and is unable to predict the axial profile of the beam. The CWinterference pattern extends thrwughallspace whereas that of pilsedwaves (Pw) is limitedtophase differences within the pulse Fost1~andHunt[9]fomdgoodagreemen tbetweenCWandPWtiels 1-a in the far field of a plane disc transducer. 'Ike near field of the pw
113
NICOLL ET AL.
Fig.
5
Alignment of mirrorsystemusingB-sznimageofwire a) before adjustment; b) after adjustment. theedgesofthephotogra@sarelOnnnapart.
114
'Ihe bright
targets. marks on
IMPROVED MIRROR SYSTEMS
sticture of the Cw solution although solution lacks the fine interference Fccussing with a spherical bawl will intrcduce minima do exist. This far field CW interference will be interference beyomi thefocus. ameliorated bytheapcdizationbutonlyattheexpenseof increasing the side lobes [lo]. Side lobe mnplitude is an important limitation in an imaging transducer. l'hus, althoughtheaveragepressureshcwnbytheCW solution will indicate the pulsed field, the actual interference structure will not exist more than a pulse length frcm the focal Zone. 'Ihe boundary ccmlitions used are those attributed to Huygens, i.e. a infinite planar baffle. These of Kirchoff (which model a totally rigid, inmmsed trausducer with an ideally rigid back, totally isolated frm the transmitting surface) are a better physical apprmcimation to the hollcw mirrcr but the two models give results which differ only in the size of the peaks in the Fresnel region, and the field close to the aperture is not of interest in the present work. There is no consensus in the literature on which parameters are most apt for describing beam shape. Kossoff [ll] uses the diameter of the first off-axis zeros. Foster andHunt[9] use full width, half maximum. Weyns [lo] refers to both the -3 dB and -10 dB contours. Since apcdization will have most effect on the lcwer part of the zero order focus and on the side lobes, we have investigatedUne radiusofthe -lOdBcontour, the first off-axis zero and the first off-axis maxims. The respmseoftheCWmcdeldescribedprevicuslyto increasir~.~ the size ofthecentralobtructionduetothe secoAaqofamirrcrsystemis shown in figures 6, 7 and 8. !Ihese figures shm calculations for the transmitted field anly. Figure6showsthebehaviourofthethree beam widthpa.mnetersdiecuss&inthelastpa?qra~. Theradiusofthe first off-axis zero (Airy disc) decreases shmingadecreas e in size of the main lobe but the -10 dE! width and the position of the first off-axis peak are unaltexed. 'Ihe peak pressure (Fig. 7) showsadecreaseapproximatelyin pmportiontothereduction insurfaceareaofreflector. Themostnotable effect is in the amplitude of the side lobe maximum relative to the peak value (Fig. 8). Thisimmasessteadily, atldBper6nunincrease in diameterofthecentralstopbetweenloand40mmdiametess. nUIlE?r.icdL ~lWdelwasusedtocalcliiatet.he~tted thedimensionsofthefinaldesign. The resulting
field beam
'IhiS
using
I
IO-
RlTdmdcumlt~=lsonml chLnd=nhn
lo-
l
l
.
.
.
1st
off-am
,'e
10 20 30 40 &
6
Fig. 7
.
lmxm
10 20 30 LO i?L
DAMTER CX=CENTW ST@ m m
Fig.
.
PEAK PRESSURE
RAD(us mm
transverse
0,ANETER OF LWTRE Sl$
Effects cnacalculatedkeamshape size of the center stop of a large Effect on~=alculatedpeakheightof centerstopofaconcavebowl.
I15
parametersofincreasing cmcave bawl. incmxtsingthesize
the of
the
NICOLL ET AL.
RELATIVE PRESSURE
dB /mm) -'
Radus
0
0
10
20
30
of cwvafwe = KOmm chord = loGmm
40
s, mm
OIAMTER OF CENTRE STOP
Fig.
8
Effect on a calculated amplitude of first off axis peak relative to the nmxinnrm of increasw the size of the center stop.
Fig.
