MULTI-ELEMENT SOURCES FOCUSING ACOUSTIC ENERGY GRAZYNA GRELOWSKA

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1 MULTI-ELEMENT SOURCES OCUSING ACOUSTIC ENERGY GRAZYNA GRELOWSKA Naval University in Gdynia Smidwicza 69, Gdynia Pland In underwater imaging the beam-frming technique plays ne f the mst imprtant rles. cusing acustic energy is ne f the methds used t imprve lateral reslutin. The paper cntains the results f the experimental research in a piezelectric fur- and sixelement annular arrays f a resnant frequency equal t 1.5 MHz. The third examined surce is built using ne PZT bwl element. The surces are cnstructed with a layer adjusting the PZT transducers t water. In that way we btained the surces f bradened band radiating in the frequency range 1. MHz MHz. The space distributin f the pressure field has been determined fr varius frequencies and varius intensity f the phenmenn f the nnlinear distrtin f the wave. The experimental data have been cmpared with the results f the numerical research carried ut with the use f a mdel cnstructed n the basis f the KZK equatin. INTRODUCTION The simplest ultrasnic transducer is an unfcused pistn transducer that cnsists f a piezelectric disc with thin electrdes depsited n bth sides f the disc. Electrical signals are applied t r prduced frm the electrdes. The transducer is unifrmly weighted (unweighted ~ ( r1, ω) = 1) and its surfaces vibrate lie an engine pistn when excited by an electrical signal. The main beamwidth prduced by this transducer is apprximately the same as the diameter f the transducer, D. in the depth f field that is defined as the Rayleigh distance [1]: a PZ max = (1) π where a and dente the radius and central wavelength f the transducer. In the far field where the raunhfer apprximatin is valid, the lateral field pattern f the beam prduced by

2 the unfcused pistn transducer is prprtinal t the urier transfrm f the aperture (assumed t be a disc) f the transducer and can be derived in frm []: r r a ( ) ( i z r z) J ( ar z) / 1, ω = e iz where J 1 ( ) is the first rder Bessel functin f the first ind. The first minimum f ( r,ω ) alng the radius is: ar / z r () z r = 0.61 (3) a Equatin (3) represents half f the main beamwidth f the unfcused pistn transducer. Hence the main beamwidth increases with the axial distance z, fr a given central wavelength, and decreases as the size f aperture f the transducer, a, increases. Cnsequently, the lateral beamwidth f the abve unfcused pistn transducer is very large and the lateral reslutin f the images btained with such a transducer is lw. ig. 1. A beam prduced by a pistn transducer (n weighting) The main beamwidth f a pistn transducer, equivalently the lateral reslutin f images, can be greatly imprved if the spherical-fcusing technique is applied. 1. OCUSED PISTON TRANSDUCER The field f a fcused pistn transducer can be calculated with the fllwing aperture weighting functin that is a spherical phase shifter alng the radial distance r 1 : t r ( r, ) 1 ω = e i + r 1 (4) where is the fcai length f the transducer. Under the resnel apprximatin, ne btains the field in the fcal plane in the fllwing frm: r J ~ ar ~ ( r, ) 1 1 ω ( ar / ) / (5)

3 where the first minimum f ( r,ω) r r alng the radius is at: r = 0.61 = 1. f (6) a in which f = /( a ) is defined as an f number. It implies that the main beamwidth increases with the f-number fr a given central wavelength. Hence, a beam cannt be prperly fcused with a larger f-number r the lateral reslutin cannt be imprved by fcusing a beam with a fcal length that is in the raunhfer regin, where equatins (3) and (6) are identical. Althugh a fcused pistn transducer can reduce the beamwidth at its fcus, its sidelbes are nt reduced (cmpare equatins () and (5). T suppress the sidelbes, varius frms f the aperture weighting functin. can be applied. As an example culd be used a fcused Gaussian-weighted beam. In this case, the field distributin (either the pressure r r1 / velcity ptential) n the surface f the transducer is a Gaussian functin, where dentes the radius at which the field amplitude drps t l/e f its maximum called the effective radius f the aperture. The Gaussian weighted beam can als be characterized by the full width at half maximum (WHM) f the Gaussian functin at the transducer surface The WHM is related t by: WHM = ln (7) G z= 0 where "G" stands fr fcused Gaussian. Under bth the resnel apprximatin and paraxial cnditin (field bserved is nt t far away frm the axis), the lateral prfile f a Gaussian beam (assume that << a )in the fcal plane is still prprtinal t a Gaussian functin [5], e.g: ~ r / (, ) ~ π ω e r r (8) The Gaussian beam specified by equatin (8) has lwer sidelbes because the Gaussian functin appraches zer faster as the radial distance increases. Because < a, the effective aperture size f the Gaussian transducer is smaller than that f the pistn transducer with the same radius a. The reduced effective aperture size f the Gaussian transducer increases the WHM f the beam in the fcal plane. Therefre, the lwer sidelbes gained by the Gaussian beam are at the expense f the larger lateral beamwidth (r lwer lateral imaging reslutin). Hwever, because the Gaussian transducer has a lwer field amplitude at its edge than the pistn transducer, edge waves are lwer in the Gaussian beam than in the pistn beam.. TRADE-OS BETWEEN LATERAL BEAMWIDTH AND DEPTH O IELD r analytical simplicity and withut the lss f generality, the fcused Gaussian beam can be used fr studying the trade-ffs between the lateral beamwidth and depth f field. If the depth f field f the fcused Gaussian beam is defined as the distance between tw ut-f- e