9
Transversebeam mcdel.
shape of finaldesigncalculatedbythe
numerical
shape is shcmn infigure9withammothcurvedrawn through the data points usinga piecewisecubic polyncmialn&hod. The CWmodel gives a -12 dB focal depth of field of 9 mm; hmeverasdiscussedearlierthe Pw field will only closely resemble the CM interference pattern close to the gemetrical focus. lbe calculated focal size will be wmpared with obsemedexperimntalperfonnancelater.
ideally
Altlmugh the reflective copper surface is thin (0.68 mm), it thin whem ampared to the wave length in capper (0.95 mm).
is
not
transducerused to drive the The pulse shape fromtheaammrcial mirror system was ewminedusingabilamimr shielded PVDF hydrophone (Marconi F&sear&Laboratories) in the far field, appmximtely1OOm from Theplsewasalso examhedata similarpath its surface (Fig. 10 (a)). length but including a stile reflection by the air backed mimr (Fig. 10 of danping, the (b) 1. Using the transducer manufac%xrer~s specification Hmewr, 2 s afterthestarkof pilselengthis increds%dby0.5cycles. the pulsetherefleckdsignalis still only -27 dBccarparedto its peak while the original pulse is reduced to -35 dEL mchdegradationwouldnot be consider&serious forourpresentpurposes. E&am Shape and Focal Zone Size ~~1ateralpointresponseofthemFrmrsystemwasexaminedbymoving atargetthrcnqhthefocalzone. Tilepcx3itionofthefocuswas&ikntobe the highestp&akpressum The relative fa.lrxI experimentally. positionsofthetwolRimrsandthe tmxdmer~adjustedtoplacethis peakatthegecmtricalfccus. very
~transversebeam~isdifficnilttoexaminebecausethefocusis l'EmXW, the predicteddiameteroftheAirydiscbeing1.1
116
axial
mm.
No
IMPROVED MIRROR SYSTEMS
Fig. 10
(a) (b)
Pulse shape in the far field (range= 100 mm) of I2 le transduoerusedtodrivethemirrorsystem. callmemial The pulse at the samepathlength but after a sing1 .e reflection by an air backed mirror.
117
NICOLL ET AL.
HolfwKfth 034m 034mm 047mm 049mm
0 66mm
011
0
5
w
Fig. 11
Transmitted beam profile observedwithaPVDFhydrophone
Fig.
Fulse-echobeamprofileatthe 2 mmdiameters@ricalsteeltaqet.
12
12 O-
mm
rod/us --mm
at the focus of the mirror (activearealmdiameter). focus ofthemirror
system
systemusinga
target was fomdwhichwassmallcmparedwiththefocus and hence expsrimental beam shape is a convolution of the beam and the target.
any
'Ihe hydrophoneavailablehadanactivediscof1m diameter. Thus when centered on thefirstmininm approximately 42% of its area falls withinthecdlculated zeroorderfccusreceivingabout2O% oftheenergyof the mainlobe. Thetransversebeamshapedetectedbythe hydrophone is directcmparison shown in figure 11. HCWeVX, forthefeasonsstated, with the calculated shape (Fig. 9) is not possible. !Ihe hydrophone is useful examiningpilse shapesbutisunabletodetenninethe shape of such anarrmbeam. As analternativetargeta2mmdiamteXstainless steelballmunted on a 19-gaugehypodermicneedlewasusedtogeneratea pulse-echo plot. This is a standafd target of the type suggested by Lapacewicz and Hill sectionislargecmparedwiththe focalsizeand [=I * Althoughitscross its curved surface pannits finer resolution than the with theh~one, flat 1 nun circle of the hydrophone. Theconvexsurface also makes it difficult to appreciate the effect of the target's size upon the resultixq plot. Smallerreflectivetargetsproved insensitive and unsatisfactory in use. Thinmetalwiretaqets didnotgivereproducible resultsbecausethe echo size was very dependent of the orientation of the wire relative to the beam. This was especially critical with the highly focused and slightly asymetric loams observed frcxn the mirror system. ApiLse-e&oplot, usingthe 2 mqhericaltaxget, is shown in figure 12. This pilse-echo plotmaybecmparedwiththetheoretical plot by approximating theconvolutionoftransmissionandreceptionbythe square 'Ihis has been done in of thetransmitted fieldpredictedbythemodel. 9), pulsetable 1 which shms the widths of the CWnumerical model (Fig. echo (Fig. 12) and hydrcphone (Fig. 11) results at cozpamble levels in the Doththeexperimentalplots areasynetric amI the half-width focal zone. hasbeenobtainedbydividingthe Aill-widthbytwo. Differences between the three beam profiles (Figs. 9, 11, 12) are between the experimental plots of clearly visible. The differences transmitted field (Fig. 11) using the hydrophone amI the pulse-echo field (Fig. 12) using aqhericaltargetcanonlybeunderstoodby considering the influenceofthetaqetupontheexperimental abservations. A=holJm
118
IMPROVED MIRROR SYSTEMS
Table 1.
Performance
of the Mirror
System
cwNLmErica1 rodeI.
Experiment Pulse-Echo Hydrcsphone
-6 dB Half-width
0.22 Rml
0.34 nun
0.44 nml
-10 ds
0.28 mm
0.47 mm
0.56 mm
-12 dE3
0.30 lmn
0.49 nml
0.59 lmn
-20 dB
0.37 mm
0.66 ml
0.74 nml
Relative height of first side lobe
-28 dB
-20 dE3
-18 dE3
Average radius of first side lobe
0.7 mm
1.8 m
1.3 nml
Feature (Transmission
and Reception)
both show a similar as-try the pattern of side lobes and their positions The effects upon presents quitedifferentlywiththedifferenttaqets. beam width, allawing approximately for transmission and reception, are Thepulse~oplotgivesthemoreaccuratedescription ShOWll in table 1. sincethelatqetargetcannot reducethebean~beluwitstruesize; however true beam there is little evidence to suggest that this represen tsthe size. It is hcwever encouraging that one side lobe at least is well defined. The differences betweenthebeamwidthpredictedbythemodelardthat faundbypulse-echoplottingaregenerallyabauttwicetherPagnitudeofthe differences between the~experimentdlplots. Contributions to this difference come fram two sources. Themodelisverysinpleanddces not repment the design exactly. 'Ibe designis ccmplicated and device constructed will not beperfect. An important si.qUfication in the nurkerical model is the use of the Cw approximation [10,13-151. Various workers have reported on the relationship of CWand FW fields although not for suchhighly focusseddevicas. Thequalitativedifferencesbetween CW andFWbeamcouldbeexpe&ed. !lkemainlobewouldbareducedinanplitude andhavea broadershape:thesidesbeingsteepernearthebase. Weyns[lO] found this effectnxxemarked forbowlswithanumericalaperture greater than 0.2. !thereduction inmainlobeamplitudewould increasethe relative size of the first side lobe. Intherealsystemthebeamis spread and then focussed bymirrors~~areatcont~~lyv~~anglesto the directionofpropagation. This will lead to variation in intensity across theannularam. SinCethemodelrepresentsthethreeelen~&nkrror system as one elementtheeffects of this apcdization, which tight be expressedasareduction intheeffectiveuuterdiameter, arenot included in its rf?sults. Differences between the design (Fig. 3) andthemfactured mirror Thedesignassumesthe mm (Fig. 4)cxeneframthreeprincipalsources. sourcetransducerpruduces anaccurate, spherically converging wavefront. The transducerus&inpracticedoesnot. Bothlnirro~~ manufactured fran moulds SIX neither cauldbemadedirectlyand this limits the precisionofthe final surface. Thedesignwithitspointed~r~fa~ isverysensitivetomisali~oftheaxesofthethree elements. Ihe
119
NICOLL ET AL.
asymmetric nature.
beasseenexperimntallysuggests
Using the foundtobe16nnn.