4 fcus planes in which the beamwidths increase t times that in the fcal plane (ig. ), we have [3]: 4 max = GZ (9) where must be s smal1 that the abve tw ut-f-fcus planes exist simultaneusly ( must be satisfied fr the ut-f-fcus planes), i.e.: 0 z π 1 (10) Neglecting the term in the denminatr f equatin (9), ne btains: ( ) ( / ) max 1 + π π GZ (11) On the ther hand frm equatin (8) the WHM f the Gaussian beam at fcus becmes: π WHM z G ln = = (1) ig.. cused Gaussian beams prduced with Gaussian aperture weighting

5 Trade-ffs between the lateral beamwidth (lateral imaging reslutin) in the fcal plane f a fcused Gaussian beam and the depth f field are demnstrated by equatins (11) and (1)..In particular, with the same effective radius f aperture a shrter fcal length prduces a beam f a smaller beamwidth at fcus and has a shrter depth f field. r a given central wavelength, t increase the lateral reslutin (reduce WHM in the fcal plane), the effective f-number, / must be reduced. Hwever, this reduces the depth f field. urthermre, fr a given effective f-number, the diffractin f Gaussian beam is strnger as the central wavelength increases. This lwers the lateral imaging reslutin but increases the depth f field. Therefre, t btain higher reslutin in imaging, high frequency (small central wavelength) is desirable. 3. INCREASING DEPTH O IELD One effective way t increase the depth f field in underwater imaging withut sacrificing the lateral beamwidth is dynamically fcused receptin r/and transmissin, in which the fcal length f an array transducer is changed with time s that eches frm different depths are in fcus. This prcess is equivalent t eeping z fr all and btaining the minimum WHM (r highest lateral reslutin) in imaging ver a large depth f field. The cncentric ring design, is ideal fr electrically mving fcus alng the beam axis. We have examined in ur investigatins tw mdels f multi-element underwater surces radiating finite amplitude wave. Special attentin was paid t bserve nnlinear phenmena in the cnditin f nn-cntinuus radiating surface in the vicinity f the surce f wave. The surces f nncntinuus surface used in experiments are in frm f annular arrays cmpsed f caxial elements [4]. The first surce cnsists f fur elements: a disc and three rings f piezelectric ceramics, and the secnd ne cnsists f six elements: a disc and five rings. The cnstructin f bth f the surces is similar. The surface area f all the radiating elements as well as the intervals is the same. ig. 3. The annular array arrangement The disc diameter equals d1. In that case the internal and external radii f the cnsecutive rings are as fllws: d = d1, d 3 = d1 3, d 4 = d1 4, d 5 = d1 5, d 6 = d1 6 and s n. Each f the elements f the array culd be driven independently. Measurements f the pressure field emitted frm the surce were carried ut using arrangement in which a PVd needle hydrphne with a nminal diameter f 1 mm was scanned alng the beam axis and acrss the beam at varius distances frm the radiating surface. The investigatin was cnducted with the use f high precisin device psitining the surce and cntrlling the mvement f the receiver. The measurements were perfrmed in 1.0 m x 1. m water tan 1.0 m high. T simulate CW peratin the tne burst with 50 cycles

6 was used. The digital strage scillscpe was used as a digital cnverter. The time wavefrm was dwnladed t the cntrlling cmputer and analysed ff-line. 4. RESULTS O INVESTIGATION Cnventinal and limited diffractin beams are usually studied under simplified cnditins, e.g., the beams prpagate in istrpic-hmgeneus and lss-free media withut bundaries. In additin we assume that the apertures fr limited diffractin beams and Gaussian beams are infinite. These cnditins are nt satisfied in practice. The results f investigatin allw t discuss the influences f same practical cnditins n beam frming. 0.4 p [MPa] z [mm] ig. 4. Changes in the n-axis pressure distributin f the 6 element annular array (btained experimentally) Limited diffractin beams and Gaussian beams can nly be prduced with a finite aperture in practice. Therefre these beams must be truncated with a finite aperture. The imprtant effect n imaging quality have the edge waves. They are appearing ahead f behind the main pulses. Their psitin and amplitudes are depth dependent. Because f that edge waves might als prduce nise in an image restratin. Mrever the edge waves may prduce ghst structures in imaging. r cnventinal spherical1y fcused beams, there are n edge waves at the fci because beams frm all pints n the aperture arrive in phase at the fci. REERENCES [1] J. Durnin, J. J. Miceli, J. H. Eberly, Diffractn free beam, Phys. Rev. Lett., Vl. 58, , [] J. W. Gdman, Intrductin t urier Optics, New Yr, McGraw-Hill, [3] G. S. Kin, Acustic waves: Devices, imaging, and analg signal prcessing, Englewd Cliffs, NJ: Pretience-Hall Inc., [4] E. Kzacza, G. Grelwsa, cusing surce cmpsed f axi-symmetric areas, Prceedings f the 16th Internatinal Sympsium n Nnlinear Acustics, Mscw, Russia, 19-3 August 00 CD edited. [5] J. Y. Lu, H. Zu, J.. Greenleaf, Bimedical ultrasund beam frming, Ultrasund in Med. & Bil., Vl. 0, N. 5, , 1994.