pulse-echo
technigue
a slightmisaligmentof
this
the -12 dB focal depth of
field
was
DISCUSSION me The mirror system perfomswellarrdis a useful imaging device. relatively sinpJle model predicts beam profiles and the effects of the annular aperture well enabling the determination of a suitable annulus for the chosenlengthandfreguehcy. Differences between model at-d observed performance are causednotonlybythe&ange fmncontinuous to pulsed (transducerandti waves but also by the presence of three elements lllirrorS) so increasing the scope for constructional imprecision. In thetransducerisnottheperfectlyfccusseddeviceassumedby partid=, theory,anddLigrrmentofthe~rel~~isnotperfect,asmaybeseen fmn the asymmetry of the txansve.rse plot. Fointedreflectorsweuse are more sensitive tomisaligmentthanaresi~@e conic reflectors. More sophisticatedtechniguesarereqiredtonmasure the beam experimentally. believe that our desigh is a significant inprovement over Firstly, the configuration of previ!Zlyreportedsystemsintwomspects. and secondly, theuseof a the mirrors reduced confus* 3zvedaation6, hollcw reflector maintains acceptablesignalstmangthdespite the four Gursystemgives successivereflections involved inapulse-echoseqence. a 20 dB lateral dynamic Lange. This is achieved withaut sacrifice in its lateral resolution and gives sufficient contrast for the variation of tissue fomd inthelccalisedregionsof interestinmanyapplications.
J. J. Nicoll H8al~.oi~of~Faulty reepectivsly, for financial
thank the Scottish Hme and of Medicine,
support.
FIEFERENCES [l]
Driscoll, WalterG. Hamdbcokofcptics -Optical pp. 6-2, 2-3 (McGraw-Hill, New York, 1978).
[2]
Piggins, J. M., Nicoll, J. J., McDi~, W.N., Kirkpatrick, Muir, B. A. ExperiencewithaVe.rsatileUltrasonicBreastSmmer. Ultzmsmnd Med. Biol. & Supplement 1, 152 (1982).
[33
Olofsson, S. 367 (1963).
[4]
Ihurstone, Ultrasonic Ultrasonic University 1966).
[53
Fry, W. J., Leichnex, G. H., Okuyam, D., Fry, F. J. and Fry, E. K. Ultrasomd visualisation system enplaying new scanning and presentation methods, J. Aamst. Sot. Amar. 4& 1324-1338 (1968).
An ultrasonic
optical
mirmr
Society
of America,
system, Acustica
A. E. and
a
361-
F. L. and McKinney, W. M. Focused TransducerArraysinan Scanning ~mfo;~ological ,Tissue, in Diagnostic - proceeding Inte-matlonal conference, New York, of Pitt&m&, 1965, 191-194 (Plenum Press,
120
IMPROVED MIRROR SYSTEMS
[6]
Patterson, M. S. and Foster, F. S. The Iqmvement and Quantitative AsmsmmtofB-Modemqel3Pmduced by an Annular Array/Cane Hybrid. Ultrasonic linaging -!+ 5 195-213 (1983).
[7]
Archer-Hall, J. A. and Ali-Bashter, A. I. Diffraction patterns of largeaperturebmltransducers, NM' International l3-51-55 (1980).
[8]
Griffirq, reflectcrs,
[9]
Foster, F. S. short pulse ul-
V. and Fox, F. E. Thsoryof intensitygainduetoconcave J. Acoust. Sot. Amer. 2& 348-351 (1949).
[lOI Weyns,
transducers,
A.
Ultrasonice [ll]
and Hunt, J. W. Thedesignandcharacterisationof transducers, Ultrasonics 16, 116-122 (1978). Radiation
part
l&
field calculations of pulsed ultrasonic sphericaldisc-and ring-&a@ transducers, 219-223 (1980). 2:
Kossoff, G., Robimcn, dimensional visualization 44, 1310-1318 (1968).
[12] Lapacewicz,
pulse-echo (1974) .
D. E. and Garrett, for medical diagnosis,
G. and Bill, C. R. equimt evaluation.
W. J. Ultrasonic twoJ. Acoust. See. Amer.
Choice of standard target for medical Ultrasound Med. Biol. L 287-289
[13] Weyns, A. Radiation field calculations of pulsed transducers,part1: Planarcimular,sguareandannulartransducers. Ultrasonics l& 183-188 (1980). [14] Beaver,
Acoust.
w. L. Sonic nearfields of a pulsed piston Sot. Am. 56- 1043-1048 (1974).
J. W., Arditi, M. and Foster, F. S. Ultrasonic pulse-echo medical imaging. IEEE Trans. Bicmed. Erq 481 (1983).
[151 Hunt,
121
ultrasonic
radiator.
J-2
transducers for BNE-30, 453-